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new file mode 100644
index 0000000000000000000000000000000000000000..6ecacd85ddd611be7b9bc74f2e1f9b50a15e7128
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Amin? Amin? Perfect. Of that charge Q, i.e. each charge has its own field, just like the earth has a field and the moon has a field. 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You know this story. Mars has a field. Every planet or every object has a field. And each object has its own electric field. It has its own field. Within a region surrounding it. Of course, it is impossible for this to be a cargo ship. Where is its field? By God, its field is in Nablus. Around it. 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Okay, girls, is there anyone who has seen the field of gravity? Yes. Anyone who has seen it? No. No one has seen it. And no one has seen this electric field. But scientists agreed on how to represent it later. We will talk about it in detail later. They represent it to be able to draw it. But in the end, did scientists see it? No one saw it. It is a field. This is logical. This is a field. This is it. 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Give me the force on it, then divide it by Q0. This is the electrical field. Okay? So, the electrical field brings the force to the deep thing where you do the test, and then you get it. So, I want to get ... Okay, I got this charge Q1, this charge Q2. Can a Coulomb's law bring the force to Q2 or not? To Q0, which is Q2? 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What is the definition of the electric field at a point? It is the electric force that affects a charge with a volume of one kilogram placed at the point. 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Is it correct or not? Good. This is the first information. 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And we agree that there are many physical quantities, because they are confined between scientists who do not care to give them their own unit. But when it becomes a task for the general public, they make it easy for them. Because not all of them have physics or engineering. 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He told me that this law is a unit vector. Where does it go? We multiply this with this. This is four times this, this is one, this is one. But this is the direction. Okay. It changes the magnitude. It changes the equation. I don't want to use it too much. He told me that it changes the magnitude. I told him that you can do this and do that. Who told me not to do this? One. 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So Q0 is positive. So how do I learn direction, girls? By drawing. By drawing. Do you remember how I drew the force? This is the same process. So what do I need to use? Two notes. The two notes are these. It should be noted that if the charge, the field is not the field of Q, then it is exclusive to Q. 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No, you can be stiff. She said let me try to be stiff. What's wrong with you, you know? You are attracted. It means that the field will be reflected. Okay, I want to notice. This is red. Can you tell me the lines of the field out of the cube? Absolutely. Out of the cube. Because it's a curve. How is it directed? Like this. 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Okay, we brought it blue. Everything happened. So I want to determine the direction of the field based on these two observations. Okay. 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Without analysis, I analyze them. Okay. And the magnitude, we learned about it. Okay. 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Is there a difference between them? Good. In today's lecture, I say F is a condition Q is equal to E is a condition. What does it belong to? It belongs to Q, right? Okay. I want E to belong to Q. I have this point. This is point B. Then I put a condition Q on it. 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Is there a difference? So, F on Q condition is equal to Q condition and there is E of Q condition. It becomes KQQ condition. Does it make any difference? It is the same rule. So, instead of getting F from the first column rule, get E, then multiply by Q condition.", "tokens": [29020, 2554, 30, 1119, 456, 257, 2649, 30, 407, 11, 479, 322, 1249, 4188, 307, 2681, 281, 1249, 4188, 293, 456, 307, 462, 295, 1249, 4188, 13, 467, 3643, 591, 48, 48, 4188, 13, 4402, 309, 652, 604, 2649, 30, 467, 307, 264, 912, 4978, 13, 407, 11, 2602, 295, 1242, 479, 490, 264, 700, 7738, 4978, 11, 483, 462, 11, 550, 12972, 538, 1249, 4188, 13], "avg_logprob": -0.6576286966309828, "compression_ratio": 1.644578313253012, "no_speech_prob": 1.7881393432617188e-06, "words": [{"start": 1254.2200000000003, "end": 1254.8200000000002, "word": "Correct?", "probability": 0.5252685546875}, {"start": 1254.8200000000002, "end": 1255.42, "word": " Is", "probability": 0.40673828125}, {"start": 1255.42, "end": 1255.48, "word": " there", "probability": 0.8935546875}, {"start": 1255.48, "end": 1255.52, "word": " a", "probability": 0.5732421875}, {"start": 1255.52, "end": 1255.7, "word": " difference?", 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It's like you're bringing me a new way and you're going to learn it better than the first way. Okay? Look, this is a quick quiz. That's why I always tell you to speak Arabic or Chinese. And you say, yes, Arabic. Look, Arabic or Chinese. Okay?", "tokens": [8297, 30, 467, 311, 411, 291, 434, 5062, 385, 257, 777, 636, 293, 291, 434, 516, 281, 1466, 309, 1101, 813, 264, 700, 636, 13, 1033, 30, 2053, 11, 341, 307, 257, 1702, 15450, 13, 663, 311, 983, 286, 1009, 980, 291, 281, 1710, 19938, 420, 4649, 13, 400, 291, 584, 11, 2086, 11, 19938, 13, 2053, 11, 19938, 420, 4649, 13, 1033, 30], "avg_logprob": -0.4658653846153846, "compression_ratio": 1.503030303030303, "no_speech_prob": 1.6093254089355469e-06, "words": [{"start": 1280.7, "end": 1281.18, "word": "Okay?", "probability": 0.1116943359375}, {"start": 1281.96, "end": 1282.14, "word": " It's", "probability": 0.5958251953125}, {"start": 1282.14, "end": 1282.34, "word": " like", "probability": 0.677734375}, {"start": 1282.34, "end": 1283.0, "word": " you're", "probability": 0.676025390625}, {"start": 1283.0, "end": 1283.38, "word": " bringing", "probability": 0.1278076171875}, {"start": 1283.38, "end": 1283.52, "word": " me", "probability": 0.76513671875}, {"start": 1283.52, "end": 1283.82, "word": " a", "probability": 0.7998046875}, {"start": 1283.82, "end": 1284.16, "word": " new", "probability": 0.8876953125}, {"start": 1284.16, "end": 1284.2, "word": " way", "probability": 0.787109375}, {"start": 1284.2, "end": 1284.92, "word": " and", "probability": 0.427490234375}, {"start": 1284.92, "end": 1285.2, "word": " you're", "probability": 0.6070556640625}, {"start": 1285.2, "end": 1285.2, "word": " going", "probability": 0.439208984375}, {"start": 1285.2, "end": 1285.22, "word": " to", "probability": 0.9599609375}, {"start": 1285.22, "end": 1285.52, "word": " learn", "probability": 0.6640625}, {"start": 1285.52, "end": 1285.94, "word": " it", "probability": 0.37158203125}, {"start": 1285.94, "end": 1286.1, "word": " better", "probability": 0.50537109375}, {"start": 1286.1, "end": 1286.34, "word": " than", "probability": 0.92138671875}, {"start": 1286.34, "end": 1287.34, "word": " the", "probability": 0.77880859375}, {"start": 1287.34, "end": 1287.5, "word": " first", "probability": 0.55322265625}, {"start": 1287.5, "end": 1288.2, "word": " way.", "probability": 0.740234375}, {"start": 1288.76, "end": 1289.08, "word": " Okay?", "probability": 0.5283203125}, {"start": 1296.96, "end": 1297.44, "word": " Look,", "probability": 0.465576171875}, {"start": 1297.46, "end": 1297.58, "word": " this", "probability": 0.8310546875}, {"start": 1297.58, "end": 1297.76, "word": " is", "probability": 0.77880859375}, {"start": 1297.76, "end": 1297.76, "word": " a", "probability": 0.61376953125}, {"start": 1297.76, "end": 1297.76, "word": " quick", "probability": 0.243896484375}, {"start": 1297.76, "end": 1297.96, "word": " quiz.", "probability": 0.9501953125}, {"start": 1299.0, "end": 1299.48, "word": " That's", "probability": 0.689208984375}, {"start": 1299.48, "end": 1299.48, "word": " why", "probability": 0.912109375}, {"start": 1299.48, "end": 1299.64, "word": " I", "probability": 0.8076171875}, {"start": 1299.64, "end": 1299.74, "word": " always", "probability": 0.783203125}, {"start": 1299.74, "end": 1299.94, "word": " tell", "probability": 0.7060546875}, {"start": 1299.94, "end": 1300.06, "word": " you", "probability": 0.96435546875}, {"start": 1300.06, "end": 1300.16, "word": " to", "probability": 0.488037109375}, {"start": 1300.16, "end": 1300.3, "word": " speak", "probability": 0.81982421875}, {"start": 1300.3, "end": 1300.54, "word": " Arabic", "probability": 0.78515625}, {"start": 1300.54, "end": 1300.7, "word": " or", "probability": 0.81201171875}, {"start": 1300.7, "end": 1301.02, "word": " Chinese.", "probability": 0.86083984375}, {"start": 1301.62, "end": 1301.86, "word": " And", "probability": 0.7255859375}, {"start": 1301.86, "end": 1301.98, "word": " you", "probability": 0.92919921875}, {"start": 1301.98, "end": 1302.18, "word": " say,", "probability": 0.6455078125}, {"start": 1302.34, "end": 1302.44, "word": " yes,", "probability": 0.2344970703125}, {"start": 1302.54, "end": 1302.82, "word": " Arabic.", "probability": 0.81005859375}, {"start": 1302.9, "end": 1303.08, "word": " Look,", "probability": 0.418212890625}, {"start": 1303.22, "end": 1303.48, "word": " Arabic", "probability": 0.685546875}, {"start": 1303.48, "end": 1303.7, "word": " or", "probability": 0.9443359375}, {"start": 1303.7, "end": 1304.06, "word": " Chinese.", "probability": 0.814453125}, {"start": 1304.64, "end": 1305.12, "word": " Okay?", "probability": 0.763671875}], "temperature": 1.0}, {"id": 53, "seek": 133338, "start": 1306.88, "end": 1333.38, "text": " It tells me a tested charge Q0 is located at point P. I'll put a point here. In an external electric field. Is this its field? No, it's not its field. E. If the tested charge is replaced by another tested charge. 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As you asked before. Good. The external electric field. What is going to happen to it? Where are my brushes? This is a pen and this is a brush. I put it here, does it fall? Does it fall? I put the brush on the table, does it fall? Both indicated that there is attraction. Good. Does this attraction change when I put a pen or a brush? 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To check if there is a gap or not, right? Well, does the gap need to be filled? No. What is the answer? The tip of charge changed. And we said that the tip of charge changed. Do I need to forget it or not? I need to forget it. Okay? So the tip changed. 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have to keep believing it. I have to keep believing it. Let's look at this question. They say that there was a storm one day and we were sitting at home. The world was crying, right or wrong? It was crying. We heard about the phenomenon of mutilation. What does mutilation mean, girls? Speak up, Sama. 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Say it. It's a word, but what does ayunat mean? It means charged. Do I want to make coffee? Ayunat means solid, it means charged, right? Is this what water is charged with? Yes, it is. 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That's it. And this is a drop of boiling water. Is this a can? That's it. What is a can? This is one and this is another one. I said, first let's start with Z1000. Is there MG or not? It was in the direction. 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right or not? Fine. He said to me, it's still hanging. It's a balance. And the Chinese must be equal to the Saudi. And the Saudi must be equal to zero. And the Chinese must be equal to zero. There is no Chinese. So in order for the Saudi forces to be equal, there must be a higher power. So what did he say to me? 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Correct? Good. This is a vector and this is a vector. This is Q, not Q0.", "tokens": [479, 307, 2681, 281, 1249, 294, 462, 11, 558, 30, 12753, 30, 2205, 13, 639, 307, 257, 8062, 293, 341, 307, 257, 8062, 13, 639, 307, 1249, 11, 406, 1249, 15, 13], "avg_logprob": -0.6141098484848485, "compression_ratio": 1.2289156626506024, "no_speech_prob": 7.450580596923828e-06, "words": [{"start": 1638.85, "end": 1639.49, "word": " F", "probability": 0.054351806640625}, {"start": 1639.49, "end": 1640.13, "word": " is", "probability": 0.4052734375}, {"start": 1640.13, "end": 1640.47, "word": " equal", "probability": 0.65576171875}, {"start": 1640.47, "end": 1640.57, "word": " to", "probability": 0.96484375}, {"start": 1640.57, "end": 1640.75, "word": " Q", "probability": 0.5166015625}, {"start": 1640.75, "end": 1641.13, "word": " in", "probability": 0.046875}, {"start": 1641.13, "end": 1641.45, "word": " E,", "probability": 0.7412109375}, {"start": 1641.75, "end": 1642.51, "word": " right?", "probability": 0.49267578125}, {"start": 1643.77, "end": 1644.19, "word": " Correct?", "probability": 0.233154296875}, {"start": 1644.71, "end": 1644.99, "word": " Good.", "probability": 0.52587890625}, {"start": 1646.21, "end": 1646.43, "word": " This", "probability": 0.66259765625}, {"start": 1646.43, "end": 1646.49, "word": " is", "probability": 0.8701171875}, {"start": 1646.49, "end": 1646.55, "word": " a", "probability": 0.6279296875}, {"start": 1646.55, "end": 1646.73, "word": " vector", "probability": 0.94189453125}, {"start": 1646.73, "end": 1646.83, "word": " and", "probability": 0.67822265625}, {"start": 1646.83, "end": 1646.93, "word": " this", "probability": 0.84765625}, {"start": 1646.93, "end": 1646.97, "word": " is", "probability": 0.92431640625}, {"start": 1646.97, "end": 1647.01, "word": " a", "probability": 0.67529296875}, {"start": 1647.01, "end": 1647.33, "word": " vector.", "probability": 0.93798828125}, {"start": 1648.13, "end": 1648.53, "word": " This", "probability": 0.7646484375}, {"start": 1648.53, "end": 1648.95, "word": " is", "probability": 0.63525390625}, {"start": 1648.95, "end": 1649.15, "word": " Q,", "probability": 0.438720703125}, {"start": 1649.45, "end": 1649.85, "word": " not", "probability": 0.7822265625}, {"start": 1649.85, "end": 1650.23, "word": " Q0.", "probability": 0.659912109375}], "temperature": 1.0}, {"id": 65, "seek": 167639, "start": 1651.03, "end": 1676.39, "text": " It's a condition. We are living. Okay. Because I said Q. My question is for you. This is East. This is negative. How is this? West. There is no such thing as Alif. Like Alif. 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Is there anyone who doesn't understand? How to get it? Tell me. The space is not ready to enter from there. What is not ready to enter from there? Did you find this red Q? 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This is how we learned that E is equal to KQ divided by R squared. Right or wrong? This is what we put here, one by one. Think of this quantity. This is an egg. It moves in this direction. You learned that the direction of the space has two possibilities. It does not come out of the container nor does it enter the container. 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If the charge is negative, that's it. I want to know how to apply it now. You say, easy, you have this point, there is room. E1, E1 is the result of Q1. Is Q1 positive or negative? Get rid of it. Get rid of it. This is going to it. That's it. That's it. Other than that. 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Come on, girls. As a magnitude, write it one by one. I say E1 as a magnitude. Who is better than me or him? Equals K. K1 as absolute value. On R1 squared or not? I'm still bringing the magnitude. Okay. K1 is important, so it's not a problem. The absolute value doesn't matter much. 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Is it clear? Good. Say it again. Say it again. Say it again. Say it again. Say it again. Say it again. Say it again. Say it again. Say it again. Say it again. Say it again. Say it again. Say it again. Say it again. Say it again. Say it again. Say it again. Say it again. Say it again. Say it again. Say it again. Say it again. Say it again. Say it again. Say it again. Say it again. Say it again. Say it again. Say it again. Say it again. Say it again. Say it again. Say it again. Say it again. Say it again. Say it again. Say it again. Say it again. Say it again. Say it again. Say it again. Say it again. Say it again. Say it again. Say it again. Say it again. Say it again. Say it again. Say it again. Say it again. Say it again. Say it again. 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By competition. Right? I'll give you another example and you won't get it. Right? It's what you're interested in. It's what you have. Right? Is this the same pie or not? By competition. I'll give you another example of a pie that's equal to a square. 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Okay, cosine of phi, this carrot, can I write it for you? Okay, thank God.", "tokens": [407, 264, 23565, 295, 13107, 307, 2681, 281, 264, 3732, 5593, 295, 341, 11, 382, 321, 848, 300, 341, 307, 288, 3732, 1804, 257, 3732, 11, 341, 307, 264, 5367, 286, 2729, 291, 570, 341, 1782, 775, 406, 362, 257, 3732, 11, 558, 30, 1033, 11, 23565, 295, 13107, 11, 341, 22767, 11, 393, 286, 2464, 309, 337, 291, 30, 1033, 11, 1309, 1265, 13], "avg_logprob": -0.7192234694957733, "compression_ratio": 1.6751592356687899, "no_speech_prob": 1.0728836059570312e-06, "words": [{"start": 2218.44, "end": 2218.78, "word": " So", "probability": 0.576171875}, {"start": 2218.78, "end": 2218.98, "word": " the", "probability": 0.1524658203125}, {"start": 2218.98, "end": 2219.26, "word": " cosine", "probability": 0.7861328125}, {"start": 2219.26, "end": 2220.36, "word": " of", "probability": 0.88330078125}, {"start": 2220.36, "end": 2220.68, "word": " phi", "probability": 0.17578125}, {"start": 2220.68, "end": 2220.96, "word": " is", "probability": 0.38037109375}, {"start": 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It equals, because I'm going to get used to this G. Instead of E1, I subtract this. It equals KQ1 E square plus Y square. Instead of the equation, send it to me. What? One and a half. And here there is one. 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This is E1 as a vector. Don't worry. Everything is written for you. Just don't get confused. 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I want to take it from here. I want to solve it. Pay attention. This is E2. I want to add this. Solve it. This is E2 cosine of theta and this is E2 sine of theta. 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So, the equation is negative. So, what is theta? It is B. Now, it is alternating. It is still alternating with cosine and sine. Cosine of theta is equal to B divided by this. Sine is equal to I divided by this. 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Right? Yes, this is the opposite of me. Yes, bravo. Good that I made a mistake. So that I can see if you are correct or not. Good that I made a mistake. Good. You are correct. They scolded me because I don't want to write a new chapter. I want to get this. I put its place B and put 3x2 here. Same thing. Same thing. 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He gave me the first double magnitude and then he calculated it. He calculated it and gave me the result. He told me to combine the sine with the sine and the cosine with the cosine. Fine. Of course, I got used to the cosine and sine. Right or wrong? He told me to look at the second requirement. 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Okay, is this going to be a lot of fun or not? Finish the question. This is easy. This is 3x2, but my kitchen is wrong. Okay? Okay? The last thing before the quiz, bear with me. Good. Okay. Look at this question, girls. Focus on me because I also wrote quizzes about it in the previous lecture. 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"end": 2895.38, "word": " the", "probability": 0.88134765625}, {"start": 2895.38, "end": 2895.46, "word": " point", "probability": 0.94091796875}, {"start": 2895.46, "end": 2895.64, "word": " of", "probability": 0.97265625}, {"start": 2895.64, "end": 2896.08, "word": " equality.", "probability": 0.92724609375}, {"start": 2897.08, "end": 2897.3, "word": " You", "probability": 0.953125}, {"start": 2897.3, "end": 2897.34, "word": " will", "probability": 0.84521484375}, {"start": 2897.34, "end": 2897.52, "word": " find", "probability": 0.845703125}, {"start": 2897.52, "end": 2897.6, "word": " a", "probability": 0.1446533203125}, {"start": 2897.6, "end": 2897.6, "word": " lot", "probability": 0.9501953125}, {"start": 2897.6, "end": 2897.6, "word": " of", "probability": 0.96875}, {"start": 2897.6, "end": 2897.8, "word": " questions", "probability": 0.84130859375}, {"start": 2897.8, "end": 2898.2, "word": " about", "probability": 0.1663818359375}, {"start": 2898.2, "end": 2898.44, "word": " models", "probability": 0.63916015625}, {"start": 2898.44, "end": 2898.64, "word": " like", "probability": 0.8837890625}, {"start": 2898.64, "end": 2899.38, "word": " this.", "probability": 0.63623046875}, {"start": 2899.4, "end": 2899.78, "word": " Quizzes", "probability": 0.615875244140625}, {"start": 2899.78, "end": 2899.96, "word": " like", "probability": 0.91357421875}, {"start": 2899.96, "end": 2900.32, "word": " this.", "probability": 0.7138671875}, {"start": 2900.66, "end": 2900.88, "word": " God", "probability": 0.403564453125}, {"start": 2900.88, "end": 2901.02, "word": " bless", "probability": 0.86376953125}, {"start": 2901.02, "end": 2901.08, "word": " you.", "probability": 0.94140625}], "temperature": 1.0}], "language": "en", "language_probability": 1.0, "duration": 2901.612, "duration_after_vad": 2779.194374999989}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZzXsCLffozucGP33XWqvBP/6EA8y2Cx6jI.srt b/PL9fwy3NUQKwZzXsCLffozucGP33XWqvBP/6EA8y2Cx6jI.srt
new file mode 100644
index 0000000000000000000000000000000000000000..707084caac148b956b72b3aced53c41d2348d9ea
--- /dev/null
+++ b/PL9fwy3NUQKwZzXsCLffozucGP33XWqvBP/6EA8y2Cx6jI.srt
@@ -0,0 +1,1991 @@
+1
+00:00:05,180 --> 00:00:11,850
+تمام، بعد بسم الله، نبدأ بهذا الشابتر السادس، وهو من
+
+2
+00:00:11,850 --> 00:00:17,970
+الشباتر المركزية في المادة، وزي ما حكينا، قلصنا منه
+
+3
+00:00:17,970 --> 00:00:22,090
+بعض الـ sections ورحلناهم على الشابتر اللي قبله، صار
+
+4
+00:00:22,090 --> 00:00:27,050
+في عندي فقط المواضيع المهمة جداً، هي اللي بدنا نتطرق
+
+5
+00:00:27,050 --> 00:00:31,390
+إليها إن شاء الله بالتفصيل. هنحكي عن التوصيل على
+
+6
+00:00:31,390 --> 00:00:35,810
+التوالي والتوازي، بس المرة هذه للمقومات، مش للمكثفات.
+
+7
+00:00:36,400 --> 00:00:39,580
+بعدين هنحكي عن الشغل اللي بتحبوها،  Kirchhoff’s Rules.
+
+8
+00:00:39,580 --> 00:00:46,620
+تمام؟ وبعد كده موضوع آخر هو الـ RC Circuits، وهي
+
+9
+00:00:46,620 --> 00:00:50,520
+الدوائر اللي فيها R و C، R مقاوم و C Capacitor، لما
+
+10
+00:00:50,520 --> 00:00:54,920
+يكونوا مع بعض. فيه بعض الشغلات العلمية اللي لازم
+
+11
+00:00:54,920 --> 00:00:57,960
+نأخذها في غاية الاعتبار، كون هذا Chapter من الشباتر
+
+12
+00:00:57,960 --> 00:01:02,360
+المهمة، وبالتالي هو أصلاً مكتّر أسئلة، ولما جينا
+
+13
+00:01:02,360 --> 00:01:06,730
+اطلعنا، واحنا قاعدين بنجمع من الأسئلة، كلهم مهمين
+
+14
+00:01:06,730 --> 00:01:12,930
+وبالتالي بعين الله، كتار شوية، كبشة يعني، بدهم
+
+15
+00:01:12,930 --> 00:01:19,510
+ينحلوا، لأن هذا شابتر مركزي طبعاً في الـ term اللي
+
+16
+00:01:19,510 --> 00:01:22,650
+موعده السبت الجاي. مش هيكون هذا داخل، لكن في الـ
+
+17
+00:01:22,650 --> 00:01:29,870
+final هيكون. ناططكم أول سؤال بيكون موجود، تمام؟ زي ما
+
+18
+00:01:29,870 --> 00:01:37,260
+انتوا شايفين، سطرين كيف بيكون حلوة؟ بدهم جلسة
+
+19
+00:01:37,260 --> 00:01:42,960
+هيك بكاسة شاي بيخلصوا، حلو.
+
+20
+00:01:42,960 --> 00:01:47,580
+بقى الجلسة مش ربع ساعة، بعد ربع ساعة تقولوا زهجنا، و
+
+21
+00:01:47,580 --> 00:01:52,460
+عديتوها. جلسة، لأ، جلسة جلسة، يعني جلسة زي بعد التوريح
+
+22
+00:01:52,460 --> 00:02:01,220
+للـ سحور. هي جلسة تعتبر، بيخلصوا كمان. أخذنا يا بنات
+
+23
+00:02:01,220 --> 00:02:07,140
+التوصيل على التوالي للمكثفات. واحنا في عندنا شغلتين
+
+24
+00:02:07,140 --> 00:02:15,040
+شغلة بتقول إن I بتساوي ΔV على R، هذا قانون I.
+
+25
+00:02:15,040 --> 00:02:28,040
+وفي عندنا I<sub>Q</sub> بتساوي C في ΔV، مظبوط ولا لأ؟ شوفوا
+
+26
+00:02:28,040 --> 00:02:32,260
+إيش اللي صار؟ R هنا في المقام، لكن C هنا في
+
+27
+00:02:32,260 --> 00:02:37,620
+البسط. عشان كده عندكم في القوانين هتشوفوا العكس، بس
+
+28
+00:02:37,620 --> 00:02:42,800
+في القوانين. لكن نيجي للمبدأ، عند التوصيل على
+
+29
+00:02:42,800 --> 00:02:47,520
+التوالي للمكثفات، إيش الثابت؟ الشحنات في البطاريات.
+
+30
+00:02:47,520 --> 00:02:51,500
+الشحنات صارت شحنات متحدة، يعني انجلب التيار. إذا
+
+31
+00:02:51,500 --> 00:02:56,580
+التيار بيكون ثابت. اختلف المبدأ؟ ما اختلفش المبدأ.
+
+32
+00:02:56,580 --> 00:03:00,960
+جالي هاي المقومتين، زي ما أنتم شايفين، وكلنا بنعرف
+
+33
+00:03:02,270 --> 00:03:07,370
+الشحنات لا تفنى ولا تستحدث، وبالتالي في عندك تيار
+
+34
+00:03:07,370 --> 00:03:12,710
+ماشي منهان. أول ما تقول تيار، يعني فيه شحنات، صح؟
+
+35
+00:03:12,710 --> 00:03:17,750
+شحنات ماشية، وأنا توي حكيتها. نفترض شارع فيه مئة
+
+36
+00:03:17,750 --> 00:03:22,690
+سيارة. هدول المئة سيارة ماشيين. لا فيه سيارة هيمشي
+
+37
+00:03:22,690 --> 00:03:26,670
+يقول الشارع بلعها، ولا في النص هتزيدلي سيارة، نقول
+
+38
+00:03:26,670 --> 00:03:29,350
+والله سيارة ولدي السيارة، مظبوط ولا لأ؟ هذا
+
+39
+00:03:29,350 --> 00:03:31,870
+conservation of سيارات، conservation of the
+
+40
+00:03:31,870 --> 00:03:36,510
+charges. تمام، ماشيين مئة سيارة، أكمل سيارة بدهم
+
+41
+00:03:36,510 --> 00:03:41,680
+يخشوها. مئة وكم صغير ابن مخشوها مئة، إذا معناته I
+
+42
+00:03:41,680 --> 00:03:45,460
+الكلية اللي طلعت من هنا، هي نفسها I<sub>1</sub>، هي نفسها I
+
+43
+00:03:45,460 --> 00:03:49,440
+<sub>2</sub>، ولا لأ؟ هذا مبدأ التوالي، هذا مبدأ الـ
+
+44
+00:03:49,440 --> 00:03:54,260
+conservation of charge. إذا لازم I<sub>equivalent</sub> وهو
+
+45
+00:03:54,260 --> 00:03:59,560
+الكلي، يساوي I<sub>1</sub> يساوي I<sub>2</sub>. إذا بالقطع عند
+
+46
+00:03:59,560 --> 00:04:07,470
+التوالي، بدي أقول، هاي التيار هذا I، هو نفسه I<sub>1</sub>، هو
+
+47
+00:04:07,470 --> 00:04:11,470
+نفسه I<sub>2</sub>. في خلاف على هذه النقطة؟ مافيش خلاف.
+
+48
+00:04:11,470 --> 00:04:19,870
+اتطلعولي هالـ gate V<sub>A</sub>-V<sub>B</sub> هذه، هل هي فرق الجهد الكلي
+
+49
+00:04:19,870 --> 00:04:26,350
+ولا لأ؟ مظبوط ولا لأ؟ تمام، بتساوي V<sub>AB</sub>. مش خلاف،
+
+50
+00:04:26,350 --> 00:04:33,080
+صح؟ خلّيني أطرح V<sub>C</sub> وأجمع V<sub>C</sub>، عملتش إيه؟ لأ، وهذه
+
+51
+00:04:33,080 --> 00:04:40,580
+ناقص V<sub>B</sub>؟ خالص، وأنا إيش عملت؟ تمام؟ قال لي، هدول طلع
+
+52
+00:04:40,580 --> 00:04:43,900
+عليهم على الرسمة، تجري إنه يقول إن هذه ΔV<sub>1</sub>، ولا
+
+53
+00:04:43,900 --> 00:04:52,120
+لأ؟ طب وهذه ΔV<sub>2</sub>، طب وهذه، قال لي هذه ΔV<sub>equivalent</sub>
+
+54
+00:04:52,120 --> 00:04:59,090
+صح ولا لأ؟ إذا عند التوصيل على التوالي،
+
+55
+00:04:59,090 --> 00:05:03,670
+فرق الجهد الكلي هو مجموع فرق الجهود، ولا لأ؟ زي
+
+56
+00:05:03,670 --> 00:05:09,490
+المكثفات بالتمام، ولها قياسها زيها. إذا صار في عندك
+
+57
+00:05:09,490 --> 00:05:13,670
+ΔV<sub>equivalent</sub> بيساوي ΔV<sub>1</sub> زائد ΔV<sub>2</sub>.
+
+58
+00:05:13,670 --> 00:05:15,330
+قال لي طيب.
+
+59
+00:05:18,080 --> 00:05:21,200
+وهذا القانون مش بيقول، مش بيقول ΔV بتساوي I في
+
+60
+00:05:21,200 --> 00:05:24,440
+R، يعني ΔV<sub>equivalent</sub> بتساوي I<sub>equivalent</sub> في R<sub>equivalent</sub>
+
+61
+00:05:24,440 --> 00:05:27,860
+و ΔV<sub>1</sub> بتساوي I<sub>1</sub> في R<sub>1</sub>
+
+62
+00:05:27,860 --> 00:05:30,800
+و ΔV<sub>2</sub> بتساوي I<sub>2</sub> في R<sub>2</sub>، ولا لأ؟
+
+63
+00:05:30,800 --> 00:05:35,380
+اه، كتبنا، كتبنا. طب
+
+64
+00:05:35,380 --> 00:05:39,020
+قال لي هذه المعادلة إيش بتقول؟ بتقول لي هذا بيساوي هذا،
+
+65
+00:05:39,020 --> 00:05:47,560
+بيساوي هذا. إذا صار R<sub>equivalent</sub> مجموع الـ R. طيب، جالي
+
+66
+00:05:47,560 --> 00:05:50,240
+برضه، أنت قلت لي منها قوانين، ماذا؟ بالصيغة قوانين،
+
+67
+00:05:50,240 --> 00:05:58,240
+جالي R بتساوي ρ L على A، صح؟ أنت لما تجمع، A
+
+68
+00:05:58,240 --> 00:06:02,080
+الصرف، المقاومة زادت ولا لأ؟ يعني هذه خمسة وهذه خمسة،
+
+69
+00:06:02,080 --> 00:06:05,700
+وصلهم على التوالي، هيك صاروا عشرة، ولا لأ؟ يعني زادت
+
+70
+00:06:05,700 --> 00:06:09,700
+المقاومة. جالي: هو أنت لما توصلهم هيك، يا تورا، A
+
+71
+00:06:09,700 --> 00:06:16,160
+الصرف، الطول زاد، وحسب هذه القاعدة، منطقي إنه يزيد الـ
+
+72
+00:06:16,160 --> 00:06:20,580
+R ولا لأ؟ إذا أنت عند التوصيل على التوالي، بتزيد
+
+73
+00:06:20,580 --> 00:06:26,320
+المقاومة، لأن أنت طول السلك تضاعف أو زاد،
+
+74
+00:06:26,320 --> 00:06:31,340
+وبالتالي R<sub>equivalent</sub> منطقي إنه تكون أكبر من R<sub>1</sub>
+
+75
+00:06:31,340 --> 00:06:35,610
+وR<sub>2</sub>، تمام يا بنات؟ فيه مشكلة في التوصيل على التوالي؟
+
+76
+00:06:35,610 --> 00:06:39,110
+التوصيل على التوالي، فأنتوا بتقولوا عكس المكثفات،
+
+77
+00:06:39,110 --> 00:06:45,230
+المبدأ اتغير، تتساوى الشحنات، تتساوى التيارات نفسها،
+
+78
+00:06:45,230 --> 00:06:50,730
+وتتجزأ الجهود. ΔV<sub>equivalent</sub> بتساوي ΔV<sub>1</sub>
+
+79
+00:06:50,730 --> 00:06:54,990
+زائد ΔV<sub>2</sub>، مافيش أي خلاف عليها. تمام.
+
+80
+00:06:58,350 --> 00:07:01,070
+قال لي: التوازي… كيف بتوصل التوازي؟ كنا
+
+81
+00:07:01,070 --> 00:07:04,710
+نوصل المكثفات، كل طرفين مع بعض، صح؟  ما
+
+82
+00:07:04,710 --> 00:07:07,290
+المقاومات، كل واحد له طرف، ما هو هي المقاومة، هي
+
+83
+00:07:07,290 --> 00:07:11,390
+طرف، وهي طرف، وهي مقاومة، هي طرف وهي طرف، كل جيب
+
+84
+00:07:11,390 --> 00:07:14,790
+هدول طرفين مع بعض، وهدول طرفين مع بعض، صار عندك
+
+85
+00:07:14,790 --> 00:07:17,790
+طرف هنا، وطرف هنا، ماذا؟ هدول الطرفين موصلهم مع
+
+86
+00:07:17,790 --> 00:07:20,830
+بعض، جهدهم واحد ولا لأ؟ وهدول الموصلين مع بعض،
+
+87
+00:07:20,830 --> 00:07:24,490
+جهدهم واحد، إذا قطعا ΔV<sub>1</sub> بتساوي ΔV
+
+88
+00:07:24,490 --> 00:07:31,230
+<sub>2</sub>، وبتساوي ΔV الكلية. اه هيها، هذه النقطة
+
+89
+00:07:31,230 --> 00:07:35,570
+هي نفسها هذه، هي نفسها هذه، وهذه النقطة، ونفس هذه
+
+90
+00:07:35,570 --> 00:07:40,610
+النقطة نفس هذه النقطة، إذا ΔV<sub>AB</sub> هي نفسها ΔV
+
+91
+00:07:40,610 --> 00:07:49,850
+<sub>1</sub> وهي نفسها ΔV<sub>2</sub>، بالقطع. إذا
+
+92
+00:07:49,850 --> 00:07:53,130
+ΔV<sub>equivalent</sub> بتساوي ΔV<sub>1</sub> زي الـ ΔV<sub>2</sub>.
+
+93
+00:07:53,130 --> 00:07:58,440
+نرجع للمئة سيارة، المئة سيارة اللي كانوا ماشيين في
+
+94
+00:07:58,440 --> 00:08:02,980
+الشارع، اجوا عند مفترق طرق، هذا مفترق الطرق، قبله
+
+95
+00:08:02,980 --> 00:08:08,430
+بيوديهم هيك، وبيوديهم هيك، على الـ gate. كل المئة بدهم
+
+96
+00:08:08,430 --> 00:08:12,110
+يروحوا مع بعض؟ لأ، لو ستين راحوا هيك، إيش ده؟
+
+97
+00:08:12,110 --> 00:08:16,710
+قطعاً أربعين، صح ولا لأ؟ إذا أنت، جماعة اللي راح
+
+98
+00:08:16,710 --> 00:08:20,510
+يمين، وجماعة اللي راح يسار، قلت بيساوي I الكلية
+
+99
+00:08:20,510 --> 00:08:24,930
+ولا لأ؟ أجي أطلق، هاي السيارات اللي هم الشحنات،
+
+100
+00:08:24,930 --> 00:08:28,170
+ماشي، نجوا هنا، قالوا كلنا بدنا نروح هناك؟ لأ،
+
+101
+00:08:28,170 --> 00:08:32,170
+نعمل زحمة، مظبوط ولا لأ؟ جزء مننا راح هنا، وجزء
+
+102
+00:08:32,170 --> 00:08:37,250
+مننا راح هنا. طبعاً، هذا زائد هذا بيساوي هذا، ولا لأ؟ إذا
+
+103
+00:08:37,250 --> 00:08:42,290
+I<sub>equivalent</sub> بتساوي I<sub>1</sub> زائد I<sub>2</sub>، مافيش خلاف
+
+104
+00:08:42,290 --> 00:08:47,570
+على هذه النقطة. إذا معناته على طول I<sub>equivalent</sub>
+
+105
+00:08:47,570 --> 00:08:52,070
+بتساوي مجموع التيارات، لأن التيارات انقسمت. تمام، دي
+
+106
+00:08:52,070 --> 00:08:55,890
+ربعكم. هذه قاعدة،  كررها في الأول، قعدنا من جهها. تمام.
+
+107
+00:08:55,890 --> 00:09:02,450
+قال لي: ارجع، قال لي إيه؟ جالي I بتساوي ΔV على R، إذا
+
+108
+00:09:02,450 --> 00:09:04,690
+I<sub>equivalent</sub> بتساوي ΔV<sub>equivalent</sub> على R<sub>equivalent</sub>
+
+109
+00:09:04,690 --> 00:09:08,850
+مظبوط ولا لأ؟ لما أجي أنا أعوض، محل هادي،
+
+110
+00:09:08,850 --> 00:09:14,170
+ومحل هادي، ومحل هادي، ده اللي طلعت هيك، صح؟
+
+111
+00:09:15,580 --> 00:09:20,000
+المعادلة الأولى بتخلي البسط كله يروح، إذا صار في
+
+112
+00:09:20,000 --> 00:09:23,540
+عندي عكس التوازي، يعني R<sub>equivalent</sub> بتساوي R<sub>1</sub> في
+
+113
+00:09:23,540 --> 00:09:27,100
+R<sub>2</sub> على R<sub>1</sub> زائد R<sub>2</sub>. يعني عندي مقاومتين
+
+114
+00:09:27,100 --> 00:09:32,460
+على التوازي، عشرة عشرة، كده، إيش النتيجة؟ خمسة، ليه؟ جالي:
+
+115
+00:09:32,460 --> 00:09:37,120
+أنت كيف وصلتهم؟ بتقول وصلتهم هيك، مظبوط؟ إيش صار
+
+116
+00:09:37,120 --> 00:09:43,480
+في العرض؟ زاد، اتسع. جيد. عندنا نرجع للشوارع، شارع فيه
+
+117
+00:09:43,480 --> 00:09:47,000
+جزيرة في النص، إجت البلدية قالت: زحمة من الجزيرة،
+
+118
+00:09:47,000 --> 00:09:53,860
+ممكن تكون one way، اتحسنت الطريق ولا لأ؟ وهذه نفس
+
+119
+00:09:53,860 --> 00:09:58,580
+العملية، إذا أنت إيش زودت؟ زودت إيش؟ إيش صرف R؟
+
+120
+00:09:58,580 --> 00:10:03,080
+قلّ، وصار صرف التوازي، شغلة منطقية إن R تقلّ، لأنك
+
+121
+00:10:03,080 --> 00:10:04,960
+أنت زودت الوسعة.
+
+122
+00:10:07,180 --> 00:10:11,000
+مظبوط ولا لأ؟ إذا عند التوصيل على التوالي تتساوى
+
+123
+00:10:11,000 --> 00:10:14,440
+التيارات، وعند التوصيل على التوازي تتساوى الجهود.
+
+124
+00:10:14,440 --> 00:10:22,400
+إذا انقسم التيار، قطعاً مش توالي، صح؟ لأ، لأ يا روان.
+
+125
+00:10:22,400 --> 00:10:29,140
+إذا توزّع التيار، انتهى التوالي، ولم يثبت التوازي، لم
+
+126
+00:10:29,140 --> 00:10:33,640
+يثبت التوازي. عشان تثبت التوازي، بدك تتحقق من ثبات
+
+127
+00:10:33,640 --> 00:10:38,540
+الجهود. أما أنت بتقول لي خلاص مش توالي، لأنه مرات لا
+
+128
+00:10:38,540 --> 00:10:42,100
+بيكون توالي ولا بيكون توازي. وعدنا هنشوف، وعدنا
+
+129
+00:10:42,100 --> 00:10:45,820
+هنرسم دائرة وبنشوف، احنا بدنا توزّع التيار، هل توازي
+
+130
+00:10:45,820 --> 00:10:50,620
+ولا لأ، تمام؟ شوفوا هالدائرة.
+
+131
+00:10:53,360 --> 00:10:57,480
+حاجات التيار بتوزع ولا لأ؟ مين بياخد أكبر نصيب؟
+
+132
+00:10:57,480 --> 00:11:02,220
+المقاومته أقل. طيب، لو كانت المقاومة صفر، إيش بتاخد
+
+133
+00:11:02,220 --> 00:11:08,080
+من التيار؟ كل التيار، كل التيار، صح ولا لأ؟ تمام. جالي:
+
+134
+00:11:08,080 --> 00:11:10,960
+اتطلع لي على الدائرة على اليسار، هذه اللي حاططها أنت
+
+135
+00:11:10,960 --> 00:11:17,720
+عليها، إيه؟ إجا التيار هنا، بده يتوزع، وين بروح؟ بروح
+
+136
+00:11:17,720 --> 00:11:23,020
+هنا، يعني هذه موجودة؟ هذه لا تهمل، أنا بقول بتعفن، هذه
+
+137
+00:11:23,020 --> 00:11:28,620
+العضو في الجسم، لما ما يخشوش دم، إيش بصير فيه؟ بيعفن.
+
+138
+00:11:28,620 --> 00:11:34,900
+تمام؟ والدم مش شحنات، قالت تهملي، أنا عفنت، راحت،
+
+139
+00:11:34,900 --> 00:11:40,400
+ما ليّش دعوة في الدائرة، تمام؟ قال لي: يعني أنت هنا كم
+
+140
+00:11:40,400 --> 00:11:46,770
+مقاومة في الدائرة هنا؟ واحدة. إذا بيقول لي: when the
+
+141
+00:11:46,770 --> 00:11:49,730
+switch in the circuit shown is closed، كان مغلق، زي ما
+
+142
+00:11:49,730 --> 00:11:54,070
+أنتم شايفينه، الأميتر… الأميتر إيش بيجيب؟ تيار
+
+143
+00:11:54,070 --> 00:11:57,670
+… الأميتر reads the current in the circuit، قرأ
+
+144
+00:11:57,670 --> 00:12:03,010
+التيار، قراءة معينة. ده اللي الآن بدي أفتح المفتاح،
+
+145
+00:12:03,010 --> 00:12:06,270
+وأشوف قراءة الأميتر إيش بده يحصل فيها لما أفتح
+
+146
+00:12:06,270 --> 00:12:09,970
+المفتاح، اللي كنت مهملتها، وقلت عنها بتعفن، بحييها
+
+147
+00:12:09,970 --> 00:12:15,280
+بإن الدم بدأ يجي فيها ولا لأ؟ بعتبرها شيء. طيب، هذه
+
+148
+00:12:15,280 --> 00:12:18,800
+مقاومة إيش صارت؟ طيب، ما في مقاومة جديدة، ولا لأ؟
+
+149
+00:12:18,800 --> 00:12:22,700
+صاروا اثنتين، كيف؟ توالي، توالي، إيش في
+
+150
+00:12:22,700 --> 00:12:26,780
+التوالي؟ بيصير مقاومة إيش مالها؟ زادت، ولما تزيدي
+
+151
+00:12:26,780 --> 00:12:29,920
+المقاومة، إيش بصير في التيار؟ بيقل التيار، إذا
+
+152
+00:12:29,920 --> 00:12:33,880
+بتوقعي قراءة الأميتر، تريد تقول لي فيها؟ تقلّ، فبقول
+
+153
+00:12:33,880 --> 00:12:38,020
+increased ولا decreased ولا unchanged عشان ما
+
+154
+00:12:38,020 --> 00:12:43,740
+تزعلوا، ولا zero في الحالتين، تمام؟ إذا أنتم
+
+155
+00:12:43,740 --> 00:12:50,320
+حللناها، وجيناها إنها decreased لزيادة R، وهناك
+
+156
+00:12:50,320 --> 00:12:54,280
+معايير علاقة عكسية بين I و R،  توجلّطوها، ولكم
+
+157
+00:12:54,280 --> 00:13:00,380
+تعرفوها، صحيح ولا لأ؟ واضح هذا الـ quiz؟ واضح، تمام؟
+
+158
+00:13:00,380 --> 00:13:06,990
+قال لي: أنا بقول لك ولو… كتبت لك سؤال، عند التوصيل
+
+159
+00:13:06,990 --> 00:13:10,310
+على التوالي، إيش بيصير في التيارات؟ بتقولي ثابتة، صح
+
+160
+00:13:10,310 --> 00:13:16,030
+ولا لأ؟ بعرفها. جبت السؤال هذا كيف متواصلين؟ هدوء.
+
+161
+00:13:16,030 --> 00:13:21,030
+قال لي: والله المقاومات مش زي بعض، ليش؟ هيه بيقول لي
+
+162
+00:13:21,030 --> 00:13:24,590
+واحدة اثنين، وواحدة أربعة، وواحدة ستة. قال لي: مين من
+
+163
+00:13:24,590 --> 00:13:29,790
+هالمقاومات بيحمل أكبر تيار؟ مش  أكبرها، ولا أعرجها،
+
+164
+00:13:29
+
+223
+00:17:44,560 --> 00:17:50,740
+الطيار Delta V على R 42 على 14 طلع تلاتة إذا هنا
+
+224
+00:17:50,740 --> 00:17:54,800
+الطيار تلاتة أمبير في خلاف؟ وأنت قلت لي هذا
+
+225
+00:17:54,800 --> 00:17:58,960
+equivalent لتنتين متواصلتين على التوالي وعند التوالي
+
+226
+00:17:58,960 --> 00:18:02,400
+I واحد بتساوي I اتنين بتساوي I equivalent I
+
+227
+00:18:02,400 --> 00:18:05,380
+equivalent بتساوي I واحد بتساوي I اتنين إذا هذه
+
+228
+00:18:05,380 --> 00:18:10,840
+تلاتة وهذه تلاتة تمام إذا قلت له هذه تلاتة مظبوط
+
+229
+00:18:10,840 --> 00:18:15,060
+هيك ولا لأ؟ قال لي ارجع، قال لي هذه كيف جاية؟ قلت له
+
+230
+00:18:15,060 --> 00:18:18,720
+تنتين على التوالي إذا هذه تلاتة وهذه تلاتة إذا هذه
+
+231
+00:18:18,720 --> 00:18:24,950
+تلاتة وهذه تلاتة، واحدة واحدة، لكن واحد قال لي طيب
+
+232
+00:18:24,950 --> 00:18:27,810
+لو بدي أشوف أنا حلي صح ولا لا؟ قلت له جدّي الجهود هذه
+
+233
+00:18:27,810 --> 00:18:31,490
+قلت له اتنين في تلاتة ستة، تلاتين وتلاتة في اتنين
+
+234
+00:18:31,490 --> 00:18:36,920
+ستة، أجمعهم وأطلع أربعة وأربعين، إذا أنا بحل صح تمام
+
+235
+00:18:36,920 --> 00:18:41,900
+قال لي حلو، قال لي هادي جاية من وين؟ قلت له جاية من
+
+236
+00:18:41,900 --> 00:18:45,400
+تنتين توازي، إيش اللي بتسوي على التوازي؟ يعني هادي
+
+237
+00:18:45,400 --> 00:18:50,180
+ستة volt، هادي قد إيش؟ وهادي ستة، إذا هادي ستة volt
+
+238
+00:18:50,180 --> 00:18:55,520
+يلا، في طيار قال لي ستة على ستة واحد، وستة على اتنين
+
+239
+00:18:55,520 --> 00:19:01,800
+المقاومة الأقل أخدت طيار أكبر ولا لأ؟ أجمع الطيارين
+
+240
+00:19:02,930 --> 00:19:06,510
+let charge is conserved, let charge is conserved
+
+241
+00:19:06,510 --> 00:19:11,910
+أيه يا بنات؟ أو ممكن قبل ما تجيب الجهد لهذه تسويه أكتر
+
+242
+00:19:11,910 --> 00:19:17,010
+يعني طيب هي هي بس بدك تطولي أنت هيك حالك كل يوم
+
+243
+00:19:17,010 --> 00:19:20,530
+بدك هي هي هيك شوفها أحلى، تجيبي الجهد وبتسويه
+
+244
+00:19:20,530 --> 00:19:24,230
+بتجيبي معادلة إن هذي بتساوي هذي وتعملي المعادلتين
+
+245
+00:19:24,230 --> 00:19:28,320
+أطول أطول.. جرب.. جرب في الدار.. ممكن أنت مخترع
+
+246
+00:19:28,320 --> 00:19:32,000
+طريقة تانية ومخك تدي بها.. بس هي أسهل.. أما
+
+247
+00:19:32,000 --> 00:19:35,400
+صحيح.. على حالك صحيح.. أيه يا بنات؟ في أي صفصة؟
+
+248
+00:19:35,400 --> 00:19:40,040
+كمان مثال.. أسهل من هذا.. برضه مثال كتاب.. ها
+
+249
+00:19:40,040 --> 00:19:42,440
+.. مش أنا.. مش أنا بنجيبهم يعني.. عشان ما
+
+250
+00:19:42,440 --> 00:19:44,960
+تتهمونيش أني أنا بدي اللي سهل.. هذا الكتاب هو
+
+251
+00:19:44,960 --> 00:19:49,760
+هيك اللي جاية..
+
+252
+00:19:49,760 --> 00:19:55,220
+كيف ما توصلين يا بنات؟ توازي.. بيقول لي three
+
+253
+00:19:55,220 --> 00:19:57,860
+resistors are connected، أي شون، أي شون يعني برا
+
+254
+00:19:57,860 --> 00:20:04,840
+ليه؟ صح ولا لا؟ طيب برا لإيش؟ بنتساوي؟ فرق الجهد
+
+255
+00:20:04,840 --> 00:20:08,560
+على كل واحدة، أنا عارف ولا لا؟ تعرف تجيب الكورة
+
+256
+00:20:08,560 --> 00:20:14,920
+فيها كل واحدة؟ صح ولا لا؟ اه، تمنتعش على تلاتة ستة
+
+257
+00:20:14,920 --> 00:20:19,860
+تمنتعش على تلاتة ستة تسعة، تمنتعش على تسعة اتنين، تسعة و
+
+258
+00:20:19,860 --> 00:20:25,440
+اتنين أحد عشر، إذا طيار كل أحد عشر، اتجسم لستة و
+
+259
+00:20:25,440 --> 00:20:31,610
+تلاتة واتنين، صح ولا لا؟ إذا I equivalent بتساوي 11
+
+260
+00:20:31,610 --> 00:20:35,970
+أمبير، صح ولا لا؟ طيب تقدروا تجيبوا لي R equivalent من
+
+261
+00:20:35,970 --> 00:20:38,890
+Delta V equivalent على I equivalent، بقدر أديها بقى
+
+262
+00:20:38,890 --> 00:20:43,070
+بقدر أديها بقى، اه، شوفوا، بده بيقول لي find the current
+
+263
+00:20:43,070 --> 00:20:47,500
+in each resistor، هيحلها، يخلص، متصنع التوازن وأنت
+
+264
+00:20:47,500 --> 00:20:50,480
+مديني الجهود والجهد الكلي، هذا هو نفس الجهد ده كل
+
+265
+00:20:50,480 --> 00:20:53,720
+واحدة، المطلوب التاني برضه عشان يصعب السؤال يقول ما
+
+266
+00:20:53,720 --> 00:20:58,520
+بستاهل وما نقولش إن هذا مغوظ لحاله وبيجيبش للأسل
+
+267
+00:20:58,520 --> 00:21:01,780
+السهلة، قال يلا نصعب هذا السؤال بيقول اوجد ال
+
+268
+00:21:01,780 --> 00:21:06,760
+power على كل واحدة والـ power الكلية، Calculate the
+
+269
+00:21:06,760 --> 00:21:09,080
+power delivered to each resistor and the total
+
+270
+00:21:09,080 --> 00:21:11,600
+power delivered to the combination، Delivered يعني
+
+271
+00:21:11,600 --> 00:21:15,960
+استهلك أو راح، مديت لأن هذه المقاومات إحنا اتفقنا
+
+272
+00:21:15,960 --> 00:21:20,080
+load، تذكرين كلمة load؟ Load يعني أجهزة، يعني هذه
+
+273
+00:21:20,080 --> 00:21:24,400
+شبكة، شبكة تتضاهر، حطت غسالة، عبء أو load، حطت
+
+274
+00:21:24,400 --> 00:21:28,240
+غسالة أو حطت مكيف أو حطت تلاجة، هذه تلت مقاومات
+
+275
+00:21:28,240 --> 00:21:32,000
+موصّلة مع التوازي مع بعض، موصلة مع التوازي، هذا هم،
+
+276
+00:21:32,000 --> 00:21:35,520
+ده اللي كل واحدة بتستهلك طاقة ولا لأ؟ طاقة يعني
+
+277
+00:21:35,520 --> 00:21:38,960
+قدرة، ما هو الطاقة والقدرة قرايب، بينهم زمن،
+
+278
+00:21:38,960 --> 00:21:42,740
+صحيح؟ قال يجيب لي القدرة لكل واحدة، قد إيش سهلة
+
+279
+00:21:42,740 --> 00:21:45,420
+كانت القدرة، وبعدين يجيب لي القدرة الكلية، القدرة
+
+280
+00:21:45,420 --> 00:21:48,180
+الكلية هي اللي جيبتها من البطارية، ما هي، قال لي
+
+281
+00:21:48,180 --> 00:21:52,760
+بسيطة، القدرة، إيش هي الصيغ؟ ولا لأ؟ لأجهزة أفضل
+
+282
+00:21:52,760 --> 00:21:55,440
+تجيبها، أي تربيع في الأرض، ليس لو أنا إيش حسبتها،
+
+283
+00:21:55,440 --> 00:21:58,260
+والأرض معطية، طب أحد يقول لي طب بدي أجيب Delta V
+
+284
+00:21:58,260 --> 00:22:03,600
+تربيع على أرض، صح؟ كل واحد، قال لي يلا، هذه قلنا
+
+285
+00:22:03,600 --> 00:22:10,520
+جيبناها، مفيش خلاف، تمام، خلينا
+
+286
+00:22:10,520 --> 00:22:15,720
+نجيب I الكلية، قد إيش؟ قلنا 11، يلا نجيب R الكلية، R
+
+287
+00:22:15,720 --> 00:22:19,880
+equivalent، قلنا على التوازي التلاتة، واحدة واحدة
+
+288
+00:22:19,880 --> 00:22:24,400
+تلاتة مع الستة إيش بتعطي؟ اتنين، اتنين في تسعة، كيف
+
+289
+00:22:24,400 --> 00:22:29,300
+بنعملها؟ اتنين ضرب تسعة على اتنين زائد تسعة، يعني
+
+290
+00:22:29,300 --> 00:22:38,350
+تمنتعش على أحد عشر، صح؟ هذه R equivalent، بقول له V أو
+
+291
+00:22:38,350 --> 00:22:43,650
+sorry، I equivalent بتساوي Delta V equivalent على R
+
+292
+00:22:43,650 --> 00:22:50,810
+equivalent، جدّي Delta V equivalent، و
+
+293
+00:22:50,810 --> 00:22:55,070
+الله، طلعت 11 أمبير، صح؟ وأنا لما جمعتهم طلعت 11
+
+294
+00:22:55,070 --> 00:22:59,490
+أمبير، صحيحة تمام، قال لي بيدي الـ power في المطلوب
+
+295
+00:22:59,490 --> 00:23:01,990
+التاني، هديها 11 أمبير وجابها بطريقة تانية، R
+
+296
+00:23:01,990 --> 00:23:07,170
+equivalent اللي هي 1.8، 11، 1.624، مش مشكلة، قال لي for
+
+297
+00:23:07,170 --> 00:23:12,010
+the power، هي P1، هي P2، وهي P3، power أي تربيع في الـ
+
+298
+00:23:12,010 --> 00:23:16,370
+R، صح ولا لأ؟ تمام، قال لي طب أجمعهم، قال لي هاد أجمعهم
+
+299
+00:23:16,370 --> 00:23:21,590
+سهل، أيا جابها هيك 198، هم الجامع تبعتهم، أو بأجيبهم
+
+300
+00:23:21,590 --> 00:23:25,690
+من الـ I equivalent تربيع في الـ R equivalent، إذا زي
+
+301
+00:23:25,690 --> 00:23:32,030
+ما اتفقنا، سؤال سهل، تمام، هنجي التوالي والتوازي
+
+302
+00:23:32,030 --> 00:23:38,130
+خلصنا، ونبدأ بدائرة، نرجع لروان، تمام، هاي دائرة
+
+303
+00:23:48,400 --> 00:23:56,040
+شوف إزايها، طب خليني أخرب بيتكم، هاي اتنين أوم،
+
+304
+00:23:56,040 --> 00:24:06,640
+تلاتة أوم، خمسة أوم، أربعة أوم، تمانية أوم، تخربطيش
+
+305
+00:24:06,640 --> 00:24:11,060
+أنا هربط لك تمانية، اتنين
+
+306
+00:24:15,300 --> 00:24:18,660
+ما أنت بتطلع على.. أنت بتطلعش على اللوح
+
+307
+00:24:18,660 --> 00:24:22,340
+بتطلع على كتاب توجيهي، قاعدة لأ، مش خنطرة يا عزيزي
+
+308
+00:24:22,340 --> 00:24:26,080
+.. مش خنطرة.. مش خنطرة.. مش.. هذه مش الخنطرة
+
+309
+00:24:26,080 --> 00:24:33,580
+أنا بدي أرجع لروان، هجت، أي تيار هنا بيتوزع، مش
+
+310
+00:24:33,580 --> 00:24:34,700
+شوالي، هدول كوازي
+
+311
+00:24:38,110 --> 00:24:41,850
+كيف هنعرف إن أنا توازي؟ مش تساوي جهود؟ تساوي
+
+312
+00:24:41,850 --> 00:24:44,970
+تساوي، ها أحكي يا مريم، هم هادي وما هادي مع بعض؟ هم
+
+313
+00:24:44,970 --> 00:24:48,490
+هادي وما هادي زي بعض؟ كيف بأعرف إنهم زي بعض ولا
+
+314
+00:24:48,490 --> 00:24:51,870
+لا؟ بدي أمشي من واحدة للتانية، بديش أمور معايا، لا
+
+315
+00:24:51,870 --> 00:24:56,410
+مقاومة ولا بطارية ولا مكثف ولا ملف، في مجال حد
+
+316
+00:24:56,410 --> 00:24:59,950
+يروح ليه من النقطة هادي للنقطة هادي من دون ما يمر
+
+317
+00:24:59,950 --> 00:25:05,790
+على أي حاجة؟ تمانية أهو! ليش؟ تمانية ما لها؟ من
+
+318
+00:25:05,790 --> 00:25:09,940
+التمانية؟ برضه تطلع على كتاب توجيهي، جادّة، بتطلعوش
+
+319
+00:25:09,940 --> 00:25:12,520
+على كتاب توجيه، الكتاب توجيه، الأرقام مختلفة،
+
+320
+00:25:12,520 --> 00:25:17,200
+الأرقام مختلفة، الرسم زيها، الأرقام مختلفة، أنت
+
+321
+00:25:17,200 --> 00:25:21,580
+حاجة تقول ده تشوف زيها، خلاص صادقة، ده ما.. ده ما
+
+322
+00:25:21,580 --> 00:25:28,200
+.. لكن الأرقام مختلفة، إذا تقسمت التيارات، انتفت
+
+323
+00:25:28,200 --> 00:25:33,260
+التوالي ولم يثبت التوازي، تمام هيك؟ حلو، قلتوا
+
+324
+00:25:33,260 --> 00:25:39,160
+بكلمة كانت حلوة، أيه، كيرشوف، قال لي بحلوة كيرشوف
+
+325
+00:25:39,160 --> 00:25:43,140
+بقى، واجع عندك، حلّ غير غير كيرشوف، أحكي يا مريم، حلّها
+
+326
+00:25:43,140 --> 00:25:51,340
+التوالية، التوازية، أطلعك على الواحد، يلا، نجلّيني بلاش
+
+327
+00:25:51,340 --> 00:26:04,520
+أطلعك، خليها مضبوطة، إيش تلاتة؟ إيش هي؟ صوتت ما عجبهاش
+
+328
+00:26:04,520 --> 00:26:14,850
+الهادي مع الخمسة توازيه، هادي واحدة
+
+329
+00:26:14,850 --> 00:26:20,990
+واحدة واحدة واحدة، تلاتة وتمانية توازي، بقول لك نص
+
+330
+00:26:20,990 --> 00:26:25,250
+توازي، لأن هدول زي بعض، لكن هادي وهادي مش زي بعض، إذا
+
+331
+00:26:25,250 --> 00:26:27,890
+مش توازي، لأ يا ماريا
+
+332
+00:26:31,700 --> 00:26:37,740
+هو ده إيش؟ ما جاله شاله بفعل
+
+333
+00:26:37,740 --> 00:26:41,420
+ما هو عشان أقول توالي، مش لازم يتحقق شرط التوالي، مش
+
+334
+00:26:41,420 --> 00:26:44,740
+لجلنا، لازم التيار ما يتجزّقش، وجلنا التيار يتجزّأ من
+
+335
+00:26:44,740 --> 00:26:45,280
+أولها
+
+336
+00:26:49,320 --> 00:26:52,840
+اه، وين؟ طب ما كنتِ وأنا بحكي روان روان روان؟ وين
+
+337
+00:26:52,840 --> 00:26:58,560
+كنتِ؟ قلت إذا تجزّأ التيار، انتفت توالي ولم يثبت
+
+338
+00:26:58,560 --> 00:27:02,420
+التوازي، يعني مش عشانه مش توالي، إذا انقطع التوازي
+
+339
+00:27:02,420 --> 00:27:05,720
+مش، يعني مش الأذن هادي والأذن هادي، لأ، فيه أذن تالتة
+
+340
+00:27:05,720 --> 00:27:11,320
+تمام؟ اه، فيه أذن تالتة هنا، تفاجأنا يا نور؟ نفي
+
+341
+00:27:11,320 --> 00:27:18,480
+التوالي لا يثبت التوازي، هذه خلصنا منها، إيه ده؟ قال
+
+342
+00:27:18,480 --> 00:27:22,020
+يكيفوا يحلّوها، طبعًا زي ما اتفقنا اللي بده يتخصّص
+
+343
+00:27:22,020 --> 00:27:25,120
+هندسة كهربية وهندسة حاسوب، هيجيها بالتفاصيل، واللي
+
+344
+00:27:25,120 --> 00:27:29,140
+فيها أكتر من شغلة، لأنها دي دوائر ولازم تكونوا
+
+345
+00:27:29,140 --> 00:27:34,400
+عارفينها، إيه ده؟ كيرشوف، كيرشوف، علم كبير، إيه ده؟ فكر
+
+346
+00:27:34,400 --> 00:27:37,880
+جالي، والله، فيه قانونين كلكم بتعرفوهم، بدي أعيدهم، و
+
+347
+00:27:37,880 --> 00:27:41,800
+أسمّيهم باسمي، بحجة اللي أتجلم، أنا بدي أضبطهم، بحجة
+
+348
+00:27:41,800 --> 00:27:45,840
+اللي إيش؟ الشيء جالي، أنت توي مشغول، التيار لما
+
+349
+00:27:45,840 --> 00:27:51,910
+بدي أجيب، بيتوزّع، ما بينفعش يتوزّع ولا جَلّ، يعني عشرة بدها
+
+350
+00:27:51,910 --> 00:27:57,350
+تتوزّع إلى تلت أجسام، اتنين وتلاتة وخمسة، صح؟ لازم
+
+351
+00:27:57,350 --> 00:28:02,090
+ترجع، عشان.. برا علينا، قال هو وين بتوزّع التيار؟
+
+352
+00:28:02,090 --> 00:28:05,750
+قلت له زي ما وين بتتوزّع السيارات عند مفترق طرق
+
+353
+00:28:05,750 --> 00:28:08,870
+المفترق الطرق بيسمّوها junction، اتباعون الهندسة
+
+354
+00:28:08,870 --> 00:28:11,110
+المدنية بيسمّوها junction، واتباعون الهندسة
+
+355
+00:28:11,110 --> 00:28:14,250
+الكهربية بيسمّوها junction، هدول للسيارات، وهدول
+
+356
+00:28:14,250 --> 00:28:20,970
+للشحنات أو للتيارات، إذا قال كيرشوف، يلي قاعدتين، أول
+
+357
+00:28:20,970 --> 00:28:22,410
+قاعدة كلكم بتعرفوها
+
+358
+00:28:25,720 --> 00:28:32,240
+هو حبيبنا كيرشوف، اتوفّى سنة الـ 1887، تمام؟
+
+359
+00:28:32,240 --> 00:28:36,200
+كيرشوف
+
+360
+00:28:36,200 --> 00:28:43,280
+روسي ولا ألماني؟ أعتقد، هي، أعتقد أنه ألماني، أهمّ
+
+361
+00:28:43,280 --> 00:28:43,500
+المعنى
+
+362
+00:28:49,120 --> 00:28:55,520
+مش مشكلة، هنا، ده بندي الجنسية الألمانية عشان تجيب
+
+363
+00:28:55,520 --> 00:29:02,000
+حاجة أو جنسية روسية، ما نطلعوش من جبرو، تمام، هو مرات
+
+364
+00:29:02,000 --> 00:29:04,760
+الاسم في كلامك صحيح، لكن لما يقولوا ألمانيا هم
+
+365
+00:29:04,760 --> 00:29:08,670
+بتطلعوا على الجنسية مش الموطن، ممكن يكون أصله اه، و
+
+366
+00:29:08,670 --> 00:29:12,690
+في الآخر إن تروحوا على أمريكا بتلاقوش مواطن أمريكي
+
+367
+00:29:12,690 --> 00:29:15,810
+اللي بيقولوا من وين أصله؟ أصلاً مفيش واحد أصله
+
+368
+00:29:15,810 --> 00:29:19,370
+أمريكي إلا الهنود والحمر، والباقين كلهم اجوا من
+
+369
+00:29:19,370 --> 00:29:20,750
+بلدان متعددة
+
+370
+00:29:23,400 --> 00:29:27,540
+قال لي إيش؟ قال لي التيار هو لما إجيت أنا وصلت على
+
+371
+00:29:27,540 --> 00:29:32,120
+التوازن، قلت التيار كان داخل نقطة وبعدين خرج من
+
+372
+00:29:32,120 --> 00:29:36,640
+النقطة، إذا الداخل بيساوي الخارج، هي صيغة قاعدة كيرشوف
+
+373
+00:29:36,640 --> 00:29:40,020
+الأولى، ماهيش قاعدة بالمعنى الآخر، مش قانون، ما هو
+
+374
+00:29:40,020 --> 00:29:43,940
+قانون الأصل هو conservation of charge، إذا القانون
+
+375
+00:29:43,940 --> 00:29:48,380
+هو conservation of charge، صيغته بقاعدة، صياغة، إعادة
+
+376
+00:29:48,380 --> 00:29:53,430
+صياغة، قال لي the sum of the currents entering، داخلة
+
+377
+00:29:53,430 --> 00:29:56,970
+any junction، وعرفنا إيش معنى junction، must equal
+
+378
+00:29:56,970 --> 00:30:00,090
+the sum of the currents leaving that junction، كيف
+
+379
+00:30:00,090 --> 00:30:03,470
+يعني؟ قال لي هاي الـ junction؟ كيف؟ البنفسجية هذه؟
+
+380
+00:30:03,470 --> 00:30:07,410
+قال لي هاي تيار دخل عليها، هجد في حد ما بعرفش إنه داخلة
+
+381
+00:30:07,410 --> 00:30:13,570
+ولا خارجها دي؟ داخلة، داخلة، طب وهدول الاتنين؟ إذن
+
+382
+00:30:13,570 --> 00:30:17,910
+بقدر أقول هذه الـ junction ولا لأ؟ هذه هي الـ
+
+383
+00:30:17,910 --> 00:30:22,270
+junction، إذا أي junction، في أي موقف في مجلس حركتين
+
+384
+00:30:22,270 --> 00:30:27,350
+كانت تتفرع، لما التيار بدّه يتفرّع، بقول هي الـ
+
+385
+00:30:27,350 --> 00:30:33,190
+junction، junction؟
+
+386
+00:30:33,190 --> 00:30:38,910
+مش كل مكتب junction، هه، هان التيار بيتفرّعش، بيلوف
+
+387
+00:30:38,910 -->
+
+445
+00:34:51,690 --> 00:34:54,890
+first rule مش تبعتى هذا مبدأ الـ conservation of
+
+446
+00:34:54,890 --> 00:34:58,270
+charge. الـ first rule is an application of the
+
+447
+00:34:58,270 --> 00:35:02,690
+conservation of charge, while the second rule is a
+
+448
+00:35:02,690 --> 00:35:05,930
+conservation of energy; it is a consequence of the
+
+449
+00:35:05,930 --> 00:35:08,970
+conservation of energy لأنه هذا مبدأ حفظ الطاقة
+
+450
+00:35:08,970 --> 00:35:13,410
+لأن فرق الجهد أضربه في Q بيصير شغل، بيصير طاقة
+
+451
+00:35:13,410 --> 00:35:17,650
+فهذا مبدأ حفظ الطاقة اللي أنا بعمل لك إياه، بقول لك VA
+
+452
+00:35:17,650 --> 00:35:22,190
+لازم تساوي VA  وأنت ماشي، بتبدأ بالطاقة، بدك ترجع لنفس
+
+453
+00:35:22,190 --> 00:35:27,770
+الطاقة تمام، حلو. قال لي: بس مشكلتي مشكلة في الثانية
+
+454
+00:35:27,770 --> 00:35:31,490
+أن الـ Delta V هذه مرة بتكون موجبة ومرة بتكون
+
+455
+00:35:31,490 --> 00:35:35,270
+سالبة، بدك تنتبه لها. قال لي: to apply the second
+
+456
+00:35:35,270 --> 00:35:38,690
+rule, we should know the following two remarks، عشان
+
+457
+00:35:38,690 --> 00:35:43,010
+تطبق وتعرف الموجب والسالب، بدك تنتبه من شغلها. قال
+
+458
+00:35:43,010 --> 00:35:47,710
+لي: لو كان عندك هنا مقاومة وأنا أديتك التيار زي ما
+
+459
+00:35:47,710 --> 00:35:52,040
+أنت شايف، تخيلوا وين الطرف الموجب والطرف السالب
+
+460
+00:35:52,040 --> 00:35:57,180
+يعني هيك صح؟ طبعاً أول ما حطيت موجب وسالب، عرفت من
+
+461
+00:35:57,180 --> 00:36:00,220
+العالي ومن الواطي، تمام. قال: إيه، أنت كده بدك تمشي
+
+462
+00:36:00,220 --> 00:36:04,040
+قلت له: إذا أنا ماشي يمين، معناته طالع من العالي إلى
+
+463
+00:36:04,040 --> 00:36:09,900
+الواطي، معناته سالب، صح؟ من العالي للواطي يعني
+
+464
+00:36:09,900 --> 00:36:13,520
+كيف؟ عالي، واطي، يعني أنا ماشي هيك، معناته الـ
+
+465
+00:36:13,520 --> 00:36:17,380
+initial موجب، والـ final سالب، هو هي ماشي. قال: إيه
+
+466
+00:36:17,380 --> 00:36:26,290
+يعني أنت لو كنت ماشي هيك، بتحط سالب، تعكس، موجب
+
+467
+00:36:26,290 --> 00:36:32,330
+الأولى رايحة يمين، والتانية رايحة يسار. بيقول لي: that change in
+
+468
+00:36:32,330 --> 00:36:37,070
+potential through any resistor is negative for a
+
+469
+00:36:37,070 --> 00:36:41,850
+move in the direction of the current, and positive
+
+470
+00:36:41,850 --> 00:36:44,730
+for a move opposite to the direction of the
+
+471
+00:36:44,730 --> 00:36:46,930
+current. هذه اللي خدناها في المدرسة، لكن عرفنا ليش؟
+
+472
+00:36:46,930 --> 00:36:50,960
+لأنه انتقال من عالي لواطي، من واطي لعالي، هذا هي
+
+473
+00:36:50,960 --> 00:36:58,680
+بصورة بسيطة جداً، هي فرق، جهود في الآخر، فرق زي ما
+
+474
+00:36:58,680 --> 00:37:01,700
+تقول لكم: خمسة ناقص ثمانية، ولا ثمانية ناقص خمسة، عشان
+
+475
+00:37:01,700 --> 00:37:05,060
+أعرف إنها تلاتة، ولا سالب تلاتة. إذا والله ثمانية
+
+476
+00:37:05,060 --> 00:37:08,340
+ناقص خمسة، تلاتة، لكن إذا خمسة ناقص ثمانية، سالب تلاتة
+
+477
+00:37:08,340 --> 00:37:13,140
+إذا أنت بتقول لي فرق: نهاية ناقص بداية، إذا كانت
+
+478
+00:37:13,140 --> 00:37:20,590
+النهاية هي الواطية، سالب، واضحة ولا لأ؟ تمام. قال لي: طيب، و
+
+479
+00:37:20,590 --> 00:37:24,170
+البطارية؟ قلت: البطارية سهلة، أنا عندي قطب سالب و
+
+480
+00:37:24,170 --> 00:37:29,790
+قطب موجب، والله إذا أنت ماشي هيك، معناته موجب، وإذا
+
+481
+00:37:29,790 --> 00:37:33,850
+ماشي العكس، معناته سالب. يعني إذا أنت ماشي مع التيار،
+
+482
+00:37:33,850 --> 00:37:38,750
+موجب، وإذا ماشي ضد التيار، فهو سالب، تمام يا بنات؟
+
+483
+00:37:38,750 --> 00:37:45,680
+قاعدة سهلة جداً، وعارفينها، وطبقناها في المدرسة. إذا الـ
+
+484
+00:37:45,680 --> 00:37:47,940
+Change in potential through an ideal battery
+
+485
+00:37:47,940 --> 00:37:50,620
+is positive for a move from the negative to the
+
+486
+00:37:50,620 --> 00:37:53,420
+positive terminal of the battery, and negative for
+
+487
+00:37:53,420 --> 00:37:58,160
+a move in the opposite direction. هذه هي الـ
+
+488
+00:37:58,160 --> 00:38:03,120
+quiz،زين، بس حطيهم، أنا حكيتهم، طلع الـ quiz، بقول: قال
+
+489
+00:38:03,120 --> 00:38:06,960
+قاعدة كيرشوف الأولى هي نتيجة لأي قانون من القوانين
+
+490
+00:38:06,960 --> 00:38:13,860
+الأربعة اللي بدك إياهم: Conservation of Charge. إذا
+
+491
+00:38:13,860 --> 00:38:19,660
+هذه معناها: الشحن لا يُفنى ولا يُستحدث، وهذا مبدأ
+
+492
+00:38:19,660 --> 00:38:24,660
+Conservation of Charge. قال: طيب، كيرشوف، second rule
+
+493
+00:38:24,660 --> 00:38:28,620
+is a consequence of من الأربعة: Conservation of
+
+494
+00:38:28,620 --> 00:38:35,200
+Energy. حكيته، بس ب...مهم، عشان نعلمه، دي نقولها
+
+495
+00:38:35,200 --> 00:38:42,460
+يللا ننقل... ننقله، مية بركة، طلعت لك، تمام؟ اه، تمام
+
+496
+00:38:42,460 --> 00:38:49,120
+يا بنات؟ حلو. جيت بدي أحل، جيت بدي أعرف الستراتيجيات
+
+497
+00:38:49,120 --> 00:38:53,540
+اللي بنحطها عشان نبدأ نحل أسئلة كيرشوف. أجاكم سؤال
+
+498
+00:38:53,540 --> 00:38:58,820
+كيرشوف اللي في التوجيهي؟ كيف تعاملتوا عليه؟ اه، حلو، الحمد
+
+499
+00:38:58,820 --> 00:39:03,930
+لله. الحلو بيكون معايا كمية، اه، مش حلو في توجيهي، بس
+
+500
+00:39:03,930 --> 00:39:09,130
+إحنا بس بنحط عليه شوية مريح، بس، اه، فيه شوية مريح
+
+501
+00:39:09,130 --> 00:39:15,490
+زيادة عشان تطلع فكرة السؤال، عشان تطلع السؤال  واضح، لأ
+
+502
+00:39:15,490 --> 00:39:18,450
+ما تبقوا بنات صغيرة، مش ضغط ولا حاجة علينا، الضغط
+
+503
+00:39:18,450 --> 00:39:22,230
+إنتوا لسة بتخافوا من الضغط، لأن إنتوا بتاكلوا طرشي
+
+504
+00:39:22,230 --> 00:39:27,770
+وفلفل مكبوس، ومش عارفين إيه، جات عليها دي، تمام. طلعش
+
+505
+00:39:27,770 --> 00:39:33,480
+مين، نسوي، جلي، عشان تحل جلي، أول حاجة، الدائرة
+
+506
+00:39:33,480 --> 00:39:35,940
+بترسمها، قلت: الحمد لله كل الدوائر مرسومة في
+
+507
+00:39:35,940 --> 00:39:40,080
+الكتاب، إذا أول خطوة already إحنا بنعملها. Draw a
+
+508
+00:39:40,080 --> 00:39:42,620
+circuit diagram and label all quantities known and
+
+509
+00:39:42,620 --> 00:39:46,220
+unknowns. إيش يعني label؟ جالي: حط رموز، يعني زي
+
+510
+00:39:46,220 --> 00:39:51,000
+هذا السؤال. هنا قال: يعني إنت هذه R، حطها R واحد، هذه
+
+511
+00:39:51,000 --> 00:39:56,340
+R، حطها R إثنين، هذه R تلاتة، هذه R أربعة، وهذه R خمسة
+
+512
+00:39:56,340 --> 00:40:01,880
+هذه بيسميها ترميز، والتيارات قال لي: هذه I واحد اللي
+
+513
+00:40:01,880 --> 00:40:04,780
+هنا، I إثنين اللي هنا، I تلاتة اللي هنا، I أربعة، انهي
+
+514
+00:40:04,780 --> 00:40:08,660
+I خمسة، هذه سميها Epsilon. إذا عندك إثنين إبسلون،
+
+515
+00:40:08,660 --> 00:40:12,500
+إبسلون واحد وإبسلون إثنين، هذا بيسميه ترميز للرموز
+
+516
+00:40:12,500 --> 00:40:15,800
+اللي عندك، وإيش قال لي؟  النون والأنون، حتى لو معطاة
+
+517
+00:40:15,800 --> 00:40:19,480
+أنت بتقول بدي أنا نفترض R1 ماهي إثنين أوم، ترجع عنها
+
+518
+00:40:19,480 --> 00:40:23,900
+في الآخر، حتى لو known ومعروفة، أديها رمز عشان تكتب
+
+519
+00:40:23,900 --> 00:40:25,860
+المعادلة صح، تمام.
+
+521
+00:40:28,070 --> 00:40:31,010
+بيقول لي: أنت قاعدة كيرشوف التانية بتقول: ابدأ من
+
+522
+00:40:31,010 --> 00:40:34,410
+النقطة وارجع لها، صح؟  حاجات اللي تتخيلوا، بتبدأ من
+
+523
+00:40:34,410 --> 00:40:37,390
+النقطة وترجع لها، في عندك خيارين: لا تالي لهما،
+
+524
+00:40:37,390 --> 00:40:39,770
+لا بتمشي مع إتجاه الساعة، لا ضد إتجاه الساعة، في
+
+525
+00:40:39,770 --> 00:40:44,250
+خلاف؟ لأ. إذا بيقول لي: أنت مع إتجاه الساعة وضد إتجاه
+
+526
+00:40:44,250 --> 00:40:46,830
+الساعة، أنا أشوف ولا أي من، ولا بحب إتجاه الساعة ولا
+
+527
+00:40:46,830 --> 00:40:50,310
+بحب ضد إتجاهه، بس قول لي: وين رايح؟  خطة للإتجاه
+
+528
+00:40:50,310 --> 00:40:54,690
+اللي بتمشي فيه، دي a sign، حدد، a direction for
+
+529
+00:40:54,690 --> 00:40:57,500
+the current، أول في الحاجة، اه...أنا جيت وقال لي
+
+530
+00:40:57,500 --> 00:41:01,080
+التيارات...قال لي: التيارات كيف بدي أعملها؟ طب أنا
+
+531
+00:41:01,080 --> 00:41:03,420
+عندي قاعدة: التيار بيجي من قطب الموجب لقطب
+
+532
+00:41:03,420 --> 00:41:07,680
+السالب، صح؟ طب مش دائماً واضحة، قال لي: عشان كده لما
+
+533
+00:41:07,680 --> 00:41:12,900
+تخليش مخك يفكر ثانية، خلي قلبك يحط الـ directions،
+
+534
+00:41:12,900 --> 00:41:16,700
+where ما يحطوا يحطوا، where ما يحطوا يحطوا، إذا
+
+535
+00:41:16,700 --> 00:41:19,480
+بيقول لي: assign a direction for the current in each
+
+536
+00:41:19,480 --> 00:41:25,030
+part of the circuit.حضّرْك ومكمّل، Don't bother ولا
+
+537
+00:41:25,030 --> 00:41:29,570
+تجلد إطلاقاً if your guess of current direction is
+
+538
+00:41:29,570 --> 00:41:33,490
+incorrect. إذا كان تخمينك غلط، خمّل وما تخافش حتى
+
+539
+00:41:33,490 --> 00:41:38,450
+لو كان تخمينك خطأ، في هذه الحالة النتيجة هتطلع معاك
+
+540
+00:41:38,450 --> 00:41:43,410
+سالبة، بس طبعاً إحنا عشان نريح ونقعد نغلب بعض في
+
+541
+00:41:43,410 --> 00:41:47,430
+التصحيح، إحنا بنحط الـ directions في الامتحان برضه
+
+542
+00:41:47,430 --> 00:41:50,270
+عشان نريحنا. في الكتاب مرات بيقول لك: أنت حط الـ
+
+543
+00:41:50,270 --> 00:41:54,250
+direction، بنبدأ ناخد وجهته و نفكر، إيه الـ direction
+
+544
+00:41:54,250 --> 00:41:58,610
+تمام، بدي
+
+545
+00:41:58,610 --> 00:42:03,550
+أبدأ بكيرشوف رولز، طبعاً إنتوا عارفين إحنا كيف بنحل
+
+546
+00:42:03,550 --> 00:42:08,790
+بنحل على الفيزياء، صحيح؟ والفيزياء بتنُتج معادلات، كل
+
+547
+00:42:08,790 --> 00:42:12,130
+معادلة بنديها درجة. ما زلنا بدنا معادلات منهم،
+
+548
+00:42:12,130 --> 00:42:15,110
+معادلات منهم اللي بتيجي؟ من قاعدة كيرشوف، قاعدة
+
+549
+00:42:15,110 --> 00:42:17,070
+كيرشوف، قال لي: القاعدة الأولى فيها حد اللي بيخربط
+
+550
+00:42:17,070 --> 00:42:20,290
+فيها، ما بيخربطش إذا أنت حاطط، بتروحي تشوفي الـ
+
+551
+00:42:20,290 --> 00:42:24,030
+junction، بتكون الداخل بيساوي الخارج. إذا apply
+
+552
+00:42:24,030 --> 00:42:28,230
+the first Kirchhoff's rule to any junction in the
+
+553
+00:42:28,230 --> 00:42:31,770
+circuit. طيب، قال لي: طب لو في إثنين junction، باخد
+
+554
+00:42:31,770 --> 00:42:35,410
+ست درجات، تلاتة وتلاتة، بقول له: مش دائماً، ليش؟ قال لي:
+
+555
+00:42:35,410 --> 00:42:40,840
+طيب، إني أشوف هذه الدائرة، مش هذه a junction، وهذه بـ
+
+556
+00:42:40,840 --> 00:42:47,760
+junction. يلا، الداخل all  هنا بيساوي الخارج، I1 زي
+
+557
+00:42:47,760 --> 00:42:53,280
+I2. نيجي لهنا، اللي هذه هنا أصلاً كانت خارجها، وهذول
+
+558
+00:42:53,280 --> 00:43:01,220
+داخلين، صارت I1 زائد I2 بتساوي I. تقدر تقولي هذه واحدة
+
+559
+00:43:01,220 --> 00:43:06,260
+وحطولك تلت درجات، وهذه وحطولك تلت درجات، نفسه ما نفعش
+
+560
+00:43:06,260 --> 00:43:12,760
+إحنا ما نعدّش عدل هيك، يعني هو إحنا ما نعدّ معادلات
+
+561
+00:43:12,760 --> 00:43:16,120
+جبرية صحيحة، عشان كده إيش بيقول لي؟ بيقول لي: in general
+
+562
+00:43:16,120 --> 00:43:19,580
+this rule is used one time fewer than the number
+
+563
+00:43:19,580 --> 00:43:22,620
+of junctions in the circuit. إذا عندك two junctions،
+
+564
+00:43:22,620 --> 00:43:27,400
+استخدمها مرة، three junctions استخدمها مرتين،
+
+565
+00:43:27,400 --> 00:43:31,960
+four junctions استخدمها تلات مرات،كذا، أما مش كل
+
+566
+00:43:31,960 --> 00:43:34,660
+junctions، ويقول لي: هي معادلات، كل معادلة تلات درجات،
+
+567
+00:43:34,850 --> 00:43:40,070
+بتضبط تمام، بقول لها:
+
+568
+00:43:40,070 --> 00:43:47,930
+جيت أختار الـ loops. نيجي لهذه، كم loop فيها؟  ادّوا،
+
+569
+00:43:47,930 --> 00:43:54,530
+ادّوا، وما تتلعبوا، تطلعوها. طلعنا تلاتة هنا، هذه
+
+570
+00:43:54,530 --> 00:44:02,450
+الصغيرة حلوة، وهي هذه، وهي هذه، تلاتة، وينها؟ والله
+
+571
+00:44:02,450 --> 00:44:10,200
+يمكن تعدّوا ستة، ستة وسبعة، هاي واحدة، إثنين، هاي تلاتة
+
+572
+00:44:10,200 --> 00:44:18,680
+هاي أربعة، هاي خمسة، هاي ستة، و تعدّوا ثمانية، اختار الـ
+
+573
+00:44:18,680 --> 00:44:25,260
+loops. جالي: اختار أي loop، ابدأ من نقطة وارجع لها، لما
+
+574
+00:44:25,260 --> 00:44:28,740
+تبدأ من نقطة وإذا ترجع لها، بدك تختار إما مع قرب
+
+575
+00:44:28,740 --> 00:44:33,560
+الساعة أو ضد قرب الساعة. إن: choose any closed
+
+576
+00:44:33,560 --> 00:44:38,100
+loop in the network، نتورك، الشبكة، الدائرة كلها، and
+
+577
+00:44:38,100 --> 00:44:41,580
+designate a direction، وحدد إتجاه، كيف بدك تلف،
+
+578
+00:44:41,580 --> 00:44:46,480
+clockwise or counter clockwise، تمام، to traverse
+
+579
+00:44:46,480 --> 00:44:52,520
+the loop، عشان تلف على الـ loop، بداية من نقطة واحدة
+
+580
+00:44:52,520 --> 00:44:56,820
+في اللوب، اذهب حول اللوب في الاتجاه، الاتجاه، أو
+
+581
+00:44:56,820 --> 00:44:58,780
+الاتجاه، أو الاتجاه، أو الاتجاه
+
+582
+00:44:58,780 --> 00:44:58,800
+الاتجاه، أو الاتجاه، أو الاتجاه
+
+583
+00:44:58,800 --> 00:44:58,840
+أو الاتجاه، الاتجاه، أو الاتجاه، الاتجاه
+
+584
+00:44:58,840 --> 00:44:59,480
+الاتجاه، الاتجاه، الاتجاه، الاتجاه، الاتجاه، الاتجاه
+
+585
+00:44:59,480 --> 00:45:01,480
+الاتجاه، الاتجاه، الاتجاه، الاتجاه، الاتجاه، الاتجاه
+
+586
+00:45:01,480 --> 00:45:02,740
+الاتجاه، الاتجاه، الاتجاه، الاتجاه، الاتجاه، الاتجاه
+
+587
+00:45:02,740 --> 00:45:04,080
+الاتجاه، الاتجاه، الاتجاه، الاتجاه، الاتجاه، الاتجاه
+
+588
+00:45:04,080 --> 00:45:07,370
+الاتجاه، الاتجاه، الاتجاه، الاتجاه، الاتجاه، الاتجاه
+
+589
+00:45:07,370 --> 00:45:11,650
+كم لوب؟ قال لك: أنت كم مجاهيل عندك؟ تلاتة، كم معادلة
+
+590
+00:45:11,650 --> 00:45:14,570
+بتحتاجها؟ لك، تظل تختار الـ loops، لما تصبح عندك تلات
+
+591
+00:45:14,570 --> 00:45:18,110
+معادلات، كل معادلة عليها تلات درجات، نفترض تلاتة
+
+592
+00:45:18,110 --> 00:45:23,350
+تلاتة وتلاتة وتلاتة، كديش؟ تسعة، تظل علامة على جابر
+
+593
+00:45:23,350 --> 00:45:31,230
+صف سابع، كيف نحل العلاقات؟ تمام، اه، in doing so you
+
+594
+00:45:31,230 --> 00:45:33,090
+should know the two remarks we discussed before.
+
+595
+00:45:33,090 --> 00:45:36,330
+جالي: وأنا قاعد بجمع، بدك think بيه، في عندك مقاومات
+
+596
+00:45:36,330 --> 00:45:39,350
+وفي عندك بطاريات، think بيه، the potential
+
+597
+00:45:39,350 --> 00:45:44,150
+difference اللي بدك تجمعه across any battery
+
+598
+00:45:44,150 --> 00:45:49,070
+across any resistor is plus epsilon، بيكون زائد، if it is
+
+599
+00:45:49,070 --> 00:45:51,350
+traversed from the negative to the positive
+
+600
+00:45:51,350 --> 00:45:55,690
+terminal، and minus epsilon، if it traversed in the
+
+601
+00:45:55,690 --> 00:45:57,970
+opposite direction. وأنت ماشي، ما أنت قلت لي: مع
+
+602
+00:45:57,970 --> 00:46:00,730
+إتجاه الساعة وضد إتجاه الساعة، ماشي. إذا أنت
+
+603
+00:46:00,730 --> 00:46:03,150
+والله جاي من الـ negative للـ positive في البطارية،
+
+604
+00:46:03,150 --> 00:46:06,670
+بتحط زائد epsilon. إذا جاي من الـ positive للـ negative،
+
+605
+00:46:06,670 --> 00:46:09,990
+بتحط ناقص إبسلون، ده دي. طيب، في الـ
+
+606
+00:46:09,990 --> 00:46:13,270
+resistor، قلت له: فرق الجهد بيساوي I في R حسب قانون
+
+607
+00:46:13,270 --> 00:46:19,570
+أوم، إذا فرق الجهد في المقاومات إما زائد IR أو ناقص
+
+608
+00:46:19,570 --> 00:46:25,130
+IR، ناقص IR إذا وأنت ماشي والتيار معاك، وزائد IR
+
+609
+00:46:25,130 --> 00:46:29,170
+إذا وأنت ماشي والتيار عكسك. بقول: choose another
+
+610
+00:46:29,170 --> 00:46:34,380
+loop، اختار loop تانية، and repeat the fifth step to
+
+6
+
+667
+00:50:38,050 --> 00:50:41,470
+ال quiz يوم الخميس، لأنه قبل الامتحان معانا الجمعة
+
+668
+00:50:41,470 --> 00:50:45,390
+للساعة بيكون تمام تمام، نقف هنا عشان هذا السؤال
+
+669
+00:50:45,390 --> 00:50:48,230
+بنحله بالتفصيل المرة الجاية، يعطيكم العافية، و
+
+670
+00:50:48,230 --> 00:50:48,950
+بنكمل إن شاء الله
diff --git a/PL9fwy3NUQKwZzXsCLffozucGP33XWqvBP/6EA8y2Cx6jI_postprocess.srt b/PL9fwy3NUQKwZzXsCLffozucGP33XWqvBP/6EA8y2Cx6jI_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..8ab5d58ca49c7ebc0cb28abd302a78695e6b88b0
--- /dev/null
+++ b/PL9fwy3NUQKwZzXsCLffozucGP33XWqvBP/6EA8y2Cx6jI_postprocess.srt
@@ -0,0 +1,2680 @@
+1
+00:00:05,180 --> 00:00:11,850
+تمامبعد بسم الله بنبدأ بهذا الشابتر السادس وهو من
+
+2
+00:00:11,850 --> 00:00:17,970
+الشباتر المركزية في المادة وزي ما حكينا قلصنا منه
+
+3
+00:00:17,970 --> 00:00:22,090
+بعض ال section ورحلناهم على الشابتر اللي جابله صار
+
+4
+00:00:22,090 --> 00:00:27,050
+في عندي فقط المواضيع المهمة جدا هي اللي بدنا نتطرق
+
+5
+00:00:27,050 --> 00:00:31,390
+إليها ان شاء الله بالتفصيل هنحكي عن التوصيل على
+
+6
+00:00:31,390 --> 00:00:35,810
+التوالي والتوازي بس المرة هذه للمقومات مش للمكثفات
+
+7
+00:00:36,400 --> 00:00:39,580
+بعدين هنحكي عن الشغل اللي بتحبوها Casual Rules
+
+8
+00:00:39,580 --> 00:00:46,620
+تمام؟ و بعد كده موضوع أخر هو الRC Circuits وهي
+
+9
+00:00:46,620 --> 00:00:50,520
+الدوائل اللي فيها R و C R مقاوم و C Capacitor لما
+
+10
+00:00:50,520 --> 00:00:54,920
+يكونوا مع بعض إيه له بعض الشغلات العلمية اللي لازم
+
+11
+00:00:54,920 --> 00:00:57,960
+نخدها في عالي اعتبار كون هذا Chapter من الشباتر
+
+12
+00:00:57,960 --> 00:01:02,360
+المهمة وبالتالي هو أصلا مكتر أسئلة و لما جينا
+
+13
+00:01:02,360 --> 00:01:06,730
+اطلعنا و احنا بقعدين بنجي من الأسئلةجلهم مهمين
+
+14
+00:01:06,730 --> 00:01:12,930
+وبالتالي بعينكم الله كتار شوية كبشة يعني بدهم
+
+15
+00:01:12,930 --> 00:01:19,510
+ينحلوا لأن هذا شبطر مركزي طبعا في ال term اللي
+
+16
+00:01:19,510 --> 00:01:22,650
+معوعده السبت الجاي مش هيكون هذا داخل لكن في ال
+
+17
+00:01:22,650 --> 00:01:29,870
+final هيكون ناططكم اول سؤال بيكون موجود تمام زي ما
+
+18
+00:01:29,870 --> 00:01:37,260
+انتوا شايفين سطرين كيف بيكون حلوه؟بدهم جاي جلسة
+
+19
+00:01:37,260 --> 00:01:42,960
+هيك بكاسة شاي بيخلصوا حلو
+
+20
+00:01:42,960 --> 00:01:47,580
+بقى الجلسة مش ربع ساعة بعد ربع ساعة تقولوا زهجنا و
+
+21
+00:01:47,580 --> 00:01:52,460
+عديتوها جلسة لأ جلسة جلسة يعني جلسة زي بعد التوريح
+
+22
+00:01:52,460 --> 00:02:01,220
+للصحور هي جلسة تعتبر بيخلصوا كمان أخدنا يا بنات
+
+23
+00:02:01,220 --> 00:02:07,140
+التوصيل على التواليف المكثفاتو احنا في عنا شغلتين
+
+24
+00:02:07,140 --> 00:02:15,040
+شغلة بتقول ان I بتسوي Delta V على R هذا قانون I
+
+25
+00:02:15,040 --> 00:02:28,040
+وفي بدل IQ بتسوي C في Delta V مظبوط ولا لأ؟ شوفوا
+
+26
+00:02:28,040 --> 00:02:32,260
+إيش اللي صار معايا R هنا في المقام لكن C هنا في
+
+27
+00:02:32,260 --> 00:02:37,620
+البسطعشان كده عندكم في القوانين هتشوفوا العكس بس
+
+28
+00:02:37,620 --> 00:02:42,800
+في القوانين لكن نيجي للمبدأ عند التوصيل على
+
+29
+00:02:42,800 --> 00:02:47,520
+التواليف المكثفات إيش الثابت؟ الشحنات في البطاريات
+
+30
+00:02:47,520 --> 00:02:51,500
+الشحنات صارت شحنات متحدقة يعني انجلب التيارة إذا
+
+31
+00:02:51,500 --> 00:02:56,580
+التيار بيكون ثابت اختلف المبدأ؟ مااختلفش المبدأ
+
+32
+00:02:56,580 --> 00:03:00,960
+جالي هاي المقومتين زي ما انتوا شايفين وكلنا بنعرف
+
+33
+00:03:02,270 --> 00:03:07,370
+الشحنات لا تفنع ولا تستحدث وبالتالي في عندك طيار
+
+34
+00:03:07,370 --> 00:03:12,710
+ماشي منهان اول ما تقول طيار يعني فيه شحنات صح؟
+
+35
+00:03:12,710 --> 00:03:17,750
+شحنات ماشية وانا توي حكيتها نفترض شارع فيه مية
+
+36
+00:03:17,750 --> 00:03:22,690
+سيارةهدول الميت سيارة ماشيين لا في سيارة هيمشي
+
+37
+00:03:22,690 --> 00:03:26,670
+يقول الشارع بلعها ولا في النص هتزيدلي سيارة نقول
+
+38
+00:03:26,670 --> 00:03:29,350
+والله سيارة ولدي السيارة، مظبوط ولا لأ؟ هذا
+
+39
+00:03:29,350 --> 00:03:31,870
+conservation of سيارات، conservation of the
+
+40
+00:03:31,870 --> 00:03:36,510
+charges تمى، ماشيين ميت سيارة، أكمل سيارة بدهم
+
+41
+00:03:36,510 --> 00:03:41,680
+يخشوهامية و كم صغير ابن مخشوها مية إذا معناته I
+
+42
+00:03:41,680 --> 00:03:45,460
+الكلية اللي طلعت من هنا هي نفسها I واحد هي نفسها I
+
+43
+00:03:45,460 --> 00:03:49,440
+اتنين ولا لا هذا مبدأ التوالي هذا مبدأ ال
+
+44
+00:03:49,440 --> 00:03:54,260
+conservation of charge إذا لازم I equivalent وهو
+
+45
+00:03:54,260 --> 00:03:59,560
+الكلي يسوي I واحد يسوي I اتنين إذا بالقطع عند
+
+46
+00:03:59,560 --> 00:04:07,470
+التواليبدي اقول هاي التيار هذا I هو نفسه I1 هو
+
+47
+00:04:07,470 --> 00:04:11,470
+نفسه I2 في خلاف على هذه النقطة؟ مافيش خلاف
+
+48
+00:04:11,470 --> 00:04:19,870
+اتطلعولي هال gate VA-VB هذي هل هي فرق الجهد الكلي
+
+49
+00:04:19,870 --> 00:04:26,350
+ولا لأ؟ مظبوط ولا لأ؟ تمام بتساوي VAVE مش خلاف،
+
+50
+00:04:26,350 --> 00:04:33,080
+صح؟خلّيني أطرح VC و أجمع VC، عملتش إيه؟ لأ، و هذه
+
+51
+00:04:33,080 --> 00:04:40,580
+ناقص VB؟ خالص و أنا إيش عملت؟ تمه؟ قاللي هدول طلّع
+
+52
+00:04:40,580 --> 00:04:43,900
+عليهم على الرسمة تجرى إنه يقول إن هذه delta V1 ولا
+
+53
+00:04:43,900 --> 00:04:52,120
+لأ؟ طب و هذه delta V2 طب و هذه قاللي هذه delta V
+
+54
+00:04:52,120 --> 00:04:59,090
+equivalentصح ولا لا؟ إذا عند التوصيل على التوالي
+
+55
+00:04:59,090 --> 00:05:03,670
+فرق الجهد الكل هو مجموع فرق الجهود ولا لا؟ زي
+
+56
+00:05:03,670 --> 00:05:09,490
+المكثفات بالتمام ولكماها زيها إذا صار في عندك
+
+57
+00:05:09,490 --> 00:05:13,670
+delta V equivalent بيسوي delta V1 بيسوي delta V2
+
+58
+00:05:13,670 --> 00:05:15,330
+قال لي طيب
+
+59
+00:05:18,080 --> 00:05:21,200
+وهذا القانون مش بيقول مش بيقول delta V بالسوء I في
+
+60
+00:05:21,200 --> 00:05:24,440
+R يعني delta V equivalent بالسوء I equivalent في R
+
+61
+00:05:24,440 --> 00:05:27,860
+equivalent و delta V واحد بالسوء I واحد في R واحد
+
+62
+00:05:27,860 --> 00:05:30,800
+و delta V اتنين بالسوء I اتنين في R اتنين ولا لأ
+
+63
+00:05:30,800 --> 00:05:35,380
+اه كتب كتبنا طب
+
+64
+00:05:35,380 --> 00:05:39,020
+قاللي هذه المعادلة ايش بتقول بتقوللي هذا بقيم هذا
+
+65
+00:05:39,020 --> 00:05:47,560
+بقيم هذا اذا صار R equivalent مجموع الريبطيب جالي
+
+66
+00:05:47,560 --> 00:05:50,240
+برضه انت قيلتني منها قوانين ماذا بالصفة قوانين
+
+67
+00:05:50,240 --> 00:05:58,240
+جالي R بتساوي ρو L على ايه صح انت لما تجمع ايه
+
+68
+00:05:58,240 --> 00:06:02,080
+الصرف المقاومة زادت ولا لأ يعني هذه خمسة وهذه خمسة
+
+69
+00:06:02,080 --> 00:06:05,700
+وصوتهم على التوالي هيك صاروا عشر ولا لأ يعني زادت
+
+70
+00:06:05,700 --> 00:06:09,700
+المقاومة جالي هو انت لما توصلهم هيك يا تورا ايه
+
+71
+00:06:09,700 --> 00:06:16,160
+الصرف الطولزاد وحسب هذه القاعدة منطقي انه يزيد ال
+
+72
+00:06:16,160 --> 00:06:20,580
+R ولا لا؟ اذا انت عند التواصيل على التوالي بتزيد
+
+73
+00:06:20,580 --> 00:06:26,320
+المقاومة لأن انت طول المخسّلك تضاعف او زاد
+
+74
+00:06:26,320 --> 00:06:31,340
+وبالتالي R equivalent منطقي انه تكون اكبر من R1
+
+75
+00:06:31,340 --> 00:06:35,610
+وR2 تمام يا بنات؟فيه مشكلة في التواصل على التوالي
+
+76
+00:06:35,610 --> 00:06:39,110
+التواصل على التوالي فانتوا تقولون عكس المكثفات
+
+77
+00:06:39,110 --> 00:06:45,230
+المبدأ اتغير تتساول الشحنات تتساول التيارات نفسها
+
+78
+00:06:45,230 --> 00:06:50,730
+وتتجزأ الجهود Delta V equivalent بتساول Delta V1
+
+79
+00:06:50,730 --> 00:06:54,990
+زي Delta V2 مافي اي خلاف عليها تم
+
+80
+00:06:58,350 --> 00:07:01,070
+قال لي انبرايريك .. كيف بتوصل الانبرايريك؟ كنا
+
+81
+00:07:01,070 --> 00:07:04,710
+نوصل المكافئة دول كل طرفين مع بعض صح؟ ما
+
+82
+00:07:04,710 --> 00:07:07,290
+المقاومات، كل واحد هي لطرف، ما هو هي المقاومة، هي
+
+83
+00:07:07,290 --> 00:07:11,390
+طرف وهي طرف، وهي مقاومة، هي طرف وهي طرف، كل جيب
+
+84
+00:07:11,390 --> 00:07:14,790
+هدول طرفين مع بعض، و هدول طرفين مع بعض، صار عندك
+
+85
+00:07:14,790 --> 00:07:17,790
+طرف هنا و طرف هنا، ماذا هدول الطرفين موصلتهم مع
+
+86
+00:07:17,790 --> 00:07:20,830
+بعض، جهدهم واحد ولا لأ؟ و هدول الموصلين مع بعض،
+
+87
+00:07:20,830 --> 00:07:24,490
+جهدهم واحد، إذا قطعا Delta V واحد بتساوي Delta V
+
+88
+00:07:24,490 --> 00:07:31,230
+اتنين، و بتساوي Delta V الكليةأه هيها هذه النقطة
+
+89
+00:07:31,230 --> 00:07:35,570
+هي نفسها هذه هي نفسها هذه و هذه النقطة و نفس هذه
+
+90
+00:07:35,570 --> 00:07:40,610
+النقطة نفس هذه النقطة اذا delta VAB هي نفسها delta
+
+91
+00:07:40,610 --> 00:07:49,850
+V1 و هي نفسها delta V2 بالقطع اذا
+
+92
+00:07:49,850 --> 00:07:53,130
+delta V equivalent بتساوي delta V1 زي ال delta V2
+
+93
+00:07:53,130 --> 00:07:58,440
+نرجع للميط سيارةالميت سيارة اللي كانوا ماشيين في
+
+94
+00:07:58,440 --> 00:08:02,980
+الشارع اجعوا عند مفترق طرق هذا مفترق الطرق قبلها
+
+95
+00:08:02,980 --> 00:08:08,430
+بيوديهم هك و بيوديهم هك على ال gateكل المية بدهم
+
+96
+00:08:08,430 --> 00:08:12,110
+يروحوا مع بعض؟ لأ، لو ستين راحوا هيك، إيش ده؟
+
+97
+00:08:12,110 --> 00:08:16,710
+قطعاً أربعين، صح ولا لأ؟ إذا انت جماعة اللي راح
+
+98
+00:08:16,710 --> 00:08:20,510
+يمين و جماعة اللي راح يسار، قلت بيساوي I الكلية
+
+99
+00:08:20,510 --> 00:08:24,930
+ولا لأ؟ أجي أطلّق، هاي السيارات اللي هم الشحنات،
+
+100
+00:08:24,930 --> 00:08:28,170
+ماشي، نجوا هنا، قالوا كلنا بدنا نروح هناك؟ لأ،
+
+101
+00:08:28,170 --> 00:08:32,170
+نعمل زحمة، مظبوط ولا لأ؟ جزء مننا راح هنا و جزء
+
+102
+00:08:32,170 --> 00:08:37,250
+مننا راح هناطبعا هدى زيد هدى بيسوي هدى ولا لأ اذا
+
+103
+00:08:37,250 --> 00:08:42,290
+I equivalent بتسوي I واحد زياد I اتنين مافيش خلاف
+
+104
+00:08:42,290 --> 00:08:47,570
+على هذه النقطة اذا معناته على طول I equivalent
+
+105
+00:08:47,570 --> 00:08:52,070
+بتسوي مجموعة التيارات لان التيارات انجسمت تمى دى
+
+106
+00:08:52,070 --> 00:08:55,890
+ربعكم هذه قاعدة كرش في الأولى قعدنا من جهها تمى
+
+107
+00:08:55,890 --> 00:09:02,450
+قاللي ارجع قاللي ايه؟جلي I بتسوى Delta V على R إذا
+
+108
+00:09:02,450 --> 00:09:04,690
+I equivalent بتسوى Delta V equivalent على R
+
+109
+00:09:04,690 --> 00:09:08,850
+equivalent مظبوط ولا لأ لما أجى انا اعوض محل هادي
+
+110
+00:09:08,850 --> 00:09:14,170
+ومحل هادي ومحل هادي ده اللي طلعت هيك صح؟
+
+111
+00:09:15,580 --> 00:09:20,000
+المعادلة الأولى بتخلي البسط كله يروح إذا صار في
+
+112
+00:09:20,000 --> 00:09:23,540
+عندي عاد توازي يعني R equivalent بيساوي R واحد في
+
+113
+00:09:23,540 --> 00:09:27,100
+R اتنين على R واحد زي R اتنين يعني عندي مقاومتين
+
+114
+00:09:27,100 --> 00:09:32,460
+على التوازي عشرة عشرة كدهش النتيجة؟ خمسة ليه؟ جالي
+
+115
+00:09:32,460 --> 00:09:37,120
+انت كيف وصلتهم؟ بتقول وصلتهم هيك، مظبوط؟ إيه صار
+
+116
+00:09:37,120 --> 00:09:43,480
+في العرض؟ زاد، وسعهجد عندنا نرجع للشوارع، شارعه في
+
+117
+00:09:43,480 --> 00:09:47,000
+جزيرة في النصر، إجت البلدية جلت زحمج من الجزيرة،
+
+118
+00:09:47,000 --> 00:09:53,860
+ممكن تكون one way، اتحسنت الطريق ولا لأ؟ وهذه نفس
+
+119
+00:09:53,860 --> 00:09:58,580
+العملية، إذا إنت إيه زودت؟ زودت إيه؟ إيه صرف R؟
+
+120
+00:09:58,580 --> 00:10:03,080
+جلت وهير صرف التوازي، شغلة منطقية إن R تجل، لأنك
+
+121
+00:10:03,080 --> 00:10:04,960
+إنت زودت الوسعة
+
+122
+00:10:07,180 --> 00:10:11,000
+مظبوطك ولا لأ؟ إذا عند التوصيل على التوالي تتساوى
+
+123
+00:10:11,000 --> 00:10:14,440
+التيارات وعند التوصيل على التوازي تتساوى الجهود
+
+124
+00:10:14,440 --> 00:10:22,400
+إذا انجسم التيار قطعا مش توالي، صح؟ لأ، لأ يا روان
+
+125
+00:10:22,400 --> 00:10:29,140
+إذا توزعت التيار انتفت توالي ولم يثبت التوازن، لم
+
+126
+00:10:29,140 --> 00:10:33,640
+يثبت التوازن عشان تثبت التوازن، بدك تتحقق من ثبات
+
+127
+00:10:33,640 --> 00:10:38,540
+الجهودأما انت بتقولي خلاص مش توالي لأنه مرات لا
+
+128
+00:10:38,540 --> 00:10:42,100
+بيكون توالي ولا بيكون توازي وعدنا هنشوف وعدنا
+
+129
+00:10:42,100 --> 00:10:45,820
+هنرسم دائرة وبنشوف احنا بدي توزع التيار هل توازي
+
+130
+00:10:45,820 --> 00:10:50,620
+ولا لأ تمام؟ شوفوا هالدائرة
+
+131
+00:10:53,360 --> 00:10:57,480
+حاجات الطيار بتوزع ولا لأ؟ مين بياخد أكبر نصيب؟
+
+132
+00:10:57,480 --> 00:11:02,220
+المقاومته أقل طيب لو كانت المقاومة سفر إيش بتاخد
+
+133
+00:11:02,220 --> 00:11:08,080
+من الطيار؟ كل الطيار كل الطيار صح ولا لأ؟ تمه جالي
+
+134
+00:11:08,080 --> 00:11:10,960
+تطلعلي على الدائرة على اليسار هذه اللي حاططلي أنت
+
+135
+00:11:10,960 --> 00:11:17,720
+عليها إيه؟ إجا الطيار هنا بده يتوزع وين بروح؟ بروح
+
+136
+00:11:17,720 --> 00:11:23,020
+هنا يعني هذه موجودة؟ هذه لاتهمل أنا بقول بتعفن هذه
+
+137
+00:11:23,020 --> 00:11:28,620
+العضو في الجسم لما ما يخشوش دم ايش بيصير فيه بعفن
+
+138
+00:11:28,620 --> 00:11:34,900
+تمام؟ والدم مش شحنات قالت تهملي انا عفنت راحت
+
+139
+00:11:34,900 --> 00:11:40,400
+ماليش دعوة في الدائرة تمام؟ قاللي يعني انت هنا اكم
+
+140
+00:11:40,400 --> 00:11:46,770
+مقاومة في الدائرة هنا واحدةإذا بيقوللي when the
+
+141
+00:11:46,770 --> 00:11:49,730
+switch in the circuit shown closed كان مغلق زي ما
+
+142
+00:11:49,730 --> 00:11:54,070
+انتوا شايفينه الاميتر .. الاميتر إيش بيجيس؟ طيار
+
+143
+00:11:54,070 --> 00:11:57,670
+.. الاميتر reads the current in the circuit قرأ
+
+144
+00:11:57,670 --> 00:12:03,010
+التيار أمين رقم معين ده اللي الأن بدي أفتح المفتاح
+
+145
+00:12:03,010 --> 00:12:06,270
+و أشوف لقراة الاميتر إيش بده يحصل فيها لما أفتح
+
+146
+00:12:06,270 --> 00:12:09,970
+المفتاح اللي كنت مهملها و قلت عنها بتعفن بحييها
+
+147
+00:12:09,970 --> 00:12:15,280
+بإن الدم بدأ يجي فيها ولا لأ؟بعتدتيشي طيب هذه
+
+148
+00:12:15,280 --> 00:12:18,800
+مقاومة إيش جيدة؟ طب مافي مقاومة جديمة ولا لأ؟
+
+149
+00:12:18,800 --> 00:12:22,700
+صارتين كلمة تصلين، كيف؟ توالي توالي إيش في
+
+150
+00:12:22,700 --> 00:12:26,780
+التوالي؟ بيصير مقاومة إيش ما لها؟ زادت ولمّا تزيدي
+
+151
+00:12:26,780 --> 00:12:29,920
+المقاومة إيش بيصير في التيار؟ بجل التيار، إذا
+
+152
+00:12:29,920 --> 00:12:33,880
+بتوقع خرقة الأمن تريد تصل فيها؟ اتجل فبقول
+
+153
+00:12:33,880 --> 00:12:38,020
+increased و لا decreased و لا unchanged عشان ما
+
+154
+00:12:38,020 --> 00:12:43,740
+تزعلوش و لا zero في الحالتينتمام؟ اذا انتوا
+
+155
+00:12:43,740 --> 00:12:50,320
+حللناها و لجيناها انها decreased لزيادة R و هناك
+
+156
+00:12:50,320 --> 00:12:54,280
+معايير علاقة عكسية بين I و R توجلطوها و كلكم
+
+157
+00:12:54,280 --> 00:13:00,380
+تعرفوها صحيح ولا لأ؟ واضح هذا ال quiz؟ واضح تمى؟
+
+158
+00:13:00,380 --> 00:13:06,990
+قال لي انا بقولك و لو ..كتبتلك سؤال عند التوصيل
+
+159
+00:13:06,990 --> 00:13:10,310
+على التوالي ايش بيصير في الطيارات بتقولي ثابتة صح
+
+160
+00:13:10,310 --> 00:13:16,030
+ولا لا بعرفها جيبت السؤال هذا كيف متواصلين هدوء
+
+161
+00:13:16,030 --> 00:13:21,030
+قالي والله المقاومات مش زي بعد ليش هيه بيقولي
+
+162
+00:13:21,030 --> 00:13:24,590
+واحدة اتنين وواحدة اربعة وواحدة ستة قالي مين من
+
+163
+00:13:24,590 --> 00:13:29,790
+هالمقاومات بيحمل اكبر طيار مش استكبرها ولا وعرجها
+
+164
+00:13:29,790 --> 00:13:35,920
+ولا عجرةمش الكبيرة بتاخد طيارة كبيرة، لأ، تشوف
+
+165
+00:13:35,920 --> 00:13:44,460
+الخيارات، Bravo علينا، مظبوط هيك ولا لأ؟ حل، و
+
+166
+00:13:44,460 --> 00:13:48,320
+بتيجي هيك و الذاتي الموضلة، ايا بكرا بتيجي زي هيك،
+
+167
+00:13:48,320 --> 00:13:53,380
+تمة؟ بس مرة ماتكونش مصحصحين و أنتوا بتحلوا، هادي
+
+168
+00:13:53,380 --> 00:13:55,080
+بعدي، تمة؟
+
+169
+00:13:58,280 --> 00:14:03,420
+طلع برضه ع اليسار اتطلعولي قال لي المفتاح مفتوح
+
+170
+00:14:03,420 --> 00:14:10,780
+يعني R2 موجودة في الدائرة؟ لأ قرأ الاميتر قراءة
+
+171
+00:14:10,780 --> 00:14:17,220
+سكر المفتاح ايه سويت وصلت مقاومة جيدة ولا لا؟ وصلت
+
+172
+00:14:17,220 --> 00:14:21,260
+مقاومة جيدة على التوازن ايه صار في المقاومة؟ ايه
+
+173
+00:14:21,260 --> 00:14:26,530
+صار في الطيار؟ عين عليكمإذاً with the switch in
+
+174
+00:14:26,530 --> 00:14:28,670
+the circuit shown open the emitter reads the
+
+175
+00:14:28,670 --> 00:14:31,710
+current in the circuit what happens to the reading
+
+176
+00:14:31,710 --> 00:14:35,250
+on the emitter when the switch is closed هل
+
+177
+00:14:35,250 --> 00:14:38,130
+increase ولا decrease ولا not change ولا it is
+
+178
+00:14:38,130 --> 00:14:43,930
+zero in both cases قلتله قولت R وزاد التيار لأنه
+
+179
+00:14:43,930 --> 00:14:52,550
+وصلته مع التوازي برضه امين صح ولا لأ تمام انشوفالـ
+
+180
+00:14:52,550 --> 00:14:57,630
+quiz مش quiz مثال جيلي هذا مثال و انا مرات بقول
+
+181
+00:14:57,630 --> 00:15:01,830
+بفرض الأمثلة دايما تكون صعبةلكن هو مرة هذي مختار
+
+182
+00:15:01,830 --> 00:15:05,470
+أسئلة الأمثلة سهلة أنا بقول لو هذي شفتهوا أنتوا في
+
+183
+00:15:05,470 --> 00:15:08,090
+متحالة توجيهي بتكيفوا بتحولوا تطوروا على الرجال و
+
+184
+00:15:08,090 --> 00:15:10,750
+بتقولوا يا رضي مثلة السؤال، مظبوط ولا لأ؟ لكن
+
+185
+00:15:10,750 --> 00:15:14,610
+جايبه، أدهي، واحنا إيش نسوي؟ أنا في آخر الشرطة
+
+186
+00:15:14,610 --> 00:15:17,470
+أجابلكم لكم سؤال من الكتاب اللي بغلبه يعني لكن
+
+187
+00:15:17,470 --> 00:15:21,710
+هدول الأمثلة بيقولوا يللا نحلهم، بيقولوا عندك أربع
+
+188
+00:15:21,710 --> 00:15:26,180
+مقاومات كيف هم تواصلين شايفينهمالشفاوة بتقدر
+
+189
+00:15:26,180 --> 00:15:30,960
+تقولولي كداش are equivalent؟ أربعة عاشر جلتوا ستة
+
+190
+00:15:30,960 --> 00:15:35,120
+و تلاتة مع بعض توازي اتنين اتنين و اربعة ستة مع
+
+191
+00:15:35,120 --> 00:15:38,520
+تمانية اربعة عاشر خلصنا و عاملهم غالب حاله بيقول
+
+192
+00:15:38,520 --> 00:15:42,060
+هال تمانية المطلوب المطلوب الأول ماهي حاليناها
+
+193
+00:15:42,060 --> 00:15:45,200
+شفاوة what is the equivalent resistance between
+
+194
+00:15:45,200 --> 00:15:49,690
+point A and C؟ A and C يعني لكلهاطيب فقعدّي يقولي
+
+195
+00:15:49,690 --> 00:15:54,110
+طيب فيما لو كان فرق الجهد بين النقطين هدول A وC 42
+
+196
+00:15:54,110 --> 00:15:59,130
+Volt بديت تيارة على كل مقاومة هده بنشمر و بنشتغل
+
+197
+00:15:59,130 --> 00:16:03,770
+على كل حال في شغل لما الأولاني شافه كيه؟ قاللي زي
+
+198
+00:16:03,770 --> 00:16:07,770
+المكثفات بنرجع وجوه صح ولا لأ؟ كيف بنحلقونا احنا
+
+199
+00:16:07,770 --> 00:16:10,450
+على التوالي والتوازي يا بنات بنتاشر كتبشي؟ كله ع
+
+200
+00:16:10,450 --> 00:16:15,710
+الرسمانهلجيت لما أجي أحل هدول التنتين في خلاف جديش
+
+201
+00:16:15,710 --> 00:16:22,600
+كيف يكونوا؟ يالا قولولي تواني إذا بكتب seriesطب
+
+202
+00:16:22,600 --> 00:16:27,400
+وهدول التنتين back to parallel طبعا عشان ما تقولش
+
+203
+00:16:27,400 --> 00:16:30,580
+ان ال calculator خربطت حطولي قانون التوالي و قانون
+
+204
+00:16:30,580 --> 00:16:33,700
+التوازي عشان لو خربطت .. خربطت ال calculator مش
+
+205
+00:16:33,700 --> 00:16:39,800
+خربطت مخ تم ها؟ حلو بقول عندي التوالي حطت بنيت
+
+206
+00:16:39,800 --> 00:16:43,420
+القانون والله جامعة بس ال calculator خربطت مسكينة
+
+207
+00:16:43,420 --> 00:16:49,600
+قدش 8 او 4 بدل ما تحط 12 حطت 15مهمش بس بيه كان كات
+
+208
+00:16:49,600 --> 00:16:54,180
+باينها جميع تمام قلتله هدول إيجت محلهم واحد اتانية
+
+209
+00:16:54,180 --> 00:16:58,380
+و أربع جديش اتناش اذا انا اتناش هي equivalent
+
+210
+00:16:58,380 --> 00:17:01,560
+تلاتين تين على التوازي ولا لا قاللي و هدول على
+
+211
+00:17:01,560 --> 00:17:04,760
+التوازي طلعت جديش اتنين قاللي التين هذه هي
+
+212
+00:17:04,760 --> 00:17:09,120
+equivalent تلاتين تين على التوازي تمام قاللي ايه
+
+213
+00:17:09,120 --> 00:17:12,760
+صحروا التنتين هدول اتناش و اتناش و اتناش و اتناش و
+
+214
+00:17:12,760 --> 00:17:13,480
+اتناش و اتناش و اتناش و اتناش و اتناش و اتناش و
+
+215
+00:17:13,480 --> 00:17:13,580
+اتناش و اتناش و اتناش و اتناش و اتناش و اتناش و
+
+216
+00:17:13,580 --> 00:17:18,190
+اتناش و اتناش و اتنصح اتناش و اتنين اربعتاش حطيتها
+
+217
+00:17:18,190 --> 00:17:23,370
+جدش are equivalent اربعتاش اربعتاش تم احنا are
+
+218
+00:17:23,370 --> 00:17:27,430
+equivalent لسه قاللي انا مطلوب التاني بتقوللي انت
+
+219
+00:17:27,430 --> 00:17:32,180
+فرق الجهد هنا اتنين و اربعين volt هذا معطىجاللي
+
+220
+00:17:32,180 --> 00:17:36,200
+بقى رجعي لجوه جاللي هاجي ال 14 من وين جاية؟ جاية
+
+221
+00:17:36,200 --> 00:17:40,400
+من تنتين، توالي ولا لأ؟ عند التوالي إيش اللي
+
+222
+00:17:40,400 --> 00:17:44,560
+بتساوى؟ الطيار جاللي بتعرفش تجيب الطيار؟ قلتله هاي
+
+223
+00:17:44,560 --> 00:17:50,740
+الطيار Delta V على R 42 على 14 طلع تلاتة إذا هنا
+
+224
+00:17:50,740 --> 00:17:54,800
+الطيار تلاتة أمبير في خلاف؟وانت قلتلي هذا
+
+225
+00:17:54,800 --> 00:17:58,960
+equivalent لتنتين متواصين على التوالي وعند التوالي
+
+226
+00:17:58,960 --> 00:18:02,400
+I واحد بتسوي I اتنين بتسوي I equivalent I
+
+227
+00:18:02,400 --> 00:18:05,380
+equivalent بتسوي I واحد بتسوي I اتنين اذا هذه
+
+228
+00:18:05,380 --> 00:18:10,840
+تلاتة وهذه تلاتة تمام اذا قلتله هذه تلاتة مظبوط
+
+229
+00:18:10,840 --> 00:18:15,060
+هيك ولا لأ قاللي ارجع قاللي هذه كيف جاية قلتله
+
+230
+00:18:15,060 --> 00:18:18,720
+تنتين على التوالي اذا هذه تلاتة وهذه تلاتة اذا هذه
+
+231
+00:18:18,720 --> 00:18:24,950
+تلاتةو هذه تلاتة واحدة واحدة لكن واحد قال لي طيب
+
+232
+00:18:24,950 --> 00:18:27,810
+لو بدي اشوف انا حلص صح ولا لا قلتله جدي الجهود هذه
+
+233
+00:18:27,810 --> 00:18:31,490
+قلتله اتنعاش في تلاتة ستة تلاتين و تلاتة في اتنين
+
+234
+00:18:31,490 --> 00:18:36,920
+ستة اجمعهم و اطلع اتنين واربعين اذا انا بحل صحتمى
+
+235
+00:18:36,920 --> 00:18:41,900
+قال لي حلو قال لي هادي جاية من وين قولتله جاية من
+
+236
+00:18:41,900 --> 00:18:45,400
+تنتين توازي ايش اللي بتسوي على التوازي يعني هادي
+
+237
+00:18:45,400 --> 00:18:50,180
+ستة volt هادي قداشر و هادي ستة اذا هادي ستة volt
+
+238
+00:18:50,180 --> 00:18:55,520
+يلا في طيار قاللي ستة ع ستة واحد و ستة ع اتنين
+
+239
+00:18:55,520 --> 00:19:01,800
+المقاومة الأقل أخدت طيار أكبر ولا لأ اجمع الطيارين
+
+240
+00:19:02,930 --> 00:19:06,510
+let charge is conserved let charge is conserved
+
+241
+00:19:06,510 --> 00:19:11,910
+آية بنات او ممكن قبل ما تجيب الجهد لهذه تسويه أكتر
+
+242
+00:19:11,910 --> 00:19:17,010
+يعني طيب هي هي بس بدك تطولي انت هيك حالك كل يوم
+
+243
+00:19:17,010 --> 00:19:20,530
+بدك هي هي هيك شوفه أحلى تجيبي الجهد و بتسويها
+
+244
+00:19:20,530 --> 00:19:24,230
+بتجيبي معادلة ان هذي بتسوي هذي وتعمل المعادلتين
+
+245
+00:19:24,230 --> 00:19:28,320
+أطولأطول .. جرب .. جرب في الدار .. ممكن انت مخترع
+
+246
+00:19:28,320 --> 00:19:32,000
+قريقة تانية و مخك تدي بيها .. بس هي أسهل .. أما
+
+247
+00:19:32,000 --> 00:19:35,400
+صحيح .. على حالك صحيح .. أيه يا بنات؟ في أي صفصة؟
+
+248
+00:19:35,400 --> 00:19:40,040
+كمان مثال .. أسهل من هذا .. برضه مثال كتاب .. ها
+
+249
+00:19:40,040 --> 00:19:42,440
+.. مش أنا .. مش أنا بنجيهم يعنى .. عشان ما
+
+250
+00:19:42,440 --> 00:19:44,960
+تتهمونيش أني أنا بديب اللي سهل .. هذه الكتاب هو
+
+251
+00:19:44,960 --> 00:19:49,760
+هيك اللي جاية ..
+
+252
+00:19:49,760 --> 00:19:55,220
+كيف ماتواصلين يا بنات؟ توازي ..بيقول لي three
+
+253
+00:19:55,220 --> 00:19:57,860
+resistors are connected أي شون أي شون يعني برا
+
+254
+00:19:57,860 --> 00:20:04,840
+ليه؟ صح ولا لا؟ طيب برا للإيش بنتساوى؟ فرق الجهد
+
+255
+00:20:04,840 --> 00:20:08,560
+على كل واحدة أنا عارف ولا لا؟ تعرف تجيب الكورة
+
+256
+00:20:08,560 --> 00:20:14,920
+فيها كل واحدة؟صح ولا لأ اه تمنتعش ع تلاتة ستة
+
+257
+00:20:14,920 --> 00:20:19,860
+تمنتعش ع تلاتة ستة تسعة تمنتعش ع تسعة اتنين تسعة و
+
+258
+00:20:19,860 --> 00:20:25,440
+اتنين احداشر اذا طيارة كل احداشر اتجسم لستة و
+
+259
+00:20:25,440 --> 00:20:31,610
+تلاتة و اتنين صح ولا لأ اذا I equivalent بتساوي11
+
+260
+00:20:31,610 --> 00:20:35,970
+امبير صح ولا لأ طيب تقدروا تجيبولي R equivalent من
+
+261
+00:20:35,970 --> 00:20:38,890
+Delta V equivalent على I equivalent بقدر اديه بقى
+
+262
+00:20:38,890 --> 00:20:43,070
+بقدر اديه بقى اه شوفش بده بيقولي find the current
+
+263
+00:20:43,070 --> 00:20:47,500
+in each resistor هيحلتهمايخلص متصنع التوازن وانت
+
+264
+00:20:47,500 --> 00:20:50,480
+مديني الجهود والجهد الكلي هذا هو نفس الجهد ده كل
+
+265
+00:20:50,480 --> 00:20:53,720
+واحدة المطلوب التاني برضه عشان يصعب السؤال يقول ما
+
+266
+00:20:53,720 --> 00:20:58,520
+بستاهل ومانقولش انه هذا مغوظ لحاله وبيجيبش للأسل
+
+267
+00:20:58,520 --> 00:21:01,780
+السهلة قال يللا نصعب هذا السؤال بيقول اوجد ال
+
+268
+00:21:01,780 --> 00:21:06,760
+power ع كل واحدة و ال power القليةCalculate the
+
+269
+00:21:06,760 --> 00:21:09,080
+power delivered to each resistor and the total
+
+270
+00:21:09,080 --> 00:21:11,600
+power delivered to the combination. Delivered يعني
+
+271
+00:21:11,600 --> 00:21:15,960
+استهلك أو راح، مديت لأن هذه المقاومات احنا اتفقنا
+
+272
+00:21:15,960 --> 00:21:20,080
+load، تذكرين كلمة load؟ Load يعني أجهزة، يعني هذه
+
+273
+00:21:20,080 --> 00:21:24,400
+شبكة، شبكة تتضاهر، حطت غسالة، عبق أو load، حطت
+
+274
+00:21:24,400 --> 00:21:28,240
+غسالة أو حطت مكيف أو حطت تلاجة، هذه تلت مقاومات
+
+275
+00:21:28,240 --> 00:21:32,000
+موصلة مع التوازي مع بعض، موصلة مع التوازي، هذا هم،
+
+276
+00:21:32,000 --> 00:21:35,520
+ده اللي كل واحدة بتستهلك طاقة ولا لأ؟طاقة يعني
+
+277
+00:21:35,520 --> 00:21:38,960
+قدرة، ما هو الطاقة و القدرة جرايب، بينهم زمن،
+
+278
+00:21:38,960 --> 00:21:42,740
+صحيح؟ قال يجيبلي القدرة لكل واحدة، قد إيش السهلة
+
+279
+00:21:42,740 --> 00:21:45,420
+كانت القدرة، و بعدين يجيبلي القدرة الكلية، القدرة
+
+280
+00:21:45,420 --> 00:21:48,180
+الكلية هي اللي جيبتها من البطارية، ما هي، قاللي
+
+281
+00:21:48,180 --> 00:21:52,760
+بسيطة، القدرة إيها ترى الصيغ، ولا لأ، لأجهزة أفضل
+
+282
+00:21:52,760 --> 00:21:55,440
+تجيبه أي تربيع في الأرض، ليس لو أنا أيه حسبتها،
+
+283
+00:21:55,440 --> 00:21:58,260
+والأرض معطية، طب أحد يقولي طب بدي أجيب Delta V
+
+284
+00:21:58,260 --> 00:22:03,600
+تربيع على أرض، صح؟ كل واحد، قاللي يلّا، هذه قلنا
+
+285
+00:22:03,600 --> 00:22:10,520
+جيبناه،مافيش خلاف تمام خلّينا
+
+286
+00:22:10,520 --> 00:22:15,720
+نجيب I الكلية جدش قلنا 11 يلّا نجيب R الكلية R
+
+287
+00:22:15,720 --> 00:22:19,880
+equivalent قلنا على التوازي التلاتة واحدة واحدة
+
+288
+00:22:19,880 --> 00:22:24,400
+تلاتة مع الستة إيش بتعطي؟ اتنين اتنين في تسعة كيف
+
+289
+00:22:24,400 --> 00:22:29,300
+بنعملها؟ اتنين ضرب تسعة على اتنين زائد تسعة يعني
+
+290
+00:22:29,300 --> 00:22:38,350
+تمنتعش على أحد عشر صح؟ هذي R equivalentبقوله V أو
+
+291
+00:22:38,350 --> 00:22:43,650
+sorry I equivalent بتساوي Delta V equivalent على R
+
+292
+00:22:43,650 --> 00:22:50,810
+equivalent جدّي Delta V equivalent و
+
+293
+00:22:50,810 --> 00:22:55,070
+الله طلعت 11 أمبير صح و أنا لما جمعتهم طلعت 11
+
+294
+00:22:55,070 --> 00:22:59,490
+أمبير صحيحةتمام قال لي بيدي ال power في المطلوب
+
+295
+00:22:59,490 --> 00:23:01,990
+التاني هديه 11 أمبير و جابها بطريقة تانية R
+
+296
+00:23:01,990 --> 00:23:07,170
+equivalent اللي هي 18 11 1.624 مش مشكلة قال لي for
+
+297
+00:23:07,170 --> 00:23:12,010
+the power هي P1 هي P2 و هي P3 power أي تربيع في ال
+
+298
+00:23:12,010 --> 00:23:16,370
+R صح ولا لأتمام قال لي طب اجمعهم قال لي هاد اجمعهم
+
+299
+00:23:16,370 --> 00:23:21,590
+سهل ايا جابها هيك 198 هم الجامع تبعتهم او باجيبهم
+
+300
+00:23:21,590 --> 00:23:25,690
+من ال I equivalent تربيع في ال R equivalent اذا زي
+
+301
+00:23:25,690 --> 00:23:32,030
+ما اتفقنا سؤال سهل تمام هجي التوالي و التوازي
+
+302
+00:23:32,030 --> 00:23:38,130
+خلصنا و نبدأ بها دائرة نرجع لاروان تمام هاي دائرة
+
+303
+00:23:48,400 --> 00:23:56,040
+شوف إزايها طب خلّيني أخرب بيتكم هاي اتنين أوم
+
+304
+00:23:56,040 --> 00:24:06,640
+تلاتة أوم خمسة أوم أربعة أوم تمانية أوم تخربطيش
+
+305
+00:24:06,640 --> 00:24:11,060
+أنا هربطك تمانية اتنين
+
+306
+00:24:15,300 --> 00:24:18,660
+ما انت بتبتطلع على .. انت بتبتطلعش على اللوح
+
+307
+00:24:18,660 --> 00:24:22,340
+بتبتطلع على كلاب توجيهي جاعدة لأ مش خنطرة يا عزيزي
+
+308
+00:24:22,340 --> 00:24:26,080
+.. مش خنطرة .. مش خنطرة .. مش .. هذه مش الخنطرة
+
+309
+00:24:26,080 --> 00:24:33,580
+أنا بدي أرضي على روان .. هجت أي تيار هنا بتوزع مش
+
+310
+00:24:33,580 --> 00:24:34,700
+شوالي هدول كوازي
+
+311
+00:24:38,110 --> 00:24:41,850
+كيف هنبقى أعرف ان انا توازي؟ مش تساوي جهود؟ تساوي
+
+312
+00:24:41,850 --> 00:24:44,970
+تساوي ها أحكي يا مريم هم هادي و ما هادي مع بعض؟ هم
+
+313
+00:24:44,970 --> 00:24:48,490
+هادي و ما هادي زي بعض؟ كيف بأعرف انهم زي بعض ولا
+
+314
+00:24:48,490 --> 00:24:51,870
+لا؟ بدي أمشي من واحدة للتانية، بديش أمور معايا، لا
+
+315
+00:24:51,870 --> 00:24:56,410
+مقاومة ولا بطارية ولا مكثف ولا ملف، في مجال حد
+
+316
+00:24:56,410 --> 00:24:59,950
+يروح ليه من النقطة هادي للنقطة هادي من دون ما يمر
+
+317
+00:24:59,950 --> 00:25:05,790
+على أي حاجة؟ تمانية أهو! ليش؟ تمانية ما لها؟ من
+
+318
+00:25:05,790 --> 00:25:09,940
+التمانية؟ برضه تطلع على كتاب توجيهي جاديتبتطلعوش
+
+319
+00:25:09,940 --> 00:25:12,520
+على كتاب توجيه، الكتاب توجيه الأرقام مختلفة،
+
+320
+00:25:12,520 --> 00:25:17,200
+الأرقام مختلفة، الرسم زيها، الأرقام مختلفة، انت
+
+321
+00:25:17,200 --> 00:25:21,580
+حاجة تقول ده تشوف زيها، خلاص صادقة، ده ما .. ده ما
+
+322
+00:25:21,580 --> 00:25:28,200
+.. لكن الأرقام مختلفة، اذا تقسمت التيارات نفت
+
+323
+00:25:28,200 --> 00:25:33,260
+التوالي ولم تثبت التوازن، تمام هيك؟ حلو، قلتوا
+
+324
+00:25:33,260 --> 00:25:39,160
+بكلمة كانت حلوة، ايه جاكيرشوف قال لي بحلوةكيرشوف
+
+325
+00:25:39,160 --> 00:25:43,140
+بقى واجع عندك حلب غير غير كيرشوف احكي يا مريم حلها
+
+326
+00:25:43,140 --> 00:25:51,340
+التواليه توازيه اطلعك على الواحد يالا نجليني بلاش
+
+327
+00:25:51,340 --> 00:26:04,520
+اطلعك خليها مضبوبة ايش تلاته ايش هي صوتت ماعجباش
+
+328
+00:26:04,520 --> 00:26:14,850
+هالهادي مع الخمسة توازيهها واحدة
+
+329
+00:26:14,850 --> 00:26:20,990
+واحدة واحدة واحدة تلاتة وتمانية توازي بقولك نص
+
+330
+00:26:20,990 --> 00:26:25,250
+توازي لإن هدول زي بعض لكن هادي وهادي مش زي بعض إذا
+
+331
+00:26:25,250 --> 00:26:27,890
+مش توازي لأ يا ماريا
+
+332
+00:26:31,700 --> 00:26:37,740
+هو دي اش ماجاله شاله بفعل
+
+333
+00:26:37,740 --> 00:26:41,420
+ما هو عشان اقول توالي مش لازم يتحقق شرط التوالي مش
+
+334
+00:26:41,420 --> 00:26:44,740
+لجلنا لازم الطيار مايتجزقش وجلنا الطيار يتجزق من
+
+335
+00:26:44,740 --> 00:26:45,280
+أولها
+
+336
+00:26:49,320 --> 00:26:52,840
+اه وين طب ما كنتي وانا بحكي روان روان روان؟ وين
+
+337
+00:26:52,840 --> 00:26:58,560
+كنتي؟ قلت إذا تجزء التيار انتفت توالي ولم يثبت
+
+338
+00:26:58,560 --> 00:27:02,420
+التوازي يعني مش عشانه مش توالي إذا انقطع انتوازي
+
+339
+00:27:02,420 --> 00:27:05,720
+مش يعني مش الودن هادي الودن هادي لأ فيه ودن تالتة
+
+340
+00:27:05,720 --> 00:27:11,320
+تمام؟ اه فيه ودن تالتة هنا تفاجنا يا نور؟ نفي
+
+341
+00:27:11,320 --> 00:27:18,480
+التوالي لا يثبت التوازي هذه خلصنا منهاإيه ده قال
+
+342
+00:27:18,480 --> 00:27:22,020
+كيبكوا تحلوها طبعا زي ما اتفقنا اللي بده يتخصص
+
+343
+00:27:22,020 --> 00:27:25,120
+هندسة كهربية و هندسة حسوب حيجيها بالتفاصيل و اللي
+
+344
+00:27:25,120 --> 00:27:29,140
+فيها أكتر من شغلة لأنها دي دوائر و لازم تكونوا
+
+345
+00:27:29,140 --> 00:27:34,400
+عارفينها إيه ده كيرشوف كيرشوف علم كبير إيه ده فكر
+
+346
+00:27:34,400 --> 00:27:37,880
+جالي والله فيه قانونين كلكم بتعرفوهم بدي أعيدهم و
+
+347
+00:27:37,880 --> 00:27:41,800
+أسميهم باسمي بحج اللي أتجلم أنا بدي أضبطهم بحج
+
+348
+00:27:41,800 --> 00:27:45,840
+اللي إيه الشيء جالي انت توي مشغولتيلي التيار لما
+
+349
+00:27:45,840 --> 00:27:51,910
+بدي جيه توزعبنفعش يتوزع ولا جل يعني عشرة بدها
+
+350
+00:27:51,910 --> 00:27:57,350
+تتوزع إلى تلت أجسام اتنين و تلاتة و خمسةصح لازم
+
+351
+00:27:57,350 --> 00:28:02,090
+ترجع عشان .. برا علينا قال هو وين بتوزع التيار
+
+352
+00:28:02,090 --> 00:28:05,750
+قلتله زي ما وين بتتوزع السيارات عند مفترق طرق
+
+353
+00:28:05,750 --> 00:28:08,870
+المفترق الطرق بيسموها junction اتباعون الهنجسة
+
+354
+00:28:08,870 --> 00:28:11,110
+المدنية بيسموها junction و اتباعون الهنجسة
+
+355
+00:28:11,110 --> 00:28:14,250
+الكهربية بيسموها junction هدول ات للسيارات و هدول
+
+356
+00:28:14,250 --> 00:28:20,970
+للشحنات او للتيارات اذا قال كيرشوف يلي قاعدتين اول
+
+357
+00:28:20,970 --> 00:28:22,410
+قاعدة كلكم بتعرفوها
+
+358
+00:28:25,720 --> 00:28:32,240
+هو حبيبنا كيرشوف اتوفى سنة الـ 1887 تمام؟
+
+359
+00:28:32,240 --> 00:28:36,200
+كيرشوف
+
+360
+00:28:36,200 --> 00:28:43,280
+روسي ولا ألماني؟ أعتقد هي أعتقد أنه ألماني أهم
+
+361
+00:28:43,280 --> 00:28:43,500
+المعنى
+
+362
+00:28:49,120 --> 00:28:55,520
+مش مشكلة هنا ده بنتدي الجنسية الألمانية عشان تجيب
+
+363
+00:28:55,520 --> 00:29:02,000
+حاجة أو جنسية روسية مانطلعوا من جبرو تمام هو مرات
+
+364
+00:29:02,000 --> 00:29:04,760
+الاسم في كلامك صحيح لكن لما يقولوا ألمانيا هم
+
+365
+00:29:04,760 --> 00:29:08,670
+بتطلعوا على الجنسية مش الموطن ممكن يكون أصلهأه و
+
+366
+00:29:08,670 --> 00:29:12,690
+في الآخر ان تروحوا على أمريكا بتلاقوش مواطن أمريكي
+
+367
+00:29:12,690 --> 00:29:15,810
+اللي بيقولوا من وين أصله؟ أصلا مافيش واحد أصله
+
+368
+00:29:15,810 --> 00:29:19,370
+أمريكي إلا الهند والحمر والباقين كلهم إجوا من
+
+369
+00:29:19,370 --> 00:29:20,750
+بلدان متعددة
+
+370
+00:29:23,400 --> 00:29:27,540
+جاللي إيش؟ جاللي التيار هو لما إجيت أنا وصلت على
+
+371
+00:29:27,540 --> 00:29:32,120
+التوازن قولت التيار كان داخل نقطة و بعدين خرج من
+
+372
+00:29:32,120 --> 00:29:36,640
+النقطة إذا الداخل بسوء الخارج هي سيغة قاعدة كرشوف
+
+373
+00:29:36,640 --> 00:29:40,020
+الأولى ماهياش قاعدة بالمعنى الأخر مش قانون ماهو
+
+374
+00:29:40,020 --> 00:29:43,940
+قانون الأصل هو conservation of charge إذا القانون
+
+375
+00:29:43,940 --> 00:29:48,380
+هو conservation of charge صاغة بقاعدة سياغة إعادة
+
+376
+00:29:48,380 --> 00:29:53,430
+سياغة جاللي the sum of the currentsentering داخلة
+
+377
+00:29:53,430 --> 00:29:56,970
+any junction وعرفنا إيش معنى junction must equal
+
+378
+00:29:56,970 --> 00:30:00,090
+the sum of the currents leaving that junction كيف
+
+379
+00:30:00,090 --> 00:30:03,470
+يعني قاللي هاي ال junction؟ كيفين البنفسجية هذه؟
+
+380
+00:30:03,470 --> 00:30:07,410
+قاللي هاي تيار دخل عليها هجد في حد بعرفش إنه داخلة
+
+381
+00:30:07,410 --> 00:30:13,570
+ولا خارجها دي؟ داخلة داخلة طب و هدول الاتنين؟ أذن
+
+382
+00:30:13,570 --> 00:30:17,910
+بقدر أقولهذه الـ junction ولا لأ؟ هذه هي الـ
+
+383
+00:30:17,910 --> 00:30:22,270
+junction إذا اي junction في أي موقف في مجلس حركتين
+
+384
+00:30:22,270 --> 00:30:27,350
+كانت تتفرع لما الطيار بديه يتفرع بقول هي ال
+
+385
+00:30:27,350 --> 00:30:33,190
+junction junction؟
+
+386
+00:30:33,190 --> 00:30:38,910
+مش كل مكتب junction هه هان الطيار بيتفرعش بيلوف
+
+387
+00:30:38,910 --> 00:30:42,790
+ميت طيارة فاشي في الشارع الشارع ميل بديه ميله كله
+
+388
+00:30:43,470 --> 00:30:48,310
+مافيش طيار مانجسمش تمام قال لي يعني اكتبلي قاعدة
+
+389
+00:30:48,310 --> 00:30:54,090
+cash off هنا قال لي داخل I1 واللي خارج I2 زائد I3
+
+390
+00:30:54,090 --> 00:30:58,110
+بالظبط زي ما توجهنا التوصيل على التوازي بقولنا هي
+
+391
+00:30:58,110 --> 00:31:06,150
+هيك هي هيك مظبوط
+
+392
+00:31:06,150 --> 00:31:11,680
+هيك ولا لأ بقولنا هذه I وهذه I1وها دي اية اتنين
+
+393
+00:31:11,680 --> 00:31:14,060
+اذا انا انا انا انا انا انا انا انا انا انا انا
+
+394
+00:31:14,060 --> 00:31:17,120
+انا
+
+395
+00:31:17,120 --> 00:31:17,680
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+396
+00:31:17,680 --> 00:31:19,000
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+397
+00:31:19,000 --> 00:31:19,200
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+398
+00:31:19,200 --> 00:31:22,520
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+399
+00:31:22,520 --> 00:31:27,140
+انا انا انا انا انا انا انا
+
+400
+00:31:27,140 --> 00:31:35,090
+انا انا اناأدبي خاشش من أدبي امسلم هو برياضيات من
+
+401
+00:31:35,090 --> 00:31:39,950
+قلع دا دي من الصف السابع قلتله ده اللي ماكانش دعوة
+
+402
+00:31:39,950 --> 00:31:41,670
+في الرياضيات أنا مالك دعوة في الرياضيات قلتله بس
+
+403
+00:31:41,670 --> 00:31:47,070
+شغلة بسيطة بدي أقول VA نقص VA يقولوا هدى معرفة صار
+
+404
+00:31:47,070 --> 00:31:52,750
+عالم رياضية جدش هدى؟ سفر هكده شوف التانية بتساوي
+
+405
+00:31:52,750 --> 00:31:58,210
+سفر فيه خلاف؟جلّي va-va طب انا دايما بقولي v final
+
+406
+00:31:58,210 --> 00:32:01,570
+نقص v initial ولا لأ؟ جلّي يعني ال final و ال
+
+407
+00:32:01,570 --> 00:32:04,670
+initial نفس النقطة جلّي وين بتحقق؟ قولتله في
+
+408
+00:32:04,670 --> 00:32:08,970
+الدوائر المغلقة، فح؟ أي حلقة ما هو دائرة، طبعا في
+
+409
+00:32:08,970 --> 00:32:11,650
+الدائرة المغلقة في الدوائر الكهربائية ما يسميها
+
+410
+00:32:11,650 --> 00:32:15,770
+loop، loop مغلقة جلّي يعني أنت بدك تبدأ من النقطة
+
+411
+00:32:15,770 --> 00:32:20,370
+وترجعلها وتسويهم بزفر، مافيش خلافقال لي طب و أنت
+
+412
+00:32:20,370 --> 00:32:23,950
+ماشي من النقطة و أنت ماشي و ترجع للنقطة ايش
+
+413
+00:32:23,950 --> 00:32:27,110
+بيجابله؟ بيقوللي بيجابلني شغلات كتيرة بيجابلني
+
+414
+00:32:27,110 --> 00:32:31,110
+كدائرة بصورة عامة مش هناخدهم كلهم بيجابلني بطارية
+
+415
+00:32:31,110 --> 00:32:41,890
+صح؟ بيجابلني مقاومة كبسيطار؟ ملف المحافظة هذا R
+
+416
+00:32:41,890 --> 00:32:48,390
+وهذه C وهذه L وهذه Epsilonقال لي بدك تشوف فرق
+
+417
+00:32:48,390 --> 00:32:51,990
+الجهود انت بتجمع قاعد طب هو فرق الجهود دايما زي
+
+418
+00:32:51,990 --> 00:32:56,290
+بعض مش مرة موجب مرة سالب اذا انت بتجمع الجامع جبري
+
+419
+00:32:56,290 --> 00:33:00,270
+الموجب و السالب ايش بده يعرفني موجب ولا سالب قاللي
+
+420
+00:33:00,270 --> 00:33:06,610
+فرق الجهود يا بنات خمسة نقص تمانية طب تمانية نقص
+
+421
+00:33:06,610 --> 00:33:11,710
+خمسة اذا انت لما تكون واطي وروحك عالي على التمانية
+
+422
+00:33:11,710 --> 00:33:17,770
+بيكون نتيجة فرق موجب وإذا العكس بيكون فرق سالبزي
+
+423
+00:33:17,770 --> 00:33:21,370
+ما نقوله نرجع للجهود ما هو طاقة هاي واحد كان هنا
+
+424
+00:33:21,370 --> 00:33:25,330
+صار هنا إيش الفرق؟ موجب لأنه انت انتقلت من واطي
+
+425
+00:33:25,330 --> 00:33:29,790
+لعالي ال final نقص ال initial طيب كنت هنا وصلت هنا
+
+426
+00:33:29,790 --> 00:33:34,370
+إذا لما تنتقل من العالي للواطي بكون سالق قلتلي طب
+
+427
+00:33:34,370 --> 00:33:37,710
+هدا كيف بدك تجلبه في الكهربا؟ قلتله هو البطارية
+
+428
+00:33:37,710 --> 00:33:42,260
+مافيش حد بيعرف إنها واحد واطي وواحد عالي؟أذا
+
+429
+00:33:42,260 --> 00:33:46,140
+المعرف في قطب السالب و القطب الموجب و السالب واطي
+
+430
+00:33:46,140 --> 00:33:50,060
+و الموجب عالي جري طب و المقاومة؟ قولتله المقاومة
+
+431
+00:33:50,060 --> 00:33:54,360
+هو بينفع يكون لها فرق جهود بدون طيار طب هو الطيار
+
+432
+00:33:54,360 --> 00:33:58,400
+لما جولك اتجاهه بتعرف لإنت الموجب و السالب ولا لأ؟
+
+433
+00:33:58,400 --> 00:34:03,290
+يعني هاي دي نرجعله هنا و أقولك هي الطيارةإذاً
+
+434
+00:34:03,290 --> 00:34:06,530
+قطعًا هذه مودب وهذه سالب لأن التيار بيمشي من
+
+435
+00:34:06,530 --> 00:34:12,230
+العالي للواطي صح ولا لأ؟ إذاً معناته بهذه القاعدة
+
+436
+00:34:12,230 --> 00:34:18,350
+بتقدر تحدد لي Delta V للبطارية أو للمقاومة مودب أو
+
+437
+00:34:18,350 --> 00:34:23,170
+سالب فتكمل المكثف والملف ناشيه هكذا تمام هيك؟ إذاً
+
+438
+00:34:23,170 --> 00:34:28,690
+جاليالقاعدة اللي سماها الـ algebraic sum اللي هي
+
+439
+00:34:28,690 --> 00:34:32,130
+القاعدة هذه ال algebraic sum of the potential
+
+440
+00:34:32,130 --> 00:34:36,550
+differences across all the elements كل عناصر
+
+441
+00:34:36,550 --> 00:34:39,750
+الدائرة، عناصر الدائرة أربعة الآن، هذا هما مش
+
+442
+00:34:39,750 --> 00:34:43,490
+هناخدهم كلهم، هناخد انتيه بس هم أربعة، all the
+
+443
+00:34:43,490 --> 00:34:46,630
+elements around any closed loop must be zero قلتله
+
+444
+00:34:46,630 --> 00:34:51,690
+تمه، قاللي the first ruleهو نفسه كيرشي بيقولك ال
+
+445
+00:34:51,690 --> 00:34:54,890
+first rule مش تبعتى هذه مبدأ ال conservation of
+
+446
+00:34:54,890 --> 00:34:58,270
+charge ال first rule is an application of the
+
+447
+00:34:58,270 --> 00:35:02,690
+conservation of charge while the second rule is a
+
+448
+00:35:02,690 --> 00:35:05,930
+conservation of energy is a consequence of the
+
+449
+00:35:05,930 --> 00:35:08,970
+conservation of energy لأنه هذا مبدأ الطاقة حفظ
+
+450
+00:35:08,970 --> 00:35:13,410
+الطاقة لأن فرق الجهد اضربه في Q بصير شغل بصير طاقة
+
+451
+00:35:13,410 --> 00:35:17,650
+فهذا مبدأ حفظ الطاقة اللى انا بعملكياه بقولك VA
+
+452
+00:35:17,650 --> 00:35:22,190
+لازم تسوى VA وانت ماشيبديت بالطاقة، بدك ترجع لنفس
+
+453
+00:35:22,190 --> 00:35:27,770
+الطاقة تمام، حلو قال له بس مشكلتي مشكلة في التانية
+
+454
+00:35:27,770 --> 00:35:31,490
+إن الـDelta V هذه مرة بتكون موجبة ومرة بتكون
+
+455
+00:35:31,490 --> 00:35:35,270
+سالبة، بدك تنتبه لها قال لي to apply the second
+
+456
+00:35:35,270 --> 00:35:38,690
+rule we should know the following two remarks عشان
+
+457
+00:35:38,690 --> 00:35:43,010
+تطبق وتعرف الموجب والسالب بدك تنتبه من شغلها قال
+
+458
+00:35:43,010 --> 00:35:47,710
+لي لو كان عندك هنا مقاومة وانا اديتك التيار زي ما
+
+459
+00:35:47,710 --> 00:35:52,040
+انت شايفتخيلوا وين الطرف الموجب و الطرف السالب
+
+460
+00:35:52,040 --> 00:35:57,180
+يعني هيك صح طبعا أول ما حط موجب و سالب عرفت من
+
+461
+00:35:57,180 --> 00:36:00,220
+العالي و من الواطي تمام قال إيه أنت كده بدك تمشي
+
+462
+00:36:00,220 --> 00:36:04,040
+قلتله إذا أنا ماشي يمين معناته طالع من العالي إلى
+
+463
+00:36:04,040 --> 00:36:09,900
+الواطي معناته سالب صح؟ من العالي إلى الواطي يعني
+
+464
+00:36:09,900 --> 00:36:13,520
+كيفي عالي الواطي يعني أنا ماشي هيك معناته ال
+
+465
+00:36:13,520 --> 00:36:17,380
+initial موجب و ال final سالب هو هي ماشي قال إيه
+
+466
+00:36:17,380 --> 00:36:26,290
+يعني أنت لو كنت ماشي هيكبحط سالب اعكس موجب
+
+467
+00:36:26,290 --> 00:36:32,330
+الفجانية الأولى والتحتانية التانية الأولى رايح
+
+468
+00:36:32,330 --> 00:36:37,070
+يمين التانية رايح يسار بيقول لي that change in
+
+469
+00:36:37,070 --> 00:36:41,850
+potential through any resistor is negative for a
+
+470
+00:36:41,850 --> 00:36:44,730
+move in the direction of the current and positive
+
+471
+00:36:44,730 --> 00:36:46,930
+for a move opposite to the direction of the
+
+472
+00:36:46,930 --> 00:36:50,960
+current هذه اللي خدناها في المدرسةلكن عرفنا ليش؟
+
+473
+00:36:50,960 --> 00:36:53,860
+لأنه انتقال من عالي لواطي من واطي لعالي هدا هي
+
+474
+00:36:53,860 --> 00:36:58,680
+بصورة بسيطة جدا هي فرق يهود في الآخر فرق زي ما
+
+475
+00:36:58,680 --> 00:37:01,700
+تقولتلكم خمسة نقص سمانية ولا تمانية نقص خمسة عشان
+
+476
+00:37:01,700 --> 00:37:05,060
+أعرف إنها تلاتة ولا سالب تلاتة إذا والله تمانية
+
+477
+00:37:05,060 --> 00:37:08,340
+نقص خمسة تلاتة لكن إذا خمسة نقص تمانية نقص سلاتة
+
+478
+00:37:08,340 --> 00:37:13,140
+إذا أنت بتقوللي فرق نهاية نقص بداية إذا كانت
+
+479
+00:37:13,140 --> 00:37:20,590
+النهاية هي الواطية سالب واضحة ولا لأ تمةقالي طيب و
+
+480
+00:37:20,590 --> 00:37:24,170
+البطارية؟ قلت البطارية سهلة أنا عندي قطب سالب و
+
+481
+00:37:24,170 --> 00:37:29,790
+قطب موجب والله إذا أنت ماشي هيك معناته موجب و إذا
+
+482
+00:37:29,790 --> 00:37:33,850
+ماشي العكس معناته سالب يعني إذا أنت ماشي مع الإنف
+
+483
+00:37:33,850 --> 00:37:38,750
+موجب و إذا ماشي ضد الإنف فهو سالب تمام يا بنات
+
+484
+00:37:38,750 --> 00:37:45,680
+قاعدة سهلة جدا و عارفينها و طبقناها في المدرسةإذا
+
+485
+00:37:45,680 --> 00:37:47,940
+الـ Change in potential through an ideal battery
+
+486
+00:37:47,940 --> 00:37:50,620
+is positive for a move from the negative to the
+
+487
+00:37:50,620 --> 00:37:53,420
+positive terminal of the battery and negative for
+
+488
+00:37:53,420 --> 00:37:58,160
+a move in the opposite direction هذه هي الـ
+
+489
+00:37:58,160 --> 00:38:03,120
+quizزين بس حطيهم أنا حكيتهم طلع ال quiz بقول قال
+
+490
+00:38:03,120 --> 00:38:06,960
+قاعدة كرشف الأولى هي نتيجة لأي قانون من القوانين
+
+491
+00:38:06,960 --> 00:38:13,860
+الأربع اللي بددك إياهمConservation of Charge إذا
+
+492
+00:38:13,860 --> 00:38:19,660
+هذه معناه تلشحن لما لا تفنع ولا تستحدر وهذا مبدأ
+
+493
+00:38:19,660 --> 00:38:24,660
+Conservation of Charge قال طيب كيرشف second rule
+
+494
+00:38:24,660 --> 00:38:28,620
+is a consequence of من الأربعة Conservation of
+
+495
+00:38:28,620 --> 00:38:35,200
+Energy حكيته بس ب ..محتوط عشان نعلمه دي نقولنا
+
+496
+00:38:35,200 --> 00:38:42,460
+يللا ننقل .. ننقله ميا بركة طلعتلك تمام؟ اه تمام
+
+497
+00:38:42,460 --> 00:38:49,120
+يا بنات؟ حلو جيت بدي أحل هجيت بدي أعرف السرتيجيات
+
+498
+00:38:49,120 --> 00:38:53,540
+اللي بنحطها عشان نبدأ نحل أسئلة كيرشوف أجاكم سؤال
+
+499
+00:38:53,540 --> 00:38:58,820
+كيرشوف اللي بتوجيهي؟ كيفتوا عليه؟ اه حلو فيه الحمد
+
+500
+00:38:58,820 --> 00:39:03,930
+للهالحلو بيكون معايا كمية اه مش حلو في توجيهه بس
+
+501
+00:39:03,930 --> 00:39:09,130
+احنا بس بنحط عليه شوية مريح بس اه فيه شوية مريح
+
+502
+00:39:09,130 --> 00:39:15,490
+زيادة عشان تطلع حجة السؤال عشان تطلع السؤال حدجلأ
+
+503
+00:39:15,490 --> 00:39:18,450
+ما تبقى بنات صغيرة مش ضغط ولا حاجة علينا الضغط
+
+504
+00:39:18,450 --> 00:39:22,230
+انتوا لسه بخافتي من الضغط لإن انتوا بتاكلوا طرشة
+
+505
+00:39:22,230 --> 00:39:27,770
+وفلفل مكبوس ومش عارفين ايه جات عليها دي تمام طلعش
+
+506
+00:39:27,770 --> 00:39:33,480
+مين نسوي جليك عشان تحل جلي أول حاجةالدائرة
+
+507
+00:39:33,480 --> 00:39:35,940
+بترسمها، قلت الحمد لله كل الدوائر مرسومة في
+
+508
+00:39:35,940 --> 00:39:40,080
+الكتاب، إذا أول خطوة already إحنا بنعملها. Draw a
+
+509
+00:39:40,080 --> 00:39:42,620
+circuit diagram and label all quantities known and
+
+510
+00:39:42,620 --> 00:39:46,220
+unknowns. إيش يعني label؟ جالي حُط رموز، يعني زي
+
+511
+00:39:46,220 --> 00:39:51,000
+هذا السؤال.هنا قال يعني انت هذه R حطها R واحد هذه
+
+512
+00:39:51,000 --> 00:39:56,340
+R حطها R اتنين هذه R تلاتة هذه R أربعة وهذه R خمسة
+
+513
+00:39:56,340 --> 00:40:01,880
+هذه بيسميها ترميز والتيارات قال لي هذه I واحد اللي
+
+514
+00:40:01,880 --> 00:40:04,780
+هنا I اتنين اللي هنا I تلاتة اللي هنا I أربعة انهي
+
+515
+00:40:04,780 --> 00:40:08,660
+I خمسة هذه سميها Epsilonإذا عندك تين تين إبسلون
+
+516
+00:40:08,660 --> 00:40:12,500
+إبسلون واحد وإبسلون اتنين هذا بيسمي ترميز ل الرموز
+
+517
+00:40:12,500 --> 00:40:15,800
+اللي عندك وإيش قال ليه النون والأنون حتى لو معطنة
+
+518
+00:40:15,800 --> 00:40:19,480
+انت بتقول بدي لنا نفترض R1 ماهي اتنين O تعود عنها
+
+519
+00:40:19,480 --> 00:40:23,900
+في الآخر حتى لو known ومعروفة اديها رمز عشان تكتب
+
+520
+00:40:23,900 --> 00:40:25,860
+المعادلة صح تمام
+
+521
+00:40:28,070 --> 00:40:31,010
+بيقولّي انت قاعدة كرشوف التانية بتقول ابدأ من
+
+522
+00:40:31,010 --> 00:40:34,410
+النقطة و ارجعلها، صح؟ حاجات اللي تتخيلوا، بتبدأ من
+
+523
+00:40:34,410 --> 00:40:37,390
+النقطة و ترجعولها، في عندك خيارين لا تالي لهمها،
+
+524
+00:40:37,390 --> 00:40:39,770
+لا بتمشي مع أقرب الساعة، لا ضد أقرب الساعة، في
+
+525
+00:40:39,770 --> 00:40:44,250
+خلاف؟ لأ. إذا بيقوللي انت مع أقرب الساعة و ضد أقرب
+
+526
+00:40:44,250 --> 00:40:46,830
+الساعة، أنا أشول ولا أي من ولا بحب أقرب الساعة ولا
+
+527
+00:40:46,830 --> 00:40:50,310
+بحب ضد المتحور، بس قوللي وين رايح؟ خطة للاتجاه
+
+528
+00:40:50,310 --> 00:40:54,690
+اللي بتمشي فيه، دي a sign، حدد، a direction for
+
+529
+00:40:54,690 --> 00:40:57,500
+the current أول في الحاجة،أه .. أنا جيت وقاللي
+
+530
+00:40:57,500 --> 00:41:01,080
+الطيارات .. قاللي الطيارات كيف بدي أعملهم؟ طب أنا
+
+531
+00:41:01,080 --> 00:41:03,420
+عندي قاعدة الطيار بيجي من قطب الموجة إلى قطب
+
+532
+00:41:03,420 --> 00:41:07,680
+السالب، صح؟ طب مش دايما واضحة، قاللي عشان كده لما
+
+533
+00:41:07,680 --> 00:41:12,900
+تخليش مخك يفكر ثانية، خلي جلمك يحط ال directions،
+
+534
+00:41:12,900 --> 00:41:16,700
+where ما يحطوا يحطوا، where ما يحطوا يحطوا، إذا
+
+535
+00:41:16,700 --> 00:41:19,480
+بيقوللي assign a direction for the current in each
+
+536
+00:41:19,480 --> 00:41:25,030
+part of the circuitحضّرْك ومكمّل Don't bother و لا
+
+537
+00:41:25,030 --> 00:41:29,570
+تجلد إتراقًا if your guess of current direction is
+
+538
+00:41:29,570 --> 00:41:33,490
+incorrect إذا كان تقمينك غلط خمّل و ما تخافش حتى
+
+539
+00:41:33,490 --> 00:41:38,450
+لو كان تقمينك خطأ في هذه الحالة النتيجة هتطلع معاك
+
+540
+00:41:38,450 --> 00:41:43,410
+سالب بس طبعًا أحنا عشان نريح و نقعد نغلب بعض في
+
+541
+00:41:43,410 --> 00:41:47,430
+التصليح أحنا بنحط ال directionsفي الامتحان برضه
+
+542
+00:41:47,430 --> 00:41:50,270
+عشان نريحنا في الكتاب مرات بيقولك انت حط ال
+
+543
+00:41:50,270 --> 00:41:54,250
+direction بناش ناخد وجهته و نفكر اين ال direction
+
+544
+00:41:54,250 --> 00:41:58,610
+تمام بدي
+
+545
+00:41:58,610 --> 00:42:03,550
+ابدأ بكرشوف رولز طبعا انتوا عارفين احنا كيف بنصلح
+
+546
+00:42:03,550 --> 00:42:08,790
+نصلح على الفيزيا صحيح؟ و الفيزيا بتنأكس معادلات كل
+
+547
+00:42:08,790 --> 00:42:12,130
+معادلة بنديها درجةما زالت بدنا معادلات منهم،
+
+548
+00:42:12,130 --> 00:42:15,110
+معادلات منهم اللي بتيجي؟ من قاعدة كيرشوف، قاعدتها
+
+549
+00:42:15,110 --> 00:42:17,070
+كيرشوف، قاللي القاعدة الأولى فيها حد اللي بيخربط
+
+550
+00:42:17,070 --> 00:42:20,290
+فيها، بيخربطش إذا انت حاطط، بتروحي تشوف ال
+
+551
+00:42:20,290 --> 00:42:24,030
+junction، بتكوني الداخل بالساوي الخارج، إذا apply
+
+552
+00:42:24,030 --> 00:42:28,230
+the first Kirshoff's rule to any junction in the
+
+553
+00:42:28,230 --> 00:42:31,770
+circuit، طيب، قاللي طب لو في اتنين junction، باخد
+
+554
+00:42:31,770 --> 00:42:35,410
+ست درجات، تلاتة وتلاتة، بقوله مش دايما، ليش؟ قاللي
+
+555
+00:42:35,410 --> 00:42:40,840
+طيب اني أشوف هذه الدائرة،مش هذه a junction وهذه بي
+
+556
+00:42:40,840 --> 00:42:47,760
+junction يالا الداخل all هيها بتساوي الخارج I1 زي
+
+557
+00:42:47,760 --> 00:42:53,280
+I2 نجي لهنا اللي هذه هنا أصلا كانت خارجها وهدول
+
+558
+00:42:53,280 --> 00:43:01,220
+داخلين صارت I1 زي I2 بتساوي I تقدر تقولي هذه واحد
+
+559
+00:43:01,220 --> 00:43:06,260
+وحطولك تلت درجات وهذه وحطولك تلت درجاتنفسه مانفعش
+
+560
+00:43:06,260 --> 00:43:12,760
+احنا مانعدش عدل هيك يعني هوا احنا مانعد معادلات
+
+561
+00:43:12,760 --> 00:43:16,120
+جبريه صحيحه عشان كده ايش بيقولي بيقولي in general
+
+562
+00:43:16,120 --> 00:43:19,580
+this rule is used one time fewer than the number
+
+563
+00:43:19,580 --> 00:43:22,620
+of junctions in the circuit اذا عندك two junctions
+
+564
+00:43:22,620 --> 00:43:27,400
+استخدمها مرتين مرة تلاتة junctions استخدمها مرتين
+
+565
+00:43:27,400 --> 00:43:31,960
+اربع junctions استخدمها تلات مرة كذا اما مش كل
+
+566
+00:43:31,960 --> 00:43:34,660
+junctions ويقولي هي معادلات كل معادلة تلاتة درجات
+
+567
+00:43:34,850 --> 00:43:40,070
+تظبطش تامة بقولها
+
+568
+00:43:40,070 --> 00:43:47,930
+جيت اختاري ال loops نيجي لهذه أكم loop فيها ادوا
+
+569
+00:43:47,930 --> 00:43:54,530
+ادوا وما تتلعبوا تطلعوه طلعنا تلاتة هنا هذه
+
+570
+00:43:54,530 --> 00:44:02,450
+الفغيرة حلوة وهي هذه وهي هذه تلاتة وينها؟ والله
+
+571
+00:44:02,450 --> 00:44:10,200
+يمكن تعدوا ستةستة و سبعة هاي واحدة تنتين هاي تلاتة
+
+572
+00:44:10,200 --> 00:44:18,680
+هاي أربعة هاي خمسة هاي ستة و تعدده تمانين اختار ال
+
+573
+00:44:18,680 --> 00:44:25,260
+loops جالي اختار أي loopابدى من نقطة ورجعلها لما
+
+574
+00:44:25,260 --> 00:44:28,740
+تبدى من نقطة و اذا ترجعلها بدك تختار اما مع قرب
+
+575
+00:44:28,740 --> 00:44:33,560
+الساعة او ضد قرب الساعة ان ا choose any closed
+
+576
+00:44:33,560 --> 00:44:38,100
+loop in the network نتورك الشبكة الدائرة كلها and
+
+577
+00:44:38,100 --> 00:44:41,580
+designate a direction وحدد اتجاه كيف بدك تلف
+
+578
+00:44:41,580 --> 00:44:46,480
+clockwise or counter clockwise تمام to traverse
+
+579
+00:44:46,480 --> 00:44:52,520
+the loop عشان تلف على ال loopبداية من نقطة واحدة
+
+580
+00:44:52,520 --> 00:44:56,820
+في اللوب، اذهب حول اللوب في الاتصال الاتصالي أو
+
+581
+00:44:56,820 --> 00:44:58,780
+الاتصال الاتصالي أو الاتصال الاتصالي أو الاتصال
+
+582
+00:44:58,780 --> 00:44:58,800
+الاتصالي أو الاتصال الاتصالي أو الاتصال الاتصالي
+
+583
+00:44:58,800 --> 00:44:58,840
+أو الاتصال الاتصال الاتصالي أو الاتصال الاتصال
+
+584
+00:44:58,840 --> 00:44:59,480
+الاتصال الاتصال الاتصال الاتصال الاتصال الاتصال
+
+585
+00:44:59,480 --> 00:45:01,480
+الاتصال الاتصال الاتصال الاتصال الاتصال الاتصال
+
+586
+00:45:01,480 --> 00:45:02,740
+الاتصال الاتصال الاتصال الاتصال الاتصال الاتصال
+
+587
+00:45:02,740 --> 00:45:04,080
+الاتصال الاتصال الاتصال الاتصال الاتصال الاتصال
+
+588
+00:45:04,080 --> 00:45:07,370
+الاتصال الاتصال الاتصال الاتصال الاتصال الاتصتم
+
+589
+00:45:07,370 --> 00:45:11,650
+اكم لوب قال لك انت اكم مجول عندك تلاتة اكم معادلة
+
+590
+00:45:11,650 --> 00:45:14,570
+بتحتاجها لك تظل تختار ال loops لما تصبح عندك تلات
+
+591
+00:45:14,570 --> 00:45:18,110
+معادلات كل معادلة عليها تلات درجات نفترض تلاتة
+
+592
+00:45:18,110 --> 00:45:23,350
+تلاتة و تلاتة و تلاتة كديش تسعة تظل علامة على جابر
+
+593
+00:45:23,350 --> 00:45:31,230
+صف سابع كيف حل العلاقاتتمام اه in doing so you
+
+594
+00:45:31,230 --> 00:45:33,090
+should know the two remarks we discussed before
+
+595
+00:45:33,090 --> 00:45:36,330
+جالي و انا قاعد بجمع بدك think بيه في عندك مقاومات
+
+596
+00:45:36,330 --> 00:45:39,350
+و في عندك بطاريات think بيه the potential
+
+597
+00:45:39,350 --> 00:45:44,150
+difference اللي بدك تجمعه across any battery
+
+598
+00:45:44,150 --> 00:45:49,070
+across any input is plus epsilonبكون زائد if it is
+
+599
+00:45:49,070 --> 00:45:51,350
+traversed from the negative to the positive
+
+600
+00:45:51,350 --> 00:45:55,690
+terminal and minus epsilon if it traversed in the
+
+601
+00:45:55,690 --> 00:45:57,970
+opposite direction وانت ماشي ما انت بقى قلتلي مع
+
+602
+00:45:57,970 --> 00:46:00,730
+القارب الساعة و ضد القارب الساعة، ماشي إذا انت
+
+603
+00:46:00,730 --> 00:46:03,150
+والله جاي من ال negative لل positive في البطارية
+
+604
+00:46:03,150 --> 00:46:06,670
+بتحط زائد epsilonإذا جاي من الـ positive لأن الـ
+
+605
+00:46:06,670 --> 00:46:09,990
+negative بتحط ناقص إبسلون ده دي طيب في الـ
+
+606
+00:46:09,990 --> 00:46:13,270
+resistor قولتله فرق الجهد بيساوي I في R حسب قانون
+
+607
+00:46:13,270 --> 00:46:19,570
+O إذا فرق الجهد ده المقاومات إما plus IR أو ناقص
+
+608
+00:46:19,570 --> 00:46:25,130
+IR ناقص IR إذا و أنت ماشي والتيار معاك و زائد IR
+
+609
+00:46:25,130 --> 00:46:29,170
+إذا و أنت ماشي التيار عكسك بقول choose another
+
+610
+00:46:29,170 --> 00:46:34,380
+loop اختار loop تانية and repeat the fifthstep to
+
+611
+00:46:34,380 --> 00:46:37,080
+get a different equation relating the unknown
+
+612
+00:46:37,080 --> 00:46:40,320
+quantities continue until you have as many
+
+613
+00:46:40,320 --> 00:46:43,640
+equations as unknowns تلت مجاهير بدك تلت معادلات
+
+614
+00:46:43,640 --> 00:46:49,360
+اربع مجاهير بدك اربع معادلات رقم سبعة عليها علامة
+
+615
+00:46:49,360 --> 00:46:52,780
+solve these equations simultaneously for the
+
+616
+00:46:52,780 --> 00:46:57,840
+unknowns عشان تجيب ال unknowns هذا السؤال يا بنات
+
+617
+00:46:57,840 --> 00:47:01,220
+موجود فين الكتاب هذا أظن بده سبعة معادلات بسبعة
+
+618
+00:47:01,220 --> 00:47:06,850
+مجاهيرطويل .. ماتكشريش .. ماتجيبوش في الامتحان ..
+
+619
+00:47:06,850 --> 00:47:11,910
+ماتكشريش .. لكن موجود في الكتاب .. عشان تتسلوا فيه
+
+620
+00:47:11,910 --> 00:47:15,010
+.. عشان تشوف حانة و لتاب .. انا قولت ليش في
+
+621
+00:47:15,010 --> 00:47:18,630
+رويحاته .. قالك لحظة يكون في طالب صار ياخد المادة
+
+622
+00:47:18,630 --> 00:47:22,090
+و هو مش مخلص سابع .. نشوف و نسقطه .. ماخد سابع ولا
+
+623
+00:47:22,090 --> 00:47:25,430
+لا .. اذا ماخد سابع بحالها .. مش مدوا جدا .. مدي و
+
+624
+00:47:25,430 --> 00:47:30,290
+اكتفوا الضغط .. مجيبوا و نمتحان ..طبعا فهذا موجود
+
+625
+00:47:30,290 --> 00:47:33,950
+عشان تجيبوا unequivalent عشان ماتقوليش هذه وهملات
+
+626
+00:47:33,950 --> 00:47:38,810
+لأن الأرقام مختلفة طبعا وقت إيش هدول بيه مال هيكون
+
+627
+00:47:38,810 --> 00:47:42,470
+فيه هدول بتساوي بعض ساعتها في طيار بيخش منها و
+
+628
+00:47:42,470 --> 00:47:47,190
+الطيار من هنا بيلغوا بعض و بيصير هذه طاعدة بناخدها
+
+629
+00:47:47,190 --> 00:47:54,090
+بعدين إذا صار فيه فرصةفي هذه الحالة طبعا يا بنات
+
+630
+00:47:54,090 --> 00:47:57,950
+احنا مدركين انه انتوا بالنسبة للتوجيه كبرتوا
+
+631
+00:47:57,950 --> 00:48:02,630
+كبرتوا و احنا مدركين هذا الكبر و هذا الندج لا
+
+632
+00:48:02,630 --> 00:48:05,830
+والزمان
+
+633
+00:48:05,830 --> 00:48:13,670
+ممشيش في مرة اصغار بس اكبر من التوجيه يعني اصغار
+
+634
+00:48:13,670 --> 00:48:19,940
+مقارنة بسنة خمسةأيه لأ بس هي اللي حواليكم
+
+635
+00:48:19,940 --> 00:48:25,920
+بيخوفوكوا بس هي مسكتة لأنه كل الجيلان بيسألوا جدي
+
+636
+00:48:25,920 --> 00:48:28,280
+الجابت في توجيهه لكن جدي الجابت في الفصل الأول حد
+
+637
+00:48:28,280 --> 00:48:33,060
+سألكه لا أخاتك ولا عمتك ولا جارتك ولا حاجة كل واحد
+
+638
+00:48:33,060 --> 00:48:37,290
+ماخد يجب أمك و أبوك يعرفه و بصراعفهخلاص كل واحد
+
+639
+00:48:37,290 --> 00:48:41,250
+كشف درجاته إيه له في الجامعة عشان كده الطالب بياخد
+
+640
+00:48:41,250 --> 00:48:45,970
+راحته لقصر بقولك ما حد شايف مش مشكلة غير عن توجيه
+
+641
+00:48:45,970 --> 00:48:50,250
+فضيحة بجلاجل زي ما بيسموها لو بتخشوا على كل مواقع
+
+642
+00:48:50,250 --> 00:48:53,890
+ال .. ال net بيقولوا بديون أسماء بعد ساعتين بيصير
+
+643
+00:48:53,890 --> 00:48:59,600
+كلها بقى أسماء بيصير فضيحة تابعأذا هذا الموضوع يا
+
+644
+00:48:59,600 --> 00:49:03,660
+بنات زي ما توي انا حكيتلها مظبوط انا بجيبه في
+
+645
+00:49:03,660 --> 00:49:06,620
+الامتحان وانا قلت هذا ال chapter كتير مهم وفي ال
+
+646
+00:49:06,620 --> 00:49:10,320
+final لازم ييجي بس بجيبه مش زي توجيهي المال يحتبعي
+
+647
+00:49:10,320 --> 00:49:13,840
+بدخل فيه شغلات معينة بدخل فيه capacitor قعدنا نشوف
+
+648
+00:49:13,840 --> 00:49:16,960
+طبعا احنا ال capacitor هو نتعلم كيف نتعامل معاهبما
+
+649
+00:49:16,960 --> 00:49:22,220
+نكون اتعلمنا لأن الـ RC أحد العلوين المهمة في هذا
+
+650
+00:49:22,220 --> 00:49:26,000
+ال chapter فحنشرحه بالتفصيل وبالتالي ممكن نزود و
+
+651
+00:49:26,000 --> 00:49:29,040
+نكون في chapter عشرة أخدنا الملافظ، ملاحظة فيه
+
+652
+00:49:29,040 --> 00:49:33,440
+كمان ملافظ؟ هم، حنا بدنا نجمع، فهو بدنا ناخد ..
+
+653
+00:49:33,440 --> 00:49:37,980
+والله كيرشوفوالله كيرشه وما هو ابلح موق دمه بس
+
+654
+00:49:37,980 --> 00:49:42,000
+شوية ملح هزودنا على الطبخ خلاص مش اكتر فأما هو
+
+655
+00:49:42,000 --> 00:49:47,040
+يعني القاعدة تبعتي ضالت زي ما هي لكن وطبعا احنا
+
+656
+00:49:47,040 --> 00:49:51,860
+مينجيمش الملح مرة واحدة ممكن احنا واحدة واحدة ممكن
+
+657
+00:49:51,860 --> 00:49:54,880
+علمناكم كده دي كيف بتتعاملوا مع المكثف كيف
+
+658
+00:49:54,880 --> 00:49:59,180
+بتتعاملوا مع البلاف وكل هذه التفاصيل بتكون انتوا
+
+659
+00:49:59,180 --> 00:50:04,960
+عرفتوهاتمام احنا امتحاننا النصفي هيكون يوم السبت
+
+660
+00:50:04,960 --> 00:50:11,320
+مثل اليوم تمام؟ بالتالي هللي quiz نخليه خميس؟ quiz
+
+661
+00:50:11,320 --> 00:50:16,810
+شبطة الخمسةيكون استويتوا و جهزتوا حالكم و ساعة
+
+662
+00:50:16,810 --> 00:50:20,590
+الزمن او مش ساعة الزمن هي عشر دقائق زمن اتحلوا ال
+
+663
+00:50:20,590 --> 00:50:24,410
+quiz تشوفوا حالكم انه هذا خصوصا هذا ال chapter
+
+664
+00:50:24,410 --> 00:50:28,250
+خصوصا هذا ال chapter يا نادا مش هيكون عليه أسئلة
+
+665
+00:50:28,250 --> 00:50:33,450
+حل هيكون بس عليه أسئلة multiple choicesأه هذا
+
+666
+00:50:33,450 --> 00:50:38,050
+الشرطة الخامس مش هذا الخامس وبالتالي جيد انه يكون
+
+667
+00:50:38,050 --> 00:50:41,470
+ال quiz يوم الخميس انه قبل الامتحان معانا الجمعة
+
+668
+00:50:41,470 --> 00:50:45,390
+للساعة بيكون تمام تمام نقف هنا عشان هذا السؤال
+
+669
+00:50:45,390 --> 00:50:48,230
+بنحله بالتفصيل المرة الجاية يعطيكوا العافية و
+
+670
+00:50:48,230 --> 00:50:48,950
+بنكمل ان شاء الله
+
diff --git a/PL9fwy3NUQKwZzXsCLffozucGP33XWqvBP/93UnIEtyPuY.srt b/PL9fwy3NUQKwZzXsCLffozucGP33XWqvBP/93UnIEtyPuY.srt
new file mode 100644
index 0000000000000000000000000000000000000000..65ccd06ab4d58f1326dd93f67c28829a70c7c33f
--- /dev/null
+++ b/PL9fwy3NUQKwZzXsCLffozucGP33XWqvBP/93UnIEtyPuY.srt
@@ -0,0 +1,1860 @@
+1
+00:00:05,570 --> 00:00:08,990
+بسم الله الرحمن الرحيم وإن شاء الله نبدأ
+
+2
+00:00:08,990 --> 00:00:15,330
+الآن بشرح chapter one زي ما حكيت أنا في المحاضرة
+
+3
+00:00:15,330 --> 00:00:18,930
+التمهيدية أن chapter one سيكون عنوانه electric
+
+4
+00:00:18,930 --> 00:00:25,730
+field أو المجال الكهربائي، ماذا سنشرح فيه؟ في هذا الـ
+
+5
+00:00:25,730 --> 00:00:29,730
+chapter، سنشرح عدة مواضيع، في منها سهل وفي منها
+
+6
+00:00:29,730 --> 00:00:34,690
+رئيسي. أول شيء، نبدأ بشرح الـElectric Charge،
+
+7
+00:00:34,690 --> 00:00:37,310
+الشحنة الكهربية. وهذه الشحنة الكهربية، نحن
+
+8
+00:00:37,310 --> 00:00:41,370
+نعتبركم أخذتوها في الابتدائية. شحنة موجبة وشحنة
+
+9
+00:00:41,370 --> 00:00:44,490
+سالبة، ألم تأخذوها؟ أخذتوها. إنها صفات، سنأخذها
+
+10
+00:00:44,490 --> 00:00:49,520
+تفصيلًا. بعد ذلك، سنشرح أنك تقولين الشحنة
+
+11
+00:00:49,520 --> 00:00:53,440
+الموجبة مع الموجبة تتنافر والموجبة مع السالبة تتجاذب
+
+12
+00:00:53,440 --> 00:00:58,740
+تنافر وتجاذب يعني قوة، هذه القوة وحدتها نيوتن، طيب
+
+13
+00:00:58,740 --> 00:01:02,060
+عشرة نيوتن أم عشرون نيوتن أم مئة نيوتن؟ من
+
+14
+00:01:02,060 --> 00:01:06,520
+المقدار، يعتمد على المقدار، جاء كولوم ووضع قانون
+
+15
+00:01:06,520 --> 00:01:10,360
+هذا القانون سمي قانون كولوم، سنشرحه بالتفصيل
+
+16
+00:01:10,360 --> 00:01:14,580
+بعدين ننتقل إلى شيء اسمه المجال الكهربائي
+
+17
+00:01:14,990 --> 00:01:19,510
+Electric Field، المجال الكهربائي، في البداية نبدأ
+
+18
+00:01:19,510 --> 00:01:24,250
+بحالة تكون الشحنة بحجم نقطة، شحنة نقطية أو
+
+19
+00:01:24,250 --> 00:01:29,930
+Point Charge، يعني صغيرة، بعد ذلك، هو لبّ الشطر
+
+20
+00:01:30,680 --> 00:01:36,100
+عندما تكون الشحنة حجمها كبير، هذا الجسم كله مشحون،
+
+21
+00:01:36,100 --> 00:01:39,760
+طبعًا من باب أولى أنه يولد مجالًا كهربائيًا أم لا، كم
+
+22
+00:01:39,760 --> 00:01:44,580
+أريد أن أحسبه، هذا موضوعنا، وهذا لبّ الشطر، وهذا يمكن
+
+23
+00:01:44,580 --> 00:01:48,920
+أن يأخذ لحاله أسبوع.الموضوع تمام، وزي ما حكينا كل
+
+24
+00:01:48,920 --> 00:01:54,760
+chapter له core  أساسي وفيه الحاشية، فهذا موضوع
+
+25
+00:01:54,760 --> 00:02:00,980
+حاشية، وهذا أقرب للقلب، الموضوع الأخير حاشية كثيرة
+
+26
+00:02:00,980 --> 00:02:06,280
+خطوط المجال الكهربائي، سمعتم بها؟ سنأخذها بسرعة وهذا
+
+27
+00:02:06,280 --> 00:02:12,180
+يحتاج ساعة ويخلص، تمام، الـ recommended problems
+
+28
+00:02:13,580 --> 00:02:19,780
+والله يا بنات خميس وجمعة كافٍ لحلها، لو لم نراجعهم
+
+29
+00:02:19,780 --> 00:02:26,060
+هم كم سؤال؟ خمسة وعشرون، يعني كل يوم اثنا عشر سؤالًا
+
+30
+00:02:26,060 --> 00:02:33,800
+أربعة أيام، كل يوم ستة، يخلصون من أول بأول يا
+
+31
+00:02:33,800 --> 00:02:37,740
+بنات، لا نرهق أنفسنا، كي لا نتعب غدًا
+
+32
+00:02:37,740 --> 00:02:38,900
+الوجد كافٍ لنا
+
+33
+00:02:41,100 --> 00:02:44,440
+كي لا نقول الوجد لم يكفينا، هذه سهلة، وفي من
+
+34
+00:02:44,440 --> 00:02:48,500
+هم لا تأخذ منكن شيئًا، واتفقنا نستعين بصديقة،
+
+35
+00:02:48,500 --> 00:02:52,860
+ونستعين بمعيدة، وتستعين بِـي، المهم نحلهم ونحن
+
+36
+00:02:52,860 --> 00:02:58,280
+لسنا نقول أنكن عمالقة ونيوتن ثانية، لا، طبعًا
+
+37
+00:02:58,280 --> 00:03:02,000
+لن تستطعن حل بعض الأسئلة، لكن بالمحاولة ستحَلُّنَّها
+
+38
+00:03:02,000 --> 00:03:10,440
+قطعا، تمام يا بنات، المهم نحلها، فلنبدأ مقارنة بـ
+
+39
+00:03:10,440 --> 00:03:16,100
+Electric Charges، خواص الشحنات، هذه الشحنات الموجبة
+
+40
+00:03:16,100 --> 00:03:21,440
+والسالبة لها خواص، يجب أن نتعرف عليها، طبعًا كلكن
+
+41
+00:03:21,440 --> 00:03:26,080
+تعرفن المعلومة البديهية، أن كم نوع من
+
+42
+00:03:26,080 --> 00:03:32,720
+الشحنات لدينا؟ اثنان، موجب وسالب، إذن فرانكلين
+
+43
+00:03:32,720 --> 00:03:36,140
+هو الذي سمّى، أول من سمّى موجب وسالب، قال أنا there
+
+44
+00:03:36,140 --> 00:03:38,980
+are two kinds of electric charges، لدي نوعان من
+
+45
+00:03:38,980 --> 00:03:43,680
+الشحنات في الطبيعة، في الدنيا، positive charges، و
+
+46
+00:03:43,680 --> 00:03:48,640
+التي يحملها جسم سمّي بروتون، جسم سمّي بروتون، إلى
+
+47
+00:03:48,640 --> 00:03:55,100
+الآن، معلومات تعرفونها، negative charges، يحملها جسم
+
+48
+00:03:55,100 --> 00:04:01,430
+اسمه electron، طبعًا، ماذا لدينا؟ لدينا شحنة الإلكترون
+
+49
+00:04:01,430 --> 00:04:07,110
+السالبة وشحنة البروتون الموجبة، نفس المقدار، بالرغم
+
+50
+00:04:07,110 --> 00:04:11,890
+من أنهما متعاكسان في النوع، لكن مقدارهما واحد، إذن الـ
+
+51
+00:04:11,890 --> 00:04:15,130
+negative charge of an electron and the positive
+
+52
+00:04:15,130 --> 00:04:18,530
+charge of a proton have the same magnitude
+
+53
+00:04:18,530 --> 00:04:24,470
+كمقدار، يعني بمعنى آخر، Q للإلكترون تساوي
+
+54
+00:04:24,470 --> 00:04:28,880
+Q للبروتون، لكن كـ absolute value، لأن أحدهما موجب
+
+55
+00:04:28,880 --> 00:04:32,320
+والآخر سالب، لكن الـ absolute value يُبطل معنى
+
+56
+00:04:32,320 --> 00:04:39,940
+للسالب، تمام، ما هي Q؟ الـ Q هي رمز الشحنة، أرجع وأقول
+
+57
+00:04:39,940 --> 00:04:45,200
+ما هو الرمز الفيزيائي للـ mass؟ M، إذن كل كمية
+
+58
+00:04:45,200 --> 00:04:48,580
+فيزيائية لها رمز مشهور، أليس كذلك؟ مثل ما هو رمز
+
+59
+00:04:48,580 --> 00:04:55,390
+السرعة؟ V، ما هو رمز الشحنة؟ طبعًا هذه كمية جديدة تمر
+
+60
+00:04:55,390 --> 00:05:01,090
+علينا، فرمزها Q، تمام، ما هو مقدارها؟ قيل لي هذه ثابتة
+
+61
+00:05:01,090 --> 00:05:07,170
+للإلكترون، وجدوا أنه يساوي واحدًا وستة أعشار في عشرة
+
+62
+00:05:07,170 --> 00:05:12,770
+أس سالب تسعة عشر، ما هي الوحدة؟ قيل لي coulomb، طبعًا هذه
+
+63
+00:05:12,770 --> 00:05:18,280
+في الـ SI system، في أنظمة أخرى وحداتها مختلفة، نحن
+
+64
+00:05:18,280 --> 00:05:21,400
+نعتمد الـ SI system، أليس كذلك؟ في الـ SI
+
+65
+00:05:21,400 --> 00:05:27,880
+system هي الـ coulomb، نحن زمان كنا نقول في م ك ث
+
+66
+00:05:27,880 --> 00:05:31,920
+الـ second، صحيح؟ meter kilogram second، ما هي
+
+67
+00:05:31,920 --> 00:05:37,980
+الرابعة؟ جاءت الرابعة coulomb، إذن هذه هي الوحدة
+
+68
+00:05:37,980 --> 00:05:42,840
+الأساسية الرابعة في الفيزياء، الكولوم، في وحدات أساسية
+
+69
+00:05:42,840 --> 00:05:48,180
+كثيرة، لكن نحن واحدة واحدة، إذن وحدة الشحنة بالنظام
+
+70
+00:05:48,180 --> 00:05:52,240
+العالمي هي الكولوم، طبعًا عندما نقدر واحدًا وستة أعشار
+
+71
+00:05:52,240 --> 00:05:56,420
+في عشرة أس سالب تسعة عشر، سالب تسعة عشر صغيرة جدًا
+
+72
+00:05:56,420 --> 00:06:01,420
+بالنسبة للواحد كولوم، كبير جدًا، هذه شحنة الـ
+
+73
+00:06:01,420 --> 00:06:06,870
+electron، طيب، قيل لي طيب نحن تعلمنا في المدارس أن
+
+74
+00:06:06,870 --> 00:06:10,970
+الذرّة فيها عدد الإلكترونات يساوي عدد البروتونات
+
+75
+00:06:10,970 --> 00:06:16,330
+وسُمّي العدد الذري، صحيح أم لا، الـ atomic number
+
+76
+00:06:16,330 --> 00:06:20,170
+ماذا يعني؟ يقول لي كل ذرة في الدنيا بطبيعتها
+
+77
+00:06:20,170 --> 00:06:26,230
+متعادلة، neutral، يعني لا هي موجبة ولا هي سالبة، حيث
+
+78
+00:06:26,230 --> 00:06:31,290
+عندما أقول هذه غير مشحونة، متعادلة، يعني هل هذا يعني
+
+79
+00:06:31,290 --> 00:06:35,700
+لا توجد فيها شحنات؟ لا، ما هي فيها Atoms، وفيها
+
+80
+00:06:35,700 --> 00:06:38,980
+إلكترونات وفيها بروتونات، هو ماذا يعني Neutral؟ هذا
+
+81
+00:06:38,980 --> 00:06:42,960
+الذي يعني أن عدد البروتونات يساوي عدد الإلكترونات
+
+82
+00:06:42,960 --> 00:06:46,820
+وبالتالي عندما تجمع الشحنة الكلية تجدينها Zero، صحيح
+
+83
+00:06:46,820 --> 00:06:52,250
+أم لا؟ لأن الموجب والسالب جمعتهم طلع Zero
+
+84
+00:06:52,250 --> 00:06:57,490
+إذن الجسم عندما يكون Neutral أو غير مشحون Uncharged
+
+85
+00:06:57,490 --> 00:07:03,470
+معناه عدد البروتونات يساوي عدد الإلكترونات، حلو
+
+86
+00:07:03,470 --> 00:07:09,950
+طبعًا هذه تعرفونها أنتم،  Electronic، ما هي شحنته؟ البروتون
+
+87
+00:07:09,950 --> 00:07:15,010
+ما هي شحنته؟ نفسه، أليس كذلك؟ نسمع في الـ Neutron، أين يوجد
+
+88
+00:07:15,010 --> 00:07:18,930
+الـ Neutron هذا؟ في النواة، برافو عليكم، لماذا سمي
+
+89
+00:07:18,930 --> 00:07:23,170
+Neutron؟ لأنه متعادل، شحنته Zero، Neutral
+
+90
+00:07:23,170 --> 00:07:28,910
+Masses، هذا مقارنةً به خفيف جدًا، لذلك كانوا
+
+91
+00:07:28,910 --> 00:07:35,630
+زمان يقولون ليش كتلة الذرّة متمركزة في النواة؟ أقول لكم
+
+92
+00:07:35,630 --> 00:07:39,490
+لأن هذين هما اللذان يوجد جوا النواة وهذا ليس جوا
+
+93
+00:07:39,490 --> 00:07:43,190
+النواة، وبالتالي كتلة الذرّة تتمركز في النواة
+
+94
+00:07:43,190 --> 00:07:47,110
+تمام، طبعًا أرقام من هذه الأرقام مطلوب منكن
+
+95
+00:07:47,110 --> 00:07:52,980
+حفظها، هذه ثوابت تُعطى لكن، لو أردتن استخدامها، صحيح
+
+96
+00:07:52,980 --> 00:07:57,340
+أم لا؟ ذكرنا الـ G في امتحان النهاية، رأيتم؟ أنه
+
+97
+00:07:57,340 --> 00:08:00,820
+موجود كان؟ نعم، كنا نضعه كي لا... لا نُجهدكنّ
+
+98
+00:08:00,820 --> 00:08:03,580
+يعني، واحدة تقول والله تعبت وحفظته وحصلت على علامة
+
+99
+00:08:03,580 --> 00:08:07,980
+عليه، لا، يوم لم يوضع، لا، ونفس الشيء، يعني شحنة
+
+100
+00:08:07,980 --> 00:08:12,540
+الإلكترون، وعدنا بأخذ الثابت كله أم كتلة الإلكترون،
+
+101
+00:08:12,540 --> 00:08:17,340
+كل شيء مُعطى لكن، لا تحفظوه، هذا للتذكرة فقط، ليس أكثر
+
+102
+00:08:19,670 --> 00:08:24,890
+طيب هذه الشحنات الموجبة والسالبة،
+لها صفات، نعم
+
+103
+00:08:24,890 --> 00:08:30,070
+هذه هي الصفات، علينا أن نتعرف عليها ونفهمها، أول
+
+104
+00:08:30,070 --> 00:08:35,850
+شيء، ربما يعرفه ابن الروضة، ما هو؟ 
+
+105
+00:08:35,850 --> 00:08:42,720
+الشحنات المتشابهة تتنافر، صحيح؟ والشحنات المتضادة أو
+
+106
+00:08:42,720 --> 00:08:47,320
+المختلفة تتجاذب، like يعني أنكم متشابهين، like أن
+
+107
+00:08:47,320 --> 00:08:51,920
+تَعرِفنَها، like charges repel، repel يعني تتنافر
+
+108
+00:08:51,920 --> 00:08:58,340
+هذا الفعل repulsion، تنافر، repel each other،  تتنافر
+
+109
+00:08:58,340 --> 00:09:03,620
+بعضها بعضًا، تمام، and unlike charges، والشحنات
+
+110
+00:09:03,620 --> 00:09:08,680
+المختلفة، attract each other، attract ماذا يعني؟
+
+111
+00:09:08,680 --> 00:09:11,420
+تنجذب بعضها لبعض، تنجذب بعضها لبعض، هل هناك من لا يعرف
+
+112
+00:09:11,420 --> 00:09:18,440
+هذه المعلومة؟ الكل يعرفها، ليس هناك من لا يعرف، حلو، ما هي
+
+113
+00:09:18,440 --> 00:09:21,660
+الصفة الثانية؟ قيل لي، يوجد شيء نسميه Conservation
+
+114
+00:09:21,660 --> 00:09:25,520
+Energy is conserved، سمعتن بها؟ Linear momentum
+
+115
+00:09:25,520 --> 00:09:29,480
+is conserved، سمعنا بها، Angular momentum is
+
+116
+00:09:29,480 --> 00:09:32,600
+conserved، لكل منها شروطها، Its charge is
+
+117
+00:09:32,600 --> 00:09:37,020
+conserved، ماذا يعني Conservation؟ لا تفنى ولا تُخلق
+
+118
+00:09:37,020 --> 00:09:41,060
+من العدم، تمام؟ يعني في مجال واحد يقول لي، لديّ
+
+119
+00:09:41,060 --> 00:09:47,890
+electron، دفنته، مات؟ لا يوجد إلكترون وُلد
+
+120
+00:09:47,890 --> 00:09:53,170
+بيننا، نعمله أسبوع؟ لا، إذن الإلكترون لا يولد ولا
+
+121
+00:09:53,170 --> 00:09:56,610
+يدفن، تمام؟ هذا معنى Conservation of Charge، ماذا
+
+122
+00:09:56,610 --> 00:09:59,810
+يحدث؟ كيف تُشحن هذه؟ لأنك تشحنها إما تعطينها
+
+123
+00:09:59,810 --> 00:10:02,750
+إلكترونات أو تأخذين منها إلكترونات، لا تقولين أن
+
+124
+00:10:02,750 --> 00:10:05,810
+الإلكترون الذي بداخلها يولد ويصبح لديه إلكترونين، لا،
+
+125
+00:10:05,810 --> 00:10:09,910
+مستحيل، أنتن تنقلن الإلكترونات، إذن هذا المبدأ
+
+126
+00:10:09,910 --> 00:10:13,830
+مبدأ Conservation of Charge يا بنات، سمعتن بـ كيرشوف؟
+
+127
+00:10:13,830 --> 00:10:18,250
+ماذا تقول قاعدة كيرشوف الأولى؟ من يذكرني بها؟
+
+128
+00:10:18,250 --> 00:10:24,530
+التيارات الداخلة تساوي التيارات الخارجة، هذا ليس بعيدًا عن
+
+129
+00:10:24,530 --> 00:10:29,310
+مبدأ الـ Conservation of Charge، كان لدي خمسة
+
+130
+00:10:29,310 --> 00:10:35,890
+أمبير، جمعتهم، صار اثنان، ثلاثة، أم مبدأ
+
+131
+00:10:35,890 --> 00:10:40,910
+Conservation of Charge، انظري إليه بهذه الطريقة، تمام؟ هذا ما
+
+132
+00:10:40,910 --> 00:10:45,610
+هو المثال، زمان عندما كنا صغارًا كان لدينا مشط بلاستيك
+
+133
+00:10:45,610 --> 00:10:49,470
+أليس كذلك؟ كنتم تحكونه بشعركن، تفهمين؟ وتضعنه على
+
+134
+00:10:49,470 --> 00:10:56,190
+الورق، الجرس حر، الورق انجذب، تمام؟ أصلاً أصبح في
+
+135
+00:10:56,190 --> 00:11:02,160
+المشط أصبح مشحونًا. طيب ولماذا حككت؟ أقول نعم
+
+136
+00:11:02,160 --> 00:11:07,180
+حككت لأخذ طاقة، أليس كذلك؟ عندما كنا نفعل هذا؟
+
+137
+00:11:07,180 --> 00:11:12,320
+يجب طاقة، وهذه المشط فيه إلكترونات والإلكترونات
+
+138
+00:11:12,320 --> 00:11:18,100
+مرتبطة بطاقة بالنواة، حككت، تأخذ طاقة، هذا الجسم
+
+139
+00:11:18,100 --> 00:11:23,270
+عندما يكون على الأرض وأريد أن أرفعه للطاولة، يحتاج إلى
+
+140
+00:11:23,270 --> 00:11:27,950
+يصل إلى الطاولة؟ أم يحتاج إلى قوة، يحتاج إلى طاقة، يحتاج إلى شغل،
+
+141
+00:11:27,950 --> 00:11:33,650
+تمام؟ إذن معناته قوة الربط بين الإلكترون والنواة
+
+142
+00:11:33,650 --> 00:11:39,250
+سالبة، دائمًا سالبة، صحيح، يأخذ طاقة، الإلكترون هذا،
+
+143
+00:11:39,250 --> 00:11:42,810
+أول ما يأخذ طاقة يَفْلِت، فين يذهب؟ يذهب إلى
+
+144
+00:11:42,810 --> 00:11:46,770
+المشط، من الشعر للمشط، يذهب إلى المشط، يصبح
+
+145
+00:11:46,770 --> 00:11:51,630
+المشط، جاءته إلكترونات أو بروتونات، وانشحن، قال لي
+
+146
+00:11:51,630 --> 00:11:55,070
+تعالي انظري لهذا الأمر مثل المشط والشعر، قال لي هي
+
+147
+00:11:55,070 --> 00:12:00,910
+عندها قطعة من الزجاج وقطعة من الحرير، حككت، يجب
+
+148
+00:12:00,910 --> 00:12:05,150
+أن تُحَكَّ كي تأخذ طاقة، تمام؟ أول ما حككت
+
+149
+00:12:05,150 --> 00:12:10,690
+الإلكترونات التي في الزجاج، رحلت، رحلت، أين ذهبت؟ إلى
+
+150
+00:12:10,690 --> 00:12:15,630
+الحرير، إذن الزجاج الذي كان متعادلًا أخذنا منه مئة
+
+151
+00:12:15,630 --> 00:12:19,570
+إلكترون، من أصبح أكثر؟ أليس البروتونات أصبحت أكثر؟
+
+152
+00:12:19,570 --> 00:12:23,530
+صار موجبًا، طيب والحرير المسكين الذي كان neutral ماذا
+
+153
+00:12:23,530 --> 00:12:28,510
+جاءه؟ جاءته إلكترونات، أصبح سالبًا، أليس كذلك؟ إذن عملية الحك
+
+154
+00:12:28,940 --> 00:12:33,720
+نقلت الـ electrons للحرير، يمكننا أن نقول أنه لم يمت
+
+155
+00:12:33,720 --> 00:12:37,900
+electron من الزجاج، لم يمت؟ وأن الذي لديه
+
+156
+00:12:37,900 --> 00:12:40,660
+الحرير، يأتي ويقول، الحرير، والله إلكتروناتي
+
+157
+00:12:40,660 --> 00:12:46,940
+ولدت؟ لا، ماذا حدث؟ انتقال، إذن يقول لي في هذه
+
+158
+00:12:46,940 --> 00:12:52,440
+العملية، when a glass rod، قضيب من الزجاج، إذا حُكَّ
+
+159
+00:12:52,440 --> 00:12:57,140
+مع silk، قطعة من الحرير، Electrons، ماذا حدث فيها؟
+
+160
+00:12:57,140 --> 00:13:01,220
+Transferred، انتقلت، Transferred from the
+
+161
+00:13:01,220 --> 00:13:05,180
+glass to the silk، ماذا يعني؟ يقول لي that is there
+
+162
+00:13:05,180 --> 00:13:09,340
+is no creation، لا يوجد خلق للإلكترونات، there is no
+
+163
+00:13:09,340 --> 00:13:14,030
+creation of charges، يعني لو تركتِ أنتِ الزجاج
+
+164
+00:13:14,030 --> 00:13:19,510
+والحرير system واحدًا، هل الشحنات الكلية تغيرت؟ لا لا
+
+165
+00:13:19,510 --> 00:13:22,150
+إذن الـ charge is conserved أم غير conserved؟ الـ
+
+166
+00:13:22,150 --> 00:13:25,570
+charge is conserved، الـ need to charge on the
+
+167
+00:13:25,570 --> 00:13:29,590
+glass silk system is not changed، بنات لا تخافن من
+
+168
+00:13:29,590 --> 00:13:32,550
+التصوير، ما هو سؤالك؟ لا تقولن تصوير، وخائفات
+
+169
+00:13:32,550 --> 00:13:38,300
+تسألن؟ لا، خذْن راحاتكن،
+
+223
+00:17:39,540 --> 00:17:43,800
+واحد منهم من neutral هو فيه قوة مع الـ neutral لأ هذه
+
+224
+00:17:43,800 --> 00:17:48,320
+اللي مسطح تمام اللي بده تقول هذه بادئ لجره رابعة
+
+225
+00:17:48,320 --> 00:17:58,160
+كبار كان الهادئ اجت على الرابعة تمام حلو حلو شح لنا
+
+226
+00:17:58,940 --> 00:18:03,520
+جسم بالحق، ذاكرين المصطرة والحريض؟ هذه لازم تحكّ
+
+227
+00:18:03,520 --> 00:18:08,120
+وبنفع أتحك بدون ما أتلامس؟ لأ، لازم المصطرة أحطها
+
+228
+00:18:08,120 --> 00:18:11,280
+على الشعر ولا أعمل من هيك وأقول بدي أعملها،
+
+229
+00:18:11,280 --> 00:18:15,600
+بينفعش، لازم أحك الشعر الآن بدي أشحن بس بدون ما
+
+230
+00:18:15,600 --> 00:18:20,500
+ألابس، مازال بديش ألامس، بدي أسمي تأثير، هذا اسم
+
+231
+00:18:20,500 --> 00:18:27,060
+عشان أشحن تأثيرياً، بدي أتعرف على المواد، هو أنت
+
+232
+00:18:28,400 --> 00:18:32,760
+النحاس زي الخشب عندك في الكهربا إيش بيفرجوا عن
+
+233
+00:18:32,760 --> 00:18:37,760
+بعض؟ هو برا وعليكم خلصنا إذا في المرحلة المقدمة
+
+234
+00:18:37,760 --> 00:18:44,160
+نفرّج بين نحاس والخشب نحاس زي زي كل المعادن
+
+235
+00:18:44,160 --> 00:18:48,800
+بنسميهم conductors ولا لأ، كل الـ metals نحاس و
+
+236
+00:18:48,800 --> 00:18:52,540
+الفضة والألمنيوم والحديد والزئبق ذاكرينهم
+
+237
+00:18:52,540 --> 00:18:57,960
+أنتوا إذا أول حاجة بتتعرفوا على حاجة بقول materials
+
+238
+00:18:57,960 --> 00:19:03,470
+المواد صنّفت لعدة تصنيفات بيناخد تلاتة منهم احنا
+
+239
+00:19:03,470 --> 00:19:07,650
+حيناخد اتنين، أول واحد بنسميه Conductors، إيش يعني
+
+240
+00:19:07,650 --> 00:19:11,690
+Conductors؟ مادة موصلة، ده اللي هذه مين بيحددها؟
+
+241
+00:19:11,690 --> 00:19:14,650
+قال لي التركيب الكيميائي تبعتها، التركيب
+
+242
+00:19:14,650 --> 00:19:19,290
+الكيميائي تبعتها في هذه المواد إيش بيكون؟ بيقول لي
+
+243
+00:19:19,290 --> 00:19:25,970
+بعض الإلكترونات مربوطة بالنواة بطاقة ضعيفة جداً جداً
+
+244
+00:19:25,970 --> 00:19:31,030
+درجة حرارة الغرفة بتخليها تفلت، ولما تفلت بتصير
+
+245
+00:19:31,030 --> 00:19:38,880
+دائرة حرة، يعني إيش؟ يعني سواحة وإن ما بدها بتتحرك
+
+246
+00:19:38,880 --> 00:19:43,120
+إذا لما يكون فيه conductor يا بنات، نفترض
+
+247
+00:19:43,120 --> 00:19:46,860
+الإلكترون مسموح له يمشي ولا لأ؟ مسموح له، الطرق
+
+248
+00:19:46,860 --> 00:19:52,080
+قدامه مسكرة ولا مفتوحة؟ هي مفتوحة، تكملي الجملة هذه
+
+249
+00:19:52,080 --> 00:19:56,580
+التعريف، لكن أنا في النهاية بدي أحملها وأفهمها إيه
+
+250
+00:19:56,580 --> 00:19:59,580
+الشعر، لما أقول conductor، لما أقول الإلكترونات بتتحرك
+
+251
+00:19:59,580 --> 00:20:03,540
+بسهولة، وينتقل عليها، بتمشي معاك صح ولا لأ؟ نيجي نقرأ
+
+252
+00:20:04,700 --> 00:20:09,260
+الـ Text اللي بدنا نِحفظُه، إيش تعريفه؟ بيقول لي are
+
+253
+00:20:09,260 --> 00:20:13,780
+materials in which some of the electrons are free
+
+254
+00:20:13,780 --> 00:20:17,000
+electrons، طبعاً أنتم بتعرفوا الذرة، هي النواة
+
+255
+00:20:17,000 --> 00:20:21,200
+وهذه الإلكترونات، فين؟ طبعاً مين اللي بيشرد؟ اللي
+
+256
+00:20:21,200 --> 00:20:24,360
+بيشرد اللي في الـ... اللي... اللي برا، عشان كده
+
+257
+00:20:24,360 --> 00:20:26,820
+بيقول some of the electrons، مش مشكلة، أنا المهم
+
+258
+00:20:26,820 --> 00:20:33,200
+عندي يكون فيه إلكترونات حرة، تمام؟ ليش؟ بيقولوا They
+
+259
+00:20:33,200 --> 00:20:36,720
+are not bound to the atoms، لأنها مش مربوطة بالنواة
+
+260
+00:20:36,720 --> 00:20:42,240
+كيف فلتت؟ فلتت من طاقة الجو، أي طاقة بتقليها تفلت
+
+261
+00:20:42,240 --> 00:20:46,020
+and can move relatively freely through the
+
+262
+00:20:46,020 --> 00:20:50,240
+material، إذن بتتحرك بحرية جوا المادة، سواحة مش
+
+263
+00:20:50,240 --> 00:20:54,500
+هيقول لنا هذه هي conductors، إيش فيه أمثلة؟ قال
+
+264
+00:20:54,500 --> 00:20:59,860
+الفضة والنحاس والألمنيوم وفي غيره لكن هدول الأشهر
+
+265
+00:20:59,860 --> 00:21:03,600
+الـ silver هو أجود أنواع المواد الـ conduction
+
+266
+00:21:03,600 --> 00:21:08,620
+والنحاس بيجي وراه، لكن احنا ما بنستخدمش الـ silver عشانّه
+
+267
+00:21:08,620 --> 00:21:12,860
+غالي، تمام؟ حلو، ولكن بنستخدم النحاس عشانّه ما شاء
+
+268
+00:21:12,860 --> 00:21:18,040
+الله متوفر ورخيص، فبنستخدمه لكل التواصلات، يعني كل
+
+269
+00:21:18,040 --> 00:21:21,080
+الأسلاك اللي جوا الحيطان هذه وفي بيوتكم وفي المكان
+
+270
+00:21:21,080 --> 00:21:25,650
+واللي في الشوارع كلها نحاس، تمام؟ قال طب والـ
+
+271
+00:21:25,650 --> 00:21:31,090
+insulators؟ قال لي كل الإلكترونات مربوطة بحبل
+
+272
+00:21:31,090 --> 00:21:37,770
+الملتحم مع الذرات، عشان كده انفخ عليها بتنفخ وهي
+
+273
+00:21:37,770 --> 00:21:43,170
+مش متحركة ولا ممكن تتحرك، تمام؟ إذا معناته are
+
+274
+00:21:43,170 --> 00:21:47,710
+materials in which all electrons are bound to
+
+275
+00:21:47,710 --> 00:21:51,630
+atoms، مربوطة بالـ atoms، and cannot move freely
+
+276
+00:21:51,630 --> 00:21:55,830
+through the material، هلجيت insulator؟ مسموح
+
+277
+00:21:55,830 --> 00:22:00,210
+للإلكترونات تتحرك؟ لأ، مش مسموح، إيش ما تسوي،
+
+278
+00:22:00,210 --> 00:22:05,490
+ممنوع، مظبوطة زي لما تقول والله هي بنتنا أو
+
+279
+00:22:05,490 --> 00:22:09,290
+زميلتنا قاعدة، بدك تطردها، بتتطرد؟ ولا في حيطة
+
+280
+00:22:09,290 --> 00:22:14,870
+مقفلة قدامها، صح ولا لأ؟ في حيطة، مسكرة، تمام؟ حلو
+
+281
+00:22:16,300 --> 00:22:22,940
+الخشب، الذّجاج، البلاستيك والـ rubber، كل الأسلاك
+
+282
+00:22:22,940 --> 00:22:29,040
+محطوطة بالـ rubber، مغلفة عشان تكون عازلة، والمثل
+
+283
+00:22:29,040 --> 00:22:32,840
+العربي بيقول عشان الحسد، امسك الخشب عشان ما ينجلش
+
+284
+00:22:32,840 --> 00:22:34,400
+تمام، عشان هو عازل
+
+285
+00:22:37,050 --> 00:22:41,230
+فيه نوع ثالث، مش مهم كتير، إحنا مهم للعلم
+
+286
+00:22:41,230 --> 00:22:44,270
+الإلكترونيات بصورة عامة، هو بيقول في بعض المواد لأ
+
+287
+00:22:44,270 --> 00:22:47,570
+أنت ممكن تصنفها conductors، ولأ أنت ممكن تصنفها
+
+288
+00:22:47,570 --> 00:22:51,390
+insulators، يعني عن ظروف معينة بتصير conductor، وعن
+
+289
+00:22:51,390 --> 00:22:53,690
+ظروف معينة بتصير insulator، كانوا يسموها
+
+290
+00:22:53,690 --> 00:22:58,630
+semiconductor، لا هي موصلة ولا هي عازلة، شيء شبه
+
+291
+00:22:58,630 --> 00:23:02,710
+موصلة، وأخطوها برضه، طبعاً ما قبلناش نخش بالتفاصيل
+
+292
+00:23:02,710 --> 00:23:07,460
+اللي هو التركيب الفيزيائي تبعتها، علم كبير، تمام،
+
+293
+00:23:07,460 --> 00:23:12,680
+إذاً سيميكوندكتّرز هم نوع ثالث... هو نوع ثالث...
+
+294
+00:23:12,680 --> 00:23:16,660
+of materials with their electrical properties، خاصة
+
+295
+00:23:16,660 --> 00:23:21,580
+الكهربائية، are somewhere between... هي متوسطة ما بين
+
+296
+00:23:21,580 --> 00:23:26,640
+الـ conductors والـ insulators، زي الجرمانيوم والسيليكون
+
+297
+00:23:26,640 --> 00:23:28,900
+طبعاً في نوع رابع، من النّجاة... أو فيه، بس سمعتوا
+
+298
+00:23:28,900 --> 00:23:33,530
+فيه superconductors، هذا superconductors، بعض المواد
+
+299
+00:23:33,530 --> 00:23:37,570
+عن درجة حرارة قليلة جداً، ولما أقول قليلة جداً مش
+
+300
+00:23:37,570 --> 00:23:40,910
+ناقص خمسة تحت الصفر، يعني مش في موسكو بتصير
+
+301
+00:23:40,910 --> 00:23:45,950
+superconductor، بدها ناقص مرات مئة عشان تصير
+
+302
+00:23:45,950 --> 00:23:51,810
+superconductor، لكن احنا بدنا نِشيها، ده اللي حلو الآن
+
+303
+00:23:51,810 --> 00:23:55,350
+عرفت لما تقول conductor، مسموح للإلكترونات تتحرك ولا
+
+304
+00:23:55,350 --> 00:24:00,720
+لأ؟ مسموح، حلو، جالي أنتم هجيتوا، عرفتوا هذه الخواص، خلّيني
+
+305
+00:24:00,720 --> 00:24:06,700
+أشوف إيش بنا نسوي يا بنات، هاي conductor، حطيته على
+
+306
+00:24:06,700 --> 00:24:12,720
+حامل من الخشب، هذا خشب يعني insulator، وهذا خشب
+
+307
+00:24:12,720 --> 00:24:16,560
+ومحطوط هذا، ما قالوه، إيش مسميته؟ conductor، هجيت هذا
+
+308
+00:24:16,560 --> 00:24:22,640
+conductor، مشحون، متعادل، متعادل، لما أقول مشحون
+
+309
+00:24:22,640 --> 00:24:26,380
+معناته موجب أكثر من السالب أو السالب أكثر من الموجب، هل
+
+310
+00:24:26,380 --> 00:24:31,920
+جيت هذا... فيه شحنات؟ فيه شحنات، لكن مشحون؟ لأ، متعادل
+
+311
+00:24:31,920 --> 00:24:36,180
+conductor، لو نفخت عليه، الإلكترونات تتحرك معه ولا لا؟
+
+312
+00:24:36,180 --> 00:24:41,460
+تتحرك، حلو، هذا هو الـ neutral، بدي أشحنه شحنة بسيطة
+
+313
+00:24:41,460 --> 00:24:45,920
+أجيب لك مادة مشحونة وأنت عارفها، إذن أولاً consider a
+
+314
+00:24:45,920 --> 00:24:49,680
+conductor insulated from the ground، أنا عازلة من
+
+315
+00:24:49,680 --> 00:24:52,340
+الأرض، مش موصلة من الأرض، من وسط الخشب، يعني أنا
+
+316
+00:24:52,340 --> 00:24:54,400
+حاطّة على الطاولة هذه، أنا عازلتها، الطاولة هذه
+
+317
+00:24:54,400 --> 00:24:59,460
+خشب ولا لأ؟ خشب، معناته مش مبتصلة بالأرض، حلو، بقول
+
+318
+00:24:59,460 --> 00:25:04,020
+now let a negatively charged object، جسم مشحون،
+
+319
+00:25:04,020 --> 00:25:07,610
+مشحون بشحنات سالبة، جاهز، to be brought near the
+
+320
+00:25:07,610 --> 00:25:12,450
+conductor without touching it، لمستُه؟  لأ،
+
+321
+00:25:12,450 --> 00:25:16,990
+لمستوش، without touching it، حلو، توجهنا، نفخ على
+
+322
+00:25:16,990 --> 00:25:22,430
+الإلكترون، بتتحرك ولا لا؟ هتتحرك، هذا سالب، هنا فيه
+
+323
+00:25:22,430 --> 00:25:25,970
+إلكترونات، ما فيش فيه إلكترونات، إلكترون مع إلكترون
+
+324
+00:25:25,970 --> 00:25:31,390
+إيش بيصير؟ فيه تنافر، يعني في واحد بيرجع فيهم، مسموح له
+
+325
+00:25:31,390 --> 00:25:34,610
+يتحرك؟ مسموح له، لأن الطرق قدامه سالكة ولا لأ؟
+
+326
+00:25:34,610 --> 00:25:38,810
+سالكة، لأنّه هذا conductor، إيش بيصير؟ قال لي كل
+
+327
+00:25:38,810 --> 00:25:42,190
+الإلكترونات الـ free بتيجي هنا، طب هو الـ free مش
+
+328
+00:25:42,190 --> 00:25:46,070
+كانت جوا atom في الأول، والـ atom لما طلع منها هذا
+
+329
+00:25:46,070 --> 00:25:49,640
+الإلكترون غصب عنها، صارت موجبة ولا لأ؟ والموجب بده
+
+330
+00:25:49,640 --> 00:25:53,660
+يُرجعها ولا لأ؟ بده يرجعها، إذا إيش صار معايا يا بنات؟
+
+331
+00:25:53,660 --> 00:25:57,800
+بيقول لي due to the attractive and repulsive forces،
+
+332
+00:25:57,800 --> 00:26:01,520
+نتيجة قوة التنافر والتجاذب اللي إتعلمتوا،
+
+333
+00:26:01,520 --> 00:26:06,440
+الإلكترونات بتنجذب والبروتونات بتتنافر، يعني
+
+334
+00:26:06,440 --> 00:26:10,800
+الإلكترونات بتبعد والبروتونات بتقرب، بيقول لي that
+
+335
+00:26:10,800 --> 00:26:13,600
+charge is redistributed، إيش يعني redistributed؟
+
+336
+00:26:13,600 --> 00:26:19,430
+يعني يُعاد توزيعها، انتبهوا لي، بدي أسأل، الكرة الحمراء
+
+337
+00:26:19,430 --> 00:26:25,030
+انشحنت؟ لأ، برافو عليكم، صح، صحّحين، إقعد، ترتيب لكن ضال
+
+338
+00:26:25,030 --> 00:26:29,610
+الموجب بيساوي السالب ولا لأ؟ لسه ما انشحنتش حاجة، طب
+
+339
+00:26:29,610 --> 00:26:34,170
+سؤالي لكم، مش هذه في حد قاعد بترجع فيها؟ ليش ما رجعتش
+
+340
+00:26:34,170 --> 00:26:41,850
+أكثر؟ فيه عازل، هو الموجب بقى بترجّح حاجة، فيه عازل
+
+341
+00:26:41,850 --> 00:26:45,810
+لأنّه هذا عازل، فيه عازل، إيش هو العازل؟ الفراغ، فمش
+
+342
+00:26:45,810 --> 00:26:50,420
+قادرة تطلع، بعد كده الطريق مسكر، اللي هو العازل،
+
+343
+00:26:50,420 --> 00:26:54,980
+الطريق مسكر، ده اللي بسيط، هذه حيطة مسكرة، لو
+
+344
+00:26:54,980 --> 00:26:59,420
+عملت خروج، بتخرج ولا بتنهج؟ بدي أعملها خروج، مش
+
+345
+00:26:59,420 --> 00:27:04,810
+نهج، خروج يعني، بدي أجيب سلك وأوصّله في الأرض، السلك
+
+346
+00:27:04,810 --> 00:27:08,690
+يعني الـ conductor، يعني الطريق سلكته ولا لا؟ سلكت
+
+347
+00:27:08,690 --> 00:27:13,330
+الطريق، زي مية مسكرة، روحت سلكتها، بتخرج ولا بتنهج
+
+348
+00:27:13,330 --> 00:27:18,270
+ريشة؟ بتخرج، فإيش بدي أسوي؟ بقول لي now let the
+
+349
+00:27:18,270 --> 00:27:21,870
+conductor be grounded، يعني وصلته بالأرض، خلاص، فادي
+
+350
+00:27:21,870 --> 00:27:27,310
+هاي، جبت السلك، عملت فتحة في الجدار المسكر، إيه صار
+
+351
+00:27:27,310 --> 00:27:31,090
+في الإلكترونات؟ خرجوا، وراحوا، ماتوا؟ راحوا على
+
+352
+00:27:31,090 --> 00:27:35,130
+الأرض، ما ماتوش، الـ charge is conserved، انتقلوا
+
+353
+00:27:35,130 --> 00:27:39,550
+إلى الأرض، انتقلوا إلى الأرض، ضايقين هنا ولا
+
+354
+00:27:39,550 --> 00:27:40,810
+خرجوا؟ لسه ما خرجوش
+
+355
+00:27:43,490 --> 00:27:47,670
+due to the repulsive force the negative charge...
+
+356
+00:27:47,670 --> 00:27:50,510
+due to the repulsive force، عشان فيه هدول مفرضين
+
+357
+00:27:50,510 --> 00:27:55,090
+أول ما فتحت الفتحة، ما صدّقوا يشردوا، due to the
+
+358
+00:27:55,090 --> 00:27:57,590
+repulsive force the negative charges move out of
+
+359
+00:27:57,590 --> 00:28:01,410
+the sphere، طلعوا من الـ sphere، راحوا، الله سهّل عليهم
+
+360
+00:28:01,410 --> 00:28:05,290
+طب سؤالي إيه لكم الآن؟ أرجع للّي توا حكت،  إسمُها
+
+361
+00:28:05,290 --> 00:28:11,200
+إيش إسمك؟ إيمان، طلع إيه؟ مش هذه أرض، والسلطة
+
+362
+00:28:11,200 --> 00:28:14,760
+والأصل الأرض بتبلع كل شيء؟ ليش الشحنة الموجبة ما
+
+363
+00:28:14,760 --> 00:28:21,420
+انْتقلتْش؟ لأنها مربوطة، ممسوكة، مين مسكها هؤلاء؟ هذ
+
+364
+00:28:21,420 --> 00:28:25,760
+الجدار، طلع يا بنات، هذه إنّه هذه، إيش بصير في هذه؟
+
+365
+00:28:25,760 --> 00:28:31,860
+بتْرجع متعادلة، الموجب بيرجع، الموجب بيرجع، طب هو إحنا ليه
+
+366
+00:28:31,860 --> 00:28:36,850
+ليه مخلّي هذه؟ قال عشان أمسكها، إذا جبت الأزرق الآن
+
+367
+00:28:36,850 --> 00:28:41,870
+ولا مرة بتشحن الكرة، هترجع متعادلة، الموجب بيشرد، إيش أسوي أول؟
+
+368
+00:28:41,870 --> 00:28:46,810
+بدي أجيب السلك، بدي أسكر الفتحة اللي
+
+369
+00:28:46,810 --> 00:28:51,690
+فتحتها، تمام؟ إذا إيش بقول لي بقى؟ Disconnect، إيش
+
+370
+00:28:51,690 --> 00:28:56,170
+يعني disconnect؟ عكس connect، افصل، Disconnect the
+
+371
+00:28:56,170 --> 00:29:00,830
+conductor from the ground، بدك تسكر الفتحة أول، أشيل
+
+372
+00:29:00,830 --> 00:29:05,210
+الأزرق، قبل ما تسكر، بتروح كل عمليتك، تمام
+
+373
+00:29:05,210 --> 00:29:09,110
+from the ground and then، وكلمة then بتعرفوا معناها
+
+374
+00:29:09,110 --> 00:29:14,110
+بعدها، أشيل الأزرق، and then remove that charged
+
+375
+00:29:14,110 --> 00:29:18,370
+object، أمين، تظهروا إيش عملت؟ في مجالها، جيتي، الموجب
+
+376
+00:29:18,370 --> 00:29:24,870
+بيشرد؟ وين بده يروح؟ ما فيش طرق، فكرنا عليه كل الطرق، إيه
+
+377
+00:29:24,870 --> 00:29:29,290
+صار في الكرة يا روان؟ انشحنت، صار الموجب أقل من
+
+378
+00:29:29,290 --> 00:29:33,850
+السالب ولا لأ؟ خلاص، أكثر، أنا قلت أقل، صار الموجب
+
+379
+00:29:33,850 --> 00:29:38,970
+أكثر من السالب، نعم، بقى الـ game هذا، إيش بده
+
+380
+00:29:38,970 --> 00:29:41,390
+يصير؟ بقول إن الشحنات الموجبة هاجرت، بتتجاذب مع
+
+381
+00:29:41,390 --> 00:29:45,270
+بعض، لأن هم زي بعض، بدهم يتنافروا ولا لأ؟ بيتبعدوا
+
+382
+00:29:45,270 --> 00:29:49,580
+توزيع حالهم على السطح، بصير عندك كرة ما شاء الله
+
+383
+00:29:49,580 --> 00:29:53,060
+عليها شحنة مشهورة بشحنات موجبة، طب، الجسم، عنّا سالب
+
+384
+00:29:53,060 --> 00:29:58,620
+قال، أجيب المؤثر الموجب، بس، وعيد نفس التفاصيل، بقول،
+
+385
+00:29:58,620 --> 00:30:01,880
+due to the repulsive force between them، بيعني
+
+386
+00:30:01,880 --> 00:30:05,460
+الشحنات اللي بيناتهم، قوة التنافر، the positive
+
+387
+00:30:05,460 --> 00:30:09,380
+charges will be
+
+445
+00:34:31,670 --> 00:34:35,370
+the object. بقولي، آه، بس مش كل الجثة هذه. هذه نص
+
+446
+00:34:35,370 --> 00:34:39,890
+صح. Attracted بس في البداية. The ball was repelled
+
+447
+00:34:39,890 --> 00:34:43,310
+away from the object. هذه للنعساة، للمسطّي، اللي
+
+448
+00:34:43,310 --> 00:34:46,150
+مايعرفش أشمعات مودي أبو سالب. صح ولا لأ؟ هذه خطأ
+
+449
+00:34:46,150 --> 00:34:50,490
+قطعا. بقولي، The ball was first attracted to the
+
+450
+00:34:50,490 --> 00:34:53,730
+object and then repelled away from the object.
+
+451
+00:34:54,250 --> 00:34:57,710
+كلمة then الوقت عايش، بعد ما فيه تلامس. أول ما
+
+452
+00:34:57,710 --> 00:35:00,870
+اتلامس وبعد ثانية بقى لجيهم التطرق. عادوا طلعوا
+
+453
+00:35:00,870 --> 00:35:05,290
+تمى الخيار الرابع the ball first repelled away
+
+454
+00:35:05,290 --> 00:35:08,870
+from the object and then attracted to it. طبعا هذه
+
+455
+00:35:08,870 --> 00:35:14,190
+اللي انفطليه تمى هذا غلط. إذا الشوية جوابها صح؟ C
+
+456
+00:35:14,190 --> 00:35:23,770
+حكينا عربي؟ الحمد لله. تمّ. بدأني أبدأ بجد حاجة هذه
+
+457
+00:35:23,770 --> 00:35:34,230
+كمزح. كلام أغلبهم بتعرفوا قانون كولوم. قانون كولوم. كولوم
+
+458
+00:35:34,230 --> 00:35:39,810
+سنة الألف وسبعمية وكسور. تصوروا وقت الألف وسبعمية من
+
+459
+00:35:39,810 --> 00:35:44,750
+كان عايش ولا جد من جدكم يعرفوا من كان عايش أصلا. صح
+
+460
+00:35:44,750 --> 00:35:51,310
+ولا لأ؟ الألف وسبعمية. هذا سنة الألف وثمانية وستة مات
+
+461
+00:35:53,100 --> 00:35:56,640
+وهو عايش عامل تجربة. أنا بجيب التاريخ عشان تقولوا
+
+462
+00:35:56,640 --> 00:36:01,300
+هاد ويقولوا كيف عملوا تجارب وبأي أدوات. أنت لو سألتي
+
+463
+00:36:01,300 --> 00:36:07,260
+بلاش جدك. سألتي أبوكي أيامكم كيف كنتوا تتواصلوا مع
+
+464
+00:36:07,260 --> 00:36:11,080
+بعض بالتليفون؟ يقول لك في كل الحارة في تليفون واحد
+
+465
+00:36:11,080 --> 00:36:16,520
+هلجيت في الدار كم جوال فيه؟ في الجواهر، في البيت
+
+466
+00:36:16,520 --> 00:36:20,680
+الواحد، تشوف كلها، تشوف كيف اختلفت الدنيا؟ اتصوروا
+
+467
+00:36:20,680 --> 00:36:26,080
+في الـ 1807، زي أنا بقول في غزة، فذاك الزمن الله
+
+468
+00:36:26,080 --> 00:36:28,080
+علم كان فيها حمير ولا فيش حمير عشان يكون فيه
+
+469
+00:36:28,080 --> 00:36:34,970
+سيارات، مصبوطا لا، فيش، الدنيا جاحِت بالرغم من ذلك
+
+470
+00:36:34,970 --> 00:36:39,550
+بهديك الإمكانيات هيعمل تجربة لحد الآن. عاشة جدر يعمل
+
+471
+00:36:39,550 --> 00:36:43,530
+تجربة ويدينا نتائج. لحد الآن بقوله صح اللي عمله
+
+472
+00:36:43,530 --> 00:36:48,870
+اعمل تجربة على قوة الجذب والتنافر. قال هدول القوة
+
+473
+00:36:48,870 --> 00:36:52,510
+بدي 1500 نيوتن ولا 100 نيوتن. بدي قانون رياضي
+
+474
+00:36:52,510 --> 00:36:55,790
+أحسبها ولا لأ؟ عشان أجيب بدي قانون رياضي. بدي
+
+475
+00:36:55,790 --> 00:37:00,450
+معلومات فرح اعمل تجربة وأستنتج التالي. أنا بأهم من
+
+476
+00:37:00,450 --> 00:37:05,050
+استنتاجاته بس عشان اتصور ايش عملوه في الـ 1800 وكيف
+
+477
+00:37:05,050 --> 00:37:08,110
+كانوا عندهم مختبرات وشغلات وعملات. لا عندهم
+
+478
+00:37:08,110 --> 00:37:14,620
+computers ولا عندهم جوالات. تمام. بيقول لي بالنسبة
+
+479
+00:37:14,620 --> 00:37:18,660
+للقوة الكهربية. ما يتعلق بالقوة الكهربية. It is
+
+480
+00:37:18,660 --> 00:37:21,820
+found that. ولما أقول it is found يعني النهاردة
+
+481
+00:37:21,820 --> 00:37:27,340
+جت ملاحظات مخبرية في المعمل. وجدت التالي. كلهم قالوا هاي
+
+482
+00:37:27,340 --> 00:37:32,060
+اللي أنا لاحظته نتيجة تجاربه. إيش أول حاجة؟ بقولي
+
+483
+00:37:32,060 --> 00:37:36,140
+لجيت هو القوة مش بتكون بين شحنتين يا بنات؟ شحنتين،
+
+484
+00:37:36,140 --> 00:37:41,240
+هذه سميها Q1 وهذه سميها Q2. لجى القوة تتناسب تناسبا
+
+485
+00:37:41,240 --> 00:37:46,340
+طرديا مع حاصل ضربهم. يعني زود واحدة بتزيد القوة. زود
+
+486
+00:37:46,340 --> 00:37:50,620
+التانية بتزيد أكتر وأكثر. تمام؟ إذا قال لي the
+
+487
+00:37:50,620 --> 00:37:56,160
+force is directly proportional. تتناسب تناسبا طرديا
+
+488
+00:37:56,160 --> 00:38:03,040
+مع حاصل ضرب مقدار الشحنتين. يعني F تتناسب مع K واحد
+
+489
+00:38:03,040 --> 00:38:05,180
+في K اتنين. بس كـ magnitude
+
+490
+00:38:08,940 --> 00:38:11,540
+عشان حاطط الـ absolute عشان تفرجش معاه موجب ولا
+
+491
+00:38:11,540 --> 00:38:17,730
+سالب. هاي أول ملاحظة. تمام؟ جالي كمان ملاحظة عملتها
+
+492
+00:38:17,730 --> 00:38:23,730
+لجيت أن الـ force تتناسب عكسيا مش مع المسافة مع
+
+493
+00:38:23,730 --> 00:38:29,330
+مربع المسافة. يعني كل ما قربت الشحنات زادت القوة و
+
+494
+00:38:29,330 --> 00:38:34,250
+كل ما بعدت الشحنات قلت القوة. يعني بمعنى آخر جبت
+
+495
+00:38:34,250 --> 00:38:38,970
+القوة والمسافة بينهم 1 متر. عملت القوة 2 متر لجيت
+
+496
+00:38:38,970 --> 00:38:46,520
+القوة نص ولا ربع؟ ربع. ربع. لأنه التربيع. تمام؟ فقال
+
+497
+00:38:46,520 --> 00:38:52,940
+لي لجيت أنه the force مقدار السرعة is inversely
+
+498
+00:38:52,940 --> 00:38:55,940
+proportional to  تربيع. واحد على اتنين بين واحد
+
+499
+00:38:55,940 --> 00:39:02,400
+واتنين. حلو. هاجي ملاحظتين حلوين بدي أحطهم بالقانون
+
+500
+00:39:03,130 --> 00:39:07,890
+مش بده أقول يساوي وأحط ثابت. بحط ثابت وخلصنا. إيه
+
+501
+00:39:07,890 --> 00:39:11,930
+أعطيك العافية. جال بس استنى شوية. بنخلص. إيه هتخلص
+
+502
+00:39:11,930 --> 00:39:20,530
+جال. هاي الشحنة هي Q1 وهي Q2. هجت قطعا الـQ1 بتتأثر
+
+503
+00:39:20,530 --> 00:39:25,390
+في الـQ2 ولا لأ؟ نفترض أنما تنافر أو تجاذب. بنفع
+
+504
+00:39:25,390 --> 00:39:29,870
+القوة تقول هيك. بينفع القوة تكون هيك؟ قال لي ولا
+
+505
+00:39:29,870 --> 00:39:34,830
+ممكن. لازم تكون باتجاه الخط الواصل بينهم. يعني اعمل
+
+506
+00:39:34,830 --> 00:39:39,690
+خط هيك وبتقول ليه القوة إما هيك أو هيك. إذا تجاذب
+
+507
+00:39:39,690 --> 00:39:43,610
+هادي وإذا تنافر هادي. إذا الملاحظة الثالثة اللي
+
+508
+00:39:43,610 --> 00:39:48,270
+جالها كولوم أن لازم اتجاه القوة يكون على طول الخط
+
+509
+00:39:48,270 --> 00:39:53,830
+الواصل بين الشحنتين. قطعا وقولا واحدا. إذا the
+
+510
+00:39:53,830 --> 00:39:58,600
+direction of the force is along the line joining
+
+511
+00:39:58,600 --> 00:40:02,960
+the two particles. هدول التلات ملاحظات أعطانا إياهم
+
+512
+00:40:02,960 --> 00:40:10,480
+كلهم. وعايشين لحتى الآن وأصبح له قانون قطعي. مش
+
+513
+00:40:10,480 --> 00:40:16,200
+theory. الـ theory لسه هتبقى مش متأكدين منها. تمام. وهذه
+
+514
+00:40:16,200 --> 00:40:21,040
+ما احنا عارفينها بس أكد ليها. ده اللي القوة بتكون
+
+515
+00:40:21,040 --> 00:40:26,520
+تجاذبية إذا كانوا الشحنتين عكس بعض. ولا لأ؟ the
+
+516
+00:40:26,520 --> 00:40:31,200
+force is attractive if the charges are of opposite
+
+517
+00:40:31,200 --> 00:40:35,940
+signs and repulsive تنافرية if the charges have
+
+518
+00:40:35,940 --> 00:40:40,700
+the same signs. هذه عارفينها. تمّ. قال لي أعطيك
+
+519
+00:40:40,700 --> 00:40:45,340
+العافية. أكل الان بنحط معادلة رياضية from these
+
+520
+00:40:45,340 --> 00:40:48,920
+observations. من هذه الملاحظات الأربع. the
+
+521
+00:40:48,920 --> 00:40:52,520
+magnitude of the force. لأن الـ force vector ولا
+
+522
+00:40:52,520 --> 00:40:56,760
+scalar. Vector. والـ vector له magnitude و direction.
+
+523
+00:40:56,760 --> 00:41:01,480
+نشتغل على الـ magnitude أولًا. قال لي the magnitude of
+
+524
+00:41:01,480 --> 00:41:06,580
+that force on a pointed charge Q1. اللي بيأثر على
+
+525
+00:41:06,580 --> 00:41:11,080
+Q1 due to another pointed charge Q2. نتيجة وجود Q2
+
+526
+00:41:11,080 --> 00:41:15,160
+جنبه. يعني بيدي القوة اللي على واحد من اتنين. تمام؟
+
+527
+00:41:15,160 --> 00:41:20,710
+كيف بتكتبها؟ قال لي بكتبها هيك. إذا هذه F من 2 إلى 1
+
+528
+00:41:20,710 --> 00:41:23,990
+يعني الـ F على 1. يعني لو بدي أرسم الـ free body
+
+529
+00:41:23,990 --> 00:41:29,110
+diagram لـ كي واحد. بتلاقي هذه. طب بدي free body
+
+530
+00:41:29,110 --> 00:41:31,470
+diagram للتانية. بقول لنيوتن. القانون بيشتغل
+
+531
+00:41:31,470 --> 00:41:36,010
+ذاكرينه؟ لكل فعل؟ رد فعل. بس بيكون معاكس. تمام،
+
+532
+00:41:36,010 --> 00:41:40,590
+قدم نجيها. جالي بتثوي ثابت التناسب. مش عارف يقول
+
+533
+00:41:40,590 --> 00:41:46,530
+عنه؟ K. في K واحد في K اتنين كـ absolute values. لكن
+
+534
+00:41:46,530 --> 00:41:50,670
+أنت بتحكي عن magnitude للقوة. تمام، على مربع
+
+535
+00:41:50,670 --> 00:41:56,670
+المسافة اللي بينهم. هو بالقانون كله؟ تمام، see him؟
+
+536
+00:41:57,010 --> 00:42:01,750
+طب الـ K إيه؟ قال لي هذا ثابت، بدي أحفظه؟ لأ. بنعطيك
+
+537
+00:42:01,750 --> 00:42:05,070
+إياه. طب قال لي ده إيش مقداره؟ قال لي هذا المقدار
+
+538
+00:42:05,070 --> 00:42:08,570
+بيعتمد على إيش؟ الوحدات اللي بتستخدمها، إيش الـ
+
+539
+00:42:08,570 --> 00:42:12,690
+system اللي بدك تستخدمه؟ الـ SI ولا الجاوسي؟
+
+540
+00:42:12,690 --> 00:42:16,590
+قال لي احنا بنستخدم إيش؟ الـ SI. بالنسبة لتخربطنا،
+
+541
+00:42:16,590 --> 00:42:20,830
+تمام؟ طبعا هذه R21 in the distance between the two
+
+542
+00:42:20,830 --> 00:42:25,330
+charges and K is the proportionality constant. إيه
+
+543
+00:42:25,330 --> 00:42:29,670
+سموه؟ ما هو سموه قانون ثابت كولوم؟ طيب سهل. ما هو
+
+544
+00:42:29,670 --> 00:42:33,790
+موجود في قانون كولوم مش بينا نسميه ثابت كولوم مش قضية
+
+545
+00:42:33,790 --> 00:42:37,930
+و اللي نافي اسمه مش نافي. احنا ناسبه. بدناش اسمه ولا
+
+546
+00:42:37,930 --> 00:42:41,550
+لا بدنا... ولا بدنا. احتمالا مقداره ما حتى بتدينيه.
+
+547
+00:42:41,550 --> 00:42:47,010
+خلاص K. وبنعرفه كمان. خلصنا الـ magnitude. قال طب الـ
+
+548
+00:42:47,010 --> 00:42:49,910
+Direction؟ قال الـ Direction إما بيكون Repulsive
+
+549
+00:42:49,910 --> 00:42:54,250
+أو Attractive. مظبوط ولا لأ؟ إما Repulsive أو
+
+550
+00:42:54,250 --> 00:42:57,590
+Attractive. إذا الـ Direction كيف بدك تحدده؟ قال
+
+551
+00:42:57,590 --> 00:43:02,650
+حسب نوع الشحنات. وأنا بعرف لما أجي أقول هي شحنة وهي
+
+552
+00:43:02,650 --> 00:43:07,860
+شحنة وهي Q1 وهي Q2. تمام؟ قال لي هادي أنت بدك
+
+553
+00:43:07,860 --> 00:43:10,760
+القوة على هادي. بعدين بتطلع هادي موجبة. أنا افترض
+
+554
+00:43:10,760 --> 00:43:18,340
+أنه هادي موجبة سالبة. بقول هادي إيه بتصير فيها؟ صح
+
+555
+00:43:18,340 --> 00:43:23,540
+ولا لأ؟ طب لو كانت هادي هيك. هي... إذا أنا بحددها
+
+556
+00:43:23,540 --> 00:43:27,780
+بناء على إيش؟ على أنواع الشحنات. إذا the direction of
+
+557
+00:43:27,780 --> 00:43:31,500
+the force is determined. تحدد according...
+
+558
+00:43:31,500 --> 00:43:34,560
+according to the sign of the two charges. وبيعرف
+
+559
+00:43:34,560 --> 00:43:39,940
+أحنا ما بناخدها كتير وبنطبقها كتير. بعيد وبكرر. It is
+
+560
+00:43:39,940 --> 00:43:45,060
+repulsive. بتكون تنافرية إذا كانوا زي بعض. إذا كانوا
+
+561
+00:43:45,060 --> 00:43:52,380
+زي بعض. and attractive if they are unlike. تمام. آخر
+
+562
+00:43:52,380 --> 00:43:57,600
+حاجة قال لي:  the proportionality constant K has a numerical
+
+563
+00:43:57,600 --> 00:44:02,920
+value. قيمة عددية. depends on the choice of units. إذن
+
+564
+00:44:02,920 --> 00:44:10,200
+هو مقداره مش دائما واحد. حسب الوحدات. قال لي حلو. أنا
+
+565
+00:44:10,200 --> 00:44:14,100
+الأساس unit of each charge اللي بدي استخدمها
+
+566
+00:44:14,100 --> 00:44:17,540
+وبنعرف إنه شرحنا إيش وحدتها في هذا الـ system كله.
+
+567
+00:44:17,540 --> 00:44:25,880
+ساعتها بيقولي الـ K بيساوي 9 في 10 أس 9. بتطلع لي
+
+568
+00:44:25,880 --> 00:44:30,820
+على القانون فوق. من القانون بدي واحد يشتق لي من دون
+
+569
+00:44:30,820 --> 00:44:32,800
+ما يطلع هنا وحدة K.
+
+570
+00:44:35,970 --> 00:44:42,010
+النيوتن متر مربع على كولوم تربيع. اتفقنا إنه هذا
+
+571
+00:44:42,010 --> 00:44:48,470
+بدناش نحفظه. بس ممكن نسألكم عن وحدته. عن وحدته من
+
+572
+00:44:48,470 --> 00:44:53,150
+القانون. قانون كولوم مطلوب منكم تحفظوه. تمام يا بنات؟
+
+573
+00:44:53,150 --> 00:44:57,950
+كمان مرة اللي إيجي جديد يلتحق بمجموعة الواتساب يا
+
+574
+00:44:57,950 --> 00:45:01,870
+بنات عشان هي وصية التواصل السهلة بيننا. يا تكل
+
+575
+00:45:01,870 --> 00:45:02,330
+عافية
diff --git a/PL9fwy3NUQKwZzXsCLffozucGP33XWqvBP/JMwSbUAxLRk_postprocess.srt b/PL9fwy3NUQKwZzXsCLffozucGP33XWqvBP/JMwSbUAxLRk_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..13f7c591b550014f49ab955cfab152a19ff304e1
--- /dev/null
+++ b/PL9fwy3NUQKwZzXsCLffozucGP33XWqvBP/JMwSbUAxLRk_postprocess.srt
@@ -0,0 +1,3980 @@
+1
+00:00:05,730 --> 00:00:09,310
+Okay, we will continue today with what is left of
+
+2
+00:00:09,310 --> 00:00:13,090
+the chapter and we are now in the heart of the
+
+3
+00:00:13,090 --> 00:00:14,810
+chapter which is the most important thing in the
+
+4
+00:00:14,810 --> 00:00:20,910
+chapter, which is how to use the law of Gauss to
+
+5
+00:00:20,910 --> 00:00:23,050
+calculate the intensity of the electric field.
+
+6
+00:00:23,730 --> 00:00:26,190
+What we have taken is the construction of an
+
+7
+00:00:26,190 --> 00:00:32,400
+effect. on a closed surface equal to E dot dA on a
+
+8
+00:00:32,400 --> 00:00:35,060
+closed surface according to Gauss's law this is
+
+9
+00:00:35,060 --> 00:00:38,800
+equal to Qm over epsilon naught. He said today I
+
+10
+00:00:38,800 --> 00:00:41,260
+don't need the word fire, I don't need to
+
+11
+00:00:41,260 --> 00:00:44,360
+calculate the flux. What is more important than
+
+12
+00:00:44,360 --> 00:00:46,940
+the flux scientifically is the value of the
+
+13
+00:00:46,940 --> 00:00:52,240
+remaining electric fields. He said Theoretically,
+
+14
+00:00:52,820 --> 00:00:56,940
+with this equation, can I calculate E? They said,
+
+15
+00:00:56,980 --> 00:00:58,900
+theoretically, yes. Because E is clear in the
+
+16
+00:00:58,900 --> 00:01:01,720
+equation, isn't it clear? It is clear. He said,
+
+17
+00:01:01,780 --> 00:01:04,720
+but you have a problem. What is this? It is
+
+18
+00:01:04,720 --> 00:01:07,240
+integration. Right or wrong? Therefore, you will
+
+19
+00:01:07,240 --> 00:01:10,640
+get bored while working. There is no way to deal
+
+20
+00:01:10,640 --> 00:01:15,200
+with it easily except if you can get out of it. If
+
+21
+00:01:15,200 --> 00:01:17,480
+you can get out of it, does every function get out
+
+22
+00:01:17,480 --> 00:01:22,780
+of it? No. It must be constant. Correct? So tell
+
+23
+00:01:22,780 --> 00:01:25,480
+me, this is the condition. Is this condition
+
+24
+00:01:25,480 --> 00:01:30,240
+always constant? I say unfortunately no. There is
+
+25
+00:01:30,240 --> 00:01:35,340
+no possibility that all forms can be left out
+
+26
+00:01:35,340 --> 00:01:38,180
+constantly. Constantly I mean on a closed surface.
+
+27
+00:01:38,800 --> 00:01:40,820
+And a closed surface is correct. God has given me
+
+28
+00:01:40,820 --> 00:01:45,140
+a closed surface. But sometimes all the closed
+
+29
+00:01:45,140 --> 00:01:47,680
+surfaces in the world do not fit with you. Okay?
+
+30
+00:01:48,160 --> 00:01:54,370
+So what does it say? He says here, the practical
+
+31
+00:01:54,370 --> 00:01:58,610
+utility of
+
+32
+00:01:58,610 --> 00:02:07,030
+Gauss's law lies largely in providing
+
+33
+00:02:07,030 --> 00:02:11,130
+a smart
+
+34
+00:02:11,130 --> 00:02:13,030
+way. What is smart?
+
+35
+00:02:19,540 --> 00:02:25,300
+a smart way to evaluate the electric field for
+
+36
+00:02:25,300 --> 00:02:26,720
+some size distribution
+
+37
+00:02:33,580 --> 00:02:42,760
+For this way to be as easy as possible, we must be
+
+38
+00:02:42,760 --> 00:02:48,800
+able to choose a hypothetical closed surface
+
+39
+00:03:03,260 --> 00:03:08,740
+Villages. Abandoned. Ran away. That's it. Okay,
+
+40
+00:03:08,960 --> 00:03:10,820
+I'm going to repeat it again so that no one messes
+
+41
+00:03:10,820 --> 00:03:13,720
+up with it. Closed roof. One of the soldiers said
+
+42
+00:03:13,720 --> 00:03:18,080
+to me, my illusion, my illusion, my illusion, my
+
+43
+00:03:18,080 --> 00:03:21,620
+illusion, my illusion, my illusion, my illusion,
+
+44
+00:03:21,620 --> 00:03:21,660
+my illusion, my illusion, my illusion, my
+
+45
+00:03:21,660 --> 00:03:22,080
+illusion, my illusion, my illusion, my illusion,
+
+46
+00:03:22,080 --> 00:03:22,400
+illusion, my illusion, my illusion, my illusion,
+
+47
+00:03:22,400 --> 00:03:22,500
+my illusion, my illusion, my illusion, my
+
+48
+00:03:22,500 --> 00:03:22,620
+illusion, my illusion, my illusion, my illusion,
+
+49
+00:03:22,620 --> 00:03:22,720
+my illusion, my illusion, my illusion, my
+
+50
+00:03:22,720 --> 00:03:23,590
+my illusion, my illusion, my illusion, my Call
+
+51
+00:03:23,590 --> 00:03:26,130
+this imaginary surface a Gauss surface. Is there a
+
+52
+00:03:26,130 --> 00:03:28,830
+difference? Call it whatever you want to call it.
+
+53
+00:03:28,890 --> 00:03:31,190
+The most important thing is that it has two
+
+54
+00:03:31,190 --> 00:03:33,970
+attributes, closed and imaginary, okay? Call this
+
+55
+00:03:33,970 --> 00:03:38,770
+rectangle a Gauss surface. Such that, this is the
+
+56
+00:03:38,770 --> 00:03:41,430
+most important thing. When you choose, the
+
+57
+00:03:41,430 --> 00:03:44,990
+electric field over its surface must be constant.
+
+58
+00:03:45,670 --> 00:03:48,470
+Why? So that I can get a complete equation.Do you
+
+59
+00:03:48,470 --> 00:03:50,910
+understand me? I have to be able to get out of the
+
+60
+00:03:50,910 --> 00:03:54,650
+complex. I agreed with him that does this happen
+
+61
+00:03:54,650 --> 00:03:59,630
+all the time? I told him unfortunately not. He
+
+62
+00:03:59,630 --> 00:04:05,730
+told me then what are the cases that I can choose.
+
+63
+00:04:06,090 --> 00:04:08,050
+I can choose any case and I want to choose it. It
+
+64
+00:04:08,050 --> 00:04:09,910
+should be E constant on it. He told me that you
+
+65
+00:04:09,910 --> 00:04:11,430
+don't have three types but they don't have a
+
+66
+00:04:11,430 --> 00:04:14,720
+fourth one. But there are three types. So the
+
+67
+00:04:14,720 --> 00:04:17,600
+first thing is the charge distribution of the
+
+68
+00:04:17,600 --> 00:04:20,060
+charged body. You bring a truck full of space,
+
+69
+00:04:20,160 --> 00:04:23,080
+right? There is space that comes without cargo. So
+
+70
+00:04:23,080 --> 00:04:24,980
+you want to have a charged body. You tell him to
+
+71
+00:04:24,980 --> 00:04:26,680
+bring a truck full of electricity. He has two
+
+72
+00:04:26,680 --> 00:04:28,740
+buckets of water. That's it. Then you look at the
+
+73
+00:04:28,740 --> 00:04:31,380
+charged body. You have to tell him that it must be
+
+74
+00:04:31,380 --> 00:04:34,880
+one of the three types.The child distribution must
+
+75
+00:04:34,880 --> 00:04:36,560
+have a high degree of symmetry.
+
+76
+00:04:52,860 --> 00:04:58,780
+These balls are loaded, big, small, empty, empty,
+
+77
+00:04:59,120 --> 00:05:00,960
+each one of them. Which one does it look like?
+
+78
+00:05:01,360 --> 00:05:05,580
+Carowin. Ok, girls? Ok, let's go back to memory
+
+79
+00:05:05,580 --> 00:05:08,280
+and if someone asks you what is the definition of
+
+80
+00:05:08,280 --> 00:05:12,860
+point? Point is a circle. No, it is a ball from a
+
+81
+00:05:12,860 --> 00:05:15,960
+circle. A ball that we drop? Zero. Does it look
+
+82
+00:05:15,960 --> 00:05:18,000
+like a carowin or not? No. So this is one of the
+
+83
+00:05:18,000 --> 00:05:22,680
+types.Each ball is bigger or smaller. Smaller
+
+84
+00:05:22,680 --> 00:05:24,300
+means that the point is smaller than it could be.
+
+85
+00:05:24,580 --> 00:05:28,120
+Good. What is the second case? He said that all
+
+86
+00:05:28,120 --> 00:05:31,700
+Egyptian shapes, but conditional. What is
+
+87
+00:05:31,700 --> 00:05:33,780
+conditional? He said that these edges do not
+
+88
+00:05:33,780 --> 00:05:36,820
+belong to them. Because these edges do not belong
+
+89
+00:05:36,820 --> 00:05:39,700
+to them, they must be very long. When it is very
+
+90
+00:05:39,700 --> 00:05:42,620
+long, girls. Keep it that way so that it fits with
+
+91
+00:05:42,620 --> 00:05:46,360
+me. This edge is in the head of the dragon. Where
+
+92
+00:05:46,360 --> 00:05:48,570
+is the head of the dragon? Do you know that it is
+
+93
+00:05:48,570 --> 00:05:50,930
+the highest point in the north of Palestine? And
+
+94
+00:05:50,930 --> 00:05:56,250
+this is a part of Egypt, in Al-Arish. In Al-Arish.
+
+95
+00:05:56,310 --> 00:05:57,410
+So this is in Al-Arish and this is in Palestine.
+
+96
+00:05:57,970 --> 00:06:01,870
+Okay? Does anyone see the edges? No. Let's not say
+
+97
+00:06:01,870 --> 00:06:07,150
+why.Okay? This is the second type. The spherical
+
+98
+00:06:07,150 --> 00:06:10,410
+shapes are of this condition. Big, small, flat,
+
+99
+00:06:10,790 --> 00:06:13,790
+empty, each one. The rectangular shapes are
+
+100
+00:06:13,790 --> 00:06:16,330
+required to be very long. How many do you want to
+
+101
+00:06:16,330 --> 00:06:19,640
+know? I will tell you. So we have to wait for him
+
+102
+00:06:19,640 --> 00:06:23,060
+to say two words, not very long, not infinitely
+
+103
+00:06:23,060 --> 00:06:28,020
+long. Infinity means infinite. Good. What is the
+
+104
+00:06:28,020 --> 00:06:32,500
+third type? The third type is plain. Plain means
+
+105
+00:06:32,500 --> 00:06:35,840
+level. Is not a level paper? It is also a
+
+106
+00:06:35,840 --> 00:06:37,560
+condition. What is the condition? He said, do you
+
+107
+00:06:37,560 --> 00:06:39,850
+see these sides? You don't have them. You don't
+
+108
+00:06:39,850 --> 00:06:41,990
+see them. In order for me not to see them, does
+
+109
+00:06:41,990 --> 00:06:44,810
+this paper have to be very big or not? It has to
+
+110
+00:06:44,810 --> 00:06:47,090
+be very big. These are the edges. This is at the
+
+111
+00:06:47,090 --> 00:06:49,590
+bottom of the sky. This is under the ground. This
+
+112
+00:06:49,590 --> 00:06:53,070
+is in the clouds and this is in the sun. So these
+
+113
+00:06:53,070 --> 00:06:57,210
+are the three types that I can apply a law based
+
+114
+00:06:57,210 --> 00:06:59,550
+on to calculate the magnitude of space. So the
+
+115
+00:06:59,550 --> 00:07:03,510
+spheres, will they fit here? No. All the problems
+
+116
+00:07:03,510 --> 00:07:08,270
+I told you about. Cylinders with infinite length.
+
+117
+00:07:09,100 --> 00:07:14,020
+The third type is planes with infinite sizes. I
+
+118
+00:07:14,020 --> 00:07:19,040
+will tell you why. Girls, this is a line. The line
+
+119
+00:07:19,040 --> 00:07:21,140
+is cylindrical, mind you. But how many lines does
+
+120
+00:07:21,140 --> 00:07:24,800
+it have? Zero. Zero. Good. If I told you that I
+
+121
+00:07:24,800 --> 00:07:27,200
+want to draw the lines of space, we start from the
+
+122
+00:07:27,200 --> 00:07:34,080
+middle. Right? Here, I bring it like this. Right?
+
+123
+00:07:34,500 --> 00:07:35,300
+So why did it happen here?
+
+124
+00:07:40,670 --> 00:07:43,190
+What are these lines? Parallel lines? Uniforms?
+
+125
+00:07:43,290 --> 00:07:46,230
+Yes? No. No. He said to me, that's why the edges
+
+126
+00:07:46,230 --> 00:07:48,470
+will be a problem for you. Take it easy. He said
+
+127
+00:07:48,470 --> 00:07:50,410
+to me, the edges that you see? No. In your
+
+128
+00:07:50,410 --> 00:07:52,330
+neighborhood? No. Not in your neighborhood.
+
+129
+00:07:52,930 --> 00:07:54,390
+Because you say that when you say that you have
+
+130
+00:07:54,390 --> 00:07:56,290
+space on a point in your neighborhood, you don't
+
+131
+00:07:56,290 --> 00:07:58,370
+say where the edges are. You don't have edges, you
+
+132
+00:07:58,370 --> 00:08:01,450
+don't have space. Okay? To stay away from the
+
+133
+00:08:01,450 --> 00:08:04,550
+uniform. Come back, I want your paper. Give it to
+
+134
+00:08:04,550 --> 00:08:08,710
+me. This is a big piece of paper. I want the lines
+
+135
+00:08:08,710 --> 00:08:11,620
+of space here.How do you draw lines in space?
+
+136
+00:08:11,660 --> 00:08:14,840
+These are all lines. You have to draw them
+
+137
+00:08:14,840 --> 00:08:20,580
+parallel to each other. Right? Up and down and up
+
+138
+00:08:20,580 --> 00:08:22,620
+and down and up and down and up and down and up
+
+139
+00:08:22,620 --> 00:08:23,380
+and down and up and down and up and down and up
+
+140
+00:08:23,380 --> 00:08:23,740
+and down and up and down and up and down and up
+
+141
+00:08:23,740 --> 00:08:24,400
+and down and up and down and up and down and up
+
+142
+00:08:24,400 --> 00:08:25,140
+and down and up and down and up and down and up
+
+143
+00:08:25,140 --> 00:08:25,920
+and down and up and down and up and down and up
+
+144
+00:08:25,920 --> 00:08:29,360
+and down and up and down and up and down and up
+
+145
+00:08:29,360 --> 00:08:30,940
+and down
+
+146
+00:08:34,420 --> 00:08:37,780
+Why should I force the cylinders to be very long
+
+147
+00:08:37,780 --> 00:08:42,020
+and the planes to be very big in order to move
+
+148
+00:08:42,020 --> 00:08:44,500
+away from the edges? The edges that they give me,
+
+149
+00:08:44,540 --> 00:08:47,860
+they give me a uniform electric field. Am I right,
+
+150
+00:08:47,920 --> 00:08:51,900
+girls? You mean that the blades are not on the gas
+
+151
+00:08:51,900 --> 00:08:54,260
+surface? Not on the gas surface. This is the
+
+152
+00:08:54,260 --> 00:08:58,780
+occupied body. The occupied body. One by one. One
+
+153
+00:08:58,780 --> 00:09:02,200
+by one. I'm coming to you all. Wait a minute. The
+
+154
+00:09:02,200 --> 00:09:03,420
+first famous person to extend his field of
+
+155
+00:09:03,420 --> 00:09:05,440
+expertise, to extend his field of expertise, to
+
+156
+00:09:05,440 --> 00:09:07,280
+extend his field of expertise, to extend his field
+
+157
+00:09:07,280 --> 00:09:07,320
+of expertise, to extend his field of expertise, to
+
+158
+00:09:07,320 --> 00:09:07,400
+extend his field of expertise, to extend his field
+
+159
+00:09:07,400 --> 00:09:08,440
+of expertise, to extend his field of expertise, to
+
+160
+00:09:08,440 --> 00:09:12,000
+extend his field of expertise, to extend his field
+
+161
+00:09:12,000 --> 00:09:15,200
+of expertise, to extend his field of expertise, to
+
+162
+00:09:15,200 --> 00:09:19,340
+extend his field of expertise.I say to him, I see
+
+163
+00:09:19,340 --> 00:09:21,440
+that the law is not the law, is it true or not? I
+
+164
+00:09:21,440 --> 00:09:25,180
+mean, if a line is one meter long, or the length
+
+165
+00:09:25,180 --> 00:09:28,200
+of the space, apply a gas law, does it work? No,
+
+166
+00:09:28,820 --> 00:09:30,680
+when I say one meter, does it mean that the edges
+
+167
+00:09:30,680 --> 00:09:33,080
+are in a map or not in a map? In a map, it doesn't
+
+168
+00:09:33,080 --> 00:09:34,860
+work. So how do I solve it? I say to him, I didn't
+
+169
+00:09:34,860 --> 00:09:37,100
+see it at first, so I gave it to you. Not because
+
+170
+00:09:37,100 --> 00:09:39,560
+it was long or short, I don't know what. I was
+
+171
+00:09:39,560 --> 00:09:43,000
+asking you. Yes, now the paper that I grabbed was
+
+172
+00:09:43,000 --> 00:09:46,740
+like a flat surface. Flat, not size. Yes. It's
+
+173
+00:09:46,740 --> 00:09:49,720
+flat, but it's very big. You can't see its edges.
+
+174
+00:09:50,340 --> 00:09:55,600
+It's flat. Plane. It's flat. It's flat, but it's
+
+175
+00:09:55,600 --> 00:09:56,440
+very big. You can't see its edges. It's flat, but
+
+176
+00:09:56,440 --> 00:09:56,860
+flat, but it's very big. It's flat, but it's very
+
+177
+00:09:56,860 --> 00:09:58,200
+big. It's flat, but it's very big. It's flat, but
+
+178
+00:09:58,200 --> 00:09:58,900
+it's very big. It's flat, but it's very big. It's
+
+179
+00:09:58,900 --> 00:10:01,080
+flat, but it's very big. It's flat, but it's very
+
+180
+00:10:01,080 --> 00:10:04,280
+big. It's flat, but it's very big. It's flat, but
+
+181
+00:10:04,280 --> 00:10:09,120
+it's very big. It's flat, but it's very big. It's
+
+182
+00:10:09,120 --> 00:10:14,760
+flat, but it's
+
+183
+00:10:14,760 --> 00:10:20,420
+very bigOkay? The next step now is to apply the
+
+184
+00:10:20,420 --> 00:10:23,180
+Gauss law. Gauss law said to me, this is a closed
+
+185
+00:10:23,180 --> 00:10:25,400
+surface, and you and I agreed that the closed
+
+186
+00:10:25,400 --> 00:10:27,980
+surface should be imaginary, closed and imaginary.
+
+187
+00:10:28,360 --> 00:10:31,020
+He said to me, well, how do I choose? He said to
+
+188
+00:10:31,020 --> 00:10:35,200
+me, I also want to help you choose.because if you
+
+189
+00:10:35,200 --> 00:10:38,260
+don't help me, I will tell you how many floors are
+
+190
+00:10:38,260 --> 00:10:39,380
+closed. Do you remember? There are many
+
+191
+00:10:39,380 --> 00:10:43,060
+rectangles, cubes, squares and curves. What did he
+
+192
+00:10:43,060 --> 00:10:45,080
+do? He said, I will make it easy for you, and hope
+
+193
+00:10:45,080 --> 00:10:48,600
+is easy. He said, the closed floor must look like
+
+194
+00:10:48,600 --> 00:10:51,700
+the full body. How many types does the full body
+
+195
+00:10:51,700 --> 00:10:55,460
+have? Three. Good. So, how many types do I have
+
+196
+00:10:55,460 --> 00:10:58,140
+compared to a closed house floor? Three. What is
+
+197
+00:10:58,140 --> 00:11:00,580
+the first thing? Do you have a disagreement? If
+
+198
+00:11:00,580 --> 00:11:03,060
+the full body is round, should I take a ball house
+
+199
+00:11:03,060 --> 00:11:06,890
+floor?Is there a difference? A ball is a ball. Is
+
+200
+00:11:06,890 --> 00:11:09,650
+there anyone who can mess it up? No. So if the
+
+201
+00:11:09,650 --> 00:11:14,750
+body is loaded with balls, a fake ball, a ball, is
+
+202
+00:11:14,750 --> 00:11:17,670
+it closed or not closed? Closed. Closed. Okay, why
+
+203
+00:11:17,670 --> 00:11:21,050
+did you work on your ball? Well, you have to wait
+
+204
+00:11:21,050 --> 00:11:23,930
+a while. One by one, one by one. He said to me,
+
+205
+00:11:23,930 --> 00:11:27,170
+what is it? He said to me, you have to bring the
+
+206
+00:11:27,170 --> 00:11:29,330
+intensity of the field to where? At a point. Not
+
+207
+00:11:29,330 --> 00:11:31,990
+at a point. Okay. He said to me, this point must
+
+208
+00:11:31,990 --> 00:11:34,750
+be on the surface that you choose. on the surface
+
+209
+00:11:34,750 --> 00:11:37,250
+you want to choose. Why? Because you are here.
+
+210
+00:11:37,870 --> 00:11:39,730
+What is this and what is this? This is the area of
+
+211
+00:11:39,730 --> 00:11:41,350
+​​Gauss, the surface of Gauss. And what does it
+
+212
+00:11:41,350 --> 00:11:45,250
+have? So the point must be on the surface. The
+
+213
+00:11:45,250 --> 00:11:46,670
+point must be on the surface. And we will pay
+
+214
+00:11:46,670 --> 00:11:49,250
+attention to it one by one. Okay, what is the
+
+215
+00:11:49,250 --> 00:11:50,890
+shape of the cylinder? I will tell you. What is
+
+216
+00:11:50,890 --> 00:11:52,990
+the shape of the surface of Gauss? Cylinder. Yes,
+
+217
+00:11:53,070 --> 00:11:55,250
+show me an example of it. Well, is the cylinder
+
+218
+00:11:55,250 --> 00:11:57,190
+the surface of a rock or not? Cylinder. Okay.
+
+219
+00:11:58,070 --> 00:12:01,750
+Cylinder. He said, okay, tell me how much? High?
+
+220
+00:12:02,050 --> 00:12:02,050
+High.
+
+221
+00:12:06,080 --> 00:12:10,440
+It's not closed. I want a closed surface. Is this
+
+222
+00:12:10,440 --> 00:12:12,640
+paper one of the types that we named mixed and not
+
+223
+00:12:12,640 --> 00:12:15,460
+mixed? No. How many times do you tell me the same
+
+224
+00:12:15,460 --> 00:12:19,480
+thing? And so on and so forth. If you put water
+
+225
+00:12:19,480 --> 00:12:21,780
+next to this paper, what comes out? Parallels.
+
+226
+00:12:22,360 --> 00:12:24,800
+Parallels. Parallels are closed or not closed?
+
+227
+00:12:25,120 --> 00:12:27,980
+This surface is closed. Okay, you told me this is
+
+228
+00:12:27,980 --> 00:12:30,000
+a rectangle or not? How did you know it was a
+
+229
+00:12:30,000 --> 00:12:30,220
+rectangle?
+
+230
+00:12:33,350 --> 00:12:38,350
+Why do you say rectangle? I want to say square,
+
+231
+00:12:39,450 --> 00:12:42,250
+right? Okay, someone said, no, I don't want a
+
+232
+00:12:42,250 --> 00:12:47,170
+square, I want a disk. Yes or right? Right or
+
+233
+00:12:47,170 --> 00:12:50,010
+wrong? And what does it mean? Who said rectangle
+
+234
+00:12:50,010 --> 00:12:53,710
+is correct or not correct? And who said disk? And
+
+235
+00:12:53,710 --> 00:12:57,510
+if you want to go and sit with someone, you should
+
+236
+00:12:57,510 --> 00:13:00,050
+put the edges to see, to know that the whole disc
+
+237
+00:13:00,050 --> 00:13:01,910
+is straight. Well, I don't understand the edges,
+
+238
+00:13:02,010 --> 00:13:04,690
+and you don't see them. If you don't know, you're
+
+239
+00:13:04,690 --> 00:13:07,650
+right and you're right. Okay, if you put a meat
+
+240
+00:13:07,650 --> 00:13:10,270
+disc next to you, what comes out of the surface?So
+
+241
+00:13:10,270 --> 00:13:12,390
+if the roof is closed, what will be the ceiling?
+
+242
+00:13:12,610 --> 00:13:14,850
+Okay, the ceiling is correct, and the equilateral
+
+243
+00:13:14,850 --> 00:13:17,670
+rectangles are correct. And I have a saying, if it
+
+244
+00:13:17,670 --> 00:13:19,930
+is chosen between two opinions, what will I take?
+
+245
+00:13:20,390 --> 00:13:22,850
+The easiest one, right or wrong? Okay, the
+
+246
+00:13:22,850 --> 00:13:24,090
+equilateral rectangles are going to be the roof,
+
+247
+00:13:24,430 --> 00:13:26,430
+and the ceiling is going to be the ceiling. What
+
+248
+00:13:26,430 --> 00:13:29,890
+will I take? The second one is the ceiling. So the
+
+249
+00:13:29,890 --> 00:13:33,250
+meaning is as follows, that the shapes are of
+
+250
+00:13:33,250 --> 00:13:34,930
+three types, but the roof is made of two types
+
+251
+00:13:34,930 --> 00:13:42,490
+only. Am I wrong or not?كل جسم مشحون قروي فضحك
+
+252
+00:13:42,490 --> 00:13:47,550
+الله وكل جسم مشحون infinite cylinders او large
+
+253
+00:13:47,550 --> 00:13:52,370
+planes cylinder وخلصنا عرفنا كيف نختار يا بطول؟
+
+254
+00:13:52,370 --> 00:13:55,590
+هزيت أنا اللي بدي أختار بس في قاعدة ولا فيش؟ في
+
+255
+00:13:55,590 --> 00:13:58,690
+قاعدة واحد يقول ليا فاب لو شذيت عن هذا الاختيار
+
+256
+00:13:58,690 --> 00:14:03,630
+ابطورت وحنجرب، حنجيب وحنا بنعمل إذا كيف ابطورت؟
+
+257
+00:14:03,630 --> 00:14:06,630
+بقولي بتنطل هدف تقدر تعمله كيف؟ يعني بقولك هدف
+
+258
+00:14:06,630 --> 00:14:11,800
+تقدر تطلعه برا All right? Good. So the meaning is
+
+259
+00:14:13,100 --> 00:14:24,960
+The Gaussian surface should have
+
+260
+00:14:24,960 --> 00:14:27,680
+the same symmetry as that of the charge
+
+261
+00:14:27,680 --> 00:14:30,540
+distribution.
+
+262
+00:14:33,000 --> 00:14:34,620
+Spheres or cylinders.
+
+263
+00:14:41,600 --> 00:14:47,940
+Look, Slender Zublin told me that I don't want to
+
+264
+00:14:47,940 --> 00:14:49,260
+go to Egypt. He told me that I want to go to
+
+265
+00:14:49,260 --> 00:14:51,700
+Egypt. And from last Saturday when he told me that
+
+266
+00:14:51,700 --> 00:14:52,680
+I want to go to Egypt, I told him where do you
+
+267
+00:14:52,680 --> 00:14:55,460
+want to go. So at a certain point, this point must
+
+268
+00:14:55,460 --> 00:14:58,060
+be on the ceiling. It should be on the surface.
+
+269
+00:14:58,360 --> 00:15:01,820
+The point at which E is to be evaluated should lie
+
+270
+00:15:01,820 --> 00:15:04,520
+on the Gaussian surface. It should lie on the
+
+271
+00:15:04,520 --> 00:15:07,200
+surface. We also apply this a lot with you. Good.
+
+272
+00:15:07,640 --> 00:15:10,480
+Once these are achieved, it means that you have
+
+273
+00:15:10,480 --> 00:15:13,740
+one of two cases, not the third one. This
+
+274
+00:15:13,740 --> 00:15:16,560
+interrelation does not get lost in a series. It
+
+275
+00:15:16,560 --> 00:15:19,000
+does not get lost in a dot product. It does not
+
+276
+00:15:19,000 --> 00:15:21,520
+get lost in a dot product plus a series, plus 90.
+
+277
+00:15:22,460 --> 00:15:25,930
+If it does not get lost, it should be constant.and
+
+278
+00:15:25,930 --> 00:15:28,410
+if it goes out, does anyone know how much it is?
+
+279
+00:15:29,030 --> 00:15:32,070
+What is it? It is the area of the roof of a house.
+
+280
+00:15:32,650 --> 00:15:35,010
+And a roof of a house is either a ball or a
+
+281
+00:15:35,010 --> 00:15:37,970
+ceiling. Ok, wait a minute. A ball does not have
+
+282
+00:15:37,970 --> 00:15:44,050
+an area of 4 square meters. 4 square meters,
+
+283
+00:15:44,890 --> 00:15:47,970
+right? The ceiling is the total area of the
+
+284
+00:15:47,970 --> 00:15:51,840
+ceiling. This area of the base is equal to the
+
+285
+00:15:51,840 --> 00:15:53,480
+area of the side, which is the circumference of
+
+286
+00:15:53,480 --> 00:15:56,340
+the base in height. Right or wrong? So I know
+
+287
+00:15:56,340 --> 00:16:00,420
+them. I know them. That's it, we continue. We say
+
+288
+00:16:00,420 --> 00:16:05,460
+what? These two cases, Fe is perpendicular to Da.
+
+289
+00:16:05,880 --> 00:16:08,740
+If E and Da were perpendicular, the object would
+
+290
+00:16:08,740 --> 00:16:11,440
+have gone away. Right or wrong? It still went
+
+291
+00:16:11,440 --> 00:16:13,800
+away. What's wrong with that? I want it to go away
+
+292
+00:16:13,800 --> 00:16:16,460
+completely and it is zero. That's it. The doctor
+
+293
+00:16:16,460 --> 00:16:21,450
+relaxed me. Or if E is parallel to the A at every
+
+294
+00:16:21,450 --> 00:16:24,470
+point and since E is constant, you will get this
+
+295
+00:16:24,470 --> 00:16:29,190
+combination Do you want me to give you a complete
+
+296
+00:16:29,190 --> 00:16:33,770
+calculation? Yes, yes, yes, yes, yes, yes, yes,
+
+297
+00:16:33,790 --> 00:16:34,290
+yes, yes, yes, yes, yes, yes, yes, yes, yes, yes,
+
+298
+00:16:34,290 --> 00:16:34,490
+yes, yes, yes, yes, yes, yes, yes, yes, yes, yes,
+
+299
+00:16:34,570 --> 00:16:35,810
+yes, yes, yes, yes, yes, yes, yes, yes, yes, yes,
+
+300
+00:16:35,810 --> 00:16:36,230
+yes, yes, yes, yes, yes, yes, yes, yes, yes, yes,
+
+301
+00:16:36,230 --> 00:16:36,330
+yes, yes, yes, yes, yes, yes, yes, yes, yes, yes,
+
+302
+00:16:36,330 --> 00:16:36,430
+yes, yes, yes, yes, yes, yes, yes, yes, yes, yes,
+
+303
+00:16:40,030 --> 00:16:40,030
+yes, yes, yes, yes, yes, yes, yes, yes, yes, yes,
+
+304
+00:16:45,310 --> 00:16:49,500
+yes, yesDid we agree on the point? Okay, if I told
+
+305
+00:16:49,500 --> 00:16:52,020
+you that I have a pointed charge and you want to
+
+306
+00:16:52,020 --> 00:16:53,760
+get its area, is there anyone who has difficulty?
+
+307
+00:16:54,160 --> 00:16:58,440
+Does it have a law? KQ on R square. He said, okay,
+
+308
+00:16:58,600 --> 00:17:00,360
+look, Gauss does not get the answer, he does not
+
+309
+00:17:00,360 --> 00:17:04,740
+get it. He said, the curvature of the area at a
+
+310
+00:17:04,740 --> 00:17:06,800
+point away from distance R, and focus now because
+
+311
+00:17:06,800 --> 00:17:10,240
+I want to apply it. At a point away from distance
+
+312
+00:17:10,240 --> 00:17:16,090
+R on the charge. First test.What is the charged
+
+313
+00:17:16,090 --> 00:17:20,310
+body? Pod. Is it one of the three types of animals
+
+314
+00:17:20,310 --> 00:17:25,350
+or not? Ball. So the first condition is fulfilled.
+
+315
+00:17:25,950 --> 00:17:28,950
+The second condition is important. I want to
+
+316
+00:17:28,950 --> 00:17:33,590
+choose a warm, humid surface. What do I choose?
+
+317
+00:17:34,350 --> 00:17:40,270
+Ball. Let's say you have 60 girls. I can imagine
+
+318
+00:17:40,270 --> 00:17:44,290
+going out with 60 girls, right? But all the floors
+
+319
+00:17:44,290 --> 00:17:46,890
+will fit. I say no, only one will fit. What does
+
+320
+00:17:46,890 --> 00:17:50,890
+it mean? This point must be on the floor. If a
+
+321
+00:17:50,890 --> 00:17:52,710
+girl came and said, I have a small line, this is
+
+322
+00:17:52,710 --> 00:17:55,430
+how I do it. Does it work? No, it doesn't work. A
+
+323
+00:17:55,430 --> 00:17:57,410
+girl came and said, it's better than me. It turned
+
+324
+00:17:57,410 --> 00:17:59,680
+out like this. Does it work?Neither of them is
+
+325
+00:17:59,680 --> 00:18:01,700
+useful. Despite the fact that both are balls or
+
+326
+00:18:01,700 --> 00:18:03,440
+not, there are two conditions that are not
+
+327
+00:18:03,440 --> 00:18:06,520
+fulfilled. One is that the point should be above
+
+328
+00:18:06,520 --> 00:18:10,440
+it. Therefore, the surface must be here or not. It
+
+329
+00:18:10,440 --> 00:18:13,660
+should start from here. Immediately after
+
+330
+00:18:13,660 --> 00:18:16,360
+confirming that the body is loaded with one of the
+
+331
+00:18:16,360 --> 00:18:20,360
+three types, she drew a gaussian surface. And this
+
+332
+00:18:20,360 --> 00:18:23,360
+is a gaussian surface. Do you see it? We make a
+
+333
+00:18:23,360 --> 00:18:26,300
+deduction to make sure that it is true or false.
+
+334
+00:18:26,940 --> 00:18:30,580
+It is false. He said to me, I did what you told me
+
+335
+00:18:30,580 --> 00:18:35,700
+to do. It means that the combination does not need
+
+336
+00:18:35,700 --> 00:18:38,480
+to be calculated, does it? I started to make sure.
+
+337
+00:18:38,900 --> 00:18:42,060
+Is it a constant or not? Do you see these dots?
+
+338
+00:18:43,460 --> 00:18:47,660
+Each one chooses a dot and the volume of each dot
+
+339
+00:18:47,660 --> 00:18:52,540
+is larger than the other. Are they all on the same
+
+340
+00:18:52,540 --> 00:18:55,940
+axis? Correct or not? So E is constant or not?
+
+341
+00:18:57,200 --> 00:19:00,280
+Half of the work you did is correct. The rest of
+
+342
+00:19:00,280 --> 00:19:04,700
+the work is the dot product. One by one. The dot
+
+343
+00:19:04,700 --> 00:19:06,740
+product. Which is the dot product between whom and
+
+344
+00:19:06,740 --> 00:19:12,660
+whom? Draw me a circle with a red dot. Do you see
+
+345
+00:19:12,660 --> 00:19:15,840
+it? It should be like this. Wait a minute. It
+
+346
+00:19:15,840 --> 00:19:17,580
+should be like this or not? It should be like
+
+347
+00:19:17,580 --> 00:19:20,680
+this. At this point, I want you to read it. How
+
+348
+00:19:20,680 --> 00:19:24,370
+does it go? How much is left? Zero. And zero
+
+349
+00:19:24,370 --> 00:19:27,450
+minus? Zero. The dot product is gone. What a
+
+350
+00:19:27,450 --> 00:19:30,950
+beautiful sight. He said, so this is what
+
+351
+00:19:30,950 --> 00:19:33,010
+happened. Yes, we can do it this way, it is better
+
+352
+00:19:33,010 --> 00:19:36,530
+this way. Did this come out or not? Yes. What? The
+
+353
+00:19:36,530 --> 00:19:38,390
+dot product is gone. What does the camera say?
+
+354
+00:19:39,030 --> 00:19:42,210
+Equal. Equal. What is the difference between the
+
+355
+00:19:42,210 --> 00:19:43,850
+size of the ball? I don't know what they want to
+
+356
+00:19:43,850 --> 00:19:46,270
+put in its place. A piece of land? A piece of
+
+357
+00:19:46,270 --> 00:19:50,010
+land. Correct or not? Correct. Come on, girls. Do
+
+358
+00:19:50,010 --> 00:19:52,870
+you see the closed surface of the tube? Yes. You
+
+359
+00:19:52,870 --> 00:19:55,590
+see it. Inside it, you know what's inside and
+
+360
+00:19:55,590 --> 00:19:58,850
+outside it, what's inside it. According to Gauss'
+
+361
+00:19:58,850 --> 00:20:01,070
+law, the Q in is the cargo inside it. Let's take a
+
+362
+00:20:01,070 --> 00:20:02,690
+small child. When he grows up, he goes to college,
+
+363
+00:20:03,370 --> 00:20:05,930
+and when he grows up, he goes to the garden. We
+
+364
+00:20:05,930 --> 00:20:07,510
+say, do you see the surface of the tube? He says,
+
+365
+00:20:07,610 --> 00:20:10,690
+I see it. Is there something red inside it? Yes.
+
+366
+00:20:10,950 --> 00:20:15,590
+He says yes or no. Yes. Okay. Is this the Q? Okay.
+
+367
+00:20:16,090 --> 00:20:19,870
+How much is it? Isn't it a cube? Give it to me. So
+
+368
+00:20:19,870 --> 00:20:22,590
+Qn is equal to Q, isn't it? Yes. Because it's the
+
+369
+00:20:22,590 --> 00:20:29,470
+end of Qn. So instead of Qn, you put Q. Right or
+
+370
+00:20:29,470 --> 00:20:32,390
+not? Because you can't from now on after you tell
+
+371
+00:20:32,390 --> 00:20:35,390
+me E times A, find out the value of E. Did you get
+
+372
+00:20:35,390 --> 00:20:44,750
+it? Yes. Look, girls. One over four pi epsilon not
+
+373
+00:20:44,750 --> 00:20:49,450
+k, isn't it k? Yes. Yes. Look. Cake you on our
+
+374
+00:20:49,450 --> 00:20:50,190
+Terbiya.
+
+375
+00:20:53,510 --> 00:20:57,970
+Which alphabet? Okay. Does this mean that I know
+
+376
+00:20:57,970 --> 00:21:00,970
+the answer or not? Okay, I know the answer without
+
+377
+00:21:00,970 --> 00:21:03,690
+any fuss. I write it down and we're done. Okay,
+
+378
+00:21:04,270 --> 00:21:12,410
+now I want you to ask me a difficult question. He
+
+379
+00:21:12,410 --> 00:21:14,230
+told me that this is a ball half-flattened and
+
+380
+00:21:14,230 --> 00:21:18,510
+isolated. Not conductor isolated. Insulating. It's
+
+381
+00:21:18,510 --> 00:21:20,810
+a factory. And look at all these red things.
+
+382
+00:21:21,590 --> 00:21:24,470
+They're all shipments. Does it generate a field or
+
+383
+00:21:24,470 --> 00:21:27,210
+not? It generates a field. What field do you want
+
+384
+00:21:27,210 --> 00:21:30,670
+it to generate? It generates a field in two
+
+385
+00:21:30,670 --> 00:21:34,050
+regions. An outer region and an inner region. An
+
+386
+00:21:34,050 --> 00:21:36,410
+outer region is like this. And an inner region is
+
+387
+00:21:36,410 --> 00:21:39,030
+like this. Right or wrong? Of course, think of
+
+388
+00:21:39,030 --> 00:21:41,630
+Gauss. If this question came up in the book on the
+
+389
+00:21:41,630 --> 00:21:44,920
+chapter before it,She wants to take an element or
+
+390
+00:21:44,920 --> 00:21:47,280
+not? And get the area of the element and then
+
+391
+00:21:47,280 --> 00:21:50,440
+complete it. Okay. This is if in the third year a
+
+392
+00:21:50,440 --> 00:21:51,440
+question comes like this, you can say that you are
+
+393
+00:21:51,440 --> 00:21:54,320
+not using Gauss law. You used the second chapter
+
+394
+00:21:54,320 --> 00:21:57,600
+completely. In order to solve it, girls, you have
+
+395
+00:21:57,600 --> 00:22:01,040
+to finish calculus A and B and C and get over 90.
+
+396
+00:22:01,980 --> 00:22:06,800
+Not Madjugzak. Okay? And you need three or four
+
+397
+00:22:06,800 --> 00:22:10,110
+pages to solve the question. Three or four pages.
+
+398
+00:22:10,250 --> 00:22:13,690
+Wait a minute. Without Gauss. If Gauss had three
+
+399
+00:22:13,690 --> 00:22:16,290
+or four pages and the beauty of using calculus, I
+
+400
+00:22:16,290 --> 00:22:18,890
+will give you a line without the beauty of using
+
+401
+00:22:18,890 --> 00:22:21,230
+calculus. You don't know the beauty of calculus A
+
+402
+00:22:21,230 --> 00:22:23,170
+and B and C and so on. Do you think that I am
+
+403
+00:22:23,170 --> 00:22:26,890
+above ninety? That I am skilled in using calculus?
+
+404
+00:22:27,530 --> 00:22:29,210
+All of this is not necessary. Of course, I will
+
+405
+00:22:29,210 --> 00:22:31,110
+tell you the rules of that year from beginning to
+
+406
+00:22:31,110 --> 00:22:33,310
+end. And you use it in the original way in three
+
+407
+00:22:33,310 --> 00:22:36,610
+or four pages. To see how to find calculus. Do you
+
+408
+00:22:36,610 --> 00:22:42,520
+use it correctly or not? Okay? Good. So now I
+
+409
+00:22:42,520 --> 00:22:45,340
+don't want to use the calculus. We didn't finish
+
+410
+00:22:45,340 --> 00:22:49,180
+it yet to finish the game. Okay? Good. He said,
+
+411
+00:22:49,260 --> 00:22:51,360
+what do you want to do? I said, I don't know. Then
+
+412
+00:22:51,360 --> 00:22:54,000
+he said, find the strength of the electric field
+
+413
+00:22:54,000 --> 00:22:57,920
+outside the sphere, a distance that is R because
+
+414
+00:22:57,920 --> 00:23:00,400
+it is outside, it should be greater than what? And
+
+415
+00:23:00,400 --> 00:23:03,100
+its diameters at a distance less than what? Good.
+
+416
+00:23:03,240 --> 00:23:05,880
+One by one, girls.Where do you want it to be? I
+
+417
+00:23:05,880 --> 00:23:08,140
+have this black point. Do you see it? This point
+
+418
+00:23:08,140 --> 00:23:09,620
+is far away. It is outside and this is not
+
+419
+00:23:09,620 --> 00:23:12,240
+outside. It is outside. What is the distance? He
+
+420
+00:23:12,240 --> 00:23:14,020
+said R. Of course, it is clear that R is bigger
+
+421
+00:23:14,020 --> 00:23:17,280
+than E. Good. You have to start working. The first
+
+422
+00:23:17,280 --> 00:23:20,460
+condition is that the charged body is a ball.
+
+423
+00:23:20,900 --> 00:23:24,150
+Right? Should I continue? Yes, because it is one
+
+424
+00:23:24,150 --> 00:23:26,270
+of the three types, isn't it? How do you get me
+
+425
+00:23:26,270 --> 00:23:31,610
+up? An insulating sphere. That's it. The word
+
+426
+00:23:31,610 --> 00:23:34,170
+sphere comes from these conditions. That's it. The
+
+427
+00:23:34,170 --> 00:23:37,850
+word sphere works. All right. The next step is to
+
+428
+00:23:37,850 --> 00:23:40,550
+choose a gaussian surface. A gaussian surface is
+
+429
+00:23:40,550 --> 00:23:42,810
+imaginary and looks like a curved body. What does
+
+430
+00:23:42,810 --> 00:23:45,550
+it have to be? A ball. Well, it has to have a
+
+431
+00:23:45,550 --> 00:23:47,850
+point on it. Imagine a gaussian surface. Did you
+
+432
+00:23:47,850 --> 00:23:55,210
+find it? This one or not?This is for sure. This is
+
+433
+00:23:55,210 --> 00:23:59,030
+for sure. Good. I will work and work as you say.
+
+434
+00:23:59,550 --> 00:24:03,890
+As the book says, as they say. Now, while you are
+
+435
+00:24:03,890 --> 00:24:09,770
+on the surface, E is fixed or not? It's fixed. So
+
+436
+00:24:09,770 --> 00:24:11,490
+in order for me to work correctly, I need an E
+
+437
+00:24:11,490 --> 00:24:14,270
+constant. I need a product against a product. I
+
+438
+00:24:14,270 --> 00:24:17,530
+need a product against a product. It means that
+
+439
+00:24:17,530 --> 00:24:21,110
+this E and this A, wherever they are, right? There
+
+440
+00:24:21,110 --> 00:24:23,330
+is no corner between them. And the cosine of zero
+
+441
+00:24:23,330 --> 00:24:28,770
+is one. This is what it means that the gas law
+
+442
+00:24:28,770 --> 00:24:33,910
+gave it a QN. Tell me what is QN? I told him I
+
+443
+00:24:33,910 --> 00:24:35,730
+wanted to bring my little son to play in the
+
+444
+00:24:35,730 --> 00:24:38,450
+garden. I told him that the kitchen is on the
+
+445
+00:24:38,450 --> 00:24:40,570
+floor. I told him that the kitchen is on the
+
+446
+00:24:40,570 --> 00:24:44,810
+floor. I told him to look inside. I told him that
+
+447
+00:24:44,810 --> 00:24:47,830
+there are red boxes. He told me that there are red
+
+448
+00:24:47,830 --> 00:24:50,330
+boxes. I told him that there are red boxes. He
+
+449
+00:24:50,330 --> 00:24:52,310
+there are red boxes. He told me that there are red
+
+450
+00:24:52,310 --> 00:24:52,370
+boxes. I told him that there are red boxes. I told
+
+451
+00:24:52,370 --> 00:24:52,530
+him that there are red boxes. I told him that
+
+452
+00:24:52,530 --> 00:24:54,210
+there are red boxes. I told him that there are red
+
+453
+00:24:54,210 --> 00:24:55,790
+boxes. I told him that there are red boxes. I told
+
+454
+00:24:55,790 --> 00:24:56,550
+him that there are red boxes. I told him that
+
+455
+00:24:56,550 --> 00:24:57,230
+there are red boxes. I told him that there are red
+
+456
+00:24:57,230 --> 00:24:57,550
+boxes. I told him that there are red boxes. I told
+
+457
+00:24:57,550 --> 00:24:59,370
+him that there are red boxesDo you put capital Q
+
+458
+00:24:59,370 --> 00:25:02,530
+or not? He said, get used to it. Is this what you
+
+459
+00:25:02,530 --> 00:25:04,790
+play with? Is there a part of it that you want to
+
+460
+00:25:04,790 --> 00:25:07,910
+get rid of? All of them inside. All of them want
+
+461
+00:25:07,910 --> 00:25:10,270
+to get rid of it. These millions want to get rid
+
+462
+00:25:10,270 --> 00:25:12,450
+of the millions. The millions are all capital Q.
+
+463
+00:25:12,630 --> 00:25:19,110
+Right or not? Get used to it. Life is hard. There
+
+464
+00:25:19,110 --> 00:25:22,970
+was a verse. I will delete it from here. The force
+
+465
+00:25:22,970 --> 00:25:28,530
+of gravity in the outer region E when R was
+
+466
+00:25:28,530 --> 00:25:31,590
+greater than A means outside, the answer came out
+
+467
+00:25:31,590 --> 00:25:35,830
+to be Q over 4 pi epsilon R squared, right or not?
+
+468
+00:25:36,350 --> 00:25:42,610
+This is the first answer, okay? I came back to the
+
+469
+00:25:42,610 --> 00:25:45,610
+second point, where is the point? Do you see this
+
+470
+00:25:45,610 --> 00:25:50,480
+yellow point? Is it visible to you? GoodCome on,
+
+471
+00:25:50,860 --> 00:25:53,420
+we have to choose a cross. How many crosses can I
+
+472
+00:25:53,420 --> 00:25:58,260
+get? One. Zero point on it. Can you imagine? I
+
+473
+00:25:58,260 --> 00:26:01,900
+draw it.
+
+474
+00:26:03,180 --> 00:26:05,560
+Isn't it a cross? Yes. Nice.
+
+475
+00:26:10,750 --> 00:26:15,850
+One by one. If I work from here, will I get a
+
+476
+00:26:15,850 --> 00:26:19,570
+fixed income or not? I brought a product, but it
+
+477
+00:26:19,570 --> 00:26:21,450
+was lost because it was minus zero. He said to me,
+
+478
+00:26:21,450 --> 00:26:25,170
+what does this have in common? I want a Q&A. We
+
+479
+00:26:25,170 --> 00:26:29,190
+came to the little boy to talk to him. I asked
+
+480
+00:26:29,190 --> 00:26:31,230
+him, where are we going? He said, there is a
+
+481
+00:26:31,230 --> 00:26:35,430
+donkey outside and a donkey inside.كله بدك إياه
+
+482
+00:26:35,430 --> 00:26:38,790
+أنا بقوله بدني الجول طيب مش كله يعني أنا بدي جزء
+
+483
+00:26:38,790 --> 00:26:43,370
+منه أه جزء طب هل الجزء هذا معلومة بقدر أقوله النص
+
+484
+00:26:43,370 --> 00:26:48,290
+أو الربع أو التل مش عشوائي عشوائي جالي طب كيه بدي
+
+485
+00:26:48,290 --> 00:26:54,450
+أعمل جالي والله علمناك أنه في حاجة اسمها كثافة لما
+
+486
+00:26:54,450 --> 00:26:59,320
+بدك حاجة جزء من كله روح للكثافاتHow much density
+
+487
+00:26:59,320 --> 00:27:02,140
+do you have in your eyes? Good. Let's go back to
+
+488
+00:27:02,140 --> 00:27:06,280
+the loaded body. Is it big or long or flat? It's
+
+489
+00:27:06,280 --> 00:27:09,640
+big. So it's going to be raw. Correct. It's still
+
+490
+00:27:09,640 --> 00:27:11,820
+going to be raw. I'm telling you here, you told me
+
+491
+00:27:11,820 --> 00:27:14,080
+Qn on Epsilon Note. When I was a child, we boiled
+
+492
+00:27:14,080 --> 00:27:16,900
+it. I said, I don't know how to work. Right? I can
+
+493
+00:27:16,900 --> 00:27:20,540
+tell you that Qn is equal to raw in those who are
+
+494
+00:27:20,540 --> 00:27:25,220
+inside the gas surface. Correct. What is inside
+
+495
+00:27:25,220 --> 00:27:29,940
+the gas surface is the yellow mass.Did anyone
+
+496
+00:27:29,940 --> 00:27:37,440
+forget the size of the ball? 4 by 3 equals to 4 by
+
+497
+00:27:37,440 --> 00:27:42,980
+3 by Artakib. Am I right or not? He said to me,
+
+498
+00:27:42,980 --> 00:27:45,140
+you brought this ball to help you and give it to
+
+499
+00:27:45,140 --> 00:27:47,360
+Al'af. She helped me and gave it to me. He said,
+
+500
+00:27:47,440 --> 00:27:50,280
+bring it to me with the glory of the givers. You
+
+501
+00:27:50,280 --> 00:27:52,820
+still brought me the uniform. Can I say that the
+
+502
+00:27:52,820 --> 00:27:55,360
+ball equals to the total load, the total size?
+
+503
+00:27:57,760 --> 00:28:00,600
+Isn't it true or not? I mean this beautiful thing
+
+504
+00:28:00,600 --> 00:28:04,180
+I can say that it is equal to capital Q divided by
+
+505
+00:28:04,180 --> 00:28:10,060
+4 divided by 3 divided by what? Is it true or not?
+
+506
+00:28:10,800 --> 00:28:14,240
+One more time, this is not a fixed rule. It is
+
+507
+00:28:14,240 --> 00:28:17,360
+equal to dQ divided by dx and equal to Q divided
+
+508
+00:28:17,360 --> 00:28:21,380
+by L. When I said dQ, I meant the length of the
+
+509
+00:28:21,380 --> 00:28:24,840
+element. But when I said the total Q, I meant the
+
+510
+00:28:24,840 --> 00:28:29,860
+total length, right? Ok, you told me that Rho is
+
+511
+00:28:29,860 --> 00:28:35,200
+equal to Q in over V in. Can you tell me the total
+
+512
+00:28:35,200 --> 00:28:38,300
+Q over the total volume? This is what you did,
+
+513
+00:28:38,860 --> 00:28:41,520
+right? Did you stop speaking Arabic?
+
+514
+00:28:44,820 --> 00:28:47,480
+Speak up. I found that the charge is distributed
+
+515
+00:28:47,480 --> 00:28:49,140
+according to the magnitude of the charge. The
+
+516
+00:28:49,140 --> 00:28:51,100
+magnitude of the charge is the same as the volume.
+
+517
+00:28:52,660 --> 00:28:55,020
+It's the same thing. It's the same thing. Look at
+
+518
+00:28:55,020 --> 00:28:57,440
+this. This is in the dictionary, isn't it? And
+
+519
+00:28:57,440 --> 00:29:01,700
+this one is in the
+
+520
+00:29:01,700 --> 00:29:01,960
+dictionary.
+
+521
+00:29:06,060 --> 00:29:15,760
+It's the same thing. It's the same thing. It's the
+
+522
+00:29:15,760 --> 00:29:21,130
+same thing. It's the same thing. And each one of
+
+523
+00:29:21,130 --> 00:29:22,690
+them took the gate other than the other one.
+
+524
+00:29:23,030 --> 00:29:25,610
+That's right or not? Depending on where the
+
+525
+00:29:25,610 --> 00:29:29,090
+information reached. You are free. They came and
+
+526
+00:29:29,090 --> 00:29:32,490
+took me from this gate. What is this? What did I
+
+527
+00:29:32,490 --> 00:29:33,030
+put instead of E?
+
+528
+00:29:36,950 --> 00:29:39,830
+What did I put instead of QN?
+
+529
+00:29:45,510 --> 00:29:49,490
+Right? Look at this. Hadi with Hadi in one house.
+
+530
+00:29:50,870 --> 00:29:58,290
+So, E is equal to Q divided by 4 by Epsilon Note
+
+531
+00:29:58,290 --> 00:30:04,330
+Here there is R and here there is A square Right?
+
+532
+00:30:06,910 --> 00:30:11,150
+Okay If
+
+533
+00:30:11,150 --> 00:30:14,350
+I spoke Arabic correctly I will tell you something
+
+534
+00:30:14,350 --> 00:30:21,770
+If the point is here Outside or inside?outside or
+
+535
+00:30:21,770 --> 00:30:24,530
+inside? inside, outside, outside, outside,
+
+536
+00:30:24,650 --> 00:30:26,030
+outside, outside, outside, outside, outside,
+
+537
+00:30:26,030 --> 00:30:29,590
+outside, outside, outside, outside, outside,
+
+538
+00:30:29,630 --> 00:30:29,870
+outside, outside,
+
+539
+00:30:33,450 --> 00:30:33,550
+outside, outside, outside, outside, outside,
+
+540
+00:30:33,550 --> 00:30:33,790
+outside, outside, outside, outside, outside,
+
+541
+00:30:33,790 --> 00:30:34,650
+outside, outside, outside, outside, outside,
+
+542
+00:30:34,650 --> 00:30:36,710
+outside, outside, outside, outside, outside,
+
+543
+00:30:36,710 --> 00:30:36,730
+outside, outside, outside, outside, outside,
+
+544
+00:30:36,970 --> 00:30:37,870
+outside, outside, outside, outside, outside,
+
+545
+00:30:37,870 --> 00:30:40,230
+outside, outside, outside, outside, outside,
+
+546
+00:30:40,230 --> 00:30:40,690
+outside, outside, outside, outside, outside,
+
+547
+00:30:40,690 --> 00:30:44,110
+outside, outside, outside,
+
+548
+00:30:44,850 --> 00:30:47,910
+outside,
+
+549
+00:30:47,910 --> 00:30:50,600
+outside, outside, outside, outside, outside Right
+
+550
+00:30:50,600 --> 00:30:55,440
+or not? Here, what should I put instead of R? A.
+
+551
+00:30:56,820 --> 00:30:58,000
+What should I put instead of R?
+
+552
+00:31:01,560 --> 00:31:05,840
+A. Nothing or right? Okay, let's connect it with
+
+553
+00:31:05,840 --> 00:31:09,720
+calculus. What is calculus that you took and
+
+554
+00:31:09,720 --> 00:31:12,580
+succeeded in? You took something called the
+
+555
+00:31:12,580 --> 00:31:17,940
+continuous function. If you were asked to test the
+
+556
+00:31:17,940 --> 00:31:21,250
+continuity of a function, how would you do it? Say
+
+557
+00:31:21,250 --> 00:31:24,610
+yes or no You were doing this from the right and
+
+558
+00:31:24,610 --> 00:31:27,250
+from the left Right and left from the outside and
+
+559
+00:31:27,250 --> 00:31:30,270
+from the inside? Yes What if you equal it?
+
+560
+00:31:31,090 --> 00:31:32,970
+Continuous The function I have is an electric
+
+561
+00:31:32,970 --> 00:31:36,610
+field The electric field is continuous You brought
+
+562
+00:31:36,610 --> 00:31:39,130
+it from the right and from the left But instead of
+
+563
+00:31:39,130 --> 00:31:41,270
+right and left From both sides, you don't know
+
+564
+00:31:41,270 --> 00:31:42,930
+which side is left and which side is right The two
+
+565
+00:31:42,930 --> 00:31:44,610
+sides I have outside and inside You brought it
+
+566
+00:31:44,610 --> 00:31:46,510
+from outside and brought it from inside The same
+
+567
+00:31:46,510 --> 00:31:49,110
+answer, does it mean continuous or not? So
+
+568
+00:31:49,110 --> 00:31:49,490
+continuous
+
+569
+00:31:54,590 --> 00:31:56,290
+What does it mean? I don't know the answer. I have
+
+570
+00:31:56,290 --> 00:31:58,470
+to get it from outside. No, no, no. This is a
+
+571
+00:31:58,470 --> 00:32:00,130
+kickback. Just to tell you to continue. Keep
+
+572
+00:32:00,130 --> 00:32:02,610
+going. Keep going. Keep going. The last part, keep
+
+573
+00:32:02,610 --> 00:32:05,070
+going if you want to. If you are confused. If he
+
+574
+00:32:05,070 --> 00:32:07,530
+is Chinese, may God make it easy for him. Chinese
+
+575
+00:32:07,530 --> 00:32:10,090
+entered your mind. Forget it. We finished the
+
+576
+00:32:10,090 --> 00:32:11,970
+question. We finished it. There is one thing. Yes.
+
+577
+00:32:12,230 --> 00:32:14,930
+I remember when we took the point outside. It
+
+578
+00:32:14,930 --> 00:32:18,550
+turned out to be in the range of Q over 4Y epsilon
+
+579
+00:32:18,550 --> 00:32:21,010
+in the upper right corner. Nice. It's like I'm
+
+580
+00:32:21,010 --> 00:32:24,110
+telling you. Point. Oh, that's why there's
+
+581
+00:32:24,110 --> 00:32:27,850
+symmetry. Because there's symmetry. Well done. An
+
+582
+00:32:27,850 --> 00:32:30,270
+important observation. That you think outside is
+
+583
+00:32:30,270 --> 00:32:38,670
+like a point. Right? Yes. Tell me. Where? Nowhere.
+
+584
+00:32:39,150 --> 00:32:43,270
+Up.Why outside the equation? Because this person
+
+585
+00:32:43,270 --> 00:32:44,850
+is not very important. I don't want to waste his
+
+586
+00:32:44,850 --> 00:32:46,830
+time. I told him that whoever enters his country
+
+587
+00:32:46,830 --> 00:32:48,570
+is an Arab and whoever does not enter his country
+
+588
+00:32:48,570 --> 00:32:52,190
+is a foreigner. Okay? Because he is not important.
+
+589
+00:32:52,890 --> 00:32:55,870
+That's why I gave him a check. Who are you asking?
+
+590
+00:32:56,370 --> 00:32:58,890
+You say it, Doha. It's okay because I consider
+
+591
+00:32:58,890 --> 00:33:01,370
+that as long as it is a ball that is represented,
+
+592
+00:33:01,670 --> 00:33:05,470
+I mean, I see it and it wants an external point, I
+
+593
+00:33:05,470 --> 00:33:07,430
+consider it directly ... I consider it, I consider
+
+594
+00:33:07,430 --> 00:33:11,510
+it, right, this is a note, this is a note, I build
+
+595
+00:33:11,510 --> 00:33:14,430
+on it, but in the end, did I prove it or not? I
+
+596
+00:33:14,430 --> 00:33:16,790
+proved it, so I don't want to keep a law and get
+
+597
+00:33:16,790 --> 00:33:20,790
+stuck in it because I don't keep a rule. That's
+
+598
+00:33:20,790 --> 00:33:23,030
+it. I noticed that it is very important and
+
+599
+00:33:23,030 --> 00:33:26,210
+written. That I make it as a point. But it is not
+
+600
+00:33:26,210 --> 00:33:28,050
+very important. I found it. Then I will say it one
+
+601
+00:33:28,050 --> 00:33:34,530
+by one. Increase your voice, Naida. What is wrong
+
+602
+00:33:34,530 --> 00:33:38,330
+with them? I asked you a question, Naida. Did you
+
+603
+00:33:38,330 --> 00:33:41,070
+put red or not? Consider it positive. Someone
+
+604
+00:33:41,070 --> 00:33:44,610
+tells me to consider it negative. Yes. I consider
+
+605
+00:33:44,610 --> 00:33:47,390
+it positive. But if you consider it negative, it
+
+606
+00:33:47,390 --> 00:33:49,370
+becomes positive for you, doesn't it? That's it.
+
+607
+00:33:49,470 --> 00:33:51,790
+Since you consider it positive from inside and
+
+608
+00:33:51,790 --> 00:33:54,710
+outside, why don't I deal with everything that
+
+609
+00:33:54,710 --> 00:33:57,830
+anyone gives me from the beginning? From the
+
+610
+00:33:57,830 --> 00:33:59,350
+beginning. We've been talking about this for a
+
+611
+00:33:59,350 --> 00:34:00,810
+long time and it's still not clear. You can
+
+612
+00:34:00,810 --> 00:34:04,790
+consider it as a point if you're only outside. The
+
+613
+00:34:04,790 --> 00:34:07,450
+point was outside, but inside it was not. There
+
+614
+00:34:07,450 --> 00:34:11,170
+was a small r in your mind. Okay, let's face the
+
+615
+00:34:11,170 --> 00:34:15,190
+small r now. He gave the answer for the capital.
+
+616
+00:34:16,010 --> 00:34:20,190
+He said, look when I got out of here, I said hi R
+
+617
+00:34:20,190 --> 00:34:22,670
+in the past. He said, okay, this is the yellow
+
+618
+00:34:22,670 --> 00:34:24,830
+point, girls. If it was in the center, what would
+
+619
+00:34:24,830 --> 00:34:27,250
+I put instead of the R always? I don't know how to
+
+620
+00:34:27,250 --> 00:34:31,330
+get the answer. Zero. If the field is stretched
+
+621
+00:34:31,330 --> 00:34:33,710
+towards the center, it's zero. Why do I say this?
+
+622
+00:34:34,310 --> 00:34:40,370
+Think about it. Bravo on you. Tell me yes. Because
+
+623
+00:34:40,370 --> 00:34:42,190
+this is the point when you are in the center
+
+624
+00:34:42,190 --> 00:34:45,670
+surrounded by all sides with equal sections or
+
+625
+00:34:45,670 --> 00:34:48,490
+not? And you are dealing with vectors or scalars?
+
+626
+00:34:48,690 --> 00:34:51,690
+Vectors. Vectors. Look at all the sections. You
+
+627
+00:34:51,690 --> 00:34:56,070
+will find that each section has a direction. So it
+
+628
+00:34:56,070 --> 00:34:59,190
+is reasonable. It is reasonable. Is it reasonable?
+
+629
+00:34:59,470 --> 00:35:01,370
+I tell him it is reasonable. Correct.
+
+630
+00:35:04,530 --> 00:35:13,590
+Okay? Like the example. found the electric field a
+
+631
+00:35:13,590 --> 00:35:18,630
+distance R from an infinite line
+
+632
+00:35:22,090 --> 00:35:26,450
+He said, I want to use the law of gauss. I said,
+
+633
+00:35:26,690 --> 00:35:29,630
+okay, but do a test. Is it one of the three types
+
+634
+00:35:29,630 --> 00:35:33,450
+or not? Cylinders very long or not very long? He
+
+635
+00:35:33,450 --> 00:35:36,710
+said, very long. I drew it. Of course, I drew it
+
+636
+00:35:36,710 --> 00:35:38,530
+because this is not his side. This is part of him.
+
+637
+00:35:38,670 --> 00:35:42,150
+His side is far away. And this is far away. Very
+
+638
+00:35:42,150 --> 00:35:48,530
+far away. Okay. This line is part of him. I want
+
+639
+00:35:48,530 --> 00:35:53,150
+someone to reach the lines of space.like this and
+
+640
+00:35:53,150 --> 00:35:56,250
+like this and like this and like this and like
+
+641
+00:35:56,250 --> 00:35:56,850
+this and like this and like this and like this and
+
+642
+00:35:56,850 --> 00:35:57,330
+like this and like this and like this and like
+
+643
+00:35:57,330 --> 00:35:58,210
+this and like this and like this and like this and
+
+644
+00:35:58,210 --> 00:35:58,250
+like this and like this and like this and like
+
+645
+00:35:58,250 --> 00:35:58,390
+this and like this and like this and like this and
+
+646
+00:35:58,390 --> 00:35:59,550
+like this and like this and like this and like
+
+647
+00:35:59,550 --> 00:36:00,770
+this and like this and like this and like this and
+
+648
+00:36:00,770 --> 00:36:01,790
+this and like this and like this and like this and
+
+649
+00:36:01,790 --> 00:36:07,110
+like this and like this and like this and
+
+650
+00:36:07,110 --> 00:36:07,290
+like this
+
+651
+00:36:23,710 --> 00:36:26,390
+Fine. Good. We imagined the lines of the circle,
+
+652
+00:36:26,690 --> 00:36:30,590
+didn't we? Fine. This is one of the three shapes
+
+653
+00:36:30,590 --> 00:36:33,530
+that you told me about. Amen. The next step. I
+
+654
+00:36:33,530 --> 00:36:36,210
+want to choose a gaussian plane. What did you
+
+655
+00:36:36,210 --> 00:36:40,870
+choose? Point. Because the point should have a
+
+656
+00:36:40,870 --> 00:36:44,350
+beautiful plane, a plane that is flat. It should
+
+657
+00:36:44,350 --> 00:36:48,090
+be on one of the three, not on the surface. The
+
+658
+00:36:48,090 --> 00:36:50,610
+point is on the surface of the pan, not on the
+
+659
+00:36:50,610 --> 00:36:52,730
+surface of the pan. On the surface of the pan.
+
+660
+00:36:53,390 --> 00:36:55,910
+Someone says, okay, should I make it bigger or
+
+661
+00:36:55,910 --> 00:36:57,990
+smaller? I say, make it smaller as much as you
+
+662
+00:36:57,990 --> 00:37:00,250
+can. Why? So that you can move away from the
+
+663
+00:37:00,250 --> 00:37:03,390
+edges. Not as much as you move away from the
+
+664
+00:37:03,390 --> 00:37:07,990
+edges. Okay?Sometimes we ask him a question like
+
+665
+00:37:07,990 --> 00:37:09,670
+this. We used to ask him this question in exams.
+
+666
+00:37:10,010 --> 00:37:11,250
+We ask him this question. We tell him it's a
+
+667
+00:37:11,250 --> 00:37:13,330
+silicon. We tell him it's infinite, but we can't
+
+668
+00:37:13,330 --> 00:37:15,970
+tell if it's infinite or not. Any student must
+
+669
+00:37:15,970 --> 00:37:17,590
+choose a surface of ice. He must say which one is
+
+670
+00:37:17,590 --> 00:37:19,090
+closer to him. This surface is ice.
+
+671
+00:37:21,980 --> 00:37:24,740
+He said, you're following the edges. I said, I'm
+
+672
+00:37:24,740 --> 00:37:27,060
+not following the edges. Did you see the edges? He
+
+673
+00:37:27,060 --> 00:37:29,480
+said, leave the edges alone. You can't draw like
+
+674
+00:37:29,480 --> 00:37:30,400
+that, because you'll get yourself in trouble.
+
+675
+00:37:31,020 --> 00:37:33,820
+You're following the problem, which is the edges.
+
+676
+00:37:33,980 --> 00:37:36,140
+Right or wrong? I said, whatever you choose. I
+
+677
+00:37:36,140 --> 00:37:38,500
+exaggerated a little bit to make you see it. It
+
+678
+00:37:38,500 --> 00:37:42,100
+should be even more. Then he told me a nice thing.
+
+679
+00:37:44,290 --> 00:37:46,890
+She mixed up the point on the top and the point on
+
+680
+00:37:46,890 --> 00:37:50,730
+the bottom. The point on the top is safe. She
+
+681
+00:37:50,730 --> 00:37:53,870
+said, now we have to apply it. Let's go back to
+
+682
+00:37:53,870 --> 00:37:56,570
+the previous example. In the previous two
+
+683
+00:37:56,570 --> 00:37:58,290
+examples, the point and the sphere, what was the
+
+684
+00:37:58,290 --> 00:38:02,630
+point on the top? A ball. The ball had a top. The
+
+685
+00:38:02,630 --> 00:38:06,390
+ball. The bottom. She said, then after that, when
+
+686
+00:38:06,390 --> 00:38:09,190
+you start writing after these words, this becomes
+
+687
+00:38:09,190 --> 00:38:11,870
+three compositions. Do you remember the equation
+
+688
+00:38:11,870 --> 00:38:14,230
+of rectangles when we got it? Didn't we divide it
+
+689
+00:38:14,230 --> 00:38:16,830
+by 6? He told me this is going to be a combination
+
+690
+00:38:16,830 --> 00:38:20,590
+of 6. So what does he say? After I did this and
+
+691
+00:38:20,590 --> 00:38:24,510
+these lines of space, he told me since the
+
+692
+00:38:24,510 --> 00:38:28,630
+cylinder has three surfaces, this sentence, does
+
+693
+00:38:28,630 --> 00:38:31,400
+anyone not know it? How many surfaces does a
+
+694
+00:38:31,400 --> 00:38:34,920
+cylinder have? Three. It means that a cylinder has
+
+695
+00:38:34,920 --> 00:38:41,500
+three surfaces. The integral in Gauss's law has to
+
+696
+00:38:41,500 --> 00:38:44,320
+be split. What does split mean? It has to be
+
+697
+00:38:44,320 --> 00:38:48,280
+divided. Split. It has to be divided. It has to be
+
+698
+00:38:48,280 --> 00:38:53,500
+split into three parts. Let's say the surface of
+
+699
+00:38:53,500 --> 00:38:58,840
+the whole star. How do they get it? How many bases
+
+700
+00:38:58,840 --> 00:39:05,100
+does it have? Base, Base, Curved Base, Base,
+
+701
+00:39:05,240 --> 00:39:11,420
+Curved. Curved is what? The side. Nice. This is
+
+702
+00:39:11,420 --> 00:39:12,240
+what I found.
+
+703
+00:39:14,840 --> 00:39:18,260
+What is this height? Raise your voice. What is
+
+704
+00:39:18,260 --> 00:39:21,540
+this height? This is the side area. One of them.
+
+705
+00:39:22,160 --> 00:39:27,260
+One of them. Should I say it? In two cases? Why
+
+706
+00:39:27,260 --> 00:39:30,220
+are they two against each other? Side area? Later.
+
+707
+00:39:31,760 --> 00:39:35,580
+Do you understand? Yes. Yes. Yes. Yes. Yes. Yes.
+
+708
+00:39:35,580 --> 00:39:36,040
+Yes. Yes. Yes. Yes. Yes. Yes. Yes. Yes. Yes. Yes.
+
+709
+00:39:36,040 --> 00:39:37,880
+Yes. Yes. Yes. Yes. Yes. Yes. Yes. Yes. Yes.
+
+710
+00:39:40,960 --> 00:39:45,240
+Yes. Yes. Yes. Yes. Yes. Yes. Yes. Yes. Yes. Yes.
+
+711
+00:39:45,360 --> 00:39:46,440
+Yes. Yes. Yes. Yes. Yes. Yes. Yes. Yes. Yes. Yes.
+
+712
+00:39:49,780 --> 00:39:50,500
+Yes.
+
+713
+00:39:53,440 --> 00:39:59,260
+Yes. Yes. Yes. Yes. Yes. Yes. Yes. Yes. Yes. Yes.
+
+714
+00:39:59,260 --> 00:39:59,400
+Yes. Yes. Yes. Yes. Yes. Yes. Yes. Yes. Yes. Yes.
+
+715
+00:39:59,400 --> 00:40:00,940
+Yes. Yes. Yes. Yes.Do you want to deal with all
+
+716
+00:40:00,940 --> 00:40:04,480
+the intermingling on one side or not? Good. Look
+
+717
+00:40:04,480 --> 00:40:09,800
+at this beauty. How is the reading of it? From
+
+718
+00:40:09,800 --> 00:40:14,240
+above. Don't give space between it and the red
+
+719
+00:40:14,240 --> 00:40:18,580
+line. The intermingling is gone. This flower is
+
+720
+00:40:18,580 --> 00:40:22,060
+beautiful. Do you know? If it wasn't yellow, it
+
+721
+00:40:22,060 --> 00:40:26,160
+would have been rotten. Why? Because this point is
+
+722
+00:40:26,160 --> 00:40:27,980
+on the surface and this point is on the surface.
+
+723
+00:40:28,920 --> 00:40:31,720
+Am I right or not? Are these two dots in the same
+
+724
+00:40:31,720 --> 00:40:35,620
+field? No. So if this one didn't go away from the
+
+725
+00:40:35,620 --> 00:40:38,700
+dot product, could I pull this one out? No, but
+
+726
+00:40:38,700 --> 00:40:43,340
+thank God, it needed to be pulled out because it
+
+727
+00:40:43,340 --> 00:40:45,900
+went away with all its problems, with all its
+
+728
+00:40:45,900 --> 00:40:50,840
+dirt, and it became zero. So this one went away.
+
+729
+00:40:52,860 --> 00:40:59,780
+One more time, if words slip, ask it. Instead of
+
+730
+00:40:59,780 --> 00:41:04,420
+reminding them to not be afraid of me because I'm
+
+731
+00:41:04,420 --> 00:41:06,820
+afraid of asking them, I'm encouraging them to ask
+
+732
+00:41:06,820 --> 00:41:14,840
+me. Okay, look at this one. Where is the E? Yes,
+
+733
+00:41:15,360 --> 00:41:20,300
+don't you want the corner? She went away. Where
+
+734
+00:41:20,300 --> 00:41:23,900
+did you go? What is left? The side. Can you
+
+735
+00:41:23,900 --> 00:41:25,760
+imagine the side and why are you walking on it?
+
+736
+00:41:26,160 --> 00:41:27,460
+Are you moving away or are you trying to walk on
+
+737
+00:41:27,460 --> 00:41:32,340
+the chain? E is constant. Wow! E is constant.
+
+738
+00:41:32,760 --> 00:41:34,620
+Okay, how many circles are there in the directions
+
+739
+00:41:34,620 --> 00:41:39,180
+of the spaces? Outside. Outside. And E? Zero. So,
+
+740
+00:41:39,300 --> 00:41:43,280
+the angle is zero. So, this is the contraction, my
+
+741
+00:41:43,280 --> 00:41:46,260
+dear. So, this is how I enlarged it.
+
+742
+00:41:49,240 --> 00:41:56,540
+Right? E to E. The problem of QN remains. Is all
+
+743
+00:41:56,540 --> 00:42:00,120
+the heat inside a gaussian surface? Part of it. I
+
+744
+00:42:00,120 --> 00:42:04,520
+want density. In the first above, infinite line,
+
+745
+00:42:04,700 --> 00:42:07,460
+right? Line means what? Lambda or sigma or rho?
+
+746
+00:42:07,820 --> 00:42:13,760
+Lambda. I can say, girls, that QN equals lambda to
+
+747
+00:42:13,760 --> 00:42:18,370
+LNWhat is the length of this whole donkey that
+
+748
+00:42:18,370 --> 00:42:24,530
+enters the roof of the house? H I reply to them,
+
+749
+00:42:24,630 --> 00:42:28,890
+but if they are your friends, tell me why H? The N
+
+750
+00:42:28,890 --> 00:42:30,850
+is equal to lambda in H, right? But it gives this
+
+751
+00:42:30,850 --> 00:42:34,670
+length, that's it? And I draw too. Thank God,
+
+752
+00:42:34,830 --> 00:42:37,090
+Corona made us overcome ourselves and draw a lot.
+
+753
+00:42:37,850 --> 00:42:41,760
+These are all words that I spoke in Arabic. He
+
+754
+00:42:41,760 --> 00:42:45,760
+said, let's do a Q&A. Let's do a Q&A. This is the
+
+755
+00:42:45,760 --> 00:42:48,100
+size. This is the circumference. The side area
+
+756
+00:42:48,100 --> 00:42:50,140
+between them. On both sides. On the edge. The base
+
+757
+00:42:50,140 --> 00:42:54,320
+area in height. Okay. He said, this is okay. This
+
+758
+00:42:54,320 --> 00:42:57,440
+is going to give a Q&A. Look at this Q&A. The ones
+
+759
+00:42:57,440 --> 00:42:59,660
+that move, do you see them? But these ones that
+
+760
+00:42:59,660 --> 00:43:03,760
+have carriers, how long are they? So lambda is in
+
+761
+00:43:03,760 --> 00:43:08,500
+the edge or not? Look what happened. Edge with
+
+762
+00:43:08,500 --> 00:43:14,020
+edge. So why did the videocutter make a loud
+
+763
+00:43:14,020 --> 00:43:17,180
+noise? Was his answer louder? No, no. It's not a
+
+764
+00:43:17,180 --> 00:43:19,720
+lie. On the contrary, he made himself heard. Okay?
+
+765
+00:43:20,360 --> 00:43:21,720
+The more you make noise, the more logical it
+
+766
+00:43:21,720 --> 00:43:21,860
+becomes.
+
+767
+00:43:26,050 --> 00:43:28,710
+I will repeat this sentence that I told you. He
+
+768
+00:43:28,710 --> 00:43:32,210
+said that if the circuit is not very long, you
+
+769
+00:43:32,210 --> 00:43:36,030
+will have the edges in your field. Right? And the
+
+770
+00:43:36,030 --> 00:43:38,950
+edges in your field and the edges in the
+
+771
+00:43:38,950 --> 00:43:42,310
+electrical field are not uniform. Therefore, you
+
+772
+00:43:42,310 --> 00:43:43,490
+will not be able to deal with the three
+
+773
+00:43:43,490 --> 00:43:43,830
+components.
+
+774
+00:43:53,000 --> 00:44:01,060
+Its end will be close to any Gaussian surface.
+
+775
+00:44:02,230 --> 00:44:04,770
+Since the electric field وبما أنه شد في المجال
+
+776
+00:44:04,770 --> 00:44:09,450
+الكهربائي أو المجال الكهربائي عند أو قريب من
+
+777
+00:44:09,450 --> 00:44:14,190
+الأطراف at يعني عند and close to the ends عند
+
+778
+00:44:14,190 --> 00:44:19,190
+الأطراف قريب is not uniform مكونش uniform وبالتالي
+
+779
+00:44:19,190 --> 00:44:23,250
+it will be impossible ولا ممكن لا calculus A ولا B
+
+780
+00:44:23,250 --> 00:44:25,450
+ولا C ولا D ولا E
+
+781
+00:44:28,440 --> 00:44:31,140
+It will be impossible to manage the integral of
+
+782
+00:44:31,140 --> 00:44:32,200
+Gauss's law.
+
+783
+00:44:43,920 --> 00:44:47,560
+I don't want a cane, I don't want to answer you, I
+
+784
+00:44:47,560 --> 00:44:49,980
+want to choose a ball, the ball is halal, it has
+
+785
+00:44:49,980 --> 00:44:52,620
+one floor, do you see the balls? How many floors
+
+786
+00:44:52,620 --> 00:44:54,680
+does it have? One floor. As long as you walk on
+
+787
+00:44:54,680 --> 00:44:56,600
+the floor, do you try to touch you or not? Yes.
+
+788
+00:44:56,680 --> 00:44:58,280
+You can try and stay away from him. So what do you
+
+789
+00:44:58,280 --> 00:45:05,180
+want? Water. Water. This is a point,
+
+790
+00:45:10,720 --> 00:45:14,290
+and this is a point. And this is a point. It's the
+
+791
+00:45:14,290 --> 00:45:18,850
+same distance on the wire. So in this uniform. So
+
+792
+00:45:18,850 --> 00:45:23,550
+if a bullet flies from it, it flies. Am I right or
+
+793
+00:45:23,550 --> 00:45:27,250
+am I lying? How?
+
+794
+00:45:30,530 --> 00:45:34,550
+Yes. Good. When they fire, you want them to fire
+
+795
+00:45:34,550 --> 00:45:37,330
+in the opposite direction, right? I'll give you an
+
+796
+00:45:37,330 --> 00:45:39,390
+example. I have a point here. How many lines does
+
+797
+00:45:39,390 --> 00:45:42,010
+the BGK have? Millions and billions of lines.
+
+798
+00:45:43,500 --> 00:45:46,640
+That's the other way around. The wrong way around.
+
+799
+00:45:47,080 --> 00:45:51,320
+Doctor, should the accumulation of the cells go
+
+800
+00:45:51,320 --> 00:45:55,240
+away? According to this question. Because we lost
+
+801
+00:45:55,240 --> 00:45:59,000
+them. Why? We lost them from the dot. Okay, so
+
+802
+00:45:59,000 --> 00:46:03,140
+what happens to the A? It's not fixed. So if it
+
+803
+00:46:03,140 --> 00:46:04,140
+doesn't go away from the dot, it will get stuck.
+
+804
+00:46:04,460 --> 00:46:06,380
+It will get stuck, my dear. It will get stuck.
+
+805
+00:46:07,220 --> 00:46:10,080
+Look at this question. He said this is a plane.
+
+806
+00:46:10,920 --> 00:46:14,360
+Plane. Machiavellian plane must have conditions.
+
+807
+00:46:14,940 --> 00:46:18,700
+Very big conditions. Let's see. Let's see this
+
+808
+00:46:18,700 --> 00:46:23,520
+sentence or word. What is this? The condition is
+
+809
+00:46:23,520 --> 00:46:26,220
+fulfilled or not fulfilled? They want to find the
+
+810
+00:46:26,220 --> 00:46:31,120
+electric field E due to non-conducting infinity
+
+811
+00:46:31,120 --> 00:46:37,720
+plane with uniform surface charges at sigma. And
+
+812
+00:46:37,720 --> 00:46:40,920
+this sigma is uniform.Sigma because it's a plane.
+
+813
+00:46:41,080 --> 00:46:42,120
+Isn't there a difference between being a plane and
+
+814
+00:46:42,120 --> 00:46:45,320
+not being a sigma? It's a surface. Does it have to
+
+815
+00:46:45,320 --> 00:46:49,020
+be a sigma or a denominator? Sigma. Of course, is
+
+816
+00:46:49,020 --> 00:46:50,420
+there anyone who doesn't know what a plane is?
+
+817
+00:46:51,520 --> 00:46:54,100
+It's a paper. Right or wrong? Yes. It's a paper.
+
+818
+00:46:55,920 --> 00:46:59,200
+Did you see the edges of the paper? No. And she
+
+819
+00:46:59,200 --> 00:47:02,240
+said, practically speaking, I choose the left
+
+820
+00:47:02,240 --> 00:47:04,740
+side, I want a surface. A cylinder. A cylinder.
+
+821
+00:47:05,200 --> 00:47:09,540
+Right or wrong? The paper is easy. My hand was the
+
+822
+00:47:09,540 --> 00:47:11,540
+paper and you can see the edges that I considered
+
+823
+00:47:11,540 --> 00:47:14,900
+to be a disk. I put five or six hands next to each
+
+824
+00:47:14,900 --> 00:47:16,280
+other and it turned out that I was sleeping like
+
+825
+00:47:16,280 --> 00:47:19,080
+this. Right or wrong? He told me that this is a
+
+826
+00:47:19,080 --> 00:47:21,280
+gaussian surface. These are the lines of space
+
+827
+00:47:21,280 --> 00:47:23,240
+that are different from each other. This is a
+
+828
+00:47:23,240 --> 00:47:27,340
+gaussian surface. And why was this time standing
+
+829
+00:47:27,340 --> 00:47:31,020
+and this time sleeping?This time the line is like
+
+830
+00:47:31,020 --> 00:47:33,980
+this. The shape that resembles it should be like
+
+831
+00:47:33,980 --> 00:47:38,060
+it. A plane. Here is a plane. A plane. She put
+
+832
+00:47:38,060 --> 00:47:40,320
+planes next to each other. Did the plane rise or
+
+833
+00:47:40,320 --> 00:47:43,100
+fall asleep? It fell asleep. Correctly or not?
+
+834
+00:47:43,360 --> 00:47:45,100
+Actually, before I say plane, there are many
+
+835
+00:47:45,100 --> 00:47:48,160
+planes and cities. They said that the surface of
+
+836
+00:47:48,160 --> 00:47:51,120
+Earth should resemble a loaded body or not. And a
+
+837
+00:47:51,120 --> 00:47:54,660
+loaded body is a part of a plane. So it should be
+
+838
+00:47:54,660 --> 00:48:00,220
+a part of a sleeping plane. Right? No, you put it
+
+839
+00:48:00,220 --> 00:48:02,960
+in a standing position. Let's say this is what
+
+840
+00:48:02,960 --> 00:48:05,720
+happened. What do you do? You put it in a standing
+
+841
+00:48:05,720 --> 00:48:08,240
+position. That's it. I don't know why this one was
+
+842
+00:48:08,240 --> 00:48:09,840
+sleeping and this one was standing. Or vice versa.
+
+843
+00:48:11,640 --> 00:48:15,120
+Yes. Look at these guys. These are girls. Do you
+
+844
+00:48:15,120 --> 00:48:17,600
+understand now? The lines of space are different,
+
+845
+00:48:17,800 --> 00:48:22,160
+girls. There is no space. This is a piece of paper
+
+846
+00:48:22,160 --> 00:48:26,940
+from my class. This is the paper. These are
+
+847
+00:48:26,940 --> 00:48:29,560
+loaded. You have to draw a line in space. Is there
+
+848
+00:48:29,560 --> 00:48:33,120
+space for you or not? From here to me. Is it
+
+849
+00:48:33,120 --> 00:48:36,540
+correct or not? Good. How many floors does an
+
+850
+00:48:36,540 --> 00:48:39,400
+astronaut have? Three. So the first thing is
+
+851
+00:48:39,400 --> 00:48:40,480
+completion. How many completions does this need?
+
+852
+00:48:40,800 --> 00:48:41,240
+Three.
+
+853
+00:48:45,840 --> 00:48:52,120
+The three. Two bases and a side floor. Base. Base
+
+854
+00:48:52,120 --> 00:48:56,170
+curved. Is it correct, girls? Correct. We come to
+
+855
+00:48:56,170 --> 00:49:01,070
+the base. The picture is like this, right? Look at
+
+856
+00:49:01,070 --> 00:49:02,970
+it and tell me if this is one of the bases or not.
+
+857
+00:49:03,250 --> 00:49:06,610
+And you are walking on it. Are you moving away or
+
+858
+00:49:06,610 --> 00:49:11,350
+getting closer to the paper? What does it mean,
+
+859
+00:49:11,610 --> 00:49:16,090
+uniform? Constant. And you are walking here. This
+
+860
+00:49:16,090 --> 00:49:18,710
+point, or this one, or this one, or this one.
+
+861
+00:49:19,010 --> 00:49:20,430
+Isn't it the same distance? And is it this
+
+862
+00:49:20,430 --> 00:49:23,630
+distance? Okay, who tells me to walk towards the
+
+863
+00:49:23,630 --> 00:49:29,120
+area here? to outside. And E means that this is
+
+864
+00:49:29,120 --> 00:49:30,180
+the area of the cube.
+
+865
+00:49:33,520 --> 00:49:38,300
+And the angle is zero. And E is constant.
+
+866
+00:49:42,550 --> 00:49:45,730
+Correct? Let's go to the base of the forehead. The
+
+867
+00:49:45,730 --> 00:49:47,530
+base of the forehead is not this line that
+
+868
+00:49:47,530 --> 00:49:49,870
+penetrates it, it is the line that I have. The
+
+869
+00:49:49,870 --> 00:49:52,610
+line that I have is on me. And this column, its
+
+870
+00:49:52,610 --> 00:49:55,690
+base is also on me. So, what does the angle mean?
+
+871
+00:50:01,510 --> 00:50:04,350
+Look, girls. It is also correct because of Arabic
+
+872
+00:50:04,350 --> 00:50:08,510
+and Chinese. Did this liquid come from the bottom
+
+873
+00:50:08,510 --> 00:50:13,390
+of the sea or not? This point and this point is
+
+874
+00:50:13,390 --> 00:50:16,110
+the same distance so what does it have? it's not
+
+875
+00:50:16,110 --> 00:50:19,450
+constant in fact, right or not? it's not constant
+
+876
+00:50:19,450 --> 00:50:24,170
+nice, it points towards the area either up or
+
+877
+00:50:24,170 --> 00:50:26,850
+sideways but how does it find it? it's not like
+
+878
+00:50:26,850 --> 00:50:28,870
+this it's like this vertically and it's like this
+
+879
+00:50:28,870 --> 00:50:30,970
+vertically so it has to be vertical, thank God,
+
+880
+00:50:31,050 --> 00:50:34,790
+even if it's rotated because it's not constant who
+
+881
+00:50:34,790 --> 00:50:39,310
+saved me? the dot product this one, can you see
+
+882
+00:50:39,310 --> 00:50:43,070
+it? Imagine the direction. Isn't this the
+
+883
+00:50:43,070 --> 00:50:46,450
+direction? This is not the angle. Go away.
+
+884
+00:50:50,030 --> 00:50:55,290
+E to the A plus E to the A. Two E to the A. Okay,
+
+885
+00:50:55,490 --> 00:51:00,230
+I have a question for you. O Hertzog, are all the
+
+886
+00:51:00,230 --> 00:51:05,450
+cargoes in Gauss? No, I only want a part of this
+
+887
+00:51:05,450 --> 00:51:10,830
+red thing. Right? Only. Let me tell you, I don't
+
+888
+00:51:10,830 --> 00:51:12,210
+want a part of everything. Should I go to the
+
+889
+00:51:12,210 --> 00:51:14,350
+density or not? And is there a difference that the
+
+890
+00:51:14,350 --> 00:51:18,910
+density is sigma? Okay, the Q and N are words that
+
+891
+00:51:18,910 --> 00:51:22,810
+are equal to sigma in A and N. Does A and N differ
+
+892
+00:51:22,810 --> 00:51:26,430
+from these? The A is the same as the A. So we
+
+893
+00:51:26,430 --> 00:51:29,510
+start with Q and N and put sigma in A. Right or
+
+894
+00:51:29,510 --> 00:51:29,590
+not?
+
+895
+00:51:33,420 --> 00:51:36,140
+this is it, and of course I play with it a little
+
+896
+00:51:36,140 --> 00:51:40,100
+bit, this is it, isn't this the part I want? isn't
+
+897
+00:51:40,100 --> 00:51:43,940
+this the part I want? I don't get it, what? it's
+
+898
+00:51:43,940 --> 00:51:47,240
+the same thing as the two roots, so QL equals
+
+899
+00:51:47,240 --> 00:51:52,520
+sigma in what? there's the answer, I got it, what
+
+900
+00:51:52,520 --> 00:51:55,560
+did he say? tell me, I reminded you weakly you,
+
+901
+00:51:56,180 --> 00:51:58,860
+tell me the last chapter solved a question on the
+
+902
+00:51:58,860 --> 00:52:03,620
+desk, And after I finish this example, I want to
+
+903
+00:52:03,620 --> 00:52:06,340
+do two tests. I put the disk at Azgula, and a
+
+904
+00:52:06,340 --> 00:52:10,320
+point came out. Right? This is Azgula's brain. And
+
+905
+00:52:10,320 --> 00:52:12,480
+there is another test. I told you that if the disk
+
+906
+00:52:12,480 --> 00:52:17,200
+was very large, I got this result. The same
+
+907
+00:52:17,200 --> 00:52:20,080
+result. If the disk is very large, does it mean
+
+908
+00:52:20,080 --> 00:52:22,680
+infinite or not infinite? I got the same answer.
+
+909
+00:52:24,120 --> 00:52:29,610
+Okay.It is clear that E does not depend on
+
+910
+00:52:29,610 --> 00:52:32,970
+dimensions. This is logical because E is big. I
+
+911
+00:52:32,970 --> 00:52:37,270
+want to go back to the book of Ola. He said, why
+
+912
+00:52:37,270 --> 00:52:40,970
+did you tell me to follow the Sunnah by choosing
+
+913
+00:52:40,970 --> 00:52:42,790
+the easiest one? I chose the easiest one, and I
+
+914
+00:52:42,790 --> 00:52:45,770
+got the answer. Then, someone came and said, I
+
+915
+00:52:45,770 --> 00:52:48,510
+have my time. Why did you choose this Sunnah? I
+
+916
+00:52:48,510 --> 00:52:50,370
+told him, because I chose the roof, didn't I? He
+
+917
+00:52:50,370 --> 00:52:54,170
+said, yes, and so on. Legs on legs, and tea next
+
+918
+00:52:54,170 --> 00:52:56,590
+to me, and coffee next to me, and I don't have
+
+919
+00:52:56,590 --> 00:52:58,330
+time for exams. I need to solve it on the basis
+
+920
+00:52:58,330 --> 00:53:02,660
+that this is a rectangle. Or secondly, what will
+
+921
+00:53:02,660 --> 00:53:04,400
+the roof of the house look like? Rectangular,
+
+922
+00:53:04,400 --> 00:53:06,280
+rectangular, rectangular, rectangular,
+
+923
+00:53:06,440 --> 00:53:07,140
+rectangular, rectangular, rectangular,
+
+924
+00:53:07,140 --> 00:53:07,600
+rectangular, rectangular, rectangular,
+
+925
+00:53:07,600 --> 00:53:09,960
+rectangular, rectangular, rectangular,
+
+926
+00:53:09,960 --> 00:53:10,000
+rectangular, rectangular, rectangular,
+
+927
+00:53:10,500 --> 00:53:13,160
+rectangular, rectangular, rectangular,
+
+928
+00:53:15,240 --> 00:53:16,400
+rectangular, rectangular, rectangular,
+
+929
+00:53:16,400 --> 00:53:16,620
+rectangular, rectangular, rectangular,
+
+930
+00:53:16,620 --> 00:53:16,980
+rectangular, rectangular, rectangular,
+
+931
+00:53:16,980 --> 00:53:17,620
+rectangular, rectangular, rectangular,
+
+932
+00:53:18,380 --> 00:53:19,780
+rectangular, rectangular, rectangular,
+
+933
+00:53:19,780 --> 00:53:19,820
+rectangular, rectangular, rectangular,
+
+934
+00:53:19,820 --> 00:53:19,840
+rectangular, rectangular, rectangular,
+
+935
+00:53:19,840 --> 00:53:19,860
+rectangular, rectangular, rectangular,
+
+936
+00:53:19,860 --> 00:53:20,280
+rectangular, rectangular, rectangular,
+
+937
+00:53:20,960 --> 00:53:22,680
+rectangular,
+
+938
+00:53:29,790 --> 00:53:32,370
+How did it go to the area? It went down, and the E
+
+939
+00:53:32,370 --> 00:53:34,850
+went up, and the one above it went down one by one
+
+940
+00:53:34,850 --> 00:53:39,230
+from the six. It stayed two. Okay, but what about
+
+941
+00:53:39,230 --> 00:53:43,650
+this one? What did this area look like to you? And
+
+942
+00:53:43,650 --> 00:53:45,610
+the angle is zero, so it's E times E, but be
+
+943
+00:53:45,610 --> 00:53:47,990
+careful, this E is not under the disc, it's under
+
+944
+00:53:47,990 --> 00:53:50,390
+the rectangle. Okay, okay. Okay, and what about
+
+945
+00:53:50,390 --> 00:53:54,570
+Bali? The same process. Okay, let's look at Qn. I
+
+946
+00:53:54,570 --> 00:53:57,410
+told him, in this case, Qn, my dear, is a part of
+
+947
+00:53:57,410 --> 00:54:01,730
+the paper equal to the rectangle. Right? If this
+
+948
+00:54:01,730 --> 00:54:03,550
+thing came directly to me, it would be a line.
+
+949
+00:54:03,890 --> 00:54:06,110
+What kind of paper is it? Is it rectangular or
+
+950
+00:54:06,110 --> 00:54:09,470
+not? So the Q in equals sigma in the area of the
+
+951
+00:54:09,470 --> 00:54:12,390
+rectangle, and this is rectangular, and this is
+
+952
+00:54:12,390 --> 00:54:16,710
+rectangular. So it became sigma in what? Get out
+
+953
+00:54:16,710 --> 00:54:21,480
+of there. Be careful what happens to you. Go to
+
+954
+00:54:21,480 --> 00:54:25,660
+our level. Three levels. Right or wrong? Right.
+
+955
+00:54:26,140 --> 00:54:32,160
+The last thing, just to say something. A long time
+
+956
+00:54:32,160 --> 00:54:35,600
+ago, there was a virus that we did not catch.
+
+957
+00:54:36,560 --> 00:54:39,500
+There was something like that. Did you see this
+
+958
+00:54:39,500 --> 00:54:43,970
+circle? What is this? He praised us and this is a
+
+959
+00:54:43,970 --> 00:54:45,470
+sign that we should follow him. He told me, what
+
+960
+00:54:45,470 --> 00:54:47,450
+is the magnifier? He told me that the magnifier is
+
+961
+00:54:47,450 --> 00:54:49,910
+two planes that are bigger than each other. One
+
+962
+00:54:49,910 --> 00:54:52,610
+positive and one negative. And these planes are
+
+963
+00:54:52,610 --> 00:54:55,070
+considered to be very big. He told me, if you want
+
+964
+00:54:55,070 --> 00:54:57,370
+to tell me which one is bigger than the two
+
+965
+00:54:57,370 --> 00:54:59,070
+planes, I will tell you that I don't want to bore
+
+966
+00:54:59,070 --> 00:55:02,890
+you. For each plane on one, can I guess the answer
+
+967
+00:55:02,890 --> 00:55:05,820
+is this one or not? Isn't it correct? Isn't this
+
+968
+00:55:05,820 --> 00:55:08,020
+the answer which is sigma over 2 epsilon naught
+
+969
+00:55:08,020 --> 00:55:09,660
+which we just got? Isn't it the answer which is
+
+970
+00:55:09,660 --> 00:55:12,780
+sigma over 2 epsilon naught which we just got?
+
+971
+00:55:12,780 --> 00:55:15,820
+Yes. This is for every big number, right? Yes. He
+
+972
+00:55:15,820 --> 00:55:17,800
+said to me, I want to have two numbers. I will
+
+973
+00:55:17,800 --> 00:55:20,000
+tell you to stretch the space which comes from two
+
+974
+00:55:20,000 --> 00:55:22,460
+spaces. From this one and from this one. Is it
+
+975
+00:55:22,460 --> 00:55:24,680
+correct or not? Correct. Does it mean to add or
+
+976
+00:55:24,680 --> 00:55:26,800
+not to add? Correct. But your answer is to add
+
+977
+00:55:26,800 --> 00:55:29,400
+vectors. Correct. Good. He said to me, this is the
+
+978
+00:55:29,400 --> 00:55:32,860
+red one, the first one. The lines of space come
+
+979
+00:55:32,860 --> 00:55:35,880
+out of the wave. She came out. Okay, I want to
+
+980
+00:55:35,880 --> 00:55:40,540
+bring blue. The lines of space enter. Right? Come
+
+981
+00:55:40,540 --> 00:55:45,440
+on. Come to this one here. But with each other,
+
+982
+00:55:45,480 --> 00:55:48,400
+it's the opposite again. Guys, the two equalities
+
+983
+00:55:48,400 --> 00:55:51,260
+are opposite again. Zero. And here it's the
+
+984
+00:55:51,260 --> 00:55:52,380
+opposite again. See, this blue is going like this.
+
+985
+00:55:52,920 --> 00:55:55,780
+And the red is like this. Also zero. Okay, look
+
+986
+00:55:55,780 --> 00:55:57,040
+here. This one is like this and this one is like
+
+987
+00:55:57,040 --> 00:56:00,170
+this. The same direction. So inside I want to add
+
+988
+00:56:00,170 --> 00:56:03,570
+sigma over 2 epsilon note and sigma over 2 epsilon
+
+989
+00:56:03,570 --> 00:56:08,010
+note, sigma over epsilon note. So in this case,
+
+990
+00:56:08,450 --> 00:56:11,450
+these people got together and said in the end, I
+
+991
+00:56:11,450 --> 00:56:14,890
+got the answer like this. Here sigma over epsilon
+
+992
+00:56:14,890 --> 00:56:18,850
+note, here zero and here zero. Of course, I'm
+
+993
+00:56:18,850 --> 00:56:21,230
+going to put this in because in chapter 4 I missed
+
+994
+00:56:21,230 --> 00:56:25,050
+it. I will remind you of it and repeat it. Okay
+
+995
+00:56:25,050 --> 00:56:27,930
+girls? God bless you.
+
diff --git a/PL9fwy3NUQKwZzXsCLffozucGP33XWqvBP/LUaz4P8Wi3Y_raw.json b/PL9fwy3NUQKwZzXsCLffozucGP33XWqvBP/LUaz4P8Wi3Y_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..3b0823e3ff62cfadacdefff623168460c973e6f0
--- /dev/null
+++ b/PL9fwy3NUQKwZzXsCLffozucGP33XWqvBP/LUaz4P8Wi3Y_raw.json
@@ -0,0 +1 @@
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This is 2 and this is 5. This is I maximum. When I get I maximum, I say after a long time, when the file becomes silk. 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What is the explanation here? Do you understand what I am doing? And T is equal to zero. How does the file work? Open circuit. 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How did he make the file? He told him to get this file and put it in the place of the switch. What is the relationship between the four eights that these people lived in? Balance. With the first four, they multiplied. Can you bring me a equivalent book? The eight and the four are thirty-two to sixteen or not? 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This is R equivalent. Can you tell me that I1 is I equivalent and I equivalent is equal to 10 over R equivalent or not? We can calculate it. This is 6.7. 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So I want to merge all the ideas that are networked and repeated in order to work on Kirchhoff? They don't work on Kirchhoff. So Kirchhoff remains Kirchhoff like salt in circles. Okay. Our topic now is energy. In magnetic field. Did you notice the name? 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So does it have a job or does it not have a job? It has a job. It's like a capacitor. 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Right? I want this information only. Did you go to the fire or not? Of course, when you go to the fire, you will take it as well. But when you go to the fire, you will not take it. But we know that there is a worker in the world and he has a job. He stores energy. What is the unit of energy? Energy of movement. What is the unit of energy? Energy of position. Energy of movement. Energy of position. Energy of position. Energy of position. Energy of position. Energy of position. Energy of position. Energy of position. Energy of position. Energy of position. Energy of position. Energy of position. Energy of position. Energy of position. Energy of position. Energy of position. Energy of position. Energy of position. Energy of position. Energy of position. Energy of position. Energy of position. Energy of position. Energy of position. Energy of position. Energy of position. Energy of position. Energy of position. Energy of position. Energy of position. Energy of position. 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Good. He said to me, enlarge it. Get a mirror and enlarge it on each term. I in epsilon, I in V, what is this? Power. Power. What is the profit in R? Power. Yes, power. I will get a fee plus a thousand, what do you say? We say that when you have quantities and they have a common denominator or equal, they must be of the same gender. Can you say power plus power plus power? 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So does the third term have to be power or not? Okay, until now, this, this, this. Is this power for whom? Battery. Is this power for whom? What is this now? So is this the power of the file? Definitely or not? Definitely. 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Yes, because it is DU over DT. So he said that this is the power of the battery and this is the power of the resistance. So he said that this is definitely the power of the file because power plus power plus power. 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Tell me, I waited for him for a long time, and I made the file in Cilic. But in the end, did it store energy or not? It stored energy. Yes, it stores energy. Any square in R, and Cilic is R.", "tokens": [2278, 5809, 3209, 13, 5115, 385, 11, 286, 15240, 337, 796, 337, 257, 938, 565, 11, 293, 286, 1027, 264, 3991, 294, 383, 388, 299, 13, 583, 294, 264, 917, 11, 630, 309, 3531, 2281, 420, 406, 30, 467, 12187, 2281, 13, 1079, 11, 309, 9512, 2281, 13, 2639, 3732, 294, 497, 11, 293, 383, 388, 299, 307, 497, 13], "avg_logprob": -0.5911885324071665, "compression_ratio": 1.4452054794520548, "no_speech_prob": 3.993511199951172e-06, "words": [{"start": 1265.61, "end": 1266.17, "word": "The", "probability": 0.0804443359375}, {"start": 1266.17, "end": 1266.53, "word": " battery", "probability": 0.47021484375}, {"start": 1266.53, "end": 1266.81, "word": " network.", "probability": 0.14599609375}, {"start": 1267.31, "end": 1267.51, "word": " Tell", "probability": 0.295166015625}, {"start": 1267.51, "end": 1267.69, "word": " me,", "probability": 0.93603515625}, {"start": 1267.85, "end": 1267.85, "word": " I", "probability": 0.58056640625}, {"start": 1267.85, "end": 1268.41, "word": " waited", "probability": 0.57275390625}, {"start": 1268.41, "end": 1268.81, "word": " for", "probability": 0.6962890625}, {"start": 1268.81, "end": 1269.31, "word": " him", "probability": 0.289794921875}, {"start": 1269.31, "end": 1269.93, "word": " for", "probability": 0.37548828125}, {"start": 1269.93, "end": 1270.37, "word": " a", "probability": 0.84033203125}, {"start": 1270.37, "end": 1271.03, "word": " long", "probability": 0.89599609375}, {"start": 1271.03, "end": 1271.35, "word": " time,", "probability": 0.8720703125}, {"start": 1271.59, "end": 1271.97, "word": " and", "probability": 0.7294921875}, {"start": 1271.97, "end": 1272.43, "word": " I", "probability": 0.5458984375}, {"start": 1272.43, "end": 1272.43, "word": " made", "probability": 0.67626953125}, {"start": 1272.43, "end": 1272.61, "word": " the", "probability": 0.65771484375}, {"start": 1272.61, "end": 1272.99, "word": " file", "probability": 0.89892578125}, {"start": 1272.99, "end": 1273.23, "word": " in", "probability": 0.505859375}, {"start": 1273.23, "end": 1273.63, "word": " Cilic.", "probability": 0.3443806966145833}, {"start": 1273.69, "end": 1273.91, "word": " But", "probability": 0.80810546875}, {"start": 1273.91, "end": 1274.03, "word": " in", "probability": 0.399658203125}, {"start": 1274.03, "end": 1274.11, "word": " the", "probability": 0.9267578125}, {"start": 1274.11, "end": 1274.23, "word": " end,", "probability": 0.92236328125}, {"start": 1274.35, "end": 1274.35, "word": " did", "probability": 0.404541015625}, {"start": 1274.35, "end": 1274.35, "word": " it", "probability": 0.5712890625}, {"start": 1274.35, "end": 1274.49, "word": " store", "probability": 0.580078125}, {"start": 1274.49, "end": 1274.77, "word": " energy", "probability": 0.5693359375}, {"start": 1274.77, "end": 1274.95, "word": " or", "probability": 0.7880859375}, {"start": 1274.95, "end": 1275.11, "word": " not?", "probability": 0.89599609375}, {"start": 1275.41, "end": 1275.75, "word": " It", "probability": 0.5205078125}, {"start": 1275.75, "end": 1276.09, "word": " stored", "probability": 0.7509765625}, {"start": 1276.09, "end": 1276.63, "word": " energy.", "probability": 0.86328125}, {"start": 1278.59, "end": 1279.15, "word": " Yes,", "probability": 0.298828125}, {"start": 1279.45, "end": 1279.57, "word": " it", "probability": 0.7158203125}, {"start": 1279.57, "end": 1279.83, "word": " stores", "probability": 0.736328125}, {"start": 1279.83, "end": 1280.19, "word": " energy.", "probability": 0.91064453125}, {"start": 1280.25, "end": 1280.39, "word": " Any", "probability": 0.806640625}, {"start": 1280.39, "end": 1280.57, "word": " square", "probability": 0.77294921875}, {"start": 1280.57, "end": 1280.73, "word": " in", "probability": 0.7998046875}, {"start": 1280.73, "end": 1281.15, "word": " R,", "probability": 0.70068359375}, {"start": 1281.49, "end": 1281.61, "word": " and", "probability": 0.45361328125}, {"start": 1281.61, "end": 1281.89, "word": " Cilic", "probability": 0.9080403645833334}, {"start": 1281.89, "end": 1282.09, "word": " is", "probability": 0.84130859375}, {"start": 1282.09, "end": 1282.27, "word": " R.", "probability": 0.09747314453125}], "temperature": 1.0}, {"id": 55, "seek": 130626, "start": 1283.92, "end": 1306.26, "text": " Yes, it stores energy. But why did the file contain a file without silicon? The file generates a magnetic field that is valuable. It's like a solenoid. But the silicon in the magnetic field is almost negligible. That's why it's called heliophilic. As for resistors, I consider them silicon. But it has another function. It stores energy. Okay, what if this was a lamp?", "tokens": [1079, 11, 309, 9512, 2281, 13, 583, 983, 630, 264, 3991, 5304, 257, 3991, 1553, 22848, 30, 440, 3991, 23815, 257, 12688, 2519, 300, 307, 8263, 13, 467, 311, 411, 257, 1404, 5808, 327, 13, 583, 264, 22848, 294, 264, 12688, 2519, 307, 1920, 32570, 964, 13, 663, 311, 983, 309, 311, 1219, 801, 72, 5317, 388, 299, 13, 1018, 337, 4597, 830, 11, 286, 1949, 552, 22848, 13, 583, 309, 575, 1071, 2445, 13, 467, 9512, 2281, 13, 1033, 11, 437, 498, 341, 390, 257, 12684, 30], "avg_logprob": -0.5958567147844294, "compression_ratio": 1.654708520179372, "no_speech_prob": 4.172325134277344e-07, "words": [{"start": 1283.92, "end": 1284.2, "word": " Yes,", "probability": 0.2003173828125}, {"start": 1284.32, "end": 1284.42, "word": " it", "probability": 0.36328125}, {"start": 1284.42, "end": 1284.56, "word": " stores", "probability": 0.4111328125}, {"start": 1284.56, "end": 1284.66, "word": " energy.", "probability": 0.443359375}, {"start": 1284.7, "end": 1284.8, 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When I turn it on, does the original light up or not? Does the original light up? Does the file exist that lights up immediately? No, it remains a light bulb. Of course, it remains a light bulb, which means that there is energy. Where does the energy come from? 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This is what I want to prove. Consider once again the RL circuit shown with the switch in the throne to point 2 after being in position 1 for a long time. So I had number 1 for the switch for a long time. This means that I made sure that everything was fine. I had a steady state condition, as we call it. 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Yes, I thought you didn't know. What does it count? Energy. But let me tell you that its unit is kilowatts times R. And this unit of energy counts Hades. 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The electrician in the bedroom is 4x4 meters. We call him Ton. Okay? Approximately 1,000 watts. 1,000 watts is one kilowatt. 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So you have to calculate how much this is. I tell him if this is the same energy that was stored in the file, I have to prove it. Right or not? Good. I tell him this is equivalent to how you make any spring in the ground or not. 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I told him to make it complete. He said yes. I said yes. He said yes. I said yes. He said yes. I said yes. He said yes. I said yes. He said yes. I said yes. He said yes. He said yes. I said yes. He said yes. He said yes. He said yes. He said yes. He said yes. He said yes. He said yes. He said yes. He said yes. He said yes. He said yes. He said yes. He said yes. He said yes. He said yes. He said yes. He said yes. He said yes. He said yes. He said yes. He said yes. He said yes. He said yes. He said yes. He said yes. He said yes. He said yes. He said yes. He said yes. He said yes. He said yes. He said yes. He said yes. He said yes. He said yes. He said yes. He said yes. He said yes. 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Let's see the meaning and go back to your question. What are our applications? He told me this is a circle. He told me this is a full capacitor. If you put a full capacitor between two wires, what happens? It diverts. It diverts. Well done. Isn't that what I told you about those files? Yes. Yes. I want to shut down the computer. What happens to the capacitor? 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After closing the switch, the charge will flow through the inductor. 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Write it down and tell him. If it is one of the two, what does it mean? 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If it has to be 2 and not 1 or 2, it's not a problem. I say it randomly. Can I write like this or not? Even if one is zero, it needs a correct equation. If this is zero, this is equal to this. If this is zero, this is equal to this. 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We don't know if it's invalid or not. We don't know if it's invalid or not. We don't know if it's invalid or not. We don't know if it's invalid or not. We don't know if it's invalid or not. 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Let's see if it's an O or not. It's a comparison, it's a second. It's a time, one over two. It's a hesitation. Is it good or not? Let's try. Hadi said to me, you need one over thousand, because it's thousand in the equation. It's equal. What's its unit, girls? And the C is a square, right? Okay?", "tokens": [1033, 11, 665, 13, 961, 311, 536, 498, 309, 311, 364, 422, 420, 406, 13, 467, 311, 257, 9660, 11, 309, 311, 257, 1150, 13, 467, 311, 257, 565, 11, 472, 670, 732, 13, 467, 311, 257, 36125, 13, 1119, 309, 665, 420, 406, 30, 961, 311, 853, 13, 18908, 848, 281, 385, 11, 291, 643, 472, 670, 4714, 11, 570, 309, 311, 4714, 294, 264, 5367, 13, 467, 311, 2681, 13, 708, 311, 1080, 4985, 11, 4519, 30, 400, 264, 383, 307, 257, 3732, 11, 558, 30, 1033, 30], "avg_logprob": -0.7135988788290338, "compression_ratio": 1.617801047120419, "no_speech_prob": 2.6881694793701172e-05, "words": [{"start": 2142.4, "end": 2142.88, "word": " Okay,", "probability": 0.0816650390625}, {"start": 2143.32, "end": 2143.32, "word": " good.", "probability": 0.177734375}, {"start": 2143.9, "end": 2144.38, "word": " Let's", "probability": 0.615234375}, {"start": 2144.38, "end": 2144.74, "word": " see", "probability": 0.548828125}, {"start": 2144.74, "end": 2144.92, "word": " if", "probability": 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He said volt second divided by ampere. So this is one over volt second divided by ampere. Take out the ampere above you. The vacuum is Q divided by V. So it is Coulomb divided by volt. Coulomb divided by volt. Ampere and Coulomb don't mix together? Ampere is Coulomb divided by second or not? 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So this is omega growing up. Omega growing up. So it means that this .. where did it go? I wrote it. I got it. Column got stuck. Who corrected it? I got it. Okay? And where did I write the excerpt?", "tokens": [40332, 365, 5962, 1437, 1314, 293, 7738, 365, 7738, 1437, 1314, 293, 472, 295, 552, 994, 380, 1852, 493, 13, 407, 341, 307, 10498, 4194, 493, 13, 27645, 4194, 493, 13, 407, 309, 1355, 300, 341, 4386, 689, 630, 309, 352, 30, 286, 4114, 309, 13, 286, 658, 309, 13, 4004, 16449, 658, 5541, 13, 2102, 31687, 309, 30, 286, 658, 309, 13, 1033, 30, 400, 689, 630, 286, 2464, 264, 454, 1776, 662, 30], "avg_logprob": -0.7010690867900848, "compression_ratio": 1.6647398843930636, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2197.04, "end": 2197.56, "word": " Volt", "probability": 0.1981201171875}, {"start": 2197.56, "end": 2197.76, "word": " with", "probability": 0.38720703125}, {"start": 2197.76, "end": 2198.2, "word": " volt", "probability": 0.6220703125}, {"start": 2198.2, "end": 2198.58, "word": " went", "probability": 0.2391357421875}, {"start": 2198.58, "end": 2199.0, "word": " away", "probability": 0.37890625}, {"start": 2199.0, 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Yes, I didn't write it. Yes, here it is, sheikh. Instead of one over L C, do I put omega R B or not? And omega equals one over L C under the root. What do you want? M? M? Tell me. Good question, what do you want from it? Did you find this frequency or not frequency? 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And why do you want the F and I don't want the Omega? Because the F and the Omega are related to each other. They are both in the F. Right? Yes. Because the frequency doesn't have two symbols, it became F and I said Omega. Right? In the F because we .. Yes, the Omega is better than one and another. Okay? Is there anything else? Can I put M? 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No. So I know it by heart. It indicates the frequency. Because the unit says the frequency for sure. If I say the F of the frequency, I say Amin. I say it doesn't ring, doesn't ring. But you bring it to me, you tell me the time, T. Does it work? No. So do you know why I chose omega? Because it is one over second. Because in hertz, frequency, you put what you said correctly. No problem. 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Does anyone know the answer? Yes, does anyone know the answer? No, she has a general rule. You didn't get it at the right time. Eight. 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twice or not? Come on girls, is there anyone who doesn't know how to write cosine?", "tokens": [13342, 29458, 510, 11, 360, 286, 362, 281, 2464, 309, 6091, 420, 406, 30, 2492, 322, 4519, 11, 307, 456, 2878, 567, 1177, 380, 458, 577, 281, 2464, 23565, 30], "avg_logprob": -0.6008064554583642, "compression_ratio": 1.1923076923076923, "no_speech_prob": 0.0, "words": [{"start": 2469.7899999999995, "end": 2470.0699999999997, "word": "To", "probability": 0.27880859375}, {"start": 2470.0699999999997, "end": 2470.35, "word": " compensate", "probability": 0.1199951171875}, {"start": 2470.35, "end": 2470.57, "word": " here,", "probability": 0.4580078125}, {"start": 2470.71, "end": 2470.71, "word": " do", "probability": 0.2841796875}, {"start": 2470.71, "end": 2470.81, "word": " I", "probability": 0.93994140625}, {"start": 2470.81, "end": 2470.81, "word": " have", "probability": 0.61279296875}, {"start": 2470.81, "end": 2470.89, "word": " to", "probability": 0.97412109375}, {"start": 2470.89, "end": 2471.05, 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It becomes Omega square Q maximum cosine Omega T. And instead of this one, I swear it turned out to be correct. So this is its solution, cosine. And if its solution is cosine, you told me that the function that goes and comes is cosine, not cosine. Cosine, I swear it worked in math. Cosine turns out to be something. Q, this is Q. It means Q turns out to be something. 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Look at it, this is square x over dt square. This here becomes plus k over n into x equals zero. This is omega square. Look at this and this. This is x cube.", "tokens": [12089, 259, 921, 3548, 289, 514, 3175, 350, 87, 293, 341, 307, 275, 67, 3732, 2031, 670, 36423, 3732, 13, 2053, 412, 309, 11, 341, 307, 3732, 2031, 670, 36423, 3732, 13, 639, 510, 3643, 1804, 350, 670, 297, 666, 2031, 6915, 4018, 13, 639, 307, 10498, 3732, 13, 2053, 412, 341, 293, 341, 13, 639, 307, 2031, 13728, 13], "avg_logprob": -0.6121926034083132, "compression_ratio": 1.7153846153846153, "no_speech_prob": 7.152557373046875e-07, "words": [{"start": 2649.2400000000002, "end": 2649.88, "word": " Machinazombarak", "probability": 0.3577728271484375}, {"start": 2649.88, "end": 2650.16, "word": " minus", "probability": 0.1556396484375}, {"start": 2650.16, "end": 2650.78, "word": " kx", "probability": 0.52099609375}, {"start": 2650.78, "end": 2651.8, "word": " and", "probability": 0.441162109375}, {"start": 2651.8, "end": 2652.16, "word": " this", "probability": 0.740234375}, {"start": 2652.16, "end": 2652.26, "word": " is", "probability": 0.6474609375}, {"start": 2652.26, "end": 2653.0, "word": " md", "probability": 0.39581298828125}, {"start": 2653.0, "end": 2653.42, "word": " square", "probability": 0.1640625}, {"start": 2653.42, "end": 2654.04, "word": " x", "probability": 0.93896484375}, {"start": 2654.04, "end": 2654.28, "word": " over", "probability": 0.330078125}, {"start": 2654.28, "end": 2654.58, "word": " dt", "probability": 0.95068359375}, {"start": 2654.58, "end": 2655.18, "word": " square.", "probability": 0.7333984375}, {"start": 2656.12, "end": 2656.7, "word": " Look", "probability": 0.3857421875}, {"start": 2656.7, "end": 2656.94, "word": " at", "probability": 0.85302734375}, {"start": 2656.94, "end": 2657.06, "word": " it,", "probability": 0.5849609375}, {"start": 2657.26, "end": 2657.48, "word": " this", "probability": 0.57421875}, {"start": 2657.48, "end": 2657.62, "word": " is", "probability": 0.9150390625}, {"start": 2657.62, "end": 2657.94, "word": " square", "probability": 0.58544921875}, {"start": 2657.94, "end": 2658.56, "word": " x", "probability": 0.92578125}, {"start": 2658.56, "end": 2659.26, "word": " over", "probability": 0.82177734375}, {"start": 2659.26, "end": 2659.7, "word": " dt", "probability": 0.931640625}, {"start": 2659.7, "end": 2660.24, "word": " square.", "probability": 0.83056640625}, {"start": 2660.32, "end": 2660.64, "word": " This", "probability": 0.116943359375}, {"start": 2660.64, "end": 2661.2, "word": " here", "probability": 0.26318359375}, {"start": 2661.2, "end": 2661.76, "word": " becomes", "probability": 0.431640625}, {"start": 2661.76, "end": 2662.08, "word": " plus", "probability": 0.755859375}, {"start": 2662.08, "end": 2662.58, "word": " k", "probability": 0.94091796875}, {"start": 2662.58, "end": 2662.88, "word": " over", "probability": 0.57958984375}, {"start": 2662.88, "end": 2663.32, "word": " n", "probability": 0.5986328125}, {"start": 2663.32, "end": 2663.86, "word": " into", "probability": 0.355712890625}, {"start": 2663.86, "end": 2664.18, "word": " x", "probability": 0.9912109375}, {"start": 2664.18, "end": 2664.58, "word": " equals", "probability": 0.55810546875}, {"start": 2664.58, "end": 2664.92, "word": " zero.", "probability": 0.5400390625}, {"start": 2665.9, "end": 2666.22, "word": " This", "probability": 0.8466796875}, {"start": 2666.22, "end": 2666.32, "word": " is", "probability": 0.904296875}, {"start": 2666.32, "end": 2666.52, "word": " omega", "probability": 0.60546875}, {"start": 2666.52, "end": 2667.04, "word": " square.", "probability": 0.7919921875}, {"start": 2667.56, "end": 2667.7, "word": " Look", "probability": 0.55615234375}, {"start": 2667.7, "end": 2667.88, "word": " at", "probability": 0.86474609375}, {"start": 2667.88, "end": 2668.04, "word": " this", "probability": 0.7119140625}, {"start": 2668.04, "end": 2668.14, "word": " and", "probability": 0.853515625}, {"start": 2668.14, "end": 2668.34, "word": " this.", "probability": 0.8994140625}, {"start": 2669.84, "end": 2670.48, "word": " This", "probability": 0.50537109375}, {"start": 2670.48, "end": 2670.56, "word": " is", "probability": 0.92724609375}, {"start": 2670.56, "end": 2670.8, "word": " x", "probability": 0.8603515625}, {"start": 2670.8, "end": 2671.1, "word": " cube.", "probability": 0.388671875}], "temperature": 1.0}, {"id": 109, "seek": 269084, "start": 2672.46, "end": 2690.84, "text": " Am I right or not? The meaning of Zimbabwe is going towards Sin and Cosine. Because this is its solution. Sin and Cosine is also a solution like this. We are back. Right or not? So from here comes the joy of mathematics. How our Lord created things in harmony in all matters.", "tokens": [2012, 286, 558, 420, 406, 30, 440, 3620, 295, 1176, 17306, 455, 826, 307, 516, 281, 4151, 7800, 82, 11187, 293, 15855, 533, 13, 1436, 341, 307, 1080, 3827, 13, 11187, 293, 15855, 533, 307, 611, 257, 3827, 411, 341, 13, 492, 366, 646, 13, 1779, 420, 406, 30, 407, 490, 510, 1487, 264, 6258, 295, 18666, 13, 1012, 527, 3257, 2942, 721, 294, 19410, 294, 439, 7001, 13], "avg_logprob": -0.5785714081355504, "compression_ratio": 1.5, "no_speech_prob": 8.165836334228516e-06, "words": [{"start": 2672.46, "end": 2672.64, "word": " Am", "probability": 0.2298583984375}, {"start": 2672.64, "end": 2672.72, "word": " I", "probability": 0.9130859375}, {"start": 2672.72, "end": 2672.88, "word": " right", "probability": 0.75439453125}, {"start": 2672.88, "end": 2673.2, "word": " or", "probability": 0.599609375}, {"start": 2673.2, "end": 2673.2, "word": " not?", "probability": 0.78564453125}, {"start": 2673.84, "end": 2673.98, "word": " 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"end": 2710.55, "text": " He said, I got this Q and I got it. I said, I want I. He said, this I is easy. This is I. So, what is I maximum? I said, when you put Q maximum in omega, right or wrong, what is the unit of Q maximum? Column. And omega? Column over second.", "tokens": [634, 848, 11, 286, 658, 341, 1249, 293, 286, 658, 309, 13, 286, 848, 11, 286, 528, 286, 13, 634, 848, 11, 341, 286, 307, 1858, 13, 639, 307, 286, 13, 407, 11, 437, 307, 286, 6674, 30, 286, 848, 11, 562, 291, 829, 1249, 6674, 294, 10498, 11, 558, 420, 2085, 11, 437, 307, 264, 4985, 295, 1249, 6674, 30, 4004, 16449, 13, 400, 10498, 30, 4004, 16449, 670, 1150, 13], "avg_logprob": -0.5008561643835616, "compression_ratio": 1.6, "no_speech_prob": 2.9206275939941406e-06, "words": [{"start": 2692.91, "end": 2693.13, "word": " He", "probability": 0.1551513671875}, {"start": 2693.13, "end": 2693.21, "word": " said,", "probability": 0.461669921875}, {"start": 2693.29, "end": 2693.37, "word": " I", "probability": 0.37109375}, {"start": 2693.37, "end": 2693.61, "word": " got", "probability": 0.31640625}, {"start": 2693.61, "end": 2693.85, "word": " this", "probability": 0.7919921875}, {"start": 2693.85, "end": 2694.03, "word": " Q", "probability": 0.3662109375}, 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2741.84, "text": " It's not a flow, it's I maximum. And usually the thing next to sine and cosine must be maximum. Because the most important value for sine and cosine is one. It's the most important value. So, the correctness must be maximum. They call it amplitude, the hour. Have you ever heard of something called the hour? The hour. The hour is the longest distance. Which is next to sine and cosine. The longest distance. Okay.", "tokens": [467, 311, 406, 257, 3095, 11, 309, 311, 286, 6674, 13, 400, 2673, 264, 551, 958, 281, 18609, 293, 23565, 1633, 312, 6674, 13, 1436, 264, 881, 1021, 2158, 337, 18609, 293, 23565, 307, 472, 13, 467, 311, 264, 881, 1021, 2158, 13, 407, 11, 264, 3006, 1287, 1633, 312, 6674, 13, 814, 818, 309, 27433, 11, 264, 1773, 13, 3560, 291, 1562, 2198, 295, 746, 1219, 264, 1773, 30, 440, 1773, 13, 440, 1773, 307, 264, 15438, 4560, 13, 3013, 307, 958, 281, 18609, 293, 23565, 13, 440, 15438, 4560, 13, 1033, 13], "avg_logprob": -0.5476973897532413, "compression_ratio": 1.9036697247706422, "no_speech_prob": 4.291534423828125e-06, "words": [{"start": 2713.4, "end": 2713.66, "word": " It's", "probability": 0.25}, {"start": 2713.66, "end": 2713.76, "word": " not", "probability": 0.382080078125}, {"start": 2713.76, "end": 2713.96, "word": " a", "probability": 0.537109375}, {"start": 2713.96, "end": 2714.28, "word": " flow,", "probability": 0.0634765625}, {"start": 2714.36, "end": 2715.02, 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He said, let's look at something specific.", "tokens": [467, 2067, 380, 472, 3353, 293, 472, 3671, 412, 700, 13, 1133, 291, 9943, 309, 11, 309, 486, 1813, 3671, 293, 3353, 13, 961, 311, 536, 294, 2607, 13, 1133, 264, 2190, 307, 4289, 5310, 484, 295, 5574, 365, 264, 4602, 11, 300, 307, 11, 562, 264, 4602, 307, 6674, 11, 264, 2190, 307, 4018, 13, 400, 562, 264, 4602, 307, 4018, 11, 264, 2190, 307, 6674, 13, 12024, 13, 634, 848, 11, 718, 311, 574, 412, 746, 2685, 13], "avg_logprob": -0.4070216049382716, "compression_ratio": 1.7121951219512195, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 2805.96, "end": 2806.14, "word": " It", "probability": 0.053466796875}, {"start": 2806.14, "end": 2806.36, "word": " wasn't", "probability": 0.62030029296875}, {"start": 2806.36, "end": 2806.8, "word": " one", "probability": 0.18994140625}, {"start": 2806.8, "end": 2807.52, "word": " positive", "probability": 0.6005859375}, {"start": 2807.52, "end": 2807.8, "word": " and", "probability": 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I told him let's try it. Instead of Q, put Q maximum cosine omega T. And instead of I, put I maximum sine omega T. Am I right or not? We exchanged. Hit your brain a little bit. 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The red is followed by L and the blue is followed by C. When the red is zero, the blue is maximum. When the red is maximum, the blue is zero. Right or not? And so on. Yes. What did I just say? One more time. How many people specialize in computers or electricity?", "tokens": [639, 307, 641, 6316, 13, 440, 2182, 307, 6263, 538, 441, 293, 264, 3344, 307, 6263, 538, 383, 13, 1133, 264, 2182, 307, 4018, 11, 264, 3344, 307, 6674, 13, 1133, 264, 2182, 307, 6674, 11, 264, 3344, 307, 4018, 13, 1779, 420, 406, 30, 400, 370, 322, 13, 1079, 13, 708, 630, 286, 445, 584, 30, 1485, 544, 565, 13, 1012, 867, 561, 37938, 294, 10807, 420, 10356, 30], "avg_logprob": -0.4132922518421227, "compression_ratio": 1.6033519553072626, "no_speech_prob": 2.086162567138672e-06, "words": [{"start": 2925.85, "end": 2926.11, "word": " This", "probability": 0.194580078125}, {"start": 2926.11, "end": 2926.15, "word": " is", "probability": 0.9052734375}, {"start": 2926.15, "end": 2926.69, "word": " their", "probability": 0.202880859375}, {"start": 2926.69, "end": 2926.69, "word": " drawing.", "probability": 0.68994140625}, {"start": 2927.69, "end": 2927.85, "word": " The", "probability": 0.57373046875}, {"start": 2927.85, 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Because this is the basis of all communications science. What is the C of the reception circle? It depends on the letter C. You know, when you change from station to station, from the island to Arabia to I don't know what, what do you do? 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When you say you found a new station, or the island station, or the car changed, what do you look for? Its frequency. 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So the LC applications are all connected to the phone. The phone is a simple receiver. We carry it in our pocket. Because it receives the wave of the mobile phone. And there is a wave for the Arab country. For the homeland. There is a wave for the homeland. Each person has his own wave. Therefore, each person's SIM card that you put depends on your receiver. It changes. Okay?", "tokens": [8297, 30, 407, 264, 42198, 5821, 366, 439, 4582, 281, 264, 2593, 13, 440, 2593, 307, 257, 2199, 20086, 13, 492, 3985, 309, 294, 527, 8963, 13, 1436, 309, 20717, 264, 5772, 295, 264, 6013, 2593, 13, 400, 456, 307, 257, 5772, 337, 264, 8625, 1941, 13, 1171, 264, 32494, 13, 821, 307, 257, 5772, 337, 264, 32494, 13, 6947, 954, 575, 702, 1065, 5772, 13, 7504, 11, 1184, 954, 311, 24738, 2920, 300, 291, 829, 5946, 322, 428, 20086, 13, 467, 2962, 13, 1033, 30], "avg_logprob": -0.6332614942528736, "compression_ratio": 1.6991150442477876, "no_speech_prob": 1.2993812561035156e-05, "words": [{"start": 3053.51, "end": 3053.83, "word": "Okay?", "probability": 0.048065185546875}, {"start": 3054.27, "end": 3054.41, "word": " So", "probability": 0.5498046875}, {"start": 3054.41, "end": 3054.53, "word": " the", "probability": 0.330322265625}, {"start": 3054.53, "end": 3055.11, "word": " LC", "probability": 0.423095703125}, {"start": 3055.11, "end": 3056.15, "word": " applications", 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The wave is a wave. You know the waves. Yes. What do you think to receive the station of the island? A person sitting at home and talking like this? 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What is the bath? He lowers his voice and his image on a magnetic wave of electricity and goes through the artificial moons and puts them in the air and reaches Gaza. It becomes full of air. Okay? He wants to receive it. What does he want? 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And after how many times? How many times did you receive one million times? I want one. Go to the receiver. The receiver wants you to change the frequency when there is a matching between the wave that you want to receive and the frequency of your receiver. It becomes what we call running. Running means that you have reached the maximum. You take the wave. 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We only had Israeli stations, that's all. Before the government came. Of course, a long time ago, when I say a long time ago, before your father was born. A long time ago, not you, I mean. Look at what we talked about. I don't care. It was like this. It was full. It was not a train. After a quarter of a cycle, it became empty. What happened to it? 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Look at the comparison. This was a curve and this is a rectangle. It is reversed. Look at the comparison again. It is reversed because it is not reversed. It is reversed. Thus, a quarter of a cycle time, half of a cycle time, three quarters of a cycle time and it continues. Okay. This is an easy question. Do you see this key? What is the value of this key? It is charged. Totally charged. 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Quiz. The last second. I tell you that there is a moment in the LC circuit. The current is maximum. What is Q? Zero. Then what is the difference between the two sides of the capacitor? Zero. Zero. If Q is negative, then it is zero. Okay. If I say that the current is zero, how much does Q mean? Maximum. 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{"start": 3284.8, "end": 3285.3, "word": " current", "probability": 0.890625}, {"start": 3285.3, "end": 3285.64, "word": " is", "probability": 0.93408203125}, {"start": 3285.64, "end": 3286.14, "word": " zero,", "probability": 0.8837890625}, {"start": 3286.34, "end": 3286.48, "word": " how", "probability": 0.281005859375}, {"start": 3286.48, "end": 3286.5, "word": " much", "probability": 0.80859375}, {"start": 3286.5, "end": 3286.5, "word": " does", "probability": 0.375732421875}, {"start": 3286.5, "end": 3286.84, "word": " Q", "probability": 0.9169921875}, {"start": 3286.84, "end": 3287.18, "word": " mean?", "probability": 0.81982421875}, {"start": 3287.74, "end": 3288.34, "word": " Maximum.", "probability": 0.83642578125}, {"start": 3288.42, "end": 3288.66, "word": " And", "probability": 0.60498046875}, {"start": 3288.66, "end": 3288.82, "word": " the", "probability": 0.5888671875}, {"start": 3288.82, "end": 3288.82, "word": " difference", "probability": 0.79833984375}, {"start": 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwZzXsCLffozucGP33XWqvBP/W6xi_v8dxGc.srt b/PL9fwy3NUQKwZzXsCLffozucGP33XWqvBP/W6xi_v8dxGc.srt
new file mode 100644
index 0000000000000000000000000000000000000000..2fbeaad26713762b805a249fdfdfad9040e65e30
--- /dev/null
+++ b/PL9fwy3NUQKwZzXsCLffozucGP33XWqvBP/W6xi_v8dxGc.srt
@@ -0,0 +1,2071 @@
+1
+00:00:05,810 --> 00:00:09,530
+ثم نبدأ باسم الله، ونكمل اليوم إن شاء الله على
+
+2
+00:00:09,530 --> 00:00:14,730
+كيرشوف، أخذنا قاعدتي كيرشوف تفصيلاً، والآن بدنا نطبق
+
+3
+00:00:14,730 --> 00:00:18,430
+عليها في بعض الدوائر، ببدأ بدائرة من الدوائر
+
+4
+00:00:18,430 --> 00:00:23,850
+البسيطة جداً. كم junction فيها؟ واحدة.
+
+5
+00:00:23,850 --> 00:00:30,390
+واحدة. كم loop فيها؟ واحدة. إذًا كم معادلة بيمكنني
+
+6
+00:00:30,390 --> 00:00:34,330
+بكيروشوف أكتب؟  إذًا ممنوع يكون لي أكثر من مجهول واحد.
+
+7
+00:00:36,850 --> 00:00:38,370
+إحنا بدنا نسهل، إحنا بدنا نسهل، إحنا بدنا نسهل، إحنا
+
+8
+00:00:38,370 --> 00:00:38,470
+بدنا نسهل، إحنا بدنا نسهل، إحنا بدنا نسهل، إحنا بدنا
+
+9
+00:00:38,470 --> 00:00:39,090
+نسهل، إحنا بدنا نسهل، إحنا بدنا نسهل، إحنا بدنا نسهل
+
+10
+00:00:39,090 --> 00:00:40,150
+إحنا بدنا نسهل، إحنا بدنا نسهل، إحنا بدنا نسهل، إحنا
+
+11
+00:00:40,150 --> 00:00:42,610
+بدنا نسهل، إحنا بدنا نسهل، إحنا بدنا نسهل، إحنا بدنا
+
+12
+00:00:42,610 --> 00:00:50,970
+نسهل، إحنا بدنا نسهل، إحنا بدنا نسهل، إحنا بدنا نسهل
+
+13
+00:00:50,970 --> 00:00:54,750
+إحنا
+
+14
+00:00:54,750 --> 00:00:59,410
+بدنا نسهل، إحنا بدنا نسهل، إحنا بدنا نسهل، إحنا بدنا
+
+15
+00:00:59,410 --> 00:01:06,160
+نسهل، إحنا بدنا نسهل الناس بتغلب حالها لما كيرشوف يتعب
+
+16
+00:01:06,160 --> 00:01:10,040
+ويغلب حاله، ويحط قانون، ويستخدمهم وخلص، ليش نخترع
+
+17
+00:01:10,040 --> 00:01:15,720
+شغلات ونقعد نجع في المحظور. بدي أستخدم كيرشوف، قال
+
+18
+00:01:15,720 --> 00:01:19,300
+لي في لوب ولا فيش لوب، في لوب، كيف نتعامل مع لوب؟ قال
+
+19
+00:01:19,300 --> 00:01:23,560
+لي ابدأ من نقطة، صح ولا لأ؟ وامشي مع عقارب الساعة
+
+20
+00:01:23,560 --> 00:01:28,420
+أو ضد عقارب الساعة، وألف لما تصل لنفس النقطة، تم.
+
+21
+00:01:29,820 --> 00:01:32,520
+بيقول لي إيه؟ إيش بده؟ جالي تيار، ما هنا جالي لأ
+
+22
+00:01:32,520 --> 00:01:35,960
+فيش غير تيار واحد، مجهول وحيد. بعد كده عشان أطول
+
+23
+00:01:35,960 --> 00:01:40,040
+السؤال، عشانه سهل، قالت جيب لي الـpower اللي استنفذ
+
+24
+00:01:40,040 --> 00:01:44,100
+في المقاومتين وفي البطارية الكبيرة. طبعاً دائماً
+
+25
+00:01:44,100 --> 00:01:48,940
+للمقاومة، الـpower تبع أي مقاومة بستخدم أنا صيغة
+
+26
+00:01:48,940 --> 00:01:53,380
+أما الـpower لأي إبسلون، لأي بطارية، I في إبسلون.
+
+27
+00:01:53,380 --> 00:01:59,250
+خلصنا. طبعاً إذا طلعت أنا I، بخلص المطلوبين التانين.
+
+28
+00:01:59,250 --> 00:02:04,530
+ولا لأ؟ سايبين. يلا يا بنات، بدنا نبدأ. قال لي،
+
+29
+00:02:04,530 --> 00:02:08,410
+التيار، أنت أديك من تجاهه، بدي أمشي مع عقارب الساعة، و
+
+30
+00:02:08,410 --> 00:02:11,670
+قلت لك أنا كيف ماشي، مع عقارب الساعة وهي السهم
+
+31
+00:02:11,670 --> 00:02:15,310
+موجود، عشان تعرفوا كيف تحلوا في فيلم بتاعها، برضه،
+
+32
+00:02:15,310 --> 00:02:18,630
+قولوا لي كيف ماشي، عشان أتبع وراكم. قلت أنا بدي
+
+33
+00:02:18,630 --> 00:02:23,060
+أبدأ من نقطة هذه. تمام. أنت بتحطه A B C D، يعني مش فارق. أحياناً
+
+34
+00:02:23,060 --> 00:02:26,540
+مرات تكون النقاط معروفة. نقول واضح، بيكون واحد من
+
+35
+00:02:26,540 --> 00:02:30,480
+وين بدأ، لحد لو ما جاش، ماشي أنا مع عقارب الساعة.
+
+36
+00:02:30,480 --> 00:02:38,560
+طلعوا إيش؟ هحط الستة موجبة، موجبة لأن إبسلون أمشي مع
+
+37
+00:02:38,560 --> 00:02:43,220
+بعضو. إحنا اتفقنا لما تكون إبسلون بنفس اتجاه حركة
+
+38
+00:02:43,220 --> 00:02:48,680
+يكون موجب. إذًا معناته إبسلون 1، وبعدين بنعوض. إذا
+
+39
+00:02:48,680 --> 00:02:54,540
+إبسلون 1، صحّيك ولا لأ؟ تم. أوصبت، بدي أنزل على R
+
+40
+00:02:54,540 --> 00:03:00,460
+واحد. وفليش هيك عينكم؟ ماشي الله، R واحد نزل تحت، و
+
+41
+00:03:00,460 --> 00:03:02,940
+التيار نزل تحت، إذًا سالب.
+
+42
+00:03:05,540 --> 00:03:13,540
+وصلت للـ 12، سالب 12، إن هي... لأنه التيار معايا ولا
+
+43
+00:03:13,540 --> 00:03:22,120
+لأ... ها... سالب. وإذا البطارية ضدي، بحطها سالب. إيش
+
+44
+00:03:22,120 --> 00:03:24,720
+ضال عندي؟ ضال عندي العشرة، التيار معايا ولا لأ؟
+
+45
+00:03:24,720 --> 00:03:34,270
+... سالب. عوض، عوضت. معادلة سهلة، مظبوط ولا لأ؟ سالب
+
+46
+00:03:34,270 --> 00:03:39,370
+زائد ستة، وسالب اثنا عشر، سالب ستة، وثمانية I، وعشرة
+
+47
+00:03:39,370 --> 00:03:44,990
+I، ثمانية عشر I، then I بتساوي ستة على ثمانية عشر، ثلث
+
+48
+00:03:44,990 --> 00:03:49,470
+بالسالب، ثلث بالسالب، مظبوط ولا لأ؟ يعني معناته
+
+49
+00:03:49,470 --> 00:03:54,830
+الاتجاه معكوس. جالي أصلاً، قالت هو أنه ممكن أنا أحلها
+
+50
+00:03:54,830 --> 00:03:58,310
+بدون كيرشوف. لو طلعتها بالتيار تبع مين بيكون؟
+
+51
+00:03:58,930 --> 00:04:04,750
+الكبيرة، مش اللي أنت رسمته. عشان كده كيرشوف قال لي
+
+52
+00:04:04,750 --> 00:04:08,450
+ما تت موجود لك، ما تغلبش حالك. ما طلعت سالب، هالي سالب
+
+53
+00:04:08,450 --> 00:04:14,950
+يعني معكوس. إذا صح الكلام، إذا طلع لما عوضت سالب،
+
+54
+00:04:14,950 --> 00:04:19,310
+والسالب بيعني أنه اتجاه التيار اللي أنت راسمه غلط،
+
+55
+00:04:19,310 --> 00:04:23,750
+معكوس. صحيح ولا لأ؟ تابعوا. أنا عارفة من الأول، بس عشان
+
+56
+00:04:23,750 --> 00:04:27,330
+نثبت. The minus sign indicates that the direction
+
+57
+00:04:27,330 --> 00:04:32,010
+of I is opposite to the assumed direction اللي أنا
+
+58
+00:04:32,010 --> 00:04:35,590
+فرضته أصلاً. ما فيش مشكلة في هذا السؤال. بعد كده
+
+59
+00:04:35,590 --> 00:04:40,310
+المطلوب الثاني، خلاص. المطلوب الثاني هذا هو، هادي
+
+60
+00:04:40,310 --> 00:04:45,710
+للمقاومتين، وهادي للبطارية اللي بدك إياها. ثم إجا
+
+61
+00:04:45,710 --> 00:04:48,950
+قال طب إيه؟ مش طالب البطارية الثانية الستة؟ قال لي
+
+62
+00:04:48,950 --> 00:04:52,450
+بعدين بتطلع لحالها عادي. بقول لكم كيف بنطلع، بنجيبوها
+
+63
+00:04:52,450 --> 00:05:00,770
+حسبت القدرة تبعت الـ 12، لاقيتها 4 واط، 4 واط. حسبت تبعت
+
+64
+00:05:00,770 --> 00:05:05,670
+واحدة من المقاومات، والثانية لاقيتها 2 واط. إذًا
+
+65
+00:05:05,670 --> 00:05:10,170
+المقاومات أكلوا 2 واط، والبطارية اللي كبيرة بتطلع 4
+
+66
+00:05:10,170 --> 00:05:13,050
+واط، و وين الـ 2 راحوا؟ إذًا هذه كانت 2 واط غصب عنها
+
+67
+00:05:13,050 --> 00:05:17,170
+ولا لأ؟ من دون ما أعملها. طب مش هنا بتطلع بقى؟ لأ.
+
+68
+00:05:17,170 --> 00:05:21,270
+هنا بتطلعش، هنا بتأخذ، هنا بتشحن، الجهد هذا عشان ليش
+
+69
+00:05:21,270 --> 00:05:24,950
+عكس الأولى. لكن اللي هو، محبة بتطلع، لكن هنا الجهد
+
+70
+00:05:24,950 --> 00:05:31,350
+بتشحن. تمام، لإنه التيار غلط، عكس التيار الأولى، كان
+
+71
+00:05:31,350 --> 00:05:34,470
+يجب الـpower. قلت له هي واحدة 0.9 والثانية 1.1
+
+72
+00:05:34,470 --> 00:05:39,150
+والإبسلون 14. لما جماعة جابت اثنين واط، فقعدت أفكر
+
+73
+00:05:39,150 --> 00:05:41,370
+طب وين اثنين واط اللي راحوا؟ قلت فيك ما البطارية
+
+74
+00:05:41,370 --> 00:05:46,510
+أكلتها. إذًا واضح بيقول لي that is half of the power
+
+75
+00:05:46,510 --> 00:05:50,570
+supplied by the 12 battery، نصهم is delivered to
+
+76
+00:05:50,570 --> 00:05:53,530
+the resistors، راحوا في المقاومات، والأصل النص
+
+77
+00:05:53,530 --> 00:05:58,400
+الثاني راح في البطارية الثانية اللي بتشحن، سهل.
+
+78
+00:05:58,400 --> 00:06:05,620
+هذا تمام، حلو. هذه دائرة سهلة، راح عليكم بهمش، تمام.
+
+79
+00:06:05,620 --> 00:06:14,720
+نجي لدائرة صعبة، هذه دائرة شوية معقدة، نبدأ. ماريا، شوفيني
+
+80
+00:06:14,720 --> 00:06:20,570
+التوالي والتوازي في هدول أكيد؟ ولا هيك حكيت إياها؟
+
+81
+00:06:20,570 --> 00:06:25,090
+في توالي وتوازي يا بنات؟ فيش توالي وتوازي، ولا
+
+82
+00:06:25,090 --> 00:06:28,550
+مقاومة، ولا في واحدة عندها رأي ثاني تقول؟ إذا واحدة
+
+83
+00:06:28,550 --> 00:06:34,610
+شكت في واحدة تقول في توالي وتوازي؟ فيش اثنين وستة
+
+84
+00:06:34,610 --> 00:06:39,870
+آه، عندك كلام. بس اثنين وستة هل توازي؟ أنت شكت
+
+85
+00:06:39,870 --> 00:06:44,070
+توازي؟ توالي، حلو. طلع لي، عشان يكون توالي، يكون
+
+86
+00:06:44,070 --> 00:06:50,710
+التيار ما ينقسمش، صح؟ هذه مش junction، هذه إذًا مش
+
+87
+00:06:50,710 --> 00:06:54,030
+توازي. طبعاً مش توازي، لأن البطارية هذه خلت هذول مش
+
+88
+00:06:54,030 --> 00:06:58,490
+توازي. إذًا لا توالي ولا توازي، كيف بدنا نحلها حبيبنا
+
+89
+00:06:58,490 --> 00:07:04,350
+كيرشوف؟ كم junction فيه، وإيش، وكم loop فيه؟
+
+90
+00:07:04,350 --> 00:07:09,230
+ثلاثة، الفجانية، والتحتانية، والكلية. قال لي يلا
+
+91
+00:07:09,230 --> 00:07:13,750
+بدنا نستخدم كيرشوف، وبدي اتجاه التيارات. هذا هو، بدي
+
+92
+00:07:13,750 --> 00:07:14,370
+أقيّمهم.
+
+93
+00:07:17,210 --> 00:07:22,990
+أنا أحكي. يلا، كم معادلة عندك؟ كم معادلة مطلوب؟
+
+94
+00:07:22,990 --> 00:07:28,470
+ثلاثة، صح ولا لأ؟ نبدأ بأول معادلة تبعت الـjunction
+
+95
+00:07:28,470 --> 00:07:34,090
+وبدي آخذ الـjunction B. الـjunction B، شوفوا لي
+
+96
+00:07:34,090 --> 00:07:39,210
+هالتيارين الحلوين هذول، هذول داخلين ولا مش داخلين؟
+
+97
+00:07:39,210 --> 00:07:45,930
+مجموع الداخل، إذًا معناته I1 زائد I2. إيش الخارج اللي
+
+98
+00:07:45,930 --> 00:07:51,530
+والله يخرج؟ إذًا هاي أول معادلة. طيب، مين ينجّلني الـ
+
+99
+00:07:51,530 --> 00:07:59,850
+junction A؟ مش به، مين الداخل؟ I3، ومين الخارج؟
+
+100
+00:08:01,760 --> 00:08:06,220
+بفرق؟ عشان كده قلنا ممنوع تقولوا بدي أعد أنا بس
+
+101
+00:08:06,220 --> 00:08:10,220
+معادلات، وأعطيني علامات. هذه نفس المعادلة، ممنوع تأخذ
+
+102
+00:08:10,220 --> 00:08:13,900
+الـjunction مرتين. إذا كانوا بس two junctions بس
+
+103
+00:08:13,900 --> 00:08:20,320
+مرة واحدة. تمه، يلا، هلّجتي الـloops؟ أحكي عايش
+
+104
+00:08:20,320 --> 00:08:24,360
+بتشغل loops، يلا.
+
+105
+00:08:24,360 --> 00:08:31,080
+تخيليها، آه، نيّح سؤالك. خربطة أي اثنين، طالع من A،
+
+106
+00:08:31,080 --> 00:08:34,760
+معلومة لازم تعرفوها: التيار بيبدأ من junction و
+
+107
+00:08:34,760 --> 00:08:39,560
+بيخلص عند junction. بيجيء اتطلع أي اثنين، من وين بدأ
+
+108
+00:08:39,560 --> 00:08:44,980
+من A، طلع من A، صح؟ وخلص عند B. طبعاً بيطلع
+
+109
+00:08:44,980 --> 00:08:50,660
+بيبدأ، بيطلع، وبدخل على B، خلص، روح انتهى. أي
+
+110
+00:08:50,660 --> 00:08:56,670
+واحد بدأ من A، يخلص عند B، ولا لأ؟ طب I3، وين بدأ؟
+
+111
+00:08:56,670 --> 00:09:01,510
+من B وخلص عند A. حليت مشكلتك، هلّجتي؟ اتجاهات
+
+112
+00:09:01,510 --> 00:09:05,590
+التيارات. بدي أجيب لكم شيء. تبقى على منبعه، فبالتالي I2
+
+113
+00:09:05,590 --> 00:09:15,610
+منبعه النقطة A، تمام هيك؟ حلو. آه، تخجلوش. هو فرضها، هو
+
+114
+00:09:15,610 --> 00:09:19,390
+فرضها، تمام؟ لو بدك تفرضي أنت حرة، بس هو فرضها عشان
+
+115
+00:09:19,390 --> 00:09:20,070
+نريح حالنا.
+
+116
+00:09:23,020 --> 00:09:29,480
+هي... آه... شوفي، ما تقوليش بدي أطلع مالاش قاعدة
+
+117
+00:09:29,480 --> 00:09:35,620
+بديك تفرضي اعتباطياً، اعتباطياً، وأنا قلت لك هاي وهاي
+
+118
+00:09:35,620 --> 00:09:40,600
+حافظي الكلمة. لحظة، ما تفكريش. خلي جلمك هو اللي يحدد، و
+
+119
+00:09:40,600 --> 00:09:45,630
+جلم له مخ؟ جلم يلو مخ؟ عشان كده بقول خلي جلمك،
+
+120
+00:09:45,630 --> 00:09:49,330
+عشان ما حد يفكر. إذا بيتفرض، ما فيش قاعدة، المهم ما فيش
+
+121
+00:09:49,330 --> 00:09:53,370
+قاعدة. اللي هو أصلاً لو في قاعدة، ليش أنا بقول لك افرض؟
+
+122
+00:09:53,370 --> 00:09:56,990
+المهم هي خلاص. لك تتبع القاعدة. هو مش قاعدة، بس غالباً
+
+123
+00:09:56,990 --> 00:10:02,750
+... المزايا
+
+124
+00:10:02,750 --> 00:10:06,470
+فيهم، مش الكل. ببطل في قاعدة. أنت هنا إحنا بدنا نقعد
+
+125
+00:10:06,470 --> 00:10:10,970
+هنا أحفظ وقتش، هذه وقتش، هذه آيات؟ مديش أحفظ؟ خلاص.
+
+126
+00:10:10,970 --> 00:10:11,750
+احكي يا روان.
+
+127
+00:10:15,510 --> 00:10:19,470
+أنتوا بتجهدوا حالكم، مش فيه زي واحد بيكون عنده رخصة
+
+128
+00:10:19,470 --> 00:10:22,670
+بيقول لك بديش آخذ فيها. طب هو الله بديك إياها. وهذه نفس
+
+129
+00:10:22,670 --> 00:10:26,810
+العملية. ليش أنتم بتأخذوا... بتعملوا قوانين، وتشغلوا
+
+130
+00:10:26,810 --> 00:10:30,050
+حالك بـ 100 ألف قانون، و100 ألف قاعدة. هذه قاعدة، ما
+
+131
+00:10:30,050 --> 00:10:33,530
+أنتوا حاططين قاعدة، صارت قاعدة، وبتتبعوها. ليش تحطوا
+
+132
+00:10:33,530 --> 00:10:37,890
+حالكم قواعد، وأنتوا أحرار. مش إحنا أحرار؟ ليش
+
+133
+00:10:37,890 --> 00:10:41,810
+القانون، قاعدة، حالنا. احكي لنا، قاعدة سيارة في حاجة
+
+134
+00:10:41,810 --> 00:10:48,660
+سهلة، نجاوبكم. آه. طب هو كان بطارية عنده، team 2، ومين
+
+135
+00:10:48,660 --> 00:10:53,600
+بيغلب. مش بعرف، الدوائر معقدة هنا، عشان كده ما فيش
+
+136
+00:10:53,600 --> 00:10:59,040
+قاعدة. مش زي دائرة دي كنت عارف مين بدي يغلب، بس هنا
+
+137
+00:10:59,040 --> 00:11:04,740
+مقدرش أعرف مقدمًا إلا كيرشوف. نتحمل جميله ونضل
+
+138
+00:11:04,740 --> 00:11:08,800
+نمشي معه للآخر، عشان أعرف موجب ولا سالب. ما فيش
+
+139
+00:11:08,800 --> 00:11:13,360
+قاعدة، يا عيالة. ابتدعوا القواعد لحالكم، يا بنات. أنتم
+
+140
+00:11:13,360 --> 00:11:16,820
+مش زعلانين يطلع سالب؟ أنتم مخالفين، زعلانين ليش؟
+
+141
+00:11:16,820 --> 00:11:20,880
+السالب يطلع؟ بتحبوش يطلع سالب؟ ومهما اجتهدتوا، هيطلع
+
+142
+00:11:20,880 --> 00:11:26,260
+سالب، هيطلع سالب بالأخر، لأنه ما فيش قاعدة تحكم هذا
+
+143
+00:11:26,260 --> 00:11:31,240
+الاجتهاد. طبعاً هيك وإلا كان حيكون شغل عشوائية.
+
+144
+00:11:32,360 --> 00:11:36,760
+الدائرة مرات بتكون معقدة زي هيك، ما نقدروش نعرف ليش؟
+
+145
+00:11:36,760 --> 00:11:40,320
+مش ببساطة قيمة البطاريات، قيمة المقاومات اللي بتلعب
+
+146
+00:11:40,320 --> 00:11:43,820
+دور كبير، إن وين المقاومات أكثر، لأن هذا التيار مش
+
+147
+00:11:43,820 --> 00:11:47,380
+بس بطارية وماشي، لأ، ما هو كل ما كترت المقاومة، وكل
+
+148
+00:11:47,380 --> 00:11:50,440
+ما قلت التيار، وبالتالي بيصير عملية معقدة جداً،
+
+149
+00:11:50,440 --> 00:11:53,200
+والمقاومة زي ما أنتم شايفينها، أنتم فاهمينها؟ في
+
+150
+00:11:53,200 --> 00:11:58,480
+قاعدة؟ لكن أيوة إحنا عارفين إيش نعمل، ولا كنا نسوي
+
+151
+00:11:58,480 --> 00:12:03,380
+في الشهادة، كله من ناس جيرخييال عنكم، لأنهم بتحبوا
+
+152
+00:12:03,380 --> 00:12:07,160
+أنتم تقيدوا حالكم. إحنا هيك البشر، زي ما بيقولوا
+
+153
+00:12:07,160 --> 00:12:10,640
+مرات المشايخ. إحنا من كثر الأسئلة اللي بتجينا
+
+154
+00:12:10,640 --> 00:12:14,580
+بنقول لهم ما تسألوش، وبنضطر إننا نجاوب، أو بيصير
+
+155
+00:12:14,580 --> 00:12:18,220
+الجواب سهل. حرام بصراحة، حرام. طبعاً طول ما تسألوش
+
+156
+00:12:18,220 --> 00:12:22,360
+قرصونا. واحد ما يقيدش حاله، خلاص، العموميات أفضل.
+
+157
+00:12:24,940 --> 00:12:26,160
+هي هي هي هي هي هي هي هي هي هي هي هي هي هي هي
+
+158
+00:12:26,160 --> 00:12:27,060
+هي هي هي هي هي هي هي هي هي هي هي هي هي هي هي
+
+159
+00:12:27,060 --> 00:12:33,700
+هي هي هي هي هي هي هي هي هي هي هي
+
+160
+00:12:33,700 --> 00:12:36,500
+هي هي هي هي هي هي هي هي هي هي هي هي هي هي هي
+
+161
+00:12:36,50
+
+223
+00:17:38,000 --> 00:17:42,960
+الإجابات I1، I2 أمبير، طلعت I2 سالب 3 أمبير و I3 سالب 1 أمبير، اتفجأنا يا بنات؟ طب أنا أجد سهل، تمام،
+
+224
+00:17:42,960 --> 00:17:48,200
+
+225
+00:17:48,200 --> 00:17:51,900
+انظروا لي، إيش اللي طلع معايا، انظروا لي على I1،
+
+226
+00:17:51,900 --> 00:17:56,180
+موجبة أم سالبة؟ موجبة، مظبوط أم لا؟ إيش يعني
+
+227
+00:17:56,180 --> 00:18:00,460
+بيقولوا أن الإتجاه اللي أنتم حاطينه غلط، صح؟ موجبة طلعت
+
+228
+00:18:00,460 --> 00:18:04,680
+I واحد؟ I واحد، آه I ثلاثة سالبة، أنا أنا أنا
+
+229
+00:18:04,680 --> 00:18:09,620
+بتطلع هذه I واحد، صح؟ آه تمام، I ثلاثة سالبة، I
+
+230
+00:18:09,620 --> 00:18:14,380
+ثلاثة سالبة، معناته هذه معكوسة وهذه صحيحة، تقدروا
+
+231
+00:18:14,380 --> 00:18:19,810
+تقولوا من أعلى A أم B، حسب هذه المعطيات؟ أيه؟ لأن
+
+232
+00:18:19,810 --> 00:18:23,730
+التيار يريد أن يمشي من العالي للواطي، إذا المفروض أيه
+
+233
+00:18:23,730 --> 00:18:27,150
+تكون موجبة وأيه سالبة؟ طلعوا المطلوب الثاني، إيش بده
+
+234
+00:18:27,150 --> 00:18:31,470
+بيقول: أوجد فرق جهد VP ناقص VA، في بنت أظن سألتني مرة
+
+235
+00:18:31,470 --> 00:18:38,370
+من المرات، VAB إيش تعني؟ مظبوط منكم، وقلت لكم كل
+
+236
+00:18:38,370 --> 00:18:42,470
+شيء، هو طريقته أم لا، وأنا عشان ما يكون ليش طريقة
+
+237
+00:18:42,470 --> 00:18:46,990
+بدي أكتب لكم، أكتب بالظبط إيش بتاعتي:Vb-Va أم Va
+
+238
+00:18:46,990 --> 00:18:51,450
+-Vb؟ طبعاً، إيش كتبت لكم؟ Vb-Va، عارفين إيش اللي بدكم
+
+239
+00:18:51,450 --> 00:19:02,200
+إياها؟ هرجيت لو قلت لكم هذه، قولي هذه بس، أفضّوها، الـ
+
+240
+00:19:02,200 --> 00:19:04,660
+Delta V، بس إيش مكتوب عندي؟ فأنت عارف أنك مش كاتب V
+
+241
+00:19:04,660 --> 00:19:09,380
+F، إيش يعني F؟ وإيش يعني I؟ حلو، بتعرفوا معنى initial
+
+242
+00:19:09,380 --> 00:19:17,400
+و final؟ من وين أبدأ؟ هجيت!
+
+243
+00:19:17,400 --> 00:19:21,160
+أنا ببدأ من النهاية وأنا من البداية، أنا ليش قلت لكم
+
+244
+00:19:21,160 --> 00:19:25,360
+إيش معنى initial؟ عشان تقولوا ابتدائي، هجيت! الواحد من
+
+245
+00:19:25,360 --> 00:19:28,220
+وين يبدأ؟ من الابتدائي أم لا؟ أنتم كيف تبدأون في
+
+246
+00:19:28,220 --> 00:19:30,180
+المدرسة؟ من الرفض أم من التوجيه، وتنزلون نزولاً
+
+247
+00:19:31,790 --> 00:19:35,830
+بنبدأ من الابتدائي، صح أم لا؟ إذا لما تكتبوا هناك، من
+
+248
+00:19:35,830 --> 00:19:40,370
+أين أبدأ؟ من الـ initial، طيب أنا إيش بدي أعمله؟ من أين
+
+249
+00:19:40,370 --> 00:19:46,270
+.. من أين أبدأ؟ من A، إذا لما يقول لي: أوجد VB ناقص
+
+250
+00:19:46,270 --> 00:19:50,670
+VA، من أين أبدأ؟ لو قال لي: أوجد VA ناقص VB، من أين
+
+251
+00:19:50,670 --> 00:19:56,260
+أبدأ؟ دلوقت، من إيش ربطتها؟ من Vfinal ناقص Vinitial،
+
+252
+00:19:56,260 --> 00:20:01,260
+رجعتها لأصلها، Final ناقص Initial، Final، عشان كده
+
+253
+00:20:01,260 --> 00:20:04,340
+قلت لكم ارفضوها، وما تعود تقولوا الـ initial، بعدين أن ده
+
+254
+00:20:04,340 --> 00:20:06,800
+بدأ من الـ final، يعني أبدأ من الـ initial في
+
+255
+00:20:06,800 --> 00:20:12,340
+العالي، في الواطي، حد فيش، هو في الواطي العالي، حدش
+
+256
+00:20:12,340 --> 00:20:16,340
+اللي هو في الواطي العالي، أبدأ من الـ initial، صح؟
+
+257
+00:20:16,340 --> 00:20:20,360
+initial، أبدأ منه، هو من الـ initial، آه الـ initial،
+
+258
+00:20:20,360 --> 00:20:24,710
+وينه؟ الأول أم الثاني؟ فوق شفها، ات من الثانية،
+
+259
+00:20:24,710 --> 00:20:28,390
+هارجت من الأعلى وما كانش في دعوة للحساب اللي بيطلع هذه
+
+260
+00:20:28,390 --> 00:20:33,750
+حالة خاصة، إذا أبدأ من الثانية، حلو، طيب برضه واحدة
+
+261
+00:20:33,750 --> 00:20:37,690
+واحدة، كرّشوها في الثانية، أول ما شرحت لكم إياها كتبت لكم
+
+262
+00:20:37,690 --> 00:20:43,040
+Va ناقص Va بتساوي صفر، مظبوط أم لا؟ قلت: تبدأ، هجيت!
+
+263
+00:20:43,040 --> 00:20:46,020
+من هنا، لأ، أصلاً تبدأ، وحالتي جاية تقول: ده تبدأ من هنا،
+
+264
+00:20:46,020 --> 00:20:49,340
+ما هي تفرق، عشان كده قلت معاها قريب الساعة، ورضّعها،
+
+265
+00:20:49,340 --> 00:20:53,260
+قريب الساعة، أنا ذاتها، ما هي تفرق، هجيت! هدول اختلفوا،
+
+266
+00:20:53,260 --> 00:20:56,380
+وبدك تبدأ من هنا، وتخلصها كاش، ترجع لنفس النقطة،
+
+267
+00:20:56,380 --> 00:21:00,500
+إذا لما دي فرق الجهد بين نقطتين مش متساويتين، تبدأ
+
+268
+00:21:00,500 --> 00:21:04,200
+من الثانية، وبدك تروح للأولى، وتخلص عندها طبعاً؟ طب و
+
+269
+00:21:04,200 --> 00:21:09,480
+أنت ماشي، هتلاقي عندك بطارية، وهتلاقي مقاومة
+
+270
+00:21:09,480 --> 00:21:12,740
+بيديك تشتغل زي ما اشتغلت، تشوف الثانية، إذا، و
+
+271
+00:21:12,740 --> 00:21:16,480
+أنت ماشي، حاجات ماشيتك، بطلت عشوائية، من الثانية
+
+272
+00:21:16,480 --> 00:21:20,840
+للأولى، ماشيتك بطلت عشوائية، فيه مصام، عين واحدة،
+
+273
+00:21:20,840 --> 00:21:24,300
+واحدة، صارت أن أنت بدك من واحدة ورايح للتانية، إذا
+
+274
+00:21:24,300 --> 00:21:28,360
+طريقك عشوائي أم محدد؟ محدد، وأنت ماشي، إذا
+
+275
+00:21:28,360 --> 00:21:32,690
+البطارية، الموجب معاك، حط موجب، وإذا التيار معاك
+
+276
+00:21:32,690 --> 00:21:37,930
+حط سالب، ماشي من التفاجؤ؟ قال لي: يلا نبدأ .. يلا
+
+277
+00:21:37,930 --> 00:21:47,610
+نبدأ .. هه .. إيش بيديك المسار؟ ماذا قلت؟ كل
+
+278
+00:21:47,610 --> 00:21:53,730
+الطرق تؤدي إلى روما، تمام؟ الواحد راح بالـ bus أم
+
+279
+00:21:53,730 --> 00:21:57,150
+بالـجطار أم بالطائرة، على روما، بدي أوصل روما أم لا؟
+
+280
+00:21:57,150 --> 00:22:02,650
+بدي أوصل روما، هي الثلاث طرق، ما انش برضه، هو مش عارف إيش
+
+281
+00:22:02,650 --> 00:22:08,800
+بيحكوا لكم كثير، أنتم عبّطتوا، مش عارف ناس، ليش؟ ليش؟ هو
+
+282
+00:22:08,800 --> 00:22:12,220
+أنت صغير؟ أنا .. أنا .. ما أنتم كبرتوا في التوجيهي،
+
+283
+00:22:12,220 --> 00:22:15,400
+.. كبرتوا .. ما ينفعش نضمّ .. نبدّغكم، اللجنة، و
+
+284
+00:22:15,400 --> 00:22:20,440
+حطّفتكم؟ مش لأخر لحظة .. فخلاص كبرتوا .. تعلموا
+
+285
+00:22:20,440 --> 00:22:24,180
+تمدّغوا .. هجيت! مش أنا طلعت التيارات، بتجيبها، و
+
+286
+00:22:24,180 --> 00:22:27,800
+بتسحبها؟ بدّك تخلي الاتجاهات .. خليهم .. ما أنتَ
+
+287
+00:22:27,800 --> 00:22:30,860
+بدّك تعود، بتسحب ساعتها .. مظبوط أم لا؟ أنا
+
+288
+00:22:30,860 --> 00:22:35,060
+هجيت! التيارات .. شايفينهم؟ يلا .. أي طريق بدّك
+
+289
+00:22:35,060 --> 00:22:41,260
+.. نبدأ فيه يا ماريان .. العدل؟ العدل، أسهل طريق،
+
+290
+00:22:41,260 --> 00:22:44,400
+التحتاني، بس خلّيني بنقول اللي رحنا من الروابط
+
+291
+00:22:44,400 --> 00:22:49,240
+الأحمر زي ما بده صاحبه، تمام؟ يلا، بنبدأ من أي نقطة
+
+292
+00:22:49,240 --> 00:22:55,220
+بده يا مريم، من أي نقطة؟ Vb ناقص Va زي ما بده، Vb
+
+293
+00:22:55,220 --> 00:22:58,600
+ناقص Va، مظبوط؟ إذا من أي نقطة بده بده؟ من A، مش
+
+294
+00:22:58,600 --> 00:23:02,960
+على خاطر .. من أيه؟ يلا، ابدأ من A وأنت رايح على B،
+
+295
+00:23:02,960 --> 00:23:07,240
+بالطريق الوسطية، هجيت! العشر of word، موجبة أم سالبة؟
+
+296
+00:23:07,240 --> 00:23:17,900
+موجبة، هجيت! الستة، قوم، التيار معاكي صحيح، سالب ستة، أي
+
+297
+00:23:17,900 --> 00:23:18,480
+واحد
+
+298
+00:23:22,480 --> 00:23:29,280
+6 في 2، أم بتكون كالكلتر كمان، عشرة ناقص اثنين، سالب
+
+299
+00:23:29,280 --> 00:23:38,440
+اثنين volt، VB ناقص VA، مين بده ينجّني؟ اللي تحت، يلا
+
+300
+00:23:38,440 --> 00:23:42,960
+يا واحد، بالموجبة
+
+301
+00:23:42,960 --> 00:23:50,630
+شايفيني ماشية؟ لأنه I عكسي، فـ اثنين I ثلاثة، أنا
+
+302
+00:23:50,630 --> 00:23:54,150
+ما غيرت اتجاه التيار، بعيبه، أخذته، معناته بدي آخذ
+
+303
+00:23:54,150 --> 00:24:02,670
+نتيجته بعيبه بالسالب، تبعته 2000 في سالب واحد، VD ناقص
+
+304
+00:24:02,670 --> 00:24:10,450
+VA، بدي المسار الثاني، احكي يا بطل، سالب
+
+305
+00:24:10,450 --> 00:24:14,230
+أربعة، مش أربعة عشر، هذه المهمة، يستبدى من أيه يا
+
+306
+00:24:14,230 --> 00:24:23,380
+بطل؟ سالب أربعة، أي اثنين أم لا؟ ناقص 14، فحكي بدي
+
+307
+00:24:23,380 --> 00:24:27,580
+أعود عن، أي اثنين سالب ثلاثة في سالب أربعة، عشر، زاد
+
+308
+00:24:27,580 --> 00:24:33,180
+اثنين، نفس
+
+309
+00:24:33,180 --> 00:24:38,280
+الرومة، كل الطرق تؤدي إلى نفس روما، إذا عرفت كيف
+
+310
+00:24:38,280 --> 00:24:41,420
+تجيب فرق جهد بين نقطتين، نبدأ من أي نقطة؟ من
+
+311
+00:24:41,420 --> 00:24:44,740
+العالية أم الواطية، هالـ gate؟ من الثانية! ما ليش زي
+
+312
+00:24:44,740 --> 00:24:48,040
+عبارة عن العالية هالـ gate، احنا اتفقنا طلع سالب، ليش
+
+313
+00:24:48,040 --> 00:24:51,840
+طلع سالب؟ قلت له: أنا متوقع أنه أيه تكون هي الأعلى
+
+314
+00:24:51,840 --> 00:24:55,820
+من اتجاهات التيار، وبالتالي لما تقول لي VB ناقص Vm،
+
+315
+00:24:55,820 --> 00:24:58,660
+هذه أكبر من هذه، إذا أنت طلعت النتيجة سالبة أم
+
+316
+00:24:58,660 --> 00:25:05,600
+ما طلعتش سالبة؟ واضح؟ احكي، لإيش
+
+317
+00:25:05,600 --> 00:25:07,960
+طلع أي ثلاثة؟
+
+318
+00:25:10,980 --> 00:25:14,740
+تجلبيش .. تجلبيش .. تجلبيش الاتجاهات، أنا بدي آخذ
+
+319
+00:25:14,740 --> 00:25:17,120
+الجواب، باعتباره سالباً أم مش بالسالب؟ بالسالب،
+
+320
+00:25:17,120 --> 00:25:20,000
+إذا خلي الاتجاه اللي أنت فرضتيه زي ما هو، يعني
+
+321
+00:25:20,000 --> 00:25:22,420
+سالب، لجلال التيارات، آه .. آه .. آه .. سالب .. عشان
+
+322
+00:25:22,420 --> 00:25:24,760
+أقول لكم هذا .. خلاص، ما .. تجلبيش التيارات اللي
+
+323
+00:25:24,760 --> 00:25:28,120
+فرضتيهم، بس عوضي من النتائج اللي طلعت معاكي، موجبة، و
+
+324
+00:25:28,120 --> 00:25:36,060
+سالبة، تمام، هيك؟ آية، بلاء، واضحة؟ سهل .. كثير سهل ..
+
+325
+00:25:36,060 --> 00:25:36,680
+احكيه
+
+326
+00:25:45,930 --> 00:25:52,230
+برضه مصمّمة، حطوا لحالهم قواعد، فشي فشي، ما بديش أسمع حتى
+
+327
+00:25:52,230 --> 00:25:55,930
+عشان أكمل، ما بديش أسمع، ما هي الحاجات اللي قلت لكم إياها، فشي
+
+328
+00:25:55,930 --> 00:25:59,250
+شيلك فيها، أنت به تحسبي، وتشوفي موجب أم سالب،
+
+329
+00:25:59,250 --> 00:26:03,800
+احسبي بقاعدة كيرشوف الثانية، وما تستخفّوا بحالكم
+
+330
+00:26:03,800 --> 00:26:06,480
+بالقواعد، يا بنات، يا بنات، أنتم لما تكبروا أنتم
+
+331
+00:26:06,480 --> 00:26:09,640
+قاعدين بتكبروا شوية شوية، القوانين كتير بتصير معاكم
+
+332
+00:26:09,640 --> 00:26:12,560
+بتأخذوها في كل المجالات، لما يتكرر القوانين، وكل
+
+333
+00:26:12,560 --> 00:26:15,700
+حاجة بتحفظوها، كل حاجة بتحفظوها بتورّط، إيش الواحد
+
+334
+00:26:15,700 --> 00:26:18,800
+بيديه يحفظ؟ لما يحفظ، عشان كده الواحد بيحفظ الشغلات
+
+335
+00:26:18,800 --> 00:26:23,100
+العامة، والشغلات، أن كل حاجة إلها، علمونا في المدرسة،
+
+336
+00:26:23,100 --> 00:26:28,680
+تخلصوا، خلاص، الواحد ما بيصدق الحرية حلوة، ما زال عنده
+
+337
+00:26:28,680 --> 00:26:34,240
+حرية، ليش يقيد حاله؟ تمام، to find، هاي الكلام اللي
+
+338
+00:26:34,240 --> 00:26:37,080
+حكيته، to find the potential difference between two
+
+339
+00:26:37,080 --> 00:26:42,060
+points، two points، يعني مختلفين، تمام، start at the
+
+340
+00:26:42,060 --> 00:26:45,100
+initial point، at the initial point، عشان كنا نسمّيها
+
+341
+00:26:45,100 --> 00:26:49,980
+initial، at the initial point، تمام، and traverse the
+
+342
+00:26:49,980 --> 00:26:53,560
+loop، ونفعل loop، toward the final point، adding
+
+343
+00:26:53,560 --> 00:26:56,680
+potential differences across all the elements you
+
+344
+00:26:56,680 --> 00:27:00,160
+encounter، وبتضيف، وبتجمع اللي بتواجههم، encounter،
+
+345
+00:27:00,160 --> 00:27:06,340
+تواجه، تمام، قال لي: يعني هي رجعنا، to find vb ناقص va،
+
+346
+00:27:06,340 --> 00:27:10,920
+الشيء الـ initial، بيقول أيه؟ من كتبتها على طول، بتجيب
+
+347
+00:27:10,920 --> 00:27:14,060
+في find، الـ ناقص v initial، الـ initial الثانية، تمام،
+
+348
+00:27:14,060 --> 00:27:18,420
+we begin at point A and follow a path toward point
+
+349
+00:27:18,420 --> 00:27:22,220
+B، through the middle، هو اختار زي ما اختارت مريم الـ
+
+350
+00:27:22,220 --> 00:27:25,140
+middle battery، قال: بدي أختار هذا المسار، قلت له:
+
+351
+00:27:25,140 --> 00:27:32,840
+مشيت هذه عشرة، صحيح، نور، هذه عشرة، وهذه ناقص 6I1،
+
+352
+00:27:32,840 --> 00:27:38,580
+أخذتها، بعكسها، عكسها، فلو كتبتها، طلعت ناقص،
+
+353
+00:27:38,580 --> 00:27:42,900
+قال لي: the minus sign here means that by chance، يا
+
+354
+00:27:42,900 --> 00:27:46,260
+صراحة، by chance، طلعت واحدة أكبر من الثانية، ما لهيش
+
+355
+00:27:46,260 --> 00:27:50,380
+قاعدة، تمام، try to follow another path from A to
+
+356
+00:27:50,380 --> 00:27:55,300
+B، to verify، عشان تتأكد، verify، أتحقق أن جوابي يطلع
+
+357
+00:27:55,300 --> 00:28:01,220
+ناقص 2 volt، أشوف حالي بتوتر الطرق أم ما بتوترش، إذا
+
+358
+00:28:01,220 --> 00:28:05,920
+توترت، بقول: والله ما غلط، والله أكيد جوابي صح، مظبوط،
+
+359
+00:28:05,920 --> 00:28:12,260
+أم لا، خلاص عملتها، هاي VB ناقص Ve، للأبر، وهي الـ
+
+360
+00:28:12,260 --> 00:28:15,280
+lower، ماشي يا نور، تمّ
+
+361
+00:28:20,240 --> 00:28:23,460
+لو طلب الـ Power، نرجع لـ Power، قانون مقاومة I
+
+362
+00:28:23,460 --> 00:28:30,000
+تربيع في R، لبطارية I في Epsilon، حلو،
+
+363
+00:28:30,000 --> 00:28:34,760
+حلو، حلو، سؤال، شو هو الـ power بالنسبة للمقاومة؟
+
+364
+00:28:34,760 --> 00:28:40,900
+قانونها، قانونها، بتفرق معاكي عكسية أم ما عكسية؟ مجلة
+
+365
+00:28:40,900 --> 00:28:47,750
+الإشارة، هو الـ power، مش المفروض يطلع سالب عشان شهد
+
+366
+00:28:47,750 --> 00:28:53,270
+فيها الشغلة .. تمام؟ مش هتطلع سالب، إذا أنت في صح
+
+367
+00:28:53,270 --> 00:28:56,290
+سيّحتوا، عارفة .. تطلعيش .. بتأخذوا الـ absolute
+
+368
+00:28:56,290 --> 00:28:58,770
+value، يعني .. واحنا ليش بنعلمكم الـ absolute value؟
+
+369
+00:28:58,770 --> 00:29:01,790
+في كل كرّشة .. عشان يديكم الشغلة .. تمام .. آه،
+
+370
+00:29:01,790 --> 00:29:05,230
+عشان رايح حالنا .. الموضوع الأخير، الـ RC circuits،
+
+371
+00:29:05,230 --> 00:29:09,670
+.. أخذتوا كبسيطر، أرضه .. وبديتوا تدرسوه أم لا؟ ..
+
+372
+00:29:09,670 --> 00:29:13,890
+آه، جربوا في الامتحان .. لازم تكونوا بديتوا .. علمتكم
+
+373
+00:29:13,890 --> 00:29:19,570
+كيف تشحنوا المكثف؟ نشبك بطارية، تنتقل الشحنات شوية،
+
+374
+00:29:19,570 --> 00:29:22,450
+.. شوية .. شوية .. شوية .. شوية .. شوية .. شوية ..
+
+375
+00:29:22,450 --> 00:29:23,270
+شوية .. شوية .. شوية .. شوية .. شوية .. شوية ..
+
+376
+00:29:23,270 --> 00:29:24,330
+شوية .. شوية .. شوية .. شوية .. شوية .. شوية ..
+
+377
+00:29:24,330 --> 00:29:29,010
+شوية .. شوية .. شوية .. شوية،
+
+378
+00:29:29,010 --> 00:29:31,650
+.. شوية .. شوية .. شوية .. شوية .. شوية .. شوية ..
+
+379
+00:29:31,650 --> 00:29:32,550
+شوية .. شوية .. شوية .. شوية .. شوية .. شوية ..
+
+380
+00:29:32,550 --> 00:29:38,730
+شوية .. شوية .. شوية .. شوية،
+
+381
+00:29:38,730 --> 00:29:40,890
+.. شوية .. شوية .. شوية .. شوية .. شوية .. شوية ..
+
+382
+00:29:40,890 --> 00:29:45,570
+شوية .. شوية .. شوية .. شايفين البطارية؟ في مكثف
+
+383
+0
+
+445
+00:34:27,850 --> 00:34:31,050
+ولا لأ؟ بدي أضرب كل المعادلة بـC أخذناها في
+
+446
+00:34:31,050 --> 00:34:34,290
+المدارس ولا لأ؟ بدي أضرب كل المعادلة بـC لما يوا
+
+447
+00:34:34,290 --> 00:34:38,910
+حد يقول لي إيش جديد؟ يرفع أيدي ويقول أنا محتاج، تمام؟
+
+448
+00:34:38,910 --> 00:34:45,290
+هذه صارت C وهذه صارت C وهذه راحت، عملتي شيء؟ لأ
+
+449
+00:34:45,290 --> 00:34:51,940
+تمام، قال لي: طيب ممكن تعملي التالي، إيش أعمل؟ قلت
+
+450
+00:34:51,940 --> 00:34:55,060
+له: هذه الحلوة، ننقلها على الطرف الثاني، تعلمتوا
+
+451
+00:34:55,060 --> 00:34:59,500
+كيف تنقلوها؟ هم أتعلمنا C في إبسلون، ماقص الـQ
+
+452
+00:34:59,500 --> 00:35:08,740
+بتساوي زائد RCDQ على DT، في مشكلة؟ ده ده ده ده، في
+
+453
+00:35:08,740 --> 00:35:18,100
+مشكلة؟ لأ، قال لي: طيب، تقدر تجسم لي على RC، أضرب في
+
+454
+00:35:18,100 --> 00:35:23,740
+DT، أجسم على RC صارت
+
+455
+00:35:23,740 --> 00:35:36,880
+C في إبسلون ناقص Q على RC في DT بتساوي DQ، مش
+
+456
+00:35:36,880 --> 00:35:41,900
+احنا ده ده ده، ماشي، في حد يحتاج لأي شيء؟ حلو
+
+457
+00:35:44,420 --> 00:35:48,700
+هل جيت؟ إيش ممكن تسوي؟ هذه Q، نديها إعكس، هذه نرجع
+
+458
+00:35:48,700 --> 00:35:52,880
+لها، نخليها في المقام، بس هذه، شايفينها؟ نخليها في
+
+459
+00:35:52,880 --> 00:35:57,540
+المقام، ينفع؟ ينفع، إيش بيصير عندكم؟ هذه T على RC
+
+460
+00:35:57,540 --> 00:36:10,180
+بتساوي هذه Q على C في إبسلون ناقص Q،  منيح؟ حلو، مصح
+
+461
+00:36:10,180 --> 00:36:16,910
+صح، صحين؟ أعمل هذه هيك وهذه هيك وهذه هيك، ضربت
+
+462
+00:36:16,910 --> 00:36:20,770
+المعادلة كلها بثلاث، بتكونش بلاش، بس الحلقة أحلى
+
+463
+00:36:20,770 --> 00:36:26,310
+يعني بس مش أكثر، هذا اللي بدي إياه، قلت له: كامل طرفي
+
+464
+00:36:26,310 --> 00:36:31,530
+المعادلة، يلا نكامل، هينا وصلنا هنا، نكامل طرفي
+
+465
+00:36:31,530 --> 00:36:37,850
+المعادلة، RC ثابتة ولا ما ثابتة؟ إذا سالب 1 على RC
+
+466
+00:36:37,850 --> 00:36:45,590
+تكامل DT بتساوي تكامل DQ على Q ناقص C في إبسلون
+
+467
+00:36:45,590 --> 00:36:53,290
+وصلنا لهنا، تمام، خلصنا المدرسة، أخذنا في التوجيهي
+
+468
+00:36:53,290 --> 00:36:57,050
+تكامل، ولسه في المدرسة، معناته لسه بدنا حدود
+
+469
+00:36:57,050 --> 00:37:02,050
+التكامل، أنت لما تبدأ، احكوا معايا، احتجت، احكوا معايا
+
+470
+00:37:03,130 --> 00:37:08,170
+التكامل، أخذناه في توجيهي، اه اه، بس أخذته في التوجيهي
+
+471
+00:37:08,170 --> 00:37:11,770
+برضه، اه اه، يعني ما بعرف، أخذته في الـ calculus بس هو
+
+472
+00:37:11,770 --> 00:37:14,570
+احنا بندخل نقول: احنا، احنا أكبرنا، لسه ما استخدمتش
+
+473
+00:37:14,570 --> 00:37:17,570
+اللي أكبرنا فيه، قعدنا فيه شغلات، حقول،  أخذناها في
+
+474
+00:37:17,570 --> 00:37:24,510
+calculus، بس ما بقدر أطلع EQ، ما بقدر أطلع EQ، مش عندي مجهول
+
+475
+00:37:24,510 --> 00:37:29,380
+ما بقدر أطلع EQ، هذه هو الفرق، المرة هذه استخدمت الـ
+
+476
+00:37:29,380 --> 00:37:34,020
+jugger، كنت مبسوط، أخذته في سفر، أبيع، أما رجعت عشان ما
+
+477
+00:37:34,020 --> 00:37:39,040
+أخدتش، بلعت، تمام، أخذته، بدي أطلع كيوب، بدي أطلع
+
+478
+00:37:39,040 --> 00:37:42,380
+النجوم، طلعناها، المرة هذه كانت اثنين وثلاثة ومش
+
+479
+00:37:42,380 --> 00:37:44,980
+عارف إيه، شفتيهم، ما طلعناها بنفس الطريقة، بس الطريقة
+
+480
+00:37:44,980 --> 00:37:51,620
+أسهل، كانت، يلا يا بنات، بدنا حدود التكامل، الزمن دائماً
+
+481
+00:37:51,620 --> 00:37:55,420
+أنا ببدأ من الـ zero ولا لأ؟ إذا الزمن دائماً يبدأ
+
+482
+00:37:55,420 --> 00:38:01,120
+من zero، لأن أي زمن، قال لي: أي زمن، طيب، مكفك لما أنت
+
+483
+00:38:01,120 --> 00:38:04,800
+أول ما بدأت كان فاضي ولا ما كانش فاضي؟ إذا الشحنات
+
+484
+00:38:04,800 --> 00:38:10,140
+من أين تبدأها؟ لكي و… أنت… نكامل الطرف هذه
+
+485
+00:38:10,140 --> 00:38:13,360
+عشان ما حد يقول لي: لسه طالعة من توجيهي، إيش تكامل هذه
+
+486
+00:38:13,360 --> 00:38:20,830
+T؟ إذا ناقص T على RC، بيساوي، لأ، كدا واحد منكم شاطرين
+
+487
+00:38:20,830 --> 00:38:26,970
+لأن أنت قلت U بتساوي Q ناقص C في إبسلون، الـ
+
+488
+00:38:26,970 --> 00:38:32,310
+substitution اللي أخذناه بتوجيهي، قلنا U بتساوي Q
+
+489
+00:38:32,310 --> 00:38:39,990
+ناقص C في إبسلون، إذا هذه U بتساوي هذه Q، بس إذا صارت
+
+490
+00:38:39,990 --> 00:38:46,930
+DU على U، فهي لنا الـ U وهي عبارة عن لنا الـ Q ناقص C
+
+491
+00:38:46,930 --> 00:38:53,510
+في إبسلون، من Zero لـ Q، صح
+
+492
+00:38:53,510 --> 00:38:56,750
+ليش؟ ليش لا؟
+
+493
+00:38:59,400 --> 00:39:06,300
+لأن الـ U والـ U، عطلتها، رجعتها، بنعوض، الفوقانية
+
+494
+00:39:06,300 --> 00:39:10,080
+ناقص التحتانية، و ln الـ B ناقص ln الـ A، يا B على A
+
+495
+00:39:10,080 --> 00:39:18,240
+صح، فصارت ناقص T على RC بتساوي ln الـ Q ناقص C في
+
+496
+00:39:18,240 --> 00:39:27,380
+إبسلون على ناقص C في إبسلون، عوضت، سفر مريم
+
+497
+00:39:27,380 --> 00:39:34,590
+أم بدي key وهالـ gate، إيش أسوي؟ الـ key جوه اللذن
+
+498
+00:39:34,590 --> 00:39:40,470
+أيوا، بدي أخذ الـ exponential، يلا نأخذ الـ
+
+499
+00:39:40,470 --> 00:39:51,290
+exponential، صحيح؟
+
+500
+00:39:51,290 --> 00:39:58,300
+ما فيش طريقة غيرها، واحنا بنكبر، ليش؟ لأ، سؤالك حلو
+
+501
+00:39:58,300 --> 00:40:02,420
+يا عياط، لأ،  عدنا بنشوف عشان البدنية، بس احنا رهجات
+
+502
+00:40:02,420 --> 00:40:07,340
+البدنية، أن كل كلمة أو أنا بقعد بحكيها، إذا أنتم
+
+503
+00:40:07,340 --> 00:40:13,200
+أنا بحكي شغلة بتعرفوها، هاش، قولوا لي، بضرب بإشارة سالب
+
+504
+00:40:13,200 --> 00:40:18,300
+وبحسب وبأعمل، وكلّه بنعرفه، تحتجوا زي مريم، ليش بدنا
+
+505
+00:40:18,300 --> 00:40:22,900
+هذه الشغلة، طول سطولتها، تمام؟ بنفسد نعملها كل مرة يا
+
+506
+00:40:22,900 --> 00:40:28,060
+عياط، مرة واحدة نفهمها، تمام، قال لي: طيب هذه الحلوة
+
+507
+00:40:28,060 --> 00:40:34,180
+اللي بالأحمر، هالـ gate، بس بدنا نرتبها، اه، نضربها في
+
+508
+00:40:34,180 --> 00:40:38,980
+إيش؟ في ناقص C في إبسلون، فست، ناقص C في إبسلون، E
+
+509
+00:40:38,980 --> 00:40:44,540
+طبعاً، ناقص T على RC بتساوي Q ناقص C في إبسلون، جيب لي
+
+510
+00:40:44,540 --> 00:40:49,060
+هذه، يعني طلعت Q ولا ما طلعتش؟ الـ Q بتساوي C في
+
+511
+00:40:49,060 --> 00:40:53,120
+إبسلون، أخذ عنهم الشراك، واحد ناقص E، طبعاً ناقص T على
+
+512
+00:40:53,120 --> 00:40:53,460
+RC
+
+513
+00:41:00,680 --> 00:41:08,140
+هيا قيو؟ بدك إياها؟ هيا قيو؟ أول نعالج عليها عشان
+
+514
+00:41:08,140 --> 00:41:11,440
+نعالج عليها، نشوف هي منطقية ولا لأ، عشان نستفيد من
+
+515
+00:41:11,440 --> 00:41:16,220
+الـ calculus اللي أخذناه، يا باتور، باتور، أخذت الـ
+
+516
+00:41:16,220 --> 00:41:23,140
+exponential؟ حلو؟ واحد واحد، براو
+
+517
+00:41:27,090 --> 00:41:32,450
+حين عليكم يا عين عليكم، قول لي: أنت هذه Q معادلة
+
+518
+00:41:32,450 --> 00:41:36,670
+بتحدد لك تصرف الـ Q عند كل زمن ولا لأ؟ طب أنت عن
+
+519
+00:41:36,670 --> 00:41:40,310
+تي بتساوي صفر، كان المكثف فاضي ولا مش فاضي؟ لازم هذه
+
+520
+00:41:40,310 --> 00:41:45,130
+المعادلة لما أحط بتساوي صفر، يظل عليه الصفر، صح؟ ليه
+
+521
+00:41:45,130 --> 00:41:49,650
+جينا نجرب، احكي، واعد، ما تستغربيش، هذه نحطها صفر، إتبار
+
+522
+00:41:49,650 --> 00:41:55,750
+صفر ولا لأ، إتبار صفر، جديش واحد ناقص واحد، زبطت، طيب
+
+523
+00:41:55,750 --> 00:42:03,310
+أنت للمكثف، وخلص، T صارت من النهاية، مظبوط، إيه، بتبقى
+
+524
+00:42:03,310 --> 00:42:07,310
+الناقص من النهاية، إذا الـ Q بيساوي C في إبسلون، طب ما
+
+525
+00:42:07,310 --> 00:42:10,550
+هو Q بيساوي C في فرق الجهود، بقول له: ما هو لما هينط
+
+526
+00:42:10,550 --> 00:42:13,390
+ليه؟ مش بيصير فرق الجهود تبعه بيساوي فرق الجهود تبع
+
+527
+00:42:13,390 --> 00:42:17,670
+البطارية، إذا معناته هذه هي Q maximum ولا مش Q
+
+528
+00:42:17,670 --> 00:42:21,550
+maximum، هذه صح
+
+529
+00:42:21,550 --> 00:42:27,890
+ولا لأ؟ عشان كده؟ عرفتي ليش بدنية؟ لأنه عشان أتذوق
+
+530
+00:42:27,890 --> 00:42:33,630
+حلوة الـ calculus، إيه، كلّه معنى؟ اه، أن هذه هو
+
+531
+00:42:33,630 --> 00:42:38,590
+المعادلة عكست الواقع ولا ما عكستش الواقع؟ عكست
+
+532
+00:42:38,590 --> 00:42:45,110
+الواقع، تمام، قال لي: أنت جبت Q في المعادلة في البداية
+
+533
+00:42:45,110 --> 00:42:49,270
+كان في عندي تيار وكان في عندي Q، صح؟ طيب في الآخر
+
+534
+00:42:49,270 --> 00:42:52,470
+أنت جبت واحد، بالطريقة الثانية، طب بدي التيار من أين
+
+535
+00:42:52,470 --> 00:42:56,990
+أجيبه؟ بدي أشتق، ذم حكت، بتقول I بيساوي DQ على DT
+
+536
+00:42:56,990 --> 00:43:02,450
+أنت مش، إيش جبته؟ بدي التيار يا بنات، بقدر أقول I
+
+537
+00:43:02,450 --> 00:43:10,890
+بيساوي DQ على DT، قبل ما أفاضل، نرجع لمريم، بدي أشتق
+
+538
+00:43:10,890 --> 00:43:16,690
+لها، هذه D على DX، إيه بتبقى ناقص AX؟ أشتقناه
+
+539
+00:43:21,600 --> 00:43:29,840
+يعني سالب AE، طبعاً ناقص AX، صح؟ لإني بدي أشتق هذه الـ
+
+540
+00:43:29,840 --> 00:43:36,260
+A هي واحد على RC هنا، صح؟ نجي نشتق هذه، اللي هجي C Y
+
+541
+00:43:36,260 --> 00:43:43,940
+في واحد ثابت، إيش اشتقاق ثابت؟ Zero، اشتق سالب C في Y
+
+542
+00:43:43,940 --> 00:43:52,840
+في سالب الـ A، صارت RC، إيه بتصير، ناقص T على RC؟
+
+543
+00:43:52,840 --> 00:43:57,640
+هذا كالكلس لسه، وبعدين بنفسر، حلوة الكالكلس، قال لي:
+
+544
+00:43:57,640 --> 00:44:02,820
+هذه ما حدش بيروح إيه؟
+
+545
+00:44:02,820 --> 00:44:07,920
+اه، إيه؟ من وين جبنا هذه الحلوة؟ والله أنا ملببت
+
+546
+00:44:07,920 --> 00:44:11,600
+عشان ما تسميش هذا السؤال، تمام؟ هذه الـ A، واحد على R
+
+547
+00:44:11,600 --> 00:44:17,890
+C، تمام؟ قال لي: شو هذه الـ إبسلون على R؟ قلت له: هذا
+
+548
+00:44:17,890 --> 00:44:23,950
+التيار، عن T بتساوي صفر، ليش؟ نرجع للعدد، T بتساوي صفر
+
+549
+00:44:23,950 --> 00:44:28,870
+إيه بتبقى صفر واحد ولا لأ، إذا لما التيار عن T بتساوي
+
+550
+00:44:28,870 --> 00:44:32,370
+صفر بتساوي Y على R ولا لأ، إذا هذا التيار عن T بتساوي
+
+551
+00:44:32,370 --> 00:44:37,930
+صفر، إذا هذا هو I not، تمام؟
+
+552
+00:44:37,930 --> 00:44:41,810
+حلو، هاجت
+
+553
+00:44:41,810 --> 00:44:46,830
+بدي أعيده يا صفا، طلع عليّ، طلع لي على الدائرة، تيار
+
+554
+00:44:46,830 --> 00:44:51,050
+هذا، المكثف كان فاضي، صح؟ فيه بطارية، اللي البطارية
+
+555
+00:44:51,050 --> 00:44:53,730
+شغلتها بتبدا تيار، لإنه بتعمل فرق جهد وبتجبر
+
+556
+00:44:53,730 --> 00:44:57,030
+الشحنات، إذا في تيار، تيار البطارية، عارفين اتجاهه؟
+
+557
+00:44:57,030 --> 00:45:02,910
+عارفين اتجاهه؟ هذا، نضبت؟ هجيت الـ… المكثف بدأ
+
+558
+00:45:02,910 --> 00:45:12,710
+يشحن، بتطلع تيار؟ ولما نفرغ أفضيه؟ طيب، سمعتوا
+
+559
+00:45:12,710 --> 00:45:18,860
+بالـ Neon الشاحن؟ تعرفوه؟ حلو، لما تقطع الكهربا
+
+560
+00:45:18,860 --> 00:45:24,620
+بضويه؟ اه، ليش؟ لأنه بيكون أنت شحنته، لو مش شحنته
+
+561
+00:45:24,620 --> 00:45:31,900
+بضويه؟ إيش بتشحن جوا مكثف؟ بيفرق شحنات؟ إذا بطلع
+
+562
+00:45:31,900 --> 00:45:37,180
+تيار وبضوي، مكثف، هل جيت تطلعوا لي على المكثف اللي
+
+563
+00:45:37,180 --> 00:45:44,040
+رسمته تبهه؟ تبلعوش، معلومات بتعرفوها تماماً، بتقول…
+
+564
+00:45:44,040 --> 00:45:47,340
+بتقول: اعتبر المكثف بطارية، شوف لي كيف تياره بالعكس
+
+565
+00:45:47,340 --> 00:45:50,680
+…عكس الأول… بديه يطلع نتعقل بالساعة ولا لأ؟
+
+566
+00:45:50,680 --> 00:45:54,980
+زيه ولا عكس الأول؟ عكس الأول، عكسه… عكسه… عكسه…
+
+567
+00:45:54,980 --> 00:45:55,820
+…عكسه… عكسه… عكسه… عكسه… عكسه… عكسه…
+
+568
+00:45:55,820 --> 00:45:57,760
+…عكسه… عكسه… عكسه… عكسه… عكسه… عكسه…
+
+569
+00:45:57,760 --> 00:46:06,160
+عكسه
+
+570
+00:46:06,160 --> 00:46:06,260
+…عكسه… عكسه… عكسه… عكسه… عكسه… عكسه…
+
+571
+00:46:07,410 --> 00:46:11,910
+إذا تساوى… كم يتخلص من 1 متر؟ صفر… وكم يتساوى؟
+
+572
+00:46:11,910 --> 00:46:15,490
+لما ينشحن كامل، لإنه صار فرق جهد وبتساوي جهد فرق
+
+573
+00:46:15,490 --> 00:46:19,130
+جهد بالبطارية، وكأنه في عندك بطاريتين نفس الجهد عكس
+
+574
+00:46:19,130 --> 00:46:23,650
+بعيد… كمّ التيار؟ صفر ولا لا؟ إذا معناته… إيش
+
+575
+00:46:23,650 --> 00:46:29,230
+اللي قالت لي… ما فهمتيهاش؟ قلت لك هذا… التيار
+
+576
+00:46:29,230 --> 00:46:33,360
+عندي بتساوي صفر، بس تبقى البطارية، لإنه ما كانش المكثف
+
+577
+00:46:33,360 --> 00:46:37,340
+مليان، بس تبقى البطارية، جي من المكثف وحط محله
+
+578
+00:46:37,340 --> 00:46:40,280
+silicon، شوفوا إيه، إيش التيار بيساوي؟ إبسلون على R
+
+579
+00:46:40,280 --> 00:46:45,700
+ولا لأ؟ إذا إبسلون على R هذا I not ولا لأ، بعد كده
+
+580
+00:46:45,700 --> 00:46:50,660
+أنت للمكثف، استنيت ساعة، ساعتين، تلاتة، طلعت على الـ
+
+581
+00:46:50,660 --> 00:46:56,460
+emitter، الأصل، إيش يقرأ؟ Zero، Zero، صح ولا لأ؟ اطلع
+
+582
+00:46:56,460 --> 00:47:00,560
+يا واعد، هدى، حجة، حطّي محلها، ما للنهاية، ما جاش تيار طلع
+
+583
+00:47:00,560 --> 00:47:05,450
+صفر، إذا بعد مدرسة طويلة، طلع صفر، ليش؟ لإنه التيارين
+
+584
+00:47:05,450 --> 00:47:10,910
+اتساووا، عكس بعض، اتعاكسوا مع بعض ولا لا؟ إذا معناته
+
+585
+00:47:10,910 --> 00:47:15,710
+هدول التيارين، IB تبع البطارية، و IC تبع الكباسيتار
+
+586
+00:47:15,710 --> 00:47:19,570
+عكس بعض، إذا اتساووا، معناته لازم يكون التيار الكلي
+
+587
+00:47:19,570 --> 00:47:23,510
+يساوي زيرو، وهذه اللي أثبتته الـ calculus والـ
+
+588
+00:47:23,510 --> 00:47:27,950
+exponential، أنت… اه، infinity… اه، أنت عارفاها من
+
+589
+00:47:27,950 --> 00:47:31,370
+…من سنة أولى يا صفراء، فصل أول، infinity، شغلة
+
+590
+00:47:31,370 --> 00:47:35,010
+نسبية، أنا عندي هنا الـ infinity ممكن تكون نص ساعة
+
+591
+00:47:35,010 --> 00:47:39,630
+نص ساعة، لإنه أنت بتتعامل مع seconds، اتصور وثلاثين
+
+592
+00:47:39,630 --> 00:47:42,990
+دقيقة تطير، يعني بالنسبة لإشي، اه، بالنسبة لإشي، أنت
+
+593
+00:47:42,990 --> 00:47:46,250
+لما قعدت الـ infinity، لما تتأكد أن المكثف أنت لا
+
+594
+00:47:46,250 --> 00:47:50,050
+وصلتي للمنال، نهاية، تمام؟ هيك وصلتي للمنال، نهاية
+
+595
+00:47:50,050 --> 00:47:53,210
+احكيه
+
+596
+00:47:53,210 --> 00:47:59,090
+واحدة فيكم يلا، اه اه اه اه اه اه اه اه اه اه
+
+597
+00:47:59,090 --> 00:47:59,150
+اه اه اه اه اه اه اه اه اه اه اه
+
+598
+00:47:59,150 --> 00:47:59,250
+اه اه اه اه اه اه اه اه اه اه اه
+
+599
+00:47:59,250 --> 00:47:59,930
+اه اه اه اه اه اه اه اه اه اه اه اه اه اه
+
+600
+00:47:59,930 --> 00:48:02,370
+اه اه اه اه اه اه اه اه اه اه اه اه اه اه
+
+601
+00:48:02,370 --> 00:48:07,970
+اه اه اه اه اه اه اه اه اه اه اه اه اه اه
+
+602
+00:48:07,970 --> 00:48:16,580
+اه اه اه اه اه اه اه اه اه اه اه اه اه اه، ازي
+
+603
+00:48:16,580 --> 00:48:19,10
+
+667
+00:53:18,760 --> 00:53:22,180
+بتساوي صفر، بدي أجيب وأحط محله سيليك
+
+668
+00:53:24,510 --> 00:53:29,630
+هلجيت جاني عنتيقوس، ثم لنهاية الطيار سوى صفر، و
+
+669
+00:53:29,630 --> 00:53:33,510
+وقتيش الطيار بيساوي صفر؟ نجرب، تطلعولي يا بنات، هاي
+
+670
+00:53:33,510 --> 00:53:40,290
+دائرة، فيه قديش طيار صفر؟ إذا إيش يسوي في المكثف لما
+
+671
+00:53:40,290 --> 00:53:44,250
+تقول لك بعد مدرسة جيب المكثف، واعتبره شباك في الدائرة
+
+672
+00:53:44,250 --> 00:53:48,110
+شباك في الدائرة، صح ولا لأ؟ لما يكون في شباك في
+
+673
+00:53:48,110 --> 00:53:54,320
+الدائرة، في طيار لأ. إذا بيقول لي after closing the
+
+674
+00:53:54,320 --> 00:53:57,860
+switch for a long time، التيار I goes to  صفر، نهاية
+
+675
+00:53:57,860 --> 00:54:01,160
+أو مرات بيقول لك steady state condition، يعني أنه
+
+676
+00:54:01,160 --> 00:54:04,560
+خلاص وقفت الشحنات، الـ steady state، the capacitor
+
+677
+00:54:04,560 --> 00:54:09,660
+acts as if it were an open switch، بعتبره open
+
+678
+00:54:09,660 --> 00:54:13,460
+switch، أو شباك في الدائرة. عيد هدول القاعدتين كتير
+
+679
+00:54:13,460 --> 00:54:17,880
+مهمات، ليش الثانية؟ عشان التيار صفر، ماشي؟ احنا
+
+680
+00:54:17,880 --> 00:54:22,300
+بنقول عند…هيا… هالطيار هنا يا… I بتساوي I
+
+681
+00:54:22,300 --> 00:54:27,520
+not،  إتوا بقى ناقص T على tau، حط لي T بيه مالانهاية
+
+682
+00:54:27,520 --> 00:54:30,700
+بصير صفر، بقول ما بيمشي ليه؟ تصير طيار صفر لما يكون
+
+683
+00:54:30,700 --> 00:54:35,220
+فيه فتحة في الدائرة، صح؟ المكثف هو الفتحة، إذا من
+
+684
+00:54:35,220 --> 00:54:38,780
+وين؟
+
+685
+00:54:38,780 --> 00:54:42,800
+هو أنت مفكر المفتاح، أنت بتعيهي أنا مفكر المفتاح
+
+686
+00:54:42,800 --> 00:54:45,980
+وأنت لا، هو أن أنا فتحت المفتاح، بنت ليه؟ بنت المكثف
+
+687
+00:54:47,300 --> 00:54:51,660
+اه، مفعش اه…ذاتم، وأنت عاملة دائرة، وأنت مسكرة
+
+688
+00:54:51,660 --> 00:54:55,180
+مفتاحك، صار التيار صفر، عادة بتقوله كأنه المكثف صار
+
+689
+00:54:55,180 --> 00:55:01,380
+هو المفتوح، المفتاح ما تمسكه، تمام هيك؟ حلو، احكيها
+
+690
+00:55:01,380 --> 00:55:05,320
+يعني
+
+691
+00:55:05,320 --> 00:55:09,220
+غالبا اه، بس اعتبريها هي قيمة التيار عندك بالساعة
+
+692
+00:55:09,220 --> 00:55:14,730
+صفر، أكثر دقة، عشان كده حطيت  I note initial، ذاكرها
+
+693
+00:55:14,730 --> 00:55:21,050
+مرات في الكتب بيكتبوها V0، تمام؟ فهذه أفضل، كتير مرات
+
+694
+00:55:21,050 --> 00:55:25,330
+بتكون كلامك صح، بس هي علميا أفضل هذا التعريف، أنه
+
+695
+00:55:25,330 --> 00:55:29,370
+قيمة التيار عندي بتساوي صفر، لأنه مرات بتتأكس، يعني
+
+696
+00:55:29,370 --> 00:55:34,930
+مرة طيب يا بنات، عارف أنه خلصت، بتعرف رسمة الـ
+
+697
+00:55:34,930 --> 00:55:42,290
+exponential كيف؟ طب ارسمولي هذه، كيف بدك ترسموها؟
+
+698
+00:55:43,830 --> 00:55:51,030
+طيب كيف تصير تسيم؟ أو صومها؟ انبسطني
+
+699
+00:55:51,030 --> 00:55:55,810
+شوية، هديك طلع
+
+700
+00:55:55,810 --> 00:56:00,830
+تيار ببدأ من I note، وهي قيمة التيار عندك بتساوي
+
+701
+00:56:00,830 --> 00:56:06,850
+صفر، يا لما، وبيضل يتناقص، يتناقص، سؤالك بيتناقص لما
+
+702
+00:56:06,850 --> 00:56:13,480
+يتلاشى، أما الشحنات بتبدأ صفر، وبتبدأ تزيد، تزيد، هذا
+
+703
+00:56:13,480 --> 00:56:18,260
+بيسموه asymptote، في القلقلص، لأنه خلاص،  تمام
+
+704
+00:56:18,260 --> 00:56:20,040
+هيك؟ العربية، هيبقى بنكمل إن شاء الله
diff --git a/PL9fwy3NUQKwZzXsCLffozucGP33XWqvBP/Z1q3A5nGXN8_raw.json b/PL9fwy3NUQKwZzXsCLffozucGP33XWqvBP/Z1q3A5nGXN8_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..50ee44c3bad2464a1c9d0707115e06dcaf979113
--- /dev/null
+++ b/PL9fwy3NUQKwZzXsCLffozucGP33XWqvBP/Z1q3A5nGXN8_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 2038, "start": 5.26, "end": 20.38, "text": "Okay girls, let's start chapter 9. Of course, we are finishing this subject step by step. We have two chapters left. Chapter 9 is a very important title for him. He found a very important law in the science of electricity. 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Faraday is the one who created this electricity. He is the one who convinced us that there is electricity that does not come from batteries and that's it. So this is the Faraday's law. Okay. The Faraday's law and the doctrine behind it has an organic interference between them. They complement each other. What are we going to explain? 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A hypothetical law that talks about electromagnetic induction. 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There is no doubt about it. So look at the law, like Newton's law, right or wrong? Newton's second law or Newton's laws. And this is a hypothetical law that was made in 1830, that is, years ago, and it was done millions of times. And it was proven. 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Was he a djinn or a mouse? What made him move? He was concentrating and started doing scientific experiments to see what happened. What were these experiments? So, what does the original say? It says that it brings us back to the previous chapter. What is in the previous chapter? The information that we got from it. 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What happened to the magnetic field that is here? Did it increase or decrease? It increased. As soon as I moved the magnet, what happened to the indicator? 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As if there was a current. If the conclusion here is that there is a current, in which direction will it be indicated? He recorded this observation. He said, okay, let's see if I want to do something else. 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It's up to you to change the flux. I tell him to change the flux in three cases. You have to change B, you have to change A, you have to change the angle, or you have to change any 2,2 or any 3 together. 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If it changes, does it stop? Yes. Does it stop with the equation? Yes. No, wait a minute. Your question is excellent. Look, we have a change. There are changes. Where did you get the calculus? I don't know, I'm forgetting your calculus. You have two changes. You took two changes, you didn't take them. 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What does crushing mean? What did you do to the area? You changed the area. You made it smaller. So a plane is born. So here it is born. It says I want it, don't give birth to it. I say this is not the choice I want. This means crushing. Exactly. You hold it and crush it as they say in Arabic in this country. Crush. 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Did the field change? Did it crash? Did it rotate? Nothing changed. This is exactly how I drew her during Corona. I told her to calm down. She came in and said, wait a minute, let's start this game. Let's start. What changed? 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Is it correct, Mona? Good. What is the fourth option? I told him the moment when the loop comes out. I told him the moment when the loop comes out. There was a value that became zero. So it changed, although it is uniform, but I changed it over time. 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Conductor means that there are charges. We say that the charges are like a mouse inside. Do you remember the mouse? If there is a mouse inside, it moves. What happens to the mouse? It moves. If there is a mouse inside, it moves. If there is a mouse inside, it moves. If there is a mouse inside, it moves. If there is a mouse inside, it moves. If there is a mouse inside, it moves. If there is a mouse inside, it moves. If there is a mouse inside, it moves. If there is a mouse inside, it moves. If there is a mouse inside, it moves. If there is a mouse inside, it moves. If there is a mouse inside, it moves. If there is a mouse inside, it moves. If there is a mouse inside, it moves. If there is a mouse inside, it moves. If there is a mouse inside, it moves. If there is a mouse inside, it moves. 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So that we can benefit from it. Okay, it turned out to be EVP-J. Is it correct or not? This is what we got. It is like chapter 7. What does it mean? It is an atom. What is negative? Where did it go? Okay, if it is positive, it should be negative, right? Because this electron is not an orphan. It is correct that it is M, which is an atom. When an atom takes an electron from it, it becomes positive. Where did it go? To the top. 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In chapter 1, there was a force called electric force. It is equal to Q. Do you remember it? 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He said to me, at first, before you separate the first person, it was the charges. You don't have an electric field. You separated. Can you say inside this ship that there is an electric field or not? 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So that we don't die one day. As you know, if we try the sun or the moon, we don't live. Everything is predetermined. 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Okay mom. One and a half. One and a half. Good. How many people need a radio remote control? Two. Two. Look at the remote control that you see every day. See how many volts are written on it. 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The clock, once we put the stone, it's enough. So it's one and a half volts. Okay, if you hold the stone between your hands, does it turn on electricity? And it's one and a half volts, so what if it's ten volts? It means that everything is in order. Take the electricity to recharge it. They said okay. Okay, good, we're not done yet. They said, where are you, my hypothesis? I made a law, this is the difference in effort, and you made a law for me. 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Wait a minute, and you will answer me. But get up. Don't give up. Okay? Good. Wait a little bit. First, you will come and say, how did the cargo ship go down? And the ship? Okay. The ship closed above the ship and below the ship. The battery died. 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He said that this is L to the power of x. Is x constant? No. Is L constant? Yes. So it is B L dx over dt. What is this? Who are you asking? Look at this. This moves. Do you see it? 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moves generates between two sides a difference of force, which is given by the relation PL to V using the law of Fermat's law or using the laws of chapter 7. Right or wrong? Right. This is a law. This is not Fermat's law. This is not. This is an interpretation after Fermat's law. Fermat's law is different from the rest of the scientists, but it is one of them. Right. Fermat's law is easy. That's it. 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And A is equal to I L cross B. Did you hear that? Good. Tell me that L is the direction of the current to the top. Right? 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J cross K I. So minus I. So how is the direction? The force is opposite to the speed. Look exactly like this. This is a man. He wants to throw himself on the ground. You shot him. Who wants to stop him?", "tokens": [1726, 363, 3175, 591, 30, 508, 3278, 591, 286, 13, 407, 3175, 286, 13, 407, 577, 307, 264, 3513, 30, 440, 3464, 307, 6182, 281, 264, 3073, 13, 2053, 2293, 411, 341, 13, 639, 307, 257, 587, 13, 634, 2738, 281, 3507, 3647, 322, 264, 2727, 13, 509, 3347, 796, 13, 2102, 2738, 281, 1590, 796, 30], "avg_logprob": -0.5420258445986386, "compression_ratio": 1.3974358974358974, "no_speech_prob": 8.940696716308594e-07, "words": [{"start": 2611.46, "end": 2611.72, "word": " Not", "probability": 0.07403564453125}, {"start": 2611.72, "end": 2611.92, "word": " B", "probability": 0.654296875}, {"start": 2611.92, "end": 2612.1, "word": " minus", "probability": 0.224609375}, {"start": 2612.1, "end": 2612.42, "word": " K?", "probability": 0.9365234375}, {"start": 2613.14, "end": 2613.66, "word": " J", "probability": 0.666015625}, {"start": 2613.66, "end": 2614.64, "word": " cross", "probability": 0.70703125}, {"start": 2614.64, "end": 2615.44, "word": " K", "probability": 0.420166015625}, {"start": 2615.44, "end": 2616.36, "word": " I.", "probability": 0.548828125}, {"start": 2616.84, "end": 2617.32, "word": " So", "probability": 0.55712890625}, {"start": 2617.32, "end": 2617.58, "word": " minus", "probability": 0.404052734375}, {"start": 2617.58, "end": 2617.92, "word": " I.", "probability": 0.9736328125}, {"start": 2618.3, "end": 2618.44, "word": " So", "probability": 0.73681640625}, {"start": 2618.44, "end": 2618.6, "word": " how", "probability": 0.48046875}, {"start": 2618.6, "end": 2618.66, "word": " is", "probability": 0.6630859375}, {"start": 2618.66, "end": 2618.72, "word": " the", "probability": 0.421875}, {"start": 2618.72, "end": 2618.96, "word": " direction?", "probability": 0.85693359375}, {"start": 2621.36, "end": 2621.88, "word": " The", "probability": 0.62451171875}, {"start": 2621.88, "end": 2622.42, "word": " force", "probability": 0.90966796875}, {"start": 2622.42, "end": 2622.96, "word": " is", "probability": 0.744140625}, {"start": 2622.96, "end": 2623.24, "word": " opposite", "probability": 0.442626953125}, {"start": 2623.24, "end": 2623.44, "word": " to", "probability": 0.72607421875}, {"start": 2623.44, "end": 2623.44, "word": " the", "probability": 0.72265625}, {"start": 2623.44, "end": 2623.78, "word": " speed.", "probability": 0.73828125}, {"start": 2624.8, "end": 2625.3, "word": " Look", "probability": 0.6064453125}, {"start": 2625.3, "end": 2625.62, "word": " exactly", "probability": 0.4501953125}, {"start": 2625.62, "end": 2625.8, "word": " like", "probability": 0.1756591796875}, {"start": 2625.8, "end": 2626.2, "word": " this.", "probability": 0.85546875}, {"start": 2626.26, "end": 2626.46, "word": " This", "probability": 0.283203125}, {"start": 2626.46, "end": 2626.54, "word": " is", "probability": 0.425048828125}, {"start": 2626.54, "end": 2626.8, "word": " a", "probability": 0.85107421875}, {"start": 2626.8, "end": 2626.8, "word": " man.", "probability": 0.410400390625}, {"start": 2627.02, "end": 2627.28, "word": " He", "probability": 0.7470703125}, {"start": 2627.28, "end": 2627.4, "word": " wants", "probability": 0.5107421875}, {"start": 2627.4, "end": 2627.42, "word": " to", "probability": 0.95849609375}, {"start": 2627.42, "end": 2627.6, "word": " throw", "probability": 0.7802734375}, {"start": 2627.6, "end": 2627.78, "word": " himself", "probability": 0.330078125}, {"start": 2627.78, "end": 2627.82, "word": " on", "probability": 0.56201171875}, {"start": 2627.82, "end": 2627.9, "word": " the", "probability": 0.916015625}, {"start": 2627.9, "end": 2628.26, "word": " ground.", "probability": 0.712890625}, {"start": 2628.78, "end": 2629.12, "word": " You", "probability": 0.29931640625}, {"start": 2629.12, "end": 2629.44, "word": " shot", "probability": 0.308837890625}, {"start": 2629.44, "end": 2629.78, "word": " him.", "probability": 0.92138671875}, {"start": 2630.22, "end": 2630.56, "word": " Who", "probability": 0.85791015625}, {"start": 2630.56, "end": 2630.8, "word": " wants", "probability": 0.56201171875}, {"start": 2630.8, "end": 2630.86, "word": " to", "probability": 0.97216796875}, {"start": 2630.86, "end": 2631.08, "word": " stop", "probability": 0.86767578125}, {"start": 2631.08, "end": 2631.28, "word": " him?", "probability": 0.84375}], "temperature": 1.0}, {"id": 110, "seek": 266106, "start": 2632.26, "end": 2661.06, "text": "The force of the interaction towards the opposite of speed or not. When I want to put it, I put a negative. The force of the interaction, right? So this force is negative, my dear. Okay, I put it negative. Okay, we put it negative. So where did this come from? I told him it came from movement. Can I say I equals epsilon over R? They said yes. And this? Okay, what happened to you? This came out of nowhere. 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Is it correct or not? It is correct. And here there is also a B. So it is B squared. And here there is also a L. So it is L squared. So I have B squared. L squared in V over A is equal to M DV. 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Because you need a V, you need a whole. And here there is a V. Give me this here, and give me this here. Do you know how to do it? Then we do it. Let's do it. Then we complete it. It became a square. What is a square? It is a square. On R, there is M. And here is DT. And here is DV. And this is the V that was here. 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"word": " also", "probability": 0.327392578125}, {"start": 3080.3, "end": 3080.3, "word": " said,", "probability": 0.5361328125}, {"start": 3080.7, "end": 3080.88, "word": " less", "probability": 0.2083740234375}, {"start": 3080.88, "end": 3081.14, "word": " than", "probability": 0.94482421875}, {"start": 3081.14, "end": 3081.48, "word": " ten", "probability": 0.595703125}, {"start": 3081.48, "end": 3082.58, "word": " volts", "probability": 0.767578125}, {"start": 3082.58, "end": 3082.58, "word": " came", "probability": 0.5341796875}, {"start": 3082.58, "end": 3082.58, "word": " out,", "probability": 0.87060546875}, {"start": 3082.62, "end": 3082.76, "word": " don't", "probability": 0.6170654296875}, {"start": 3082.76, "end": 3083.12, "word": " worry,", "probability": 0.53173828125}, {"start": 3083.86, "end": 3084.48, "word": " because", "probability": 0.81982421875}, {"start": 3084.48, "end": 3085.34, "word": " B,", "probability": 0.312744140625}, {"start": 3085.78, "end": 3086.14, "word": " which", "probability": 0.818359375}, {"start": 3086.14, "end": 3086.48, "word": " our", "probability": 0.5419921875}, {"start": 3086.48, "end": 3086.48, "word": " Lord", "probability": 0.75390625}, {"start": 3086.48, "end": 3086.88, "word": " created,", "probability": 0.83251953125}, {"start": 3087.14, "end": 3087.32, "word": " is", "probability": 0.787109375}, {"start": 3087.32, "end": 3087.66, "word": " small,", "probability": 0.91650390625}, {"start": 3088.24, "end": 3088.54, "word": " so", "probability": 0.481201171875}, {"start": 3088.54, "end": 3088.92, "word": " don't", "probability": 0.7841796875}, {"start": 3088.92, "end": 3089.32, "word": " worry,", "probability": 0.79150390625}, {"start": 3090.12, "end": 3090.46, "word": " okay?", "probability": 0.73583984375}, {"start": 3090.84, "end": 3091.02, "word": " So", "probability": 0.796875}, {"start": 3091.02, "end": 3091.2, "word": " it", "probability": 0.49951171875}, {"start": 3091.2, "end": 3091.4, "word": " turned", "probability": 0.197265625}, {"start": 3091.4, "end": 3091.48, "word": " out", "probability": 0.89453125}, {"start": 3091.48, "end": 3091.56, "word": " to", "probability": 0.66064453125}, {"start": 3091.56, "end": 3091.64, "word": " be", "probability": 0.94970703125}, {"start": 3091.64, "end": 3091.82, "word": " this", "probability": 0.6142578125}, {"start": 3091.82, "end": 3092.26, "word": " much.", "probability": 0.60302734375}, {"start": 3092.66, "end": 3093.1, "word": " Nice!", "probability": 0.29296875}, {"start": 3095.34, "end": 3095.94, "word": " For", "probability": 0.349365234375}, {"start": 3095.94, "end": 3096.38, "word": " next", "probability": 0.6201171875}, {"start": 3096.38, "end": 3096.46, "word": " time,", "probability": 0.88818359375}, {"start": 3096.92, "end": 3097.26, "word": " okay?", "probability": 0.69921875}, {"start": 3097.82, "end": 3098.1, "word": " God", "probability": 0.51806640625}, {"start": 3098.1, "end": 3098.22, "word": " bless", "probability": 0.85986328125}, {"start": 3098.22, "end": 3098.3, "word": " you", "probability": 0.943359375}, {"start": 3098.3, "end": 3098.38, "word": " all.", "probability": 0.411376953125}], "temperature": 1.0}], "language": "en", "language_probability": 1.0, "duration": 3099.05125, "duration_after_vad": 3011.5962499999873}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZzXsCLffozucGP33XWqvBP/bW5S0SLU8ho_raw.srt b/PL9fwy3NUQKwZzXsCLffozucGP33XWqvBP/bW5S0SLU8ho_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..582890b3d00a1e6836c2f19e530ccebf6051c441
--- /dev/null
+++ b/PL9fwy3NUQKwZzXsCLffozucGP33XWqvBP/bW5S0SLU8ho_raw.srt
@@ -0,0 +1,1252 @@
+1
+00:00:05,360 --> 00:00:11,080
+تماما بنات نستكمل ما تبقى من هذا ال chapter حكينا
+
+2
+00:00:11,080 --> 00:00:17,300
+على الداي Electric وإيش مفعوله فقلنا إن C بيساوي
+
+3
+00:00:17,300 --> 00:00:24,600
+Kappa في C Note وبيساوي Kappa Epsilon Note A على D
+
+4
+00:00:25,770 --> 00:00:30,030
+لو كان برا للبيت capacitor وبالتالي صار بدل ال
+
+5
+00:00:30,030 --> 00:00:33,930
+epsilon note او مرات انا بكتبها كيف بتسوي epsilon
+
+6
+00:00:33,930 --> 00:00:39,370
+a على d وهذه epsilon حسب المادة بتسوي قعبة في
+
+7
+00:00:39,370 --> 00:00:42,990
+epsilon note زي ما انتوا شايفين تمام يعني ايش
+
+8
+00:00:42,990 --> 00:00:48,070
+بتسوي الضايلكترك في الcapacitor بتزود ساعته حلو
+
+9
+00:00:48,070 --> 00:00:54,280
+بقولي hi two capacitors كم توصلين يا بنات؟توالي
+
+10
+00:00:54,280 --> 00:00:57,340
+حلو هذه برمجة حلوه اول حاجه لو حد يعرف اشي اللي
+
+11
+00:00:57,340 --> 00:01:02,680
+بيسويها تمه نشوف اش بدك جالي two capacitors are
+
+12
+00:01:02,680 --> 00:01:07,060
+connected in series بتعرفوا اش معناه ال series اش
+
+13
+00:01:07,060 --> 00:01:12,240
+اللي بتساوي في ال series الشحنات حلو جالي as shown
+
+14
+00:01:12,240 --> 00:01:16,170
+in the figure و الفيجر يبين ان ال series أصلاإيه
+
+15
+00:01:16,170 --> 00:01:20,590
+سويه؟ قال لي واحد من ال two capacitors حطيت جواه
+
+16
+00:01:20,590 --> 00:01:28,870
+تضايق electric واحد بس is inserted between the
+
+17
+00:01:28,870 --> 00:01:33,830
+blades of C1 C2 اللي لعبت فيه؟ لأ which of the
+
+18
+00:01:33,830 --> 00:01:38,050
+following is correct؟
+
+19
+00:01:38,050 --> 00:01:42,380
+لأليش؟ ايش الغلط؟ C2 اللي اللي اللي اللي اللي اللي
+
+20
+00:01:42,380 --> 00:01:42,780
+اللي اللي اللي اللي اللي اللي اللي اللي اللي اللي
+
+21
+00:01:42,780 --> 00:01:43,740
+اللي اللي اللي اللي اللي اللي اللي اللي اللي اللي
+
+22
+00:01:43,740 --> 00:01:45,520
+اللي اللي اللي اللي اللي اللي اللي اللي اللي اللي
+
+23
+00:01:45,520 --> 00:01:47,040
+اللي اللي اللي اللي اللي اللي اللي اللي اللي اللي
+
+24
+00:01:47,040 --> 00:01:47,160
+اللي اللي اللي اللي اللي اللي اللي اللي اللي اللي
+
+25
+00:01:47,160 --> 00:01:47,420
+اللي اللي اللي اللي اللي اللي اللي اللي اللي اللي
+
+26
+00:01:47,420 --> 00:01:47,420
+اللي اللي اللي اللي اللي اللي اللي اللي اللي اللي
+
+27
+00:01:47,420 --> 00:01:47,420
+اللي اللي اللي اللي اللي اللي اللي اللي اللي اللي
+
+28
+00:01:47,420 --> 00:01:50,600
+اللي اللي اللي اللي اللي اللي اللي اللي اللي اللي
+
+29
+00:01:50,600 --> 00:02:04,740
+اللي اللي اللي اللي اللي اللي اللي اللي
+
+30
+00:02:04,740 --> 00:02:04,740
+اللي الل
+
+31
+00:02:13,160 --> 00:02:19,820
+أه حلو بس إيش خبرة Q1 و Q2؟ بخترفوا عن بعض؟ بس إيش
+
+32
+00:02:19,820 --> 00:02:23,440
+بيفرج؟ بدون die electric و مع die electric؟ زي بقى
+
+33
+00:02:23,440 --> 00:02:28,060
+بيبقى ده اللي ما هو Q؟ هل جيت مش C1 زادت؟ طب في
+
+34
+00:02:28,060 --> 00:02:31,760
+equivalent إيه صار فيها؟ بدأت زيد إذا الشحنات اللي
+
+35
+00:02:31,760 --> 00:02:36,100
+ع C1 زادتوما زالوا متواصلين على التوالي إذا
+
+36
+00:02:36,100 --> 00:02:38,580
+الشحنات اللي على التانية غصب عنها بدها تزيد زي
+
+37
+00:02:38,580 --> 00:02:46,280
+الأولى صح ولا لأ نشوف الخيارات اللي وراها قاللي
+
+38
+00:02:46,280 --> 00:02:51,940
+هذه للأعمى هذه للسكران صح هذه هيك بس نشوف هذه
+
+39
+00:02:51,940 --> 00:02:55,380
+للواحدة
+
+40
+00:02:55,380 --> 00:02:58,930
+الأولى بيقولي ممكن هذه تكون صحإذا مش متواصين على
+
+41
+00:02:58,930 --> 00:03:03,390
+التوازي لكن عشان هم متواصين على التوازي هجت زيادة
+
+42
+00:03:03,390 --> 00:03:05,950
+السحب زيدي الشحنات ما زال البطارية موجودة ولا لأ
+
+43
+00:03:05,950 --> 00:03:10,730
+بزيدي الشحنات جالي هو بنفع الأولى تكون شحناتها عشر
+
+44
+00:03:10,730 --> 00:03:14,230
+أو تانية تمانية بنفعش ما زال زودتي الأولى ايش
+
+45
+00:03:14,230 --> 00:03:18,910
+تتعرف التانية بتزيد لإنهم متواصين على التوازي طيب
+
+46
+00:03:18,910 --> 00:03:22,430
+اتخيلوا الرسمة وهدول متواصين على التوازي وشوفوا
+
+47
+00:03:22,430 --> 00:03:26,730
+اليمين من الخيارات صح الاخيرة الاخيرة براولو كانوا
+
+48
+00:03:26,730 --> 00:03:29,790
+متواصلين على التوازي بقوله هدول مش متواصلين على
+
+49
+00:03:29,790 --> 00:03:33,090
+التوالي وبالتالي كل واحد بيلعب لحاله كل واحد
+
+50
+00:03:33,090 --> 00:03:37,830
+شحناته بتلعب لحالها وبالتالي في واحد زودها زودت
+
+51
+00:03:37,830 --> 00:03:41,630
+كيو واحد في اتنين مالعبتش فيها اذا كيو اتنين دلت
+
+52
+00:03:41,630 --> 00:03:43,570
+زي ما هي تمام يا بنات؟
+
+53
+00:03:47,470 --> 00:03:51,570
+أه صح هو ايش اللي زود الـQ واحد؟ وجود البطارية
+
+54
+00:03:51,570 --> 00:03:56,750
+تمام؟ مثلا هذه القاعدة بيقول لو ماوجدتش البطارية
+
+55
+00:03:56,750 --> 00:04:01,170
+يعني الـQ مضمنة تتغير بس طبعا تخبلك هنا هو دول
+
+56
+00:04:01,170 --> 00:04:04,930
+اتنين وممكن واحد ياخد من التاني لكن الـQ الكلية حد
+
+57
+00:04:04,930 --> 00:04:09,950
+دالها ثابتة صح هيجزك وعشان كده وافقتك الـQ الكلية
+
+58
+00:04:09,950 --> 00:04:13,170
+لكن ممكن واحد ياخد من التاني لإن هو دول اتنين لو
+
+59
+00:04:13,170 --> 00:04:16,710
+واحد بيقولك الـQ ومفيش غيرها دالها ثابتةممكن ياخد
+
+60
+00:04:16,710 --> 00:04:22,390
+واحد ياخد من التاني اه يعني بمعنى اخر انت مجسمة
+
+61
+00:04:22,390 --> 00:04:27,270
+شحنات عندك عشرة مافيش غيرهم مظبوط جسمتيهم هنا هذا
+
+62
+00:04:27,270 --> 00:04:31,570
+خمسة و هذا خمسة روحت قولتله هذا وصلي بطنه وصلي
+
+63
+00:04:31,570 --> 00:04:34,230
+بطنه وصلي بطنه وصلي بطنه وصلي بطنه وصلي بطنه وصلي
+
+64
+00:04:34,230 --> 00:04:34,630
+بطنه وصلي بطنه وصلي بطنه وصلي بطنه وصلي بطنه وصلي
+
+65
+00:04:34,630 --> 00:04:34,630
+بطنه وصلي بطنه وصلي بطنه وصلي بطنه وصلي بطنه وصلي
+
+66
+00:04:34,630 --> 00:04:38,630
+بطنه وصلي بطنه وصلي بطنه وصلي بطنه وصلي بطنه وصلكن
+
+67
+00:04:38,630 --> 00:04:42,930
+في الأخر المجموع ضالة عشرة أخد سبعة التانية ضالة
+
+68
+00:04:42,930 --> 00:04:46,310
+تلاتة صح احنا لما قولنا لما نفوق البطارية ال total
+
+69
+00:04:46,310 --> 00:04:51,610
+charge ممنوع تزيد ل .. بالتالي لكن ممكن واحد ياخد
+
+70
+00:04:51,610 --> 00:04:54,530
+من التاني تحكي يعني .. يعني هرجتها لو أنا ماعنديش
+
+71
+00:04:54,530 --> 00:04:59,190
+بطارية بنحكي سواء Q واحد بتزيد و سواء اتنين بتزيد
+
+72
+00:04:59,190 --> 00:05:02,470
+براو عليكي اه لما بديت تاخد من أختها هاملهم ازاي
+
+73
+00:05:02,470 --> 00:05:06,250
+اخد لكن لما مافيش أختها ليهاش تاخد بيضالها زي ما
+
+74
+00:05:06,250 --> 00:05:13,810
+هيتمام هيك؟ حلو بحكي عربي؟ تمام
+
+75
+00:05:13,810 --> 00:05:21,150
+جاني شوف هالسؤال الحلو جالي هذا capacitor حلو إيه
+
+76
+00:05:21,150 --> 00:05:25,010
+سويت فيه؟ جالي جيبتي لك جطعة من انحاس الصفار
+
+77
+00:05:25,010 --> 00:05:28,510
+شايفينه؟ انحاس .. انحاس conductor دي بالكم مظبوط
+
+78
+00:05:28,510 --> 00:05:33,160
+ولا لأ؟ وحطيتها في النصقال ليه صار عندك بتدي السي
+
+79
+00:05:33,160 --> 00:05:36,680
+على هالجهاز اللي انت عملته؟ قلت له هذا كبسطر في
+
+80
+00:05:36,680 --> 00:05:42,180
+النهاية بقدر اقول فيش ضايق electric ولا لا فوق فيه
+
+81
+00:05:42,180 --> 00:05:47,320
+هواء و تحت فيه هواء بقدر اقول كابها دي واحد عشان
+
+82
+00:05:47,320 --> 00:05:52,160
+هواء ابسل نوت ايه على دي بقولك لا ليش لا بقولك هو
+
+83
+00:05:52,160 --> 00:05:58,940
+المسافة دي ضلاطواللي دي انخسفت انخسفت دي جالي طب
+
+84
+00:05:58,940 --> 00:06:02,760
+كيف بيكي تسويها جالي المسافة الفجانية والمسافة
+
+85
+00:06:02,760 --> 00:06:05,520
+التحتانية جات بعض اعتبرها لأنه جالي انا حاططها دي
+
+86
+00:06:05,520 --> 00:06:09,240
+بالنص بالظبط هذا معطيها للسؤال طلعوا أبارع ال
+
+87
+00:06:09,240 --> 00:06:12,900
+blade capacitor has a blade separation دي المسافة
+
+88
+00:06:12,900 --> 00:06:16,800
+بين الفجانية والتحتانية دي شي واضحة في الرسمةحلو
+
+89
+00:06:16,800 --> 00:06:20,120
+.. an uncharged metallic slab .. metal يعني ال
+
+90
+00:06:20,120 --> 00:06:24,020
+conductor ولا لأ؟ metallic slab .. of thickness A
+
+91
+00:06:24,020 --> 00:06:30,640
+.. ثمكه A حلو .. is inserted midway .. midway يعني
+
+92
+00:06:30,640 --> 00:06:33,460
+في النص بالظبط .. يعني المسافة اللي فوق بتساوي
+
+93
+00:06:33,460 --> 00:06:36,100
+المسافة اللي تحت .. من يقول المسافة اللي فوق جديش
+
+94
+00:06:36,100 --> 00:06:37,260
+و المسافة اللي تحت جديش؟
+
+95
+00:06:40,140 --> 00:06:44,400
+دى ناقص ا على اتنين صح ولا لأ دى ناقص ا على اتنين
+
+96
+00:06:44,400 --> 00:06:48,060
+كل واحد عله تمام قال انت ايه سويت قولتله اعتبر ان
+
+97
+00:06:48,060 --> 00:06:52,860
+انا جسمت ال capacitor الكبير الى two capacitors صح
+
+98
+00:06:52,860 --> 00:06:59,090
+ولا لأ الفجاني لحالوالتحتاني لحالي وانت قلتولي
+
+99
+00:06:59,090 --> 00:07:03,510
+هادي دي ناقص ا ع اتنين و هادي زيها دي ناقص ا ع
+
+100
+00:07:03,510 --> 00:07:08,150
+اتنين صح ولا لأ؟ هنا الكابة بيساوي واحد يعني هادي
+
+101
+00:07:08,150 --> 00:07:13,490
+فيه اي نوت و هادي اي نوت فراخ جالي أيه شويت منهم؟
+
+102
+00:07:13,490 --> 00:07:17,330
+جالتلي مش هادي conductor السفار؟ يعني بنفع تحميلهم
+
+103
+00:07:17,330 --> 00:07:20,790
+و تعملهم سلك هيك؟ ماهي نفس العملية، السلك خملته
+
+104
+00:07:20,790 --> 00:07:25,880
+ولا رفعته؟ وكأنك لمشتهم بعيدالذي يعتبر هذا الـ
+
+105
+00:07:25,880 --> 00:07:27,580
+Capacitor هو هذا الـ Capacitor كم من التواصلين
+
+106
+00:07:27,580 --> 00:07:32,260
+هؤلاء؟ توازي .. توازي .. توازي .. توازي .. توازي
+
+107
+00:07:32,260 --> 00:07:33,700
+.. توازي .. توازي .. توازي .. توازي .. توازي ..
+
+108
+00:07:33,700 --> 00:07:33,880
+توازي .. توازي .. توازي .. توازي .. توازي .. توازي
+
+109
+00:07:33,880 --> 00:07:33,880
+.. توازي .. توازي .. توازي .. توازي .. توازي ..
+
+110
+00:07:33,880 --> 00:07:34,560
+توازي .. توازي .. توازي .. توازي .. توازي .. توازي
+
+111
+00:07:34,560 --> 00:07:37,700
+.. توازي .. توازي .. توازي .. توازي .. توازي ..
+
+112
+00:07:37,700 --> 00:07:38,900
+توازي .. توازي .. توازي .. توازي .. توازي .. توازي
+
+113
+00:07:38,900 --> 00:07:39,320
+.. توازي .. توازي .. توازي .. توازي .. توازي ..
+
+114
+00:07:39,320 --> 00:07:48,380
+توازي .. توازي .. توازي .. توازي .. تواز
+
+115
+00:07:50,890 --> 00:07:57,790
+بتساوي C1 بتساوي epsilon note A على D ناقص A ع 2
+
+116
+00:07:57,790 --> 00:08:04,930
+بيصير اتنين هنا طب و التاني نفسه عندك two
+
+117
+00:08:04,930 --> 00:08:07,410
+capacitors واحد تمانية و التاني تمانية و وصلتهم
+
+118
+00:08:07,410 --> 00:08:10,870
+على التوالي جاتيش النتيجة اربعة اذا لما يكونوا
+
+119
+00:08:10,870 --> 00:08:13,090
+اتنين متساويين و توصلوا على التوالي بتاخدوا النص
+
+120
+00:08:13,090 --> 00:08:18,670
+ولا لا اذا C equivalent من هنا جسم ع 2
+
+121
+00:08:22,230 --> 00:08:26,970
+واحدة تمام هى C equivalent هى المطلوب الأول إذا
+
+122
+00:08:26,970 --> 00:08:30,270
+إيش بدك في الأول can you find the capacitance of
+
+123
+00:08:30,270 --> 00:08:34,910
+the device الكباسيتر الكليهيها إذا عبارة عن two
+
+124
+00:08:34,910 --> 00:08:38,030
+capacitors موصلينا على التوالي شوف المطلوب التاني
+
+125
+00:08:38,030 --> 00:08:44,030
+هيك tricky يعني حيلة إيش بقول بقول show that if
+
+126
+00:08:45,490 --> 00:08:47,310
+show that the capacitance of the original
+
+127
+00:08:47,310 --> 00:08:51,490
+capacitor is unaffected by the insertion of the
+
+128
+00:08:51,490 --> 00:08:56,030
+metallic slab if the slab is infinitesimally thin
+
+129
+00:08:56,030 --> 00:08:59,830
+قال لي لو هذه الجطعة الصفرية كتير رفيعة كتير رفيعة
+
+130
+00:08:59,830 --> 00:09:05,170
+يعني ايه goes to zero اثبتلي ان الكباسيتر ساعته
+
+131
+00:09:05,170 --> 00:09:08,690
+بتتغيرش وكأنه مش موجود للميتاليك سلاب فقوله قلت له
+
+132
+00:09:08,690 --> 00:09:15,000
+مش هي الجواب اخده اللي مثل ما ايه goes to zeroأيش
+
+133
+00:09:15,000 --> 00:09:33,160
+مرجع ايش مرجع ايش مرجع ايش مرجع ايش مرجع ايش
+
+134
+00:09:33,160 --> 00:09:38,600
+مرجع ايش مرجع ايش مرجع ايش مرجع
+
+135
+00:09:40,690 --> 00:09:45,610
+وبالتالي الـ C على اليدي ده هي equivalent مكافئة
+
+136
+00:09:45,610 --> 00:09:51,210
+لمكثفين كيف متواصلي؟ توالي equivalent to two
+
+137
+00:09:51,210 --> 00:09:54,670
+capacitors in series each having a blade
+
+138
+00:09:54,670 --> 00:09:57,490
+separation وكل واحد ما انتوا قولتولي دي ناقص إيه
+
+139
+00:09:57,490 --> 00:10:00,670
+على اتنين دي ناقص إيه على اتنين قاللي خلاص جيب C
+
+140
+00:10:00,670 --> 00:10:04,350
+equivalent قاللي هاي واحد على C ثم واحد على C واحد
+
+141
+00:10:04,350 --> 00:10:07,430
+زاد واحد على C اتنين قاللي طلعت و C واحد C اتنين
+
+142
+00:10:07,430 --> 00:10:12,370
+جبتلك إياها قاللي معناتهC equivalent بتسوي نص واحد
+
+143
+00:10:12,370 --> 00:10:17,250
+منهم و طلعتها epsilon not A على D نقص A المطلوب
+
+144
+00:10:17,250 --> 00:10:20,950
+التاني جالي نبين بده الشطارة خد ال limit جالي
+
+145
+00:10:20,950 --> 00:10:26,530
+طلعتها ده نفس الساعة ولا لأ نفس الساعة أي استفسار
+
+146
+00:10:26,530 --> 00:10:34,290
+جالي طب هدى وحطها فى مخكك وشوف له هالسؤال هذا
+
+147
+00:10:34,290 --> 00:10:39,540
+الخضار مش conductor die electricجدش كابا قال لي
+
+148
+00:10:39,540 --> 00:10:45,120
+كابا هل هذا الخضار ملة كل المنطقة لأ جالي بتقدر
+
+149
+00:10:45,120 --> 00:10:48,760
+تكتب ليه كابا إبسلو نوت إيه على دي بقولك لأ هو هاد
+
+150
+00:10:48,760 --> 00:10:53,300
+كابا ماخد كل اللي عال لأ في فراغ ولا مافيش فراغ
+
+151
+00:10:53,300 --> 00:10:56,900
+جالي أيه سوى في ال capacitor جالي برضه جسمت ال
+
+152
+00:10:56,900 --> 00:11:04,090
+capacitor إلى نصين مش نصين جسمين جسمالفراغ موجود و
+
+153
+00:11:04,090 --> 00:11:08,270
+الجسم بدون فراغ إذا الجسم هدى .. هدى موجودة و
+
+154
+00:11:08,270 --> 00:11:12,770
+الجسم هدى واحد طيب إذا معناه اعتبرهم كام كاباسيتار
+
+155
+00:11:12,770 --> 00:11:19,390
+اتنين كيف متواصلين برضه توالي ده اللي حلوقال لي
+
+156
+00:11:19,390 --> 00:11:25,290
+طيب هال D للفجاني نفس D للتحتاني واحدة تلتة وتانية
+
+157
+00:11:25,290 --> 00:11:32,390
+تلتة اذا مافيش شيء أسهل مني أقولك ان C1 اللي هو
+
+158
+00:11:32,390 --> 00:11:38,290
+الفجاني C1 بتسوي Epsilon Note Epsilon هي دي كعبة
+
+159
+00:11:38,290 --> 00:11:44,530
+Epsilon Note في ايه جديش ال D قال لي تلتة DC2
+
+160
+00:11:44,530 --> 00:11:49,750
+بقوله كابعو بالساوي واحد ابسلون نوت A على تلتين D
+
+161
+00:11:49,750 --> 00:11:54,770
+ايش ضال عليها اقول C equivalent ايش بالساويبقولي
+
+162
+00:11:54,770 --> 00:11:58,370
+توالي و يعطيك العافية و بتقولي C equivalent ايش
+
+163
+00:11:58,370 --> 00:12:04,230
+بيساوي C1 في C2 على C1 زي C2 و فلت حساب تبع صفر 4
+
+164
+00:12:04,230 --> 00:12:08,270
+عليا اللي بيخربط فيه بس اكتبلي C equivalent بيساوي
+
+165
+00:12:08,270 --> 00:12:13,410
+C1 في C2 على C1 زي C2 او اكتبلي 1 ع C equivalent
+
+166
+00:12:13,410 --> 00:12:21,130
+بيساوي 1 ع C2 زي 1 ع C2 و يعطيك العافية ايش هو؟ من
+
+167
+00:12:21,130 --> 00:12:21,670
+اللي بتحكي؟
+
+168
+00:12:25,350 --> 00:12:30,110
+وقتش في القابة بيستوي واحد؟ اي برا عليكي ذاكرها
+
+169
+00:12:30,110 --> 00:12:35,170
+وين الفراخ؟ فوق ولا تحت؟ تحت تحت C2 هتفتفت القابة
+
+170
+00:12:35,170 --> 00:12:40,230
+كده؟ واحد عشان الفراخ مش قولنا قابل الفراخ واحد
+
+171
+00:12:40,230 --> 00:12:46,610
+تمام؟ حلو ليش توالي؟
+
+172
+00:12:46,610 --> 00:13:00,480
+حلو وانا أحطهم هنا حاجة هي هذاتمام؟ وهي هدا. بدي
+
+173
+00:13:00,480 --> 00:13:04,900
+أوصل هدي بهدي بس ماعنديش سلك. إيش هسوي؟ ألزقهم
+
+174
+00:13:04,900 --> 00:13:12,880
+البعض؟ لما لزقتهم البعض صار هداك ها دي شايفينها؟
+
+175
+00:13:12,880 --> 00:13:17,190
+هجيت لو أعملت هيك في خلاف عنها توالي؟طبعا هاجد
+
+176
+00:13:17,190 --> 00:13:21,050
+هادى اللى مغلباكم انا مش معايا فى المختبر سيك
+
+177
+00:13:21,050 --> 00:13:25,250
+زيادة روح تقولى تعالى هادى انت جربى هنا خلينى
+
+178
+00:13:25,250 --> 00:13:31,370
+ارسمها بلون تانى احمها لحم او مس امس صار تلامس
+
+179
+00:13:31,370 --> 00:13:32,410
+وماصاراش
+
+180
+00:13:36,140 --> 00:13:41,880
+اه هذا هو السؤال طب هذا مش conductor يعني سؤالكم
+
+181
+00:13:41,880 --> 00:13:46,240
+انت بتقول هذا مش conductor صح طب أنت و قلتلكم في
+
+182
+00:13:46,240 --> 00:13:50,600
+المثال السابق لو اتخيلتوا conductor سمكه تقريبا
+
+183
+00:13:50,600 --> 00:13:56,280
+سفر بيفرج معاكم اتخيلوا موجود conductor الفيع كتير
+
+184
+00:13:56,280 --> 00:14:03,860
+تمام أثر عليكم بحل مشكلتكم اللي سألته عنها هذا
+
+185
+00:14:03,860 --> 00:14:11,330
+conductorافتراضي بافترضه بأثرش طبعا واحد بيقول لك
+
+186
+00:14:11,330 --> 00:14:15,270
+اه مادخلتش المعلومة مادخلتش افترضش عيلنا و اتغلب
+
+187
+00:14:15,270 --> 00:14:19,670
+اه و اما و قلنا conductor و conductor و بينهم مادة
+
+188
+00:14:19,670 --> 00:14:24,170
+ال conductor اللي افترضته هنا موجود هم هاي اللي
+
+189
+00:14:24,170 --> 00:14:29,070
+غلبهم انه لو حطت ال conductor hand الشاشة لو حطت
+
+190
+00:14:29,070 --> 00:14:33,050
+ال conductor hand بحل مشكلتكم مسبوط ولا ها ده
+
+191
+00:14:33,050 --> 00:14:33,970
+افترضي افتراض
+
+192
+00:14:37,260 --> 00:14:42,080
+هو وقت إيش التوازي لازم يتواصل لباس هادي مع حادي
+
+193
+00:14:42,080 --> 00:14:47,340
+وخلاص ولا لازم تاني تانيين مصريين تاني تانيين لأ
+
+194
+00:14:47,990 --> 00:14:52,530
+ماشي يا نور؟ مش موصل ايه؟ مافعش توازي و هو الواحد
+
+195
+00:14:52,530 --> 00:14:55,410
+دي بيقول إذا مش الوديان هادى هادى الوديان لأ
+
+196
+00:14:55,410 --> 00:15:00,970
+التوالي و التوازي مش صح إذا مش توالي قطعا توازي لأ
+
+197
+00:15:00,970 --> 00:15:04,810
+تمام؟ مش تغلبوا عالكم ماحسبتوش التوالي تقولوا
+
+198
+00:15:04,810 --> 00:15:12,570
+توازي هي الشغل مش هادى فادى تمام؟ هاي سؤالكم اللي
+
+199
+00:15:12,570 --> 00:15:18,710
+سألت ورا تمام إذا مش بيقولليعادي بديجيكي مثال آخر
+
+200
+00:15:18,710 --> 00:15:25,710
+وبنشوف بقولي solutionthe capacitor is equivalent
+
+201
+00:15:25,710 --> 00:15:32,730
+to two capacitors in series in series قال لي الأول
+
+202
+00:15:32,730 --> 00:15:38,650
+هضربت بكابة الأول ضربت بكابة الفجاني والتاني
+
+203
+00:15:38,650 --> 00:15:43,850
+اعتبرتي الكابة تبعت واحد واحد دي تبعته تلت والتاني
+
+204
+00:15:43,850 --> 00:15:49,610
+تلتين قال لي see equivalent عشان هم توالي اعمل هيك
+
+205
+00:15:49,610 --> 00:15:51,990
+و اللي ماشاء الله خدش صف رابع بقى انا بعمله اياه
+
+206
+00:15:53,010 --> 00:15:58,550
+تمام؟ قال لي هاي سي طيب هاجيتنا نعلق على هذه
+
+207
+00:15:58,550 --> 00:16:05,550
+النتيجة لو هذا القابة شايفينها كان فراغ ايش بيجي
+
+208
+00:16:05,550 --> 00:16:11,770
+تحط بمكان القابة؟ حط واحد تلاتة في واحد تلاتة
+
+209
+00:16:11,770 --> 00:16:17,350
+اتنين ذات واحد تلاتة ع تلاتة رجع واحد لأنه بيبطل
+
+210
+00:16:17,350 --> 00:16:26,800
+فيه جسمه صح ولا؟ والله صح الجوابغيره طيب مازال
+
+211
+00:16:26,800 --> 00:16:30,300
+سألت على التوالي والتوازي يا نور خلّيني أشوف
+
+212
+00:16:30,300 --> 00:16:33,280
+هالسؤال السؤال في الكتاب طبعا أنا جايبه بس يعني
+
+213
+00:16:33,280 --> 00:16:42,260
+يلا فرصة ها capacitor روحت جيبت مادة جسرت معايا
+
+214
+00:16:42,260 --> 00:16:49,060
+مملتش المنطقة كلها بس ملت لهنا هكابة
+
+215
+00:16:49,060 --> 00:16:54,010
+هاني اللي خليتهاكوبستر واحد هدا كله ممكن اعتبره؟
+
+216
+00:16:54,010 --> 00:17:00,070
+لأ، أكمل واحد كيف نتواصليه؟ هدول بالظبط زي ما كأنه
+
+217
+00:17:00,070 --> 00:17:10,890
+هذا هيو و هذا هيو روح أسوت هيك هيك صار توازي طيب،
+
+218
+00:17:10,890 --> 00:17:16,170
+إما سؤال في الكتاب ده اللي أحكيه حلو، إيه شرط
+
+219
+00:17:16,170 --> 00:17:22,210
+التوازي؟ أوصل كتبتين مع بعض أتوصلوا مع بعض؟كل تن
+
+220
+00:17:22,210 --> 00:17:23,350
+تن تن تن تن تن تن تن تن تن تن تن تن تن تن تن تن تن
+
+221
+00:17:23,350 --> 00:17:25,850
+تن تن تن تن تن تن تن تن تن تن تن تن تن تن تن تن تن
+
+222
+00:17:25,850 --> 00:17:33,850
+تن تن تن تن تن تن تن تن تن تن تن تن تن تن تن تن تن
+
+223
+00:17:33,850 --> 00:17:34,610
+تن تن تن تن تن تن تن تن تن تن تن تن تن تن تن تن تن
+
+224
+00:17:34,610 --> 00:17:35,930
+تن تن تن تن تن تن تن تن تن تن تن تن تن تن تن تن تن
+
+225
+00:17:35,930 --> 00:17:36,950
+تن تن تن تن تن تن تن تن تن تن تن تن تن تن تن تن تن
+
+226
+00:17:36,950 --> 00:17:50,510
+تن تن تن تن تن تن تن
+
+227
+00:17:50,510 --> 00:18:01,900
+تن تبتصرف تحكي صيني؟ مانا جاوبت اللي بتسأل هل هدى
+
+228
+00:18:01,900 --> 00:18:07,540
+هو هدى؟ اتنين؟ تقدر تقول هدى لملامس هدى؟ هدى هدى
+
+229
+00:18:07,540 --> 00:18:11,140
+مشاية ملامس هدى ملازقة فيها؟ و هدى ملازقة فيه هدى؟
+
+230
+00:18:11,140 --> 00:18:16,580
+جود هدى؟ كنتين مع بعض متساويين و جود هدول متساويات
+
+231
+00:18:16,580 --> 00:18:19,200
+ماعنديه فرق هنا بس هو الفرق هنا وهيش فرقات توازي
+
+232
+00:18:19,200 --> 00:18:24,920
+طيبيالا يا بنات فتشنا في الكتاب في ال recommended
+
+233
+00:18:24,920 --> 00:18:33,200
+problem نجينا هالسؤال كيه؟ قال لي هيه قاللي
+
+234
+00:18:33,200 --> 00:18:36,480
+هدول تلات مواد هيكابا واحد هيكابا اتنين هيكابا
+
+235
+00:18:36,480 --> 00:18:43,760
+تلاتة بدي C equivalent اكمل كبسطة هدول كم نتصلين
+
+236
+00:18:43,760 --> 00:18:52,830
+احكي لما هدول ببدأ فيهم توالي مع حد توازيكيف عرفت؟
+
+237
+00:18:52,830 --> 00:19:01,810
+نرجع لك كيف عرفت وكأنهم هيك صحيك؟
+
+238
+00:19:01,810 --> 00:19:09,470
+تنتين توالي ما حد توازي يا رب أحكي عربي تمام
+
+239
+00:19:09,470 --> 00:19:15,610
+هنا؟ هقيت؟ طيب قاللي هذا سؤال ما زال خلصنا بدري
+
+240
+00:19:15,610 --> 00:19:19,210
+جيبنا سؤال من الكتاب نحله مش مثال هذا سؤال الكتاب
+
+241
+00:19:20,560 --> 00:19:26,480
+problem 22 في الكتاب يقول شايف هالرسم اعدوا كم كم
+
+242
+00:19:26,480 --> 00:19:32,780
+كثف هدول؟ سبعة هدول سبعة موصلين زي ما انت شايف وكل
+
+243
+00:19:32,780 --> 00:19:36,880
+واحد منهم انا مديك قيمته هدي A B هدي C 1 و هده C 1
+
+244
+00:19:36,880 --> 00:19:42,420
+زيه هده C 3 C 3 ما انتوا شايفينين 2 ميكروفراد C 1
+
+245
+00:19:42,420 --> 00:19:47,420
+خمسة ميكروفراد C 2 عشرة ميكروفراد هده C 2 و هده C
+
+246
+00:19:47,420 --> 00:19:52,760
+2 طب مش بدكجالي find the equivalent capacitance
+
+247
+00:19:52,760 --> 00:19:57,240
+between A and B طيب و بعدين جالي لو كان فرق جهد
+
+248
+00:19:57,240 --> 00:20:01,520
+بين النقطين A و B 60 volt جيبلي الشحنات على هذه
+
+249
+00:20:01,520 --> 00:20:05,460
+الغلبات بس طبعا واحد بيقولي على هذا طبعا بجيبهم
+
+250
+00:20:05,460 --> 00:20:10,920
+كلهم ولا لأ بجيبهم كلهم نيجي احنا برمجين في
+
+251
+00:20:10,920 --> 00:20:16,920
+المدارس مرات غلط كل اتنين فوق بعض توازي اكم واحد
+
+252
+00:20:16,920 --> 00:20:20,740
+بيدحطلي كل اتنين فوق بعض توازيقعدنا نشوف في امتحان
+
+253
+00:20:20,740 --> 00:20:27,400
+جرّا .. نشوف .. 184 .. نشوف .. تمام .. حطوت ال 22
+
+254
+00:20:27,400 --> 00:20:31,140
+هدول .. أحط برا ليه؟ و اللي بيحط برا ليه؟
+
+255
+00:20:31,140 --> 00:20:40,160
+بالتفجير؟ تمام .. طب هدول كيف؟ توالي .. و هدول ..
+
+256
+00:20:40,930 --> 00:20:44,090
+توالي .. طب شوفوا هدول .. طلعي بقى تقولي هدول زي
+
+257
+00:20:44,090 --> 00:20:47,890
+هدول .. اللي أولا صمتم قلتلي كم عملتم توازي ..
+
+258
+00:20:47,890 --> 00:20:51,670
+قلتلك هادي و هادي يلهم نفس الجهود .. و هادي و هادي
+
+259
+00:20:51,670 --> 00:20:54,030
+يلهم نفس الجهود .. إذا هدول توازي
+
+260
+00:20:57,410 --> 00:21:02,310
+تمام واحدة واحدة هل جيت في التوالي مش C1 C2 ع C1
+
+261
+00:21:02,310 --> 00:21:07,590
+زي C2 وفي التوازي مش بجمع نيجي له دول series قاللي
+
+262
+00:21:07,590 --> 00:21:13,770
+series C1 وC2 C1 خمسة وC2 عشرة خمسة في عشرةخمسين
+
+263
+00:21:13,770 --> 00:21:18,030
+على عشر زي خمسة خمس طعش خمسين على خمس طعش بيطلع
+
+264
+00:21:18,030 --> 00:21:21,290
+تلاتة و تلت لأن خمس طعش في تلاتة خمسة واربعين
+
+265
+00:21:21,290 --> 00:21:25,790
+بيبقى الخمسة خمسة بالنسبة لخمس طعش تلت و التلت تلت
+
+266
+00:21:25,790 --> 00:21:30,830
+عشر و التلاتة بتخلصش دوري براو عليكم خلينا ناخد
+
+267
+00:21:30,830 --> 00:21:35,010
+عشانهم تلتات ناخد تلتة واحدة لو ستات بصير سبعة
+
+268
+00:21:35,680 --> 00:21:39,900
+ساكرين لكن التلاتات عجل من خمسة مدخلش الا واحد قال
+
+269
+00:21:39,900 --> 00:21:43,920
+يعني هذه التنين حال ما حالهم واحد هذا ال
+
+270
+00:21:43,920 --> 00:21:47,740
+equivalent تبع C1 و C2 و هدول التنين حال ما حالهم
+
+271
+00:21:47,740 --> 00:21:51,880
+واحد احسب بال calculator و هدول حالهم واحد هذا
+
+272
+00:21:51,880 --> 00:21:55,000
+تلاتة بقون تلاتة و هذا تلاتة بقون تلاتة تمام و هذه
+
+273
+00:21:55,000 --> 00:21:58,800
+عشرين ليش توازي عشرة و عشرة عشري
+
+274
+00:22:01,940 --> 00:22:06,620
+الفكر توازي قال لي والله هدول توازي ما هدول زي
+
+275
+00:22:06,620 --> 00:22:13,060
+هدول بس تلاتة توازي حلو توازي اجمع تلاتة و تلاتة و
+
+276
+00:22:13,060 --> 00:22:16,540
+تلاتة و تلاتة ستة و ستة ستة و ستة و ستة و تلاتة
+
+277
+00:22:16,540 --> 00:22:24,060
+اتنين تمانية و ستة تمانية و ستةيواردى مثالى لقضية
+
+278
+00:22:24,060 --> 00:22:28,740
+لما تتلطب واحدة واحدة بتمشى زى الحلاوة واحنا انتوا
+
+279
+00:22:28,740 --> 00:22:31,500
+عارفين من تجربتكم ايه كام امتحان اخدتهوا في عمركم
+
+280
+00:22:31,500 --> 00:22:36,500
+كتير لما يكون السؤال بيجي جراه بتقوله ساكنها بالحل
+
+281
+00:22:36,500 --> 00:22:41,600
+صح ولمّا يعترس .. ولمّا يعترس بتقوله كتير قاعدى
+
+282
+00:22:41,600 --> 00:22:47,260
+بينعكوامفروض اللي لأ؟ تمام جالي يا دو كيف؟ وردي
+
+283
+00:22:47,260 --> 00:22:51,420
+محلقه عشرين في تمانية point ستة ع تمانية عشرين
+
+284
+00:22:51,420 --> 00:22:55,440
+point ستة رضعت معايا ال calculator طلعتها ستة
+
+285
+00:22:55,440 --> 00:23:00,940
+تمام؟ جالي انت ايش بتقوللي؟ بتقوللي فرق الجهد بين
+
+286
+00:23:00,940 --> 00:23:05,200
+النقطين a و b ستين volt طب a و b هو نفسه فرق الجهد
+
+287
+00:23:05,200 --> 00:23:10,450
+بين اخر واحد؟حلو يعني فرق الجهد بين الستة
+
+288
+00:23:10,450 --> 00:23:14,250
+مايكروفاراد هو ستين volt بتقدر تجيبلي شحناته
+
+289
+00:23:14,250 --> 00:23:19,550
+كيوبيت سواء C في V ستين في ستة تراتمية و ستين
+
+290
+00:23:19,550 --> 00:23:25,970
+مايكروكلوم بنرجع الآن بقول هذا جاي من اتنين كيف
+
+291
+00:23:25,970 --> 00:23:32,030
+وصلتهأيش اللي بتساوى في التوازي؟ الشحنات ارجع بقول
+
+292
+00:23:32,030 --> 00:23:34,990
+يعني الـQ equivalent بتساوي الـQ واحد بتساوي الـQ
+
+293
+00:23:34,990 --> 00:23:39,770
+اتنين الـQ equivalent بتساوي هذه بتساوي هذه اذا كل
+
+294
+00:23:39,770 --> 00:23:45,150
+واحد عرفت شحناته ولا لأ؟ هذا الخطوة عرفتها ولا لأ؟
+
+295
+00:23:45,150 --> 00:23:50,530
+تمام، ارجع ده اللي حلو، هدول كيف جاية؟ توازي، ايش
+
+296
+00:23:50,530 --> 00:23:54,470
+بتساوي في التوازي؟قال لي معناته جهود هذا بيسوي
+
+297
+00:23:54,470 --> 00:23:57,230
+جهود هذا بيسوي جهود هذا بيسوي جهود هذا بيدي جهود
+
+298
+00:23:57,230 --> 00:24:01,130
+هذا قال لي الشحنة على السعة الشحنة طو جبتها تلت
+
+299
+00:24:01,130 --> 00:24:04,190
+منها ستين ع تمانية بون ستة طلعت اتنين واربعين فولت
+
+300
+00:24:04,190 --> 00:24:10,010
+اذا كل واحد منهم جد جهده خلاص
+
+301
+00:24:10,010 --> 00:24:13,830
+متهج بذكية وصلت قال لي هذا جهده اتنين واربعين
+
+302
+00:24:13,830 --> 00:24:20,760
+ومقداره اتنين42×2 يعني 84 طب لو بدي أكمل بقولك
+
+303
+00:24:20,760 --> 00:24:25,880
+يالا نكمل هذا من وين اجا اتنين توالي صح ولا لأ
+
+304
+00:24:25,880 --> 00:24:32,500
+وبالتالي شحنة هذه اللي هي 42×3.3 هي نفس هذه هي نفس
+
+305
+00:24:32,500 --> 00:24:37,020
+هذه وهذا نفس العملية هذا عشان تعرف بقوله هذا جهود
+
+306
+00:24:37,020 --> 00:24:40,160
+هذا بيسوي جهود هذا بيسوي جهود هذا وجهود هذا هي
+
+307
+00:24:40,160 --> 00:24:47,510
+سعته هي شحنته بجيب جهده وهكذا بكمل أيصف صارتمام؟
+
+308
+00:24:47,510 --> 00:24:50,110
+انتوا طبعا على أخر المحاضرة وبالتالي اتفجنا مع
+
+309
+00:24:50,110 --> 00:24:53,450
+الشباب ان ال quiz هذا الشبطر يكون يوم الخميس نتصحر
+
+310
+00:24:53,450 --> 00:24:58,310
+عليه أول يوم في رمضان تمام؟ خلاص اتفجنا يعني أنا
+
+311
+00:24:58,310 --> 00:25:01,430
+كنت حابب أكون أقدر قالوا الشباب لأ خليها الخميس
+
+312
+00:25:01,430 --> 00:25:05,790
+فقلنا أمين و الكل بحب يأجل وبالتالي الميزة أكيد
+
+313
+00:25:05,790 --> 00:25:11,630
+هتوافجوا على التأجيل تمام؟ خلص الشبطر الرابع
+
diff --git a/PL9fwy3NUQKwZzXsCLffozucGP33XWqvBP/sPp_M6pXBWo_postprocess.srt b/PL9fwy3NUQKwZzXsCLffozucGP33XWqvBP/sPp_M6pXBWo_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..0f1a1bc6f332dae2dbe07c32fae153e88c732c3f
--- /dev/null
+++ b/PL9fwy3NUQKwZzXsCLffozucGP33XWqvBP/sPp_M6pXBWo_postprocess.srt
@@ -0,0 +1,2604 @@
+1
+00:00:05,090 --> 00:00:07,710
+تمام نكمل
+
+2
+00:00:09,130 --> 00:00:15,170
+أخر حاجة أخدناها هو كيف حساب الطاقة اللي تخزن داخل
+
+3
+00:00:15,170 --> 00:00:20,410
+أي Capacitor قولنا U بتساوي Q تربيع عكنين C وفي
+
+4
+00:00:20,410 --> 00:00:25,250
+عندي قانون بيقول C بتساوي Q على Delta V وبالتالي
+
+5
+00:00:25,250 --> 00:00:31,510
+في صغطين إجداد بدل ما أحط C بدي أحط بدل C Q على V
+
+6
+00:00:31,510 --> 00:00:40,210
+فهذه بتصير نص Q Delta Vأو بيتساوي نص بدل Q C تربيع
+
+7
+00:00:40,210 --> 00:00:44,790
+بيساوي نص C Delta V تربيع هذا وصيغة تانية لليوم
+
+8
+00:00:44,790 --> 00:00:51,770
+تمام مانا كوزين و انا في عندي quiz ايش بقول بقول
+
+9
+00:00:51,770 --> 00:00:57,630
+في عندي تلاتة capacitors و بدك توصلهم بطريقة ما
+
+10
+00:00:58,450 --> 00:01:04,350
+بحيث تحصل على أكبر قدر من الطاقة طبعا كيف توصلهم
+
+11
+00:01:04,350 --> 00:01:08,870
+احنا اتعلمنا كام طريقة توصيل فيه توالي و توازن دي
+
+12
+00:01:08,870 --> 00:01:13,250
+رباكم في التوالي الساعة بتجلي ولا بتجليش؟ وقتيش
+
+13
+00:01:13,250 --> 00:01:17,280
+الساعة بتزيد؟بالتوازي بقولي هدول التلاتة في الآخر
+
+14
+00:01:17,280 --> 00:01:21,340
+انت بتوصلهم ببطارية وبالتالي الجهود واحد انت
+
+15
+00:01:21,340 --> 00:01:25,400
+بتوصلهم ببطارية مقدارها 12 volt نفترض مزال بتطلع
+
+16
+00:01:25,400 --> 00:01:28,800
+مزال في الجهود نفسه في كل أحوال جهود البطارية لأ
+
+17
+00:01:28,800 --> 00:01:31,700
+باخد هذه لأ باخد هذه هدف إيش فيها C ناخد هذه
+
+18
+00:01:31,700 --> 00:01:37,140
+السهلة بقوله انت بدك تزود U مفروض تزود C ولا لأ
+
+19
+00:01:37,140 --> 00:01:43,680
+كيف اوصل عشان ازود Cتوازي اذا الاصل انك توصل على
+
+20
+00:01:43,680 --> 00:01:49,140
+التوازي بتزود C واذا زودت C الطاقة الكلية بتزيد
+
+21
+00:01:49,140 --> 00:01:55,540
+قطعا فبقولت series ولا parallel ولا either series
+
+22
+00:01:55,540 --> 00:01:59,100
+or parallel يعني لا هيك لا هيك كل واحد ولا لا هيك
+
+23
+00:01:59,100 --> 00:02:03,890
+ولا هيك بقوله لافي الـ Parallel C بتزيد وحسب هذا
+
+24
+00:02:03,890 --> 00:02:09,490
+القانون زيادة C بتعطيك زيادة في U ولا لأ إذا
+
+25
+00:02:09,490 --> 00:02:13,970
+معناته ال Parallel لأ هذه القانون Parallel هو الصح
+
+26
+00:02:13,970 --> 00:02:19,590
+طيب نشوف كمان هال Quiz قللي عندك Two Capacitors
+
+27
+00:02:20,570 --> 00:02:24,550
+واحد جد التاني ولا واحد أصغر من التاني؟ واحد أصغر
+
+28
+00:02:24,550 --> 00:02:29,870
+من التاني أنا بدي ياك اتوصلهم بطريقة ما بحيث
+
+29
+00:02:29,870 --> 00:02:34,410
+الأربع اللي هو الصغير يكون طاقته أكبر من التمانية
+
+30
+00:02:34,410 --> 00:02:38,290
+اللي هو الكبير الصغير بدي يكون فيه طاقة أكبر من
+
+31
+00:02:38,290 --> 00:02:43,370
+الكبير يعني بده القانون يكون فيه تناسب عكسي ولا
+
+32
+00:02:43,370 --> 00:02:49,860
+ترضي بنيوسي عكسيبدي طريقة طلع فيش ما هي ده الغلباء
+
+33
+00:02:49,860 --> 00:02:55,240
+اللي فيه C في المقام صح ولا لأ طيب بتثبت هذه و تلو
+
+34
+00:02:55,240 --> 00:03:00,480
+اكتشف تثبت هي Q ع التوالي ع التوالي يعني بمعنى اخر
+
+35
+00:03:00,480 --> 00:03:05,100
+لو عملت هيك هدول ايش و كيف وصلتهم يا بنات هاي
+
+36
+00:03:05,100 --> 00:03:09,000
+أربعة مايكروفارات و هاي تمانية مايكروفارات لو اديت
+
+37
+00:03:09,000 --> 00:03:14,540
+حسبت الطاقة مين بتطلع أكبر الاربعة اتنين اللي هو
+
+38
+00:03:14,540 --> 00:03:19,810
+نفس ال Q ولا لأ ليشلأنه مصالين توالي وشرط التوالي
+
+39
+00:03:19,810 --> 00:03:23,210
+تساوي الشحنات هذا إيه له نفس الشحنة و هذا إيه له
+
+40
+00:03:23,210 --> 00:03:28,330
+نفس الشحنة حسب هذا القانون اللي كان سعته أقل بدأت
+
+41
+00:03:28,330 --> 00:03:32,390
+تكون ميول تبعته أكبر إذا كيف بدأ أوصله ده اللي
+
+42
+00:03:32,390 --> 00:03:37,050
+هتوصله على ال series رجال
+
+43
+00:03:37,050 --> 00:03:43,330
+آه يا بنات واضح تمام إذا هدول أقولكوا إزاي عن اللي
+
+44
+00:03:43,330 --> 00:03:47,900
+وقفنا عندهم قال لي في سؤال في الكتابمعطيني هيك
+
+45
+00:03:47,900 --> 00:03:52,000
+التالي بيقولي عندك two capacitors مش متساويين واحد
+
+46
+00:03:52,000 --> 00:03:56,060
+أكبر من التاني السؤال في الكتاب مش حاطط أرقام أنا
+
+47
+00:03:56,060 --> 00:04:00,700
+حاطط أرقام للوضوح مش أكتر جالي C1 أكبر من C2 قولي
+
+48
+00:04:00,700 --> 00:04:06,000
+تخلي C1 اتنين و C2 واحد واحد ضعف التاني ميح جالي
+
+49
+00:04:06,000 --> 00:04:10,360
+هدوري الكنين بيكتشحني هيهم من بطارية بطارية معلومة
+
+50
+00:04:10,360 --> 00:04:16,030
+الجهد يقول بطارية جهدة معروفاشحن كل واحد على حدى و
+
+51
+00:04:16,030 --> 00:04:23,010
+فُكهم و احتفظ بشحناتهم يعني اذا جهد الاول او جهد
+
+52
+00:04:23,010 --> 00:04:26,790
+البطارية عشرة اللي ساعته اتنين بدي ياخد عشرين
+
+53
+00:04:26,790 --> 00:04:31,470
+مايكرو كلوم ولا لأ؟ و اللي ساعته واحد عشرة في واحد
+
+54
+00:04:31,470 --> 00:04:35,410
+بدي اخد عشرة مايكرو كلوم قال لي حلو شحنتهم و
+
+55
+00:04:35,410 --> 00:04:39,750
+اتأكدت انهم انت له يعني جهدهم هو جهد البطارية انت
+
+56
+00:04:39,750 --> 00:04:44,630
+قاعدين تفكتهم البطاريةبقولي two capacitors C1 أكبر
+
+57
+00:04:44,630 --> 00:04:48,930
+من C2 فقولي تخلي C1 اتنين مايكروفراد و C2 بيسوي
+
+58
+00:04:48,930 --> 00:04:54,030
+واحد مايكروفراد طيب are charged شحنتهم to the same
+
+59
+00:04:54,030 --> 00:04:57,390
+potential من نفس البطارية هذه البطارية جهد هذه
+
+60
+00:04:57,390 --> 00:05:02,830
+نوحة تعتبر عشرة فولتالـ Charge Capacitor اللي
+
+61
+00:05:02,830 --> 00:05:05,950
+شعنتهم انت فكتهم البطارية بعد ما شعنتهم are
+
+62
+00:05:05,950 --> 00:05:09,750
+removed from the battery and are then connected
+
+63
+00:05:09,750 --> 00:05:13,110
+together as shown لكي توصلياهم مع بعض كيف اوصلهم
+
+64
+00:05:13,110 --> 00:05:16,550
+قال لي لكي توصلهم هيك طلعت الرسمة قلت ان انت حامل
+
+65
+00:05:16,550 --> 00:05:21,310
+الموجب مع السالب مظبوط الموجب مع السالب هي هذه
+
+66
+00:05:21,310 --> 00:05:26,450
+سالبة وهذه موجبةبديك توصلهم كما .. نرجع للمثال
+
+67
+00:05:26,450 --> 00:05:29,570
+نربط الحمار زي ما بده صاحبه ايش بده المثال؟
+
+68
+00:05:29,570 --> 00:05:33,710
+بنوصلهم زي ما بده طب ايش بدك؟ جالي بدي ال
+
+69
+00:05:33,710 --> 00:05:39,260
+potential difference between A وBبنات هالجيتها دي
+
+70
+00:05:39,260 --> 00:05:41,300
+بده اوصلهم مع بعض تطلعولي على ال two plates اللي
+
+71
+00:05:41,300 --> 00:05:46,420
+هناك conductor conductor صح بده اوصلهم بسلك تنتقل
+
+72
+00:05:46,420 --> 00:05:49,620
+الشحنات من الجهد الأعلى إلى الجهد الأقل حتى تتساوي
+
+73
+00:05:49,620 --> 00:05:52,620
+الجهود و نفس ال plate اللي جوا اللي على الطرف
+
+74
+00:05:52,620 --> 00:05:56,760
+التاني بعد ما اوصلهم بأضمن ان فرق الجهد الفجاني
+
+75
+00:05:56,760 --> 00:06:00,020
+بيسوي فرق الجهد التحتاني بيسوي فرق الجهد بين A و B
+
+76
+00:06:00,020 --> 00:06:03,340
+ولا لأ و انا بدي فرق الجهد بين A و B بقولوا بجيلك
+
+77
+00:06:03,340 --> 00:06:07,120
+فرق الجهد واحدة منهم بكفي صح ولا لأبس في نقل
+
+78
+00:06:07,120 --> 00:06:10,900
+الشحنات ولا فيش؟ فيه بقى تنتقل الشحنات صح ولا ..
+
+79
+00:06:10,900 --> 00:06:17,320
+بكفي ما هي واحدة منهم ماهو ايش بده الكمان؟ جالي مش
+
+80
+00:06:17,320 --> 00:06:23,260
+انت خدت طاقة؟ صح أول واحد مليته خزن طاقة ولا
+
+81
+00:06:23,260 --> 00:06:28,900
+ماخزنيش؟ خزن حسبت الطاقة اللي فيه والتاني خزن طاقة
+
+82
+00:06:28,900 --> 00:06:32,820
+ولا ماخزنيش؟ خزنيش معنايهم تمام هذه الطاقة قبل ما
+
+83
+00:06:32,820 --> 00:06:38,080
+وصلهمكل واحد مقدر أحسبها تب بعد ما وصلتهم حطلها
+
+84
+00:06:38,080 --> 00:06:41,980
+الطاقة زي ما هي ولا لأ بدنا نشوف ونفسر إذا صار فيه
+
+85
+00:06:41,980 --> 00:06:46,400
+تغيير find the total energy stored before and
+
+86
+00:06:46,400 --> 00:06:48,900
+after closing the switches شايفيهم اللي ال
+
+87
+00:06:48,900 --> 00:06:52,200
+switches أول ما أسكر تبدأ الشحنات تنتقل صح ولا لأ
+
+88
+00:06:52,200 --> 00:06:57,440
+حلو نبدأ نحب و اتنين تبهولي هال gate هي بطاريته
+
+89
+00:06:57,440 --> 00:07:01,880
+عشرة voltتمام؟ هذه بطارية أعطانيها قلتله تعالي يا
+
+90
+00:07:01,880 --> 00:07:05,760
+ال capacitor الأول لمقدار ساعتك اتنين مايكرو فراد
+
+91
+00:07:05,760 --> 00:07:10,660
+وصلته استنيت عليه انتلاه احسبولي جداش فيه شحنات
+
+92
+00:07:10,660 --> 00:07:19,280
+عشرين مايكرو كلهم تم فكته و جبته قلتله هذا رشيك
+
+93
+00:07:19,280 --> 00:07:19,480
+هذه
+
+94
+00:07:23,170 --> 00:07:27,830
+تمام مش عارف ليش الرسم عينكم هيك عاملة تمام هدى
+
+95
+00:07:27,830 --> 00:07:33,910
+سالب وهدى موجب تمام حلو بقدر اعملها بسرعة بقدر
+
+96
+00:07:33,910 --> 00:07:38,330
+بقدر بقدر هنا زبطة اه اه اه وين الكابوسة ده راحه
+
+97
+00:07:38,330 --> 00:07:45,110
+اصلا هنا سرحها دى لو انا بقى لا والله في اشي غلط
+
+98
+00:07:45,110 --> 00:07:49,290
+اه مش مشكلة اتخيلوها
+
+99
+00:07:51,890 --> 00:07:57,230
+طب هو كانت عندي شباب حلوة هي بتلاقي زاحة هذه
+
+100
+00:07:57,230 --> 00:08:00,550
+السالب عشرين وهذه الزايدة عشرين مش مشكلة بتخيلينها
+
+101
+00:08:00,550 --> 00:08:07,750
+جبت تاني جت دسعة واحد انشحن عشرة وعشرة جالي بس دي
+
+102
+00:08:07,750 --> 00:08:10,930
+البالك وانت بتوصلهم اجلبني الموجب مع السالب
+
+103
+00:08:10,930 --> 00:08:15,810
+والسالب مع الموجب هاي جلبت تمام هذه ظابطة بس هو
+
+104
+00:08:15,810 --> 00:08:20,200
+كله لزاح انا كنت حاططهم تحت بعد تمامقال ايش بقى
+
+105
+00:08:20,200 --> 00:08:24,440
+كنت تسوي؟ قال بدي أشبكهم مع بعض هالجد هدول حسبته
+
+106
+00:08:24,440 --> 00:08:28,380
+راحت البطارية و بدي أشبكهم مع بعض كيف تنشبكوا؟
+
+107
+00:08:28,380 --> 00:08:32,600
+شبكوا في شبكه؟ طبعا هدول .. هدى .. هدى ايه المشكلة
+
+108
+00:08:32,600 --> 00:08:35,860
+اللي فيها ده؟ كله بدي انزح طبعا؟ يعني هيك صاروا يا
+
+109
+00:08:35,860 --> 00:08:40,360
+بنات من بعين الله هاي
+
+110
+00:08:40,360 --> 00:08:48,520
+الأحمر وهي الأحمرو هاي الأزرق و هاي الأزرق ميحك
+
+111
+00:08:48,520 --> 00:08:56,720
+تمام هال gate بدي أشبكهم مع بعض بدي أشبكهم مع بعض
+
+112
+00:08:56,720 --> 00:09:00,820
+كان في الأول هادي زائد عشرين و هادي نقص عشرين و
+
+113
+00:09:00,820 --> 00:09:06,700
+هادي نقص عشرة و هادي زائد عشرة مظبوط ولا لأ هذا
+
+114
+00:09:06,700 --> 00:09:12,710
+كان .. نرجعكان زيادة عشرين يا بنات تمام؟ وهذا ناقص
+
+115
+00:09:12,710 --> 00:09:15,530
+عشرة وصلتهم بعيد كده الشعورات اللي كله I love you
+
+116
+00:09:15,530 --> 00:09:20,090
+زيادة
+
+117
+00:09:20,090 --> 00:09:25,430
+عشرين ناقص عشر اجمعوه عشرة اذا ال total ع التنتين
+
+118
+00:09:25,430 --> 00:09:30,610
+عشرة بدي اوزحهم ع التنين اوزحهم خمسة خمسة دائما
+
+119
+00:09:30,610 --> 00:09:35,110
+خمسة خمسةما تخافوش بتظلموش لما تقولوا واحد اقتمر
+
+120
+00:09:35,110 --> 00:09:39,930
+من التاني حسب سعته صح؟ حسب سعته هيتوزعوا لكن لو
+
+121
+00:09:39,930 --> 00:09:43,230
+أخد تمانية هذا جديش ضال هذا نعم نعم لو أخد سبعة
+
+122
+00:09:43,230 --> 00:09:47,010
+هذا جديش زي اللي هو ثلاثة اذا في عندش احكي طب ايش؟
+
+123
+00:09:47,010 --> 00:09:53,710
+خلصنا؟ تمام اذا بدي اوزعهم بقولهم اتوزعهم دلبلك في
+
+124
+00:09:53,710 --> 00:09:56,510
+شرط لازم يتحقق ان الجهد الفجاني لازم يسوي الجهد
+
+125
+00:09:56,510 --> 00:10:01,850
+التحتاني صح ولا لأ؟ لأنه انت وصلتهم مع بعضبحكي
+
+126
+00:10:01,850 --> 00:10:06,930
+عربي؟ تمام؟ إذا بدي أوزحهم الآن يا بنات وما زال
+
+127
+00:10:06,930 --> 00:10:13,430
+بدك توزحهم بين هذا و هذا لازم delta V1 يسوى delta
+
+128
+00:10:13,430 --> 00:10:21,030
+V2 لازم و لازم المجموع يكون عشرة ولا لأ و لازم Q1
+
+129
+00:10:21,030 --> 00:10:29,060
+زاد Q2 يسوى عشرة صحيك هيك ولا لأ؟ تمام نجي لأهه
+
+130
+00:10:29,060 --> 00:10:32,780
+اتطلع فلتكمل الرسمة اللي عوجة هديك ميجي لهذه طلعه
+
+131
+00:10:32,780 --> 00:10:38,240
+هدول التنين المصريين مع بعض بس موح جهتهم يتغير ولا
+
+132
+00:10:38,240 --> 00:10:41,280
+هيك بتقولي لأ انت مش مقتنع بشوفك ايه بتقولي يعني
+
+133
+00:10:41,280 --> 00:10:48,440
+تو كوندكتور توصل لسلة قد جهودهم هدهي طب و هدول اذا
+
+134
+00:10:48,440 --> 00:10:52,670
+Delta V واحد لازم يسوي Delta V اتنىصح ولا لأ؟ طيب
+
+135
+00:10:52,670 --> 00:10:57,550
+Delta V مش متساوي قالني والله Q1 ع C1 و هذه Q2 ع
+
+136
+00:10:57,550 --> 00:11:05,190
+C2 صح ولا لأ؟ طب هذه مش اتنين و هذه واحد إذا بتقدر
+
+137
+00:11:05,190 --> 00:11:12,380
+تقوللي ان Q1 بيساوي 2Q2عوض هنا معناته واحد هيكون
+
+138
+00:11:12,380 --> 00:11:16,340
+عشرة ع تلاتة و واحد عشرين ع تلاتة اجمع عشر ع تلاتة
+
+139
+00:11:16,340 --> 00:11:20,780
+زاد عشرين ع تلاتة تلاتين ع تلاتة يعني عشرة صح اذا
+
+140
+00:11:20,780 --> 00:11:25,600
+واحد شحناته ضعف تاني ولا لأ لأن واحد سعته ضعف تاني
+
+141
+00:11:25,600 --> 00:11:31,100
+اصلاتمام اذا هتوزع الشحنات بنسبة واحد الى اتنين
+
+142
+00:11:31,100 --> 00:11:34,960
+واحد الى اتنين واحد بده ياخد حص واتنين بده ياخد
+
+143
+00:11:34,960 --> 00:11:38,120
+حصين وبالتالي لو كانوا تلاتة واحد بده ياخد واحد
+
+144
+00:11:38,120 --> 00:11:43,080
+واحد واتنين بده ياخد اتنين مظبوط او لأ؟ تمام حلو
+
+145
+00:11:43,080 --> 00:11:49,500
+احكي احكي مش فاهم مش هم اتواصلوا مع بعض اه يعني
+
+146
+00:11:49,500 --> 00:11:52,880
+المفروض الجهد على هدك المجموع كان مصارفه نكتة دماغ
+
+147
+00:11:52,880 --> 00:11:53,540
+اه حلو
+
+148
+00:11:58,650 --> 00:12:03,530
+فتح هدف الشحنات فرق الجهود ليش؟ ايش فرق الجهود
+
+149
+00:12:03,530 --> 00:12:13,190
+بيساوي؟ فرق الجهود بتساوي Q على C صح؟ C توصل و
+
+150
+00:12:13,190 --> 00:12:19,310
+هالجد كيف توازي وبالتالي C1 زي C2 اذا انا عشرة على
+
+151
+00:12:19,310 --> 00:12:26,550
+تلاتة صح انت جبت المطلوب عرق من الآخر صحيح؟ تمام
+
+152
+00:12:28,370 --> 00:12:35,270
+واحد على اتنين شهل انك .. اه صراحتى اه
+
+153
+00:12:35,270 --> 00:12:42,190
+قدسى واحد اتنين اه فانا قبل ما امحيها حكيت طبعا لو
+
+154
+00:12:42,190 --> 00:12:46,870
+صراحة بيجيبون وين راحت زى مثلا معاكى حلو احنا كنا
+
+155
+00:12:46,870 --> 00:12:50,430
+ماخدار من بيته و احنا ماخدار من بيته و احنا ماخدار
+
+156
+00:12:50,430 --> 00:12:50,450
+من بيته و احنا ماخدار من بيته و احنا ماخدار من
+
+157
+00:12:50,450 --> 00:12:50,510
+بيته و احنا ماخدار من بيته و احنا ماخدار من بيته و
+
+158
+00:12:50,510 --> 00:12:50,850
+احنا ماخدار من بيته و احنا ماخدار من بيته و احنا
+
+159
+00:12:50,850 --> 00:12:55,470
+ماخدار من بيته و احنا ماخدار من بيته و احنا ماخدار
+
+160
+00:12:55,470 --> 00:13:01,610
+من بيته وهدول شفاهم كانوا واحدة عشرين وواحدة سالب
+
+161
+00:13:01,610 --> 00:13:07,530
+عشرة ضالوهم زي ما هم نرجع هذه عزيزي عشرين وهذه
+
+162
+00:13:07,530 --> 00:13:12,910
+سالب عشرة بيضالوا العشرين هنا والسالب هنا مسموح
+
+163
+00:13:12,910 --> 00:13:17,930
+مشرجت هدول صاروا خلطة صارتا صاروا صارتا النتيجة
+
+164
+00:13:17,930 --> 00:13:23,190
+إيش؟ زياد عشرة لأنه زياد عشرين نقص عشرة هدول
+
+165
+00:13:23,190 --> 00:13:28,010
+العشرة بيتاخدهم كلهم هدىولا بدهم يتوزعوا بناءً على
+
+166
+00:13:28,010 --> 00:13:33,570
+ساعاتهم فها دي أخدت عشرة أو عشرين ع تلاتة وده أخدت
+
+167
+00:13:33,570 --> 00:13:36,840
+عشر ع تلاتةفاهمتي كيف؟ اذا هدولي الشحنات مابيضلولي
+
+168
+00:13:36,840 --> 00:13:41,280
+زي ما هما اول ما وصلتهم مش انا عندي قاعدة بتقول
+
+169
+00:13:41,280 --> 00:13:45,040
+تنتقل الشحنات من الجود الأعلى لجود الأقل اذا
+
+170
+00:13:45,040 --> 00:13:48,400
+بيسمحي لها تبقى هادي و هي جودة غير عنهادي اذا لازم
+
+171
+00:13:48,400 --> 00:13:53,540
+تنتقل الشحنات تنتقل الشحنات و في الآخر انا عندي زي
+
+172
+00:13:53,540 --> 00:13:56,940
+ما قلتلكم ان لو في عندي هنا غرفة روحت جنس الحيطة
+
+173
+00:13:57,950 --> 00:14:01,350
+تمام؟ مش بيصير في الغرفة الكبيرة انتوا اللي
+
+174
+00:14:01,350 --> 00:14:04,570
+جامكوا؟ تمام؟ هل جيت لهم و اصلا انه هذه غرفة
+
+175
+00:14:04,570 --> 00:14:09,110
+صغيرة؟ بقول لما اختلطكم كلكم يمكنكوا تروحوا هناك
+
+176
+00:14:09,110 --> 00:14:10,690
+أو كلكم يمكنكوا تجيهوا هناك مش بيمكنكوا تتوزعوا
+
+177
+00:14:10,690 --> 00:14:13,810
+الغرفة الكبيرة بتاخد بنات أكبر و الغرفة الصغيرة
+
+178
+00:14:13,810 --> 00:14:17,610
+بنات أقل صحيح ولا لأ؟ تمام؟ لو في موجة أبو سالب
+
+179
+00:14:17,610 --> 00:14:22,270
+يعني و في واحدة بتاكل التانية ساعتها يكون النتيجة
+
+180
+00:14:22,270 --> 00:14:27,130
+اللي اتاكل و راحه و الموجة بتاكل التسالب كأنهتمام
+
+181
+00:14:27,130 --> 00:14:33,730
+هيك؟ حلو بحكيش عربي بطولة اظنك تمام؟ تصرحوش انا
+
+182
+00:14:33,730 --> 00:14:38,050
+باخد اكتر حاجة اكتر منظر بأذينا ان الواحد يكون
+
+183
+00:14:38,050 --> 00:14:45,990
+مبلل فده بيأذي تمام حلو اذا قاللي عيها انا جمعت
+
+184
+00:14:45,990 --> 00:14:50,550
+بنات جمعت الاثنين زي السلب عشر قبل هنا قديشسالة
+
+185
+00:14:50,550 --> 00:14:54,590
+بعشرة سالة بعشرة تجميعها عادية جالي طرعت ك
+
+186
+00:14:54,590 --> 00:14:59,110
+absolute value عشرة micro farad كلهم جالي ليش
+
+187
+00:14:59,110 --> 00:15:01,990
+اتراحت كنت قول ان واحدة موجة بواحدة سالبة مظبوط
+
+188
+00:15:01,990 --> 00:15:07,210
+ولا لأ حلو الان since the two capacitors ايه يا
+
+189
+00:15:07,210 --> 00:15:09,690
+لما هذا سؤالك since the two capacitors are
+
+190
+00:15:09,690 --> 00:15:13,070
+connected together this charge will be distributed
+
+191
+00:15:13,070 --> 00:15:18,040
+between the two capacitors بشرط تساوي جهودبشرط
+
+192
+00:15:18,040 --> 00:15:21,820
+تساوي جهود طبعا كلمة final انا حاططها يعني بعد ما
+
+193
+00:15:21,820 --> 00:15:25,460
+اغلق المفاتيح هيبقى عنى فيها لأنه فيه كان كاتب ليه
+
+194
+00:15:25,460 --> 00:15:29,020
+بدى طاقة جابل و بعد فجابل ما ا سكر مفاتيحي كاتبها
+
+195
+00:15:29,020 --> 00:15:31,880
+initial و بعدى اللي انا جاعة بشتغل عليه بعد ما
+
+196
+00:15:31,880 --> 00:15:36,820
+سكرت مفاتيحي وانتقلت الشحنات تمام؟ حلوجالي إذا
+
+197
+00:15:36,820 --> 00:15:41,600
+الشرط التاني إن إذا واحدة أخدت تلاتة تانية سبعة،
+
+198
+00:15:41,600 --> 00:15:44,420
+إذا واحدة أخدت أربعة تانية ستة، إذا واحدة أخدت
+
+199
+00:15:44,420 --> 00:15:48,240
+تمانية تانية اتنين، يعني المجموعيش لازم يدله عشرة،
+
+200
+00:15:48,240 --> 00:15:57,760
+تمام؟ اعمل كالتو سألتيأيش بيقولي هنا 2 وحطت هنا 2
+
+201
+00:15:57,760 --> 00:16:02,660
+وحطت هنا 1 فطلعت ال Q1 final بتساوي 2 Q2 final
+
+202
+00:16:02,660 --> 00:16:08,480
+عوضت وطلعت منهم ال Q1 final بتساوي 20 ع تلاتة وQ2
+
+203
+00:16:08,480 --> 00:16:12,680
+final بتساوي 10 ع تلاتة اجمعوهما اتنين اتنين عشرة
+
+204
+00:16:12,680 --> 00:16:17,770
+عشرة اللي هو الشرط اللي انت حاطل ليه هنالأنه عشرين
+
+205
+00:16:17,770 --> 00:16:20,730
+ع تلاتة زي عشر ع تلاتة صرف رابع قلنا بالصير
+
+206
+00:16:20,730 --> 00:16:24,510
+التلاتة عامل مشترك وعشر زي عشرين تلاتين و تلاتين ع
+
+207
+00:16:24,510 --> 00:16:29,390
+تلاتة عشرات مظبوط ولا لا؟ تمام حلو ده اللي الآن
+
+208
+00:16:29,390 --> 00:16:34,230
+بديش انا ال cues انا بدي فرق الجهل بجيب واحد منهم
+
+209
+00:16:34,230 --> 00:16:38,440
+بكفيهيه في واحد فانى طب واحد بيقول لأ انا بدي
+
+210
+00:16:38,440 --> 00:16:41,620
+التاني برضه بيصحله كله بيطلع كل الطرق تؤدي إلى
+
+211
+00:16:41,620 --> 00:16:47,000
+روما عشرة ع تلاتة بطلت عشرة يالمه الجهد اتغير ليش
+
+212
+00:16:47,000 --> 00:16:55,520
+قال الشحنات انتقلت الشحنات انتقلت وإيه
+
+213
+00:16:55,520 --> 00:17:01,000
+الواحد من وين جابت التلاتة انا من وين جابت التلاتة
+
+214
+00:17:06,220 --> 00:17:14,800
+يلا يلا ايش هحط بدل كيو واحد final هنا احكي اتنين
+
+215
+00:17:14,800 --> 00:17:19,460
+كيو اتنين final زاد كيو اتنين final بتساوي عشرة
+
+216
+00:17:19,460 --> 00:17:27,460
+اسمها ايه اجت تلاتة اجت التلاتة تمام غيرها بيهمش
+
+217
+00:17:27,460 --> 00:17:31,100
+ان دي أسئلة حلوة بيهمش ولا .. ولا انهي سلاسلة حلوة
+
+218
+00:17:31,100 --> 00:17:33,160
+مش معنى مين احكي يا بنتي احكي
+
+219
+00:17:38,060 --> 00:17:45,480
+VAB يعني VB نقص VA او V ..
+
+220
+00:17:45,480 --> 00:17:51,860
+اه سؤالك حلو و هذا بدينا ال .. الهيز اللي كان
+
+221
+00:17:51,860 --> 00:17:56,940
+عندنا في المدارس VAB هي VB نقص VA ولا VA نقص VB مش
+
+222
+00:17:56,940 --> 00:18:03,220
+هيك بديك كل شيخ وليه طريقته كل كتاب وليه طريقته
+
+223
+00:18:03,220 --> 00:18:08,370
+معناتهطلعيها من مخكك من نفسك إلى اللي فيه انا
+
+224
+00:18:08,370 --> 00:18:12,130
+بقولك هي ايش بالثانوية لإن كل شيخ و الوطن يكتبوا
+
+225
+00:18:12,130 --> 00:18:16,570
+VAB هي VB نقص VA ولا VA نقص VB انت ممكن تقولليه
+
+226
+00:18:16,570 --> 00:18:20,950
+لإن انا مش عارف طريقتك الشيية اتشهدك دعوة مافيش
+
+227
+00:18:20,950 --> 00:18:23,850
+قانون يبقوا ممكن تقولوا احطوا قانون انا بقولك انت
+
+228
+00:18:23,850 --> 00:18:27,550
+مافيش دعوة انا بعدين أقولكما لهاش جواب، أنا هيبقى
+
+229
+00:18:27,550 --> 00:18:30,790
+بواصلك، ما لهاش جواب، في مصطلحات وبتتغير هذه
+
+230
+00:18:30,790 --> 00:18:34,910
+المصطلحات، يعني كل كتاب بيكون كاتب VAB، أنا إيش
+
+231
+00:18:34,910 --> 00:18:38,490
+بعني فيها، فهمت عليها؟ عندكم في توجيهي كانت اللي
+
+232
+00:18:38,490 --> 00:18:42,930
+لها معنى، بيكون حاطة، أنا عارف، السؤال على طول،
+
+233
+00:18:42,930 --> 00:18:46,050
+بيكون تعودته عليه، بس in general مالهاش قانون،
+
+234
+00:18:46,050 --> 00:18:49,150
+انسي، انسي، هذه شغلات بسيطة، فالكشف الحين أنا بقصد
+
+235
+00:18:49,150 --> 00:18:54,010
+VAB، أنا بقولك، أنا عمري ما هجيبلك سؤال VAB، هقولك
+
+236
+00:18:54,010 --> 00:19:01,740
+أوجد VB نقص VA،رايحتك؟ خلصنا مش هجيبلك VAB انا
+
+237
+00:19:01,740 --> 00:19:06,120
+هرجيت ماكنتش بحطلك إياها AB لما تكون مديش إشارة
+
+238
+00:19:06,120 --> 00:19:09,240
+السرب مش هتفرجوا عن بعض إشارة السرب ولا لأ هجيت
+
+239
+00:19:09,240 --> 00:19:17,920
+لما أقولك VAB وعملك هيك تفرج معاك؟ خلاص هتخافش مش
+
+240
+00:19:17,920 --> 00:19:22,420
+هجيبلك لهيك وإذا جيبتلك ويدون هيك مكون أنا حددت VA
+
+241
+00:19:22,420 --> 00:19:28,650
+-VB و لا VB-VA مش هجيبتك سؤال؟طلعيه من مخك مانا
+
+242
+00:19:28,650 --> 00:19:33,190
+بتخافوش منه حلو لأنه عن جد يعني في كتير رموز
+
+243
+00:19:33,190 --> 00:19:37,870
+الكتاب دايما في أولى الصفحات بيكون حاططها اني انا
+
+244
+00:19:37,870 --> 00:19:42,750
+اشبعنك ككاتب وهذه ماهياش قانون ثابت ومصطلحات
+
+245
+00:19:42,750 --> 00:19:47,710
+بتتغيرش تمام؟ انا .. انا بتوقع انه هي اللي كان
+
+246
+00:19:47,710 --> 00:19:53,820
+جسدك .. لأ هي هيك دلوقتي او أنا بتتوقع .. تمامإحنا
+
+247
+00:19:53,820 --> 00:19:58,120
+نستعمل التعامل مع الواحد واتنين و final و initial
+
+248
+00:19:58,120 --> 00:20:02,800
+أنه إيش ال A و B من ون أجت في الأمر؟ماظنش هدي
+
+249
+00:20:02,800 --> 00:20:05,920
+قصدات، لأ سني شوية، انت هجيت قصدك، انت ماكنش
+
+250
+00:20:05,920 --> 00:20:10,680
+تعرفيها، هجيت A، B، هي الطرف تبعي مش التانين
+
+251
+00:20:10,680 --> 00:20:14,640
+وساطهم بعيد، هاي واحد منهم A، والطرفين التانين
+
+252
+00:20:14,640 --> 00:20:18,420
+وساطهم بعيد، انت لو شفت الرسمة، شفتيها؟ شفتيها
+
+253
+00:20:18,420 --> 00:20:22,880
+الرسمة هالجيت؟ A وB يا بنات، رمزين محتوطين في
+
+254
+00:20:22,880 --> 00:20:27,050
+الكتاب وفي السؤال، أول رسمة، صح شفتهو؟اذا ايه بيه
+
+255
+00:20:27,050 --> 00:20:32,730
+هدول مش مجهولين؟ اه اعيده او ارجحه؟ شفتهوا؟ تمام
+
+256
+00:20:32,730 --> 00:20:39,970
+يلّا هالجيت بدى الطاقات before closing the
+
+257
+00:20:39,970 --> 00:20:45,450
+switches قبل ما انا اشبك المفتاحين و اشبكهم اتبعد
+
+258
+00:20:45,450 --> 00:20:49,950
+مش كل واحد كان مشحون وانه طاقته واحد عشرة جول
+
+259
+00:20:49,950 --> 00:20:55,170
+والتاني خمسة جول صعب اقولك جديش الطاقة الكلية؟لأ
+
+260
+00:20:55,170 --> 00:20:59,730
+طب شوف ليه أول واحد جديش خزان طاقه ايه اه ايه اذا
+
+261
+00:20:59,730 --> 00:21:05,070
+عرفت ال Q و C معروفة مقدرش تعرف ال U بقرأ براش هده
+
+262
+00:21:05,070 --> 00:21:08,730
+مشرت شبكته ببطارية معروفة ان موجود و C معروفة اذا
+
+263
+00:21:08,730 --> 00:21:14,310
+بتقدر يجيب U لكل واحد جبت U لكل واحد هده طلعت 150
+
+264
+00:21:14,310 --> 00:21:22,430
+micro joule في اي مشكلة هدى هل جيت شبكته
+
+265
+00:21:24,010 --> 00:21:28,290
+هل جهودهم ضلوا عشر قوات؟ لأ لأ لأ لأ لأ لأ لأ لأ
+
+266
+00:21:28,290 --> 00:21:29,870
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+267
+00:21:29,870 --> 00:21:30,250
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+268
+00:21:30,250 --> 00:21:31,830
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+269
+00:21:31,830 --> 00:21:32,370
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+270
+00:21:32,370 --> 00:21:37,360
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لبعد ما سكرت مش
+
+271
+00:21:37,360 --> 00:21:43,340
+VD Delta V1 بتسوي Delta V2 بتسوي VAB ماكلش زي بعض
+
+272
+00:21:43,340 --> 00:21:47,100
+قالي طب يلا جيبها قالي after closing the switches
+
+273
+00:21:47,100 --> 00:21:51,220
+برضه ال final زي ادي ال final بس ال final كله زي
+
+274
+00:21:51,220 --> 00:21:57,020
+بعض V final ماكتبتش V1 final و V2 final لأن هم
+
+275
+00:21:57,020 --> 00:22:03,780
+متساويين حسبتهم و حطيتهم AB ارجعت برضه نفس الكلام
+
+276
+00:22:07,840 --> 00:22:13,820
+الكالكولياتر طلعتلي 16 طلعوا كم كانوا 150 شوفوا
+
+277
+00:22:13,820 --> 00:22:19,120
+هال drop نزل نزلة كبيرة طب مش أنتوا علمتونا أن
+
+278
+00:22:19,120 --> 00:22:23,620
+الطاقة لا تفنى ولا تستحدث معناته عشان نفهم بدي
+
+279
+00:22:23,620 --> 00:22:29,940
+أعرف وراحتها الطاقة حلو لو مسكت الأسلاك بتشوفهم
+
+280
+00:22:29,940 --> 00:22:34,530
+سخنين ولا لأاذا هدول فقدوا طب مين جت الحرارة؟
+
+281
+00:22:34,530 --> 00:22:38,190
+قلتله هي الشحنات مش بدها تنتقل بدها تتحرك هتتعب
+
+282
+00:22:38,190 --> 00:22:42,470
+ولا مش هتتعب؟ بتعمل شغل وهذا الشغل بالنسبة إنا
+
+283
+00:22:42,470 --> 00:22:47,430
+فيزيائيا يعني طاقة هذا الشغل الذي بذله عند انتقال
+
+284
+00:22:47,430 --> 00:22:50,630
+الشحنات من الجهد الأعلى إلى الجهد الأقل حتى تساوت
+
+285
+00:22:50,630 --> 00:22:55,730
+الجهود معناته هذه الشحنات تعبت وخسرت طاقة وهذا
+
+286
+00:22:55,730 --> 00:23:01,150
+التفسير وين راحوا ال 150 وصلهم لل 16؟ اذا بيقوللي
+
+287
+00:23:02,780 --> 00:23:05,800
+الطاقة المفقودة، الطاقة المفقودة عشان ما تسألش
+
+288
+00:23:05,800 --> 00:23:09,100
+عنها Is it transferred out of the system by
+
+289
+00:23:09,100 --> 00:23:12,960
+mechanism of electromagnetic waves؟ كنت قوله زي ما
+
+290
+00:23:12,960 --> 00:23:16,900
+قلت حرارة أو أي إن كانت، تذكرين لما جيبنا الرسمة
+
+291
+00:23:16,900 --> 00:23:21,700
+في فيزيا ألف؟ قلنا كيف الطاقة تفقد مرة بكست الشاي
+
+292
+00:23:21,700 --> 00:23:25,840
+و كست المزوج، تذكرين؟ فهات فيه ست طرقكيف تفقدوا
+
+293
+00:23:25,840 --> 00:23:28,900
+الصوت و مش الصوت هذه طريقة من الطرق مش مهم انه
+
+294
+00:23:28,900 --> 00:23:33,860
+انتوا امنتوا انه في طاقة تفقد نتيجة حركة الشحنات
+
+295
+00:23:33,860 --> 00:23:37,700
+لان انت على طول قلتلي اول ما وصلت انتقلت الشحنات
+
+296
+00:23:37,700 --> 00:23:42,120
+من الجهد الاعلى الى الجهد الاقل زي واحد عنده طاقة
+
+297
+00:23:42,120 --> 00:23:46,900
+ميت جول و بدى امشي من هان لهان هذه فيها احتكاك ده
+
+298
+00:23:46,900 --> 00:23:52,260
+بالكمبتدلها 100 جول هنا؟ بصير انك العشي جول صح؟
+
+299
+00:23:52,260 --> 00:23:55,700
+ليش؟ بقولوا احتكاكوا ايش قامت ما هي ماشيت و هي
+
+300
+00:23:55,700 --> 00:24:00,000
+بتمشي تقبض معناته ان احتكاك عامل الشغل ضيقة علمية
+
+301
+00:24:00,000 --> 00:24:06,200
+تخلهم عشرين وهذه نفس العملية اه يا بنات اي صفصة
+
+302
+00:24:06,200 --> 00:24:14,220
+مسموح اي صفصة تمام يا بتول؟ تمام؟
+
+303
+00:24:17,830 --> 00:24:21,770
+capacitance or capacitors with dielectric اعنوان
+
+304
+00:24:21,770 --> 00:24:26,170
+الشبطار capacitance and dielectric أصلا وعرفت كلمة
+
+305
+00:24:26,170 --> 00:24:29,450
+dielectric هي نوع من أنواع المواد العازلة، مادة
+
+306
+00:24:29,450 --> 00:24:34,230
+عازلة جالي تمام جالي المادة العازلة لحتى الآن أنت
+
+307
+00:24:34,230 --> 00:24:37,450
+لما تصمتلي، إيش هذا الفراغ؟ إيش هذا فراغ؟ المادة
+
+308
+00:24:37,450 --> 00:24:41,850
+العازلة فراغ تمام فراغ هو بالأصل و الهو ذا الفراغ
+
+309
+00:24:41,850 --> 00:24:45,860
+عادة ما تشوف هو الفراغ الأصلزمان زمان قبل مئات
+
+310
+00:24:45,860 --> 00:24:50,920
+السنين عملوا تجارب وبالنسبالي انا اعرف شغل علميا
+
+311
+00:24:50,920 --> 00:24:57,640
+انه نتيجة التجربة لما تطلع و تتكرر عدة مرات من عدة
+
+312
+00:24:57,640 --> 00:25:01,560
+بني أدمين في عدة بلدان و يصلوا نفس النتيجة بيصير
+
+313
+00:25:01,560 --> 00:25:06,820
+fact وبال English لما نقول sun rise ولا rises
+
+314
+00:25:06,820 --> 00:25:12,940
+لأنها fact مظبوط ولا .. خلاص prison .. prison
+
+315
+00:25:12,940 --> 00:25:18,960
+simple تمامهان هذه صارت fact ايش real fact؟ كانوا
+
+316
+00:25:18,960 --> 00:25:22,780
+عملنا عدة تجارب و اتكررت مرات كتيرة و في أمريكا و
+
+317
+00:25:22,780 --> 00:25:26,720
+في ألمانيا و في بريطانيا كلهم طلعوا لنتيجة واحدة
+
+318
+00:25:26,720 --> 00:25:32,700
+لما تحط مادة غير الفراغ السعة بتزيد السعة بتزيد
+
+319
+00:25:32,700 --> 00:25:38,440
+على طول هذه fact طيب السعة بتزيد تحط plastic تحط
+
+320
+00:25:38,440 --> 00:25:42,140
+خشب زي بعض جلاب لو حطيت خشب بتزيد لكن لو حطيت
+
+321
+00:25:42,140 --> 00:25:45,920
+plastic بتزيد بمقدار اقل او اكترتمام إذا إيش
+
+322
+00:25:45,920 --> 00:25:49,040
+بيقوللي a dielectric is an insulating material
+
+323
+00:25:49,040 --> 00:25:52,480
+عشان يذكرني إيش هي a dielectric قاللي it is found
+
+324
+00:25:52,480 --> 00:25:57,200
+that ما زال it is found that يعني بتجارب إن عملت
+
+325
+00:25:57,200 --> 00:26:03,580
+تجارب وكتيرة تواترت وزي ما بيقولوا تعون علم الحديث
+
+326
+00:26:03,580 --> 00:26:09,290
+إنه أقوىالأحاديث هي المتواترة تمام بعدين بيجي
+
+327
+00:26:09,290 --> 00:26:13,630
+الصحيح لكن المتواتر هو أقوى من الصحيح الصحيح
+
+328
+00:26:13,630 --> 00:26:17,790
+بيسموه أحد أحد يعني نقلوا واحد عن واحد لكن
+
+329
+00:26:17,790 --> 00:26:21,710
+المتواتر نقلوا أربعين عن أربعين عن أربعين جمع
+
+330
+00:26:21,710 --> 00:26:26,250
+ويصعب الكذب عليهم زي ما بقوله طيب المهم و هنا
+
+331
+00:26:26,250 --> 00:26:30,110
+تواترت التجربة والنتيجة وصلت حقيقة you found that
+
+332
+00:26:30,110 --> 00:26:35,460
+انتهينا ايشعندما يتم إضافة مادة ديالكريكية إلى
+
+333
+00:26:35,460 --> 00:26:43,560
+حوشيرات بين قطع قطع قطع قطع قطع قطع قطع قطع قطع
+
+334
+00:26:43,560 --> 00:26:47,220
+قطع قطع قطع قطع قطع قطع قطع قطع قطع قطع قطع قطع
+
+335
+00:26:47,220 --> 00:26:49,180
+قطع قطع قطع قطع قطع قطع قطع قطع قطع قطع قطع قطع
+
+336
+00:26:49,180 --> 00:26:49,560
+قطع قطع قطع قطع قطع قطع قطع قطع قطع قطع قطع قطع
+
+337
+00:26:49,560 --> 00:26:52,860
+قطع قطع قطع قطع قطع قطع قطع قطع قطع
+
+338
+00:27:01,300 --> 00:27:04,040
+كل الـ dielectric constant of the material ثابت
+
+339
+00:27:04,040 --> 00:27:08,780
+الـ dielectric يعني C بتسوي Kappa في C0 طبعا
+
+340
+00:27:08,780 --> 00:27:13,440
+ذاكرين Epsilon Note احنا؟ اه دايما Note بتعني فراخ
+
+341
+00:27:13,440 --> 00:27:21,620
+وبالتالي C بدون فراخ وC0 فراخ انشأ علاقة C مع C0
+
+342
+00:27:21,620 --> 00:27:24,620
+بيقولوا C زادت معناته هذه لازم تكون أكبر من واحد
+
+343
+00:27:25,310 --> 00:27:28,670
+عشان هذه الزيادة لازم تكون هذه أكبر من واحد بنات
+
+344
+00:27:28,670 --> 00:27:33,750
+لو حطت هنا C نوت انا هش بقولي C بيساوي كابا C نوت
+
+345
+00:27:33,750 --> 00:27:37,250
+لو حطت هنا C نوت جديش كابا جديش كابا على الفراغ
+
+346
+00:27:37,250 --> 00:27:42,130
+واحد محط كابا على الفراغ واحد ولا لأ وهي أصغر قيمة
+
+347
+00:27:42,130 --> 00:27:47,190
+لكابا أصغر قيمة لكابا كابا كابا لازم تكون أكبر من
+
+348
+00:27:47,190 --> 00:27:52,350
+واحد تمام دكتور مش فاهم ايش زي الفرق بين الناس مش
+
+349
+00:27:52,350 --> 00:27:55,910
+عارف انت بتقولي C بتزيدمش .. مش هذه التجارة ..
+
+350
+00:27:55,910 --> 00:28:01,250
+التجارة بهجالات؟ حاجات هذه بتديش ايه اكبر من واحد
+
+351
+00:28:01,250 --> 00:28:07,270
+بدي ارضيكي؟ بتخليها تمان عشر؟ هه .. هذا مفهوش و
+
+352
+00:28:07,270 --> 00:28:10,210
+احنا بيقول التجارة مش بتقول زادت اذا لازم تكون
+
+353
+00:28:10,210 --> 00:28:15,750
+قابة اكبر من واحد لكل مادة ثابتة مش كل مواد واحدة
+
+354
+00:28:15,750 --> 00:28:23,210
+عادي بديكي في حد بحكي هناك اه سن شويةبالرغم من أن
+
+355
+00:28:23,210 --> 00:28:27,970
+C هو دائما أكبر من C نقطة، يجب أن يكون قابة القبض
+
+356
+00:28:27,970 --> 00:28:33,190
+أكبر من Unity وهذه قبض بعد المواد، لن نحفظهم يا
+
+357
+00:28:33,190 --> 00:28:39,190
+بنات، لن نحفظهم، هذه تُعطيكم، طلعوا، هذي إيش؟
+
+358
+00:28:39,190 --> 00:28:43,590
+Vacuum الفرار، هذي إيش؟ طلعوا، زي بعد تقريبا ولا
+
+359
+00:28:43,590 --> 00:28:49,140
+لأ؟طبعا نمشي مش مشكلة كل مادة ده إيه اللي بخص بيها
+
+360
+00:28:49,140 --> 00:28:54,200
+ومبتدأش أحفظها لإنه أكتب على Google بجيبها تمام؟
+
+361
+00:28:54,200 --> 00:28:59,560
+نفسها
+
+362
+00:28:59,560 --> 00:29:04,320
+بس بنفع تكون أصغر؟ لأ يعني دي أم جزي إنه لما تحط
+
+363
+00:29:04,320 --> 00:29:10,370
+مادة غير الفراغة هي جزي تمام؟هه هه بدك يعملها ال
+
+364
+00:29:10,370 --> 00:29:16,010
+gate و لا اجلها الخانة التالتة طلع عليها ايش
+
+365
+00:29:16,010 --> 00:29:21,130
+وحدتها في وقت عالميته المجال الكهربائي صح عمكم
+
+366
+00:29:21,130 --> 00:29:26,390
+شفتوا جهاز انحرق شمته ريحته اول ما ينحرق تطلع
+
+367
+00:29:26,390 --> 00:29:30,030
+ريحته خلنا نحكي بهم مش هالتليفزيون مش شاغل وقتين
+
+368
+00:29:30,030 --> 00:29:35,530
+تطلع ريحت البامية لما تستويلما تطلع ريحتي الـ
+
+369
+00:29:35,530 --> 00:29:39,690
+Capacitor معنوة المادة اللي جوا استوت، ايش استوت؟
+
+370
+00:29:39,690 --> 00:29:43,190
+جاللي اتغيرت، بطلت الـ Insulator، صلت Conductor،
+
+371
+00:29:43,190 --> 00:29:49,520
+اتأينت علميا، اتأينتإيش اللي بيخلّيها تتأين وتخرب
+
+372
+00:29:49,520 --> 00:29:53,420
+هذا المقدار؟ إذا اتجاوزته، أنا هاطلق المادة
+
+373
+00:29:53,420 --> 00:29:57,180
+طبيعتها أنا بعرفها، إذا اتجاوزته، حطيت جهود أعلى
+
+374
+00:29:57,180 --> 00:30:01,460
+من اللي أنا كتبلكيها، المادة بتنحرج، بتطلع ريحته،
+
+375
+00:30:01,460 --> 00:30:04,980
+معناته اليوم وابطلت Insulator، صارت Conductor، إيش
+
+376
+00:30:04,980 --> 00:30:09,180
+يصيبوا الـCapacitor رمي في سبالة؟بتصلحش خلاص لأن
+
+377
+00:30:09,180 --> 00:30:13,300
+المادة اتغيرت طبيعتها اتغيرت طبيعتها انا هتطلعك زي
+
+378
+00:30:13,300 --> 00:30:17,780
+لما هنقول الميه ل pure ميه insulator صح ولا لأ
+
+379
+00:30:17,780 --> 00:30:20,780
+هجيت لما تلعبوا انتوا في الكهربا ابوك وامك ايش
+
+380
+00:30:20,780 --> 00:30:23,380
+بيقول ابعدوا الميه عن حالكم مع ان الميه insulator
+
+381
+00:30:23,380 --> 00:30:27,180
+ليش لأن الميه مش صافية اللي عندك كلها أملاح و
+
+382
+00:30:27,180 --> 00:30:32,620
+بتتأين بسهولة و بال circumductor اذا معناته هذا
+
+383
+00:30:32,620 --> 00:30:38,230
+العمود هرجعله كمان مرةبيعني إن في حظ معين كل
+
+384
+00:30:38,230 --> 00:30:43,770
+capacitor بيقدرش يتجاوز وإلا بيخرب إيش يعني بيخرب؟
+
+385
+00:30:43,770 --> 00:30:47,690
+بتطلع ريحته إيش يعني بتطلع ريحته؟ لإن هو بقتل ال
+
+386
+00:30:47,690 --> 00:30:53,730
+insulator استوى استوى زي البانيا تمام حلو ولو إنه
+
+387
+00:30:53,730 --> 00:31:00,830
+عرفكم أغلبكم ماتحبوش البانيا تمام منت
+
+388
+00:31:00,830 --> 00:31:05,880
+أول سألني ليش زادت السعة؟ أنتيأحنا اتفقنا ان هذه
+
+389
+00:31:05,880 --> 00:31:10,540
+الحقيقة طلعت من المختبر فاش فيها مجال حد يكذبها و
+
+390
+00:31:10,540 --> 00:31:12,580
+اللي بيكذبها بابا بيعمل استجابة و بابا بيلاقيها صح
+
+391
+00:31:13,430 --> 00:31:17,910
+بعد كده بصير شغل العلماء يفسروا إيش اللي خلّص
+
+392
+00:31:17,910 --> 00:31:22,010
+ساعات زيد. اتفجنا؟ قالوا إيش أنت اللي بسويته؟ قلت
+
+393
+00:31:22,010 --> 00:31:25,690
+له حطيت مادة داي Electric طيب ارجع إيش هي الداي
+
+394
+00:31:25,690 --> 00:31:28,850
+Electric؟ قال لي مادة عازلة ليه سنتها داي؟ قال لي
+
+395
+00:31:28,850 --> 00:31:33,970
+من ثنائي يعني جواها فيه دايبولز أخدت كلمة دايبولز
+
+396
+00:31:33,970 --> 00:31:38,430
+زمان يعني ثنائي قطبة أو جزيء خليني أسميه قال لي
+
+397
+00:31:38,430 --> 00:31:43,150
+الجزيء ارسم ليه؟ قلت له هايهي جزيه اعتبروه جزيه
+
+398
+00:31:43,150 --> 00:31:48,850
+هذا بدي احطه زي المغناطيس زي بس هو فيه سبال قالوا
+
+399
+00:31:48,850 --> 00:31:51,470
+انت بدي تحطه جوه ال capacitor ولا لا؟ هاي ال
+
+400
+00:31:51,470 --> 00:31:55,170
+capacitor حبيبنا نمحيه عشان على الأسف ماعرفش نكتب
+
+401
+00:31:55,170 --> 00:32:01,910
+هناك على اللوح قيدونا هذا
+
+402
+00:32:01,910 --> 00:32:09,900
+موجب و هذا سالب رسمولي خطوط المجال براو عليناعشان
+
+403
+00:32:09,900 --> 00:32:15,820
+تكون نفس الرسمة فيه لون أخضر أظنه هي E صح ولا لأ؟
+
+404
+00:32:15,820 --> 00:32:21,280
+طب هذا اللي انت حاطيته جوا هذا موجب و هذا سالب و
+
+405
+00:32:21,280 --> 00:32:25,000
+في عنده قانون أخدته في ال chapter الأول بيقول F
+
+406
+00:32:25,000 --> 00:32:29,740
+بساوي Q في ال E لو كانت هذه موجب و هذه
+
+407
+00:32:38,700 --> 00:32:42,780
+بلوفها ده ولا بلوفهش هالجهة دي؟ بلوف .. بلوف ..
+
+408
+00:32:42,780 --> 00:32:48,600
+لما .. بلوف .. لما صير موجب سالم .. فح؟ هجت هي قوة
+
+409
+00:32:48,600 --> 00:32:52,740
+و هي قوة .. بلوف؟ فش عزم .. القوة بتمر في محور
+
+410
+00:32:52,740 --> 00:32:57,640
+الدوران .. إذا كل اللي زي هدول جوا المادة، بديوا
+
+411
+00:32:57,640 --> 00:33:01,400
+يصيروا زي هدول ولا لأ؟بدهم يتصفطوا ويترتبوا
+
+412
+00:33:01,400 --> 00:33:05,660
+اتطلعوا ايش بصير قال لي الـ electric field of the
+
+413
+00:33:05,660 --> 00:33:09,240
+capacitance اللي هو هذا الأخضر اللي سمتليا E نوت
+
+414
+00:33:09,240 --> 00:33:13,700
+يعني قبل ما تحط في المادة تمام؟ exerts a torque on
+
+415
+00:33:13,700 --> 00:33:17,320
+the dipoles of the material so that it tends to
+
+416
+00:33:17,320 --> 00:33:19,880
+rotate these dipoles into the direction of E نوت
+
+417
+00:33:19,880 --> 00:33:28,920
+لفه من بلديه إكساره هذا همحتى الآن صح صحين لفوا ها
+
+418
+00:33:28,920 --> 00:33:36,140
+هي الرسمة هي اللي بيطلع عليها هذا الأحمر والأزرق
+
+419
+00:33:36,140 --> 00:33:41,840
+شايفها الأحمر موجب والأزرق سالب وحسب هذه القاعدة
+
+420
+00:33:42,670 --> 00:33:46,170
+بتقول إن القوة بتكون باتجاه المجال إذا هذه موجبة
+
+421
+00:33:46,170 --> 00:33:50,610
+وعكسها سالبة هي هذه موجبة إذا القوة باتجاه المجال
+
+422
+00:33:50,610 --> 00:33:55,770
+المجال هيه وهذه هيك هجت واحد بشد هيك واحد بشد هيك
+
+423
+00:33:55,770 --> 00:33:59,930
+بيخليها هيك صح؟ إيش يعنيه بيخليه تدور بحيث إنها
+
+424
+00:33:59,930 --> 00:34:06,290
+تترتب باتجاه المجال صارت هيك جيبينها جت ممكن تلوف؟
+
+425
+00:34:06,290 --> 00:34:10,150
+لأ خلاص تمام هيك؟ طلع
+
+426
+00:34:12,720 --> 00:34:19,780
+هي مادة كيف هدول موزعين أبراو عليكم عشوائي بدي
+
+427
+00:34:19,780 --> 00:34:23,800
+أحملها و أحطها جوه كبسيطر هي كبسيطر شايفين خطوط
+
+428
+00:34:23,800 --> 00:34:29,000
+المجال؟ حلو مالها
+
+429
+00:34:29,000 --> 00:34:34,600
+دي معوجة عادلات الحمد لله إيه أصبح فيهم هدول كانوا
+
+430
+00:34:34,600 --> 00:34:41,090
+عشوائين؟ اترتبواتطلعوا انتبهولي هلجيت تجاوزا مش
+
+431
+00:34:41,090 --> 00:34:45,550
+هذه بتلغي هذه و هذه بتلغي هذه بس هذه مافيش حاجة
+
+432
+00:34:45,550 --> 00:34:50,130
+جنبها هذه على الطرف على الوجه تبع المادة و هذه على
+
+433
+00:34:50,130 --> 00:34:59,930
+الوجه بصير و كأنه هذه المادة هيك صارت امصح
+
+434
+00:34:59,930 --> 00:35:05,060
+صحين بدي اعيد عيلك اللي سالتني ليك زادت الساعةطيب،
+
+435
+00:35:05,060 --> 00:35:09,400
+جوه المادة الآن بدي تولد مجال كهرباء إشجيط، كيف
+
+436
+00:35:09,400 --> 00:35:15,580
+اتجاهه؟ من الموجب للسالب، صح ولا لأ؟ جوه المادة
+
+437
+00:35:15,580 --> 00:35:20,880
+صار في عندك مجال إشجيط نتيجة التركيب، طيب، هذا
+
+438
+00:35:20,880 --> 00:35:24,900
+المجال الأسود، اتطلعولي ياه بالنسبة للأخضر، بنفس
+
+439
+00:35:24,900 --> 00:35:29,120
+الاتجاه ولا عكسه؟ عكسه، هجيت لما بدي جيه بالنت،
+
+440
+00:35:29,120 --> 00:35:36,350
+أجمع ولا أطرح؟ أطرحهنطرح له عكس بيض طب لما أطرح
+
+441
+00:35:36,350 --> 00:35:42,470
+بينجس ولا بيزيد إذا المجال نجس المجال نجس طيب
+
+442
+00:35:42,470 --> 00:35:51,190
+قاللي مش دلتة V بيسوي تكامل E Dot DD جلت E جلت V
+
+443
+00:35:51,190 --> 00:35:57,070
+إيه الصفة C زادت عرفتي ليه زادت C هجيتليه زادت C
+
+444
+00:35:57,070 --> 00:36:04,030
+بتقوليلي عشان E جلت وعشان دلتة V جلت صح؟عرفت ليش
+
+445
+00:36:04,030 --> 00:36:08,770
+بالزيد C قالوا العلماء هاي سبب الزيادة عرفوا سبب
+
+446
+00:36:08,770 --> 00:36:12,170
+الزيادة قالوا بسيطة و الشغل اللي لما تيني عرف
+
+447
+00:36:12,170 --> 00:36:17,970
+السبب إذا عرف السبب بطلوا العجل مظبوط ولا لأ فهي
+
+448
+00:36:17,970 --> 00:36:22,170
+ده هي قال لي هاي هم عكس بعض و الله طلعوا عكس بعض
+
+449
+00:36:22,860 --> 00:36:27,600
+تمام بقول دي في الـ charges اللي هم هدول و هدول it
+
+450
+00:36:27,600 --> 00:36:31,160
+creates an electric field سمي إيه الشرطة opposite
+
+451
+00:36:31,160 --> 00:36:35,500
+to E0 E0 اللي كان قبل ما حط المادة opposite يعني
+
+452
+00:36:35,500 --> 00:36:40,800
+ال electric field جمعته أو حطته الطريقةعشان الـ
+
+453
+00:36:40,800 --> 00:36:45,680
+Opposite اللي يعني بالبلدي انه that is a reduction
+
+454
+00:36:45,680 --> 00:36:49,620
+صار فيه نقصان reduction من reduce a reduction is
+
+455
+00:36:49,620 --> 00:36:52,760
+occurred in the electric field صار فيه نقصان في
+
+456
+00:36:52,760 --> 00:36:57,640
+المجال الكهربائي ال net وبما انه Delta V بتسوي E
+
+457
+00:36:57,640 --> 00:37:00,480
+في D أخدتها في الشرطر الماضي the potential
+
+458
+00:37:00,480 --> 00:37:02,920
+difference across the capacitor decreases
+
+459
+00:37:02,920 --> 00:37:10,150
+consequently كنتيجةإذا E جلت بمقدار كعبة إذا Delta
+
+460
+00:37:10,150 --> 00:37:17,490
+V جلت معناته C زادت بمقدار كعبة احكي ما هو إيش
+
+461
+00:37:17,490 --> 00:37:21,770
+اختلف اتجاهها
+
+462
+00:37:21,770 --> 00:37:29,850
+عندك عشرة شرقا اتولد تمانية اتنين غربا جيبين ال
+
+463
+00:37:29,850 --> 00:37:30,070
+net
+
+464
+00:37:34,230 --> 00:37:39,710
+عشرة و اتنين ثم تمانية مظبوط ولا لأ؟ في الأول كنت
+
+465
+00:37:39,710 --> 00:37:43,450
+بادئ بعشرة صفيت بتمانية ايه صار في ال .. انت صرا
+
+466
+00:37:43,450 --> 00:37:47,370
+مانجيص ايش؟ مانجيص لأن انت طرحت لكن لو كانوا في
+
+467
+00:37:47,370 --> 00:37:52,610
+نفس الاتجاه عشرة و اتنين بيصيروا اتناشر ما هو الله
+
+468
+00:37:52,610 --> 00:37:59,190
+.. خلاص حلو عندك two vectors two vectors مصحصها؟
+
+469
+00:37:59,730 --> 00:38:06,970
+عشرة شمالا لأ فوق وتلاتة أسفلا إيش تسوي؟ هاي
+
+470
+00:38:06,970 --> 00:38:14,330
+بتراحتي، ليش تراحتي؟ ليش هذا قيمة؟ هم هدول القيم
+
+471
+00:38:14,330 --> 00:38:17,990
+لمين؟ لكمية vector ولا مش vector؟ إذن بتاخد فعلا
+
+472
+00:38:17,990 --> 00:38:21,590
+اعتبار الاتجاه ولا لأ؟ إذن لما يكون عكس بعيد بتحط
+
+473
+00:38:21,590 --> 00:38:25,450
+شرط سالف ولا لأ؟ عشان كده اتراحت، تمام؟
+
+474
+00:38:29,040 --> 00:38:33,640
+السؤال اللي أخر تيرمها دا في جدول بيقول should be
+
+475
+00:38:33,640 --> 00:38:37,380
+noted that a limited value of the potential can be
+
+476
+00:38:37,380 --> 00:38:40,620
+applied across a capacitor جالي كل capacitor
+
+477
+00:38:40,620 --> 00:38:45,320
+هتلاقي فيه رقم تاني غير سعته هذا بتقول لا تجديش
+
+478
+00:38:45,320 --> 00:38:49,900
+أكبر جهد بتحطه أو أكبر مجالاللي تاول حكيناها
+
+479
+00:38:49,900 --> 00:38:54,420
+البامية بس بنعيدها مزيد سعجلتنا تمام if the
+
+480
+00:38:54,420 --> 00:38:58,360
+potential is الجهد exceeds تجاوز الحد اللي انت
+
+481
+00:38:58,360 --> 00:39:01,660
+محطوط عليك the insulating properties of the
+
+482
+00:39:01,660 --> 00:39:06,380
+dielectric will break down الصفات كونوا insulator
+
+483
+00:39:06,380 --> 00:39:10,820
+تبقى ال dielectric بتنهارو ايش بيصير فيه form a
+
+484
+00:39:10,820 --> 00:39:13,320
+conducting medium بيصير عندك conducting medium
+
+485
+00:39:13,320 --> 00:39:16,140
+بيصير عندك conductor conductor بينهم conductor
+
+486
+00:39:16,140 --> 00:39:22,140
+كبسيطر هذا بوديه ع الزبالة تمام؟تمام This limiting
+
+487
+00:39:22,140 --> 00:39:24,520
+value called the breakdown potential depends on
+
+488
+00:39:24,520 --> 00:39:27,060
+the dielectric strength اللي توا حطتهوه which is
+
+489
+00:39:27,060 --> 00:39:30,020
+the maximum value of the electric field that the
+
+490
+00:39:30,020 --> 00:39:35,200
+dielectric can tolerate without breakdown هذه
+
+491
+00:39:35,200 --> 00:39:43,040
+تفاصلناها بالعربي من قصة البامية خلصناها تمام مثال
+
+492
+00:39:43,040 --> 00:39:47,060
+هجيت اشي احب ان انا اخطبق منها النتيجة انه لما احط
+
+493
+00:39:47,060 --> 00:39:52,040
+dielectric جوا كبسطراش بصرف الساعةبزيت بس اكتر من
+
+494
+00:39:52,040 --> 00:39:55,280
+كده بديش بزيت بمقدار المادة تبع للمادة اللي حطيتها
+
+495
+00:39:55,280 --> 00:39:58,560
+ولا لأ والمادة اللي حطيتها هيقولك إيش هي و هيقولك
+
+496
+00:39:58,560 --> 00:40:01,880
+جديش قابة تبعتها يعني تضرب في واحد و اتنين و عشرة
+
+497
+00:40:01,880 --> 00:40:05,660
+ولا واحد و نص ولا اتنين ولا تلاتة و هيقول لأ تمام
+
+498
+00:40:05,660 --> 00:40:19,620
+طلعش بقول السؤالهو كباسيتر بطارية
+
+499
+00:40:19,620 --> 00:40:23,900
+معلومة الجهود مازال بدي أشحنه بمعلومة الجهود وبعرف
+
+500
+00:40:23,900 --> 00:40:28,060
+ساعته وبعرف شحناته و لا لأ بعرف شحناته طيب هاي
+
+501
+00:40:28,060 --> 00:40:34,440
+شبكته شحنته خلاص عرفش شحناته صح ولا لأ تمام طبعا
+
+502
+00:40:34,440 --> 00:40:38,750
+ماش بقولينThe battery is then removed سكّرت
+
+503
+00:40:38,750 --> 00:40:44,330
+المصورة، صح؟ سكّرت المصورة تبع الشحنات أول ما جيّم
+
+504
+00:40:44,330 --> 00:40:49,710
+البطارية معناته Q مسموح لتتغير؟ لأ لأ، تمام؟ إذن
+
+505
+00:40:49,710 --> 00:40:54,350
+المعلومة اللي أخدتها من المرة ديك لما أفك البطارية
+
+506
+00:40:54,350 --> 00:40:59,810
+إيش بيثبت؟ولمّا خلّي البطارية ايش بثبات؟ Delta V
+
+507
+00:40:59,810 --> 00:41:06,210
+حلو هذه المعلومة اخدناها طيب اذا فكيت البطارية بعد
+
+508
+00:41:06,210 --> 00:41:10,210
+كده روحت جيب ال dielectric وحطيته جوا ايه صار في
+
+509
+00:41:10,210 --> 00:41:15,440
+الساعات؟صح ولا لأ؟ بيقوللي the battery is then
+
+510
+00:41:15,440 --> 00:41:19,540
+removed and a dielectric slab of dielectric
+
+511
+00:41:19,540 --> 00:41:23,560
+constant Kappa is inserted between the plates of
+
+512
+00:41:23,560 --> 00:41:27,760
+the capacitor I shown جابت البطارية ثبتت Q صح؟
+
+513
+00:41:27,760 --> 00:41:31,420
+ألعب في ال capacitor ألعبت إيه سويته ال capacitor؟
+
+514
+00:41:31,420 --> 00:41:37,560
+زود سعته بإني حطيت مادة dielectric طيب بيقوللي إيش
+
+515
+00:41:37,560 --> 00:41:39,880
+بدك؟ بيقوللي find the energy stored in the
+
+516
+00:41:39,880 --> 00:41:44,630
+capacitorقبل ما تحط المادة الخضراء وبعد ما حطيت
+
+517
+00:41:44,630 --> 00:41:48,430
+المادة الخضراء قبل ما حطيت المادة الخضراء بتعرفش
+
+518
+00:41:48,430 --> 00:41:52,630
+شحنات ولا بتعرفهاش؟ بتعرفها من وين عرفتها؟ عرفتها
+
+519
+00:41:52,630 --> 00:41:57,530
+إن الجهود معروف، مظبوطة أو لأ، والسيعة معروفة، إما
+
+520
+00:41:57,530 --> 00:42:01,710
+بتستخدم هذا القانون أو بتستخدم هذا جاهز، ما هذه
+
+521
+00:42:01,710 --> 00:42:04,650
+تبعت البطارية، ما هذه السيعة اللي تعرفها، مظبوطة
+
+522
+00:42:04,650 --> 00:42:09,350
+أو لأ؟ إذا جبتلك إياها، جالي طب وبعد ما حطيتها،
+
+523
+00:42:09,350 --> 00:42:12,800
+إيش بده يصير في اليوم؟بنشوف وإذا بده يتغير بيبقى
+
+524
+00:42:12,800 --> 00:42:19,120
+أفسر ليش تمه جالي في الأول the battery إيه سوى في
+
+525
+00:42:19,120 --> 00:42:22,480
+ال capacitor ده اللي شحنته جالي دي شحنته جالي هاي
+
+526
+00:42:22,480 --> 00:42:27,060
+شحنته C note اللي هي قبل ما حط ال dielectric يعني
+
+527
+00:42:27,060 --> 00:42:31,480
+و delta V delta V note هي مقدار فرق جهد من طرفين
+
+528
+00:42:31,480 --> 00:42:33,900
+ال capacitor قبل ما تحط ال dielectric هي تبعات
+
+529
+00:42:33,900 --> 00:42:38,960
+البطارية مش تحت البطارية بتاعة البطارية حلوقال
+
+530
+00:42:38,960 --> 00:42:45,800
+يجيب ليه بسيط هايو the energy بتسوى نصي نوت دلتا
+
+531
+00:42:45,800 --> 00:42:50,180
+في نوت او هدى كل واحد طلعش قال ليه after removing
+
+532
+00:42:50,180 --> 00:42:53,560
+the battery هدى ال charge اللى انت حسبتها مسموعها
+
+533
+00:42:53,560 --> 00:42:59,500
+تتغير will not be changed اذا جيبتلك انا you جابل
+
+534
+00:43:00,240 --> 00:43:03,900
+بدي U بعيد U بعيد أنا هتخطط لك U Note يعني Double
+
+535
+00:43:03,900 --> 00:43:09,860
+صح بالفرار هجيجي أصلا أحط U بتساوي Q تربيع ع 2C
+
+536
+00:43:09,860 --> 00:43:17,500
+مظبوط هيك ولا لأ هجيت هادي مسموحلي أحط هيك لأ لأ
+
+537
+00:43:17,500 --> 00:43:21,640
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+538
+00:43:21,640 --> 00:43:21,820
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+539
+00:43:21,820 --> 00:43:27,000
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+540
+00:43:27,000 --> 00:43:34,660
+لأ لأ لأ لولّا صارت كابا سينوت بحكي
+
+541
+00:43:34,660 --> 00:43:41,200
+عربي طيب بس هتتبهى شوية بس اخلي واحد ع كابا و أحط
+
+542
+00:43:41,200 --> 00:43:47,380
+جوز you note تربيع اتنين سينوت عملتيش ايه؟ you
+
+543
+00:43:47,380 --> 00:43:56,200
+note اذا you note you طلعت you note ع كابا يجلد
+
+544
+00:43:57,920 --> 00:44:01,700
+يجلد بيقولي ايه الراحة؟ قلتله انت بتفكر ال
+
+545
+00:44:01,700 --> 00:44:06,420
+capacitor بيقولك انت بتفكرني انا وكالة بدون بواب؟
+
+546
+00:44:06,420 --> 00:44:11,240
+بنفع تخش هيك بدون ما اقولك ان انت اول ما خشت ال
+
+547
+00:44:11,240 --> 00:44:16,000
+die electric سرطوشة ال capacitor جتلها في حد بيسمح
+
+548
+00:44:16,000 --> 00:44:19,760
+لو حد غريب يخش داره؟ هذه شغل غريبة بدأت تفجر و هو
+
+549
+00:44:19,760 --> 00:44:25,160
+ال capacitorنطوا كل السكان وعملوا فزعة جاتلوها
+
+550
+00:44:25,160 --> 00:44:28,820
+لمّا زهجوا في الأخرين هزموها نقول دخلت لكن بيكونوا
+
+551
+00:44:28,820 --> 00:44:32,820
+تعبوا ولا ماتعبوش تعبوا هذا التعب بتكلف طاقة ولا
+
+552
+00:44:32,820 --> 00:44:38,200
+لأ إذا ال reduction سببه أنه في شغل بدل ال
+
+553
+00:44:38,200 --> 00:44:43,540
+capacitor عشان يقوم دخول هذه المادة وبالتالي شغلة
+
+554
+00:44:43,540 --> 00:44:49,090
+مطيقية لجلد الطاقة صح ولا لأ بحكيش عربي شكلهاحنا
+
+555
+00:44:49,090 --> 00:44:54,270
+حكينا إنه كيوتر ده فلما حطينا ركابة زادت السعة
+
+556
+00:44:54,270 --> 00:44:58,830
+فبتالي حجيل .. زادت السعة فبتالي حجيل الصارت بظبط
+
+557
+00:44:58,830 --> 00:45:02,810
+بس احنا بنفسر بيقول راحت، راحت على هيئة شغل، كلامك
+
+558
+00:45:02,810 --> 00:45:08,330
+صحيح رياضيا، تمام، عيد، احكوا، احكوا معايا عشان
+
+559
+00:45:08,330 --> 00:45:09,050
+يسمعوا غيركم
+
+560
+00:45:11,790 --> 00:45:16,830
+جلّت you ليش جلّت؟ لأن في طاقة باعت بتعب بقى
+
+561
+00:45:16,830 --> 00:45:20,610
+مقاومة دخول المادة مش هذه المادة اللي عادة بتدخل؟
+
+562
+00:45:20,610 --> 00:45:24,770
+وحكينا توي صار فيه فزعة و السكان تعوني الكباسيتر
+
+563
+00:45:24,770 --> 00:45:30,310
+قاوموا الدخول تفرض واحد منهم مات من السكان طاقة
+
+564
+00:45:30,310 --> 00:45:34,610
+لأن هي التعب دائما انت لما تقاومي معناته فقدتي
+
+565
+00:45:34,610 --> 00:45:40,460
+طاقة ولا لأ فدائما مقاومة شيء تقدل طاقةوانا قاعد
+
+566
+00:45:40,460 --> 00:45:44,420
+كباسيتراش بقولك انا وكالة بدون بواب؟ لأ. ايش
+
+567
+00:45:44,420 --> 00:45:47,500
+معناته؟ اي واحد بده يفوت، بده يقاومه ولا لأ؟ وانت
+
+568
+00:45:47,500 --> 00:45:50,600
+المادة الخضراء، مش انت دخلتيها، هذه المادة الخضراء
+
+569
+00:45:50,600 --> 00:45:56,060
+مش جديدة، اذا جسم غريب ولا لأ؟ اذا المكثف بيقاوم
+
+570
+00:45:56,060 --> 00:46:01,540
+ويبذل الشغل لمقاومة دخول هذه المادة الخضراء، بلغة
+
+571
+00:46:01,540 --> 00:46:07,730
+الطاقة، هذه المقاومة بتكلف طاقة.كان عندى ميت جول
+
+572
+00:46:07,730 --> 00:46:12,090
+صفت على ستين جول معناته اربعين راحوا اربعين وين هو
+
+573
+00:46:12,090 --> 00:46:17,930
+التعب اللى تعبته عشان المقاومة انت عليا بما هو
+
+574
+00:46:17,930 --> 00:46:22,890
+برضه كل هذه كلام صحيح بس بلغة الطقه المعناته بلغة
+
+575
+00:46:22,890 --> 00:46:26,920
+الطقه المعناته هو الراحت اما كلامكم كله صحيحقال لي
+
+576
+00:46:26,920 --> 00:46:31,800
+ايجيت اطلع وهي كحط U ليش حط كيو نوت ماحطش كيو
+
+577
+00:46:31,800 --> 00:46:36,980
+لأنها مابتفرجش كيو نوت نفسها لما عملها زي ما تمومي
+
+578
+00:46:36,980 --> 00:46:41,100
+عملتها انا وياكم طلعت كيو نوت على كابة وهذا يعني
+
+579
+00:46:41,100 --> 00:46:46,160
+انه U قلت وقال لي الاختلاف في الطاقة يمكن انه يتم
+
+580
+00:46:46,160 --> 00:46:51,420
+تفسيره بعمل الكمبيوتر مقاومة الكمبيوتر الشغل
+
+581
+00:46:51,420 --> 00:46:55,400
+الكمبيوتر اللي بذله في مقاومة التغيير اه يا بنات
+
+582
+00:46:56,130 --> 00:47:03,950
+بنحكي عربي تمام؟ تمام، كويس، هذه برضه أغلاط في
+
+583
+00:47:03,950 --> 00:47:06,930
+الحركة بهم، مش تتحملوني، مش عارف معانا بعمل test
+
+584
+00:47:06,930 --> 00:47:13,270
+كتيرة، لكن لا حول ولا تمام، أ fully charged برا ال
+
+585
+00:47:13,270 --> 00:47:17,430
+blade capacitor، capacitor أنا ماليه؟ ماليه؟ وخلتي
+
+586
+00:47:17,430 --> 00:47:18,770
+البطارية مشموكة
+
+587
+00:47:22,010 --> 00:47:24,470
+Remains connected to the battery. ما هو الثابت؟
+
+588
+00:47:24,470 --> 00:47:28,650
+Delta V. Bravo. هذا معطيات أسلة يا بنات. معطيات.
+
+589
+00:47:29,530 --> 00:47:32,450
+To a battery while you slide a dielectric between
+
+590
+00:47:32,450 --> 00:47:35,070
+the plates. وحطي ال dielectric. إيه صار في الساعة؟
+
+591
+00:47:35,070 --> 00:47:38,750
+ذاتة. Do the following quantities increase,
+
+592
+00:47:38,870 --> 00:47:42,490
+decrease or stay the same؟ نفس المصطلح مرة علينا.
+
+593
+00:47:43,410 --> 00:47:47,640
+الشمّة جلبتهاي شايفين كيف؟ هاي الـ dielectric
+
+594
+00:47:47,640 --> 00:47:51,380
+بيدخلها والبطارية موجودة ولا لأ؟ البطارية موجودة
+
+595
+00:47:51,380 --> 00:47:54,300
+ده اللي شوف ليه يا أخش أخبار الـC وإيش أخبار الـQ
+
+596
+00:47:54,300 --> 00:47:58,200
+وإيش أخبار الـDelta V دلتا V توا حلتوه ثابتة بظبط
+
+597
+00:47:58,200 --> 00:48:01,440
+ثابتة هاي وانتوا حلتوها على طول عشان كده في بعض
+
+598
+00:48:01,440 --> 00:48:05,100
+الأسئلة بتيجي بس بتقول للناس بعرض الله هي جواب بس
+
+599
+00:48:05,100 --> 00:48:10,500
+حطوه يعني مواضح بدونش تفكير Delta V وبعدين بالـD E
+
+600
+00:48:10,500 --> 00:48:15,040
+بقوله أول حاجة أسفر في الـC قلتوا ليه؟زادت و احنا
+
+601
+00:48:15,040 --> 00:48:18,640
+شخصيا خدنا اخر معلومة اصلا اليوم ايه من C لما تحط
+
+602
+00:48:18,640 --> 00:48:22,120
+ديالكتركش من صنفه C؟ من C وما تقوليش قدش زادت وما
+
+603
+00:48:22,120 --> 00:48:28,600
+تقوليش ياك قدش زادت زادت وخلاص تمى قاللي الـQ دلتا
+
+604
+00:48:28,600 --> 00:48:35,040
+V ثابتة وC زادت اذا الـQ زادت بقول الـQ بساوي الـC
+
+605
+00:48:35,040 --> 00:48:39,040
+في دلتا V C زادت ودلتا V فظلة زي ما هي اذا الـQ
+
+606
+00:48:39,040 --> 00:48:45,660
+increasesنجي Delta V من أول ثابتة لأن البطارية
+
+607
+00:48:45,660 --> 00:48:48,960
+مشبوكة since the battery is still connected هذه
+
+608
+00:48:48,960 --> 00:48:52,000
+المعلومة اللي حاولت أدخلها في مخكم المرة الماضية
+
+609
+00:48:52,000 --> 00:48:55,320
+أول ما أقول البطارية ما زالت مشبوكة إذا Delta V is
+
+610
+00:48:55,320 --> 00:48:58,860
+constant if it's still connected then Delta V stay
+
+611
+00:48:58,860 --> 00:49:03,380
+the same هجيت E قاللي إي إي إي انت قلتلي سيجما على
+
+612
+00:49:03,380 --> 00:49:08,230
+أبسل و نوتر مرة هديكصح؟ طيب ليش حطيتها؟ قلتله لأن
+
+613
+00:49:08,230 --> 00:49:11,970
+Epsilon كان ثابتا طب هالجيث Epsilon اتحضرها زي ما
+
+614
+00:49:11,970 --> 00:49:17,770
+هي؟ ده ليه فراغ؟ Epsilon لفراغ قال لي معناته هذا
+
+615
+00:49:17,770 --> 00:49:24,270
+القانون هيغلبني ليش؟ لأن انت بتقوللي هي .. الـQ
+
+616
+00:49:24,270 --> 00:49:30,050
+إيه صار فيها؟ زادت زادت، هذه متغيرة وهذه هتتغير،
+
+617
+00:49:30,050 --> 00:49:34,840
+هتصير هيكفح؟ إذا شوف ليه قانون غيرها القانون جال
+
+618
+00:49:34,840 --> 00:49:39,340
+ليه فتش فتش فتش فيها slides ومسموح لها نفتش كمعا
+
+619
+00:49:39,340 --> 00:49:45,480
+في ال quizات لجيت إنه في E بتساوي إذا كنتوا ذاكرين
+
+620
+00:49:45,480 --> 00:49:54,260
+عبارة عن delta V على D حلو إلعبت في ال DNA طب وما
+
+621
+00:49:54,260 --> 00:49:57,560
+زال مشبوك في البطارية delta V إيش أخبارها إذا E
+
+622
+00:49:57,560 --> 00:50:01,670
+constantاذن هذا سلّي و قالوا والله موجود في ال
+
+623
+00:50:01,670 --> 00:50:06,330
+slides بتاوي استخدمته قال لي إذا معناته بس أنا ليش
+
+624
+00:50:06,330 --> 00:50:10,810
+حجبت هذا عشان ما حد يقول .. وين راحت؟ عشان ما حد
+
+625
+00:50:10,810 --> 00:50:13,210
+يقول بضحك عليه أنا مرة بستخدم هذا و مرة بستخدم هذا
+
+626
+00:50:13,210 --> 00:50:16,630
+و يقول ليش مستخدملاش هذا عارفين ليش مستخدملهوش؟
+
+627
+00:50:16,630 --> 00:50:20,190
+لأنه حيورطك طبعا يجي واحد يقول طيب عنزة ورا وطارت
+
+628
+00:50:20,190 --> 00:50:25,310
+بدي أشوف هذا إيش بديني بقوله هذه زادت صح؟ و هذه
+
+629
+00:50:25,310 --> 00:50:30,450
+زادتلو نفسي زيادة بتطلع constant برضه بتودي لنفس
+
+630
+00:50:30,450 --> 00:50:35,290
+روم تمام بس هيخبطني لأ شوف القانون تاني أعرف ليش
+
+631
+00:50:35,290 --> 00:50:43,590
+دي بتهدأ أسهللي تمام آية بنات تمام عليه
+
+632
+00:50:43,590 --> 00:50:48,950
+صوتك صوتك عليك حلو هي جذبها أترجمها جذبك هي بتقولي
+
+633
+00:50:48,950 --> 00:50:54,320
+انت بتقولي إيه ثابتة و طب قلتيلي إيه جلة صح؟طب ليش
+
+634
+00:50:54,320 --> 00:50:57,740
+هنا ثابتة؟ طب ادرعوا عليك عشان البطارية موجودة
+
+635
+00:50:57,740 --> 00:51:03,060
+النقصان مين عوضه؟ البطارية هالمرة دي كانت فاكتها
+
+636
+00:51:03,060 --> 00:51:07,940
+كنت فاكتها اي اقوى يعني و أنا بشرح اه قولت انه E
+
+637
+00:51:07,940 --> 00:51:13,640
+جلت ليش؟ لأن هنا E جلت بس اول ما جلت E البطارية
+
+638
+00:51:13,640 --> 00:51:18,880
+عوضت النقصانإدت شحنات، تمام؟ عرفتي جواب سؤالك
+
+639
+00:51:18,880 --> 00:51:23,860
+ممتازة أن E .. هي أصلا ما لازم تجلب لكن كون ما
+
+640
+00:51:23,860 --> 00:51:28,020
+زالت البطارية موجودة عوض بضط النخصان فرجعت ثابت ال
+
+641
+00:51:28,020 --> 00:51:33,520
+E سؤاليك حلو، تمام طب شوف هالسؤال، جلي نفس السؤال،
+
+642
+00:51:33,520 --> 00:51:39,920
+بس إيش بدي أسوي؟ جلي بدي أفق البطارية ال Q ثبتت و
+
+643
+00:51:39,920 --> 00:51:46,820
+حضب ال electric أثر في CC بده Z بقوله هيا C
+
+644
+00:51:46,820 --> 00:51:51,680
+increases since the battery is disconnected it
+
+645
+00:51:51,680 --> 00:51:55,500
+used to be the same ارجعت قلتله it used to be the
+
+646
+00:51:55,500 --> 00:52:01,820
+same و هادي زادت اذا دلتا V decreases ارجع لإيه
+
+647
+00:52:01,820 --> 00:52:05,440
+دلتا V على ديه مالعبتش فيه ده V جلت اذا ايه جلت
+
+648
+00:52:05,440 --> 00:52:09,200
+نجي لها ده القانون اخر حاجة و من راح ايوة هجيت
+
+649
+00:52:09,200 --> 00:52:14,350
+هادي اي صف فيه زاد هادي ضل زي ما هيإذا إيه جلّت؟
+
+650
+00:52:14,350 --> 00:52:19,430
+إيه جلّت؟ هنا إيه جلّت؟ في حد عوضها؟ جلّت هي جت
+
+651
+00:52:19,430 --> 00:52:22,110
+معاكي عشان مافيش بطارية
+
diff --git a/PL9fwy3NUQKwZzXsCLffozucGP33XWqvBP/syXP7Tyo4Ag.srt b/PL9fwy3NUQKwZzXsCLffozucGP33XWqvBP/syXP7Tyo4Ag.srt
new file mode 100644
index 0000000000000000000000000000000000000000..9414692c874ac5cb3cc29707fd6f7e2c9edc3efe
--- /dev/null
+++ b/PL9fwy3NUQKwZzXsCLffozucGP33XWqvBP/syXP7Tyo4Ag.srt
@@ -0,0 +1,1988 @@
+1
+00:00:04,960 --> 00:00:09,060
+تمام يا بنات، هنبدأ اليوم إن شاء الله بالـ chapter
+
+2
+00:00:09,060 --> 00:00:12,980
+اللي قبل الأخر وإن شاء الله يوم الأربعاء بيخلص هذا
+
+3
+00:00:12,980 --> 00:00:16,340
+الـ chapter، قولوا بسم الله عشان بالمرة الـ خمسة نعمله
+
+4
+00:00:16,340 --> 00:00:22,400
+كويس، تمام، هلا نخلص، تمام، هذا الـ chapter، بده
+
+5
+00:00:22,400 --> 00:00:27,820
+يكمل الـ chapter الماضي عنوانه الـ Inductance أو
+
+6
+00:00:27,820 --> 00:00:31,260
+الحث هو فرضيه، إيش بيحكي؟ ما هو بيحكي عن الحث ولا مش
+
+7
+00:00:31,260 --> 00:00:35,480
+عن الحث؟ فرضيه بيحكي عن الحث، هذا أكثر تفصيلاً، إيش
+
+8
+00:00:35,480 --> 00:00:39,800
+بدنا نشرحه؟ قليل، فيه حاجة مسميها الحث الذاتي، بدنا
+
+9
+00:00:39,800 --> 00:00:45,880
+ناخذه، وحاجة اسمها الـ RL Circuit، فيه حاجة زيها
+
+10
+00:00:45,880 --> 00:00:51,980
+خدناها، الـ RC Circuit، برا، علينا، تم. Energy in
+
+11
+00:00:51,980 --> 00:00:53,740
+magnetic field بقى، اللي فيه Energy في الـ
+
+12
+00:00:53,740 --> 00:00:58,000
+Capacitor، الـ Q تربيع على 2C، ذاكرينها؟ هذه بتشبهها
+
+13
+00:00:58,000 --> 00:01:05,000
+LC Circuit، خلّينا نكمل RC و LC و RL، خلّيني أشوف إيش
+
+14
+00:01:05,000 --> 00:01:13,070
+بده يصير فيها. طبعاً نرجع ونقول، هدول الأسئلة حلوهم، لأن
+
+15
+00:01:13,070 --> 00:01:17,230
+واحد منهم مرشح يكون في الـ final، أيوة، اكتبوا، طب أنا
+
+16
+00:01:17,230 --> 00:01:21,070
+بغششكم ولا ما بغششكم؟ بغششكم، بس بعرف أجيبهم
+
+17
+00:01:21,070 --> 00:01:23,790
+علامات حلوة، تمام
+
+18
+00:01:27,460 --> 00:01:30,800
+إذاً أنا إيش قلت لكم يا بنات؟ هذا الـ chapter بدي أكمل
+
+19
+00:01:30,800 --> 00:01:34,920
+الـ chapter الماضي، هو الـ chapter الماضي إيش قاله؟
+
+20
+00:01:34,920 --> 00:01:38,380
+قال في الشرح لهذه الفكرة قانون فاراداي، وإيش نفس
+
+21
+00:01:38,380 --> 00:01:42,880
+يساعد فاراداي في الشرح، طيب إيش هو قانون فاراداي؟ قال
+
+22
+00:01:42,880 --> 00:01:50,140
+لي، في induced emf بسالب ناقص d phi magnetic على
+
+23
+00:01:50,140 --> 00:01:55,040
+dt، ذكيين ولا لأ؟ هي قانون فاراداي، إيش فاراداي بيقول
+
+24
+00:01:55,040 --> 00:02:00,840
+بيقول: إذا تغير الـ flux بتولد تيار مستحث، ولا لا؟ تمام
+
+25
+00:02:00,840 --> 00:02:06,700
+الـ flux عشان يتغير، بدي واحد من ثلاثة يتغير، إما B
+
+26
+00:02:06,700 --> 00:02:10,760
+أو الـ area أو الزاوية، حلو، تنسوش أن B مين بيدّيها؟
+
+27
+00:02:10,760 --> 00:02:18,840
+مين مصدر B؟ I، حلو، قال لي خلّيني أشوف، قال لي شوف
+
+28
+00:02:18,840 --> 00:02:23,170
+هالدائرة، إيش هذه التيار؟ فيها بطارية، شايفينها؟
+
+29
+00:02:23,170 --> 00:02:28,130
+وفيها مقاومة، وفيها شغلة جديدة، سلك، بس ملفوف، ع شكل
+
+30
+00:02:28,130 --> 00:02:31,910
+ملف، هو الملف ما هو سلك، ولا لا؟ سلك بس ملفوف،
+
+31
+00:02:31,910 --> 00:02:36,450
+طيب، أمّا سؤالي إليكم الآن، في هذا الشكل، المفتاح
+
+32
+00:02:36,450 --> 00:02:41,670
+مفتوح، صح؟ قديش التيار؟ Bravo، في مجال مغناطيسي؟
+
+33
+00:02:41,670 --> 00:02:44,970
+لأ، لو صار في تيار، بصير في مجال مغناطيسي؟ طيب،
+
+34
+00:02:44,970 --> 00:02:48,530
+وكتيش بده يصير تيار، ما أسكر؟ أول ما أسكر، صار في
+
+35
+00:02:48,530 --> 00:02:53,110
+تيار، صار في مجال، معناه المجال بيتغير من صفر لقيمة
+
+36
+00:02:53,110 --> 00:02:58,440
+ولا لا؟ اشتغل فاراداي، صح؟ تشتغل فاراداي، طيب فاراداي إيش
+
+37
+00:02:58,440 --> 00:03:03,960
+بيقول؟ لينز ساعده، قال: إذا الـ flux بيزيد، في عندك معاكسة، وإذا الـ flux بينقص، في عندك معاكسة، إذا
+
+38
+00:03:03,960 --> 00:03:08,880
+أول ما تسكر المفتاح، صار في عندك مجال مغناطيسي، when
+
+39
+00:03:08,880 --> 00:03:14,820
+the switch is closed, the current and through the
+
+40
+00:03:14,820 --> 00:03:18,260
+magnetic field through the circuit increases، كفزة
+
+41
+00:03:18,260 --> 00:03:22,160
+يبقى لك أنزلّه وصلّه قيمة كان سي فرصة العشرة، كان سي
+
+42
+00:03:22,160 --> 00:03:26,300
+فرصة المئة، كل زيادة، ده اللي اشتغل فاراداي، هادها، و
+
+43
+00:03:26,300 --> 00:03:31,620
+سكّرت، ولينز قال: التغير بالزيادة، يعني في معاكسة،
+
+44
+00:03:31,620 --> 00:03:39,420
+الآن بالمرة، بدل معاكسة بالمجال، بدي أقول معاكسة في
+
+45
+00:03:39,420 --> 00:03:42,500
+التيار، كان في عندك تيار البطارية، والمُلف حسب فاراداي
+
+46
+00:03:42,500 --> 00:03:47,640
+بده يطلع لك induced emf، يعني بده يطلع لك induced
+
+47
+00:03:47,640 --> 00:03:51,180
+current، ولا لا؟ حسب، لازم بده يكونوا عكس بعض، ولا لا؟
+
+48
+00:03:51,180 --> 00:03:54,060
+حاجة مع عكس بعض، لو سألتكم عن التيار الكل، مجموع ولا
+
+49
+00:03:54,060 --> 00:03:58,800
+طرح؟ Bravo، في الأقل ذكيين، متساويين، قال لي بس هذا
+
+50
+00:03:58,800 --> 00:04:03,940
+غالباً هذا إيش بيسمّوه؟ عمره، مدة عمره قصيرة، فقط عند
+
+51
+00:04:03,940 --> 00:04:12,160
+التغيير، عندي الإغلاق، وبعد كده بموت، برجع التيار
+
+52
+00:04:12,160 --> 00:04:16,440
+تبع مين؟ تبع البطارية، بس قبل ما يموت،  بيصير
+
+53
+00:04:16,440 --> 00:04:21,760
+التيار في اتجاه عكسه، من اللي عكسه؟ قال لي ظهرت في
+
+54
+00:04:21,760 --> 00:04:25,920
+فاراداي، صح ولا لأ؟ إذاً إيش بيقول لي؟ The increasing
+
+55
+00:04:25,920 --> 00:04:31,400
+magnetic flux، لأن بيزيد من زيادة I، The increasing
+
+56
+00:04:31,400 --> 00:04:36,980
+magnetic flux induces an emf، طلع لك emf حسب فاراداي
+
+57
+00:04:36,980 --> 00:04:43,160
+تمام، This induced emf by Lenz’s law opposes the
+
+58
+00:04:43,160 --> 00:04:48,640
+change in the magnetic flux، لأنه زيادة، تمام؟ حلو
+
+59
+00:04:48,640 --> 00:04:53,820
+قال لي هيك، صح
+
+60
+00:04:53,820 --> 00:04:54,780
+قال لي هيك، صح
+
+61
+00:04:57,680 --> 00:05:03,200
+هذا التيار مهمّته إعاقة التيار الأول، عشان نعكسه ولا
+
+62
+00:05:03,200 --> 00:05:08,180
+لأ؟ عشان نعكسه. The effect of this induced emf is
+
+63
+00:05:08,180 --> 00:05:12,520
+to retard. Retard يعني يعيق. نفس كلمة hinder. برضه
+
+64
+00:05:12,520 --> 00:05:16,380
+hinder لغوياً معناها يعيق. Retard، تمام. The change
+
+65
+00:05:16,380 --> 00:05:19,780
+of the original current that is retarded is
+
+66
+00:05:19,780 --> 00:05:23,840
+increasing. بيقول له هذا قاعد بده يطلع إيجابي، حد
+
+67
+00:05:23,840 --> 00:05:31,060
+اللي استنى عكسه لفترة زمنية معينة، تم… بيقول لي
+
+68
+00:05:31,060 --> 00:05:35,760
+نفس القضية بصير لما تفتح المفتاح، لأن لما تفتح
+
+69
+00:05:35,760 --> 00:05:39,120
+المفتاح كان فيه تيار وفيه مجال، وبعدين صار صفر، بس
+
+70
+00:05:39,120 --> 00:05:43,180
+اتغير، نقصان ولا زيادة؟ نقصان، إيش شاف؟ جاله
+
+71
+00:05:43,180 --> 00:05:46,600
+اللينز، جاله بس العكس صحيح ولا لا؟ لكن اشتغل في كل
+
+72
+00:05:46,600 --> 00:05:50,000
+أحوال، هذا ولا لا؟ اشتغل، إذا the same phenomena
+
+73
+00:05:50,000 --> 00:05:56,210
+occurred، تحصل when the switch is opened، والدرجة في
+
+74
+00:05:56,210 --> 00:06:01,190
+هذه الحالة بتتغير من قيمة محددة إلى نقصان، نقصان
+
+75
+00:06:01,190 --> 00:06:04,430
+نقصان نقصان نقصان نقصان نقصان نقصان نقصان نقصان
+
+76
+00:06:04,430 --> 00:06:10,230
+نقصان نقصان نقصان نقصان نقصان نقصان نقصان نقصان
+
+77
+00:06:10,230 --> 00:06:12,310
+نقصان نقصان نقصان نقصان نقصان نقصان نقصان نقصان
+
+78
+00:06:12,310 --> 00:06:12,950
+نقصان نقصان نقصان نقصان نقصان نقصان نقصان نقصان
+
+79
+00:06:12,950 --> 00:06:20,130
+نقصان نقصان نقصان نقصان نقصان نقصان نقصان نقصان
+
+80
+00:06:21,120 --> 00:06:27,000
+مظبوط ولا لا؟ إذا بعيق الزيادة وبعيق النقصان، دخلت
+
+81
+00:06:27,000 --> 00:06:30,880
+هذه المعلومة؟ هذه المعلومة حسب فاراداي ولينز، بس هذه
+
+82
+00:06:30,880 --> 00:06:34,500
+بيجب أن أترجمها رياضيات وأقتنع فيها، بدي أشتقّ
+
+83
+00:06:34,500 --> 00:06:39,700
+معادلات رياضية، تؤكّد هذا المفهوم، بعدين واحدة واحدة
+
+84
+00:06:41,080 --> 00:06:46,140
+كانت هذه الظاهرة بيسمّوها الحث الذاتي، وليش كلمة
+
+85
+00:06:46,140 --> 00:06:49,760
+ذاتي؟ قال: لأنّ الدائرة، في عندك، ما فيش غيرها دائرة.
+
+86
+00:06:50,020 --> 00:06:53,960
+وبالتالي كل شيء جاء منها، الشغل ذاتي، إذًا
+
+87
+00:06:53,960 --> 00:06:57,760
+this phenomena is called phenomena، يعني ظاهرة، صح؟
+
+88
+00:06:57,760 --> 00:06:59,980
+أه، عرفنا. this phenomena is called the self
+
+89
+00:06:59,980 --> 00:07:06,160
+induction، الحث الذاتي. ليش؟ since، عشان التغيير في
+
+90
+00:07:06,160 --> 00:07:12,700
+الـ flux من نفس الدائرة
+
+91
+00:07:12,700 --> 00:07:18,460
+تمام، الـ emf induced بسبب هذه الظاهرة، تسمّى emf induced
+
+92
+00:07:18,460 --> 00:07:18,500
+نفسي
+
+93
+00:07:23,190 --> 00:07:26,110
+بيقول لي: طيب لو كان في دائرتين، بيقول لي في هذه
+
+94
+00:07:26,110 --> 00:07:29,530
+الحالة بيسمّوها حث ذاتي؟ بيسمّوها حث متبادل، عندك
+
+95
+00:07:29,530 --> 00:07:33,270
+دائرتين، ما بنعش ناخذها، بس ذكر، بيقول لي the emf
+
+96
+00:07:33,270 --> 00:07:36,890
+induced in a circuit due to the changing of the
+
+97
+00:07:36,890 --> 00:07:40,150
+magnetic flux set up by another circuit، عندك
+
+98
+00:07:40,150 --> 00:07:44,150
+دائرتين، we have the mutual induction phenomena
+
+99
+00:07:44,150 --> 00:07:49,510
+المتبادلة، بس هي كده للذكر، قوانينها كنت في توجيهها
+
+100
+00:07:49,510 --> 00:07:50,250
+موجودة، تمام
+
+101
+00:07:53,340 --> 00:07:59,120
+أه، ما هو فيه متبادل، وبرضه لنا، تمام، بيقول لي الآن
+
+102
+00:07:59,120 --> 00:08:05,060
+أعرفنا أنّ الملف شغلته إعاقة التيار من الوصول إلى
+
+103
+00:08:05,060 --> 00:08:08,600
+قيمته النهائية، إما زيادة أو نقصان، تمام؟ قال لي هذه
+
+104
+00:08:08,600 --> 00:08:12,420
+الشغلات بدي أديها قوانين، ما ينفعش كلّه نظري، مدرّسش تاريخ
+
+105
+00:08:12,420 --> 00:08:16,340
+إحنا، صح ولا لا؟ بدنا رياضيات، إحنا لما نشوف القوانين
+
+106
+00:08:16,340 --> 00:08:21,430
+بنفرق، بنصير نعرف نتعامل معه، ونبدأ نتعامل معه، إذًا to
+
+107
+00:08:21,430 --> 00:08:24,310
+obtain a quantitative description of the self
+
+108
+00:08:24,310 --> 00:08:27,770
+-induction، اللي هو القانون تبعه اللي أخذناه في
+
+109
+00:08:27,770 --> 00:08:31,030
+الشرح اللي جابه، صح ولا لأ؟ طيب، هيجي لو كتبت لكم
+
+110
+00:08:31,030 --> 00:08:37,070
+يا بنات، Φ هذا، إيش هي Φ؟ Magnetic flux، ولا لأ؟
+
+111
+00:08:37,070 --> 00:08:41,960
+بتناسب مع I، ولا لأ؟ أه، ما هي Φ بتساوي إيش؟ طيب، جالي
+
+112
+00:08:41,960 --> 00:08:46,740
+هذه Φ من وين جت؟ اجت من التيارات؟ حلو، يعني بنجيب
+
+113
+00:08:46,740 --> 00:08:50,900
+فيه علاقة، فيها، تحط محلها I، أه، بس بتحط ثابت تجديد، إذا
+
+114
+00:08:50,900 --> 00:08:58,020
+صار عندك emf induced بتساوي ناقص، بدل dΦ يقول dI
+
+115
+00:08:58,020 --> 00:09:06,560
+على dt، وين حط لك ثابت التناسب، سمّوه L،  نموه؟
+
+116
+00:09:06,560 --> 00:09:14,320
+هيك سمّيته؟ تمام، هو ممكن مش نموه، موته بصير موته، تمام؟
+
+117
+00:09:14,320 --> 00:09:19,940
+تغيير التيار، تغيير التيار أحلى رياضياً، تمام؟ جان
+
+118
+00:09:19,940 --> 00:09:25,360
+يشهدوا، قولت له ثابت التناسب، صح؟ دوره، دوره جوا، بيعتمد
+
+119
+00:09:25,360 --> 00:09:31,300
+على طبيعة الملف، إيش يسمّوها؟ قالوا: سمّوها المحاثة
+
+120
+00:09:31,300 --> 00:09:39,300
+سمّوها المحاثة، ذكرناها؟ هذه المحاثة، تمام؟ طب Φ إيش
+
+121
+00:09:39,300 --> 00:09:43,200
+بتساوي؟ قولت له: مش Φ بتساوي Φ؟ لو أجيت Φ، عملت
+
+122
+00:09:43,200 --> 00:09:49,960
+هيك، ناقص N dΦ على dt، مش Φ مع Φ بتروح، تمام؟
+
+123
+00:09:49,960 --> 00:09:59,740
+إذا صارت L بتساوي NΦ على I، تمام؟
+
+124
+00:09:59,740 --> 00:10:03,660
+حركة Φ قانوني الأصلي
+
+125
+00:10:05,940 --> 00:10:09,940
+الرئيسي في هذا الـ chapter، هذا قانون فرعي، إيه كلّه
+
+126
+00:10:09,940 --> 00:10:16,120
+تمام، من اللي زعلت المرة هذيك على هنري، أنتِ مش زعلتِ
+
+127
+00:10:16,120 --> 00:10:19,140
+على هنري؟ قولت له: ما يعني، صمم القانون فاراداي، عشان
+
+128
+00:10:19,140 --> 00:10:21,300
+ما يزعلوش، ما يجرحوش، ما يصمّموش، ما يجرحوش، يقولوا له يا
+
+129
+00:10:21,300 --> 00:10:25,520
+هنري، ما يروح حقه، أعطوه هنري، هذي فرع، إيش شرح هذي الـ
+
+130
+00:10:25,520 --> 00:10:30,860
+Henry، لكن هنري لما نيجي نتطلع، إيش وحدتها؟ Volt
+
+131
+00:10:30,860 --> 00:10:33,800
+second على أمبير، ولا لأ؟ هي أصلاً Volt second
+
+132
+00:10:33,800 --> 00:10:37,860
+على أمبير، بس عشان ما يزعجوش هنري، سمّوها يا هنري، تمام؟
+
+133
+00:10:37,860 --> 00:10:46,660
+إذاً الكميات الفيزيائية، ذاكرين C، وذاكرين R، وهيّئة L
+
+134
+00:10:46,660 --> 00:10:51,700
+هدول كتير بيشبهوا بعض، لو إجينا أنا وياكم نقول C
+
+135
+00:10:51,700 --> 00:10:59,300
+بتساوي Q على ΔV، وR بتساوي V على I، صح؟
+
+136
+00:10:59,300 --> 00:11:06,380
+و L بتساوي، تمام، تم، جل زمان كنا نقول C بتعتمد
+
+137
+00:11:06,380 --> 00:11:11,430
+على Q، بتعتمد على V؟ R بتعتمد على V؟ ولا بتعتمد على I؟
+
+138
+00:11:11,430 --> 00:11:16,110
+هنا قلنا ε₀ A على d، وهذه عبارة عن روح الـ
+
+139
+00:11:16,110 --> 00:11:24,210
+على A، ذكرناها؟ إذن هذه صفات للعنصر الكهربائي، هذه
+
+140
+00:11:24,210 --> 00:11:29,170
+الصفة بتكون بتعتمد على من إيش بتتركّب الـ capacitor؟
+
+141
+00:11:29,170 --> 00:11:34,950
+من إيش بتتركّب المقاومة؟ وهنا نفس العملية، إلا إنّ
+
+142
+00:11:34,950 --> 00:11:41,090
+يطلع عندك حاجة بتتعلق بتركيبة الملف، تمام؟ فصار
+
+143
+00:11:41,090 --> 00:11:45,670
+عندك عناصر الدوائر الكهربائية لحد هذه اللحظة، بطارية
+
+144
+00:11:45,670 --> 00:11:51,750
+في خلاف عليها، وهذه عارفينها، وهذه، وهذه ثانية، كلهم
+
+145
+00:11:51,750 --> 00:11:55,010
+بيشبهوا بعض، فيه كتير تشابه بينهم، هذه عناصر الدائرة
+
+146
+00:11:55,010 --> 00:11:57,930
+الكهربائية، لأن إذا بدي أذكر كيرشوف الثاني إيش
+
+147
+00:11:57,930 --> 00:12:03,430
+بيقول؟ بيقول: فرق الجهود بين جميع عناصر أي لوب مغلقة
+
+148
+00:12:03,430 --> 00:12:07,730
+بساوي صفر، جميع عناصر، هيجي، العناصر تبع إيش هي؟
+
+149
+00:12:07,730 --> 00:12:11,690
+بيقولوا: في مقاومة، بطارية، في مقاومة، في مكثف، وهيّجي
+
+150
+00:12:11,690 --> 00:12:13,330
+الملف، تمّ
+
+151
+00:12:16,290 --> 00:12:19,950
+الكلام اللي اتوه، عكيته، طلعت هذا قانوني، هو القانون
+
+152
+00:12:19,950 --> 00:12:24,170
+الرئيسي في هذا الـ chapter، مش فاراداي، إيه بس بدل ما
+
+153
+00:12:24,170 --> 00:12:28,370
+يقول لي غير Φ، بقول له هنا إيش يبقى يغيّر Φ؟ I
+
+154
+00:12:28,370 --> 00:12:32,730
+فجيبها من الأول، جيبها من الـ I على طول، فخطّيتها، و
+
+155
+00:12:32,730 --> 00:12:38,990
+صار في عندي حاجة بنسمّيها L، The constant L is called
+
+156
+00:12:38,990 --> 00:12:42,730
+the self-inductance، المحاثة الذاتية، ده كلمة ذاتي
+
+157
+00:12:42,730 --> 00:12:47,690
+جيبها للتسهيل، فبسمّوها المحاثة، تمام؟ Or simply the
+
+158
+00:12:47,690 --> 00:12:53,030
+inductance، هيجي inductance، محاثة، Inductor، الملف
+
+159
+00:12:53,030 --> 00:12:58,730
+Inductor هو الاسم العلمي للملف، الاسم اللغوي coil،
+
+160
+00:12:58,730 --> 00:13:03,450
+ملف، Capacitor، لو قلنا إيش معناه على Google،
+
+161
+00:13:03,450 --> 00:13:08,760
+بيقولوا Condenser، مكثّف، مش كوندنسر، كوندنس معناها يكثّف
+
+162
+00:13:08,760 --> 00:13:12,720
+لكن الاسم العلمي Capacitor من capacitance، ونفس
+
+163
+00:13:12,720 --> 00:13:16,860
+العملية، coil ملف لغة، لكن علمياً ده اللي سمّوه
+
+164
+00:13:16,860 --> 00:13:20,900
+Inductor، تمام، ده اللي، طب هو الـ Capacitor مش إله
+
+165
+00:13:20,900 --> 00:13:25,660
+رمز، أخذناه هيك، وهذا هيك، طب هذه اللي جبناها، ده
+
+166
+00:13:25,660 --> 00:13:28,660
+الرمز، اللي بيتـ Capacitor، أشهر أنواع الـ Capacitor
+
+16
+
+223
+00:17:57,660 --> 00:18:02,700
+current is constant تتكمليش؟ غلط لأن لو ال current
+
+224
+00:18:02,700 --> 00:18:08,280
+constant اشتغل الفرض، لا في A ولا في B ولا شيء،
+
+225
+00:18:08,280 --> 00:18:13,840
+ده زي ما حد بيصيروا The current is decreasing، اه
+
+226
+00:18:13,840 --> 00:18:17,780
+اشتغل الفرض، بالنقصان، معناته لازم التيار
+
+227
+00:18:17,780 --> 00:18:22,280
+المستحث يكون زي الأصلي، كيف تخيلتوا المستحث؟ مش
+
+228
+00:18:22,280 --> 00:18:28,480
+أنت كنت تتخيل أنها من B لـ A، إذا معناته نقصان لازم
+
+229
+00:18:28,480 --> 00:18:32,060
+يكون برضه من B إلى A. أنت إيش بتقول لي؟ من A لـ B؟
+
+230
+00:18:32,060 --> 00:18:37,020
+غلط! لو قلت لي من B إلى A، بقول لك صح، زي ما دي غلط!
+
+231
+00:18:37,960 --> 00:18:44,120
+إيش أياد؟ صراحتي؟ تمام! هل جئت، إيش بقول؟ صراحتي
+
+232
+00:18:44,120 --> 00:18:48,360
+لما قلت لي قالوا لي زي ميراتك تخيلناها، هل جئت لو هدي
+
+233
+00:18:48,360 --> 00:18:55,610
+سَكرتيها؟ سَكرتيها؟ تيارها؟ تيارها المستحث كيف بيكون
+
+234
+00:18:55,610 --> 00:18:59,470
+مش من موجة بالسالب؟ إذا في تيار مستحث بيجي من B
+
+235
+00:18:59,470 --> 00:19:04,990
+لإيه؟ من B لإيه؟ هذا المستحث، طب هذا من أين جاء؟
+
+236
+00:19:04,990 --> 00:19:09,270
+أجي من تيار أصلي تغير، تغير، هنا جالي ما تغيرش،
+
+237
+00:19:09,270 --> 00:19:12,690
+قلت لك فيش قصة مرة، أنسى، هنا تغير، decreasing،
+
+238
+00:19:12,690 --> 00:19:16,730
+قلت له لينز، بيقول إذا decreasing، بيكونوا زي بعض،
+
+239
+00:19:16,730 --> 00:19:20,090
+المستحث من B لإيه؟ إذا الأصلي بيكون من B لإيه؟ و
+
+240
+00:19:20,090 --> 00:19:23,970
+تجي لي من إيه؟ لطبيعي غلط صح؟ ليه جاللي تاني؟ جاللي
+
+241
+00:19:23,970 --> 00:19:26,770
+increasing، قلت له صح، تشتغل في الأضداد بس
+
+242
+00:19:26,770 --> 00:19:30,710
+increasing، لازم يكون عكس، طب أنت بتقول لي من B
+
+243
+00:19:30,710 --> 00:19:38,170
+لـ A، إذا لازم يكون من A لـ B. أنت مش بتقول لي غلط، طيب
+
+244
+00:19:38,170 --> 00:19:44,410
+صح ولا لأ؟ تمام؟
+
+245
+00:19:44,410 --> 00:19:49,770
+كله بحكي صيني؟ تمام؟ احكيها ماريا
+
+246
+00:19:55,170 --> 00:19:59,090
+أنت كنت معنا المرة دي قبل الحرب؟ ممكن تلاقيش آخر
+
+247
+00:19:59,090 --> 00:20:07,990
+محاضرة؟ قاعدة لينز سمعت فيها؟ اه، إيش بتقول؟ بسمح
+
+248
+00:20:07,990 --> 00:20:13,930
+فيها، بس طيب ما هو يعني أسوأ، شرحها، ما أنت متحت
+
+249
+00:20:13,930 --> 00:20:19,770
+وجيهها، أنا شرحتها هنا، الناس بيقولوا إذا التيار أو أي
+
+250
+00:20:19,770 --> 00:20:23,750
+حاجة بتتغير إيجابا، موجبا، بيكون فيه معاكسة يا
+
+251
+00:20:23,750 --> 00:20:29,170
+مريم، معاكسة، وإذا نقصان، بتروح المعاكسة، فهمت
+
+252
+00:20:29,170 --> 00:20:32,210
+عليها كيف؟ هاي قاعدة لينز اللي قاعدة بشرحها
+
+253
+00:20:32,210 --> 00:20:37,570
+فبالتالي لما يقول لي decreasing بقول له ما فيش معاكسة
+
+254
+00:20:37,570 --> 00:20:40,990
+إيش يعني معاكسة بين مين ومين هنا الآن؟ بين التيار
+
+255
+00:20:40,990 --> 00:20:45,030
+الأصلي والتيار المستحث في هذا الـ chapter، التياري
+
+256
+00:20:45,030 --> 00:20:49,070
+العصلي أنت اللي بتحكي عنه، المستحث من B لـ A وأنت
+
+257
+00:20:49,070 --> 00:20:52,610
+هنا بتقول لي من B to A، إذا ما فيش معاكس، غلط هنا
+
+258
+00:20:52,610 --> 00:20:55,810
+increasing يا مريم، increasing يعني لازم يكون فيه
+
+259
+00:20:55,810 --> 00:21:00,530
+معاكسة، معاكسة من B لـ A، إذا اللي من A لـ B أنت جاي لي
+
+260
+00:21:00,530 --> 00:21:04,030
+من B to A غلط، إذا هذا هو الصح، تمام
+
+261
+00:21:06,520 --> 00:21:09,960
+هذا سؤال سهل، وإحنا… هجاتي أفهمنا، لما أقول سهل
+
+262
+00:21:09,960 --> 00:21:16,320
+معناته؟ هذا إيه؟ كما… هذا بقول لي أريد أثبت لك أن
+
+263
+00:21:16,320 --> 00:21:21,160
+الـ L لا تعتمد إلا على التركيبة تبع الملف، إيش أشهر
+
+264
+00:21:21,160 --> 00:21:26,560
+الملف؟ قال لي solenoid، صح؟ قال لي find the
+
+265
+00:21:26,560 --> 00:21:29,740
+inductance، هذا ما solenoid، يعني الملف، الـ و الـ
+
+266
+00:21:29,740 --> 00:21:34,550
+ولا ما له الـ؟ الـ و الـ، حسب لي إياها of an ideal
+
+267
+00:21:34,550 --> 00:21:40,870
+solenoid، مريم، أخذنا solenoid، كلمة ideal بتلمع في
+
+268
+00:21:40,870 --> 00:21:48,250
+مخي حاجة، بي، برا سفر، وجوا ميو نوت إن في الـ I، إذا
+
+269
+00:21:48,250 --> 00:21:57,790
+for an ideal solenoid
+
+270
+00:21:57,790 --> 00:22:04,470
+بي، بيساوي، سفر، N، بي بتساوي ميو نوت N في الـ I، صح
+
+271
+00:22:04,470 --> 00:22:09,290
+ولا لأ؟ تمام، لو بدي أرسم الساينوسويد، أنا مش هو هيك
+
+272
+00:22:09,290 --> 00:22:13,590
+كيف
+
+273
+00:22:13,590 --> 00:22:19,310
+بي، بقوله بي، بس يوه، هاي بي، طب بدي reflex، الـ reflex
+
+274
+00:22:19,310 --> 00:22:22,690
+بس بيكون في المساحة الجوانية، طب المساحة الجوانية
+
+275
+00:22:22,690 --> 00:22:26,650
+لو أخد مساحة أنا هيك، مش الـ area برضه بتكون هيك، إذا
+
+276
+00:22:26,650 --> 00:22:30,890
+إزاي أوجدها بينهم؟ سفر كوساين السفر، طيب أنت إيش بدك؟
+
+277
+00:22:30,890 --> 00:22:37,410
+قلت له بدي L، شايفينها L؟ بدي  Φ، جئت جوا بيه
+
+278
+00:22:37,410 --> 00:22:41,010
+uniform ولا مش uniform؟ بدل B . دي إيه؟ جوا
+
+279
+00:22:41,010 --> 00:22:45,650
+التكامل بتطلع، حبر التكامل، وتكامل الـ دي إيه؟ A، إذا
+
+280
+00:22:45,650 --> 00:22:51,920
+صارت Φ بتساوي B في إيه؟ طب و B إيش بتساوي؟ ميو
+
+281
+00:22:51,920 --> 00:23:02,120
+نوت، ميو نوت، ميو نوت، ميو نوت، ميو
+
+282
+00:23:02,120 --> 00:23:15,580
+نوت، ميو نوت، ميو نوت، ميو نوت، ميو
+
+283
+00:23:15,580 --> 00:23:26,040
+نوت، ميو نوت، القنوات الوسطى اللي جوا فراغ، صح، إن عدد
+
+284
+00:23:26,040 --> 00:23:33,240
+اللفات من جنس الملف ولا لأ، إيه عرض الملف، الطول
+
+285
+00:23:33,240 --> 00:23:36,660
+الملف عشان أخطوه في توجيهي، من جول عنه هذا مش مهم
+
+286
+00:23:36,660 --> 00:23:43,700
+عشان كده من جول عنه مش مهم، تمه سهل، لأنه تمه، عشان
+
+287
+00:23:43,700 --> 00:23:45,320
+كده اتعرفوا كده توجيهي، سهل يعني
+
+288
+00:23:49,010 --> 00:23:54,290
+مش إيه؟ إيش هو؟ جئت في، بيساوي بيه في إيه؟ مش بيه
+
+289
+00:23:54,290 --> 00:23:59,150
+تبع الـ solenoid هيها، ميو نوت إن في إيه، إن هذه
+
+290
+00:23:59,150 --> 00:24:05,930
+عدد الليفات للطول والـ A، تمام، جئت الـ بيساوي
+
+291
+00:24:05,930 --> 00:24:11,150
+إن في Φ على إيه، صح؟ مش إنها تتوج منها إن هو عمل
+
+292
+00:24:11,150 --> 00:24:19,670
+مستحث، اه أنا عارفة، من جالي، اه أنا غلطانة، أنا خربطتك
+
+293
+00:24:19,670 --> 00:24:25,730
+طب إيش نسوي؟ الرموز بتتكرر، الـ الطول غير عن الـ تبع
+
+294
+00:24:25,730 --> 00:24:36,150
+المحاثة هناك، الطول تمام؟ اه، المهم حلّيناها وحطّينا
+
+295
+00:24:36,150 --> 00:24:41,820
+اسمه الـ عشان ما نخرّبط الكلام، إذن معناته L of the
+
+296
+00:24:41,820 --> 00:24:46,380
+solenoid depends on its geometric features، يعني
+
+297
+00:24:46,380 --> 00:24:53,000
+خصائصه الهندسية، طوله، عرضه، عدد لفاتِه، الوسط اللي
+
+298
+00:24:53,000 --> 00:24:56,800
+جواه فراغ، طبعا تعرفوا إنه لما أغيّر الفراغ بيتغير
+
+299
+00:24:56,800 --> 00:25:01,180
+بيصير بدل ميو نوت، ميو، وبيتغيّر زيّك، إذا كان إبسلون
+
+300
+00:25:01,180 --> 00:25:06,980
+نوت وإبسلون، المهم، جالي هذا المثال، أنا اعتقدت إنه جاي
+
+301
+00:25:06,980 --> 00:25:10,980
+في section مش مكانه، فجبته لمكانه، هذا محطوط في
+
+302
+00:25:10,980 --> 00:25:17,260
+section أربعة، شايفين؟ مثال أربعة، وهذا يوم أنا حاطه
+
+303
+00:25:17,260 --> 00:25:21,280
+هنا لإنه طلع جاي في مكان غلط، فجبناه في
+
+304
+00:25:21,280 --> 00:25:25,060
+مكانه، لإنه طلع ما بده هو بده، علم ما هنا بالمرة، نجيب
+
+305
+00:25:25,060 --> 00:25:30,020
+علم، قال لي هذا ملف، بس كيف؟ قال لي هذا عبارة عن كابل
+
+306
+00:25:30,020 --> 00:25:34,160
+ذاكرين السلك اللي جاي من الـ dish وخشّ على الصيفر
+
+307
+00:25:34,160 --> 00:25:38,720
+هذلك، بس ترجع تتمر هنا ملف، قال لي إيش هو؟ قال لي
+
+308
+00:25:38,720 --> 00:25:41,820
+a long coaxial cable of a thin cylindrical conducting
+
+309
+00:25:41,820 --> 00:25:46,260
+shell، conducting shell، هذا، هذا الشكل عبارة
+
+310
+00:25:46,260 --> 00:25:50,180
+عن سيلندر ولا لأ؟ تمام، نسقطه بيه، حلو، إيش جوا فيه
+
+311
+00:25:50,180 --> 00:25:54,800
+المركز، جالي فيه silicon، فيه، ياء، نسقطه إيه، تمام
+
+312
+00:25:54,800 --> 00:25:59,420
+طبعا إيش كتب فوق؟ long، long، بقدر أستخدم قانون أمبير
+
+313
+00:25:59,420 --> 00:26:06,340
+عشان كده جالي long، عشان هو أسهل من صفّار، صح؟ اه، عشان
+
+314
+00:26:06,340 --> 00:26:11,580
+بدك بيه، طب ليش بدك بيه؟ عشان بدي Φ، صح؟ لأن هو إيش
+
+315
+00:26:11,580 --> 00:26:16,300
+بده، بده الـ Φ، طب الـ Φ بدها بيه، فيه، بدي
+
+316
+00:26:16,300 --> 00:26:21,380
+ميه؟ طيب، طلعش كتب لي the conductors carry the same
+
+317
+00:26:21,380 --> 00:26:24,580
+current I in opposite directions، شايفين التيارات
+
+318
+00:26:24,580 --> 00:26:29,480
+واحد فوق، واحد تحت، عكس بعض، هذا معتاد سؤال، أمبير إيش
+
+319
+00:26:29,480 --> 00:26:32,080
+بده؟ قال لي calculate the inductance L of the
+
+320
+00:26:32,080 --> 00:26:37,420
+length l of the length L، لـ L، هذه l small، l of this
+
+321
+00:26:37,420 --> 00:26:40,880
+cable، قال لي هذا طويل جدا، بس أنا بدي l لجزء منها
+
+322
+00:26:40,880 --> 00:26:45,820
+طوله small l، حلو، هل جئت يا بنات؟ بدي المجال
+
+323
+00:26:45,820 --> 00:26:50,940
+المغناطيسي هنا… خذوا Amperian Loop وتشوفوا لي I
+
+324
+00:26:50,940 --> 00:26:57,020
+enclosed، جدّيش لي إيش؟ احكيها، لأن فيه تيارين، واحد
+
+325
+00:26:57,020 --> 00:27:01,700
+عكس الثاني، إذا معناته هنا التيار صفر، ولو هذا من
+
+326
+00:27:01,700 --> 00:27:05,820
+جوا فاضي، وهذا cable، معناته برضه جوا ما فيش مجال، صح
+
+327
+00:27:05,820 --> 00:27:08,900
+ولا لأ؟ وفي مجال؟ كنت اللي هنا بين هادي وبين هادي
+
+328
+00:27:08,900 --> 00:27:12,220
+طب خذ أمبير اللي هو بالخضرة، شايفينها؟ إيه، شو
+
+329
+00:27:12,220 --> 00:27:15,860
+التيار اللي بيخترقها، اثنين ولا واحد؟ ولا عليكم
+
+330
+00:27:15,860 --> 00:27:21,980
+قلنا أمبير يا ورد، دي محاضرة أمبير، بيقول، الله مش بدي
+
+331
+00:27:21,980 --> 00:27:26,760
+أكتب لكم كتير، مش قادر أكتب هناك، اتحملوني، تمام، أنا
+
+332
+00:27:26,760 --> 00:27:31,720
+في مغاوظ عند الشباب، بكتب كتير، عشان لو، بأخذ راحتي
+
+333
+00:27:31,720 --> 00:27:36,440
+بهمّش، first we want to find the magnetic field، طبعا
+
+334
+00:27:36,440 --> 00:27:41,620
+بدك تجيب لي flux، بدك الـ magnetic field using
+
+335
+00:27:41,620 --> 00:27:46,630
+Ampere's law، ليش؟ لأنه أنت جاي اللي long، لو قال ليّش
+
+336
+00:27:46,630 --> 00:27:50,510
+long، بنفعك، ما بنفعش، أنت جاي اللي long، ساعتها بيه
+
+337
+00:27:50,510 --> 00:27:55,150
+صفّار، دي وردة، مصعبها شغلة، بدنا نشتغل فيها، قال ها قانون
+
+338
+00:27:55,150 --> 00:28:00,110
+أمبير، ها دي ثابتة، دوّت، بردك بتروح، تكلموا لي الـ d
+
+339
+00:28:00,110 --> 00:28:03,950
+اللي بالخضرة، 2πR ولا لأ؟ وقلتوا لي التيار I
+
+340
+00:28:03,950 --> 00:28:08,050
+enclosed هو I، خلصنا، هذا المجال اللي جوا يا روان،
+
+341
+00:28:08,640 --> 00:28:12,340
+اللي جواها بين السلكين، حلو، جالي هذا كيف اتجاهه؟
+
+342
+00:28:12,340 --> 00:28:16,300
+قلت له هو عوض من الضوّير، بيخترق مساحات هيك عاملة
+
+343
+00:28:16,300 --> 00:28:20,000
+تمام، أنا جئت بدي الـ flux على أحد من مساحاتها دي
+
+344
+00:28:20,000 --> 00:28:22,800
+قال لي خذ واحدة، قلت له هي هذه، شايفينها الدهبية؟
+
+345
+00:28:22,800 --> 00:28:26,580
+مسميها، شايفين هذه المسافة الدهبية؟ طب دي بتعتمد على
+
+346
+00:28:26,580 --> 00:28:31,990
+القُطر ولا لأ؟ يعني بيه هنا زي هنا زي هنا، إذا معناته
+
+347
+00:28:31,990 --> 00:28:36,690
+B بتقدر تطلع لي بيه برا التكامل؟ لأ، لأن بيه
+
+348
+00:28:36,690 --> 00:28:41,490
+يعتمد على r، معناته بدك دي إيه؟ صح، بدك دي إيه؟ يعني
+
+349
+00:28:41,490 --> 00:28:47,360
+جزء من الـ area، قال لي شايف هذه الغامقة؟ شايفينها؟
+
+350
+00:28:47,360 --> 00:28:51,180
+بدي أخذها، قلت له إيش مساحتها؟ قلت له عرضها اللي
+
+351
+00:28:51,180 --> 00:28:56,080
+هو سمكها dr، طولها اللي هو l، تمام؟ قال لي دي dΦ،
+
+352
+00:28:56,080 --> 00:28:58,760
+قلت له يلا، dΦ، not that the
+
+353
+00:28:58,760 --> 00:29:02,220
+magnetic field is zero for r أكبر من b، قلت لكم
+
+354
+00:29:02,220 --> 00:29:05,660
+ماي، قلتوا لي لأ، ليش؟ لأ، قلتوا لي، إنه عكس بعض
+
+355
+00:29:05,660 --> 00:29:10,350
+التيارات، هذا خلصنا؟ يقول إن هذا المجلد، المجلد يجعل
+
+356
+00:29:10,350 --> 00:29:12,570
+مجلد مجلد مجلد مجلد مجلد مجلد مجلد مجلد مجلد مجلد
+
+357
+00:29:12,570 --> 00:29:13,330
+مجلد مجلد مجلد مجلد مجلد مجلد مجلد مجلد مجلد مجلد
+
+358
+00:29:13,330 --> 00:29:16,670
+مجلد مجلد مجلد مجلد مجلد مجلد مجلد مجلد مجلد مجلد
+
+359
+00:29:16,670 --> 00:29:16,950
+مجلد مجلد مجلد مجلد مجلد مجلد مجلد مجلد مجلد مجلد
+
+360
+00:29:16,950 --> 00:29:36,410
+مجلد مجلد م
+
+361
+00:29:36,870 --> 00:29:42,550
+هذه هي، هذه، قال لي هذه مستطيل، مساحته طوله بعرضه، طوله
+
+362
+00:29:42,550 --> 00:29:48,910
+l وعرضه dr، قال لي هذه هي l dr، تمام، عشان بدك تكامل، و
+
+363
+00:29:48,910 --> 00:29:55,990
+قلت له بدك تكامل من هنا لهنا صح؟ إذا من A لـ B كملت
+
+364
+00:29:55,990 --> 00:29:59,330
+إحنا
+
+365
+00:29:59,330 --> 00:30:04,030
+خلصنا منه عشان نجيب B، طيب وكيف… مش فاهم أنا كيف
+
+366
+00:30:04,030 --> 00:30:08,450
+قشة هذه اللي قلتها، اه، جئت دي تجيبها، وخلصتي، أخلف
+
+367
+00:30:08,450 --> 00:30:11,330
+عليك يا أمبير، الله يسّهّل عليك، نعم، خلصنا من الأمبير
+
+368
+00:30:11,330 --> 00:30:16,800
+بدي أجيب الـ flux، الـ flux إيش بيساوي؟ B في d A
+
+369
+00:30:16,800 --> 00:30:20,100
+B في d A؟ خلص من… من الأمبير أعطاني B، روح
+
+370
+00:30:20,100 --> 00:30:25,660
+جئت بدي flux، بقول له بدي مساحة، هذه المساحة دي
+
+371
+00:30:25,660 --> 00:30:31,040
+الذهبية كلها واللي جوا غامقة، ده اللي ما ينفعش تقول
+
+372
+00:30:31,040 --> 00:30:34,640
+الـ flux بيساوي B في A، لأن B مش ثابت خلال
+
+373
+00:30:34,640 --> 00:30:39,850
+المساحة، لأنه يعتمد على r، لأنه يعتمد على r صح؟
+
+374
+00:30:39,850 --> 00:30:44,170
+وبالتالي أخذت جزء منها، جزء منها اللي هو الغامق هذا
+
+375
+00:30:44,170 --> 00:30:50,690
+اللي هو هذا، شايفينها؟ هذا جزء من الدهبي، هذا الغامق
+
+376
+00:30:50,690 --> 00:30:56,430
+جزء من مساحة، عشان دي إيه؟ إذا الـ integration خلصنا منه
+
+377
+00:30:56,430 --> 00:31:04,990
+هجيب، نتعامل كذا بـ flux، آخر مثال في الشابتر الثامن
+
+378
+00:31:05,990 --> 00:31:11,610
+كامل، جبنا فيه flux، ذاكرين أخذنا نفس الفكرة، أيوة
+
+379
+00:31:11,610 --> 00:31:16,130
+برافو عليكي، صحيح، وقلنا ليش أخذنا طولي، اه، أو هنا
+
+380
+00:31:16,130 --> 00:31:19,990
+عشان كده أخذنا طولي، ما أخذناهوش هيك، وما أخذناهوش مربع
+
+381
+00:31:19,990 --> 00:31:26,030
+صغير، برافو عليكي، تمام، طلعنا، وطلعنا، طلع النتيجة، ميو
+
+382
+00:31:26,030 --> 00:31:32,820
+نوت الوسط، l، الطول، b و a أنصاف الأقطار، إذا بيعتمد
+
+383
+00:31:32,820 --> 00:31:40,100
+على التركيبة الداخلية تبع الملف، تمام، حلو، نعيد
+
+384
+00:31:40,100 --> 00:
+
+445
+00:36:59,320 --> 00:37:06,080
+لـ 80 هجيتها  DX X0 لـ X إيش X not بالساوي؟ جديش ..
+
+446
+00:37:06,080 --> 00:37:08,420
+لأن وراها X شايفيها؟ عن T بالساوي شايفيها؟ إيش
+
+447
+00:37:08,420 --> 00:37:12,700
+قولتي اللي تطيّكها؟ إذا X not بالساوي Y ولا لأ؟
+
+448
+00:37:12,700 --> 00:37:16,360
+إذا X not Y .. هذي دلوقتي هذي بالساوي Y بنرجع لها
+
+449
+00:37:16,360 --> 00:37:22,100
+يلا يا بنا Calculus تكامل DX على X من X not لـ X يا
+
+450
+00:37:22,100 --> 00:37:28,880
+ماريا لأن X على X not إذا من هالـ بقول لن X على X
+
+451
+00:37:28,880 --> 00:37:37,220
+not بالساوي ناقص R على L في T بدي X إيش هسوي؟ آخدي
+
+452
+00:37:37,220 --> 00:37:43,440
+الـ exponential صح؟ صارت X بتساوي X node + 1
+
+453
+00:37:43,440 --> 00:37:49,560
+ناقص R على L في T ولا لأ؟ خلصت الرياضية طلعت لك
+
+454
+00:37:49,560 --> 00:37:54,640
+اللي بدك إياه ارجع عوض لمحل X الـ C احكي مين بيقول
+
+455
+00:37:54,640 --> 00:37:59,920
+إيش؟ في عنده حد طريقة أسرع؟
+
+456
+00:38:10,800 --> 00:38:17,320
+طب أنا معجب في السؤال عشان كده نمشي من هنا let X
+
+457
+00:38:17,320 --> 00:38:20,880
+بيساوي Y نقص أيفل آه والله في الساعة دي إذا أخدنا
+
+458
+00:38:20,880 --> 00:38:26,740
+let صح؟ واحدة .. هذي تمام أخدناها فضل تحظي
+
+459
+00:38:26,740 --> 00:38:33,080
+المعادلة الـ J أخدناه يعني الـ J مافيش اسم الـ J
+
+460
+00:38:33,080 --> 00:38:43,060
+عوضنا هدّق X و DI بيساوي DX على A مش هي DI إيش
+
+461
+00:38:43,060 --> 00:38:48,760
+بتساوي مش DX على R بالثالث؟ حطيتها اضرب و جسمت
+
+462
+00:38:48,760 --> 00:38:54,100
+بقعدتها في رابع جديدة و خلاص و جمت من طرف ده طرف
+
+463
+00:38:54,100 --> 00:38:59,840
+حطت ثالث جديد طب والتكامل؟ واحنا بناخده K plus B
+
+464
+00:38:59,840 --> 00:39:05,660
+مش خدناه عشان نكامل؟ خلاص هذا هو اللي صح و ما نيش
+
+465
+00:39:05,660 --> 00:39:12,380
+جديد والله بتعرفي تعمليه بس أنت ارتعبتي من الخطوات
+
+466
+00:39:12,380 --> 00:39:19,800
+السريعة خفتي لأ بس
+
+467
+00:39:19,800 --> 00:39:23,120
+مينفعش تقولي إنّي بقى مافيش أعمله آه مينفعش تقولي
+
+468
+00:39:23,120 --> 00:39:28,440
+بقى احنا قلنا أنا ما بعلمش عشان نمتحن أنا ما بعلم
+
+469
+00:39:28,440 --> 00:39:32,760
+عشان نمتحن هذا عشان كده أنا عجبت في سؤالك هذا
+
+470
+00:39:32,760 --> 00:39:38,070
+خطوات لازم تعرفيها كيف إجت لازم تقولوا إيمت بتكون
+
+471
+00:39:38,070 --> 00:39:41,130
+ده عيال اللي وجدت في الامتحان لأنّ هذه شغلها سهلة
+
+472
+00:39:41,130 --> 00:39:49,510
+سهلة تمام طيب نرجع حاجة خلصت رياضية ده الـ X مش أنت
+
+473
+00:39:49,510 --> 00:39:55,590
+فرضتها ارجع اكتبها حاجة بدل هذه بدي أقول X Y ناقص
+
+474
+00:39:55,590 --> 00:40:03,170
+I في R بتساوي إيش X not؟ Y بتساوي Y إيه تمير ناقص
+
+475
+00:40:03,170 --> 00:40:12,280
+R على N في T طب يلا بدي I عام المشترك إذا I بتساوي
+
+476
+00:40:12,280 --> 00:40:16,960
+.. جيبلي هدّان طلع عليها هتجيبلي هدّان أفريقيا دي
+
+477
+00:40:16,960 --> 00:40:22,260
+تمام؟ بالسر Y العام المشترك واحد ناقص E تبقى واحد
+
+478
+00:40:22,260 --> 00:40:30,580
+ناقص R على الـ T على R أيوة؟ لأ كنتوا تابعين معايا
+
+479
+00:40:30,580 --> 00:40:40,830
+طب بدي حد يرسم لي بدي ارجع لك Calculus one بيسمّي
+
+480
+00:40:40,830 --> 00:40:49,310
+واحد ناقص E to power ناقص X سمّيه؟ كيف بتوصل إنّ أنت
+
+481
+00:40:49,310 --> 00:40:56,210
+بتاخدي معادلة، صح؟ بقول خلي X صفر E to power صفر
+
+482
+00:40:56,210 --> 00:41:03,350
+واحد ناقص واحد، إذا هذه هي رسمتها، صفر،
+
+483
+00:41:03,350 --> 00:41:04,670
+العكس
+
+484
+00:41:07,970 --> 00:41:13,350
+طب آسفة الطيار؟ زاد مرة واحدة؟ ولا خدم شوية واجد؟
+
+485
+00:41:13,350 --> 00:41:17,490
+مين عوجها عشان يوصل مرة واحدة؟ الملف، الطيار
+
+486
+00:41:17,490 --> 00:41:23,570
+المستحاف، الملف، إذًا هذه الرسمة زبطت، تمام؟ طيب،
+
+487
+00:41:23,570 --> 00:41:27,150
+واحدة واحدة لسه، هه؟ هذا الكلام اللي عملنا،
+
+488
+00:41:27,150 --> 00:41:34,100
+شايفاني مش عاجبك؟ أنا بدمش عنه، تمام؟ وصلت لهذه I
+
+489
+00:41:34,100 --> 00:41:39,260
+maximum هو Y على R طيب أنا وصلت لهنا صح هدى إيش
+
+490
+00:41:39,260 --> 00:41:46,480
+وحدتها هدى إيش وحدتها أمبير أمبير معناته ممنوع
+
+491
+00:41:46,480 --> 00:41:50,260
+الجثة ده كله وحدات لأنه أمبير بيساوي أمبير خلصنا
+
+492
+00:41:50,260 --> 00:41:55,000
+جالي كيف وهدى سكنت جالي معناته هدى على هدى لازم
+
+493
+00:41:55,000 --> 00:42:00,500
+يكون واحد على سكنت صح يلا نجانب IR على L إيش وحدة
+
+494
+00:42:00,500 --> 00:42:08,950
+R يا بنات وهدى طب واخدناها صاحبنا هنري تمام يلا
+
+495
+00:42:08,950 --> 00:42:14,790
+يا آيات هذه عبارة عن volt على ambeer هذه هذه
+
+496
+00:42:14,790 --> 00:42:19,430
+تقول لي me volt second على ambeer والله وحدتها
+
+497
+00:42:19,430 --> 00:42:26,130
+second وحدتها second صح طيب أنت قولتي لي المرة دي RC
+
+498
+00:42:26,130 --> 00:42:32,650
+ذاكرينها كانت second وسميتها tau الـ T على Tau صح؟
+
+499
+00:42:32,650 --> 00:42:37,970
+هذه لو بتقول واحد على تاو معناته L على R صح؟ لو
+
+500
+00:42:37,970 --> 00:42:43,170
+بدك تحط هذه هيك تحط تاو تصير تاو بتساوي L على R
+
+501
+00:42:43,170 --> 00:42:46,630
+بعد الـ R على L صح ولا لأ؟ فماشي تسميها هذه؟ فماشي
+
+502
+00:42:46,630 --> 00:42:48,750
+تسميها؟ الـ Time Constant ولا مش الـ Time
+
+503
+00:42:48,750 --> 00:42:52,190
+Constant؟ وهذه الـ Time Constant فكيب يدفنك بينهم
+
+504
+00:42:52,190 --> 00:42:54,970
+وقال هذه الـ Time Constant للـ RC Circuit هذه الـ
+
+505
+00:42:54,970 --> 00:42:59,150
+Time Constant للـ RL Circuit تمام يا بنات؟ حلو
+
+506
+00:42:59,150 --> 00:43:00,390
+خلصنا
+
+507
+00:43:03,580 --> 00:43:09,240
+قال لي اه نجي لعند هذه الدائرة و نشوفها قال لي اه
+
+508
+00:43:09,240 --> 00:43:12,640
+maximum طلقة Y على R صح ولا لأ هيها Y على R
+
+509
+00:43:12,640 --> 00:43:16,460
+شايفينها؟ تطلعوا يا بنا تشوفوا لي الدائرة انسوا
+
+510
+00:43:16,460 --> 00:43:22,930
+الملف اعتبروه short عادي من يجيب للتيار؟ Epsilon على
+
+511
+00:43:22,930 --> 00:43:30,150
+R إذا معناته اي maximum بيكون قيمة التيار لما
+
+512
+00:43:30,150 --> 00:43:33,190
+الملف يكون short عادي ولا لأ وهذا لم يكن يحصل
+
+513
+00:43:33,190 --> 00:43:38,950
+عليه بعد زمن طويل طب لما تيبك سوى صفر في هذه
+
+514
+00:43:38,950 --> 00:43:43,870
+العلاقة إيه تبقى ور صفر واحد واحد نقص واحد صفر زي
+
+515
+00:43:43,870 --> 00:43:47,490
+التيار zero وماكتشت تيار في دائرة بيكون zero لما
+
+516
+00:43:47,490 --> 00:43:52,150
+تكون الـ circuit مفتوحة إذا معناته الملف عكس المكثف
+
+517
+00:43:52,670 --> 00:43:57,690
+نذكر حالنا في المكثف أنت بتساوي الصفر بيكون short
+
+518
+00:43:57,690 --> 00:44:02,670
+circuit وأنتي goes to ملا نهاية open circuit اعكس
+
+519
+00:44:02,670 --> 00:44:07,490
+أنت بتساوي الصفر الملف open circuit وأنت بتساوي
+
+520
+00:44:07,490 --> 00:44:14,450
+ملا نهاية الملف short عشان تسهل عليكم الملف طبيعته
+
+521
+00:44:14,450 --> 00:44:20,720
+من إيش مصنوع؟ short صح بيشتغل بس عند الإغلاق ولا لأ
+
+522
+00:44:20,720 --> 00:44:25,440
+بعد ما نغلق بعد مدة طويلة برجع لطبيعته short إذا
+
+523
+00:44:25,440 --> 00:44:29,900
+بيصير short بعد مدة طويلة دخلت إذا هو بيشتغلش اللي
+
+524
+00:44:29,900 --> 00:44:32,660
+عند الإغلاق بعد ما يغلق واثنين عليه اتنين
+
+525
+00:44:32,660 --> 00:44:38,020
+ثلاثة خلاص بيشتغل برجع لطبيعته short عادي تمام يا
+
+526
+00:44:38,020 --> 00:44:44,980
+بنات حلو قال لي طيب إيش سوى target في المفتاح؟ طلع
+
+527
+00:44:44,980 --> 00:44:49,940
+سويت فيه، سوى وين المفتاح راح؟ إيش صار فيه بطارية؟
+
+528
+00:44:49,940 --> 00:44:54,160
+الأصل ده الطيار؟ لأ، بس أنت إيش بتقوله؟ بتقول
+
+529
+00:44:54,160 --> 00:44:57,960
+الملف يرتبط بالطيار بروح السفر مرة واحدة، في حد
+
+530
+00:44:57,960 --> 00:45:02,320
+بعوجه، كيف يعني؟ هيوصل هنا، شايفين وصل هنا؟ ده
+
+531
+00:45:02,320 --> 00:45:05,940
+اللي أنت دي بكتب فيه، الأصل هنا نزل، لكن الملف
+
+532
+00:45:05,940 --> 00:45:10,920
+خليه ينزل هيك، شوف كيف، بالبطء، قال لي طب شوف لي
+
+533
+00:45:10,920 --> 00:45:15,400
+في الرياضيات إيش بيصير؟ انتبهوا .. قولوا اللي هي المرة
+
+534
+00:45:15,400 --> 00:45:21,100
+عايزه .. هاه .. if the battery is suddenly removed
+
+535
+00:45:21,100 --> 00:45:24,740
+.. جمت البطارية .. by throwing the switch to point
+
+536
+00:45:24,740 --> 00:45:28,100
+2 in the circuit and applying Kirchhoff rule ..
+
+537
+00:45:28,100 --> 00:45:33,540
+هجيت كيرشوف هذه اللوة بقى كم عنصر فيها؟ هدى .. نهر
+
+538
+00:45:33,540 --> 00:45:36,280
+.. رحت البطارية .. بالتالي بيصير بس هيك
+
+539
+00:45:39,370 --> 00:45:43,910
+خوصت الفيزياء نشوف هنجيبش لا X ولا حاجة بدناشي
+
+540
+00:45:43,910 --> 00:45:50,330
+جميلة X جالي يلا ارجع لصف رابع ابتدائي جسم على I
+
+541
+00:45:50,330 --> 00:45:56,590
+جسمتي على I واضرب في DT ضربنا في DT وجسم على L
+
+542
+00:45:56,590 --> 00:46:01,830
+وخط واحدة عند واحدة طلعت هيك والله هذا تبع صف رابع
+
+543
+00:46:03,020 --> 00:46:07,220
+صح؟ هيجيت نقطتين لتوجيهي، بدنا نكامل عشان، وصف رابع
+
+544
+00:46:07,220 --> 00:46:11,360
+حرام، همم، ما عملوا نص، ده كمان، همم؟ هالـ gate لحد
+
+545
+00:46:11,360 --> 00:46:15,300
+الآن صف رابع وخامس وسادس، كامل الطرفين المعادلة،
+
+546
+00:46:15,300 --> 00:46:20,480
+كامل؟ قال لي الطيار كان في I maximum، كان في تيار،
+
+547
+00:46:20,480 --> 00:46:24,080
+لعند أي I، رجعنا وشغلنا الساعة من أول جديد، لعند
+
+548
+00:46:24,080 --> 00:46:28,760
+أي زمان، إيش أكمل دي I على I؟ لين، إيه؟ إيش تغيب؟
+
+549
+00:46:28,760 --> 00:46:37,460
+طلعت هيك عليها خط تيمة لأنها والله راجع سفر طلعك
+
+550
+00:46:37,460 --> 00:46:42,320
+هي رسمتها هذه المعادلة هي رسمتها آه طبعًا في اللي
+
+551
+00:46:42,320 --> 00:46:46,180
+ماعرف أنا ما أجيبش لآخر أنا ما أجيب عند أي زمن عند أي
+
+552
+00:46:46,180 --> 00:46:51,960
+تيار دلي مظبوط طبعًا إذا معناته I maximum is the
+
+553
+00:46:51,960 --> 00:46:54,990
+initial current before removing the battery قال
+
+554
+00:46:54,990 --> 00:46:58,650
+ليه؟ الـ Variation لما قاعد أرسل قال لي هيك الرسل
+
+555
+00:46:58,650 --> 00:47:03,310
+هذه زيادة وهذه نقصانة when connecting the battery
+
+556
+00:47:03,310 --> 00:47:06,490
+the current takes some time تأخذ بعض الوقت to
+
+557
+00:47:06,490 --> 00:47:09,390
+reach its maximum value أخذ بعض الوقت عشان يصل
+
+558
+00:47:09,390 --> 00:47:11,710
+لقيمته النهائية هذا ما يسمونه asymptote في عالم
+
+559
+00:47:11,710 --> 00:47:17,670
+الـ calculus ها قال لي the تيار the current The
+
+560
+00:47:17,670 --> 00:47:19,770
+current will remove it from the battery. The
+
+561
+00:47:19,770 --> 00:47:22,270
+current takes some time to reach its zero value.
+
+562
+00:47:22,790 --> 00:47:28,570
+إذن برضه برجع Zero بس بعد وقت معين. تمام In
+
+563
+00:47:28,570 --> 00:47:34,250
+another word، إيش؟ نلخص، إيش مهمة البلاث؟ بقول لي
+
+564
+00:47:34,250 --> 00:47:38,890
+in another word، the inductor has the effect to
+
+565
+00:47:38,890 --> 00:47:42,960
+hinder، هندر يعني retard، نفس الكلمة يعني إيه؟ to
+
+566
+00:47:42,960 --> 00:47:47,000
+hinder the current from reaching its final value
+
+567
+00:47:47,000 --> 00:47:51,800
+for some time هنا أخذ وقت لما يصل القيمة النهائية
+
+568
+00:47:51,800 --> 00:47:56,120
+وهنا أخذ وقت عشان يصل القيمة النهائية طيب قال لي
+
+569
+00:47:56,120 --> 00:47:59,440
+طب لو جيت أنت شفت إيش الفرق مع موجود ملف وعدم
+
+570
+00:47:59,440 --> 00:48:05,120
+موجود ملف قال لي هاي تيار وفي عندك نقطة هاي الفترة
+
+571
+00:48:05,120 --> 00:48:08,720
+الزمنية اللي بدك تشبك البطارية قبل ما تشبك التيار
+
+572
+00:48:08,720 --> 00:48:13,840
+البطارية ليه داش تيار وبعد ما تشبك البطارية شبكة
+
+573
+00:48:13,840 --> 00:48:19,320
+التيار بدون ملف ده ليك صارت هذا بدون ملف تيجي
+
+574
+00:48:19,320 --> 00:48:24,700
+أبيجي وسميتها pulse ذاكرين النبضة الكهربية ده اللي
+
+575
+00:48:24,700 --> 00:48:31,300
+الملف طلع إيش بيسوي بيأخر
+
+576
+00:48:31,300 --> 00:48:36,760
+أو بيخلي التغيير بطيء بيخلي التغيير بطيء طبعًا أنت
+
+577
+00:48:36,760 --> 00:48:39,540
+أنت بقولي شغلة معينة واحد بيقولش هالملف هذي اللي
+
+578
+00:48:39,540 --> 00:48:42,800
+بيشتغلش إلا لحظة الإغلاق أو الفتح صح ولا ..
+
+579
+00:48:44,170 --> 00:48:49,970
+هذا في دوائر التيار المستمر هذا الضوء تيار مستمر؟
+
+580
+00:48:49,970 --> 00:48:56,670
+إيش يعني إيه؟ تيار إيش؟ لسه متردد بتغير مع الزمن
+
+581
+00:48:56,670 --> 00:49:01,710
+على طول ولا لأ؟ إذا الملف في دوائر التيار المتردد
+
+582
+00:49:01,710 --> 00:49:06,610
+شغال على طول ما بيحتاجش فتح وإغلاق لأن التيار متغير مع
+
+583
+00:49:06,610 --> 00:49:10,390
+الزمن على طول ولا لأ غير مستمر، بتغيرش مع الزمن
+
+584
+00:49:10,390 --> 00:49:14,750
+إلا لحظة الإغلاق والفتح لكن هذا ما هو متغير،
+
+585
+00:49:14,750 --> 00:49:17,890
+ذاكرة رسمة الـ Sine والـ Cosine؟ مش بتزيد وتنقص، بتزيد
+
+586
+00:49:17,890 --> 00:49:23,030
+وتنقص؟ إذا إن في دوائر التيار المتردد، الملف شغال
+
+587
+00:49:23,030 --> 00:49:27,310
+حسب قاعدة فرضه على طول، ما يحتاجش إغلاق وفتح بس،
+
+588
+00:49:27,310 --> 00:49:32,730
+تمام؟ شبكة رجالي، هنحكي عن الموضوع، تمام، يلا
+
+589
+00:49:32,730 --> 00:49:40,560
+يا بناتي Quiz هجيت أنت بتساوي صفر الملف open
+
+590
+00:49:40,560 --> 00:49:45,140
+circuit أنت بتساوي مالانهاية الملف برجع سلك مظبوط
+
+591
+00:49:45,140 --> 00:49:50,600
+ولا لأ؟ حلو بيقول لي هاي دائرة طلعش بيقول لي just
+
+592
+00:49:50,600 --> 00:49:54,540
+after closing the switch يعني أنت بتساوي صفر ولا
+
+593
+00:49:54,540 --> 00:49:58,220
+لأ؟ for the circuit shown in the figure just after
+
+594
+00:49:58,220 --> 00:50:01,440
+closing the switch حلو بيقول لي across which of
+
+595
+00:50:01,440 --> 00:50:03,780
+the following if the voltage equal to the inf of
+
+596
+00:50:03,780 --> 00:50:07,480
+the battery نفس الـ Quiz تبع عرسي الـ circuit حلو إيش
+
+597
+00:50:07,480 --> 00:50:11,340
+تبع كيرشوف بيقول بيقول لي فرق الجهد بين طرفي
+
+598
+00:50:11,340 --> 00:50:14,380
+البطارية بيساوي فرق الجهد بين طرفي المقاومة زي
+
+599
+00:50:14,380 --> 00:50:19,550
+آدي الملف صح طب إذا واحد منهم صفر إذا هذاك بيساوي
+
+600
+00:50:19,550 --> 00:50:22,810
+هذاك ولا لأ؟ إيش اللي بيساوي صفر؟ قلت له الـ I
+
+601
+00:50:22,810 --> 00:50:27,250
+بيساوي صفر مش الملف يصير open؟ جديش التيار إذا
+
+602
+00:50:27,250 --> 00:50:30,850
+الـ IFR اللي هو فرق جهد بين طرفين المقاومة جديش إذا
+
+603
+00:50:30,850 --> 00:50:33,630
+معناته فرق جهد بين طرفين البطارية هو نفس فرق جهد
+
+604
+00:50:33,630 --> 00:50:36,670
+بين طرفين الملف ولا لأ؟ إذا معناته إيش؟ بقول ليه؟
+
+605
+00:50:36,670 --> 00:50:42,170
+مين من هدول؟ قلت له باسئلة باسئلة صح ولا لأ؟ حلو
+
+606
+00:50:45,020 --> 00:50:48,960
+قال لي نفس السؤال إيش بده؟ قال لي after a long
+
+607
+00:50:48,960 --> 00:50:53,300
+time after closing the switch for a long time إيش
+
+608
+00:50:53,300 --> 00:50:56,760
+بيصير للملف؟ طيب دلوقت أسألكم الآن في هذه الدائرة
+
+609
+00:50:56,760 --> 00:51:00,500
+مين يقول لي فرق الجهد بين نقطة هذه ونقطة هذه؟ صفر
+
+610
+00:51:00,500 --> 00:51:03,700
+براو أنت بتساوي مالانهاية ديش فرق الجهد بين هذه و
+
+611
+00:51:03,700 --> 00:51:07,720
+هذه؟ لأنه نفس السلك صفر قال لي إذا معناته فرق
+
+612
+00:51:07,720 --> 00:51:10,060
+الجهد اللي هيبقى ساويه اللي هو R
+
+613
+00:51:12,990 --> 00:51:16,670
+تمام يا
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZzXsCLffozucGP33XWqvBP/x74s_bROvTc_raw.json b/PL9fwy3NUQKwZzXsCLffozucGP33XWqvBP/x74s_bROvTc_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..0f60848d45d469a69d89d38e40f10b8b50ae56a4
--- /dev/null
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On Saturday, we said", "tokens": [13267, 11, 718, 311, 20858, 437, 321, 848, 322, 8803, 13, 1282, 8803, 11, 321, 848], "avg_logprob": -0.5675551470588235, "compression_ratio": 1.1166666666666667, "no_speech_prob": 0.0, "words": [{"start": 6.5, "end": 7.26, "word": "Now,", "probability": 0.10455322265625}, {"start": 7.26, "end": 8.02, "word": " let's", "probability": 0.650634765625}, {"start": 8.02, "end": 8.42, "word": " summarize", "probability": 0.5517578125}, {"start": 8.42, "end": 8.7, "word": " what", "probability": 0.79638671875}, {"start": 8.7, "end": 8.88, "word": " we", "probability": 0.9267578125}, {"start": 8.88, "end": 9.26, "word": " said", "probability": 0.55810546875}, {"start": 9.26, "end": 10.34, "word": " on", "probability": 0.485595703125}, {"start": 10.34, "end": 10.8, "word": " Saturday.", "probability": 0.91357421875}, {"start": 11.6, "end": 12.36, "word": " On", "probability": 0.56201171875}, {"start": 12.36, "end": 12.72, "word": " Saturday,", "probability": 0.91259765625}, {"start": 12.82, "end": 12.86, "word": " we", "probability": 0.9208984375}, {"start": 12.86, "end": 13.02, "word": " said", "probability": 0.9052734375}], "temperature": 1.0}, {"id": 2, "seek": 3963, "start": 14.39, "end": 39.63, "text": "that the origin of the magnetic field is moving charges. This is the origin. That is, the source of the magnetic field is moving charges. 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Where did the course of good and bad go? Up to 91. 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As they are still moving, and I told the guys to take a picture, this is a picture, inside there is an ant, not a mouse as I told the guys, an ant, and the ant agreed to move, do they take a brush from the pen or not? They move. So who moved the pen? 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He said, I want a law that says you can't move the worm on the wire. I want to get it out. You can say that the worm is the ant. The force on the worm is the total force on the ant, right?", "tokens": [6455, 11, 562, 264, 2511, 6067, 11, 264, 23835, 6067, 886, 13, 634, 848, 11, 286, 528, 257, 2101, 300, 1619, 291, 393, 380, 1286, 264, 23835, 322, 264, 6234, 13, 286, 528, 281, 483, 309, 484, 13, 509, 393, 584, 300, 264, 23835, 307, 264, 2511, 13, 440, 3464, 322, 264, 23835, 307, 264, 3217, 3464, 322, 264, 2511, 11, 558, 30], "avg_logprob": -0.6967773260548711, "compression_ratio": 1.6934306569343065, "no_speech_prob": 9.5367431640625e-07, "words": [{"start": 745.1199999999999, "end": 745.56, "word": "So,", "probability": 0.412353515625}, {"start": 745.7, "end": 746.08, "word": " when", "probability": 0.65673828125}, {"start": 746.08, "end": 746.18, "word": " the", "probability": 0.455322265625}, {"start": 746.18, "end": 746.18, "word": " ant", "probability": 0.79248046875}, {"start": 746.18, "end": 747.02, "word": " moves,", "probability": 0.7783203125}, {"start": 747.3, "end": 747.84, "word": " the", "probability": 0.6611328125}, {"start": 747.84, "end": 748.04, "word": " worm", "probability": 0.29638671875}, {"start": 748.04, "end": 748.04, "word": " moves", "probability": 0.7685546875}, {"start": 748.04, "end": 748.26, "word": " too.", "probability": 0.3271484375}, {"start": 748.44, "end": 748.62, "word": " He", "probability": 0.164306640625}, {"start": 748.62, "end": 748.62, "word": " said,", "probability": 0.443603515625}, {"start": 748.68, "end": 749.2, "word": " I", "probability": 0.2301025390625}, {"start": 749.2, "end": 749.98, "word": " want", "probability": 0.305908203125}, {"start": 749.98, "end": 750.32, "word": " a", "probability": 0.57958984375}, {"start": 750.32, "end": 750.62, "word": " law", "probability": 0.7158203125}, {"start": 750.62, "end": 750.98, "word": " that", "probability": 0.6396484375}, {"start": 750.98, "end": 751.16, "word": " says", "probability": 0.51025390625}, {"start": 751.16, "end": 751.24, "word": " you", "probability": 0.1787109375}, {"start": 751.24, "end": 751.48, "word": " can't", "probability": 0.662841796875}, {"start": 751.48, "end": 751.62, "word": " move", "probability": 0.27001953125}, {"start": 751.62, "end": 751.62, "word": " the", "probability": 0.337890625}, {"start": 751.62, "end": 751.88, "word": " worm", "probability": 0.271484375}, {"start": 751.88, "end": 752.04, "word": " on", "probability": 0.2587890625}, {"start": 752.04, "end": 752.18, "word": " the", "probability": 0.402587890625}, {"start": 752.18, "end": 752.4, "word": " wire.", "probability": 0.1156005859375}, {"start": 753.92, "end": 754.36, "word": " I", "probability": 0.3251953125}, {"start": 754.36, "end": 754.78, "word": " want", "probability": 0.59375}, {"start": 754.78, "end": 754.98, "word": " to", "probability": 0.88916015625}, {"start": 754.98, "end": 755.2, "word": " get", "probability": 0.1513671875}, {"start": 755.2, "end": 755.4, "word": " it", "probability": 0.5869140625}, {"start": 755.4, "end": 755.4, "word": " out.", "probability": 0.80419921875}, {"start": 756.1, "end": 756.24, "word": " You", "probability": 0.77880859375}, {"start": 756.24, "end": 756.46, "word": " can", "probability": 0.8828125}, {"start": 756.46, "end": 756.74, "word": " say", "probability": 0.83203125}, {"start": 756.74, "end": 756.92, "word": " that", "probability": 0.69580078125}, {"start": 756.92, "end": 757.42, "word": " the", "probability": 0.67919921875}, {"start": 757.42, "end": 757.72, "word": " worm", "probability": 0.481689453125}, {"start": 757.72, "end": 757.9, "word": " is", "probability": 0.258056640625}, {"start": 757.9, "end": 758.08, "word": " the", "probability": 0.36962890625}, {"start": 758.08, "end": 758.34, "word": " ant.", "probability": 0.90087890625}, {"start": 758.96, "end": 759.4, "word": " The", "probability": 0.361328125}, {"start": 759.4, "end": 759.62, "word": " force", "probability": 0.282470703125}, {"start": 759.62, "end": 759.98, "word": " on", "probability": 0.81201171875}, {"start": 759.98, "end": 760.78, "word": " the", "probability": 0.90185546875}, {"start": 760.78, "end": 761.1, "word": " worm", "probability": 0.70458984375}, {"start": 761.1, "end": 761.34, "word": " is", "probability": 0.78662109375}, {"start": 761.34, "end": 761.48, "word": " the", "probability": 0.7080078125}, {"start": 761.48, "end": 761.7, "word": " total", "probability": 0.14892578125}, {"start": 761.7, "end": 762.12, "word": " force", "probability": 0.9228515625}, {"start": 762.12, "end": 762.34, "word": " on", "probability": 0.8623046875}, {"start": 762.34, "end": 762.46, "word": " the", "probability": 0.912109375}, {"start": 762.46, "end": 762.62, "word": " ant,", "probability": 0.69482421875}, {"start": 762.78, "end": 762.82, "word": " right?", "probability": 0.467041015625}], "temperature": 1.0}, {"id": 33, "seek": 78136, "start": 763.82, "end": 781.36, "text": " When you have 5 ants or 100 ants, which one moves faster? Which one moves faster? Which one moves faster? Which one moves faster? Which one moves faster? Which one moves faster? Which one moves faster? Which one moves faster? Which one moves faster? Which one moves faster? Which one moves faster? Which one moves faster? Which one moves faster? Which one moves faster? Which one moves faster? Which one moves faster? Which one moves faster? Which one moves faster? Which one moves faster? Which one moves faster? Which one moves faster? Which one moves faster? Which one moves faster? Which one moves faster? Which one moves faster? Which one moves faster? Which one moves faster? Which one moves faster? Which one moves faster? Which one moves faster? Which one moves faster? Which one moves faster? Which one moves faster? Which one moves faster? Which one moves faster? Which one moves faster? Which one moves faster? Which one moves faster? Which one moves faster? Which one moves faster? Which one moves faster? Which one moves faster? Which one moves faster?", "tokens": [1133, 291, 362, 1025, 23355, 420, 2319, 23355, 11, 597, 472, 6067, 4663, 30, 3013, 472, 6067, 4663, 30, 3013, 472, 6067, 4663, 30, 3013, 472, 6067, 4663, 30, 3013, 472, 6067, 4663, 30, 3013, 472, 6067, 4663, 30, 3013, 472, 6067, 4663, 30, 3013, 472, 6067, 4663, 30, 3013, 472, 6067, 4663, 30, 3013, 472, 6067, 4663, 30, 3013, 472, 6067, 4663, 30, 3013, 472, 6067, 4663, 30, 3013, 472, 6067, 4663, 30, 3013, 472, 6067, 4663, 30, 3013, 472, 6067, 4663, 30, 3013, 472, 6067, 4663, 30, 3013, 472, 6067, 4663, 30, 3013, 472, 6067, 4663, 30, 3013, 472, 6067, 4663, 30, 3013, 472, 6067, 4663, 30, 3013, 472, 6067, 4663, 30, 3013, 472, 6067, 4663, 30, 3013, 472, 6067, 4663, 30, 3013, 472, 6067, 4663, 30, 3013, 472, 6067, 4663, 30, 3013, 472, 6067, 4663, 30, 3013, 472, 6067, 4663, 30, 3013, 472, 6067, 4663, 30, 3013, 472, 6067, 4663, 30, 3013, 472, 6067, 4663, 30, 3013, 472, 6067, 4663, 30, 3013, 472, 6067, 4663, 30, 3013, 472, 6067, 4663, 30, 3013, 472, 6067, 4663, 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Definitely, if there is a current, then definitely there is a magnetic field or not. Do you hear about electric magnetism? This is his idea. Electric magnetism is when you put a current, then there is a magnetism. 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This means that any current carrying wire must experience a magnetic force will be placed in a magnetic field.", "tokens": [3522, 307, 2570, 300, 257, 2190, 307, 257, 12590, 295, 2684, 12235, 295, 264, 912, 2744, 13, 639, 1355, 300, 604, 2190, 9792, 6234, 1633, 1752, 257, 12688, 3464, 486, 312, 7074, 294, 257, 12688, 2519, 13], "avg_logprob": -0.2481496600728286, "compression_ratio": 1.4210526315789473, "no_speech_prob": 3.3974647521972656e-06, "words": [{"start": 840.76, "end": 841.0, "word": "It", "probability": 0.441162109375}, {"start": 841.0, "end": 841.16, "word": " is", "probability": 0.904296875}, {"start": 841.16, "end": 841.36, "word": " known", "probability": 0.74267578125}, {"start": 841.36, "end": 841.8, "word": " that", "probability": 0.943359375}, {"start": 841.8, "end": 842.46, "word": " a", "probability": 0.841796875}, {"start": 842.46, "end": 842.76, "word": " current", "probability": 0.88427734375}, {"start": 842.76, "end": 843.08, "word": " is", "probability": 0.9345703125}, {"start": 843.08, "end": 843.34, "word": " a", "probability": 0.9765625}, {"start": 843.34, "end": 843.84, "word": " collective", "probability": 0.73828125}, {"start": 843.84, "end": 844.18, "word": " of", "probability": 0.876953125}, {"start": 844.18, "end": 844.58, "word": " moving", "probability": 0.896484375}, {"start": 844.58, "end": 845.06, "word": " charges", "probability": 0.88427734375}, {"start": 845.06, "end": 845.48, "word": " of", "probability": 0.8505859375}, {"start": 845.48, "end": 845.62, "word": " the", "probability": 0.921875}, {"start": 845.62, "end": 845.9, "word": " same", "probability": 0.90185546875}, {"start": 845.9, "end": 846.32, "word": " size.", "probability": 0.716796875}, {"start": 848.9, "end": 849.74, "word": " This", "probability": 0.3623046875}, {"start": 849.74, "end": 851.9, "word": " means", "probability": 0.89111328125}, {"start": 851.9, "end": 852.28, "word": " that", "probability": 0.9365234375}, {"start": 852.28, "end": 853.42, "word": " any", "probability": 0.7861328125}, {"start": 853.42, "end": 854.04, "word": " current", "probability": 0.91259765625}, {"start": 854.04, "end": 854.76, "word": " carrying", "probability": 0.880859375}, {"start": 854.76, "end": 855.3, "word": " wire", "probability": 0.8056640625}, {"start": 855.3, "end": 857.84, "word": " must", "probability": 0.5341796875}, {"start": 857.84, "end": 859.1, "word": " experience", "probability": 0.76025390625}, {"start": 859.1, "end": 859.48, "word": " a", "probability": 0.97021484375}, {"start": 859.48, "end": 859.84, "word": " magnetic", "probability": 0.90869140625}, {"start": 859.84, "end": 861.8, "word": " force", "probability": 0.953125}, {"start": 861.8, "end": 862.46, "word": " will", "probability": 0.1876220703125}, {"start": 862.46, "end": 862.64, "word": " be", "probability": 0.408935546875}, {"start": 862.64, "end": 862.94, "word": " placed", "probability": 0.90869140625}, {"start": 862.94, "end": 863.18, "word": " in", "probability": 0.9384765625}, {"start": 863.18, "end": 863.34, "word": " a", "probability": 0.96044921875}, {"start": 863.34, "end": 863.72, "word": " magnetic", "probability": 0.8974609375}, {"start": 863.72, "end": 864.3, "word": " field.", "probability": 0.9306640625}], "temperature": 1.0}, {"id": 37, "seek": 87768, "start": 864.96, "end": 877.68, "text": "This force is the vector sum of the individual forces on the charged particle.", "tokens": [5723, 3464, 307, 264, 8062, 2408, 295, 264, 2609, 5874, 322, 264, 11109, 12359, 13], "avg_logprob": -0.4204101674258709, "compression_ratio": 1.0833333333333333, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 864.96, "end": 865.44, "word": "This", "probability": 0.048248291015625}, {"start": 865.44, "end": 867.48, "word": " force", "probability": 0.8046875}, {"start": 867.48, "end": 868.3, "word": " is", "probability": 0.689453125}, {"start": 868.3, "end": 873.16, "word": " the", "probability": 0.75146484375}, {"start": 873.16, "end": 873.54, "word": " vector", "probability": 0.88916015625}, {"start": 873.54, "end": 874.04, "word": " sum", "probability": 0.8876953125}, {"start": 874.04, "end": 874.3, "word": " of", "probability": 0.9326171875}, {"start": 874.3, "end": 874.42, "word": " the", "probability": 0.66455078125}, {"start": 874.42, "end": 875.36, "word": " individual", "probability": 0.8056640625}, {"start": 875.36, "end": 876.08, "word": " forces", "probability": 0.912109375}, {"start": 876.08, "end": 876.4, "word": " on", "probability": 0.884765625}, {"start": 876.4, "end": 876.54, "word": " the", "probability": 0.740234375}, {"start": 876.54, "end": 876.96, "word": " charged", "probability": 0.83056640625}, {"start": 876.96, "end": 877.68, "word": " particle.", "probability": 0.7958984375}], "temperature": 1.0}, {"id": 38, "seek": 89817, "start": 881.41, "end": 898.17, "text": " And the force is a vector or not a vector? It's a vector. And you notice that when you add vectors, I and J don't add up. Right or wrong? It's right. He told me that he wanted to calculate it. I told him to calculate it. He brought me a wire. A wire. 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Come on! It's not always L. Don't worry, everyone is confused like you. Because it's a vector, the answer can be zero.", "tokens": [467, 311, 257, 1622, 294, 264, 21267, 13, 2492, 322, 0, 467, 311, 406, 1009, 441, 13, 1468, 380, 3292, 11, 1518, 307, 9019, 411, 291, 13, 1436, 309, 311, 257, 8062, 11, 264, 1867, 393, 312, 4018, 13], "avg_logprob": -0.826562476158142, "compression_ratio": 1.2357723577235773, "no_speech_prob": 2.980232238769531e-07, "words": [{"start": 1137.14, "end": 1137.36, "word": " It's", "probability": 0.3720245361328125}, {"start": 1137.36, "end": 1137.58, "word": " a", "probability": 0.429443359375}, {"start": 1137.58, "end": 1137.8, "word": " line", "probability": 0.1119384765625}, {"start": 1137.8, "end": 1138.88, "word": " in", "probability": 0.5283203125}, {"start": 1138.88, "end": 1139.04, "word": " the", "probability": 0.359130859375}, {"start": 1139.04, "end": 1139.5, "word": " combinations.", "probability": 0.030487060546875}, {"start": 1139.82, "end": 1140.0, "word": " Come", "probability": 0.084228515625}, {"start": 1140.0, "end": 1140.36, "word": " on!", "probability": 0.83154296875}, {"start": 1141.4, "end": 1141.92, "word": " It's", "probability": 0.5372314453125}, {"start": 1141.92, "end": 1141.92, "word": " not", "probability": 0.301513671875}, {"start": 1141.92, "end": 1143.88, "word": " always", "probability": 0.763671875}, {"start": 1143.88, "end": 1144.18, "word": " L.", "probability": 0.1802978515625}, {"start": 1146.26, "end": 1146.78, "word": " Don't", "probability": 0.62646484375}, {"start": 1146.78, "end": 1147.58, "word": " worry,", "probability": 0.66015625}, {"start": 1147.84, "end": 1148.0, "word": " everyone", "probability": 0.2330322265625}, {"start": 1148.0, "end": 1148.06, "word": " is", "probability": 0.369384765625}, {"start": 1148.06, "end": 1148.28, "word": " confused", "probability": 0.681640625}, {"start": 1148.28, "end": 1148.36, "word": " like", "probability": 0.57958984375}, {"start": 1148.36, "end": 1148.62, "word": " you.", "probability": 0.7265625}, {"start": 1150.82, "end": 1151.34, "word": " Because", "probability": 0.295654296875}, {"start": 1151.34, "end": 1158.5, "word": " it's", "probability": 0.858154296875}, {"start": 1158.5, "end": 1158.6, "word": " a", "probability": 0.923828125}, {"start": 1158.6, "end": 1158.86, "word": " vector,", "probability": 0.94873046875}, {"start": 1159.22, "end": 1160.02, "word": " the", "probability": 0.76123046875}, {"start": 1160.02, "end": 1160.2, "word": " answer", "probability": 0.9482421875}, {"start": 1160.2, "end": 1160.3, "word": " can", "probability": 0.314208984375}, {"start": 1160.3, "end": 1160.44, "word": " be", "probability": 0.92822265625}, {"start": 1160.44, "end": 1160.72, "word": " zero.", "probability": 0.515625}], "temperature": 1.0}, {"id": 49, "seek": 118485, "start": 1162.84, "end": 1184.86, "text": " Do you remember when we used to get a DE? And when we used to complete the DE, we used to tell you to pay attention before you complete it and look at the directions. If the direction is all in the same direction, it becomes the completion of the DEE. And if it's not in the same direction, solve the sine by itself and the cosine by itself. Right or wrong? Well, what if the sine and the sine cancel each other and the cosine and the cosine cancel each other? Does it go to zero or not?", "tokens": [1144, 291, 1604, 562, 321, 1143, 281, 483, 257, 10113, 30, 400, 562, 321, 1143, 281, 3566, 264, 10113, 11, 321, 1143, 281, 980, 291, 281, 1689, 3202, 949, 291, 3566, 309, 293, 574, 412, 264, 11095, 13, 759, 264, 3513, 307, 439, 294, 264, 912, 3513, 11, 309, 3643, 264, 19372, 295, 264, 413, 7258, 13, 400, 498, 309, 311, 406, 294, 264, 912, 3513, 11, 5039, 264, 18609, 538, 2564, 293, 264, 23565, 538, 2564, 13, 1779, 420, 2085, 30, 1042, 11, 437, 498, 264, 18609, 293, 264, 18609, 10373, 1184, 661, 293, 264, 23565, 293, 264, 23565, 10373, 1184, 661, 30, 4402, 309, 352, 281, 4018, 420, 406, 30], "avg_logprob": -0.46681415085243966, "compression_ratio": 2.033333333333333, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 1162.84, "end": 1163.14, "word": " Do", "probability": 0.1688232421875}, {"start": 1163.14, "end": 1163.14, "word": " you", "probability": 0.95458984375}, {"start": 1163.14, "end": 1163.46, "word": " remember", 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Tell me what you want to do with this whole thing. I want it to be B is uniform as you told me. The rule will be F is equal to I DL cross B and B is subtracted from outside. Leave it like that. What is the problem with this?", "tokens": [12024, 13, 5115, 385, 437, 291, 528, 281, 360, 365, 341, 1379, 551, 13, 286, 528, 309, 281, 312, 363, 307, 9452, 382, 291, 1907, 385, 13, 440, 4978, 486, 312, 479, 307, 2681, 281, 286, 413, 43, 3278, 363, 293, 363, 307, 16390, 292, 490, 2380, 13, 9825, 309, 411, 300, 13, 708, 307, 264, 1154, 365, 341, 30], "avg_logprob": -0.7494877010095314, "compression_ratio": 1.4171779141104295, "no_speech_prob": 3.874301910400391e-06, "words": [{"start": 1185.71, "end": 1186.19, "word": " Fine.", "probability": 0.0703125}, {"start": 1186.55, "end": 1186.77, "word": " Tell", "probability": 0.1785888671875}, {"start": 1186.77, "end": 1186.87, "word": " me", "probability": 0.9150390625}, {"start": 1186.87, "end": 1186.97, "word": " what", "probability": 0.60888671875}, {"start": 1186.97, "end": 1187.13, "word": " you", "probability": 0.2213134765625}, {"start": 1187.13, "end": 1187.27, "word": " want", "probability": 0.2744140625}, {"start": 1187.27, "end": 1187.27, "word": " to", "probability": 0.796875}, {"start": 1187.27, "end": 1187.47, "word": " do", "probability": 0.31005859375}, {"start": 1187.47, "end": 1187.59, "word": " with", "probability": 0.74365234375}, {"start": 1187.59, "end": 1187.77, "word": " this", "probability": 0.479736328125}, {"start": 1187.77, "end": 1188.13, "word": " whole", "probability": 0.279296875}, {"start": 1188.13, "end": 1188.21, "word": " thing.", "probability": 0.197021484375}, {"start": 1188.65, "end": 1188.75, "word": " I", "probability": 0.10357666015625}, {"start": 1188.75, "end": 1189.01, "word": " want", "probability": 0.67919921875}, {"start": 1189.01, "end": 1189.23, "word": " it", "probability": 0.314453125}, {"start": 1189.23, "end": 1189.29, "word": " to", "probability": 0.72705078125}, {"start": 1189.29, "end": 1189.29, "word": " be", "probability": 0.568359375}, {"start": 1189.29, "end": 1189.45, "word": " B", "probability": 0.388916015625}, {"start": 1189.45, "end": 1189.67, "word": " is", "probability": 0.8251953125}, {"start": 1189.67, "end": 1190.09, "word": " uniform", "probability": 0.85009765625}, {"start": 1190.09, "end": 1190.27, "word": " as", "probability": 0.36669921875}, {"start": 1190.27, "end": 1190.51, "word": " you", "probability": 0.89306640625}, {"start": 1190.51, "end": 1190.67, "word": " told", "probability": 0.444091796875}, {"start": 1190.67, "end": 1191.05, "word": " me.", "probability": 0.91796875}, {"start": 1191.39, "end": 1191.87, "word": " The", "probability": 0.323974609375}, {"start": 1191.87, "end": 1192.31, "word": " rule", "probability": 0.382080078125}, {"start": 1192.31, "end": 1192.59, "word": " will", "probability": 0.37060546875}, {"start": 1192.59, "end": 1192.77, "word": " be", "probability": 0.356201171875}, {"start": 1192.77, "end": 1193.13, "word": " F", "probability": 0.71484375}, {"start": 1193.13, "end": 1194.07, "word": " is", "probability": 0.1392822265625}, {"start": 1194.07, "end": 1194.31, "word": " equal", "probability": 0.76318359375}, {"start": 1194.31, "end": 1194.41, "word": " to", "probability": 0.9609375}, {"start": 1194.41, "end": 1194.81, "word": " I", "probability": 0.94189453125}, {"start": 1194.81, "end": 1196.93, "word": " DL", "probability": 0.42877197265625}, {"start": 1196.93, "end": 1197.63, "word": " cross", "probability": 0.25927734375}, {"start": 1197.63, "end": 1198.11, "word": " B", "probability": 0.84033203125}, {"start": 1198.11, "end": 1198.41, "word": " and", "probability": 0.351806640625}, {"start": 1198.41, "end": 1198.59, "word": " B", "probability": 0.8662109375}, {"start": 1198.59, "end": 1198.69, "word": " is", "probability": 0.176025390625}, {"start": 1198.69, "end": 1199.07, "word": " subtracted", "probability": 0.55548095703125}, {"start": 1199.07, "end": 1199.07, "word": " from", "probability": 0.54443359375}, {"start": 1199.07, "end": 1199.37, "word": " outside.", "probability": 0.405029296875}, {"start": 1199.63, "end": 1199.79, "word": " Leave", "probability": 0.335693359375}, {"start": 1199.79, "end": 1199.97, "word": " it", "probability": 0.890625}, {"start": 1199.97, "end": 1200.19, "word": " like", "probability": 0.5166015625}, {"start": 1200.19, "end": 1200.51, "word": " that.", "probability": 0.6455078125}, {"start": 1200.61, "end": 1201.03, "word": " What", "probability": 0.42041015625}, {"start": 1201.03, "end": 1202.25, "word": " is", "probability": 0.49365234375}, {"start": 1202.25, "end": 1202.29, "word": " the", "probability": 0.81005859375}, {"start": 1202.29, "end": 1202.57, "word": " problem", "probability": 0.85107421875}, {"start": 1202.57, "end": 1202.73, "word": " with", "probability": 0.397216796875}, {"start": 1202.73, "end": 1203.05, "word": " this?", "probability": 0.63818359375}], "temperature": 1.0}, {"id": 51, "seek": 123194, "start": 1204.24, "end": 1231.94, "text": " How much does this equal to if they have the same direction? The same direction. Right or wrong? If they have the same direction. How much does this equal to if they have the same direction? I told him if it's a straight line, it's a straight line. It's not a straight line, we didn't finish it. There are circles. It's not a straight line, we didn't finish it together. Okay, okay. You're in a hurry to tell me. Is it a straight line or a straight line? He looked at me and said no. 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Do you understand? You see one by one. He told me that if C is straight regardless of how you look at it.", "tokens": [407, 510, 264, 6562, 295, 413, 293, 441, 1177, 380, 652, 441, 13, 1144, 291, 1223, 30, 509, 536, 472, 538, 472, 13, 634, 1907, 385, 300, 498, 383, 307, 2997, 10060, 295, 577, 291, 574, 412, 309, 13], "avg_logprob": -0.658593763411045, "compression_ratio": 1.246031746031746, "no_speech_prob": 8.940696716308594e-07, "words": [{"start": 1234.9, "end": 1235.38, "word": " So", "probability": 0.164306640625}, {"start": 1235.38, "end": 1235.82, "word": " here", "probability": 0.497802734375}, {"start": 1235.82, "end": 1236.32, "word": " the", "probability": 0.45166015625}, {"start": 1236.32, "end": 1236.6, "word": " combination", "probability": 0.296875}, {"start": 1236.6, "end": 1236.8, "word": " of", "probability": 0.88720703125}, {"start": 1236.8, "end": 1236.96, "word": " D", "probability": 0.48291015625}, {"start": 1236.96, "end": 1237.04, "word": " and", "probability": 0.62353515625}, {"start": 1237.04, 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Right or wrong? The length which is L is Pi x R and Pi is 3 and something. But the combination of D and L became 2R. Stop speaking Arabic. Isn't it, Batool? You corrected it. You corrected it. Look at it. This is a semicircle, Batool.", "tokens": [47, 72, 2031, 497, 13, 1779, 420, 2085, 30, 440, 4641, 597, 307, 441, 307, 17741, 2031, 497, 293, 17741, 307, 805, 293, 746, 13, 583, 264, 6562, 295, 413, 293, 441, 3062, 568, 49, 13, 5535, 4124, 19938, 13, 6998, 380, 309, 11, 10066, 1092, 30, 509, 31687, 309, 13, 509, 31687, 309, 13, 2053, 412, 309, 13, 639, 307, 257, 27515, 347, 2160, 11, 10066, 1092, 13], "avg_logprob": -0.5660714404923576, "compression_ratio": 1.3988439306358382, "no_speech_prob": 1.5616416931152344e-05, "words": [{"start": 1357.09, "end": 1357.43, "word": "Pi", "probability": 0.513336181640625}, {"start": 1357.43, "end": 1357.55, "word": " x", "probability": 0.0288848876953125}, {"start": 1357.55, "end": 1357.79, "word": " R.", "probability": 0.85009765625}, {"start": 1357.91, "end": 1358.03, "word": " Right", "probability": 0.2493896484375}, {"start": 1358.03, "end": 1358.21, "word": " or", "probability": 0.85693359375}, {"start": 1358.21, "end": 1358.31, "word": " wrong?", "probability": 0.465576171875}, {"start": 1358.89, "end": 1358.99, "word": " The", "probability": 0.6748046875}, {"start": 1358.99, "end": 1359.39, "word": " length", "probability": 0.61962890625}, {"start": 1359.39, "end": 1359.93, "word": " which", "probability": 0.449951171875}, {"start": 1359.93, "end": 1360.17, "word": " is", "probability": 0.888671875}, {"start": 1360.17, "end": 1360.45, "word": " L", "probability": 0.8935546875}, {"start": 1360.45, "end": 1360.81, "word": " is", "probability": 0.325439453125}, {"start": 1360.81, "end": 1361.03, "word": " Pi", "probability": 0.87744140625}, {"start": 1361.03, "end": 1361.17, "word": " x", "probability": 0.91552734375}, {"start": 1361.17, "end": 1361.45, "word": " R", "probability": 0.97412109375}, {"start": 1361.45, "end": 1361.59, "word": " and", "probability": 0.5341796875}, {"start": 1361.59, "end": 1361.79, "word": " Pi", "probability": 0.7021484375}, {"start": 1361.79, "end": 1361.87, "word": " is", "probability": 0.662109375}, {"start": 1361.87, "end": 1362.03, "word": " 3", "probability": 0.248046875}, {"start": 1362.03, "end": 1362.19, "word": " and", "probability": 0.7138671875}, {"start": 1362.19, "end": 1362.45, "word": " something.", "probability": 0.334228515625}, {"start": 1363.51, "end": 1363.95, "word": " But", "probability": 0.7119140625}, {"start": 1363.95, "end": 1365.09, "word": " the", "probability": 0.619140625}, {"start": 1365.09, "end": 1365.51, "word": " combination", "probability": 0.3662109375}, {"start": 1365.51, "end": 1365.77, "word": " of", "probability": 0.82177734375}, {"start": 1365.77, "end": 1365.97, "word": " D", "probability": 0.226318359375}, {"start": 1365.97, "end": 1366.11, "word": " and", "probability": 0.55029296875}, {"start": 1366.11, "end": 1366.33, "word": " L", "probability": 0.9716796875}, {"start": 1366.33, "end": 1366.55, "word": " became", "probability": 0.189697265625}, {"start": 1366.55, "end": 1367.17, "word": " 2R.", "probability": 0.8759765625}, {"start": 1369.15, "end": 1369.47, "word": " Stop", "probability": 0.455078125}, {"start": 1369.47, "end": 1369.73, "word": " speaking", "probability": 0.70849609375}, {"start": 1369.73, "end": 1370.07, "word": " Arabic.", "probability": 0.83349609375}, {"start": 1370.43, "end": 1370.53, "word": " Isn't", "probability": 0.5919189453125}, {"start": 1370.53, "end": 1370.61, "word": " it,", "probability": 0.63916015625}, {"start": 1370.63, "end": 1370.93, "word": " Batool?", "probability": 0.5531005859375}, {"start": 1371.13, "end": 1371.23, "word": " You", "probability": 0.3486328125}, {"start": 1371.23, "end": 1371.47, "word": " corrected", "probability": 0.09954833984375}, {"start": 1371.47, "end": 1371.81, "word": " it.", "probability": 0.454833984375}, {"start": 1372.17, "end": 1372.61, "word": " You", "probability": 0.361083984375}, {"start": 1372.61, "end": 1372.81, "word": " corrected", "probability": 0.87744140625}, {"start": 1372.81, "end": 1373.15, "word": " it.", "probability": 0.93408203125}, {"start": 1373.33, "end": 1373.55, "word": " Look", "probability": 0.798828125}, {"start": 1373.55, "end": 1373.73, "word": " at", "probability": 0.947265625}, {"start": 1373.73, "end": 1373.89, "word": " it.", "probability": 0.572265625}, {"start": 1374.51, "end": 1374.83, "word": " This", "probability": 0.70263671875}, {"start": 1374.83, "end": 1374.97, "word": " is", "probability": 0.9208984375}, {"start": 1374.97, "end": 1375.05, "word": " a", "probability": 0.286376953125}, {"start": 1375.05, "end": 1375.57, "word": " semicircle,", "probability": 0.8479817708333334}, {"start": 1375.67, "end": 1376.05, "word": " Batool.", "probability": 0.907958984375}], "temperature": 1.0}, {"id": 58, "seek": 140515, "start": 1377.59, "end": 1405.15, "text": "Okay? I want the combination of D and L. I tell you that the combination of D and L is only the Chinese. And the Chinese from now on is Qatar or not Qatar? But if the combination of D and L was L, it would have turned out to be Pi into R. Half a circle. And this is not two R's, it's three and a little. So it's always the combination of D and L equals L? 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He didn't give me a break. He told me, come on, I want to gather the Chinese. I gathered the Chinese, the Reds alone, and the Browns alone, and as you well know, I told him that they were all in the same direction when I gathered them. I used to be handsome when I used to work with them ten years ago. If you work with them in a different way, maybe they don't like each other. A little bit. 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You know it's going to be an answer like this. If you speak Chinese, it's going to come out. Wait a minute, Yoman. Wait a minute, I swear I know what you want to say. Wait a minute. What condition is this that I want to name it?", "tokens": [467, 311, 257, 6555, 6329, 11, 457, 309, 311, 257, 6555, 6329, 411, 341, 11, 558, 30, 509, 458, 309, 311, 516, 281, 312, 364, 1867, 411, 341, 13, 759, 291, 1710, 4649, 11, 309, 311, 516, 281, 808, 484, 13, 3802, 257, 3456, 11, 398, 4277, 13, 3802, 257, 3456, 11, 286, 11902, 286, 458, 437, 291, 528, 281, 584, 13, 3802, 257, 3456, 13, 708, 4188, 307, 341, 300, 286, 528, 281, 1315, 309, 30], "avg_logprob": -0.5929487240620148, "compression_ratio": 1.7309941520467835, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1438.47, "end": 1438.71, "word": " It's", "probability": 0.3383331298828125}, {"start": 1438.71, "end": 1438.83, "word": " a", "probability": 0.423828125}, {"start": 1438.83, "end": 1438.91, "word": " quarter", "probability": 0.806640625}, {"start": 1438.91, "end": 1439.27, "word": " circle,", "probability": 0.47119140625}, {"start": 1439.35, "end": 1439.43, "word": " but", "probability": 0.75732421875}, 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I want to ask you, if the circuit is closed, what is the condition? Bravo to us. Right? Bravo to us. So I can generalize and say the following, if you have a closed circuit in a magnetic field with the condition that it is uniform, what is the force on it? Zero directly. 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He's telling you. Do you think you can fool me? You don't have to answer my questions. All the answers I'm going to give you will be clear and in a straight line. Okay, let's go. So he's telling me,", "tokens": [5205, 311, 3585, 291, 11, 43731, 13, 634, 311, 3585, 291, 13, 1144, 291, 519, 291, 393, 7979, 385, 30, 509, 500, 380, 362, 281, 1867, 452, 1651, 13, 1057, 264, 6338, 286, 478, 516, 281, 976, 291, 486, 312, 1850, 293, 294, 257, 2997, 1622, 13, 1033, 11, 718, 311, 352, 13, 407, 415, 311, 3585, 385, 11], "avg_logprob": -0.6343749990065892, "compression_ratio": 1.4050632911392404, "no_speech_prob": 6.556510925292969e-07, "words": [{"start": 1574.25, "end": 1574.71, "word": "He's", "probability": 0.12255859375}, {"start": 1574.71, "end": 1575.01, "word": " telling", "probability": 0.467529296875}, {"start": 1575.01, "end": 1575.23, "word": " you,", "probability": 0.927734375}, {"start": 1575.31, "end": 1575.55, "word": " Mona.", "probability": 0.65966796875}, {"start": 1576.31, "end": 1576.65, "word": " He's", "probability": 0.80322265625}, {"start": 1576.65, "end": 1576.87, "word": " telling", "probability": 0.6923828125}, {"start": 1576.87, "end": 1577.09, "word": " you.", "probability": 0.9619140625}, {"start": 1577.25, "end": 1577.73, "word": " Do", "probability": 0.171142578125}, {"start": 1577.73, "end": 1578.07, "word": " you", "probability": 0.96533203125}, {"start": 1578.07, "end": 1578.35, "word": " think", "probability": 0.861328125}, {"start": 1578.35, "end": 1578.47, "word": " you", "probability": 0.487548828125}, {"start": 1578.47, "end": 1578.55, "word": " can", "probability": 0.349853515625}, {"start": 1578.55, "end": 1578.71, "word": " fool", "probability": 0.469970703125}, {"start": 1578.71, "end": 1579.11, "word": " me?", "probability": 0.896484375}, {"start": 1579.59, "end": 1579.97, "word": " You", "probability": 0.2183837890625}, {"start": 1579.97, "end": 1580.09, "word": " don't", "probability": 0.798583984375}, {"start": 1580.09, "end": 1580.29, "word": " have", "probability": 0.330322265625}, {"start": 1580.29, "end": 1580.51, "word": " to", "probability": 0.81640625}, {"start": 1580.51, "end": 1580.61, "word": " answer", "probability": 0.280517578125}, {"start": 1580.61, "end": 1580.69, "word": " my", "probability": 0.1363525390625}, {"start": 1580.69, "end": 1581.53, "word": " questions.", "probability": 0.87158203125}, {"start": 1582.01, "end": 1582.49, "word": " All", "probability": 0.85546875}, {"start": 1582.49, "end": 1582.65, "word": " the", "probability": 0.7294921875}, {"start": 1582.65, "end": 1583.07, "word": " answers", "probability": 0.296875}, {"start": 1583.07, "end": 1583.43, "word": " I'm", "probability": 0.44439697265625}, {"start": 1583.43, "end": 1583.43, "word": " going", "probability": 0.53076171875}, {"start": 1583.43, "end": 1583.43, "word": " to", "probability": 0.96728515625}, {"start": 1583.43, "end": 1583.49, "word": " give", "probability": 0.783203125}, {"start": 1583.49, "end": 1583.67, "word": " you", "probability": 0.861328125}, {"start": 1583.67, "end": 1583.97, "word": " will", "probability": 0.36279296875}, {"start": 1583.97, "end": 1584.13, "word": " be", "probability": 0.9267578125}, {"start": 1584.13, "end": 1584.55, "word": " clear", "probability": 0.50439453125}, {"start": 1584.55, "end": 1585.21, "word": " and", "probability": 0.73388671875}, {"start": 1585.21, "end": 1585.31, "word": " in", "probability": 0.1873779296875}, {"start": 1585.31, "end": 1585.55, "word": " a", "probability": 0.869140625}, {"start": 1585.55, "end": 1585.81, "word": " straight", "probability": 0.5615234375}, {"start": 1585.81, "end": 1586.03, "word": " line.", "probability": 0.947265625}, {"start": 1586.63, "end": 1587.01, "word": " Okay,", "probability": 0.334716796875}, {"start": 1587.63, "end": 1588.09, "word": " let's", "probability": 0.62744140625}, {"start": 1588.09, "end": 1588.19, "word": " go.", "probability": 0.6220703125}, {"start": 1589.85, "end": 1590.19, "word": " So", "probability": 0.7333984375}, {"start": 1590.19, "end": 1590.43, "word": " he's", "probability": 0.4954833984375}, {"start": 1590.43, "end": 1590.59, "word": " telling", "probability": 0.6201171875}, {"start": 1590.59, "end": 1590.81, "word": " me,", "probability": 0.86279296875}], "temperature": 1.0}, {"id": 66, "seek": 161926, "start": 1591.68, "end": 1619.26, "text": "Note that for a closed loop, the condition as Batool said would be zero. So I made it bigger and I said, the magnetic force on any closed loop, on condition that the magnetic field is uniform. Because if the magnetic field is not uniform, you can't let anything go out. And it has to go inside, it becomes a complicated process. Okay? The magnetic force on any closed current loop in a uniform magnetic field must be zero. Must be zero. 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Instead of this, let's look at it. The law says that FM equals IL cross B. Is it correct or not? How do you get this direction? Don't you put your finger on the fourth direction? Speed. Turn towards B and give F. And what do I do here? He told me that there is no V. 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Why? Because the angle is zero. Of course, even if it is 180, it is still zero. So the force there is zero. This is just one. Right or not? As magnitude. Well, look at the difference between A and B. Why is A greater? Because the angle is 90 and the angle is 25. So A is greater than B. 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Okay, girls? Good. So, subtract A, then B and C, then D. Okay, girls? Okay. 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In the end, when I find a solution, to know whether my solution is correct or not, if both sides are not equal and opposite each other, my answer will be correct? 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Good. 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Look at our hands. Can four fingers do this? 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So that I can rotate. If you do that, can I rotate towards B? Sorry. Sorry. You can't move. So I have to do that, girls. It's not the direction of the current. Do you rotate towards B or not? Understand how? Out of the beige. Did it come out like this or not? Out of the beige. Nice. Let's come to green. Green is the condition. 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It is the definition of verses from the beginning of the word to the end of the word. How do you know the beginning of the word to the end of the word? The direction. Not someone who always says these things in English from left to right. No, the direction of the direction. The green means what is the condition? What is the direction? 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We don't have airplanes here, right? Do you know about air conditioners? They're not air conditioners, but airplanes are better. Do you know about airplanes? If you turn it on, does it work? Or does it have a button that you have to press? What happens when you press the button? A plane enters the plane enters the plane. Do you know about airplanes? You have very few eyes that I can see. 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And all this is a movement, movement, movement. Its origin is this. Its origin is this law. Did you get it? When we say movement and rotation, does it mean torque or not? The torque. 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What do you mean by bravo? What are you talking about? In the direction of the rotation of the clock, or this one. Does it mean that it is rotated horizontally? The opposite of each other? No, not with each other. How can you say that it is rotated? With each other. So it is not rotated horizontally. Does it rotate or does it not rotate? The total torque, the total torque is H plus H because they are together. 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we rotate, we want to get torque. Does torque equal power in agriculture or not?", "tokens": [1033, 11, 321, 13121, 11, 321, 528, 281, 483, 16437, 13, 4402, 16437, 2681, 1347, 294, 14837, 420, 406, 30], "avg_logprob": -0.8571428344363258, "compression_ratio": 1.1012658227848102, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2745.33, "end": 2745.93, "word": " Okay,", "probability": 0.1634521484375}, {"start": 2746.57, "end": 2746.83, "word": " we", "probability": 0.2364501953125}, {"start": 2746.83, "end": 2747.11, "word": " rotate,", "probability": 0.3154296875}, {"start": 2747.75, "end": 2748.83, "word": " we", "probability": 0.200439453125}, {"start": 2748.83, "end": 2749.17, "word": " want", "probability": 0.1771240234375}, {"start": 2749.17, "end": 2749.33, "word": " to", "probability": 0.64111328125}, {"start": 2749.33, "end": 2749.55, "word": " get", "probability": 0.64208984375}, {"start": 2749.55, "end": 2750.13, "word": " torque.", "probability": 0.490234375}, {"start": 2750.43, "end": 2750.67, "word": " Does", "probability": 0.23046875}, {"start": 2750.67, "end": 2751.61, "word": " torque", "probability": 0.61474609375}, {"start": 2751.61, "end": 2751.91, "word": " equal", "probability": 0.489990234375}, {"start": 2751.91, "end": 2752.21, "word": " power", "probability": 0.35205078125}, {"start": 2752.21, "end": 2752.31, "word": " in", "probability": 0.83984375}, {"start": 2752.31, "end": 2752.65, "word": " agriculture", "probability": 0.6630859375}, {"start": 2752.65, "end": 2752.77, "word": " or", "probability": 0.42041015625}, {"start": 2752.77, "end": 2753.01, "word": " not?", "probability": 0.91455078125}], "temperature": 1.0}, {"id": 113, "seek": 278056, "start": 2753.78, "end": 2780.56, "text": "and the agriculture here is equal to this distance and this distance is half distance and half torque, right? He said let's try He said I brought you with me because you are beautiful He said this is what you call out of the bush So this torque is 2 and this torque is 4, okay? When I came and saw the forces, one was like this and the other was like this The force is zero but the torque is not zero, okay?", "tokens": [474, 264, 14837, 510, 307, 2681, 281, 341, 4560, 293, 341, 4560, 307, 1922, 4560, 293, 1922, 16437, 11, 558, 30, 634, 848, 718, 311, 853, 634, 848, 286, 3038, 291, 365, 385, 570, 291, 366, 2238, 634, 848, 341, 307, 437, 291, 818, 484, 295, 264, 19910, 407, 341, 16437, 307, 568, 293, 341, 16437, 307, 1017, 11, 1392, 30, 1133, 286, 1361, 293, 1866, 264, 5874, 11, 472, 390, 411, 341, 293, 264, 661, 390, 411, 341, 440, 3464, 307, 4018, 457, 264, 16437, 307, 406, 4018, 11, 1392, 30], "avg_logprob": -0.6055107373063282, "compression_ratio": 1.8584474885844748, "no_speech_prob": 5.4836273193359375e-06, "words": [{"start": 2753.78, "end": 2753.98, "word": "and", "probability": 0.1800537109375}, {"start": 2753.98, "end": 2754.08, "word": " the", "probability": 0.4169921875}, {"start": 2754.08, "end": 2754.4, "word": " agriculture", "probability": 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"probability": 0.9111328125}], "temperature": 1.0}, {"id": 121, "seek": 295782, "start": 2943.5, "end": 2957.82, "text": " Chapter 1. This is a magnetic dipole moment. We'll talk about it later. It's not a problem. It's one of the solutions. It's not the first time. It's not a problem. 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diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/0HTI94jFUyM.srt b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/0HTI94jFUyM.srt
new file mode 100644
index 0000000000000000000000000000000000000000..8794ce399659bf0a742f89e80f301e690e3791a9
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/0HTI94jFUyM.srt
@@ -0,0 +1,2075 @@
+1
+00:00:21,290 --> 00:00:23,210
+بسم الله الحمد لله والصلاة والسلام علي رسول الله
+
+2
+00:00:23,210 --> 00:00:26,290
+اليوم إن شاء الله شباب هنشوف الـ section الأخير
+
+3
+00:00:26,290 --> 00:00:29,810
+مؤقتا في الـ chapter الأول بحيث أن في عندنا section
+
+4
+00:00:29,810 --> 00:00:33,410
+ثاني المفروض اللي هو طرق الإثبات الرياضي بس هأخره
+
+5
+00:00:33,410 --> 00:00:36,690
+شوية عشان نشوف كيف تمشي الأمور معنا لكن الـ role
+
+6
+00:00:36,690 --> 00:00:40,930
+of inferences لما بتكلم inferences طرق الاستنباط
+
+7
+00:00:40,930 --> 00:00:45,370
+أو التخمين، استنباط أو التخمين، قوانين الاستنباط أو
+
+8
+00:00:45,370 --> 00:00:49,400
+قوانين الاختزال، سميها زي ما بدك، في الآخر أنا هكون
+
+9
+00:00:49,400 --> 00:00:53,020
+شوف مجموعة من القوانين هتلزمني في الإثبات الرياضي
+
+10
+00:00:53,020 --> 00:00:55,120
+عشان هيك بقول لك ممكن أنا هذا الـ section أرجع له
+
+11
+00:00:55,120 --> 00:01:02,420
+لاحقا، بشكل عام، بشكل عام أي نظرية بدنا نثبتها، تمام
+
+12
+00:01:02,420 --> 00:01:07,460
+لازم يكون فيها جزئيتين واضحتين جدا، الأولى الـ
+
+13
+00:01:07,460 --> 00:01:10,620
+condition أو الـ hypothesis أو الـ premises حسب
+
+14
+00:01:10,620 --> 00:01:15,900
+التسمية، الشرط، والـ conclusion المحصلة، تعال نشوف مع
+
+15
+00:01:15,900 --> 00:01:23,260
+بعض مثال بسيط التالي، بقول لي حاصل جمع the sum
+
+16
+00:01:23,260 --> 00:01:34,220
+of any two odd integers is
+
+17
+00:01:34,220 --> 00:01:41,820
+an even number.
+
+18
+00:01:41,820 --> 00:01:42,600
+even integer
+
+19
+00:01:45,350 --> 00:01:50,350
+true، هذه نظرية لأن فيها condition، اه فيها
+
+20
+00:01:50,350 --> 00:01:54,350
+condition، ايش الـ condition؟ أن يكون في عندي two
+
+21
+00:01:54,350 --> 00:02:00,710
+integers ووصفهم ايش؟ odd، يعني أنا في عندي a والـ
+
+22
+00:02:00,710 --> 00:02:09,550
+b are odd integers، طيب
+
+23
+00:02:09,550 --> 00:02:13,610
+conclusion، هاي condition، كم condition يا شباب؟
+
+24
+00:02:13,610 --> 00:02:20,280
+موجود عندي اثنين، a is an integer و b is an integer،
+
+25
+00:02:20,280 --> 00:02:26,800
+conclusion، a + b، عارف ليش لما قلت لك two
+
+26
+00:02:26,800 --> 00:02:31,040
+conditions؟ لأن هذا عبارة عن preposition، a is an odd
+
+27
+00:02:31,040 --> 00:02:35,120
+integer، تقدر تحكملي إياها ولا تقدرش؟، b is an odd integer،
+
+28
+00:02:35,120 --> 00:02:41,380
+second preposition، والرابط اللي بينهم الـ and، والـ
+
+29
+00:02:41,380 --> 00:02:51,120
+conclusion، a + b is an even integer، هذه الخلاصة، one
+
+30
+00:02:51,120 --> 00:02:54,040
+conclusion، one proposition، لاحظ أن أنا اتكلم على
+
+31
+00:02:54,040 --> 00:02:58,880
+three propositions، اثنين منهم يقولوا للتالت
+
+32
+00:02:58,880 --> 00:03:04,440
+الآن هذه الـ conditions مهمة جدا عشان أنا أقدر أثبت
+
+33
+00:03:04,440 --> 00:03:10,620
+النظريات، طيب، هنرجع للمثال هذا، الـ correct proof هو
+
+34
+00:03:10,620 --> 00:03:16,980
+الإثبات الرياضي الصحيح هو بتكون من التالي: لو كانت الـ
+
+35
+00:03:16,980 --> 00:03:21,680
+condition true، لو كانت الـ condition true هتقول إن
+
+36
+00:03:21,680 --> 00:03:26,320
+الـ conclusion صحيحة، الـ conclusion هتكون true، و
+
+37
+00:03:26,320 --> 00:03:29,540
+بالتالي الـ conditions تقول الـ conclusion دائما
+
+38
+00:03:29,540 --> 00:03:36,860
+هتكون توتولوجي، دائما الـ true تقول الـ true، فبتكلم
+
+39
+00:03:36,860 --> 00:03:39,640
+قاعد على true لأن الـ true تقول الـ true دائما هتكون
+
+40
+00:03:39,640 --> 00:03:44,740
+قيمتها يعني هيك: true implies true، equivalent to
+
+41
+00:03:44,740 --> 00:03:52,240
+true، وبالتالي توتولوجي، تمام، دعونا نشوف هذا المثال
+
+42
+00:03:52,240 --> 00:03:55,840
+كيف ممكن أن أنا أروح أثبته؟ لو أنا بدأت أروح أثبت
+
+43
+00:03:55,840 --> 00:03:59,380
+بدي أبدأ من مين يا شباب؟ بدي أبدأ من الـ conditions
+
+44
+00:03:59,380 --> 00:04:11,720
+أبدأ أفسر شو يعني؟ a is odd، معناته a = 2k
+
+45
+00:04:12,260 --> 00:04:21,360
+± 1، والـ k تنتمي إلى الـ Z، لأي عدد
+
+46
+00:04:21,360 --> 00:04:28,920
+فردي يُكتب على صورة 2 في عدد صحيح ± 1
+
+47
+00:04:28,920 --> 00:04:32,620
+اثنين في العدد الصحيح دائما الشباب، اثنين في
+
+48
+00:04:32,620 --> 00:04:37,790
+أي عدد، الناتج بيطلع عدد زوجي، و لا بصبوط؟ طب والعدد
+
+49
+00:04:37,790 --> 00:04:42,090
+الفردي، إما أكبر من عدد زوجي بواحد أو أقل منه
+
+50
+00:04:42,090 --> 00:04:47,470
+بواحد، فأنت ممكن تعتمد على الصيغة هذه بشكل عام، أو
+
+51
+00:04:47,470 --> 00:04:50,050
+تعتمد على واحدة منهم، ± حسب أنت إيش بدك
+
+52
+00:04:50,050 --> 00:04:54,390
+تمام، والـ k هي عبارة عن، عشان أقول arbitrary، لأنه
+
+53
+00:04:54,390 --> 00:04:58,090
+محددليش هو الثلاثه، محددليش الخمسة، جايب لي أي odd number
+
+54
+00:04:58,090 --> 00:05:00,410
+فبالتالي أنا بدي أروح أكتب صورة الـ odd number بشكل
+
+55
+00:05:00,410 --> 00:05:06,180
+عام، طيب، عشان أمثل الخمسة، الـ k لازم تكون ثلاثة
+
+56
+00:05:06,180 --> 00:05:10,960
+اثنين في ثلاثة ستة، ناقص واحد، أول k بتبقى تساوي اثنين
+
+57
+00:05:10,960 --> 00:05:14,980
+اثنين في اثنين أربعة، زائد واحد، فلنكن نعتمد على
+
+58
+00:05:14,980 --> 00:05:23,400
+واحدة بس و نسيب الثانية، تمام، الـ b أسقط، معناته
+
+59
+00:05:23,400 --> 00:05:29,500
+الـ b بتبقى تساوي 2h + 1
+
+60
+00:05:31,040 --> 00:05:37,360
+والـ h تنتمي لـ Z، بالمناسبة، ما بنفعش أقول ثلاثة فاصلة
+
+61
+00:05:37,360 --> 00:05:45,980
+خمسة is odd، هذا الكلام الصحيح، ليش؟ لأن الـ odd فقط
+
+62
+00:05:45,980 --> 00:05:49,160
+الـ odd with even، مع الأعداد الصحيحة، مش مع الأعداد
+
+63
+00:05:49,160 --> 00:05:53,100
+الـ real number، تمام؟ هاي الـ conditions، هاي الـ conditions
+
+64
+00:05:53,100 --> 00:05:58,740
+اللي عندي، طيب، تمام، يعني هدول هيك، وأنا قاعد بقول لك
+
+65
+00:05:58,740 --> 00:06:05,240
+true، A is odd، هيها، B is odd، هيها، true، true، and true
+
+66
+00:06:05,240 --> 00:06:10,300
+true، لأن هذا اللي لازم يوصلني للـ conclusion إن الـ
+
+67
+00:06:10,300 --> 00:06:13,960
+A + B is even، ولازم تكون true، تعال نشوف
+
+68
+00:06:13,960 --> 00:06:16,880
+معناته إن أنا بدي أروح للـ conclusion، A + B
+
+69
+00:06:16,880 --> 00:06:24,440
+يساوي، عوض عن قيمة A بقيمتها: 2k + 1 +
+
+70
+00:06:24,440 --> 00:06:29,040
+لقيمة B: 2h + 1، اجمع
+
+71
+00:06:30,370 --> 00:06:41,790
+2k + 2h + 2
+
+72
+00:06:41,790 --> 00:06:49,030
+k + h + 2، مصبوط؟ الآن هذا الرقم بغض النظر إيش
+
+73
+00:06:49,030 --> 00:06:58,240
+كانت قيمته، ينتمي إلى Z، لأن k is an integer، h هو integer
+
+74
+00:06:58,240 --> 00:07:02,680
+و 2 هو integer، وحاصل جمع integers بيؤدي إلى
+
+75
+00:07:02,680 --> 00:07:08,720
+integer، وبالتالي اثنين في integer، integer، ومش بس هيك
+
+76
+00:07:08,720 --> 00:07:14,620
+even number، even integer، مش هي صورة الـ integer، مش هي
+
+77
+00:07:14,620 --> 00:07:18,180
+صورة الـ even integer، وبالتالي إحنا وصلنا، وصارت الـ
+
+78
+00:07:18,180 --> 00:07:23,060
+conclusion تبعتنا هذه true، true، فكانت الـ condition
+
+79
+00:07:23,060 --> 00:07:28,650
+true، قالت إن الـ conclusion تبعتنا المحصلة true، هذا
+
+80
+00:07:28,650 --> 00:07:33,150
+الكلام مهم لما أنا بدي أجي أثبت القوانين كلها
+
+81
+00:07:33,150 --> 00:07:38,310
+فلازم أنا أتسلسل أو أمشي مع البرهان بكلام منطقي
+
+82
+00:07:38,310 --> 00:07:42,670
+100%، بيبدأ من وين؟ بيبدأ من عند الـ condition اللي
+
+83
+00:07:42,670 --> 00:07:47,490
+لازم تكون true، ما بينفعش في لحظة من اللحظات أجي أقول
+
+84
+00:07:47,490 --> 00:07:54,190
+الـ b، هيها،
+
+85
+00:07:54,190 --> 00:07:59,470
+b is not odd، صار الـ condition false، تعال اجمع
+
+86
+00:07:59,470 --> 00:08:04,290
+هتلاقي إن الـ output، الـ conclusion is all is false
+
+87
+00:08:04,290 --> 00:08:07,110
+لأن القيمة اللي كانت عندي معي odd ما كانتش even
+
+88
+00:08:07,110 --> 00:08:11,570
+لأن 2k + 1 + 2h + 1 تساوي
+
+89
+00:08:11,570 --> 00:08:15,810
+2(k+h) + 2، وهذا صورة
+
+90
+00:08:15,810 --> 00:08:20,110
+العدد الزوجي، فلما كانت الـ condition عندي false، أدت
+
+91
+00:08:20,110 --> 00:08:23,960
+إلى أن الـ conclusion بتطلع معي false، وبالتالي أي
+
+92
+00:08:23,960 --> 00:08:27,060
+نظرية صحيحة، لازم تكون الشروط تبعتها، الـ condition
+
+93
+00:08:27,060 --> 00:08:31,520
+أو الـ hypothesis تبعتها true، تمام، بتقدم لي
+
+94
+00:08:31,520 --> 00:08:34,840
+conclusion true، otherwise بتكون النظرية دي ما بتصحش
+
+95
+00:08:34,840 --> 00:08:43,700
+نرميها بعيد عنها لما تكونش صحيحة، تمام، الآن العلاقة
+
+96
+00:08:43,700 --> 00:08:48,940
+بين الـ condition والـ conclusion، هتعامل معاهم
+
+97
+00:08:55,710 --> 00:09:00,650
+أو عوامل إثبات صحة النظرية اللي موجودة عندنا بين
+
+98
+00:09:00,650 --> 00:09:05,440
+الاثنين، إن الـ condition تقول لي الـ
+
+99
+00:09:05,440 --> 00:09:08,360
+conclusion، هذه العوامل اللي هي الـ biconditional، مش
+
+100
+00:09:08,360 --> 00:09:11,480
+إحنا قلنا p implies q، سمينا الـ implies
+
+101
+00:09:11,480 --> 00:09:16,280
+operator، وسمينا الـ p والـ q عبارة عن argument
+
+102
+00:09:16,280 --> 00:09:19,100
+للمسألة، أو الـ operand تبع المسألة اللي عندها
+
+103
+00:09:19,100 --> 00:09:24,480
+وبالتالي هتعامل معاهم as conclusion، طيب، الآن شو
+
+104
+00:09:24,480 --> 00:09:27,880
+علاقة هذا في الإثبات؟ هو أساس الإثبات إنه فعليا
+
+105
+00:09:27,880 --> 00:09:30,640
+اللي تقول، والـ condition اللي موجودة عندها، و
+
+106
+00:09:30,640 --> 00:09:34,800
+بالتالي الـ argument connected by proper rules of
+
+107
+00:09:34,800 --> 00:09:37,600
+inferences، وبالتالي الـ argument تبعتي هذه أنا
+
+108
+00:09:37,600 --> 00:09:43,060
+بنتقل، ممكن من خلال الـ rules of inferences، الـ rules
+
+109
+00:09:43,060 --> 00:09:46,840
+of inferences، قوانين التخمين أو الاستنباط أو
+
+110
+00:09:46,840 --> 00:09:47,500
+الإثبات
+
+111
+00:09:49,970 --> 00:09:52,550
+أو الـ Step Down، سميهم زي ما بدك، أي ترجمة ممكن تجي
+
+112
+00:09:52,550 --> 00:09:59,490
+على بالك إن فرنسية، التخمين بالمناسبة، الآن بتزودني
+
+113
+00:09:59,490 --> 00:10:04,510
+بتفسير لكل step في البرهان، لما أروح أنا بـ step
+
+114
+00:10:04,510 --> 00:10:08,890
+لمقطع بمقطع، ليش؟ ليش أنا بدلتها؟ بناء على إيش؟
+
+115
+00:10:08,890 --> 00:10:12,830
+تمام؟ بناء على إن هذا الـ role أصبح fact وأنا بقدر
+
+116
+00:10:12,830 --> 00:10:18,860
+أعتمد عليها في الإثبات، تمام؟ دعونا نشوف واحد من الـ
+
+117
+00:10:18,860 --> 00:10:23,140
+rules of inferences، بقول كتابة هاي الـ argument
+
+118
+00:10:23,140 --> 00:10:27,520
+تبعتي، كل آياتها، هذا الـ rule، الآن من الـ conditions
+
+119
+00:10:27,520 --> 00:10:34,340
+p، و p implies q، والعلاقة بين الـ two conditions
+
+120
+00:10:34,340 --> 00:10:46,770
+دائما and، يقول لي q، يعني بين قوسين p and p implies
+
+121
+00:10:46,770 --> 00:10:53,370
+q، الكل يقول لي q، هذا الـ rule أو هذا القانون أنا
+
+122
+00:10:53,370 --> 00:10:57,970
+بقدر أشوفه، بمجرد ما أشوف في الإثبات الرياضي تبعي حصلت
+
+123
+00:10:57,970 --> 00:11:03,070
+على الـ two conditions هدول، بقدر أشيلهم، أشيلهم
+
+124
+00:11:03,070 --> 00:11:09,560
+أحذفهم وأحط بدلهم مين؟ q، وحط بدلهم q، وهنا بصير دور
+
+125
+00:11:09,560 --> 00:11:13,920
+أو أهمية الـ rules of inferences في الإثبات، تعال
+
+126
+00:11:13,920 --> 00:11:18,860
+نشوف أساسا هل فعليا هذا زي ما هو بقول، إن هذه دائما
+
+127
+00:11:18,860 --> 00:11:22,300
+لازم تكون توتولوجي عشان أثبتها، توتولوجي، كيف بدي
+
+128
+00:11:22,300 --> 00:11:26,280
+أعمل يا شباب؟ عشان
+
+129
+00:11:26,280 --> 00:11:31,040
+أثبت إن هذه عبارة عن توتولوجي، إيش المفروض أسوي؟
+
+130
+00:11:31,040 --> 00:11:33,820
+افكر، الـ implies
+
+131
+00:11:37,090 --> 00:11:41,270
+100%، يعني أنا بدي أستخدم الطرق اللي شفناها سابقا
+
+132
+00:11:41,270 --> 00:11:49,850
+عشان أثبت القيمة اللي عندي، تمام، p and p implies
+
+133
+00:11:49,850 --> 00:11:58,210
+q، الكل implies q، بأظبط بقول إن هذا توتولوجي
+
+134
+00:11:58,210 --> 00:12:04,490
+الآن بدي أذكرك، p implies q equivalent to not p or q، وفي
+
+135
+00:12:04,490 --> 00:12:09,660
+equivalent لشغلة ثانية بس ما بتلزمنيش الآن، not p or q
+
+136
+00:12:09,660 --> 00:12:13,480
+implies، not p، not q implies not p، الآن ليش
+
+137
+00:12:13,480 --> 00:12:22,120
+هاد ما بتلزمنيش لأن هو عم يقعد يقول لي أثبت أو بدرس
+
+138
+00:12:22,120 --> 00:12:25,460
+بتقول لي إن هذا tautology، tautology يعني بدي true، عشان
+
+139
+00:12:29,740 --> 00:12:37,020
+بدي true، لو أنا قدرت أحصل على true، ونفيها ستكون حصيلة
+
+140
+00:12:37,020 --> 00:12:41,180
+على الـ true، وهذا ما يلزم، الآن إن أنا بتلزمني
+
+141
+00:12:41,180 --> 00:12:44,260
+الصورة الثانية اللي موجودة عندي، وبالتالي هذه تكافئ
+
+142
+00:12:44,260 --> 00:12:55,640
+أبدأ بالأول، نفي الـ p and نفي الـ p
+
+143
+00:12:55,640 --> 00:13:00,880
+implies q، مظبوط؟
+
+144
+00:13:02,320 --> 00:13:06,660
+أنا بكل حولتها مرة واحدة، نفي الجملة هذا كله هو نفي
+
+145
+00:13:06,660 --> 00:13:12,820
+للجملة، والجملة هذه p implies q برضه بدلتها not p or q
+
+146
+00:13:12,820 --> 00:13:22,160
+الآن بدأت أدخل النفي على الجملة هذه، نفي الـ p or نفي
+
+147
+00:13:22,160 --> 00:13:29,800
+الجملة هذه، نفي الجملة هذه معناته p and not q الكل or
+
+148
+00:13:29,800 --> 00:13:37,680
+مظبوط هيك؟ هي ما زالت قيمتها هيك، الآن بدي أدخل بدي
+
+149
+00:13:37,680 --> 00:13:54,920
+أوزع، نفي الـ p، نفي الـ p or  p and نفي الـ p or نفي الـ q or q
+
+150
+00:13:54,920 --> 00:14:05,490
+مظبوط؟ p or not p = true، طيب هذه صارت true، الـ true and x
+
+151
+00:14:05,490 --> 00:14:09,990
+إحنا في عندنا قانون بيقول لي إن الـ true and الـ x
+
+152
+00:14:09,990 --> 00:14:14,190
+تكافئ الـ x، لا تكافئ الـ true مع الـ or تكافئ
+
+153
+00:14:14,190 --> 00:14:24,150
+وبالتالي هذه تكافئ هيك، صارت not p or not q or
+
+154
+00:14:24,150 --> 00:14:29,550
+q، خلصنا
+
+155
+00:14:29,550 --> 00:14:33,810
+من دي مورغان، دي مورغان كانت فوق لأن هان إحنا الآن
+
+156
+00:14:33,810 --> 00:14:37,050
+كل العمليات اللي عندي من نفس الرتبة اللي هي الـ or
+
+157
+00:14:37,050 --> 00:14:40,690
+وبالتالي بقدر أشتغل معها، توزيع، التوزيع كانت فوق
+
+158
+00:14:40,690 --> 00:14:47,550
+توزيع الـ or على الـ and والعكس، بس الآن تجميع، معناته
+
+159
+00:14:47,550 --> 00:14:56,370
+أنا عندي not p or not q or q، هذه صارت true، وهذه
+
+160
+00:14:56,370 --> 00:15:00,850
+تكافئ not p or true، تكافئ
+
+161
+00:15:02,300 --> 00:15:05,980
+true، وبالتالي هي عبارة عن tautology
+
+162
+00:15:08,820 --> 00:15:11,840
+إذا كان الحل الثاني لو إحنا مش قادرين نثبت بالشكل
+
+163
+00:15:11,840 --> 00:15:15,980
+هذا الشيء، ماذا نسوي؟ نستخدم جدول الاحتمالات، هستخدم
+
+164
+00:15:15,980 --> 00:15:18,720
+جدول الاحتمالات كمان شوية بس لشغلة ثانية، وبالمرة
+
+165
+00:15:18,720 --> 00:15:22,540
+بنكون أثبتناها بالشكل الثاني، وبالتالي أصبحت عندي الـ
+
+166
+00:15:22,540 --> 00:15:26,680
+rules of inferences، هذه اللي اسمها Modus Ponens
+
+167
+00:15:26,680 --> 00:15:29,780
+بغض النظر عن التسميات يا شباب، مش ضروري تحفظها لأن
+
+168
+00:15:29,780 --> 00:15:33,120
+كلها مسميات لاتينية، ما بتعنيني كتير، قبل ما يعنيني
+
+169
+00:15:33,120 --> 00:15:37,530
+أنا التطبيق تبع في القانون اللي موجود عندي، هنتبع
+
+170
+00:15:37,530 --> 00:15:42,470
+الـ rule، مين الـ hypothesis؟ هيهم p and p implies q
+
+171
+00:15:42,470 --> 00:15:45,970
+يعني في عندي two conditions، مجموعين في compound
+
+172
+00:15:45,970 --> 00:15:50,150
+condition بينهم and، مكتوبين بالصورة هذه، therefore
+
+173
+00:15:50,150 --> 00:15:56,990
+ولذلك الـ conclusion قادتني إلى q، الآن
+
+223
+00:20:22,180 --> 00:20:28,270
+اللي منها وفاق بقول لو كانت عندك الـ AB لو كانت عندك
+
+224
+00:20:28,270 --> 00:20:28,530
+الـ B
+
+225
+00:20:35,640 --> 00:20:40,000
+P implies P or Q لو كانت عندك الـ condition P
+
+226
+00:20:40,000 --> 00:20:45,340
+لحالها is it true فتحط الـ D نقلة أو تقدي إلى true
+
+227
+00:20:45,340 --> 00:20:51,100
+كـ conclusion فأنت ضمنت عندك الـ P مع or يعني الـ P
+
+228
+00:20:51,100 --> 00:20:54,360
+بتعامل معها as a true value أصبحت true أيش ما تحط
+
+229
+00:20:54,360 --> 00:20:58,500
+لها مع الـ or فبتكون الـ conclusion تبعتك أيش؟ true
+
+230
+00:20:58,500 --> 00:21:01,740
+وبالتالي هذا الـ role مهم جدا يا شباب لما نيجي
+
+231
+00:21:01,740 --> 00:21:05,320
+نتكلم على الاختزال أو اثبات لأن فعلا هنشوف كمان
+
+232
+00:21:05,320 --> 00:21:10,480
+مرة مثال أو اتنين من أجل اثبات النظريات بالاعتماد
+
+233
+00:21:10,480 --> 00:21:15,840
+على الـ role of inferences طيب تمام الآن أنا في
+
+234
+00:21:15,840 --> 00:21:21,080
+عندي شغلة مهمة بقدر الـ role of inferences اللي
+
+235
+00:21:21,080 --> 00:21:24,400
+احنا بنسميها الـ argument اتفقنا الـ argument هي
+
+236
+00:21:24,400 --> 00:21:29,510
+عبارة عن مجموعة أيش؟ مجموعة عوامل عوامل أيش؟
+
+237
+00:21:29,510 --> 00:21:33,350
+مجموعة الـ conditions والـ conclusion مع بعض الـ
+
+238
+00:21:33,350 --> 00:21:36,650
+condition والـ conclusion مع بعض مثلا منهم أيش؟
+
+239
+00:21:36,650 --> 00:21:43,930
+argument الـ argument تبعتي هذه علاقتها مع بعض مثل
+
+240
+00:21:43,930 --> 00:21:48,970
+الـ rule of inferences أن عندي أكثر من hypothesis
+
+241
+00:21:48,970 --> 00:21:54,230
+بتؤدي لـ conclusion بقول عن الـ argument valid بقول
+
+242
+00:21:54,230 --> 00:21:59,960
+عن الـ argument valid whenever وين ما بلاقي أن الـ
+
+243
+00:21:59,960 --> 00:22:04,180
+hypothesis مع بعضهم كلهم are true  واتذكر أن الـ
+
+244
+00:22:04,180 --> 00:22:11,640
+hypothesis بواحد and باتنين and بتلاتة إلى and بمليون
+
+245
+00:22:11,640 --> 00:22:15,140
+لما يكونوا كلهم مع بعض true طب عشان كلهم مع بعض
+
+246
+00:22:15,140 --> 00:22:20,140
+يكونوا true لازم كل واحدة بشكل مستقل تكون true
+
+247
+00:22:20,140 --> 00:22:24,220
+هتؤدي إلى أن الـ conclusion تبعتي لازم تكون .. طيب لو
+
+248
+00:22:24,220 --> 00:22:28,860
+واحدة كانت منهم false يعني ليش أفحص؟ يعني ليش؟
+
+249
+00:22:28,860 --> 00:22:32,080
+أنا يعني حالة واحدة فقط أن وين ما تكون الـ
+
+250
+00:22:32,080 --> 00:22:36,300
+condition كلها true لازم الـ conclusion يكون true
+
+251
+00:22:36,300 --> 00:22:39,400
+وبالتالي هذا الـ argument أو هذه التركيبة أو هذه
+
+252
+00:22:39,400 --> 00:22:43,380
+التوليفة أو هذه النظرية الـ argument تبعتها يا أستاذ
+
+253
+00:22:44,210 --> 00:22:47,990
+valid valid بقدر أسعى في اثباتها أو أقدر أتكلم
+
+254
+00:22:47,990 --> 00:22:52,190
+عليها بالشكل هذا عشان ما أطولش كثير احنا في
+
+255
+00:22:52,190 --> 00:22:56,530
+الموضوع هذا تعالَ نشوف أول role of inferences اللي
+
+256
+00:22:56,530 --> 00:22:57,710
+احنا شفناها قبل شوية
+
+257
+00:23:14,870 --> 00:23:20,550
+هو أيش قاعد بيقول لي whenever P implies the
+
+258
+00:23:20,550 --> 00:23:26,570
+condition is true يعني P لازم تكون true وأن هذه
+
+259
+00:23:26,570 --> 00:23:30,250
+تكون true هتقول لمين؟ لو بدي أتكلمها بشكل بسيط
+
+260
+00:23:30,250 --> 00:23:32,910
+whenever  نتيجة هذا الكلام بيكون true هذه ما تكون
+
+261
+00:23:32,910 --> 00:23:38,130
+true وهذه لازم تكون true هذه متى بتكون true بي
+
+262
+00:23:38,130 --> 00:23:43,170
+تقول أو true تقول إلى .. فش غير هيك هذه الحالة
+
+263
+00:23:43,170 --> 00:23:48,660
+الوحيدة اللي عندي  مصدوق ولا لأ؟ هذه حالات ثانية
+
+264
+00:23:48,660 --> 00:23:53,320
+ممكن تتمشي فيها false تقول إلى true و false تقول
+
+265
+00:23:53,320 --> 00:23:56,160
+إلى false هذه برضه بتعطيني الـ implication true بس
+
+266
+00:23:56,160 --> 00:24:01,320
+ما أقدرش استخدمهم ليش؟ لأن حددت قيمة الـ B مسبقا
+
+267
+00:24:01,320 --> 00:24:04,400
+بإعتماد على مين؟ الـ and أو بين جملة الـ and اللي
+
+268
+00:24:04,400 --> 00:24:08,580
+ألزمتني أشتغل بـ هذه الحالة وبالتالي أنا صرت هي
+
+269
+00:24:08,580 --> 00:24:12,920
+هي الحالة الوحيدة اللي عندي الحالة الوحيدة B is
+
+270
+00:24:12,920 --> 00:24:17,470
+true و Q is true وبالتالي بتروح تفحص الـ implication
+
+271
+00:24:17,470 --> 00:24:22,730
+true implies true true وبالتالي هتصبح  الـ
+
+272
+00:24:22,730 --> 00:24:28,030
+implication true and true implies true الكل
+
+273
+00:24:28,030 --> 00:24:38,010
+implies true  تلقى true true and true true implies
+
+274
+00:24:38,010 --> 00:24:41,830
+true معناته هذا بتكلم على valid argument بتتكلم على
+
+275
+00:24:41,830 --> 00:24:45,710
+valid argument ولو بدي أروح بشغل أطول شوية ممكن
+
+276
+00:24:45,710 --> 00:24:48,750
+يكون أسهل بالنسبة إليك الآن ابني جدول الاحتمالات
+
+277
+00:24:48,750 --> 00:24:53,370
+لـ tautology هذه عبارة عن أيش يا شباب؟ عبارة عن
+
+278
+00:24:53,370 --> 00:24:57,810
+tautology يعني قيمة الـ condition هذا أو الـ .. هي
+
+279
+00:24:57,810 --> 00:25:04,550
+عبارة عن الـ true كان variable عندي أيش؟  B و Q
+
+280
+00:25:04,550 --> 00:25:12,220
+true true false false true false true false بعد هيك
+
+281
+00:25:12,220 --> 00:25:21,880
+P implies Q true false true true P and P implies Q
+
+282
+00:25:21,880 --> 00:25:31,500
+هاي هم true false false لا بس لحظة شوية هنا الـ
+
+283
+00:25:31,500 --> 00:25:37,890
+true false false false تمام أيش الضغط اللي عندي ضغط
+
+284
+00:25:37,890 --> 00:25:42,830
+اللي عندي الـ role الأخير زي ما هو هيك P and P
+
+285
+00:25:42,830 --> 00:25:49,910
+implies Q الكل implies Q هذا يقول إلى هذا الـ true
+
+286
+00:25:49,910 --> 00:25:57,590
+implies true true false implies true true false
+
+287
+00:25:57,590 --> 00:26:03,000
+implies true true false implies false true لازم
+
+288
+00:26:03,000 --> 00:26:06,320
+يكون كلهم true لأنها عبارة عن tautology لازم يكون
+
+289
+00:26:06,320 --> 00:26:13,700
+كلهم true  مضبوط بس أصبر شوية أصبر كلهم لازم يكونوا
+
+290
+00:26:13,700 --> 00:26:17,100
+true لأن هذه عبارة عن tautology بس ليش أنا بقول
+
+291
+00:26:17,100 --> 00:26:22,680
+valid argument لأن whenever all the hypothesis are
+
+292
+00:26:22,680 --> 00:26:26,100
+true وين الصف اللي فيه الـ hypothesis تبعوني كلهم مع
+
+293
+00:26:26,100 --> 00:26:29,800
+بعض الـ true كم hypothesis أنا عندي؟ كم hypothesis
+
+294
+00:26:29,800 --> 00:26:35,230
+أنا عندي؟ هي الـ hypothesis اللي عندي عندي إثنتين بي
+
+295
+00:26:35,230 --> 00:26:40,510
+هي الـ P والـ P implies Q هيهم متى القيمتين
+
+296
+00:26:40,510 --> 00:26:44,290
+هدول بيكونوا مع بعض true لو طلعناها بس في الصف
+
+297
+00:26:44,290 --> 00:26:51,990
+الأول هان وهان whenever all its hypothesis are
+
+298
+00:26:51,990 --> 00:26:56,390
+true وين ما بتكون الفرضيات تبعها true whenever the
+
+299
+00:26:56,390 --> 00:27:02,110
+hypothesis are true it will lead to the conclusion Is
+
+300
+00:27:02,110 --> 00:27:05,270
+it true؟ وبالتالي هذا الصف هو الوحيد اللي يعنيني
+
+301
+00:27:05,270 --> 00:27:09,470
+عشان أقول عليها valid أو invalid argument. هذه
+
+302
+00:27:09,470 --> 00:27:13,490
+valid argument. ليش؟ لأن وين الـ two arguments أو الـ
+
+303
+00:27:13,490 --> 00:27:18,100
+two hypothesis تبعوني كانوا true؟  بِعطوني true طب
+
+304
+00:27:18,100 --> 00:27:22,100
+الباقي يا أستاذ true وfalse .. false وfalse ..
+
+305
+00:27:22,100 --> 00:27:24,000
+false وfalse .. ماليش داخل فيهم .. خلاص معناته
+
+306
+00:27:24,000 --> 00:27:27,880
+أنا بص بالصف اللي بيحقق الشرط عشان أفحص الـ validity
+
+307
+00:27:27,880 --> 00:27:32,700
+تبع الـ argument اللي عندي otherwise لو كان هذا
+
+308
+00:27:32,700 --> 00:27:37,460
+يقول إلى false معناته
+
+309
+00:27:37,460 --> 00:27:40,360
+خلصنا .. معناته invalid argument .. invalid
+
+310
+00:27:40,360 --> 00:27:42,320
+argument .. تمام؟
+
+311
+00:27:48,350 --> 00:27:55,170
+تعالَ نشوف الـ argument اللي موجود عندي هنا في
+
+312
+00:27:55,170 --> 00:27:58,970
+عند الـ rule of inferences بقول P implies Q و
+
+313
+00:27:58,970 --> 00:28:05,650
+Q implies R therefore P implies R هذا
+
+314
+00:28:05,650 --> 00:28:09,950
+واحد من الـ rules لو بدنا نرجع هنا هيو لا مش الآخر
+
+315
+00:28:09,950 --> 00:28:16,380
+الثالث هيو طيب .. الآن هذا الـ rule .. لما أنا بدي ..
+
+316
+00:28:16,380 --> 00:28:19,420
+كمان مرة أنا جالس يا شباب مش جالس بأثبت أن rule of
+
+317
+00:28:19,420 --> 00:28:23,900
+inferences تمام؟ أنا بدي أثبت أنه valid argument
+
+318
+00:28:23,900 --> 00:28:26,460
+.. جالس بقول لي أفحص الـ argument هذه valid ولا
+
+319
+00:28:26,460 --> 00:28:31,610
+invalid .. من الـ argument اللي عندي أنا هانيجيهم
+
+320
+00:28:31,610 --> 00:28:34,990
+واحد إثنين تلاتة الـ argument هم عبارة عن الـ
+
+321
+00:28:34,990 --> 00:28:39,550
+conditions بالإضافة لمين؟ لـ الـ conclusion لما بدنا
+
+322
+00:28:39,550 --> 00:28:45,810
+جدول الاحتمالات بيهمني الصفوف فقط اللي بتكون فيها الـ
+
+323
+00:28:45,810 --> 00:28:51,570
+two conditions are true  هيبني جدول الاحتمالات هي
+
+324
+00:28:51,570 --> 00:28:55,530
+P وهي Q وهي R مع أن أنا بتكلم عن جدول مكون من
+
+325
+00:28:55,530 --> 00:29:00,790
+تمام صفوف P implies Q و Q implies R
+
+326
+00:29:05,250 --> 00:29:11,290
+روحنا فحصنا الـ argument اللي موجودة عندها hand
+
+327
+00:29:11,290 --> 00:29:18,230
+true الصف هذا لازم أنا أتأكد من قيمته ممتاز ننتقل
+
+328
+00:29:18,230 --> 00:29:23,350
+للي بعده لأ اللي بعده اللي بعده هيو هذا لازم يكون
+
+329
+00:29:23,350 --> 00:29:29,240
+الـ output تبعته true هيو هذا الـ output تبعته true
+
+330
+00:29:29,240 --> 00:29:32,040
+للبعده الـ output تبعته true طب اللي في النص هدول
+
+331
+00:29:32,040 --> 00:29:35,900
+ما يهمنيش لأن هم ما حققوش الـ condition تبع مين؟ تبع الـ
+
+332
+00:29:35,900 --> 00:29:39,260
+valid argument الـ valid argument كان بيقول لي بقول
+
+333
+00:29:39,260 --> 00:29:43,400
+عن هدول valid argument لما بتكون whenever all the
+
+334
+00:29:43,400 --> 00:29:46,920
+hypothesis all the conditions are true وين هم اللي
+
+335
+00:29:46,920 --> 00:29:50,420
+بتبدأ true عليهم في الصفوف المحددة ده باللون
+
+336
+00:29:50,420 --> 00:29:55,060
+الأخضر وبالتالي كانت تعمل lead الصحيحة فهذه صحيحة
+
+337
+00:29:55,060 --> 00:30:00,560
+فهذه صحيحة أيش؟ الـ argument لو أنت جيت هذه
+
+338
+00:30:00,560 --> 00:30:05,800
+الاختلافات ما تكملش خلاص ما تفحصش invalid طب ما هم
+
+339
+00:30:05,800 --> 00:30:11,240
+بيجاوبو في فروع ثانية not all صار في  there
+
+340
+00:30:11,240 --> 00:30:11,840
+exist
+
+341
+00:30:14,330 --> 00:30:17,090
+one row where all the arguments or the hypothesis
+
+342
+00:30:17,090 --> 00:30:21,390
+are true lead to false وبالتالي نفينا الـ
+
+343
+00:30:21,390 --> 00:30:26,490
+definition تبع العناصر اللي موجودة عندها تعالَ
+
+344
+00:30:26,490 --> 00:30:31,350
+نشوف المثال هذا بنعمله ترجمة ونشوف هل هو بيطلع
+
+345
+00:30:31,350 --> 00:30:36,870
+valid argument ولا لأ if I like discrete
+
+346
+00:30:36,870 --> 00:30:40,830
+mathematics إذا
+
+347
+00:30:40,830 --> 00:30:48,440
+أنا حبيت الرياضيات المنفصلة أول شرط false طيب I'll
+
+348
+00:30:48,440 --> 00:30:55,400
+study it معناته أنا بقدر أجي أقول P I like
+
+349
+00:30:55,400 --> 00:31:04,880
+discrete mathematics Q I will study discrete
+
+350
+00:31:04,880 --> 00:31:10,230
+mathematics طبعا لاحظ أن أنا عمال بأفصل .. بدي أوصل
+
+351
+00:31:10,230 --> 00:31:13,810
+الـ conditions تبعي ..الآن لاحظ أنا عمال بأفصل
+
+352
+00:31:13,810 --> 00:31:19,030
+الشباب في .. بأفصل في مين .. بحاول أترجم كل المسألة
+
+353
+00:31:19,030 --> 00:31:22,990
+..الآن صار في عندي الـ argument أو الـ condition
+
+354
+00:31:22,990 --> 00:31:27,360
+الأول P implies Q هذا الـ condition الأول لسة
+
+355
+00:31:27,360 --> 00:31:31,400
+ما وصلتش لـ conclusion either I study I study هي مش
+
+356
+00:31:31,400 --> 00:31:35,220
+مشكلة أو I study مش قضية كثير discrete mathematics
+
+357
+00:31:35,220 --> 00:31:42,120
+or I fail the course هي Q أو هي R I fail رسبت the
+
+358
+00:31:42,120 --> 00:31:47,520
+course الـ course رسبت في المساق معناته الـ
+
+359
+00:31:47,520 --> 00:31:52,540
+condition الثاني عندي either I study I study when
+
+360
+00:31:52,540 --> 00:32:01,190
+Q or R  نقطة حط لي Therefore عشان يقول لي اللي جاي هو
+
+361
+00:32:01,190 --> 00:32:06,350
+عبارة عن إيش؟ عن الـ conclusion Therefore
+
+362
+00:32:06,350 --> 00:32:13,010
+if I fail the course then I don't like discrete
+
+363
+00:32:13,010 --> 00:32:18,770
+mathematics إذا أنا رسبت الـ R تقول إلى  الـ P
+
+364
+00:32:18,770 --> 00:32:28,340
+الـ P مضبوط؟ الآن لاحظ أول شيء ترجمت النص لـ
+
+365
+00:32:28,340 --> 00:32:31,740
+simple proposition بعدين حولته لـ compound
+
+366
+00:32:31,740 --> 00:32:35,060
+proposition بناء على فهم المعادلة therefore كانت
+
+367
+00:32:35,060 --> 00:32:39,180
+الفيصل تقول كل اللي فات عبارة عن الـ conclusion
+
+368
+00:32:39,180 --> 00:32:44,300
+وكانت أنا بتلاحظ الـ first top هذه كانت بتقول لي الـ
+
+369
+00:32:44,300 --> 00:32:47,420
+condition الأول خلص الـ condition الثاني بدأ وما
+
+370
+00:32:47,420 --> 00:32:50,120
+شبه تمام
+
+371
+00:32:50,930 --> 00:32:57,850
+الآن بقول أفحص هل هذا valid argument ولا لأ؟ عشان
+
+372
+00:32:57,850 --> 00:33:00,930
+تفحص الـ validity معناته تبدأ تجيب كل احتمالات اللي
+
+373
+00:33:00,930 --> 00:33:05,050
+بتكون هذه فيها true ف أسهل حاجة بالنسبة لك الجدول
+
+374
+00:33:05,050 --> 00:33:12,130
+الاحتمالات هذا كلام أكيد طيب في
+
+375
+00:33:12,130 --> 00:33:19,310
+جدول الاحتمالات كم صفر محتاجين احنا؟ P وimplies
+
+376
+00:33:19,310 --> 00:33:26,520
+Q و R بعده تمانية true true true true false false
+
+377
+00:33:26,520 --> 00:33:34,540
+false false true true false false true true false
+
+378
+00:33:34,540 --> 00:33:39,680
+false true
+
+379
+00:33:39,680 --> 00:33:46,700
+false true false true false
+
+380
+00:33:50,450 --> 00:33:57,190
+الـ condition الأول P implies Q true implies true
+
+381
+00:33:57,190 --> 00:34:04,770
+true true false false لحظة شوية عشان أنا هحط كل
+
+382
+00:34:04,770 --> 00:34:11,670
+قيمة ما نجوش نضرب هات true هات false هات false
+
+383
+00:34:11,670 --> 00:34:16,410
+هات true true true true
+
+384
+00:34:18,930 --> 00:34:22,910
+P implies Q true implies true true true false
+
+385
+00:34:22,910 --> 00:34:30,170
+false والباقي كله true الـ condition الثاني Q
+
+386
+00:34:30,170 --> 00:34:43,610
+or R Q or R true true true false true true true
+
+387
+00:34:43,610 --> 00:34:51,210
+false Q و R هايهم الإثنتين صحيح صحيح صحيح صحيح خاطئ
+
+388
+00:34:51,210 --> 00:34:56,210
+صحيح صحيح صحيح صحيح خاطئ الآن الشغلة اللي هو عشان
+
+389
+00:34:56,210 --> 00:35:00,770
+تكون هذه valid argument whenever وين ما بتكون عندك
+
+390
+00:35:00,770 --> 00:35:07,650
+الصفوف الإثنتين مع بعض صحيح هاي
+
+391
+00:35:07,650 --> 00:35:13,830
+الصف  هاي الثاني اللي بعده لأ اللي بعده هاي واحدة
+
+392
+00:35:13,830 --> 00:35:19,770
+هاي الإثنتين هاي التلاتة هدول التلات صفوف اللي أنا
+
+393
+00:35:19,770 --> 00:35:25,290
+معني فيهم إذا هدول التلات صفوف عملوا lead implies
+
+394
+00:35:25,290 --> 00:35:28,910
+لـ true معكوا هذا valid argument لو واحدة منهم
+
+395
+00:35:28,910 --> 00:35:32,410
+عملت implies لـ false والباقي عمل لـ true فهي بتكون
+
+396
+00:35:32,410 --> 00:35:38,430
+invalid argument تعالَ نشوف الأخيرة اللي هي الـ R
+
+397
+00:35:38,430 --> 00:35:44,790
+implies الـ P هاي الـ R وهي الـ P true
+
+398
+00:35:44,790 --> 00:35:54,010
+implies false true implies false true
+
+399
+00:35:54,010 --> 00:36:02,070
+implies false false خلصنا نفي نقطة يعني ع ما بنا
+
+400
+00:36:02,070 --> 00:36:06,170
+فيه بقول لك الـ true implies false بناء على الـ role
+
+401
+00:36:06,170 --> 00:36:10,230
+اللي عندها الـ false أكمل لا ما تكملش خلصنا
+
+402
+00:36:14,510 --> 00:36:17,850
+أه لما تشوف .. لو هذا كله true .. فتبحث اللي
+
+403
+00:36:17,
+
+445
+00:39:47,760 --> 00:39:53,320
+فهذه قيمتها false ولا عمرها حسب ال condition هذه
+
+446
+00:39:53,320 --> 00:39:57,140
+هتكون true عندي عشان تكون true بدي استخدم النفي
+
+447
+00:39:57,140 --> 00:40:01,060
+وبالتالي هذا القانون الشكل هذا لا يحقق عندي أو لا 
+
+448
+00:40:01,060 --> 00:40:04,680
+يتحقق وبالتالي هذه عبارة عن invalid argument
+
+449
+00:40:04,680 --> 00:40:10,540
+ال conclusion incorrect لأن فعمليا كمان الأربعة لا
+
+450
+00:40:10,540 --> 00:40:15,800
+تقبل قسمتها على التسعة، اللي هي 1012، اجمع الأرقام وقسمها
+
+451
+00:40:15,800 --> 00:40:20,520
+على 9.
+
+452
+00:40:20,520 --> 00:40:24,200
+سعيد إنك بتشتغل على هيك هاي ال rules لإن هذا ال
+
+453
+00:40:24,200 --> 00:40:26,180
+rule هي اللي قعدت أرتّبه عشان يطابق الصورة اللي
+
+454
+00:40:26,180 --> 00:40:30,680
+موجودة عندي في الجدول، تمام؟ لكن اختلف في وين؟ في ال
+
+455
+00:40:30,680 --> 00:40:34,080
+Q الآن، وبالتالي هو الصحيح اللي يجب أن يطلع عندي، نفي
+
+456
+00:40:34,080 --> 00:40:37,020
+الـ B، لازم يطلع، هي القانون اللي عندي أنا بقوله أنا
+
+457
+00:40:37,020 --> 00:40:41,360
+بحصل على نفي الـ B، لكن تهلأ، بمعنى آخر، إن هذا الكلام
+
+458
+00:40:41,360 --> 00:40:44,570
+غير صحيح. ليش غير صحيح؟ تهاني، الراجل، ال conditions
+
+459
+00:40:44,570 --> 00:40:49,910
+اللي هي 101 لا تقبل القسمة على ثلاثة، و 1012 لا تقبل
+
+460
+00:40:49,910 --> 00:40:53,030
+القسمة على تسعة، وبالتالي مستحيل هذا ال condition
+
+461
+00:40:53,030 --> 00:40:57,610
+يكون true، وبالتالي هذا invalid argument. هذا مثال
+
+462
+00:40:57,610 --> 00:41:01,910
+واحد من الكتاب عشان تصححه، بقول لك لو اليوم بتشي
+
+463
+00:41:01,910 --> 00:41:08,350
+طبعا؟ المعنى: أنت مش حنأشيه الليلة، حنحكيه على
+
+464
+00:41:08,350 --> 00:41:13,720
+الآخر كمان، وبعض السنّين بينت زي حالتي طبعاً؟ إذا
+
+465
+00:41:13,720 --> 00:41:22,440
+كانت اليوم مطرّة، فلن نحصل على باربيكيو اليوم. إذا
+
+466
+00:41:22,440 --> 00:41:26,720
+لم نحصل على باربيكيو اليوم،
+
+467
+00:41:26,720 --> 00:41:30,960
+فلن نحصل
+
+468
+00:41:30,960 --> 00:41:42,800
+على باربيكيو غير اليوم. إذا لم نحصل على باربيكيو غير
+
+469
+00:41:42,800 --> 00:41:46,480
+اليوم، في train studio، لو بتشي اليوم معناته إحنا
+
+470
+00:41:46,480 --> 00:41:53,740
+هنشويه؟ بكرا بتشي بكرا، خلاص، بتقلّق نفس الكلام، طيب
+
+471
+00:41:53,740 --> 00:41:58,960
+الآن، تعالَ
+
+472
+00:41:58,960 --> 00:42:02,240
+شوف، سيبك من الحل هذا، لو كمان هشكل حل ثاني بالنسبة
+
+473
+00:42:02,240 --> 00:42:07,240
+لليك. تعالَ الآن، لاحظ ال condition الأول هو عبارة
+
+474
+00:42:07,240 --> 00:42:12,600
+عن implies، صح؟ ال condition الأول implies إيش؟
+
+475
+00:42:12,600 --> 00:42:13,180
+بيقول إيش؟
+
+476
+00:42:25,700 --> 00:42:30,780
+ممكن أكتب له نط Q، على إنك اليوم لديك باربيكيو.
+
+477
+00:42:36,000 --> 00:42:39,020
+الـ Q، خلصت من ال condition الأول، ال condition
+
+478
+00:42:39,020 --> 00:42:43,260
+الثاني if، برضه ما زال فيه if و then، معناته هو
+
+479
+00:42:43,260 --> 00:42:48,440
+عبارة عن implication. if we don't have a barbecue
+
+480
+00:42:48,440 --> 00:42:54,480
+today، معناته not Q، then
+
+481
+00:42:54,480 --> 00:42:57,380
+we will have a barbecue tomorrow. وهدي إيش؟ دي
+
+482
+00:42:57,380 --> 00:42:59,900
+بالنسبة لنا، have a barbecue tomorrow، اللي هتكون
+
+483
+00:42:59,900 --> 00:43:00,820
+إيش؟ R
+
+484
+00:43:03,980 --> 00:43:11,600
+خلصنا. Therefore، إذا B، تقول
+
+485
+00:43:11,600 --> 00:43:16,420
+إلى We will have a barbecue tomorrow، إلى R. إيش
+
+486
+00:43:16,420 --> 00:43:25,400
+أفرجت عن الحل هذا؟ لما عرف ال symbol proposition Q
+
+487
+00:43:25,400 --> 00:43:32,130
+عرفه، will not have، يعني دخل النافي في بنية أو في
+
+488
+00:43:32,130 --> 00:43:35,850
+تعريف الـ Simple Proposition، فصارت عنده P implies
+
+489
+00:43:35,850 --> 00:43:41,330
+Q، و Q implies R. بيفرق معنا الحاجة هان؟ لأ، لاحظ
+
+490
+00:43:41,330 --> 00:43:46,990
+الـ Proposition هذا هو نفسه هذا هون، وبالتالي أي حل
+
+491
+00:43:46,990 --> 00:43:50,190
+من الإثنين هذا، برجعنا للكلام الأول اللي قلت لك إياه
+
+492
+00:43:50,190 --> 00:43:55,010
+سابقا. طالما إنك بتفسر صح، بغض النظر كيف حصلت الـ
+
+493
+00:43:55,010 --> 00:43:58,550
+Proposition، المهم لما تكتب الـ Definition، اكتبه صح.
+
+494
+00:44:01,660 --> 00:44:04,640
+ممكن أتعرف أروح هناك أقول الـ Q، إحنا حسب ال
+
+495
+00:44:04,640 --> 00:44:07,500
+definition بتاعتنا، إياه، We have a barbecue today
+
+496
+00:44:07,500 --> 00:44:13,020
+هي الـ Q؟ وبالتالي بي implies not the Q، مافي
+
+497
+00:44:13,020 --> 00:44:19,240
+الـ Q، تمام؟ valid ولا invalid؟ valid argument، لأن
+
+498
+00:44:19,240 --> 00:44:22,640
+هذه بتطبّق ال rule of inferences اللي اسمه
+
+499
+00:44:22,640 --> 00:44:29,940
+hypothetical syllogism أو ال chaining اللي هي سلسلة
+
+500
+00:44:30,920 --> 00:44:37,960
+الآن هي ال rule موجودة عندنا هنا هي
+
+501
+00:44:37,960 --> 00:44:42,960
+وإن السلسلة .. السلسلة بمثابة ال Q، الحلقة ما بين
+
+502
+00:44:42,960 --> 00:44:48,120
+الإثنين. إذا كانت A تقول إلى B، و B تقول إلى C،
+
+503
+00:44:48,120 --> 00:44:54,240
+فمعناته A تقول إلى C، تمام.
+
+504
+00:44:54,240 --> 00:44:57,240
+نشوف المثال اللي بعده.
+
+505
+00:45:10,470 --> 00:45:20,730
+Okay، مش مشكلة، صاحبة. طيب، الآن إيش بقول لي؟ بقول لي
+
+506
+00:45:20,730 --> 00:45:27,610
+Gary is either an intelligent or a good actor. Gary
+
+507
+00:45:27,610 --> 00:45:35,460
+is intelligent، هاي P، وهاي R. A good actor، Q. Gary is
+
+508
+00:45:35,460 --> 00:45:39,160
+a good actor، Q. هال condition الأول، If Gary is
+
+509
+00:45:39,160 --> 00:45:46,340
+intelligent، P، implies then he can count from one to
+
+510
+00:45:46,340 --> 00:45:53,200
+ten. لو كان Gary ذكي، أو شاطر، هيعد من واحد لعشرة. هدي
+
+511
+00:45:53,200 --> 00:46:00,080
+R. Gary can only count from one to three. Gary بس
+
+512
+00:46:00,080 --> 00:46:06,410
+بيعد من واحد إلى ثلاثة. نط R. Therefore,
+
+513
+00:46:06,690 --> 00:46:11,990
+ال conclusion بتاعتنا، Gary is a good actor، هي مين؟
+
+514
+00:46:11,990 --> 00:46:18,090
+الـ Q فقط، الـ Q. تعالَ، ورمزنا لهم بـ P و R و Q. الـ
+
+515
+00:46:18,090 --> 00:46:23,230
+condition الأول، P، implies الـ R، نط الـ R.
+
+516
+00:46:24,390 --> 00:46:30,990
+Therefore، الـ Q. هاد الآن، هاد ال argument بتاعتنا.
+
+517
+00:46:34,800 --> 00:46:40,600
+هل هي valid argument ولا invalid argument؟ بدك
+
+518
+00:46:40,600 --> 00:46:45,160
+تبدأ تجد الاحتمالات، وتبدأ تشتغل وتحسب. ممكن تأخذ
+
+519
+00:46:45,160 --> 00:46:49,440
+وقت كثير، لكن لو إحنا رجعنا لل rule of inferences
+
+520
+00:46:49,440 --> 00:46:55,680
+الصادقة، ممكن يقولوا لي هذا الكلام صحيح ولا لأ؟ أيوة
+
+521
+00:46:55,680 --> 00:47:01,100
+..الآن ..الآن ..تعالَ نشوف الترتيب هذا يا شباب.
+
+522
+00:47:01,100 --> 00:47:05,480
+هدول التلات عناصر، وبينهم and، وإحنا ال and عملية
+
+523
+00:47:05,480 --> 00:47:09,340
+ابدالية. ال and هون بين ال conditions هدول بتاعتي
+
+524
+00:47:09,340 --> 00:47:14,020
+conditions، واللي بينهم and، وال and عملية ابدالية.
+
+525
+00:47:14,020 --> 00:47:16,880
+يعني بقدر أبدّل كل اثنين وأجمعهم زي ما بدي ولا لأ؟
+
+526
+00:47:16,880 --> 00:47:21,220
+حسب خواص ال and. طيب، تعالَ نشوف الخطوات التالية.
+
+527
+00:47:21,220 --> 00:47:23,940
+يعني لو أنا روحت اشتغلت كالتالي، هي ال hypothesis
+
+528
+00:47:23,940 --> 00:47:28,550
+اللي موجودة عندي، هو حتى أنا اشتغلت في ال hypothesis
+
+529
+00:47:28,550 --> 00:47:32,230
+كالتالي، اقعد أرتّبهم، نط ال R، ال hypothesis الأول
+
+530
+00:47:32,230 --> 00:47:39,550
+بي implies ال R، ال hypothesis الثاني هيه، يعني بين
+
+531
+00:47:39,550 --> 00:47:42,510
+جثتين، أنا ببدأ اشتغل على هدول، التاني اللي حالهم
+
+532
+00:47:42,510 --> 00:47:48,350
+بينفع؟ اه، بينفع. يعني هو كأنه جالس بيقول هيك high
+
+533
+00:47:48,350 --> 00:47:55,070
+condition، P or Q and
+
+534
+00:47:55,650 --> 00:48:04,930
+أفتح قوس كبير، نقطة ال R، and P implies ال R، صح
+
+535
+00:48:04,930 --> 00:48:10,450
+ولا لا؟ وبدي أحل القوس الكبير في الأول حسب القوانين
+
+536
+00:48:10,450 --> 00:48:14,490
+الصادقة اللي في الجدول. الشكل هذا، هيديني مين يا
+
+537
+00:48:14,490 --> 00:48:21,270
+شباب؟ نقطة ال B، هذا حسب المدرسة تيليناس واحد
+
+538
+00:48:21,270 --> 00:48:24,630
+واثنين، اللي هو أول قانونين الموجودين عندنا في
+
+539
+00:48:24,630 --> 00:48:25,230
+الجدول هنا.
+
+540
+00:48:28,720 --> 00:48:41,880
+هي نقطة ال R، P implies R، تديني نفي ال P، تمام.
+
+541
+00:48:41,880 --> 00:48:46,620
+أعطاني نفي ال P، الآن نفي ال P هي عبارة عن المحصلة
+
+542
+00:48:46,620 --> 00:48:51,480
+تبع ال two conditions هدول. بلّ أعملها إنتَ مع مين؟
+
+543
+00:48:51,480 --> 00:48:58,910
+مع ال condition هذا، P or Q، مية بالمية P or Q، وفي
+
+544
+00:48:58,910 --> 00:49:05,990
+عندي نقطة P بتديني مين؟ ال Q بتديني ال Q. هتوصلّي
+
+545
+00:49:05,990 --> 00:49:11,110
+ليها ال Q، بنفس الترتيب هذا. لو بدنا نرجع لورا
+
+546
+00:49:11,110 --> 00:49:16,330
+للقوانين، مهمّة مرة ثانية، مش ورا تتعب وأنت بترجع
+
+547
+00:49:16,330 --> 00:49:25,170
+معايا، وين القوانين هاي؟ مضبوط؟ مضبوط؟ فتديني مين؟ P
+
+548
+00:49:25,170 --> 00:49:29,180
+أنا فعلياً في عندي النفي موجود فوق في التنتين، في
+
+549
+00:49:29,180 --> 00:49:35,940
+المسألة هان، فأصبحت
+
+550
+00:49:35,940 --> 00:49:42,300
+عندها بتديني مين؟ بتديني الـ Q، أعطتني الـ Q حسب الـ
+
+551
+00:49:42,300 --> 00:49:47,060
+rule of inferences، معناه إن هذه وصلت إلى
+
+552
+00:49:47,060 --> 00:49:52,600
+ال conclusion. ال rules أو ال hypothesis اللي فوق وصلوا
+
+553
+00:49:52,600 --> 00:49:54,600
+إلى ال conclusion باعتماد على ال rule of
+
+554
+00:49:54,600 --> 00:49:58,080
+inferences، وال rule of inferences هي عبارة عن
+
+555
+00:49:58,080 --> 00:50:02,300
+valid argument already، وتم إثباتها، وبالتالي أنا
+
+556
+00:50:02,300 --> 00:50:07,140
+بقدر أتحقّق من ال validity من خاصية ال argument هذه.
+
+557
+00:50:07,140 --> 00:50:10,840
+هل هي valid ولا invalid؟ لو فعلياً قدرت أستغل ال
+
+558
+00:50:10,840 --> 00:50:15,820
+rule of inferences عشان من ال hypothesis أصل لمين
+
+559
+00:50:15,820 --> 00:50:22,270
+لل conclusion اللي موجودة. كيف تحلها؟ ما هي نفسها
+
+560
+00:50:22,270 --> 00:50:29,890
+هيّا، هتبقى تحلّها هيك؟ ما هي هذه، وهذه حسب ال rule
+
+561
+00:50:29,890 --> 00:50:33,230
+of inferences مش موجودات، بس بتقدر تعيد ترتيب
+
+562
+00:50:33,230 --> 00:50:37,290
+العناصر، تمام؟ بحيث إنك تقول: والله، أنا بدي أرتّبهم
+
+563
+00:50:37,290 --> 00:50:43,310
+هيك، تصير هيك. P implies ال R، نقطة ال R، بي oricate
+
+564
+00:50:43,310 --> 00:50:48,330
+إيش أفرجت معاك؟ ولا إشي، بس قعدت أرتّب. الآن حليت
+
+565
+00:50:48,330 --> 00:50:55,270
+اللي فوق هذه، وطلعت معايا نط ال B، صارت عندي نط الـ
+
+566
+00:50:55,270 --> 00:51:01,990
+B، P R Q، معناته تقريباً هتعطيني Q، وبالتالي وصلت لمين؟
+
+567
+00:51:01,990 --> 00:51:06,750
+لل conclusion اللي موجودة عندي، وبالتالي هدول عبارة
+
+568
+00:51:06,750 --> 00:51:10,430
+عن valid argument للمسألة اللي موجودة، وبالتالي
+
+569
+00:51:10,430 --> 00:51:14,710
+Gary is a good actor، نعم.
+
+570
+00:51:15,960 --> 00:51:25,680
+من ضمن
+
+571
+00:51:25,680 --> 00:51:32,800
+ال rule of inferences. الـ
+
+572
+00:51:32,800 --> 00:51:35,660
+rule of inferences ممكن أسقطها كمان على مين يا
+
+573
+00:51:35,660 --> 00:51:39,040
+شباب؟ على ال quantifiers وال predicate function.
+
+574
+00:51:39,040 --> 00:51:48,580
+يا ريت. طيب، تعالَ نشوف for all x، b(x). for all x، b(x)،
+
+575
+00:51:48,580 --> 00:51:51,980
+يعني هيك بقول: لأي x في ال domain، ال b(x) is true.
+
+576
+00:51:51,980 --> 00:51:58,960
+معناته إذا b(x) is true، إيش؟ من وين ال c؟ هي عبارة
+
+577
+00:51:58,960 --> 00:52:02,400
+عن عنصر في ال domain، عنصر في ال domain، في ال
+
+578
+00:52:02,400 --> 00:52:06,640
+domain اللي أخذنا منه x، يعني هي حالة خاصة من ال x
+
+579
+00:52:06,640 --> 00:52:11,760
+المعروفة. لو كان في  b(c)، for any
+
+580
+00:52:11,760 --> 00:52:16,030
+arbitrary c، لو هذا الكلام بيتحقق، ال predicate
+
+581
+00:52:16,030 --> 00:52:20,070
+function بتتحقق على أي arbitrary element c في
+
+582
+00:52:20,070 --> 00:52:25,030
+ال domain، معناته تجي هذه تكافئ for all x، b(x). نفس
+
+583
+00:52:25,030 --> 00:52:31,090
+المعنى، عكس التاني بالضبط. there exist b(c)، معناته بيه
+
+584
+00:52:31,090 --> 00:52:38,720
+c is true for some element c، على الأقل واحد. b(c) for
+
+585
+00:52:38,720 --> 00:52:42,300
+some element c. معناته تقرأ: بقدر أستبدلها، الفكرة وين
+
+586
+00:52:42,300 --> 00:52:45,200
+يا شباب، أثناء الإثبات. لو أنت وصلت لهذه، تقدر
+
+587
+00:52:45,200 --> 00:52:48,020
+تستبدلها بهذه، وهذه تقدر تحط مكانها بهذه. هذه
+
+588
+00:52:48,020 --> 00:52:51,900
+المفهوم، إنك أنت تقدر تستخدم بعض ال facts، بعض
+
+589
+00:52:51,900 --> 00:52:58,180
+الحقائق، من أجل تسهيل عملية الإثبات الرياضي. every
+
+590
+00:52:58,180 --> 00:53:02,380
+IUG student is genius. طلاب الجامعة الإسلامية
+
+591
+00:53:02,380 --> 00:53:12,500
+عَباقرة. إيش رأيك يا رامي؟ اقرأ: 100% أحمد طالب في
+
+592
+00:53:12,500 --> 00:53:19,180
+الجامعة الإسلامية. تمام. مع ال conclusion therefore
+
+593
+00:53:19,180 --> 00:53:22,900
+أحمد is a genius. إذا كل طلاب الجامعة الإسلامية
+
+594
+00:53:22,900 --> 00:53:27,560
+عَباقرة، وأحمد مسجل في الجامعة الإسلامية كطالب، فهو
+
+595
+00:53:27,560 --> 00:53:32,380
+عَبْقري. و ليش رأيك؟ خلّصنا فعلياً هذا الكلام. هي step
+
+596
+00:53:32,380 --> 00:53:39,760
+الأولى. for all x، ux، إيش ux؟ اللي هو طالب في الجامعة
+
+597
+00:53:39,760 --> 00:53:45,120
+university student، implies genius student، تمام.
+
+598
+00:53:45,120 --> 00:53:51,240
+step 2. for all أحمد، أحمد طالب في الجامعة، يقعد إلى
+
+599
+00:53:51,240 --> 00:53:54,780
+ثلاثة.
+
+600
+00:53:54,780 --> 00:53:58,940
+أحمد طالب، وأحمد genius، وخلصنا من العناصر الموجودة.
+
+601
+00:53:58,940 --> 00:54:06,250
+for all x، b(c). ليش أحمد؟ b(Ahmed)، if c تنتمي لل
+
+602
+00:54:06,250 --> 00:54:09,110
+domain اللي موجودة. اه، هو هذا القانون، وهذا هو
+
+603
+00:54:09,110 --> 00:54:15,370
+القانون اللي موجود عندنا هنا، وسلامتكم. هي خلص الـ
+
+604
+00:54:15,370 --> 00:54:18,610
+section هذا، وبدنا نقول: الشابتر الأول، الله يعطيه
+
+605
+00:54:18,610 --> 00:54:21,870
+العافية. وضلّ فيه عندنا section مهم جداً، طرق الإثبات
+
+606
+00:54:21,870 --> 00:54:25,150
+الرياضية، بس هأؤجّله شوية، إيه كده، عشان ما تتخمروا شوية
+
+607
+00:54:25,150 --> 00:54:28,430
+في الرياضيات معنا. اه، هنؤجّله إن شاء الله بس لاحقاً.
+
+608
+00:54:28,430 --> 00:54:31,530
+في أي سؤال يا شباب؟ اللي قرّحنا اليوم، بإذن الله
+
+609
+00:54:31,530 --> 00:54:32,250
+يعطيكم العافية، شباب.
+
diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/0HTI94jFUyM_postprocess.srt b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/0HTI94jFUyM_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..4c5e34f53dda89549c4cb28a06c63d863e1b5553
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/0HTI94jFUyM_postprocess.srt
@@ -0,0 +1,2436 @@
+1
+00:00:21,290 --> 00:00:23,210
+بسم الله الحمد لله والصلاة والسلام علي رسول الله
+
+2
+00:00:23,210 --> 00:00:26,290
+اليوم ان شاء الله شباب هنشوف ال section الأخير
+
+3
+00:00:26,290 --> 00:00:29,810
+مؤقتا في ال chapter الأول بحيث ان في عندنا section
+
+4
+00:00:29,810 --> 00:00:33,410
+تاني المفروض اللي هو طرق الاثبات الرياضي بس هأخره
+
+5
+00:00:33,410 --> 00:00:36,690
+شوية عشان نشوف كيف تمشي الأمور معانا لكن ال role
+
+6
+00:00:36,690 --> 00:00:40,930
+of inferences لما بتكلم inferences طرق الاستنباط
+
+7
+00:00:40,930 --> 00:00:45,370
+او التخمين استنباط او التخمين قوانين الاستنباط او
+
+8
+00:00:45,370 --> 00:00:49,400
+قوانين الاختزال سميها زي ما بدكفي الآخر انا هكون
+
+9
+00:00:49,400 --> 00:00:53,020
+شوف مجموعة من القوانين هتلزمني في الاثبات الرياضي
+
+10
+00:00:53,020 --> 00:00:55,120
+عشان هيك بقولك ممكن انا هذا ال section ارجعله
+
+11
+00:00:55,120 --> 00:01:02,420
+لاحقا بشكل عام بشكل عام اي نظرية بدنا نثبتها تمام
+
+12
+00:01:02,420 --> 00:01:07,460
+لازم يكون فيها جزئيتين واضحات جدا الاولة ال
+
+13
+00:01:07,460 --> 00:01:10,620
+condition او ال hypothesis او ال premises حسب
+
+14
+00:01:10,620 --> 00:01:15,900
+التسمية الشرطوال conclusion المحصرة تعالى نشوف مع
+
+15
+00:01:15,900 --> 00:01:23,260
+بعض المثال البسيط التالي بقول لي حاصل جمع the sum
+
+16
+00:01:23,260 --> 00:01:34,220
+of any two odd integers is
+
+17
+00:01:34,220 --> 00:01:41,820
+integer is even number is even number is
+
+18
+00:01:41,820 --> 00:01:42,600
+even integer
+
+19
+00:01:45,350 --> 00:01:50,350
+true هذه نظرية لان فيها condition اه فيها
+
+20
+00:01:50,350 --> 00:01:54,350
+condition ايش ال condition ان يكون في عندي two
+
+21
+00:01:54,350 --> 00:02:00,710
+integers وصفتهم ايش odd يعني انا في عندي a and ال
+
+22
+00:02:00,710 --> 00:02:09,550
+b are odd integers طيب
+
+23
+00:02:09,550 --> 00:02:13,610
+conclusion هاي condition كام condition يا شباب
+
+24
+00:02:13,610 --> 00:02:20,280
+موجود عندى2 2 a is integer و b is integer
+
+25
+00:02:20,280 --> 00:02:26,800
+conclusion a زائد b عارف ليش لما قلتلك two
+
+26
+00:02:26,800 --> 00:02:31,040
+conditions لأن هاد عبارة عن preposition a is odd
+
+27
+00:02:31,040 --> 00:02:35,120
+integer تقدر تحكمليها ولا تقدرش بي is odd integer
+
+28
+00:02:35,120 --> 00:02:41,380
+second preposition و الرابط اللي بينهم ال and و ال
+
+29
+00:02:41,380 --> 00:02:51,120
+conclusion a زائد bis even integer هذه الخلاصة one
+
+30
+00:02:51,120 --> 00:02:54,040
+conclusion one proposition لاحظ ان انا اتكلم على
+
+31
+00:02:54,040 --> 00:02:58,880
+three propositions اتنين منهم يقولوا الى التالت
+
+32
+00:02:58,880 --> 00:03:04,440
+الان هذه ال conditions مهمة جدا عشان انا اقدر اثبت
+
+33
+00:03:04,440 --> 00:03:10,620
+النظريات طيب هنرجع لالمثال هذا ال correct proof هو
+
+34
+00:03:10,620 --> 00:03:16,980
+اثبات الرياض الصحيح هو بتكون منالتالي لو كانت ال
+
+35
+00:03:16,980 --> 00:03:21,680
+condition true لو كانت ال condition true هتقول انه
+
+36
+00:03:21,680 --> 00:03:26,320
+ال conclusion صحيحة ال conclusion هتكون true و
+
+37
+00:03:26,320 --> 00:03:29,540
+بالتالي ال conditions تقول ال conclusion دائما
+
+38
+00:03:29,540 --> 00:03:36,860
+هتكون تتولجي دائما ال true تقول ال true فبتكلم
+
+39
+00:03:36,860 --> 00:03:39,640
+جاعد على true لإن ال true تقول ال true دائما هتكون
+
+40
+00:03:39,640 --> 00:03:44,740
+قيمتها يعني هيك true implies trueequivalent to
+
+41
+00:03:44,740 --> 00:03:52,240
+true وبالتالي تاتولوجي تمام دعونا نشوف هذا المثال
+
+42
+00:03:52,240 --> 00:03:55,840
+كيف ممكن أن انا أروح أثبته لو أنا بدأ أروح أثبت
+
+43
+00:03:55,840 --> 00:03:59,380
+بدي أبدأ من مين يا شباب؟ بدي أبدأ من ال conditions
+
+44
+00:03:59,380 --> 00:04:11,720
+أبدأ أفسر شو يعني؟ odd a is odd معناته a equal 2k
+
+45
+00:04:12,260 --> 00:04:21,360
+زائد او ناقص واحد وال K تنتمي إلى ال Z لأي عدد
+
+46
+00:04:21,360 --> 00:04:28,920
+فردي يُكتب على صورة 2 برب عدد صحيح زائد او ناقص
+
+47
+00:04:28,920 --> 00:04:32,620
+واحد اتنين في العدد الصحيح دائما الشباب اتنين في
+
+48
+00:04:32,620 --> 00:04:37,790
+اي عددالنتش بيطلع عدد زوجي و لا بصبوط طب و العدد
+
+49
+00:04:37,790 --> 00:04:42,090
+الفردي اما اكبر من عدد الزوج بواحد او اقل منه
+
+50
+00:04:42,090 --> 00:04:47,470
+بواحد فانت ممكن تعتمد على الصيغة هذه بشكل عام او
+
+51
+00:04:47,470 --> 00:04:50,050
+تعتمد على واحدة منهم زائد او نقص حسب انت ايش بدك
+
+52
+00:04:50,050 --> 00:04:54,390
+تمام و ال K هي عبارة عشان اقول arbitrary لانه
+
+53
+00:04:54,390 --> 00:04:58,090
+مجليش هو التلاتة مجليش الخمسة جالي اي odd number
+
+54
+00:04:58,090 --> 00:05:00,410
+فبالتالي انا بده اروح اكتب صورة odd number بشكل
+
+55
+00:05:00,410 --> 00:05:06,180
+عام طيب عشان امثل الخمسةالـ K لازم تكون ثلاثة
+
+56
+00:05:06,180 --> 00:05:10,960
+اتنين في ثلاثة ستة نقص واحد اول K بيبقى تسوى اتنين
+
+57
+00:05:10,960 --> 00:05:14,980
+اتنين في اتنين اربعة زائد واحد فلنكون نعتمد على
+
+58
+00:05:14,980 --> 00:05:23,400
+واحدة بس و نسيبها من التانية تمام ال B أسقط معناته
+
+59
+00:05:23,400 --> 00:05:29,500
+ال B بيبقى تسوى اتنين H زائد واحد
+
+60
+00:05:31,040 --> 00:05:37,360
+والقدش تنتمي لزد بالمناسبة بنفعش أقول تلاتة فاصلة
+
+61
+00:05:37,360 --> 00:05:45,980
+خمسة is odd هذا الكلام الصحيح ليش؟ لأن ال odd فقط
+
+62
+00:05:45,980 --> 00:05:49,160
+ال odd will even مع الأعداد الصحيحة مش معريها ال
+
+63
+00:05:49,160 --> 00:05:53,100
+number تمام؟ هاي ال conditions هاي ال conditions
+
+64
+00:05:53,100 --> 00:05:58,740
+اللي عندي طيب تمام يعني هدولة هيك و أنا جاعة بقولك
+
+65
+00:05:58,740 --> 00:06:05,240
+trueA is odd هيها B is odd هيها true true and true
+
+66
+00:06:05,240 --> 00:06:10,300
+true لأن هذا اللي لازم يوصلني لل conclusion ان ال
+
+67
+00:06:10,300 --> 00:06:13,960
+A زائد B is even و لازم تكون true تعالى نشوف
+
+68
+00:06:13,960 --> 00:06:16,880
+معناته ان انا بدي اروح ال conclusion A زائد B
+
+69
+00:06:16,880 --> 00:06:24,440
+يساوي عوض عن قيمة A بتامتها اتنين K زائد واحد زائد
+
+70
+00:06:24,440 --> 00:06:29,040
+لقيمة B اتنين H زائد واحد اجبع
+
+71
+00:06:30,370 --> 00:06:41,790
+تنين K زائد اتنين H زائد اتنين K زائد
+
+72
+00:06:41,790 --> 00:06:49,030
+H زائد واحد مصبوط؟ الان هذا الرقم بغض النظر ايش
+
+73
+00:06:49,030 --> 00:06:58,240
+كانت قيمته ينتمي الى Z لان K is integerH هو انتجار
+
+74
+00:06:58,240 --> 00:07:02,680
+و 1 هو انتجار وحاصل جامعي الانتجار هيقدي إلى
+
+75
+00:07:02,680 --> 00:07:08,720
+انتجار وبالتالي اتنين في انتجار انتجار ومش بس هيك
+
+76
+00:07:08,720 --> 00:07:14,620
+even number even انتجار مش هي صورة الانتجار مش هي
+
+77
+00:07:14,620 --> 00:07:18,180
+صورة ال even انتجار وبالتالي احنا وصلنا وصارت ال
+
+78
+00:07:18,180 --> 00:07:23,060
+conclusion تبعتنا هذه true true فكانت ال condition
+
+79
+00:07:23,060 --> 00:07:28,650
+true قالت ان ال conclusion تبعتناالمحصلة true هذا
+
+80
+00:07:28,650 --> 00:07:33,150
+الكلام مهم لما انا بدي اتي اثبت القوانين كلها
+
+81
+00:07:33,150 --> 00:07:38,310
+فلازم انا اتسلسل او امشي مع البرهان بكلام منطقي
+
+82
+00:07:38,310 --> 00:07:42,670
+100% بيبدأ من وين؟ بيبدأ من عند ال condition اللي
+
+83
+00:07:42,670 --> 00:07:47,490
+لازم تكون true بينفعش في لحظة من اللحظات اتي اقول
+
+84
+00:07:47,490 --> 00:07:54,190
+ال B هيها ال
+
+85
+00:07:54,190 --> 00:07:59,470
+B is not oddصار ال condition false تعالى جمع
+
+86
+00:07:59,470 --> 00:08:04,290
+هتلاقي ان ال output ال conclusion is all is false
+
+87
+00:08:04,290 --> 00:08:07,110
+لان القملة اللى كانت عندى معايا odd ماكنتش even
+
+88
+00:08:07,110 --> 00:08:11,570
+لان اتنين K زائد واحد زائد اتنين H زائد واحد تساوي
+
+89
+00:08:11,570 --> 00:08:15,810
+اتنين افتحقوص K زائد H الكل زائد واحد وهدا صورة
+
+90
+00:08:15,810 --> 00:08:20,110
+العدد الفردي فلما كانت ال condition عندي false أدت
+
+91
+00:08:20,110 --> 00:08:23,960
+إلى ان ال conclusion بتطلع معاياfalse وبالتالي اي
+
+92
+00:08:23,960 --> 00:08:27,060
+نظرية صحيحة لازم تكون الشروط تبعتها ال condition
+
+93
+00:08:27,060 --> 00:08:31,520
+او ال hypothesis تبعتها true تمام بتقدم معايا ل
+
+94
+00:08:31,520 --> 00:08:34,840
+conclusion true otherwise بتكون النظرية دي بدهاش
+
+95
+00:08:34,840 --> 00:08:43,700
+رمى بعيد عنها لما تكونش صحيحة تمام الآن العلاقة
+
+96
+00:08:43,700 --> 00:08:48,940
+بين ال condition و ال conclusion هتعامل معاهم
+
+97
+00:08:55,710 --> 00:09:00,650
+أو عوامل اثبات صحة النظرية اللي موجودة عندنا بين
+
+98
+00:09:00,650 --> 00:09:05,440
+جثين ان ال conclusion ال condition تقولإلى ال
+
+99
+00:09:05,440 --> 00:09:08,360
+conclusion هذه عوامل اللي هي ال by conditional مش
+
+100
+00:09:08,360 --> 00:09:11,480
+احنا قولنا بي implies كيو سمينا ال implies
+
+101
+00:09:11,480 --> 00:09:16,280
+operator وسمينا ال بي و ال كيو عبارة عن argument
+
+102
+00:09:16,280 --> 00:09:19,100
+للمسألة او ال operand تبع المسألة اللي عندها
+
+103
+00:09:19,100 --> 00:09:24,480
+وبالتالي هتعامل معاهم as conclusionطيب، الآن شو
+
+104
+00:09:24,480 --> 00:09:27,880
+علاقة هذا في الإثبات؟ هو أساس الإثبات إنه فعليا
+
+105
+00:09:27,880 --> 00:09:30,640
+اللي تقول و ال condition اللي موجودة عندها و
+
+106
+00:09:30,640 --> 00:09:34,800
+بالتالي ال argument connected by proper rules of
+
+107
+00:09:34,800 --> 00:09:37,600
+inferences و بالتالي ال argument تبعتي هذي أنا
+
+108
+00:09:37,600 --> 00:09:43,060
+بنتقل ممكن من خلال ال rule of inferences ال rule
+
+109
+00:09:43,060 --> 00:09:46,840
+of inferences قوانين التخمين أو الاستنباب أو
+
+110
+00:09:46,840 --> 00:09:47,500
+الإثبات
+
+111
+00:09:49,970 --> 00:09:52,550
+أو الـ Step Down سميهم زي ما بأي ترجمة ممكن تجي
+
+112
+00:09:52,550 --> 00:09:59,490
+على بالك ان فرنسية التخمين بالمناسبة الآن بتزودني
+
+113
+00:09:59,490 --> 00:10:04,510
+بتفسير لكل step في البرهان لما بروح أنا بstep
+
+114
+00:10:04,510 --> 00:10:08,890
+لمقطع بمقطع ليش؟ ليش أنا بدلته؟ بناء على إيش؟
+
+115
+00:10:08,890 --> 00:10:12,830
+تمام؟ بناء على إن هذا ال role أصبحت fact وانا بقدر
+
+116
+00:10:12,830 --> 00:10:18,860
+أعتمد عليها في الإثبات تمام؟ دعونا نشوفوحد من ال
+
+117
+00:10:18,860 --> 00:10:23,140
+role of inferences بقول كتابة هاي ال argument
+
+118
+00:10:23,140 --> 00:10:27,520
+تبعتي كل آياتهم هذا ال role الآن من ال conditions
+
+119
+00:10:27,520 --> 00:10:34,340
+P و P implies Q و العلاقة بين ال two conditions
+
+120
+00:10:34,340 --> 00:10:46,770
+دائما and يقول إلى Q يعني بين قصين P andB implies
+
+121
+00:10:46,770 --> 00:10:53,370
+Q الكل يقول الى Q هذا ال role أو هذا القانون انا
+
+122
+00:10:53,370 --> 00:10:57,970
+بقدر اشوف بمجرد اشوف في الاثبات الرياضي تبعي حصلت
+
+123
+00:10:57,970 --> 00:11:03,070
+على ال two condition هدول بقدر اشيلهم اشيلهم
+
+124
+00:11:03,070 --> 00:11:09,560
+احذفهم وحق بدلهم مينEQ وحط بدلهم EQ وهنا بصير دورة
+
+125
+00:11:09,560 --> 00:11:13,920
+او أهمية ال role of inferences في الإثبات تعالى
+
+126
+00:11:13,920 --> 00:11:18,860
+نشوف أساسا هل فعليا هذا زي ما هو بقول ان هذه دائما
+
+127
+00:11:18,860 --> 00:11:22,300
+لازم تكون تيتولوجيا عشان أثبتها تيتولوجيا كيف بدي
+
+128
+00:11:22,300 --> 00:11:26,280
+أسوي الشباب عشان
+
+129
+00:11:26,280 --> 00:11:31,040
+أثبت ان هذه عبارة عن تيتولوجيا ايش المفروض أسوي
+
+130
+00:11:31,040 --> 00:11:33,820
+افكر ال implies
+
+131
+00:11:37,090 --> 00:11:41,270
+100% يعني انا بدى استخدم الطرق اللى شوفناها سابقا
+
+132
+00:11:41,270 --> 00:11:49,850
+عشان اثبت القيمة اللى عندي تمام بي and بي implies
+
+133
+00:11:49,850 --> 00:11:58,210
+كيو الكل implies كيو أظبط بقول ان هذا تاتولوجي
+
+134
+00:11:58,210 --> 00:12:04,490
+الآن بدى أذكرك بي implies كيو equivalent to نط ال
+
+135
+00:12:04,490 --> 00:12:09,660
+بيor q وفي
+
+136
+00:12:09,660 --> 00:12:13,480
+equivalent لشغل تانية بس بتلزمنيش الان نط ال q
+
+137
+00:12:13,480 --> 00:12:22,120
+implies نط ال b نط ال q implies نط ال b الان ليش
+
+138
+00:12:22,120 --> 00:12:25,460
+هاد بتلزمنيش لإن هو عم يقعد يقولي اثبت او بدرس
+
+139
+00:12:25,460 --> 00:12:29,740
+بتقولي ان هاد Totology Totology يعني بدي true عشان
+
+140
+00:12:29,740 --> 00:12:37,020
+بدي true لو انا قدرت احصل orX ونفيها ستكون حصالة
+
+141
+00:12:37,020 --> 00:12:41,180
+على الـ True وهذا لا يلزمني الآن ان انا بتلزمني
+
+142
+00:12:41,180 --> 00:12:44,260
+الصورة التانية اللى موجودة عندي وبالتالي هذه تكافئ
+
+143
+00:12:44,260 --> 00:12:55,640
+اتجدم في الأول نفي ال B بس لحظة شوية and نفي ال B
+
+144
+00:12:55,640 --> 00:13:00,880
+RQ مظبوط RQ
+
+145
+00:13:02,320 --> 00:13:06,660
+أنا بكل حولته مرة واحدة نفي الجوس هذا كله هي النفي
+
+146
+00:13:06,660 --> 00:13:12,820
+للجوس والجوس هذا P implies Q برضه بدلته not P or Q
+
+147
+00:13:12,820 --> 00:13:22,160
+الآن بدأ أدخل النفي على الجوس هذا نفي ال P or نفي
+
+148
+00:13:22,160 --> 00:13:29,800
+الجوس هذا نفي الجوس هذا معناته P and not Q الكل or
+
+149
+00:13:29,800 --> 00:13:37,680
+مصبوط هيك؟هي مازال قصها يهيك الان بدي ادخل بدي
+
+150
+00:13:37,680 --> 00:13:54,920
+اوزع نفل B نفل B or ال B and نفل B or نفل Q or Q
+
+151
+00:13:54,920 --> 00:14:05,490
+بصبت B or not B trueطيب هذه بال true ال true and x
+
+152
+00:14:05,490 --> 00:14:09,990
+احنا في عندنا قانون بيقول اللي ال true and ال b
+
+153
+00:14:09,990 --> 00:14:14,190
+تكافئ ال b لا تكافئ ال true مع ال or تكافئ
+
+154
+00:14:14,190 --> 00:14:24,150
+وبالتالي هذه تكافئ هيك صارت نقطة ال b or نقطة q or
+
+155
+00:14:24,150 --> 00:14:29,550
+q خلصنا
+
+156
+00:14:29,550 --> 00:14:33,810
+من دي مورجان دي مورجان كانت فوقلأن هان احنا الان
+
+157
+00:14:33,810 --> 00:14:37,050
+كل العمليات اللي عندي من نفس الرتبة اللي هي ال R
+
+158
+00:14:37,050 --> 00:14:40,690
+وبالتالي بقدر اشتجم معناش توزيع التوزيع كانت فوق
+
+159
+00:14:40,690 --> 00:14:47,550
+توزيع ال R على الان و العكس بس الان تجميع معناته
+
+160
+00:14:47,550 --> 00:14:56,370
+انا عندي نط ال B or نط Q or Q هذه صارت true وهذه
+
+161
+00:14:56,370 --> 00:15:00,850
+تكافئ نط ال B or true تكافئ
+
+162
+00:15:02,300 --> 00:15:05,980
+True وبالتالي هي عبارة عن Tautology
+
+163
+00:15:08,820 --> 00:15:11,840
+إذا كان الحل التاني لو احنا مش قادرين نثبت بالشكل
+
+164
+00:15:11,840 --> 00:15:15,980
+هذا الشيء ماذا نسوي نستخدم جدول الاحتمالات هستخدم
+
+165
+00:15:15,980 --> 00:15:18,720
+جدول الاحتمالات كمان شوية بس لشغل تانية و بالمرة
+
+166
+00:15:18,720 --> 00:15:22,540
+بنكون أثبتناها بالشك تاني وبالتالي أصبحت عندي ال
+
+167
+00:15:22,540 --> 00:15:26,680
+role of inferences هذه اللي اسمها Medus Boninus
+
+168
+00:15:26,680 --> 00:15:29,780
+بغض النظر عن التسميات الشباب مش ضروري تحفظها لأن
+
+169
+00:15:29,780 --> 00:15:33,120
+كلها مسميات لاتينية متعنينيش كتير قبل ما يعنيني
+
+170
+00:15:33,120 --> 00:15:37,530
+أنا التطبيق تبع في القانون اللي موجود عندي هناتبعت
+
+171
+00:15:37,530 --> 00:15:42,470
+ال role مين ال hypothesis هيهم P and P implies Q
+
+172
+00:15:42,470 --> 00:15:45,970
+يعني في عندي two conditions مجموعين في compound
+
+173
+00:15:45,970 --> 00:15:50,150
+condition بينهم and مكتوبهم بالصورة هذه therefore
+
+174
+00:15:50,150 --> 00:15:56,990
+و لذلك ال conclusion قدت إلى Q الآن في أي اثبات لو
+
+175
+00:15:56,990 --> 00:16:01,850
+لجأت انا two conditions يتوفروا عندي بالصورة هذه P
+
+176
+00:16:01,850 --> 00:16:10,100
+و P implies Q مباشرة بستبدلهم بينبـ Q لاحظوا الان
+
+177
+00:16:10,100 --> 00:16:13,720
+في عندى proposition اتنين تلاتة مشكلة ما بينهم
+
+178
+00:16:13,720 --> 00:16:16,280
+compound و proposition انا خلصت منهم ب simple
+
+179
+00:16:16,280 --> 00:16:19,740
+proposition حقيت من اللي هم الـ Q وبالتالي سبصير
+
+180
+00:16:19,740 --> 00:16:23,360
+عندى موضوع الاثبات اسهل بحيث ان انا اقدر انتقل ل
+
+181
+00:16:23,360 --> 00:16:26,540
+next step عشان هيك بنقول ان ال role of inferences
+
+182
+00:16:26,540 --> 00:16:31,380
+تديني justification تديني تبرير ليش انا انتقلت
+
+183
+00:16:31,380 --> 00:16:34,280
+الخطوة هذه للخطوة هذه ليش انا اختسرت هذه و بدلتها
+
+184
+00:16:34,280 --> 00:16:41,200
+بهذهلما بكون في عندي اكتر من condition ان من ال
+
+185
+00:16:41,200 --> 00:16:44,180
+conditions و هذا الكلام ممكن لما باجي اقول على
+
+186
+00:16:44,180 --> 00:16:50,700
+سبيل المثال في المثلث قائم الزاوية طول الوتر تربيه
+
+187
+00:16:50,700 --> 00:16:56,540
+يساوي مجموع مربعات الضلعين الآخرين قانون في الثغرس
+
+188
+00:16:56,540 --> 00:17:02,800
+في عندي condition في عندي condition في عندي
+
+189
+00:17:02,800 --> 00:17:07,260
+condition ايش هو ال condition؟إن المثلث لازم يكون
+
+190
+00:17:07,260 --> 00:17:11,660
+قائم الزاوية إن المثلث لازم يكون قائم الزاوية
+
+191
+00:17:11,660 --> 00:17:14,920
+بالضبط الآن لما بكون .. هذا طبعا مثال في one
+
+192
+00:17:14,920 --> 00:17:17,940
+condition لما بكون في عندي أكثر من condition بدك
+
+193
+00:17:17,940 --> 00:17:21,240
+تفهم إن العلاقة ما بين ال conditions المختلفات
+
+194
+00:17:21,240 --> 00:17:26,480
+هدول and الرابط ما بين ال simple proposition هدول
+
+195
+00:17:26,480 --> 00:17:32,760
+او ال conditions هو مثال بت ال and هذه
+
+196
+00:17:32,760 --> 00:17:33,680
+مجموعة ال rules
+
+197
+00:17:36,370 --> 00:17:41,890
+هي اول احنا شوفنا اول واحد P and P implies Q اذا Q
+
+198
+00:17:41,890 --> 00:17:49,890
+هى فى عندى بقول نقطة Q and P implies Q هذا يمثل
+
+199
+00:17:49,890 --> 00:17:59,910
+نقطة ال P نقطة ال P P implies Q Q implies R اذا او
+
+200
+00:17:59,910 --> 00:18:04,640
+therefore ال conclusion P impliesألاحظ ان تتولجي
+
+201
+00:18:04,640 --> 00:18:11,860
+تبعتي شكل التتولجي هيها موجودة بي قره كيو و نطق ال
+
+202
+00:18:11,860 --> 00:18:25,280
+دي و لذلك بي قره كيو بي و كيو و لذلك بي قره كيو بي
+
+203
+00:18:25,280 --> 00:18:30,300
+قره كيو بي قره كيو تؤدي
+
+204
+00:18:30,300 --> 00:18:42,900
+إلى بيهدف التتولوجي صح هو اللي بقولها صح صح نفي
+
+205
+00:18:42,900 --> 00:18:54,960
+هدف التتولوجي نفي P and Q or ال P وزع النفي نقطة P
+
+206
+00:18:54,960 --> 00:18:59,660
+or نقطة Q or P
+
+207
+00:19:01,710 --> 00:19:09,030
+true تتولوجي بس طبعا بكتمل توزية توزية في الأول اه
+
+208
+00:19:09,030 --> 00:19:12,930
+عفوا تبديل وبعدين تجميع عشان جيب ال B نقطة ال B مع
+
+209
+00:19:12,930 --> 00:19:15,990
+ال D بال orb في الآخر المحصة هي تتولوجي فهي
+
+210
+00:19:15,990 --> 00:19:20,230
+تتولوجي وبالتالي هذا القانون صح طيب برضه لحد ت
+
+211
+00:19:20,230 --> 00:19:24,210
+اللحظة مش قادر استوعب انه ايش صح تعالى نشوف شكلة
+
+212
+00:19:24,210 --> 00:19:27,210
+تانية او شغلة تانية احنا هيك اثبتنا انها تتولوجي
+
+213
+00:19:27,210 --> 00:19:31,200
+تعالى نشوفهل الكلام هذا بالكلام البسيط منطقي ولا
+
+214
+00:19:31,200 --> 00:19:38,700
+لأ؟ بقول لو كانت B and Q معناته true لو كانت B and
+
+215
+00:19:38,700 --> 00:19:47,400
+Q is true تمام ال conclusion تبعتنا B طيب هذا role
+
+216
+00:19:47,400 --> 00:19:53,540
+of inferences ال condition يؤدي إلى conclusion ال
+
+217
+00:19:53,540 --> 00:19:59,440
+condition true ال conclusion trueB and Q عشان تكون
+
+218
+00:19:59,440 --> 00:20:03,900
+صحيحة، ايش لازم يكون عندك؟ لازم تنتينيكونه صحيحة
+
+219
+00:20:03,900 --> 00:20:10,580
+هذي صحيحة و هذي صحيحة يعني للـB نفسها صحيحة و مش
+
+220
+00:20:10,580 --> 00:20:14,080
+بس هيك ممكن تستبدل الـB هذي بإيش بـQ عند الحاجة
+
+221
+00:20:14,080 --> 00:20:18,480
+وبالتالي تبقى المسألة صحيحة هنا بدأت بدأت تشغل
+
+222
+00:20:18,480 --> 00:20:22,180
+دماغك فعليا في العناصر الموجودة دعالي نشوف المسألة
+
+223
+00:20:22,180 --> 00:20:28,270
+اللي منها وفاق بقول لو كانت عندك ABلو كانت عندك
+
+224
+00:20:28,270 --> 00:20:28,530
+الـ B
+
+225
+00:20:35,640 --> 00:20:40,000
+P implies P or Q لو كانت عندك ال condition P
+
+226
+00:20:40,000 --> 00:20:45,340
+لحالها is it true فتحط ال D نقلة او تقدي إلى true
+
+227
+00:20:45,340 --> 00:20:51,100
+ك conclusion فانت ضمنت عندك ال P مع or يعني ال P
+
+228
+00:20:51,100 --> 00:20:54,360
+بتتعامل معها as a true value أصبحت true أيش ما تحط
+
+229
+00:20:54,360 --> 00:20:58,500
+لها مع ال or فبتكون ال conclusion تبعتك أيش؟true
+
+230
+00:20:58,500 --> 00:21:01,740
+وبالتالي هذا ال role مهم جدا يا شباب لما نيجي
+
+231
+00:21:01,740 --> 00:21:05,320
+نتكلم على الاختزال او اثبات لان فعلا هنشوف كمان
+
+232
+00:21:05,320 --> 00:21:10,480
+مرة مثال او اتنين من اجل اثبات النظريات بالاعتماد
+
+233
+00:21:10,480 --> 00:21:15,840
+على ال role of inferences طيب تمام الان انا في
+
+234
+00:21:15,840 --> 00:21:21,080
+عندي شغلة مهمة بقدر ال role of inferences اللي
+
+235
+00:21:21,080 --> 00:21:24,400
+احنا بيسميها ال argument اتفقنا ال argument هي
+
+236
+00:21:24,400 --> 00:21:29,510
+عبارة عن مجموعة ايش؟مجموعة عوامل عوامل ايه اش
+
+237
+00:21:29,510 --> 00:21:33,350
+مجموعة ال conditions وال conclusion مع بعض ال
+
+238
+00:21:33,350 --> 00:21:36,650
+condition وال conclusion مع بعض مثلا منهم ايه اش
+
+239
+00:21:36,650 --> 00:21:43,930
+argument ال argument تباعتي هذه علاقتها مع بعض مثل
+
+240
+00:21:43,930 --> 00:21:48,970
+ال rule of inferences ان عندي اكثر من hypothesis
+
+241
+00:21:48,970 --> 00:21:54,230
+بتقدي ل conclusion بقول عن ال argument valid بقول
+
+242
+00:21:54,230 --> 00:21:59,960
+عن ال argument validwhenever وين ما بلاقي ان ال
+
+243
+00:21:59,960 --> 00:22:04,180
+hypothesis مع بعضهم كلهم are true و اتذكر ان ال
+
+244
+00:22:04,180 --> 00:22:11,640
+hypothesis بواحد and باتنين and بتلاتة إلى and بم
+
+245
+00:22:11,640 --> 00:22:15,140
+لما يكونوا كلهم مع بعض true طب عشان كلهم مع بعض
+
+246
+00:22:15,140 --> 00:22:20,140
+يكونوا true لازم كل واحدة بشكل مستقل تكوناش true
+
+247
+00:22:20,140 --> 00:22:24,220
+هيقدّي ان ال conclusion تبعتي لازم تكون .. طيب لو
+
+248
+00:22:24,220 --> 00:22:28,860
+واحدة كانت منهم falseبيعني ليش افحص؟ بيعني ليش؟
+
+249
+00:22:28,860 --> 00:22:32,080
+انا بيعني حالة واحدة فقط ان وين ما تكون ال
+
+250
+00:22:32,080 --> 00:22:36,300
+condition كلها true لازم ال conclusion يكون true
+
+251
+00:22:36,300 --> 00:22:39,400
+وبالتالي هذا ال argument او هذه التركيبة او هذه
+
+252
+00:22:39,400 --> 00:22:43,380
+التوليفة او هذه النظرية ال argument تبعتها ياشهي
+
+253
+00:22:44,210 --> 00:22:47,990
+valid valid بقدراش أسعى في أثباتها أو أقدر أتكلم
+
+254
+00:22:47,990 --> 00:22:52,190
+عليها بالشكل هذا عشان ما انتهش كتير احنا في
+
+255
+00:22:52,190 --> 00:22:56,530
+الموضوع هذا تعالى نشوف اول role of inferences اللي
+
+256
+00:22:56,530 --> 00:22:57,710
+احنا شوفناها قبل شوية
+
+257
+00:23:14,870 --> 00:23:20,550
+هو ايش قاعد بيقوللي whenever P implies the
+
+258
+00:23:20,550 --> 00:23:26,570
+condition is true يعني P لازم تكون true و ان هذي
+
+259
+00:23:26,570 --> 00:23:30,250
+تكون true هتقول لمين؟ لو بدني اتكلمها بشكل بسيط
+
+260
+00:23:30,250 --> 00:23:32,910
+whenever نتي هذي الكلام بيكون true هذي ما تكون
+
+261
+00:23:32,910 --> 00:23:38,130
+true و هذي لازم تكون true هذي متى بتكون true بي
+
+262
+00:23:38,130 --> 00:23:43,170
+تقول او true تقول الى .. فش غير هيك هذا الحالة
+
+263
+00:23:43,170 --> 00:23:48,660
+الوحيدة اللي عندىمصدوق ولا لأ؟ هذه حالات تانية
+
+264
+00:23:48,660 --> 00:23:53,320
+ممكن تتمشي فيها false تقول الى true و false تقول
+
+265
+00:23:53,320 --> 00:23:56,160
+الى false هذه برضه بتديني ال implication true بس
+
+266
+00:23:56,160 --> 00:24:01,320
+مقدرش استخدمهم ليش؟ لإن حددت قيمة ال B مسبقا
+
+267
+00:24:01,320 --> 00:24:04,400
+باعتماد على مين ال and او بين جثنين ال and اللي
+
+268
+00:24:04,400 --> 00:24:08,580
+ألزمتني أشتغل بسمع الحالة هذه وبالتالي أنا صرت هي
+
+269
+00:24:08,580 --> 00:24:12,920
+هي الحالة الوحيدة اللي عندي الحالة الوحيدة B is
+
+270
+00:24:12,920 --> 00:24:17,470
+trueو Q is true وبالتالي بتروح فحص ال implication
+
+271
+00:24:17,470 --> 00:24:22,730
+true implies true true وبالتالي هتصبح and ال
+
+272
+00:24:22,730 --> 00:24:28,030
+implication true and true implies true الكل
+
+273
+00:24:28,030 --> 00:24:38,010
+implies true تلقى true true and true true implies
+
+274
+00:24:38,010 --> 00:24:41,830
+true معناته هذا بتكلم على validargument بتتكلم على
+
+275
+00:24:41,830 --> 00:24:45,710
+valid argument و لو بدى أروح بشغل أطول شوية ممكن
+
+276
+00:24:45,710 --> 00:24:48,750
+يكون أسهل بالنسبة إليك الآن ابني جدول الاحتمالات
+
+277
+00:24:48,750 --> 00:24:53,370
+لل tautology هذه عبارة عن ايش يا شباب؟ عبارة عن
+
+278
+00:24:53,370 --> 00:24:57,810
+tautology يعني قيمة ال condition هذا او ال .. هي
+
+279
+00:24:57,810 --> 00:25:04,550
+عبارة عن ال true كان variable عندى ايه؟ 2 B و Q
+
+280
+00:25:04,550 --> 00:25:12,220
+true true false false true falsetrue false بعد هيك
+
+281
+00:25:12,220 --> 00:25:21,880
+P implies Q true false true true P and P implies Q
+
+282
+00:25:21,880 --> 00:25:31,500
+هاي هم true false false لا بس لحظة شوية هنا ال
+
+283
+00:25:31,500 --> 00:25:37,890
+true falsefalse false تمام ايه الضغط اللي عندي ضغط
+
+284
+00:25:37,890 --> 00:25:42,830
+اللي عندي ال role الأخير زي ما هو هيك P and P
+
+285
+00:25:42,830 --> 00:25:49,910
+implies Q الكل implies Q هذا يقول إلى هذا ال true
+
+286
+00:25:49,910 --> 00:25:57,590
+implies true true false implies true true false
+
+287
+00:25:57,590 --> 00:26:03,000
+implies true true false implies falsetrue لازم
+
+288
+00:26:03,000 --> 00:26:06,320
+يكون كلهم true لأنها عبارة عن تيتولوجي لازم يكون
+
+289
+00:26:06,320 --> 00:26:13,700
+كلهم true مصبوط بس أصبر شوية أصبر كلهم لازم يكونوا
+
+290
+00:26:13,700 --> 00:26:17,100
+true لأن هذه عبارة عن تيتولوجي بس ليش أنا بقول
+
+291
+00:26:17,100 --> 00:26:22,680
+valid argument لأن whenever all the hypothesis are
+
+292
+00:26:22,680 --> 00:26:26,100
+true وين الصف اللي فيه ال hypothesis تعوني كلهم مع
+
+293
+00:26:26,100 --> 00:26:29,800
+بعض ال true كم hypothesis أنا عندى؟ كم hypothesis
+
+294
+00:26:29,800 --> 00:26:35,230
+أنا عندى؟هي ال hypothesis اللي عندي عندي تنتين بي
+
+295
+00:26:35,230 --> 00:26:40,510
+هي ال بي و ال بي in boys queue هيهم متى القيمتين
+
+296
+00:26:40,510 --> 00:26:44,290
+هدول بيكونوا مع بعض true لو طلعناها بس في الصف
+
+297
+00:26:44,290 --> 00:26:51,990
+الأول هان و هان whenever all its hypothesis are
+
+298
+00:26:51,990 --> 00:26:56,390
+true وينما بتكون الفرضيات تبعتها true whenever the
+
+299
+00:26:56,390 --> 00:27:02,110
+hypothesis are true it will lead the conclusionIs
+
+300
+00:27:02,110 --> 00:27:05,270
+it true؟ وبالتالي هذا الصف هو الوحيد اللي يعنيني
+
+301
+00:27:05,270 --> 00:27:09,470
+عشان اقول عليها valid ولا invalid argument. هذي
+
+302
+00:27:09,470 --> 00:27:13,490
+valid argument. ليش؟ لأن وين ال two argument او ال
+
+303
+00:27:13,490 --> 00:27:18,100
+two hypothesis تعوني كانوا true؟تدوني true طب
+
+304
+00:27:18,100 --> 00:27:22,100
+الباقى يا أستاذ true و false .. false و false ..
+
+305
+00:27:22,100 --> 00:27:24,000
+false و false .. ماليش داخل فيهم .. خلاص معناته
+
+306
+00:27:24,000 --> 00:27:27,880
+أنا بص بالصف اللى بحقق الشرق عشان أفحص ال validity
+
+307
+00:27:27,880 --> 00:27:32,700
+تبعت ال argument اللى عندي otherwise لو كان هذا
+
+308
+00:27:32,700 --> 00:27:37,460
+يقول الى false معناته
+
+309
+00:27:37,460 --> 00:27:40,360
+خلصنا .. معناته invalid argument .. invalid
+
+310
+00:27:40,360 --> 00:27:42,320
+argument .. تمام؟
+
+311
+00:27:48,350 --> 00:27:55,170
+تعالى نشوف الـ argument اللى موجود عندى هنا في
+
+312
+00:27:55,170 --> 00:27:58,970
+عند ال rule of inferences بقول بي implies كيو و
+
+313
+00:27:58,970 --> 00:28:05,650
+كيو implies الار therefore كيو بي implies الار هذا
+
+314
+00:28:05,650 --> 00:28:09,950
+واحد من ال rules لو بدنا نرجع هنا هيو لا مش الآخر
+
+315
+00:28:09,950 --> 00:28:16,380
+تالت هيوطيب .. الآن هذا ال rule .. لما انا بدي ..
+
+316
+00:28:16,380 --> 00:28:19,420
+كمان مرة انا جاعد شباب مش جاعد بأثبت انه rule of
+
+317
+00:28:19,420 --> 00:28:23,900
+inferences تمام؟ انا بدي أثبت انه valid argument
+
+318
+00:28:23,900 --> 00:28:26,460
+.. جاعد بقوللي افحص ال argument هذه valid ولا
+
+319
+00:28:26,460 --> 00:28:31,610
+invalid .. من ال argument اللي عندي انا هانهيهم
+
+320
+00:28:31,610 --> 00:28:34,990
+واحد اتنين تلاتة ال argument هم عبارة عن ال
+
+321
+00:28:34,990 --> 00:28:39,550
+conditions بالإضافة لمين ل ال conclusion لما بدن
+
+322
+00:28:39,550 --> 00:28:45,810
+جدول الاحتمالات بتهم الصفوف فقط اللي بتكون فيها ال
+
+323
+00:28:45,810 --> 00:28:51,570
+two conditions are true هيبني الجدول الاحتمالات هي
+
+324
+00:28:51,570 --> 00:28:55,530
+B و هي Q و هي R مع ان انا بتتكلم عن جدول مكون من
+
+325
+00:28:55,530 --> 00:29:00,790
+تمام صفوف B implies Q و Q implies R
+
+326
+00:29:05,250 --> 00:29:11,290
+روحتنا فحصنا ال argument اللي موجودة عندها hand
+
+327
+00:29:11,290 --> 00:29:18,230
+true الصف هذا لازم انا اتكد منه قيمته ممتاز بنتقل
+
+328
+00:29:18,230 --> 00:29:23,350
+للي بعده لأ اللي بعده اللي بعده هيو هذا لازم يكون
+
+329
+00:29:23,350 --> 00:29:29,240
+ال output تبعته true هيو هذاالـ output تبعته true
+
+330
+00:29:29,240 --> 00:29:32,040
+لبعده الـ output تبعته true طب اللي في النص هدول
+
+331
+00:29:32,040 --> 00:29:35,900
+بيعنونيش لإن هم حققوش ال condition تبع مين تبع ال
+
+332
+00:29:35,900 --> 00:29:39,260
+valid argument ال valid argument كان بيقولي بقول
+
+333
+00:29:39,260 --> 00:29:43,400
+عن هدولة valid argument لما بتكون whenever all the
+
+334
+00:29:43,400 --> 00:29:46,920
+hypothesis all the conditions are true وين هم اللي
+
+335
+00:29:46,920 --> 00:29:50,420
+بتبتدوا true عليهم في الصوفة المحددة ده باللون
+
+336
+00:29:50,420 --> 00:29:55,060
+الأخضر وبالتالي كانت تعمل leadالصحيحة فهذه صحيحة
+
+337
+00:29:55,060 --> 00:30:00,560
+فهذه صحيحة ايش؟ الارجومنت لو انت لجيت هذه
+
+338
+00:30:00,560 --> 00:30:05,800
+الاختلافات ماتكملش خلاص تفحصش انفاليد طب ماهم
+
+339
+00:30:05,800 --> 00:30:11,240
+يجايفوا في فروع تانية not all صار في اندي there
+
+340
+00:30:11,240 --> 00:30:11,840
+exist
+
+341
+00:30:14,330 --> 00:30:17,090
+one row where all the arguments or the hypothesis
+
+342
+00:30:17,090 --> 00:30:21,390
+are true lead to false وبالتالي نفينا ال
+
+343
+00:30:21,390 --> 00:30:26,490
+definition تبعت العناصر اللي موجودة عندها تعالى
+
+344
+00:30:26,490 --> 00:30:31,350
+نشوف المثال هذا بنعمله ترجمة ونشوف هل هو بطلع
+
+345
+00:30:31,350 --> 00:30:36,870
+valid argument ولا لأ if I like discrete
+
+346
+00:30:36,870 --> 00:30:40,830
+mathematics إذا
+
+347
+00:30:40,830 --> 00:30:48,440
+أنا حبيت الرياضة المنفصلةأول شرط false طيب I'll
+
+348
+00:30:48,440 --> 00:30:55,400
+study it معناته انا بقدر اجي اقول P I like
+
+349
+00:30:55,400 --> 00:31:04,880
+discrete mathematics Q I will study discrete
+
+350
+00:31:04,880 --> 00:31:10,230
+mathematicsطبعا لاحظ ان انا عمال بفصل .. بدي اوصل
+
+351
+00:31:10,230 --> 00:31:13,810
+ال conditions تبعتي ..الان لاحظ انا عمال بفصل
+
+352
+00:31:13,810 --> 00:31:19,030
+الشباب في .. بفصل في مين .. بحاول اترجم كل المسألة
+
+353
+00:31:19,030 --> 00:31:22,990
+..الان صار في اندهان ال argument او ال condition
+
+354
+00:31:22,990 --> 00:31:27,360
+الأولB implies Q هذا ال condition الأول لسه
+
+355
+00:31:27,360 --> 00:31:31,400
+ماوصلتش ل conclusion either I study I study هي مش
+
+356
+00:31:31,400 --> 00:31:35,220
+مشكلة او I study مش قضية كتير discrete mathematics
+
+357
+00:31:35,220 --> 00:31:42,120
+or I fail the course هي Q او هي R I fail رصبت the
+
+358
+00:31:42,120 --> 00:31:47,520
+course ال course رصبت في المساق معناته ال
+
+359
+00:31:47,520 --> 00:31:52,540
+condition التاني عندى either I study I study when
+
+360
+00:31:52,540 --> 00:32:01,190
+QQ or R نقطة حطلي Therefore عشان يقولي اللي جاي هو
+
+361
+00:32:01,190 --> 00:32:06,350
+عبارة عنين؟ عن ال conclusion Therefore
+
+362
+00:32:06,350 --> 00:32:13,010
+if I fail the course then I don't like discrete
+
+363
+00:32:13,010 --> 00:32:18,770
+mathematics إذا أنا رصبت ال R تقول إلى نقطة ال B
+
+364
+00:32:18,770 --> 00:32:28,340
+نقطة ال B مصبوط؟الان لاحظ اول شي ترجمت النص ل
+
+365
+00:32:28,340 --> 00:32:31,740
+simple proposition بعدين حولته ل compound
+
+366
+00:32:31,740 --> 00:32:35,060
+proposition بناء على فهم المعادلة therefore كانت
+
+367
+00:32:35,060 --> 00:32:39,180
+الفيصل تقول كل اللي فات عبارة عن ال conclusion
+
+368
+00:32:39,180 --> 00:32:44,300
+وكنت انا بتلاحظ ال forest top هذي كانت بتقولي ال
+
+369
+00:32:44,300 --> 00:32:47,420
+condition الأول خلص ال condition التاني بدأ وما
+
+370
+00:32:47,420 --> 00:32:50,120
+شبه تمام
+
+371
+00:32:50,930 --> 00:32:57,850
+الان بقول افحص هل هذا valid argument ولا لأ؟ عشان
+
+372
+00:32:57,850 --> 00:33:00,930
+تفحص ال validity معناته تبدا تجيب كل احتمالات اللي
+
+373
+00:33:00,930 --> 00:33:05,050
+بتكون هذه فيها true فاسهل حاجة بالنسبالك الجدول
+
+374
+00:33:05,050 --> 00:33:12,130
+الاحتمالات هذا كلام اكيد طيب في
+
+375
+00:33:12,130 --> 00:33:19,310
+جدول الاحتمالات كام صفر محتاجين احنا؟ B و implies
+
+376
+00:33:19,310 --> 00:33:26,520
+a Q وRبعده تمانية true true true true false false
+
+377
+00:33:26,520 --> 00:33:34,540
+false false true true false false true true false
+
+378
+00:33:34,540 --> 00:33:39,680
+false true
+
+379
+00:33:39,680 --> 00:33:46,700
+false true false true false
+
+380
+00:33:50,450 --> 00:33:57,190
+ال condition الأول B implies Q true implies true
+
+381
+00:33:57,190 --> 00:34:04,770
+true true false false لحظة شوية عشان انا هحط كل
+
+382
+00:34:04,770 --> 00:34:11,670
+قيمة مانجوحش الخربط هات true هات false هات false
+
+383
+00:34:11,670 --> 00:34:16,410
+هات true true true true
+
+384
+00:34:18,930 --> 00:34:22,910
+B implies Q true implies true true true false
+
+385
+00:34:22,910 --> 00:34:30,170
+false و الباقي كله true ال condition التاني Q
+
+386
+00:34:30,170 --> 00:34:43,610
+or R Q or R true true true false true true true
+
+387
+00:34:43,610 --> 00:34:51,210
+false Q و R هايهمالتنتين صحيح صحيح صحيح صحيح خاطئ
+
+388
+00:34:51,210 --> 00:34:56,210
+صحيح صحيح صحيح صحيح خاطئ الانشبوك اللي هو عشان
+
+389
+00:34:56,210 --> 00:35:00,770
+تكون هذه valid argument whenever وينما بتكون عندك
+
+390
+00:35:00,770 --> 00:35:07,650
+الصفوف التنتين مع بعض صحيح هاي
+
+391
+00:35:07,650 --> 00:35:13,830
+الصف هاي التاني اللي بعده لأ اللي بعده هاي واحدة
+
+392
+00:35:13,830 --> 00:35:19,770
+هاي التنتين هاي التلاتةهدولة التلات صفوف اللي أنا
+
+393
+00:35:19,770 --> 00:35:25,290
+معنى فيهم إذا هدولة التلخمس صفوف عملوا lie implies
+
+394
+00:35:25,290 --> 00:35:28,910
+ل true معاكوا هذا valid argument لو واحدة منهم
+
+395
+00:35:28,910 --> 00:35:32,410
+عملت implies ل false والباقي عمل ل true فهي بتكون
+
+396
+00:35:32,410 --> 00:35:38,430
+invalid argument تعالى نشوف الأخيرة اللي هي ال R
+
+397
+00:35:38,430 --> 00:35:44,790
+implies نقطة ال B هاي ال R وهي نقطة ال B true
+
+398
+00:35:44,790 --> 00:35:54,010
+implies falsetrue implies false true
+
+399
+00:35:54,010 --> 00:36:02,070
+implies false false خلصنا نفي نقطة بيعني ع مال بنا
+
+400
+00:36:02,070 --> 00:36:06,170
+فيها بقولك ال true implies false بناء على ال role
+
+401
+00:36:06,170 --> 00:36:10,230
+اللي عندها ال false أكمل لا تكملش خلصنا
+
+402
+00:36:14,510 --> 00:36:17,850
+أه لما تشوف .. لو هذا كلها true .. فتبحث اللي
+
+403
+00:36:17,850 --> 00:36:22,210
+باقيها .. خلاص اتكملش .. انا مسئول علي الكلام ..
+
+404
+00:36:22,210 --> 00:36:25,490
+لإن وين بتصير .. صار في عندك واحدة أو الشرط مختلف
+
+405
+00:36:25,490 --> 00:36:29,190
+.. لإن كان الشرط بيقول إيه .. عند كل هدولة لازم
+
+406
+00:36:29,190 --> 00:36:33,530
+تكون ال conclusion true .. عند هي أول واحدة طلعت
+
+407
+00:36:33,530 --> 00:36:37,230
+ال conclusion false .. تمام؟ معينة و أنا بقدر أقول
+
+408
+00:36:37,230 --> 00:36:41,180
+عنها invalid ..Argument بدون ان اكمل الجدول و لو
+
+409
+00:36:41,180 --> 00:36:44,160
+كملت يا رامي هطلع معاك الجدول زي ما هو هنا انا
+
+410
+00:36:44,160 --> 00:36:46,720
+بكملك ايه على ال slide طبعا عشان اريح راسي
+
+411
+00:36:50,910 --> 00:36:54,890
+من أوليتها false معناته لأن بمجرد ان انا كملت جدول
+
+412
+00:36:54,890 --> 00:37:00,790
+الاحتمالات وفحصت هيلاحظ اول تنتين conditions true
+
+413
+00:37:00,790 --> 00:37:03,310
+and true لازم تعمل lead معايا او تكون ال
+
+414
+00:37:03,310 --> 00:37:07,610
+conclusion معايا true بمجرد اني لاجيتها false فهذا
+
+415
+00:37:07,610 --> 00:37:12,270
+هو invalid argument كملت الجدول ولا ماكملتهش بطل
+
+416
+00:37:12,270 --> 00:37:15,990
+اتفرج كتير خلاص معك فانا ضمنت ان هذا الكلام false
+
+417
+00:37:15,990 --> 00:37:17,750
+invalid argument
+
+418
+00:37:21,000 --> 00:37:28,060
+جاهز بيقول لي شوف لهذا المثال if 101 is divisible
+
+419
+00:37:28,060 --> 00:37:32,200
+by 3 إذا كان 101 تقبل الجسم على 3 معناته 112 تقبل
+
+420
+00:37:32,200 --> 00:37:38,980
+الجسم على 9 101 تقبل الجسم على 3 for stop
+
+421
+00:37:38,980 --> 00:37:43,900
+consequently therefore conclusion 102 is divisible
+
+422
+00:37:43,900 --> 00:37:48,500
+byتسعة او ألف و أتناش عفوية تجبل الجسم علاقة تسعة
+
+423
+00:37:48,500 --> 00:37:52,840
+هاي ال conditions اللي عندي الاول ال condition
+
+424
+00:37:52,840 --> 00:37:55,340
+الاول هي ال simple arguments او عفر ال simple
+
+425
+00:37:55,340 --> 00:38:03,540
+proposition بي اندواز كيو اللي بعده بي لإن هي جميع
+
+426
+00:38:03,540 --> 00:38:10,220
+واحد is divisible by three therefore كيو
+
+427
+00:38:10,220 --> 00:38:17,890
+كلامه ك argument هيهمهذه الاختصارات وهذه
+
+428
+00:38:17,890 --> 00:38:20,790
+الاختصارات وهذه الاختصارات هل هذا valid argument
+
+429
+00:38:20,790 --> 00:38:26,650
+ولا invalid افحص ممكن استخدم جدول الاحتجازات و
+
+430
+00:38:26,650 --> 00:38:34,190
+اشوف و ممكن اذهب للقوانين هاي القانون عندي هاي
+
+431
+00:38:34,190 --> 00:38:39,830
+الشكل اللي عندي هاي
+
+432
+00:38:39,830 --> 00:38:43,940
+الشكل B implies Qcondition الأول condition التاني
+
+433
+00:38:43,940 --> 00:38:53,520
+B therefore Q شجبه عشان أحصل على الترتيب الترتيب
+
+434
+00:38:53,520 --> 00:38:57,300
+ليش؟ عشان الطابق هان مع role of conferences اللي
+
+435
+00:38:57,300 --> 00:39:02,900
+موجود عندي هيه هيه لاحظ هذا و لاحظ هذا شوف التنين
+
+436
+00:39:02,900 --> 00:39:09,760
+هدول مهمات و عليهم هو إيش الشغل بعد
+
+437
+00:39:09,760 --> 00:39:15,780
+ما رتبنا هانهذا هيك .. therefore Q لأ بس الأصل هذا
+
+438
+00:39:15,780 --> 00:39:21,440
+إيش بيطلع بيطلع بـQ و لا بيطلع بـB حسب القانون هذه
+
+439
+00:39:21,440 --> 00:39:24,140
+القوانين كلها بتطلع معايا هيك وبالتالي هذا ال
+
+440
+00:39:24,140 --> 00:39:28,360
+condition is false وبالتالي invalid argument
+
+441
+00:39:28,360 --> 00:39:31,160
+معناته هذا ال hypothesis تبعتي مش سليمة يعني
+
+442
+00:39:31,160 --> 00:39:35,780
+invalid argument عارف ليش invalid argument؟ شوية
+
+443
+00:39:35,780 --> 00:39:39,960
+بس .. عشان أقولك أن ال hypothesis تبعتي false 101
+
+444
+00:39:39,960 --> 00:39:47,760
+لا تقبل قسم ع 3101 هيها هذه لا تقبل قسمها تلاتة
+
+445
+00:39:47,760 --> 00:39:53,320
+فهذه قيمتها false ولا عمرها حسب ال condition هذه
+
+446
+00:39:53,320 --> 00:39:57,140
+هتكون true عندي عشان تكون true بدي استخدم النفي
+
+447
+00:39:57,140 --> 00:40:01,060
+وبالتالي هذا القانون الشكل هذا لا يحقق عندي أو لا
+
+448
+00:40:01,060 --> 00:40:04,680
+يتحقق وبالتالي هذه عبارة عن invalid argument ال
+
+449
+00:40:04,680 --> 00:40:10,540
+conclusion incorrect لأن فعمليا كمان الأربعة لا
+
+450
+00:40:10,540 --> 00:40:15,800
+تقبل قسمها التسعةاللي هي 1012 اجمع الأرقام و جسمه
+
+451
+00:40:15,800 --> 00:40:20,520
+على 9 انت
+
+452
+00:40:20,520 --> 00:40:24,200
+سعيد ان انت بتشتغل على هيك هاي ال rules لإن هذا ال
+
+453
+00:40:24,200 --> 00:40:26,180
+rule هي اللي قعدت ترتيبه عشان طابق الصورة اللي
+
+454
+00:40:26,180 --> 00:40:30,680
+موجود عندي في الجدول تمام؟ لكن اختلف في وين؟ في ال
+
+455
+00:40:30,680 --> 00:40:34,080
+Q الآن وبالتالي هو الصحي اللي يجب أن يطلع عندي نفي
+
+456
+00:40:34,080 --> 00:40:37,020
+ال B لازم يطلع هي القانون اللي عندي انا بقوله انا
+
+457
+00:40:37,020 --> 00:40:41,360
+بحصل على نفي ال B لكن تهلأ بمعنى اخر ان هذا الكلام
+
+458
+00:40:41,360 --> 00:40:44,570
+غير صحيحليش غير صحيح؟ تهانى الراجل ال conditions
+
+459
+00:40:44,570 --> 00:40:49,910
+تبعتى 101 لا تقبل القسم على ثلاثة و 1012 لا تقبل
+
+460
+00:40:49,910 --> 00:40:53,030
+القسم على تسعة وبالتالي مستحيل هذا ال condition
+
+461
+00:40:53,030 --> 00:40:57,610
+يكون true وبالتالي هذا invalid argument هذا مثال
+
+462
+00:40:57,610 --> 00:41:01,910
+قريف من الكتاب عشان تصحصه بقولك لو اليوم بتشتي
+
+463
+00:41:01,910 --> 00:41:08,350
+طبعا؟ المعنى انت مش حنشه الليلة بحكته بحكته على
+
+464
+00:41:08,350 --> 00:41:13,720
+الآخر كمان و بعض السنان بينت زى حالتي طبعا؟إذا
+
+465
+00:41:13,720 --> 00:41:22,440
+كانت اليوم مطبرة، فلن نحصل على باربيكو اليوم إذا
+
+466
+00:41:22,440 --> 00:41:26,720
+لم نحصل على باربيكو اليوم،
+
+467
+00:41:26,720 --> 00:41:30,960
+فلن نحصل
+
+468
+00:41:30,960 --> 00:41:42,800
+على باربيكو غير اليوم إذا لم نحصل على باربيكو غير
+
+469
+00:41:42,800 --> 00:41:46,480
+اليومفي train studio لو تشت اليوم معناته احنا
+
+470
+00:41:46,480 --> 00:41:53,740
+هنشويه؟ بكرا شتت بكرا خلاص بتقلق نفس الكلام طيب
+
+471
+00:41:53,740 --> 00:41:58,960
+الان تعالى
+
+472
+00:41:58,960 --> 00:42:02,240
+شوف سيبك من الحل هذا لو كمان هشكل حل تاني بالنسبة
+
+473
+00:42:02,240 --> 00:42:07,240
+اليك تعالى الان لاحظ ال condition الأول هو عبارة
+
+474
+00:42:07,240 --> 00:42:12,600
+عن implies صح ال condition الأول implies ايهش
+
+475
+00:42:12,600 --> 00:42:13,180
+بيقول ايه؟
+
+476
+00:42:25,700 --> 00:42:30,780
+ممكن اكتب له نط كيو على انك اليوم لديك باربيكو
+
+477
+00:42:36,000 --> 00:42:39,020
+الـ Q خلصت من ال condition الأول ال condition
+
+478
+00:42:39,020 --> 00:42:43,260
+التاني if برضه ما زال فيه if و then معناته هو
+
+479
+00:42:43,260 --> 00:42:48,440
+عبارة عن implication if we don't have a barbecue
+
+480
+00:42:48,440 --> 00:42:54,480
+today معناته not Q then
+
+481
+00:42:54,480 --> 00:42:57,380
+we will have a barbecue tomorrow وهدش دي إيه ده
+
+482
+00:42:57,380 --> 00:42:59,900
+بالنسبة لنا have a barbecue tomorrow اللي هتكون
+
+483
+00:42:59,900 --> 00:43:00,820
+إيش R
+
+484
+00:43:03,980 --> 00:43:11,600
+خلصنا Therefore إذا B تقول
+
+485
+00:43:11,600 --> 00:43:16,420
+إلى We will have a barbecue tomorrow إلى R إيش
+
+486
+00:43:16,420 --> 00:43:25,400
+فرجت عن الحل هذا؟ لما عرف ال symbol proposition Q
+
+487
+00:43:25,400 --> 00:43:32,130
+عرفه will not haveيعني دخّل النافي في بنية أو في
+
+488
+00:43:32,130 --> 00:43:35,850
+تعريف الـ Simple Proposition فصارت عنده P implies
+
+489
+00:43:35,850 --> 00:43:41,330
+Q و Q implies R بيفرق معانا الحاجة هان؟ لأ لاحظ
+
+490
+00:43:41,330 --> 00:43:46,990
+الـ Proposition هذا هو نفسه هيوهان وبالتالي أي حل
+
+491
+00:43:46,990 --> 00:43:50,190
+من اتنين هذا برجعنا للكلام الأول اللي قلتلك إياه
+
+492
+00:43:50,190 --> 00:43:55,010
+سابقا طالما أنك بتفسر صح بغض النظر كيف حصلت الـ
+
+493
+00:43:55,010 --> 00:43:58,550
+Proposition المهم لما تكتب الـ Definition اكتبه صح
+
+494
+00:44:01,660 --> 00:44:04,640
+ممكن اتعرف تروح هناك تقول الـQ احنا حسب ال
+
+495
+00:44:04,640 --> 00:44:07,500
+definition تابعتنا ايها We have a barbecue today
+
+496
+00:44:07,500 --> 00:44:13,020
+هل هي الـQ؟ وبالتالي بي implies not the Q مافي
+
+497
+00:44:13,020 --> 00:44:19,240
+الـQ، تمام؟ valid ولا invalid؟ valid argument لأن
+
+498
+00:44:19,240 --> 00:44:22,640
+هذه بالطبق ال rule of inferences اللي اسمه
+
+499
+00:44:22,640 --> 00:44:29,940
+hypothetical soligism او ال chaining اللي هي سلسلة
+
+500
+00:44:30,920 --> 00:44:37,960
+الان هى ال role موجود عندنا هنا هى
+
+501
+00:44:37,960 --> 00:44:42,960
+وان السلسلة .. السلسلة بمثابة ال Q الحلقة ما بين
+
+502
+00:44:42,960 --> 00:44:48,120
+الاتنين اذا كانت A تقول الى B و B تقول الى C
+
+503
+00:44:48,120 --> 00:44:54,240
+فمعناته A تقول الى C تمام
+
+504
+00:44:54,240 --> 00:44:57,240
+نشوف المثال اللى بعده
+
+505
+00:45:10,470 --> 00:45:20,730
+Okay مش مشكلة صاحبة طيب الآن ايش بقوللي بقوللي
+
+506
+00:45:20,730 --> 00:45:27,610
+Gary is either an intelligent or a good actor Gary
+
+507
+00:45:27,610 --> 00:45:35,460
+is intelligent هاي P و هاي RA good actor Q Gary is
+
+508
+00:45:35,460 --> 00:45:39,160
+a good actor Q هال condition الأول If Gary is
+
+509
+00:45:39,160 --> 00:45:46,340
+intelligent B implies then he count from one to
+
+510
+00:45:46,340 --> 00:45:53,200
+ten لو كان Gary ذكي أو شاطر هيعد من واحد لعشرة هدي
+
+511
+00:45:53,200 --> 00:46:00,080
+R Gary can only count from one to three Gary بس
+
+512
+00:46:00,080 --> 00:46:06,410
+بيعد من واحد إلى تلاتةنط ال R. Therefore,
+
+513
+00:46:06,690 --> 00:46:11,990
+conclusion تبعتنا, Gary is a good actor. الهي مين؟
+
+514
+00:46:11,990 --> 00:46:18,090
+ال Q فقط ال Q. تعالى و ردتوهم بي او ري كيو. ال
+
+515
+00:46:18,090 --> 00:46:23,230
+condition الأول بي implies ال R نط ال R.
+
+516
+00:46:24,390 --> 00:46:30,990
+Therefore, ال Q. هاد الآن هاد ال argument تبعتى.
+
+517
+00:46:34,800 --> 00:46:40,600
+هل هي valid argument ولا invalid argument؟ بدك
+
+518
+00:46:40,600 --> 00:46:45,160
+تبدأ تجدوا الاحتمالات وتبدأ تشتغل و تحسب ممكن تاخد
+
+519
+00:46:45,160 --> 00:46:49,440
+وقت كتير لكن لو احنا رجعنا لل role of inferences
+
+520
+00:46:49,440 --> 00:46:55,680
+السادقات ممكن يقولولي هذا الكلام صحيح ولا لأ؟ ايوة
+
+521
+00:46:55,680 --> 00:47:01,100
+..الان ..الان ..تعالى نشوفالترتيب هذا يا شباب
+
+522
+00:47:01,100 --> 00:47:05,480
+هدولة التلت عناصر و بينهم and و احنا ال and عملية
+
+523
+00:47:05,480 --> 00:47:09,340
+ابدالية and هان بين ال conditions هدولة بتايعي
+
+524
+00:47:09,340 --> 00:47:14,020
+conditions و اللي بينهم and و ال and عملية ابدالية
+
+525
+00:47:14,020 --> 00:47:16,880
+يعني بقدر ابدل كل اتنين و اجملهم زي ما بدي ولا لأ
+
+526
+00:47:16,880 --> 00:47:21,220
+حسب خواص ال and طيب تعالى نشوف الخطوات التالية
+
+527
+00:47:21,220 --> 00:47:23,940
+يعني لو انا روحت اشتغلت كالتالية هي ال hypothesis
+
+528
+00:47:23,940 --> 00:47:28,550
+اللي موجودة عندىهو حتى انا اشتغلت في ال hypothesis
+
+529
+00:47:28,550 --> 00:47:32,230
+كالتالي اقعد ترتيبهم نط ال R ال hypothesis الأول
+
+530
+00:47:32,230 --> 00:47:39,550
+بي implies ال R ال hypothesis التاني هيه يعني بين
+
+531
+00:47:39,550 --> 00:47:42,510
+جثين انا بدأ اشتغل على هدول التاني اللي حالهم
+
+532
+00:47:42,510 --> 00:47:48,350
+بينفع اه بينفع يعني هو كأنه جالس بقوله هيك high
+
+533
+00:47:48,350 --> 00:47:55,070
+condition بي or Q and
+
+534
+00:47:55,650 --> 00:48:04,930
+أفتح جوس كبير نقطة الـ R and B implies الـ R صح
+
+535
+00:48:04,930 --> 00:48:10,450
+ولا لا؟ وبدي أحل الجو الجوس في الأول حسب القوانين
+
+536
+00:48:10,450 --> 00:48:14,490
+السادقة اللي في الجدول الشكل هذا هيدين مين يا
+
+537
+00:48:14,490 --> 00:48:21,270
+شباب؟ نقطة الـ B هذا حسب المدرسة تيليناس واحد
+
+538
+00:48:21,270 --> 00:48:24,630
+واتنين اللي هو أول قانونين الموجودة عندنا في
+
+539
+00:48:24,630 --> 00:48:25,230
+الجدول هنا
+
+540
+00:48:28,720 --> 00:48:41,880
+هي نقطة ال R P implies R تديني نفي ال P تمام
+
+541
+00:48:41,880 --> 00:48:46,620
+اداني نفي ال P الان نفي ال P هي عبارة عن المحصلة
+
+542
+00:48:46,620 --> 00:48:51,480
+تبع ال two conditions هدول بل اعملها انت مع مين؟
+
+543
+00:48:51,480 --> 00:48:58,910
+مع ال condition هدى P or Q مية لمية P or Qو في
+
+544
+00:48:58,910 --> 00:49:05,990
+عندي نقطة P بتديني مين؟ ال Q بتديني ال Q هتوصلي
+
+545
+00:49:05,990 --> 00:49:11,110
+ليها ال Q بنفس الترتيب هذا لو بدنا نرجع لورا
+
+546
+00:49:11,110 --> 00:49:16,330
+للقوانين مهمش مرة تانية مش ورا تتعب و انت بترجع
+
+547
+00:49:16,330 --> 00:49:25,170
+معايا وين القوار هايو؟ مصبوط؟ مصبوط؟ فتديني مين؟ P
+
+548
+00:49:25,170 --> 00:49:29,180
+انا فعليا في عندي النف موجود فوق في التنتينفي
+
+549
+00:49:29,180 --> 00:49:35,940
+المسألة هان فأصبحت
+
+550
+00:49:35,940 --> 00:49:42,300
+عند بتديني مين؟ بتديني الـQ، قدتني الـQ حسب ال
+
+551
+00:49:42,300 --> 00:49:47,060
+role of inferences، معناه أن هذه وصلت إلى
+
+552
+00:49:47,060 --> 00:49:52,600
+conclusionال rules أو ال hypothesis اللي فوق وصلون
+
+553
+00:49:52,600 --> 00:49:54,600
+إلى ال conclusion باعتماد على ال rule of
+
+554
+00:49:54,600 --> 00:49:58,080
+inferences وال rule of inferences هي عبارة عن
+
+555
+00:49:58,080 --> 00:50:02,300
+valid argument already و تم إثباتها وبالتالي أنا
+
+556
+00:50:02,300 --> 00:50:07,140
+بقدر أتحقق من ال validity من خاصية ال argument هذه
+
+557
+00:50:07,140 --> 00:50:10,840
+هل هي valid ولا invalid لو فعليا قدرت أستغل ال
+
+558
+00:50:10,840 --> 00:50:15,820
+rule of inferences عشان من ال hypothesis أصل لمين
+
+559
+00:50:15,820 --> 00:50:22,270
+لل conclusionاللي موجودة كيف تحلها؟ ما هي نفسها
+
+560
+00:50:22,270 --> 00:50:29,890
+هيها تهيب تحل هام هيك؟ مايب هذه و هذه حسب ال rule
+
+561
+00:50:29,890 --> 00:50:33,230
+of inferences مش موجودات بس بتقدر تعيد ترتيب
+
+562
+00:50:33,230 --> 00:50:37,290
+العناصر تمام بحيث انك تقول و الله انا بدي ارطبهم
+
+563
+00:50:37,290 --> 00:50:43,310
+هيك تصير هيك ب implies ال R نقطة ال R ب oricute
+
+564
+00:50:43,310 --> 00:50:48,330
+ايش افرجت معاك؟ولا إشي بس قعدت الترتيب الآن حليت
+
+565
+00:50:48,330 --> 00:50:55,270
+اللي فوق هذه و طلعت معايا نط ال B صارت عندي نط ال
+
+566
+00:50:55,270 --> 00:51:01,990
+B PRQ معناه تقريبا هتعطيني EQ وبالتالي وصلت لمين
+
+567
+00:51:01,990 --> 00:51:06,750
+لل conclusion اللي موجودة عندي وبالتالي هدول عبارة
+
+568
+00:51:06,750 --> 00:51:10,430
+عن valid argument للمسألة اللي موجودة وبالتالي
+
+569
+00:51:10,430 --> 00:51:14,710
+Gary is a good actor نعم
+
+570
+00:51:15,960 --> 00:51:25,680
+من ضمن
+
+571
+00:51:25,680 --> 00:51:32,800
+ال role of inferences ال
+
+572
+00:51:32,800 --> 00:51:35,660
+role of inferences ممكن أسقطها كمان على مين يا
+
+573
+00:51:35,660 --> 00:51:39,040
+شباب؟ على ال quantifiers و ال predicate function
+
+574
+00:51:39,040 --> 00:51:48,580
+يا رطيف طيب تعالى نشوف for all x بxfor all x بيكس
+
+575
+00:51:48,580 --> 00:51:51,980
+يعني هيك بقول لأي x في ال domain ال بيكس is true
+
+576
+00:51:51,980 --> 00:51:58,960
+معناته اذا بيكس is true ايش من وين ال c هي عبارة
+
+577
+00:51:58,960 --> 00:52:02,400
+عن عنصر في ال domain عنصر في ال domain في ال
+
+578
+00:52:02,400 --> 00:52:06,640
+domain اللي أخدنا منه x يعني هي حالة خاصة من ال x
+
+579
+00:52:06,640 --> 00:52:11,760
+المعرفة اللي فاج لو كان في اندي بيكس for any
+
+580
+00:52:11,760 --> 00:52:16,030
+arbitrary cلو هذا الكلام بتحقق الـ predicate
+
+581
+00:52:16,030 --> 00:52:20,070
+function بتتحقق على أي arbitrary element c في
+
+582
+00:52:20,070 --> 00:52:25,030
+الدمين معناه تجيه هذه تكافئ for all x,b,x نفس
+
+583
+00:52:25,030 --> 00:52:31,090
+المعنى عكس التاني بالضبط there exist b,x معناه بيه
+
+584
+00:52:31,090 --> 00:52:38,720
+c is true for some element c على الأقل واحدBC for
+
+585
+00:52:38,720 --> 00:52:42,300
+some element C معناه تقرأ بقدر أستبدلها الفكرة وين
+
+586
+00:52:42,300 --> 00:52:45,200
+الشباب أثناء الإثبات لو انت وصليت لهذه تقدر
+
+587
+00:52:45,200 --> 00:52:48,020
+تستبدلها بهذه وهذه تقدر تحط مكانها بهذه هذه
+
+588
+00:52:48,020 --> 00:52:51,900
+المفهوم انك انت تقدر تستخدم بعض ال facts بعض
+
+589
+00:52:51,900 --> 00:52:58,180
+الحقائق من أجل تسهيل عملية الإثبات الرياضي every
+
+590
+00:52:58,180 --> 00:53:02,380
+IUG student is genius طلاب الجامعة الإسلامية
+
+591
+00:53:02,380 --> 00:53:12,500
+عذاكرة أيش رأيك يا رامي؟اقرأي 100% أحمد طالب في
+
+592
+00:53:12,500 --> 00:53:19,180
+الجامعة الإسلامية تمام مع ال conclusion therefore
+
+593
+00:53:19,180 --> 00:53:22,900
+أحمد is a genius اذا كل غلاب الجامعة الإسلامية
+
+594
+00:53:22,900 --> 00:53:27,560
+عباقرة و أحمد مسجل في الجامعة الإسلامية كطالب فهو
+
+595
+00:53:27,560 --> 00:53:32,380
+عبقري و ليش رأيك؟ خلصنا فعليا هذا الكلام هي step
+
+596
+00:53:32,380 --> 00:53:39,760
+الأولىfor all x ux ايش ux اللي هو طالب في الجامعة
+
+597
+00:53:39,760 --> 00:53:45,120
+university student implies genius student تمام
+
+598
+00:53:45,120 --> 00:53:51,240
+step 2 for all أحمد أحمد طالب في الجامعة يقعد إلى
+
+599
+00:53:51,240 --> 00:53:54,780
+تلاتة
+
+600
+00:53:54,780 --> 00:53:58,940
+أحمد طالب و أحمد genius وخلصنا من العلاصر الموجودة
+
+601
+00:53:58,940 --> 00:54:06,250
+for all x bc ليه أحمدB of Ahmed if C تنتمي لل
+
+602
+00:54:06,250 --> 00:54:09,110
+domain اللي موجودة اه هو هذا القانون وهذا هو
+
+603
+00:54:09,110 --> 00:54:15,370
+القانون اللي موجود عندنا هنا و سلامتكم هي خلص ال
+
+604
+00:54:15,370 --> 00:54:18,610
+section هذا و بدنا نقول الشبتر الأول الله يعطيه
+
+605
+00:54:18,610 --> 00:54:21,870
+العافية و ضال فيه عنا section مهم جدا طرق الإثبات
+
+606
+00:54:21,870 --> 00:54:25,150
+الرياضة بس هأخره شوية ايه كده عبل ما تتخمروا شوية
+
+607
+00:54:25,150 --> 00:54:28,430
+في الرياضيات معنا اه هناخره ان شاء الله بس لاحقا
+
+608
+00:54:28,430 --> 00:54:31,530
+في اي سؤال الشباب اللي اقرحنا اليوم باشي الله
+
+609
+00:54:31,530 --> 00:54:32,250
+يعطيكوا العافية شباب
+
diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/0HTI94jFUyM_raw.json b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/0HTI94jFUyM_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..44f5b78acd12999b6d9a87f69e056b2cdb9a1585
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/0HTI94jFUyM_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4745, "start": 21.29, "end": 47.45, "text": "بسم الله الحمد لله والصلاة والسلام علي رسول الله اليوم ان شاء الله شباب هنشوف ال section الأخير مؤقتا في ال chapter الأول بحيث ان في عندنا section تاني المفروض اللي هو طرق الاثبات الرياضي بس هأخره شوية عشان نشوف كيف تمشي الأمور معانا لكن ال role of inferences لما بتكلم inferences طرق الاستنباط او التخمين استنباط او التخمين قوانين الاستنباط او قوانين الاختزال سميها زي ما بدك", "tokens": [3555, 38251, 21984, 21542, 2304, 3215, 24976, 3224, 16070, 9381, 15040, 3660, 16070, 3794, 37440, 25894, 12602, 3794, 12610, 21984, 45595, 20498, 16472, 13412, 16606, 21984, 13412, 3555, 16758, 8032, 1863, 8592, 38688, 2423, 3541, 16247, 9778, 13546, 3714, 33604, 38149, 995, 8978, 2423, 7187, 16247, 12610, 4724, 5016, 1829, 12984, 16472, 8978, 43242, 8315, 3541, 6055, 7649, 1829, 9673, 5172, 32887, 11242, 13672, 1829, 31439, 23032, 2288, 4587, 2423, 5718, 104, 3555, 9307, 2423, 16572, 46958, 1829, 4724, 3794, 8032, 10721, 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بعض", "probability": 0.9794921875}, {"start": 1601.65, "end": 1602.01, "word": " true", "probability": 0.57080078125}, {"start": 1602.01, "end": 1603.25, "word": " لو", "probability": 0.884765625}, {"start": 1603.25, "end": 1603.83, "word": " طلعناها", "probability": 0.844140625}, {"start": 1603.83, "end": 1603.99, "word": " بس", "probability": 0.90478515625}, {"start": 1603.99, "end": 1604.13, "word": " في", "probability": 0.82763671875}, {"start": 1604.13, "end": 1604.29, "word": " الصف", "probability": 0.968017578125}, {"start": 1604.29, "end": 1604.77, "word": " الأول", "probability": 0.754638671875}, {"start": 1604.77, "end": 1606.35, "word": " هان", "probability": 0.521240234375}, {"start": 1606.35, "end": 1607.41, "word": " و", "probability": 0.77099609375}, {"start": 1607.41, "end": 1607.73, "word": " هان", "probability": 0.905517578125}, {"start": 1607.73, "end": 1608.43, "word": " whenever", "probability": 0.9111328125}, {"start": 1608.43, "end": 1609.79, "word": " all", "probability": 0.87353515625}, {"start": 1609.79, "end": 1611.05, "word": " its", "probability": 0.488525390625}, {"start": 1611.05, "end": 1611.59, "word": " hypothesis", "probability": 0.71923828125}, {"start": 1611.59, "end": 1611.99, "word": " are", "probability": 0.8232421875}, {"start": 1611.99, "end": 1612.37, "word": " true", "probability": 0.9873046875}, {"start": 1612.37, "end": 1613.31, "word": " وينما", "probability": 0.7257486979166666}, {"start": 1613.31, "end": 1613.73, "word": " بتكون", "probability": 0.81005859375}, {"start": 1613.73, "end": 1614.47, "word": " الفرضيات", "probability": 0.976318359375}, {"start": 1614.47, "end": 1614.89, "word": " تبعتها", "probability": 0.9134521484375}, {"start": 1614.89, "end": 1615.23, "word": " true", "probability": 0.98974609375}, {"start": 1615.23, "end": 1615.79, "word": " whenever", "probability": 0.87255859375}, {"start": 1615.79, "end": 1616.39, "word": " the", "probability": 0.787109375}, {"start": 1616.39, "end": 1617.21, 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"probability": 0.8582763671875}, {"start": 1647.38, "end": 1647.5, "word": " ال", "probability": 0.9453125}, {"start": 1647.5, "end": 1647.88, "word": " validity", "probability": 0.94677734375}, {"start": 1647.88, "end": 1648.72, "word": " تبعت", "probability": 0.7960611979166666}, {"start": 1648.72, "end": 1648.84, "word": " ال", "probability": 0.96630859375}, {"start": 1648.84, "end": 1649.38, "word": " argument", "probability": 0.9287109375}, {"start": 1649.38, "end": 1650.5, "word": " اللى", "probability": 0.963134765625}, {"start": 1650.5, "end": 1650.78, "word": " عندي", "probability": 0.937255859375}, {"start": 1650.78, "end": 1651.48, "word": " otherwise", "probability": 0.78564453125}, {"start": 1651.48, "end": 1652.26, "word": " لو", "probability": 0.9443359375}, {"start": 1652.26, "end": 1652.48, "word": " كان", "probability": 0.99169921875}, {"start": 1652.48, "end": 1652.7, "word": " هذا", "probability": 0.79736328125}, {"start": 1652.7, "end": 1652.98, "word": " يقول", "probability": 0.907470703125}, {"start": 1652.98, "end": 1653.2, "word": " الى", "probability": 0.6126708984375}, {"start": 1653.2, "end": 1653.72, "word": " false", "probability": 0.86181640625}, {"start": 1653.72, "end": 1657.46, "word": " معناته", "probability": 0.7556966145833334}, {"start": 1657.46, "end": 1657.96, "word": " خلصنا", "probability": 0.77215576171875}, {"start": 1657.96, "end": 1658.24, "word": " ..", "probability": 0.4052734375}, {"start": 1658.24, "end": 1658.5, "word": " معناته", "probability": 0.8453776041666666}, {"start": 1658.5, "end": 1658.86, "word": " invalid", "probability": 0.962890625}, {"start": 1658.86, "end": 1659.56, "word": " argument", "probability": 0.9365234375}, {"start": 1659.56, "end": 1659.72, "word": " ..", "probability": 0.69189453125}, {"start": 1659.72, "end": 1660.36, "word": " invalid", "probability": 0.98291015625}, {"start": 1660.36, "end": 1661.04, "word": " argument", "probability": 0.93603515625}, {"start": 1661.04, "end": 1661.8, 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" R", "probability": 0.7724609375}, {"start": 2087.47, "end": 2087.83, "word": " هايهم", "probability": 0.6625162760416666}], "temperature": 1.0}, {"id": 78, "seek": 211723, "start": 2088.35, "end": 2117.23, "text": "التنتين صحيح صحيح صحيح صحيح خاطئ صحيح صحيح صحيح صحيح خاطئ الانشبوك اللي هو عشان تكون هذه valid argument whenever وينما بتكون عندك الصفوف التنتين مع بعض صحيح هاي الصف هاي التاني اللي بعده لأ اللي بعده هاي واحدة هاي التنتين هاي التلاتة", "tokens": [6027, 2655, 29399, 9957, 20328, 5016, 1829, 5016, 20328, 5016, 1829, 5016, 20328, 5016, 1829, 5016, 20328, 5016, 1829, 5016, 16490, 41193, 19986, 20328, 5016, 1829, 5016, 20328, 5016, 1829, 5016, 20328, 5016, 1829, 5016, 20328, 5016, 1829, 5016, 16490, 41193, 19986, 2423, 7649, 8592, 3555, 2407, 4117, 13672, 1829, 31439, 6225, 8592, 7649, 6055, 30544, 29538, 7363, 6770, 5699, 4032, 9957, 15042, 39894, 30544, 43242, 4117, 31767, 5172, 38688, 16712, 29399, 9957, 20449, 45030, 11242, 20328, 5016, 1829, 5016, 8032, 47302, 31767, 5172, 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2141.31, "end": 2143.31, "word": " هاي", "probability": 0.431884765625}, {"start": 2143.31, "end": 2143.45, "word": " ال", "probability": 0.9677734375}, {"start": 2143.45, "end": 2143.73, "word": " R", "probability": 0.9658203125}, {"start": 2143.73, "end": 2143.97, "word": " وهي", "probability": 0.734619140625}, {"start": 2143.97, "end": 2144.19, "word": " نقطة", "probability": 0.9853515625}, {"start": 2144.19, "end": 2144.27, "word": " ال", "probability": 0.880859375}, {"start": 2144.27, "end": 2144.43, "word": " B", "probability": 0.98193359375}, {"start": 2144.43, "end": 2144.79, "word": " true", "probability": 0.95068359375}, {"start": 2144.79, "end": 2145.09, "word": " implies", "probability": 0.9755859375}, {"start": 2145.09, "end": 2145.73, "word": " false", "probability": 0.904296875}], "temperature": 1.0}, {"id": 80, "seek": 217023, "start": 2147.91, "end": 2170.23, "text": "true implies false true implies false false خلصنا نفي نقطة بيعني ع مال بنا فيها بقولك ال true implies false بناء على ال role اللي عندها ال false أكمل لا تكملش خلصنا", "tokens": [6903, 622, 18779, 7908, 2074, 18779, 7908, 7908, 16490, 1211, 9381, 8315, 8717, 41185, 8717, 47432, 3660, 4724, 40228, 22653, 6225, 3714, 6027, 4724, 8315, 8978, 11296, 4724, 39648, 4117, 2423, 2074, 18779, 7908, 44945, 16606, 15844, 2423, 3090, 13672, 1829, 43242, 11296, 2423, 7908, 5551, 24793, 1211, 20193, 6055, 24793, 1211, 8592, 16490, 1211, 9381, 8315], "avg_logprob": -0.42025862839715233, "compression_ratio": 1.6206896551724137, "no_speech_prob": 4.172325134277344e-07, "words": [{"start": 2147.91, "end": 2148.93, "word": "true", "probability": 0.6329345703125}, {"start": 2148.93, "end": 2149.95, "word": " implies", "probability": 0.8515625}, {"start": 2149.95, "end": 2150.59, "word": " false", "probability": 0.90625}, {"start": 2150.59, "end": 2154.01, "word": " true", "probability": 0.267333984375}, {"start": 2154.01, "end": 2154.69, "word": " implies", "probability": 0.9091796875}, {"start": 2154.69, 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argument", "probability": 0.9140625}], "temperature": 1.0}, {"id": 84, "seek": 226419, "start": 2241.0, "end": 2264.2, "text": "جاهز بيقول لي شوف لهذا المثال if 101 is divisible by 3 إذا كان 101 تقبل الجسم على 3 معناته 112 تقبل الجسم على 9 101 تقبل الجسم على 3 for stop consequently therefore conclusion 102 is divisible by", "tokens": [7435, 40294, 11622, 4724, 1829, 39648, 32239, 13412, 38688, 46740, 15730, 9673, 12984, 6027, 498, 21055, 307, 25974, 964, 538, 805, 11933, 15730, 25961, 21055, 6055, 4587, 36150, 25724, 38251, 15844, 805, 20449, 8315, 47395, 45835, 6055, 4587, 36150, 25724, 38251, 15844, 1722, 21055, 6055, 4587, 36150, 25724, 38251, 15844, 805, 337, 1590, 47259, 4412, 10063, 45937, 307, 25974, 964, 538], "avg_logprob": -0.3213205736490988, "compression_ratio": 1.598802395209581, "no_speech_prob": 0.0, "words": [{"start": 2241.0, "end": 2241.34, "word": "جاهز", "probability": 0.4597981770833333}, {"start": 2241.34, "end": 2241.58, "word": " بيقول", "probability": 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0.97900390625}, {"start": 2248.82, "end": 2249.14, "word": " 101", "probability": 0.70068359375}, {"start": 2249.14, "end": 2249.48, "word": " تقبل", "probability": 0.75439453125}, {"start": 2249.48, "end": 2249.74, "word": " الجسم", "probability": 0.7587890625}, {"start": 2249.74, "end": 2249.9, "word": " على", "probability": 0.806640625}, {"start": 2249.9, "end": 2250.28, "word": " 3", "probability": 0.70556640625}, {"start": 2250.28, "end": 2251.16, "word": " معناته", "probability": 0.6287434895833334}, {"start": 2251.16, "end": 2251.68, "word": " 112", "probability": 0.330078125}, {"start": 2251.68, "end": 2252.2, "word": " تقبل", "probability": 0.9034830729166666}, {"start": 2252.2, "end": 2252.44, "word": " الجسم", "probability": 0.984130859375}, {"start": 2252.44, "end": 2252.6, "word": " على", "probability": 0.8623046875}, {"start": 2252.6, "end": 2253.0, "word": " 9", "probability": 0.96875}, {"start": 2253.0, "end": 2255.84, "word": " 101", "probability": 0.82470703125}, 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"text": "هذا هيك .. therefore Q لأ بس الأصل هذا إيش بيطلع بيطلع بـQ و لا بيطلع بـB حسب القانون هذه القوانين كلها بتطلع معايا هيك وبالتالي هذا ال condition is false وبالتالي invalid argument معناته هذا ال hypothesis تبعتي مش سليمة يعني invalid argument عارف ليش invalid argument؟ شوية بس .. عشان أقولك أن ال hypothesis تبعتي false 101 لا تقبل قسم ع 3", "tokens": [3224, 15730, 39896, 4117, 4386, 4412, 1249, 5296, 10721, 4724, 3794, 16247, 36520, 23758, 11933, 1829, 8592, 4724, 1829, 9566, 1211, 3615, 4724, 1829, 9566, 1211, 3615, 4724, 39184, 48, 4032, 20193, 4724, 1829, 9566, 1211, 3615, 4724, 39184, 33, 11331, 35457, 25062, 7649, 11536, 29538, 25062, 2407, 7649, 9957, 28242, 11296, 39894, 9566, 1211, 3615, 20449, 995, 25528, 39896, 4117, 46599, 6027, 2655, 6027, 1829, 23758, 2423, 4188, 307, 7908, 46599, 6027, 2655, 6027, 1829, 34702, 6770, 20449, 8315, 47395, 23758, 2423, 17291, 6055, 3555, 3615, 31371, 37893, 8608, 20292, 46007, 37495, 22653, 34702, 6770, 6225, 9640, 5172, 32239, 8592, 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"temperature": 1.0}, {"id": 95, "seek": 258082, "start": 2556.0, "end": 2580.82, "text": "الـ Q خلصت من ال condition الأول ال condition التاني if برضه ما زال فيه if و then معناته هو عبارة عن implication if we don't have a barbecue today معناته not Q then we will have a barbecue tomorrow وهدش دي إيه ده بالنسبة لنا have a barbecue tomorrow اللي هتكون إيش R", "tokens": [6027, 39184, 1249, 16490, 1211, 9381, 2655, 9154, 2423, 4188, 16247, 12610, 2423, 4188, 16712, 7649, 1829, 498, 4724, 43042, 3224, 19446, 30767, 6027, 8978, 3224, 498, 4032, 550, 20449, 8315, 47395, 31439, 6225, 3555, 9640, 3660, 18871, 37814, 498, 321, 500, 380, 362, 257, 21877, 965, 20449, 8315, 47395, 406, 1249, 550, 321, 486, 362, 257, 21877, 4153, 37037, 3215, 8592, 11778, 1829, 11933, 1829, 3224, 11778, 3224, 20666, 1863, 35457, 3660, 5296, 8315, 362, 257, 21877, 4153, 13672, 1829, 8032, 2655, 30544, 11933, 1829, 8592, 497], "avg_logprob": -0.24157303906558605, "compression_ratio": 1.63013698630137, "no_speech_prob": 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" actor", "probability": 0.9453125}, {"start": 2724.55, "end": 2727.61, "word": " Gary", "probability": 0.76904296875}, {"start": 2727.61, "end": 2727.87, "word": " is", "probability": 0.9404296875}, {"start": 2727.87, "end": 2728.63, "word": " intelligent", "probability": 0.76171875}, {"start": 2728.63, "end": 2729.01, "word": " هاي", "probability": 0.53759765625}, {"start": 2729.01, "end": 2729.37, "word": " P", "probability": 0.72412109375}, {"start": 2729.37, "end": 2730.85, "word": " و", "probability": 0.65625}, {"start": 2730.85, "end": 2731.03, "word": " هاي", "probability": 0.7783203125}, {"start": 2731.03, "end": 2731.47, "word": " R", "probability": 0.95703125}], "temperature": 1.0}, {"id": 101, "seek": 276158, "start": 2732.38, "end": 2761.58, "text": "A good actor Q Gary is a good actor Q هال condition الأول If Gary is intelligent B implies then he count from one to ten لو كان Gary ذكي أو شاطر هيعد من واحد لعشرة هدي R Gary can only count from one to three Gary بس بيعد من واحد إلى تلاتة", "tokens": [32, 665, 8747, 1249, 13788, 307, 257, 665, 8747, 1249, 8032, 6027, 4188, 16247, 12610, 759, 13788, 307, 13232, 363, 18779, 550, 415, 1207, 490, 472, 281, 2064, 45164, 25961, 13788, 29910, 4117, 1829, 34051, 13412, 41193, 2288, 39896, 22488, 9154, 36764, 24401, 5296, 3615, 8592, 25720, 8032, 16254, 497, 13788, 393, 787, 1207, 490, 472, 281, 1045, 13788, 4724, 3794, 4724, 1829, 22488, 9154, 36764, 24401, 30731, 6055, 1211, 9307, 3660], "avg_logprob": -0.2930222668059885, "compression_ratio": 1.5126903553299493, "no_speech_prob": 2.980232238769531e-07, "words": [{"start": 2732.38, "end": 2732.6, "word": "A", "probability": 0.11737060546875}, {"start": 2732.6, "end": 2732.84, "word": " good", "probability": 0.8037109375}, {"start": 2732.84, "end": 2733.38, "word": " actor", "probability": 0.93115234375}, {"start": 2733.38, "end": 2734.56, "word": " Q", "probability": 0.22216796875}, {"start": 2734.56, "end": 2735.32, "word": " Gary", "probability": 0.0947265625}, {"start": 2735.32, "end": 2735.46, "word": " is", "probability": 0.85107421875}, {"start": 2735.46, "end": 2735.58, "word": " a", "probability": 0.96484375}, {"start": 2735.58, "end": 2735.72, "word": " good", "probability": 0.93017578125}, {"start": 2735.72, "end": 2736.1, "word": " actor", "probability": 0.95849609375}, {"start": 2736.1, "end": 2736.54, "word": " Q", "probability": 0.3427734375}, {"start": 2736.54, "end": 2737.18, "word": " هال", "probability": 0.55914306640625}, {"start": 2737.18, "end": 2737.48, "word": " condition", "probability": 0.85693359375}, {"start": 2737.48, "end": 2737.9, "word": " الأول", "probability": 0.91015625}, {"start": 2737.9, "end": 2738.54, "word": " If", "probability": 0.374755859375}, {"start": 2738.54, "end": 2738.9, "word": " Gary", "probability": 0.8642578125}, {"start": 2738.9, "end": 2739.16, "word": " is", "probability": 0.95166015625}, {"start": 2739.16, "end": 2740.58, "word": " intelligent", "probability": 0.7841796875}, {"start": 2740.58, "end": 2741.5, "word": " B", "probability": 0.63671875}, {"start": 2741.5, "end": 2742.88, "word": " implies", "probability": 0.93505859375}, {"start": 2742.88, "end": 2744.2, "word": " then", "probability": 0.57568359375}, {"start": 2744.2, "end": 2744.4, "word": " he", "probability": 0.9580078125}, {"start": 2744.4, "end": 2744.9, "word": " count", "probability": 0.537109375}, {"start": 2744.9, "end": 2745.34, "word": " from", "probability": 0.9052734375}, {"start": 2745.34, "end": 2746.18, "word": " one", "probability": 0.5888671875}, {"start": 2746.18, "end": 2746.34, "word": " to", "probability": 0.97998046875}, {"start": 2746.34, "end": 2746.62, "word": " ten", "probability": 0.9013671875}, {"start": 2746.62, "end": 2747.16, "word": " لو", "probability": 0.88232421875}, {"start": 2747.16, "end": 2747.58, "word": " كان", "probability": 0.9912109375}, {"start": 2747.58, "end": 2748.28, "word": " Gary", "probability": 0.55615234375}, {"start": 2748.28, "end": 2749.38, "word": " ذكي", "probability": 0.9405924479166666}, {"start": 2749.38, "end": 2749.68, "word": " أو", "probability": 0.72119140625}, {"start": 2749.68, "end": 2750.06, "word": " شاطر", "probability": 0.9954427083333334}, {"start": 2750.06, "end": 2750.38, "word": " هيعد", "probability": 0.6175537109375}, {"start": 2750.38, "end": 2750.48, "word": " من", "probability": 0.95703125}, {"start": 2750.48, "end": 2750.72, "word": " واحد", "probability": 0.9619140625}, {"start": 2750.72, "end": 2751.44, "word": " لعشرة", "probability": 0.878662109375}, {"start": 2751.44, "end": 2753.2, "word": " هدي", "probability": 0.532958984375}, {"start": 2753.2, "end": 2753.54, "word": " R", "probability": 0.7666015625}, {"start": 2753.54, "end": 2755.96, "word": " Gary", "probability": 0.75634765625}, {"start": 2755.96, "end": 2756.26, "word": " can", "probability": 0.73388671875}, {"start": 2756.26, "end": 2757.22, "word": " only", "probability": 0.69580078125}, {"start": 2757.22, "end": 2757.88, "word": " count", "probability": 0.91845703125}, {"start": 2757.88, "end": 2758.3, "word": " from", "probability": 0.91015625}, {"start": 2758.3, "end": 2758.54, "word": " one", "probability": 0.9130859375}, {"start": 2758.54, "end": 2758.66, "word": " to", "probability": 0.98046875}, {"start": 2758.66, "end": 2758.96, "word": " three", "probability": 0.95068359375}, {"start": 2758.96, "end": 2759.82, "word": " Gary", "probability": 0.5712890625}, {"start": 2759.82, "end": 2760.08, "word": " بس", "probability": 0.958984375}, {"start": 2760.08, "end": 2760.32, "word": " بيعد", "probability": 0.7408854166666666}, {"start": 2760.32, "end": 2760.46, "word": " من", "probability": 0.9892578125}, {"start": 2760.46, "end": 2760.84, "word": " واحد", "probability": 0.972412109375}, {"start": 2760.84, "end": 2761.08, "word": " إلى", "probability": 0.76123046875}, {"start": 2761.08, "end": 2761.58, "word": " تلاتة", "probability": 0.9759521484375}], "temperature": 1.0}, {"id": 102, "seek": 279099, "start": 2762.91, "end": 2790.99, "text": "نط ال R. Therefore, conclusion تبعتنا, Gary is a good actor. الهي مين؟ ال Q فقط ال Q. تعالى و ردتوهم بي او ري كيو. ال condition الأول بي implies ال R نط ال R. Therefore, ال Q. هاد الآن هاد ال argument تبعتى.", "tokens": [1863, 9566, 2423, 497, 13, 7504, 11, 10063, 6055, 3555, 34268, 8315, 11, 13788, 307, 257, 665, 8747, 13, 2423, 3224, 1829, 3714, 9957, 22807, 2423, 1249, 6156, 47432, 2423, 1249, 13, 37279, 6027, 7578, 4032, 12602, 3215, 2655, 2407, 16095, 4724, 1829, 1975, 2407, 12602, 1829, 9122, 1829, 2407, 13, 2423, 4188, 16247, 12610, 4724, 1829, 18779, 2423, 497, 8717, 9566, 2423, 497, 13, 7504, 11, 2423, 1249, 13, 8032, 18513, 6024, 48506, 8032, 18513, 2423, 6770, 6055, 3555, 34268, 7578, 13], "avg_logprob": -0.5048363116525468, "compression_ratio": 1.4947916666666667, "no_speech_prob": 0.0, "words": [{"start": 2762.91, "end": 2763.31, "word": "نط", "probability": 0.56591796875}, {"start": 2763.31, "end": 2763.47, "word": " ال", "probability": 0.712890625}, {"start": 2763.47, "end": 2763.75, "word": " R.", "probability": 0.58203125}, {"start": 2765.73, "end": 2766.41, "word": " Therefore,", "probability": 0.666015625}, {"start": 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"word": " هاد", "probability": 0.77978515625}, {"start": 2790.01, "end": 2790.11, "word": " ال", "probability": 0.96728515625}, {"start": 2790.11, "end": 2790.47, "word": " argument", "probability": 0.9208984375}, {"start": 2790.47, "end": 2790.99, "word": " تبعتى.", "probability": 0.8382568359375}], "temperature": 1.0}, {"id": 103, "seek": 281872, "start": 2794.8, "end": 2818.72, "text": "هل هي valid argument ولا invalid argument؟ بدك تبدأ تجدوا الاحتمالات وتبدأ تشتغل و تحسب ممكن تاخد وقت كتير لكن لو احنا رجعنا لل role of inferences السادقات ممكن يقولولي هذا الكلام صحيح ولا لأ؟ ايوة ..الان ..الان ..تعالى نشوف", "tokens": [3224, 1211, 39896, 7363, 6770, 49429, 34702, 6770, 22807, 47525, 4117, 6055, 44510, 10721, 6055, 7435, 3215, 14407, 42963, 33753, 2304, 6027, 9307, 34683, 44510, 10721, 6055, 8592, 2655, 17082, 1211, 4032, 6055, 5016, 35457, 3714, 43020, 6055, 47283, 3215, 4032, 38149, 9122, 2655, 13546, 44381, 45164, 1975, 5016, 8315, 12602, 7435, 3615, 8315, 24976, 3090, 295, 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ابدالية يعني بقدر ابدل كل اتنين و اجملهم زي ما بدي ولا لأ حسب خواص ال and طيب تعالى نشوف الخطوات التالية يعني لو انا روحت اشتغلت كالتالية هي ال hypothesis اللي موجودة عندى", "tokens": [6027, 2655, 2288, 31371, 3555, 23758, 35186, 13412, 3555, 16758, 8032, 3215, 12610, 3660, 16712, 1211, 2655, 18871, 33546, 2288, 4032, 49374, 16095, 293, 4032, 1975, 5016, 8315, 2423, 293, 6225, 42213, 10632, 1975, 44510, 6027, 10632, 293, 8032, 7649, 49374, 2423, 4487, 8032, 3215, 12610, 3660, 39894, 995, 40228, 1829, 4487, 4032, 13672, 1829, 49374, 16095, 293, 4032, 2423, 293, 6225, 42213, 10632, 1975, 44510, 6027, 10632, 37495, 22653, 4724, 28543, 2288, 48127, 3215, 1211, 28242, 1975, 2655, 1863, 9957, 4032, 1975, 7435, 42213, 16095, 30767, 1829, 19446, 4724, 16254, 49429, 5296, 10721, 11331, 35457, 16490, 14407, 9381, 2423, 293, 23032, 1829, 3555, 37279, 6027, 7578, 8717, 8592, 38688, 33962, 9566, 2407, 9307, 16712, 6027, 10632, 37495, 22653, 45164, 1975, 8315, 12602, 2407, 33753, 1975, 8592, 2655, 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2842.42, "word": " روحت", "probability": 0.7101236979166666}, {"start": 2842.42, "end": 2842.82, "word": " اشتغلت", "probability": 0.8932291666666666}, {"start": 2842.82, "end": 2843.3, "word": " كالتالية", "probability": 0.88291015625}, {"start": 2843.3, "end": 2843.48, "word": " هي", "probability": 0.443115234375}, {"start": 2843.48, "end": 2843.58, "word": " ال", "probability": 0.9580078125}, {"start": 2843.58, "end": 2843.94, "word": " hypothesis", "probability": 0.78076171875}, {"start": 2843.94, "end": 2844.2, "word": " اللي", "probability": 0.83642578125}, {"start": 2844.2, "end": 2844.58, "word": " موجودة", "probability": 0.9820556640625}, {"start": 2844.58, "end": 2844.9, "word": " عندى", "probability": 0.838134765625}], "temperature": 1.0}, {"id": 105, "seek": 287507, "start": 2846.47, "end": 2875.07, "text": "هو حتى انا اشتغلت في ال hypothesis كالتالي اقعد ترتيبهم نط ال R ال hypothesis الأول بي implies ال R ال hypothesis التاني هيه يعني بين جثين انا بدأ اشتغل على هدول التاني اللي حالهم بينفع اه بينفع يعني هو كأنه جالس بقوله هيك high condition بي or Q and", "tokens": [3224, 2407, 11331, 49975, 1975, 8315, 1975, 8592, 2655, 17082, 1211, 2655, 8978, 2423, 17291, 9122, 6027, 2655, 6027, 1829, 1975, 4587, 22488, 6055, 2288, 31371, 3555, 16095, 8717, 9566, 2423, 497, 2423, 17291, 16247, 12610, 4724, 1829, 18779, 2423, 497, 2423, 17291, 16712, 7649, 1829, 39896, 3224, 37495, 22653, 49374, 10874, 12984, 9957, 1975, 8315, 47525, 10721, 1975, 8592, 2655, 17082, 1211, 15844, 8032, 3215, 12610, 16712, 7649, 1829, 13672, 1829, 11331, 6027, 16095, 4724, 9957, 5172, 3615, 1975, 3224, 4724, 9957, 5172, 3615, 37495, 22653, 31439, 9122, 33456, 3224, 10874, 6027, 3794, 4724, 39648, 3224, 39896, 4117, 1090, 4188, 4724, 1829, 420, 1249, 293], "avg_logprob": -0.31103971572679895, "compression_ratio": 1.7935779816513762, "no_speech_prob": 0.0, "words": [{"start": 2846.47, "end": 2846.79, "word": "هو", "probability": 0.517578125}, {"start": 2846.79, "end": 2846.93, "word": " 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هنا و سلامتكم هي خلص ال section هذا و بدنا نقول الشبتر الأول الله يعطيه العافية و ضال فيه عنا section مهم جدا طرق الإثبات الرياضة بس هأخره شوية ايه كده عبل ما تتخمروا شوية في الرياضيات معنا اه هناخره ان شاء الله بس لاحقا في اي سؤال الشباب اللي اقرحنا اليوم باشي الله يعطيكوا العافية شباب", "tokens": [33, 295, 39189, 498, 383, 6055, 29399, 2304, 1829, 24976, 9274, 13672, 1829, 3714, 29245, 23328, 3660, 1975, 3224, 31439, 23758, 25062, 7649, 11536, 37037, 15730, 31439, 25062, 7649, 11536, 13672, 1829, 3714, 29245, 23328, 43242, 8315, 34105, 4032, 8608, 37440, 2655, 24793, 39896, 16490, 1211, 9381, 2423, 3541, 23758, 4032, 47525, 8315, 8717, 39648, 25124, 3555, 2655, 2288, 16247, 12610, 21984, 37495, 9566, 1829, 3224, 18863, 31845, 10632, 4032, 48812, 6027, 8978, 3224, 6225, 8315, 3541, 3714, 16095, 10874, 28259, 23032, 2288, 4587, 33688, 12984, 3555, 9307, 2423, 16572, 46958, 3660, 4724, 3794, 8032, 10721, 34740, 3224, 13412, 2407, 10632, 1975, 1829, 3224, 9122, 3215, 3224, 6225, 36150, 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"word": " اللي", "probability": 0.965576171875}, {"start": 3250.25, "end": 3250.57, "word": " موجود", "probability": 0.9884440104166666}, {"start": 3250.57, "end": 3250.87, "word": " عندنا", "probability": 0.6522216796875}, {"start": 3250.87, "end": 3251.03, "word": " هنا", "probability": 0.6103515625}, {"start": 3251.03, "end": 3254.01, "word": " و", "probability": 0.24462890625}, {"start": 3254.01, "end": 3254.51, "word": " سلامتكم", "probability": 0.95166015625}, {"start": 3254.51, "end": 3254.67, "word": " هي", "probability": 0.366455078125}, {"start": 3254.67, "end": 3255.15, "word": " خلص", "probability": 0.8291015625}, {"start": 3255.15, "end": 3255.37, "word": " ال", "probability": 0.78955078125}, {"start": 3255.37, "end": 3255.65, "word": " section", "probability": 0.908203125}, {"start": 3255.65, "end": 3256.03, "word": " هذا", "probability": 0.72412109375}, {"start": 3256.03, "end": 3256.23, "word": " و", "probability": 0.833984375}, {"start": 3256.23, "end": 3256.45, "word": " بدنا", "probability": 0.89306640625}, {"start": 3256.45, "end": 3256.63, "word": " نقول", "probability": 0.882080078125}, {"start": 3256.63, "end": 3257.13, "word": " الشبتر", "probability": 0.69378662109375}, {"start": 3257.13, "end": 3257.65, "word": " الأول", "probability": 0.8291015625}, {"start": 3257.65, "end": 3258.31, "word": " الله", "probability": 0.7841796875}, {"start": 3258.31, "end": 3258.61, "word": " يعطيه", "probability": 0.79351806640625}, {"start": 3258.61, "end": 3259.09, "word": " العافية", "probability": 0.9549153645833334}, {"start": 3259.09, "end": 3259.29, "word": " و", "probability": 0.6015625}, {"start": 3259.29, "end": 3259.51, "word": " ضال", "probability": 0.6181640625}, {"start": 3259.51, "end": 3259.69, "word": " فيه", "probability": 0.822265625}, {"start": 3259.69, "end": 3259.81, "word": " عنا", "probability": 0.55499267578125}, {"start": 3259.81, "end": 3260.11, "word": " section", "probability": 0.833984375}, {"start": 3260.11, "end": 3260.41, "word": " مهم", "probability": 0.98388671875}, {"start": 3260.41, "end": 3260.87, "word": " جدا", "probability": 0.9921875}, {"start": 3260.87, "end": 3261.51, "word": " طرق", "probability": 0.94140625}, {"start": 3261.51, "end": 3261.87, "word": " الإثبات", "probability": 0.77288818359375}, {"start": 3261.87, "end": 3262.23, "word": " الرياضة", "probability": 0.8192138671875}, {"start": 3262.23, "end": 3262.39, "word": " بس", "probability": 0.97900390625}, {"start": 3262.39, "end": 3262.85, "word": " هأخره", "probability": 0.8333740234375}, {"start": 3262.85, "end": 3263.11, "word": " شوية", "probability": 0.8785807291666666}, {"start": 3263.11, "end": 3263.33, "word": " ايه", "probability": 0.5958251953125}, {"start": 3263.33, "end": 3263.91, "word": " كده", "probability": 0.82080078125}, {"start": 3263.91, "end": 3264.25, "word": " عبل", "probability": 0.6080322265625}, {"start": 3264.25, "end": 3264.35, "word": " ما", "probability": 0.88037109375}, {"start": 3264.35, "end": 3264.91, "word": " تتخمروا", "probability": 0.9806640625}, {"start": 3264.91, "end": 3265.15, "word": " شوية", "probability": 0.9482421875}, {"start": 3265.15, "end": 3265.31, "word": " في", "probability": 0.78271484375}, {"start": 3265.31, "end": 3265.77, "word": " الرياضيات", "probability": 0.91826171875}, {"start": 3265.77, "end": 3266.05, "word": " معنا", "probability": 0.777099609375}, {"start": 3266.05, "end": 3266.91, "word": " اه", "probability": 0.7088623046875}, {"start": 3266.91, "end": 3267.29, "word": " هناخره", "probability": 0.8052734375}, {"start": 3267.29, "end": 3267.37, "word": " ان", "probability": 0.841796875}, {"start": 3267.37, "end": 3267.55, "word": " شاء", "probability": 0.968017578125}, {"start": 3267.55, "end": 3267.63, "word": " الله", "probability": 0.97021484375}, {"start": 3267.63, "end": 3267.97, "word": " بس", "probability": 0.93603515625}, {"start": 3267.97, "end": 3268.43, "word": " لاحقا", "probability": 0.95849609375}, {"start": 3268.43, "end": 3269.01, "word": " في", "probability": 0.63330078125}, {"start": 3269.01, "end": 3269.15, "word": " اي", "probability": 0.820556640625}, {"start": 3269.15, "end": 3269.39, "word": " سؤال", "probability": 0.9894205729166666}, {"start": 3269.39, "end": 3269.69, "word": " الشباب", "probability": 0.9501953125}, {"start": 3269.69, "end": 3269.83, "word": " اللي", "probability": 0.855712890625}, {"start": 3269.83, "end": 3270.17, "word": " اقرحنا", "probability": 0.7560546875}, {"start": 3270.17, "end": 3270.49, "word": " اليوم", "probability": 0.76123046875}, {"start": 3270.49, "end": 3271.29, "word": " باشي", "probability": 0.7470703125}, {"start": 3271.29, "end": 3271.53, "word": " الله", "probability": 0.85791015625}, {"start": 3271.53, "end": 3271.79, "word": " يعطيكوا", "probability": 0.776513671875}, {"start": 3271.79, "end": 3271.97, "word": " العافية", "probability": 0.8478190104166666}, {"start": 3271.97, "end": 3272.25, "word": " شباب", "probability": 0.83935546875}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3272.457875, "duration_after_vad": 3124.021249999986}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/0HTI94jFUyM_raw.srt b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/0HTI94jFUyM_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..4c5e34f53dda89549c4cb28a06c63d863e1b5553
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/0HTI94jFUyM_raw.srt
@@ -0,0 +1,2436 @@
+1
+00:00:21,290 --> 00:00:23,210
+بسم الله الحمد لله والصلاة والسلام علي رسول الله
+
+2
+00:00:23,210 --> 00:00:26,290
+اليوم ان شاء الله شباب هنشوف ال section الأخير
+
+3
+00:00:26,290 --> 00:00:29,810
+مؤقتا في ال chapter الأول بحيث ان في عندنا section
+
+4
+00:00:29,810 --> 00:00:33,410
+تاني المفروض اللي هو طرق الاثبات الرياضي بس هأخره
+
+5
+00:00:33,410 --> 00:00:36,690
+شوية عشان نشوف كيف تمشي الأمور معانا لكن ال role
+
+6
+00:00:36,690 --> 00:00:40,930
+of inferences لما بتكلم inferences طرق الاستنباط
+
+7
+00:00:40,930 --> 00:00:45,370
+او التخمين استنباط او التخمين قوانين الاستنباط او
+
+8
+00:00:45,370 --> 00:00:49,400
+قوانين الاختزال سميها زي ما بدكفي الآخر انا هكون
+
+9
+00:00:49,400 --> 00:00:53,020
+شوف مجموعة من القوانين هتلزمني في الاثبات الرياضي
+
+10
+00:00:53,020 --> 00:00:55,120
+عشان هيك بقولك ممكن انا هذا ال section ارجعله
+
+11
+00:00:55,120 --> 00:01:02,420
+لاحقا بشكل عام بشكل عام اي نظرية بدنا نثبتها تمام
+
+12
+00:01:02,420 --> 00:01:07,460
+لازم يكون فيها جزئيتين واضحات جدا الاولة ال
+
+13
+00:01:07,460 --> 00:01:10,620
+condition او ال hypothesis او ال premises حسب
+
+14
+00:01:10,620 --> 00:01:15,900
+التسمية الشرطوال conclusion المحصرة تعالى نشوف مع
+
+15
+00:01:15,900 --> 00:01:23,260
+بعض المثال البسيط التالي بقول لي حاصل جمع the sum
+
+16
+00:01:23,260 --> 00:01:34,220
+of any two odd integers is
+
+17
+00:01:34,220 --> 00:01:41,820
+integer is even number is even number is
+
+18
+00:01:41,820 --> 00:01:42,600
+even integer
+
+19
+00:01:45,350 --> 00:01:50,350
+true هذه نظرية لان فيها condition اه فيها
+
+20
+00:01:50,350 --> 00:01:54,350
+condition ايش ال condition ان يكون في عندي two
+
+21
+00:01:54,350 --> 00:02:00,710
+integers وصفتهم ايش odd يعني انا في عندي a and ال
+
+22
+00:02:00,710 --> 00:02:09,550
+b are odd integers طيب
+
+23
+00:02:09,550 --> 00:02:13,610
+conclusion هاي condition كام condition يا شباب
+
+24
+00:02:13,610 --> 00:02:20,280
+موجود عندى2 2 a is integer و b is integer
+
+25
+00:02:20,280 --> 00:02:26,800
+conclusion a زائد b عارف ليش لما قلتلك two
+
+26
+00:02:26,800 --> 00:02:31,040
+conditions لأن هاد عبارة عن preposition a is odd
+
+27
+00:02:31,040 --> 00:02:35,120
+integer تقدر تحكمليها ولا تقدرش بي is odd integer
+
+28
+00:02:35,120 --> 00:02:41,380
+second preposition و الرابط اللي بينهم ال and و ال
+
+29
+00:02:41,380 --> 00:02:51,120
+conclusion a زائد bis even integer هذه الخلاصة one
+
+30
+00:02:51,120 --> 00:02:54,040
+conclusion one proposition لاحظ ان انا اتكلم على
+
+31
+00:02:54,040 --> 00:02:58,880
+three propositions اتنين منهم يقولوا الى التالت
+
+32
+00:02:58,880 --> 00:03:04,440
+الان هذه ال conditions مهمة جدا عشان انا اقدر اثبت
+
+33
+00:03:04,440 --> 00:03:10,620
+النظريات طيب هنرجع لالمثال هذا ال correct proof هو
+
+34
+00:03:10,620 --> 00:03:16,980
+اثبات الرياض الصحيح هو بتكون منالتالي لو كانت ال
+
+35
+00:03:16,980 --> 00:03:21,680
+condition true لو كانت ال condition true هتقول انه
+
+36
+00:03:21,680 --> 00:03:26,320
+ال conclusion صحيحة ال conclusion هتكون true و
+
+37
+00:03:26,320 --> 00:03:29,540
+بالتالي ال conditions تقول ال conclusion دائما
+
+38
+00:03:29,540 --> 00:03:36,860
+هتكون تتولجي دائما ال true تقول ال true فبتكلم
+
+39
+00:03:36,860 --> 00:03:39,640
+جاعد على true لإن ال true تقول ال true دائما هتكون
+
+40
+00:03:39,640 --> 00:03:44,740
+قيمتها يعني هيك true implies trueequivalent to
+
+41
+00:03:44,740 --> 00:03:52,240
+true وبالتالي تاتولوجي تمام دعونا نشوف هذا المثال
+
+42
+00:03:52,240 --> 00:03:55,840
+كيف ممكن أن انا أروح أثبته لو أنا بدأ أروح أثبت
+
+43
+00:03:55,840 --> 00:03:59,380
+بدي أبدأ من مين يا شباب؟ بدي أبدأ من ال conditions
+
+44
+00:03:59,380 --> 00:04:11,720
+أبدأ أفسر شو يعني؟ odd a is odd معناته a equal 2k
+
+45
+00:04:12,260 --> 00:04:21,360
+زائد او ناقص واحد وال K تنتمي إلى ال Z لأي عدد
+
+46
+00:04:21,360 --> 00:04:28,920
+فردي يُكتب على صورة 2 برب عدد صحيح زائد او ناقص
+
+47
+00:04:28,920 --> 00:04:32,620
+واحد اتنين في العدد الصحيح دائما الشباب اتنين في
+
+48
+00:04:32,620 --> 00:04:37,790
+اي عددالنتش بيطلع عدد زوجي و لا بصبوط طب و العدد
+
+49
+00:04:37,790 --> 00:04:42,090
+الفردي اما اكبر من عدد الزوج بواحد او اقل منه
+
+50
+00:04:42,090 --> 00:04:47,470
+بواحد فانت ممكن تعتمد على الصيغة هذه بشكل عام او
+
+51
+00:04:47,470 --> 00:04:50,050
+تعتمد على واحدة منهم زائد او نقص حسب انت ايش بدك
+
+52
+00:04:50,050 --> 00:04:54,390
+تمام و ال K هي عبارة عشان اقول arbitrary لانه
+
+53
+00:04:54,390 --> 00:04:58,090
+مجليش هو التلاتة مجليش الخمسة جالي اي odd number
+
+54
+00:04:58,090 --> 00:05:00,410
+فبالتالي انا بده اروح اكتب صورة odd number بشكل
+
+55
+00:05:00,410 --> 00:05:06,180
+عام طيب عشان امثل الخمسةالـ K لازم تكون ثلاثة
+
+56
+00:05:06,180 --> 00:05:10,960
+اتنين في ثلاثة ستة نقص واحد اول K بيبقى تسوى اتنين
+
+57
+00:05:10,960 --> 00:05:14,980
+اتنين في اتنين اربعة زائد واحد فلنكون نعتمد على
+
+58
+00:05:14,980 --> 00:05:23,400
+واحدة بس و نسيبها من التانية تمام ال B أسقط معناته
+
+59
+00:05:23,400 --> 00:05:29,500
+ال B بيبقى تسوى اتنين H زائد واحد
+
+60
+00:05:31,040 --> 00:05:37,360
+والقدش تنتمي لزد بالمناسبة بنفعش أقول تلاتة فاصلة
+
+61
+00:05:37,360 --> 00:05:45,980
+خمسة is odd هذا الكلام الصحيح ليش؟ لأن ال odd فقط
+
+62
+00:05:45,980 --> 00:05:49,160
+ال odd will even مع الأعداد الصحيحة مش معريها ال
+
+63
+00:05:49,160 --> 00:05:53,100
+number تمام؟ هاي ال conditions هاي ال conditions
+
+64
+00:05:53,100 --> 00:05:58,740
+اللي عندي طيب تمام يعني هدولة هيك و أنا جاعة بقولك
+
+65
+00:05:58,740 --> 00:06:05,240
+trueA is odd هيها B is odd هيها true true and true
+
+66
+00:06:05,240 --> 00:06:10,300
+true لأن هذا اللي لازم يوصلني لل conclusion ان ال
+
+67
+00:06:10,300 --> 00:06:13,960
+A زائد B is even و لازم تكون true تعالى نشوف
+
+68
+00:06:13,960 --> 00:06:16,880
+معناته ان انا بدي اروح ال conclusion A زائد B
+
+69
+00:06:16,880 --> 00:06:24,440
+يساوي عوض عن قيمة A بتامتها اتنين K زائد واحد زائد
+
+70
+00:06:24,440 --> 00:06:29,040
+لقيمة B اتنين H زائد واحد اجبع
+
+71
+00:06:30,370 --> 00:06:41,790
+تنين K زائد اتنين H زائد اتنين K زائد
+
+72
+00:06:41,790 --> 00:06:49,030
+H زائد واحد مصبوط؟ الان هذا الرقم بغض النظر ايش
+
+73
+00:06:49,030 --> 00:06:58,240
+كانت قيمته ينتمي الى Z لان K is integerH هو انتجار
+
+74
+00:06:58,240 --> 00:07:02,680
+و 1 هو انتجار وحاصل جامعي الانتجار هيقدي إلى
+
+75
+00:07:02,680 --> 00:07:08,720
+انتجار وبالتالي اتنين في انتجار انتجار ومش بس هيك
+
+76
+00:07:08,720 --> 00:07:14,620
+even number even انتجار مش هي صورة الانتجار مش هي
+
+77
+00:07:14,620 --> 00:07:18,180
+صورة ال even انتجار وبالتالي احنا وصلنا وصارت ال
+
+78
+00:07:18,180 --> 00:07:23,060
+conclusion تبعتنا هذه true true فكانت ال condition
+
+79
+00:07:23,060 --> 00:07:28,650
+true قالت ان ال conclusion تبعتناالمحصلة true هذا
+
+80
+00:07:28,650 --> 00:07:33,150
+الكلام مهم لما انا بدي اتي اثبت القوانين كلها
+
+81
+00:07:33,150 --> 00:07:38,310
+فلازم انا اتسلسل او امشي مع البرهان بكلام منطقي
+
+82
+00:07:38,310 --> 00:07:42,670
+100% بيبدأ من وين؟ بيبدأ من عند ال condition اللي
+
+83
+00:07:42,670 --> 00:07:47,490
+لازم تكون true بينفعش في لحظة من اللحظات اتي اقول
+
+84
+00:07:47,490 --> 00:07:54,190
+ال B هيها ال
+
+85
+00:07:54,190 --> 00:07:59,470
+B is not oddصار ال condition false تعالى جمع
+
+86
+00:07:59,470 --> 00:08:04,290
+هتلاقي ان ال output ال conclusion is all is false
+
+87
+00:08:04,290 --> 00:08:07,110
+لان القملة اللى كانت عندى معايا odd ماكنتش even
+
+88
+00:08:07,110 --> 00:08:11,570
+لان اتنين K زائد واحد زائد اتنين H زائد واحد تساوي
+
+89
+00:08:11,570 --> 00:08:15,810
+اتنين افتحقوص K زائد H الكل زائد واحد وهدا صورة
+
+90
+00:08:15,810 --> 00:08:20,110
+العدد الفردي فلما كانت ال condition عندي false أدت
+
+91
+00:08:20,110 --> 00:08:23,960
+إلى ان ال conclusion بتطلع معاياfalse وبالتالي اي
+
+92
+00:08:23,960 --> 00:08:27,060
+نظرية صحيحة لازم تكون الشروط تبعتها ال condition
+
+93
+00:08:27,060 --> 00:08:31,520
+او ال hypothesis تبعتها true تمام بتقدم معايا ل
+
+94
+00:08:31,520 --> 00:08:34,840
+conclusion true otherwise بتكون النظرية دي بدهاش
+
+95
+00:08:34,840 --> 00:08:43,700
+رمى بعيد عنها لما تكونش صحيحة تمام الآن العلاقة
+
+96
+00:08:43,700 --> 00:08:48,940
+بين ال condition و ال conclusion هتعامل معاهم
+
+97
+00:08:55,710 --> 00:09:00,650
+أو عوامل اثبات صحة النظرية اللي موجودة عندنا بين
+
+98
+00:09:00,650 --> 00:09:05,440
+جثين ان ال conclusion ال condition تقولإلى ال
+
+99
+00:09:05,440 --> 00:09:08,360
+conclusion هذه عوامل اللي هي ال by conditional مش
+
+100
+00:09:08,360 --> 00:09:11,480
+احنا قولنا بي implies كيو سمينا ال implies
+
+101
+00:09:11,480 --> 00:09:16,280
+operator وسمينا ال بي و ال كيو عبارة عن argument
+
+102
+00:09:16,280 --> 00:09:19,100
+للمسألة او ال operand تبع المسألة اللي عندها
+
+103
+00:09:19,100 --> 00:09:24,480
+وبالتالي هتعامل معاهم as conclusionطيب، الآن شو
+
+104
+00:09:24,480 --> 00:09:27,880
+علاقة هذا في الإثبات؟ هو أساس الإثبات إنه فعليا
+
+105
+00:09:27,880 --> 00:09:30,640
+اللي تقول و ال condition اللي موجودة عندها و
+
+106
+00:09:30,640 --> 00:09:34,800
+بالتالي ال argument connected by proper rules of
+
+107
+00:09:34,800 --> 00:09:37,600
+inferences و بالتالي ال argument تبعتي هذي أنا
+
+108
+00:09:37,600 --> 00:09:43,060
+بنتقل ممكن من خلال ال rule of inferences ال rule
+
+109
+00:09:43,060 --> 00:09:46,840
+of inferences قوانين التخمين أو الاستنباب أو
+
+110
+00:09:46,840 --> 00:09:47,500
+الإثبات
+
+111
+00:09:49,970 --> 00:09:52,550
+أو الـ Step Down سميهم زي ما بأي ترجمة ممكن تجي
+
+112
+00:09:52,550 --> 00:09:59,490
+على بالك ان فرنسية التخمين بالمناسبة الآن بتزودني
+
+113
+00:09:59,490 --> 00:10:04,510
+بتفسير لكل step في البرهان لما بروح أنا بstep
+
+114
+00:10:04,510 --> 00:10:08,890
+لمقطع بمقطع ليش؟ ليش أنا بدلته؟ بناء على إيش؟
+
+115
+00:10:08,890 --> 00:10:12,830
+تمام؟ بناء على إن هذا ال role أصبحت fact وانا بقدر
+
+116
+00:10:12,830 --> 00:10:18,860
+أعتمد عليها في الإثبات تمام؟ دعونا نشوفوحد من ال
+
+117
+00:10:18,860 --> 00:10:23,140
+role of inferences بقول كتابة هاي ال argument
+
+118
+00:10:23,140 --> 00:10:27,520
+تبعتي كل آياتهم هذا ال role الآن من ال conditions
+
+119
+00:10:27,520 --> 00:10:34,340
+P و P implies Q و العلاقة بين ال two conditions
+
+120
+00:10:34,340 --> 00:10:46,770
+دائما and يقول إلى Q يعني بين قصين P andB implies
+
+121
+00:10:46,770 --> 00:10:53,370
+Q الكل يقول الى Q هذا ال role أو هذا القانون انا
+
+122
+00:10:53,370 --> 00:10:57,970
+بقدر اشوف بمجرد اشوف في الاثبات الرياضي تبعي حصلت
+
+123
+00:10:57,970 --> 00:11:03,070
+على ال two condition هدول بقدر اشيلهم اشيلهم
+
+124
+00:11:03,070 --> 00:11:09,560
+احذفهم وحق بدلهم مينEQ وحط بدلهم EQ وهنا بصير دورة
+
+125
+00:11:09,560 --> 00:11:13,920
+او أهمية ال role of inferences في الإثبات تعالى
+
+126
+00:11:13,920 --> 00:11:18,860
+نشوف أساسا هل فعليا هذا زي ما هو بقول ان هذه دائما
+
+127
+00:11:18,860 --> 00:11:22,300
+لازم تكون تيتولوجيا عشان أثبتها تيتولوجيا كيف بدي
+
+128
+00:11:22,300 --> 00:11:26,280
+أسوي الشباب عشان
+
+129
+00:11:26,280 --> 00:11:31,040
+أثبت ان هذه عبارة عن تيتولوجيا ايش المفروض أسوي
+
+130
+00:11:31,040 --> 00:11:33,820
+افكر ال implies
+
+131
+00:11:37,090 --> 00:11:41,270
+100% يعني انا بدى استخدم الطرق اللى شوفناها سابقا
+
+132
+00:11:41,270 --> 00:11:49,850
+عشان اثبت القيمة اللى عندي تمام بي and بي implies
+
+133
+00:11:49,850 --> 00:11:58,210
+كيو الكل implies كيو أظبط بقول ان هذا تاتولوجي
+
+134
+00:11:58,210 --> 00:12:04,490
+الآن بدى أذكرك بي implies كيو equivalent to نط ال
+
+135
+00:12:04,490 --> 00:12:09,660
+بيor q وفي
+
+136
+00:12:09,660 --> 00:12:13,480
+equivalent لشغل تانية بس بتلزمنيش الان نط ال q
+
+137
+00:12:13,480 --> 00:12:22,120
+implies نط ال b نط ال q implies نط ال b الان ليش
+
+138
+00:12:22,120 --> 00:12:25,460
+هاد بتلزمنيش لإن هو عم يقعد يقولي اثبت او بدرس
+
+139
+00:12:25,460 --> 00:12:29,740
+بتقولي ان هاد Totology Totology يعني بدي true عشان
+
+140
+00:12:29,740 --> 00:12:37,020
+بدي true لو انا قدرت احصل orX ونفيها ستكون حصالة
+
+141
+00:12:37,020 --> 00:12:41,180
+على الـ True وهذا لا يلزمني الآن ان انا بتلزمني
+
+142
+00:12:41,180 --> 00:12:44,260
+الصورة التانية اللى موجودة عندي وبالتالي هذه تكافئ
+
+143
+00:12:44,260 --> 00:12:55,640
+اتجدم في الأول نفي ال B بس لحظة شوية and نفي ال B
+
+144
+00:12:55,640 --> 00:13:00,880
+RQ مظبوط RQ
+
+145
+00:13:02,320 --> 00:13:06,660
+أنا بكل حولته مرة واحدة نفي الجوس هذا كله هي النفي
+
+146
+00:13:06,660 --> 00:13:12,820
+للجوس والجوس هذا P implies Q برضه بدلته not P or Q
+
+147
+00:13:12,820 --> 00:13:22,160
+الآن بدأ أدخل النفي على الجوس هذا نفي ال P or نفي
+
+148
+00:13:22,160 --> 00:13:29,800
+الجوس هذا نفي الجوس هذا معناته P and not Q الكل or
+
+149
+00:13:29,800 --> 00:13:37,680
+مصبوط هيك؟هي مازال قصها يهيك الان بدي ادخل بدي
+
+150
+00:13:37,680 --> 00:13:54,920
+اوزع نفل B نفل B or ال B and نفل B or نفل Q or Q
+
+151
+00:13:54,920 --> 00:14:05,490
+بصبت B or not B trueطيب هذه بال true ال true and x
+
+152
+00:14:05,490 --> 00:14:09,990
+احنا في عندنا قانون بيقول اللي ال true and ال b
+
+153
+00:14:09,990 --> 00:14:14,190
+تكافئ ال b لا تكافئ ال true مع ال or تكافئ
+
+154
+00:14:14,190 --> 00:14:24,150
+وبالتالي هذه تكافئ هيك صارت نقطة ال b or نقطة q or
+
+155
+00:14:24,150 --> 00:14:29,550
+q خلصنا
+
+156
+00:14:29,550 --> 00:14:33,810
+من دي مورجان دي مورجان كانت فوقلأن هان احنا الان
+
+157
+00:14:33,810 --> 00:14:37,050
+كل العمليات اللي عندي من نفس الرتبة اللي هي ال R
+
+158
+00:14:37,050 --> 00:14:40,690
+وبالتالي بقدر اشتجم معناش توزيع التوزيع كانت فوق
+
+159
+00:14:40,690 --> 00:14:47,550
+توزيع ال R على الان و العكس بس الان تجميع معناته
+
+160
+00:14:47,550 --> 00:14:56,370
+انا عندي نط ال B or نط Q or Q هذه صارت true وهذه
+
+161
+00:14:56,370 --> 00:15:00,850
+تكافئ نط ال B or true تكافئ
+
+162
+00:15:02,300 --> 00:15:05,980
+True وبالتالي هي عبارة عن Tautology
+
+163
+00:15:08,820 --> 00:15:11,840
+إذا كان الحل التاني لو احنا مش قادرين نثبت بالشكل
+
+164
+00:15:11,840 --> 00:15:15,980
+هذا الشيء ماذا نسوي نستخدم جدول الاحتمالات هستخدم
+
+165
+00:15:15,980 --> 00:15:18,720
+جدول الاحتمالات كمان شوية بس لشغل تانية و بالمرة
+
+166
+00:15:18,720 --> 00:15:22,540
+بنكون أثبتناها بالشك تاني وبالتالي أصبحت عندي ال
+
+167
+00:15:22,540 --> 00:15:26,680
+role of inferences هذه اللي اسمها Medus Boninus
+
+168
+00:15:26,680 --> 00:15:29,780
+بغض النظر عن التسميات الشباب مش ضروري تحفظها لأن
+
+169
+00:15:29,780 --> 00:15:33,120
+كلها مسميات لاتينية متعنينيش كتير قبل ما يعنيني
+
+170
+00:15:33,120 --> 00:15:37,530
+أنا التطبيق تبع في القانون اللي موجود عندي هناتبعت
+
+171
+00:15:37,530 --> 00:15:42,470
+ال role مين ال hypothesis هيهم P and P implies Q
+
+172
+00:15:42,470 --> 00:15:45,970
+يعني في عندي two conditions مجموعين في compound
+
+173
+00:15:45,970 --> 00:15:50,150
+condition بينهم and مكتوبهم بالصورة هذه therefore
+
+174
+00:15:50,150 --> 00:15:56,990
+و لذلك ال conclusion قدت إلى Q الآن في أي اثبات لو
+
+175
+00:15:56,990 --> 00:16:01,850
+لجأت انا two conditions يتوفروا عندي بالصورة هذه P
+
+176
+00:16:01,850 --> 00:16:10,100
+و P implies Q مباشرة بستبدلهم بينبـ Q لاحظوا الان
+
+177
+00:16:10,100 --> 00:16:13,720
+في عندى proposition اتنين تلاتة مشكلة ما بينهم
+
+178
+00:16:13,720 --> 00:16:16,280
+compound و proposition انا خلصت منهم ب simple
+
+179
+00:16:16,280 --> 00:16:19,740
+proposition حقيت من اللي هم الـ Q وبالتالي سبصير
+
+180
+00:16:19,740 --> 00:16:23,360
+عندى موضوع الاثبات اسهل بحيث ان انا اقدر انتقل ل
+
+181
+00:16:23,360 --> 00:16:26,540
+next step عشان هيك بنقول ان ال role of inferences
+
+182
+00:16:26,540 --> 00:16:31,380
+تديني justification تديني تبرير ليش انا انتقلت
+
+183
+00:16:31,380 --> 00:16:34,280
+الخطوة هذه للخطوة هذه ليش انا اختسرت هذه و بدلتها
+
+184
+00:16:34,280 --> 00:16:41,200
+بهذهلما بكون في عندي اكتر من condition ان من ال
+
+185
+00:16:41,200 --> 00:16:44,180
+conditions و هذا الكلام ممكن لما باجي اقول على
+
+186
+00:16:44,180 --> 00:16:50,700
+سبيل المثال في المثلث قائم الزاوية طول الوتر تربيه
+
+187
+00:16:50,700 --> 00:16:56,540
+يساوي مجموع مربعات الضلعين الآخرين قانون في الثغرس
+
+188
+00:16:56,540 --> 00:17:02,800
+في عندي condition في عندي condition في عندي
+
+189
+00:17:02,800 --> 00:17:07,260
+condition ايش هو ال condition؟إن المثلث لازم يكون
+
+190
+00:17:07,260 --> 00:17:11,660
+قائم الزاوية إن المثلث لازم يكون قائم الزاوية
+
+191
+00:17:11,660 --> 00:17:14,920
+بالضبط الآن لما بكون .. هذا طبعا مثال في one
+
+192
+00:17:14,920 --> 00:17:17,940
+condition لما بكون في عندي أكثر من condition بدك
+
+193
+00:17:17,940 --> 00:17:21,240
+تفهم إن العلاقة ما بين ال conditions المختلفات
+
+194
+00:17:21,240 --> 00:17:26,480
+هدول and الرابط ما بين ال simple proposition هدول
+
+195
+00:17:26,480 --> 00:17:32,760
+او ال conditions هو مثال بت ال and هذه
+
+196
+00:17:32,760 --> 00:17:33,680
+مجموعة ال rules
+
+197
+00:17:36,370 --> 00:17:41,890
+هي اول احنا شوفنا اول واحد P and P implies Q اذا Q
+
+198
+00:17:41,890 --> 00:17:49,890
+هى فى عندى بقول نقطة Q and P implies Q هذا يمثل
+
+199
+00:17:49,890 --> 00:17:59,910
+نقطة ال P نقطة ال P P implies Q Q implies R اذا او
+
+200
+00:17:59,910 --> 00:18:04,640
+therefore ال conclusion P impliesألاحظ ان تتولجي
+
+201
+00:18:04,640 --> 00:18:11,860
+تبعتي شكل التتولجي هيها موجودة بي قره كيو و نطق ال
+
+202
+00:18:11,860 --> 00:18:25,280
+دي و لذلك بي قره كيو بي و كيو و لذلك بي قره كيو بي
+
+203
+00:18:25,280 --> 00:18:30,300
+قره كيو بي قره كيو تؤدي
+
+204
+00:18:30,300 --> 00:18:42,900
+إلى بيهدف التتولوجي صح هو اللي بقولها صح صح نفي
+
+205
+00:18:42,900 --> 00:18:54,960
+هدف التتولوجي نفي P and Q or ال P وزع النفي نقطة P
+
+206
+00:18:54,960 --> 00:18:59,660
+or نقطة Q or P
+
+207
+00:19:01,710 --> 00:19:09,030
+true تتولوجي بس طبعا بكتمل توزية توزية في الأول اه
+
+208
+00:19:09,030 --> 00:19:12,930
+عفوا تبديل وبعدين تجميع عشان جيب ال B نقطة ال B مع
+
+209
+00:19:12,930 --> 00:19:15,990
+ال D بال orb في الآخر المحصة هي تتولوجي فهي
+
+210
+00:19:15,990 --> 00:19:20,230
+تتولوجي وبالتالي هذا القانون صح طيب برضه لحد ت
+
+211
+00:19:20,230 --> 00:19:24,210
+اللحظة مش قادر استوعب انه ايش صح تعالى نشوف شكلة
+
+212
+00:19:24,210 --> 00:19:27,210
+تانية او شغلة تانية احنا هيك اثبتنا انها تتولوجي
+
+213
+00:19:27,210 --> 00:19:31,200
+تعالى نشوفهل الكلام هذا بالكلام البسيط منطقي ولا
+
+214
+00:19:31,200 --> 00:19:38,700
+لأ؟ بقول لو كانت B and Q معناته true لو كانت B and
+
+215
+00:19:38,700 --> 00:19:47,400
+Q is true تمام ال conclusion تبعتنا B طيب هذا role
+
+216
+00:19:47,400 --> 00:19:53,540
+of inferences ال condition يؤدي إلى conclusion ال
+
+217
+00:19:53,540 --> 00:19:59,440
+condition true ال conclusion trueB and Q عشان تكون
+
+218
+00:19:59,440 --> 00:20:03,900
+صحيحة، ايش لازم يكون عندك؟ لازم تنتينيكونه صحيحة
+
+219
+00:20:03,900 --> 00:20:10,580
+هذي صحيحة و هذي صحيحة يعني للـB نفسها صحيحة و مش
+
+220
+00:20:10,580 --> 00:20:14,080
+بس هيك ممكن تستبدل الـB هذي بإيش بـQ عند الحاجة
+
+221
+00:20:14,080 --> 00:20:18,480
+وبالتالي تبقى المسألة صحيحة هنا بدأت بدأت تشغل
+
+222
+00:20:18,480 --> 00:20:22,180
+دماغك فعليا في العناصر الموجودة دعالي نشوف المسألة
+
+223
+00:20:22,180 --> 00:20:28,270
+اللي منها وفاق بقول لو كانت عندك ABلو كانت عندك
+
+224
+00:20:28,270 --> 00:20:28,530
+الـ B
+
+225
+00:20:35,640 --> 00:20:40,000
+P implies P or Q لو كانت عندك ال condition P
+
+226
+00:20:40,000 --> 00:20:45,340
+لحالها is it true فتحط ال D نقلة او تقدي إلى true
+
+227
+00:20:45,340 --> 00:20:51,100
+ك conclusion فانت ضمنت عندك ال P مع or يعني ال P
+
+228
+00:20:51,100 --> 00:20:54,360
+بتتعامل معها as a true value أصبحت true أيش ما تحط
+
+229
+00:20:54,360 --> 00:20:58,500
+لها مع ال or فبتكون ال conclusion تبعتك أيش؟true
+
+230
+00:20:58,500 --> 00:21:01,740
+وبالتالي هذا ال role مهم جدا يا شباب لما نيجي
+
+231
+00:21:01,740 --> 00:21:05,320
+نتكلم على الاختزال او اثبات لان فعلا هنشوف كمان
+
+232
+00:21:05,320 --> 00:21:10,480
+مرة مثال او اتنين من اجل اثبات النظريات بالاعتماد
+
+233
+00:21:10,480 --> 00:21:15,840
+على ال role of inferences طيب تمام الان انا في
+
+234
+00:21:15,840 --> 00:21:21,080
+عندي شغلة مهمة بقدر ال role of inferences اللي
+
+235
+00:21:21,080 --> 00:21:24,400
+احنا بيسميها ال argument اتفقنا ال argument هي
+
+236
+00:21:24,400 --> 00:21:29,510
+عبارة عن مجموعة ايش؟مجموعة عوامل عوامل ايه اش
+
+237
+00:21:29,510 --> 00:21:33,350
+مجموعة ال conditions وال conclusion مع بعض ال
+
+238
+00:21:33,350 --> 00:21:36,650
+condition وال conclusion مع بعض مثلا منهم ايه اش
+
+239
+00:21:36,650 --> 00:21:43,930
+argument ال argument تباعتي هذه علاقتها مع بعض مثل
+
+240
+00:21:43,930 --> 00:21:48,970
+ال rule of inferences ان عندي اكثر من hypothesis
+
+241
+00:21:48,970 --> 00:21:54,230
+بتقدي ل conclusion بقول عن ال argument valid بقول
+
+242
+00:21:54,230 --> 00:21:59,960
+عن ال argument validwhenever وين ما بلاقي ان ال
+
+243
+00:21:59,960 --> 00:22:04,180
+hypothesis مع بعضهم كلهم are true و اتذكر ان ال
+
+244
+00:22:04,180 --> 00:22:11,640
+hypothesis بواحد and باتنين and بتلاتة إلى and بم
+
+245
+00:22:11,640 --> 00:22:15,140
+لما يكونوا كلهم مع بعض true طب عشان كلهم مع بعض
+
+246
+00:22:15,140 --> 00:22:20,140
+يكونوا true لازم كل واحدة بشكل مستقل تكوناش true
+
+247
+00:22:20,140 --> 00:22:24,220
+هيقدّي ان ال conclusion تبعتي لازم تكون .. طيب لو
+
+248
+00:22:24,220 --> 00:22:28,860
+واحدة كانت منهم falseبيعني ليش افحص؟ بيعني ليش؟
+
+249
+00:22:28,860 --> 00:22:32,080
+انا بيعني حالة واحدة فقط ان وين ما تكون ال
+
+250
+00:22:32,080 --> 00:22:36,300
+condition كلها true لازم ال conclusion يكون true
+
+251
+00:22:36,300 --> 00:22:39,400
+وبالتالي هذا ال argument او هذه التركيبة او هذه
+
+252
+00:22:39,400 --> 00:22:43,380
+التوليفة او هذه النظرية ال argument تبعتها ياشهي
+
+253
+00:22:44,210 --> 00:22:47,990
+valid valid بقدراش أسعى في أثباتها أو أقدر أتكلم
+
+254
+00:22:47,990 --> 00:22:52,190
+عليها بالشكل هذا عشان ما انتهش كتير احنا في
+
+255
+00:22:52,190 --> 00:22:56,530
+الموضوع هذا تعالى نشوف اول role of inferences اللي
+
+256
+00:22:56,530 --> 00:22:57,710
+احنا شوفناها قبل شوية
+
+257
+00:23:14,870 --> 00:23:20,550
+هو ايش قاعد بيقوللي whenever P implies the
+
+258
+00:23:20,550 --> 00:23:26,570
+condition is true يعني P لازم تكون true و ان هذي
+
+259
+00:23:26,570 --> 00:23:30,250
+تكون true هتقول لمين؟ لو بدني اتكلمها بشكل بسيط
+
+260
+00:23:30,250 --> 00:23:32,910
+whenever نتي هذي الكلام بيكون true هذي ما تكون
+
+261
+00:23:32,910 --> 00:23:38,130
+true و هذي لازم تكون true هذي متى بتكون true بي
+
+262
+00:23:38,130 --> 00:23:43,170
+تقول او true تقول الى .. فش غير هيك هذا الحالة
+
+263
+00:23:43,170 --> 00:23:48,660
+الوحيدة اللي عندىمصدوق ولا لأ؟ هذه حالات تانية
+
+264
+00:23:48,660 --> 00:23:53,320
+ممكن تتمشي فيها false تقول الى true و false تقول
+
+265
+00:23:53,320 --> 00:23:56,160
+الى false هذه برضه بتديني ال implication true بس
+
+266
+00:23:56,160 --> 00:24:01,320
+مقدرش استخدمهم ليش؟ لإن حددت قيمة ال B مسبقا
+
+267
+00:24:01,320 --> 00:24:04,400
+باعتماد على مين ال and او بين جثنين ال and اللي
+
+268
+00:24:04,400 --> 00:24:08,580
+ألزمتني أشتغل بسمع الحالة هذه وبالتالي أنا صرت هي
+
+269
+00:24:08,580 --> 00:24:12,920
+هي الحالة الوحيدة اللي عندي الحالة الوحيدة B is
+
+270
+00:24:12,920 --> 00:24:17,470
+trueو Q is true وبالتالي بتروح فحص ال implication
+
+271
+00:24:17,470 --> 00:24:22,730
+true implies true true وبالتالي هتصبح and ال
+
+272
+00:24:22,730 --> 00:24:28,030
+implication true and true implies true الكل
+
+273
+00:24:28,030 --> 00:24:38,010
+implies true تلقى true true and true true implies
+
+274
+00:24:38,010 --> 00:24:41,830
+true معناته هذا بتكلم على validargument بتتكلم على
+
+275
+00:24:41,830 --> 00:24:45,710
+valid argument و لو بدى أروح بشغل أطول شوية ممكن
+
+276
+00:24:45,710 --> 00:24:48,750
+يكون أسهل بالنسبة إليك الآن ابني جدول الاحتمالات
+
+277
+00:24:48,750 --> 00:24:53,370
+لل tautology هذه عبارة عن ايش يا شباب؟ عبارة عن
+
+278
+00:24:53,370 --> 00:24:57,810
+tautology يعني قيمة ال condition هذا او ال .. هي
+
+279
+00:24:57,810 --> 00:25:04,550
+عبارة عن ال true كان variable عندى ايه؟ 2 B و Q
+
+280
+00:25:04,550 --> 00:25:12,220
+true true false false true falsetrue false بعد هيك
+
+281
+00:25:12,220 --> 00:25:21,880
+P implies Q true false true true P and P implies Q
+
+282
+00:25:21,880 --> 00:25:31,500
+هاي هم true false false لا بس لحظة شوية هنا ال
+
+283
+00:25:31,500 --> 00:25:37,890
+true falsefalse false تمام ايه الضغط اللي عندي ضغط
+
+284
+00:25:37,890 --> 00:25:42,830
+اللي عندي ال role الأخير زي ما هو هيك P and P
+
+285
+00:25:42,830 --> 00:25:49,910
+implies Q الكل implies Q هذا يقول إلى هذا ال true
+
+286
+00:25:49,910 --> 00:25:57,590
+implies true true false implies true true false
+
+287
+00:25:57,590 --> 00:26:03,000
+implies true true false implies falsetrue لازم
+
+288
+00:26:03,000 --> 00:26:06,320
+يكون كلهم true لأنها عبارة عن تيتولوجي لازم يكون
+
+289
+00:26:06,320 --> 00:26:13,700
+كلهم true مصبوط بس أصبر شوية أصبر كلهم لازم يكونوا
+
+290
+00:26:13,700 --> 00:26:17,100
+true لأن هذه عبارة عن تيتولوجي بس ليش أنا بقول
+
+291
+00:26:17,100 --> 00:26:22,680
+valid argument لأن whenever all the hypothesis are
+
+292
+00:26:22,680 --> 00:26:26,100
+true وين الصف اللي فيه ال hypothesis تعوني كلهم مع
+
+293
+00:26:26,100 --> 00:26:29,800
+بعض ال true كم hypothesis أنا عندى؟ كم hypothesis
+
+294
+00:26:29,800 --> 00:26:35,230
+أنا عندى؟هي ال hypothesis اللي عندي عندي تنتين بي
+
+295
+00:26:35,230 --> 00:26:40,510
+هي ال بي و ال بي in boys queue هيهم متى القيمتين
+
+296
+00:26:40,510 --> 00:26:44,290
+هدول بيكونوا مع بعض true لو طلعناها بس في الصف
+
+297
+00:26:44,290 --> 00:26:51,990
+الأول هان و هان whenever all its hypothesis are
+
+298
+00:26:51,990 --> 00:26:56,390
+true وينما بتكون الفرضيات تبعتها true whenever the
+
+299
+00:26:56,390 --> 00:27:02,110
+hypothesis are true it will lead the conclusionIs
+
+300
+00:27:02,110 --> 00:27:05,270
+it true؟ وبالتالي هذا الصف هو الوحيد اللي يعنيني
+
+301
+00:27:05,270 --> 00:27:09,470
+عشان اقول عليها valid ولا invalid argument. هذي
+
+302
+00:27:09,470 --> 00:27:13,490
+valid argument. ليش؟ لأن وين ال two argument او ال
+
+303
+00:27:13,490 --> 00:27:18,100
+two hypothesis تعوني كانوا true؟تدوني true طب
+
+304
+00:27:18,100 --> 00:27:22,100
+الباقى يا أستاذ true و false .. false و false ..
+
+305
+00:27:22,100 --> 00:27:24,000
+false و false .. ماليش داخل فيهم .. خلاص معناته
+
+306
+00:27:24,000 --> 00:27:27,880
+أنا بص بالصف اللى بحقق الشرق عشان أفحص ال validity
+
+307
+00:27:27,880 --> 00:27:32,700
+تبعت ال argument اللى عندي otherwise لو كان هذا
+
+308
+00:27:32,700 --> 00:27:37,460
+يقول الى false معناته
+
+309
+00:27:37,460 --> 00:27:40,360
+خلصنا .. معناته invalid argument .. invalid
+
+310
+00:27:40,360 --> 00:27:42,320
+argument .. تمام؟
+
+311
+00:27:48,350 --> 00:27:55,170
+تعالى نشوف الـ argument اللى موجود عندى هنا في
+
+312
+00:27:55,170 --> 00:27:58,970
+عند ال rule of inferences بقول بي implies كيو و
+
+313
+00:27:58,970 --> 00:28:05,650
+كيو implies الار therefore كيو بي implies الار هذا
+
+314
+00:28:05,650 --> 00:28:09,950
+واحد من ال rules لو بدنا نرجع هنا هيو لا مش الآخر
+
+315
+00:28:09,950 --> 00:28:16,380
+تالت هيوطيب .. الآن هذا ال rule .. لما انا بدي ..
+
+316
+00:28:16,380 --> 00:28:19,420
+كمان مرة انا جاعد شباب مش جاعد بأثبت انه rule of
+
+317
+00:28:19,420 --> 00:28:23,900
+inferences تمام؟ انا بدي أثبت انه valid argument
+
+318
+00:28:23,900 --> 00:28:26,460
+.. جاعد بقوللي افحص ال argument هذه valid ولا
+
+319
+00:28:26,460 --> 00:28:31,610
+invalid .. من ال argument اللي عندي انا هانهيهم
+
+320
+00:28:31,610 --> 00:28:34,990
+واحد اتنين تلاتة ال argument هم عبارة عن ال
+
+321
+00:28:34,990 --> 00:28:39,550
+conditions بالإضافة لمين ل ال conclusion لما بدن
+
+322
+00:28:39,550 --> 00:28:45,810
+جدول الاحتمالات بتهم الصفوف فقط اللي بتكون فيها ال
+
+323
+00:28:45,810 --> 00:28:51,570
+two conditions are true هيبني الجدول الاحتمالات هي
+
+324
+00:28:51,570 --> 00:28:55,530
+B و هي Q و هي R مع ان انا بتتكلم عن جدول مكون من
+
+325
+00:28:55,530 --> 00:29:00,790
+تمام صفوف B implies Q و Q implies R
+
+326
+00:29:05,250 --> 00:29:11,290
+روحتنا فحصنا ال argument اللي موجودة عندها hand
+
+327
+00:29:11,290 --> 00:29:18,230
+true الصف هذا لازم انا اتكد منه قيمته ممتاز بنتقل
+
+328
+00:29:18,230 --> 00:29:23,350
+للي بعده لأ اللي بعده اللي بعده هيو هذا لازم يكون
+
+329
+00:29:23,350 --> 00:29:29,240
+ال output تبعته true هيو هذاالـ output تبعته true
+
+330
+00:29:29,240 --> 00:29:32,040
+لبعده الـ output تبعته true طب اللي في النص هدول
+
+331
+00:29:32,040 --> 00:29:35,900
+بيعنونيش لإن هم حققوش ال condition تبع مين تبع ال
+
+332
+00:29:35,900 --> 00:29:39,260
+valid argument ال valid argument كان بيقولي بقول
+
+333
+00:29:39,260 --> 00:29:43,400
+عن هدولة valid argument لما بتكون whenever all the
+
+334
+00:29:43,400 --> 00:29:46,920
+hypothesis all the conditions are true وين هم اللي
+
+335
+00:29:46,920 --> 00:29:50,420
+بتبتدوا true عليهم في الصوفة المحددة ده باللون
+
+336
+00:29:50,420 --> 00:29:55,060
+الأخضر وبالتالي كانت تعمل leadالصحيحة فهذه صحيحة
+
+337
+00:29:55,060 --> 00:30:00,560
+فهذه صحيحة ايش؟ الارجومنت لو انت لجيت هذه
+
+338
+00:30:00,560 --> 00:30:05,800
+الاختلافات ماتكملش خلاص تفحصش انفاليد طب ماهم
+
+339
+00:30:05,800 --> 00:30:11,240
+يجايفوا في فروع تانية not all صار في اندي there
+
+340
+00:30:11,240 --> 00:30:11,840
+exist
+
+341
+00:30:14,330 --> 00:30:17,090
+one row where all the arguments or the hypothesis
+
+342
+00:30:17,090 --> 00:30:21,390
+are true lead to false وبالتالي نفينا ال
+
+343
+00:30:21,390 --> 00:30:26,490
+definition تبعت العناصر اللي موجودة عندها تعالى
+
+344
+00:30:26,490 --> 00:30:31,350
+نشوف المثال هذا بنعمله ترجمة ونشوف هل هو بطلع
+
+345
+00:30:31,350 --> 00:30:36,870
+valid argument ولا لأ if I like discrete
+
+346
+00:30:36,870 --> 00:30:40,830
+mathematics إذا
+
+347
+00:30:40,830 --> 00:30:48,440
+أنا حبيت الرياضة المنفصلةأول شرط false طيب I'll
+
+348
+00:30:48,440 --> 00:30:55,400
+study it معناته انا بقدر اجي اقول P I like
+
+349
+00:30:55,400 --> 00:31:04,880
+discrete mathematics Q I will study discrete
+
+350
+00:31:04,880 --> 00:31:10,230
+mathematicsطبعا لاحظ ان انا عمال بفصل .. بدي اوصل
+
+351
+00:31:10,230 --> 00:31:13,810
+ال conditions تبعتي ..الان لاحظ انا عمال بفصل
+
+352
+00:31:13,810 --> 00:31:19,030
+الشباب في .. بفصل في مين .. بحاول اترجم كل المسألة
+
+353
+00:31:19,030 --> 00:31:22,990
+..الان صار في اندهان ال argument او ال condition
+
+354
+00:31:22,990 --> 00:31:27,360
+الأولB implies Q هذا ال condition الأول لسه
+
+355
+00:31:27,360 --> 00:31:31,400
+ماوصلتش ل conclusion either I study I study هي مش
+
+356
+00:31:31,400 --> 00:31:35,220
+مشكلة او I study مش قضية كتير discrete mathematics
+
+357
+00:31:35,220 --> 00:31:42,120
+or I fail the course هي Q او هي R I fail رصبت the
+
+358
+00:31:42,120 --> 00:31:47,520
+course ال course رصبت في المساق معناته ال
+
+359
+00:31:47,520 --> 00:31:52,540
+condition التاني عندى either I study I study when
+
+360
+00:31:52,540 --> 00:32:01,190
+QQ or R نقطة حطلي Therefore عشان يقولي اللي جاي هو
+
+361
+00:32:01,190 --> 00:32:06,350
+عبارة عنين؟ عن ال conclusion Therefore
+
+362
+00:32:06,350 --> 00:32:13,010
+if I fail the course then I don't like discrete
+
+363
+00:32:13,010 --> 00:32:18,770
+mathematics إذا أنا رصبت ال R تقول إلى نقطة ال B
+
+364
+00:32:18,770 --> 00:32:28,340
+نقطة ال B مصبوط؟الان لاحظ اول شي ترجمت النص ل
+
+365
+00:32:28,340 --> 00:32:31,740
+simple proposition بعدين حولته ل compound
+
+366
+00:32:31,740 --> 00:32:35,060
+proposition بناء على فهم المعادلة therefore كانت
+
+367
+00:32:35,060 --> 00:32:39,180
+الفيصل تقول كل اللي فات عبارة عن ال conclusion
+
+368
+00:32:39,180 --> 00:32:44,300
+وكنت انا بتلاحظ ال forest top هذي كانت بتقولي ال
+
+369
+00:32:44,300 --> 00:32:47,420
+condition الأول خلص ال condition التاني بدأ وما
+
+370
+00:32:47,420 --> 00:32:50,120
+شبه تمام
+
+371
+00:32:50,930 --> 00:32:57,850
+الان بقول افحص هل هذا valid argument ولا لأ؟ عشان
+
+372
+00:32:57,850 --> 00:33:00,930
+تفحص ال validity معناته تبدا تجيب كل احتمالات اللي
+
+373
+00:33:00,930 --> 00:33:05,050
+بتكون هذه فيها true فاسهل حاجة بالنسبالك الجدول
+
+374
+00:33:05,050 --> 00:33:12,130
+الاحتمالات هذا كلام اكيد طيب في
+
+375
+00:33:12,130 --> 00:33:19,310
+جدول الاحتمالات كام صفر محتاجين احنا؟ B و implies
+
+376
+00:33:19,310 --> 00:33:26,520
+a Q وRبعده تمانية true true true true false false
+
+377
+00:33:26,520 --> 00:33:34,540
+false false true true false false true true false
+
+378
+00:33:34,540 --> 00:33:39,680
+false true
+
+379
+00:33:39,680 --> 00:33:46,700
+false true false true false
+
+380
+00:33:50,450 --> 00:33:57,190
+ال condition الأول B implies Q true implies true
+
+381
+00:33:57,190 --> 00:34:04,770
+true true false false لحظة شوية عشان انا هحط كل
+
+382
+00:34:04,770 --> 00:34:11,670
+قيمة مانجوحش الخربط هات true هات false هات false
+
+383
+00:34:11,670 --> 00:34:16,410
+هات true true true true
+
+384
+00:34:18,930 --> 00:34:22,910
+B implies Q true implies true true true false
+
+385
+00:34:22,910 --> 00:34:30,170
+false و الباقي كله true ال condition التاني Q
+
+386
+00:34:30,170 --> 00:34:43,610
+or R Q or R true true true false true true true
+
+387
+00:34:43,610 --> 00:34:51,210
+false Q و R هايهمالتنتين صحيح صحيح صحيح صحيح خاطئ
+
+388
+00:34:51,210 --> 00:34:56,210
+صحيح صحيح صحيح صحيح خاطئ الانشبوك اللي هو عشان
+
+389
+00:34:56,210 --> 00:35:00,770
+تكون هذه valid argument whenever وينما بتكون عندك
+
+390
+00:35:00,770 --> 00:35:07,650
+الصفوف التنتين مع بعض صحيح هاي
+
+391
+00:35:07,650 --> 00:35:13,830
+الصف هاي التاني اللي بعده لأ اللي بعده هاي واحدة
+
+392
+00:35:13,830 --> 00:35:19,770
+هاي التنتين هاي التلاتةهدولة التلات صفوف اللي أنا
+
+393
+00:35:19,770 --> 00:35:25,290
+معنى فيهم إذا هدولة التلخمس صفوف عملوا lie implies
+
+394
+00:35:25,290 --> 00:35:28,910
+ل true معاكوا هذا valid argument لو واحدة منهم
+
+395
+00:35:28,910 --> 00:35:32,410
+عملت implies ل false والباقي عمل ل true فهي بتكون
+
+396
+00:35:32,410 --> 00:35:38,430
+invalid argument تعالى نشوف الأخيرة اللي هي ال R
+
+397
+00:35:38,430 --> 00:35:44,790
+implies نقطة ال B هاي ال R وهي نقطة ال B true
+
+398
+00:35:44,790 --> 00:35:54,010
+implies falsetrue implies false true
+
+399
+00:35:54,010 --> 00:36:02,070
+implies false false خلصنا نفي نقطة بيعني ع مال بنا
+
+400
+00:36:02,070 --> 00:36:06,170
+فيها بقولك ال true implies false بناء على ال role
+
+401
+00:36:06,170 --> 00:36:10,230
+اللي عندها ال false أكمل لا تكملش خلصنا
+
+402
+00:36:14,510 --> 00:36:17,850
+أه لما تشوف .. لو هذا كلها true .. فتبحث اللي
+
+403
+00:36:17,850 --> 00:36:22,210
+باقيها .. خلاص اتكملش .. انا مسئول علي الكلام ..
+
+404
+00:36:22,210 --> 00:36:25,490
+لإن وين بتصير .. صار في عندك واحدة أو الشرط مختلف
+
+405
+00:36:25,490 --> 00:36:29,190
+.. لإن كان الشرط بيقول إيه .. عند كل هدولة لازم
+
+406
+00:36:29,190 --> 00:36:33,530
+تكون ال conclusion true .. عند هي أول واحدة طلعت
+
+407
+00:36:33,530 --> 00:36:37,230
+ال conclusion false .. تمام؟ معينة و أنا بقدر أقول
+
+408
+00:36:37,230 --> 00:36:41,180
+عنها invalid ..Argument بدون ان اكمل الجدول و لو
+
+409
+00:36:41,180 --> 00:36:44,160
+كملت يا رامي هطلع معاك الجدول زي ما هو هنا انا
+
+410
+00:36:44,160 --> 00:36:46,720
+بكملك ايه على ال slide طبعا عشان اريح راسي
+
+411
+00:36:50,910 --> 00:36:54,890
+من أوليتها false معناته لأن بمجرد ان انا كملت جدول
+
+412
+00:36:54,890 --> 00:37:00,790
+الاحتمالات وفحصت هيلاحظ اول تنتين conditions true
+
+413
+00:37:00,790 --> 00:37:03,310
+and true لازم تعمل lead معايا او تكون ال
+
+414
+00:37:03,310 --> 00:37:07,610
+conclusion معايا true بمجرد اني لاجيتها false فهذا
+
+415
+00:37:07,610 --> 00:37:12,270
+هو invalid argument كملت الجدول ولا ماكملتهش بطل
+
+416
+00:37:12,270 --> 00:37:15,990
+اتفرج كتير خلاص معك فانا ضمنت ان هذا الكلام false
+
+417
+00:37:15,990 --> 00:37:17,750
+invalid argument
+
+418
+00:37:21,000 --> 00:37:28,060
+جاهز بيقول لي شوف لهذا المثال if 101 is divisible
+
+419
+00:37:28,060 --> 00:37:32,200
+by 3 إذا كان 101 تقبل الجسم على 3 معناته 112 تقبل
+
+420
+00:37:32,200 --> 00:37:38,980
+الجسم على 9 101 تقبل الجسم على 3 for stop
+
+421
+00:37:38,980 --> 00:37:43,900
+consequently therefore conclusion 102 is divisible
+
+422
+00:37:43,900 --> 00:37:48,500
+byتسعة او ألف و أتناش عفوية تجبل الجسم علاقة تسعة
+
+423
+00:37:48,500 --> 00:37:52,840
+هاي ال conditions اللي عندي الاول ال condition
+
+424
+00:37:52,840 --> 00:37:55,340
+الاول هي ال simple arguments او عفر ال simple
+
+425
+00:37:55,340 --> 00:38:03,540
+proposition بي اندواز كيو اللي بعده بي لإن هي جميع
+
+426
+00:38:03,540 --> 00:38:10,220
+واحد is divisible by three therefore كيو
+
+427
+00:38:10,220 --> 00:38:17,890
+كلامه ك argument هيهمهذه الاختصارات وهذه
+
+428
+00:38:17,890 --> 00:38:20,790
+الاختصارات وهذه الاختصارات هل هذا valid argument
+
+429
+00:38:20,790 --> 00:38:26,650
+ولا invalid افحص ممكن استخدم جدول الاحتجازات و
+
+430
+00:38:26,650 --> 00:38:34,190
+اشوف و ممكن اذهب للقوانين هاي القانون عندي هاي
+
+431
+00:38:34,190 --> 00:38:39,830
+الشكل اللي عندي هاي
+
+432
+00:38:39,830 --> 00:38:43,940
+الشكل B implies Qcondition الأول condition التاني
+
+433
+00:38:43,940 --> 00:38:53,520
+B therefore Q شجبه عشان أحصل على الترتيب الترتيب
+
+434
+00:38:53,520 --> 00:38:57,300
+ليش؟ عشان الطابق هان مع role of conferences اللي
+
+435
+00:38:57,300 --> 00:39:02,900
+موجود عندي هيه هيه لاحظ هذا و لاحظ هذا شوف التنين
+
+436
+00:39:02,900 --> 00:39:09,760
+هدول مهمات و عليهم هو إيش الشغل بعد
+
+437
+00:39:09,760 --> 00:39:15,780
+ما رتبنا هانهذا هيك .. therefore Q لأ بس الأصل هذا
+
+438
+00:39:15,780 --> 00:39:21,440
+إيش بيطلع بيطلع بـQ و لا بيطلع بـB حسب القانون هذه
+
+439
+00:39:21,440 --> 00:39:24,140
+القوانين كلها بتطلع معايا هيك وبالتالي هذا ال
+
+440
+00:39:24,140 --> 00:39:28,360
+condition is false وبالتالي invalid argument
+
+441
+00:39:28,360 --> 00:39:31,160
+معناته هذا ال hypothesis تبعتي مش سليمة يعني
+
+442
+00:39:31,160 --> 00:39:35,780
+invalid argument عارف ليش invalid argument؟ شوية
+
+443
+00:39:35,780 --> 00:39:39,960
+بس .. عشان أقولك أن ال hypothesis تبعتي false 101
+
+444
+00:39:39,960 --> 00:39:47,760
+لا تقبل قسم ع 3101 هيها هذه لا تقبل قسمها تلاتة
+
+445
+00:39:47,760 --> 00:39:53,320
+فهذه قيمتها false ولا عمرها حسب ال condition هذه
+
+446
+00:39:53,320 --> 00:39:57,140
+هتكون true عندي عشان تكون true بدي استخدم النفي
+
+447
+00:39:57,140 --> 00:40:01,060
+وبالتالي هذا القانون الشكل هذا لا يحقق عندي أو لا
+
+448
+00:40:01,060 --> 00:40:04,680
+يتحقق وبالتالي هذه عبارة عن invalid argument ال
+
+449
+00:40:04,680 --> 00:40:10,540
+conclusion incorrect لأن فعمليا كمان الأربعة لا
+
+450
+00:40:10,540 --> 00:40:15,800
+تقبل قسمها التسعةاللي هي 1012 اجمع الأرقام و جسمه
+
+451
+00:40:15,800 --> 00:40:20,520
+على 9 انت
+
+452
+00:40:20,520 --> 00:40:24,200
+سعيد ان انت بتشتغل على هيك هاي ال rules لإن هذا ال
+
+453
+00:40:24,200 --> 00:40:26,180
+rule هي اللي قعدت ترتيبه عشان طابق الصورة اللي
+
+454
+00:40:26,180 --> 00:40:30,680
+موجود عندي في الجدول تمام؟ لكن اختلف في وين؟ في ال
+
+455
+00:40:30,680 --> 00:40:34,080
+Q الآن وبالتالي هو الصحي اللي يجب أن يطلع عندي نفي
+
+456
+00:40:34,080 --> 00:40:37,020
+ال B لازم يطلع هي القانون اللي عندي انا بقوله انا
+
+457
+00:40:37,020 --> 00:40:41,360
+بحصل على نفي ال B لكن تهلأ بمعنى اخر ان هذا الكلام
+
+458
+00:40:41,360 --> 00:40:44,570
+غير صحيحليش غير صحيح؟ تهانى الراجل ال conditions
+
+459
+00:40:44,570 --> 00:40:49,910
+تبعتى 101 لا تقبل القسم على ثلاثة و 1012 لا تقبل
+
+460
+00:40:49,910 --> 00:40:53,030
+القسم على تسعة وبالتالي مستحيل هذا ال condition
+
+461
+00:40:53,030 --> 00:40:57,610
+يكون true وبالتالي هذا invalid argument هذا مثال
+
+462
+00:40:57,610 --> 00:41:01,910
+قريف من الكتاب عشان تصحصه بقولك لو اليوم بتشتي
+
+463
+00:41:01,910 --> 00:41:08,350
+طبعا؟ المعنى انت مش حنشه الليلة بحكته بحكته على
+
+464
+00:41:08,350 --> 00:41:13,720
+الآخر كمان و بعض السنان بينت زى حالتي طبعا؟إذا
+
+465
+00:41:13,720 --> 00:41:22,440
+كانت اليوم مطبرة، فلن نحصل على باربيكو اليوم إذا
+
+466
+00:41:22,440 --> 00:41:26,720
+لم نحصل على باربيكو اليوم،
+
+467
+00:41:26,720 --> 00:41:30,960
+فلن نحصل
+
+468
+00:41:30,960 --> 00:41:42,800
+على باربيكو غير اليوم إذا لم نحصل على باربيكو غير
+
+469
+00:41:42,800 --> 00:41:46,480
+اليومفي train studio لو تشت اليوم معناته احنا
+
+470
+00:41:46,480 --> 00:41:53,740
+هنشويه؟ بكرا شتت بكرا خلاص بتقلق نفس الكلام طيب
+
+471
+00:41:53,740 --> 00:41:58,960
+الان تعالى
+
+472
+00:41:58,960 --> 00:42:02,240
+شوف سيبك من الحل هذا لو كمان هشكل حل تاني بالنسبة
+
+473
+00:42:02,240 --> 00:42:07,240
+اليك تعالى الان لاحظ ال condition الأول هو عبارة
+
+474
+00:42:07,240 --> 00:42:12,600
+عن implies صح ال condition الأول implies ايهش
+
+475
+00:42:12,600 --> 00:42:13,180
+بيقول ايه؟
+
+476
+00:42:25,700 --> 00:42:30,780
+ممكن اكتب له نط كيو على انك اليوم لديك باربيكو
+
+477
+00:42:36,000 --> 00:42:39,020
+الـ Q خلصت من ال condition الأول ال condition
+
+478
+00:42:39,020 --> 00:42:43,260
+التاني if برضه ما زال فيه if و then معناته هو
+
+479
+00:42:43,260 --> 00:42:48,440
+عبارة عن implication if we don't have a barbecue
+
+480
+00:42:48,440 --> 00:42:54,480
+today معناته not Q then
+
+481
+00:42:54,480 --> 00:42:57,380
+we will have a barbecue tomorrow وهدش دي إيه ده
+
+482
+00:42:57,380 --> 00:42:59,900
+بالنسبة لنا have a barbecue tomorrow اللي هتكون
+
+483
+00:42:59,900 --> 00:43:00,820
+إيش R
+
+484
+00:43:03,980 --> 00:43:11,600
+خلصنا Therefore إذا B تقول
+
+485
+00:43:11,600 --> 00:43:16,420
+إلى We will have a barbecue tomorrow إلى R إيش
+
+486
+00:43:16,420 --> 00:43:25,400
+فرجت عن الحل هذا؟ لما عرف ال symbol proposition Q
+
+487
+00:43:25,400 --> 00:43:32,130
+عرفه will not haveيعني دخّل النافي في بنية أو في
+
+488
+00:43:32,130 --> 00:43:35,850
+تعريف الـ Simple Proposition فصارت عنده P implies
+
+489
+00:43:35,850 --> 00:43:41,330
+Q و Q implies R بيفرق معانا الحاجة هان؟ لأ لاحظ
+
+490
+00:43:41,330 --> 00:43:46,990
+الـ Proposition هذا هو نفسه هيوهان وبالتالي أي حل
+
+491
+00:43:46,990 --> 00:43:50,190
+من اتنين هذا برجعنا للكلام الأول اللي قلتلك إياه
+
+492
+00:43:50,190 --> 00:43:55,010
+سابقا طالما أنك بتفسر صح بغض النظر كيف حصلت الـ
+
+493
+00:43:55,010 --> 00:43:58,550
+Proposition المهم لما تكتب الـ Definition اكتبه صح
+
+494
+00:44:01,660 --> 00:44:04,640
+ممكن اتعرف تروح هناك تقول الـQ احنا حسب ال
+
+495
+00:44:04,640 --> 00:44:07,500
+definition تابعتنا ايها We have a barbecue today
+
+496
+00:44:07,500 --> 00:44:13,020
+هل هي الـQ؟ وبالتالي بي implies not the Q مافي
+
+497
+00:44:13,020 --> 00:44:19,240
+الـQ، تمام؟ valid ولا invalid؟ valid argument لأن
+
+498
+00:44:19,240 --> 00:44:22,640
+هذه بالطبق ال rule of inferences اللي اسمه
+
+499
+00:44:22,640 --> 00:44:29,940
+hypothetical soligism او ال chaining اللي هي سلسلة
+
+500
+00:44:30,920 --> 00:44:37,960
+الان هى ال role موجود عندنا هنا هى
+
+501
+00:44:37,960 --> 00:44:42,960
+وان السلسلة .. السلسلة بمثابة ال Q الحلقة ما بين
+
+502
+00:44:42,960 --> 00:44:48,120
+الاتنين اذا كانت A تقول الى B و B تقول الى C
+
+503
+00:44:48,120 --> 00:44:54,240
+فمعناته A تقول الى C تمام
+
+504
+00:44:54,240 --> 00:44:57,240
+نشوف المثال اللى بعده
+
+505
+00:45:10,470 --> 00:45:20,730
+Okay مش مشكلة صاحبة طيب الآن ايش بقوللي بقوللي
+
+506
+00:45:20,730 --> 00:45:27,610
+Gary is either an intelligent or a good actor Gary
+
+507
+00:45:27,610 --> 00:45:35,460
+is intelligent هاي P و هاي RA good actor Q Gary is
+
+508
+00:45:35,460 --> 00:45:39,160
+a good actor Q هال condition الأول If Gary is
+
+509
+00:45:39,160 --> 00:45:46,340
+intelligent B implies then he count from one to
+
+510
+00:45:46,340 --> 00:45:53,200
+ten لو كان Gary ذكي أو شاطر هيعد من واحد لعشرة هدي
+
+511
+00:45:53,200 --> 00:46:00,080
+R Gary can only count from one to three Gary بس
+
+512
+00:46:00,080 --> 00:46:06,410
+بيعد من واحد إلى تلاتةنط ال R. Therefore,
+
+513
+00:46:06,690 --> 00:46:11,990
+conclusion تبعتنا, Gary is a good actor. الهي مين؟
+
+514
+00:46:11,990 --> 00:46:18,090
+ال Q فقط ال Q. تعالى و ردتوهم بي او ري كيو. ال
+
+515
+00:46:18,090 --> 00:46:23,230
+condition الأول بي implies ال R نط ال R.
+
+516
+00:46:24,390 --> 00:46:30,990
+Therefore, ال Q. هاد الآن هاد ال argument تبعتى.
+
+517
+00:46:34,800 --> 00:46:40,600
+هل هي valid argument ولا invalid argument؟ بدك
+
+518
+00:46:40,600 --> 00:46:45,160
+تبدأ تجدوا الاحتمالات وتبدأ تشتغل و تحسب ممكن تاخد
+
+519
+00:46:45,160 --> 00:46:49,440
+وقت كتير لكن لو احنا رجعنا لل role of inferences
+
+520
+00:46:49,440 --> 00:46:55,680
+السادقات ممكن يقولولي هذا الكلام صحيح ولا لأ؟ ايوة
+
+521
+00:46:55,680 --> 00:47:01,100
+..الان ..الان ..تعالى نشوفالترتيب هذا يا شباب
+
+522
+00:47:01,100 --> 00:47:05,480
+هدولة التلت عناصر و بينهم and و احنا ال and عملية
+
+523
+00:47:05,480 --> 00:47:09,340
+ابدالية and هان بين ال conditions هدولة بتايعي
+
+524
+00:47:09,340 --> 00:47:14,020
+conditions و اللي بينهم and و ال and عملية ابدالية
+
+525
+00:47:14,020 --> 00:47:16,880
+يعني بقدر ابدل كل اتنين و اجملهم زي ما بدي ولا لأ
+
+526
+00:47:16,880 --> 00:47:21,220
+حسب خواص ال and طيب تعالى نشوف الخطوات التالية
+
+527
+00:47:21,220 --> 00:47:23,940
+يعني لو انا روحت اشتغلت كالتالية هي ال hypothesis
+
+528
+00:47:23,940 --> 00:47:28,550
+اللي موجودة عندىهو حتى انا اشتغلت في ال hypothesis
+
+529
+00:47:28,550 --> 00:47:32,230
+كالتالي اقعد ترتيبهم نط ال R ال hypothesis الأول
+
+530
+00:47:32,230 --> 00:47:39,550
+بي implies ال R ال hypothesis التاني هيه يعني بين
+
+531
+00:47:39,550 --> 00:47:42,510
+جثين انا بدأ اشتغل على هدول التاني اللي حالهم
+
+532
+00:47:42,510 --> 00:47:48,350
+بينفع اه بينفع يعني هو كأنه جالس بقوله هيك high
+
+533
+00:47:48,350 --> 00:47:55,070
+condition بي or Q and
+
+534
+00:47:55,650 --> 00:48:04,930
+أفتح جوس كبير نقطة الـ R and B implies الـ R صح
+
+535
+00:48:04,930 --> 00:48:10,450
+ولا لا؟ وبدي أحل الجو الجوس في الأول حسب القوانين
+
+536
+00:48:10,450 --> 00:48:14,490
+السادقة اللي في الجدول الشكل هذا هيدين مين يا
+
+537
+00:48:14,490 --> 00:48:21,270
+شباب؟ نقطة الـ B هذا حسب المدرسة تيليناس واحد
+
+538
+00:48:21,270 --> 00:48:24,630
+واتنين اللي هو أول قانونين الموجودة عندنا في
+
+539
+00:48:24,630 --> 00:48:25,230
+الجدول هنا
+
+540
+00:48:28,720 --> 00:48:41,880
+هي نقطة ال R P implies R تديني نفي ال P تمام
+
+541
+00:48:41,880 --> 00:48:46,620
+اداني نفي ال P الان نفي ال P هي عبارة عن المحصلة
+
+542
+00:48:46,620 --> 00:48:51,480
+تبع ال two conditions هدول بل اعملها انت مع مين؟
+
+543
+00:48:51,480 --> 00:48:58,910
+مع ال condition هدى P or Q مية لمية P or Qو في
+
+544
+00:48:58,910 --> 00:49:05,990
+عندي نقطة P بتديني مين؟ ال Q بتديني ال Q هتوصلي
+
+545
+00:49:05,990 --> 00:49:11,110
+ليها ال Q بنفس الترتيب هذا لو بدنا نرجع لورا
+
+546
+00:49:11,110 --> 00:49:16,330
+للقوانين مهمش مرة تانية مش ورا تتعب و انت بترجع
+
+547
+00:49:16,330 --> 00:49:25,170
+معايا وين القوار هايو؟ مصبوط؟ مصبوط؟ فتديني مين؟ P
+
+548
+00:49:25,170 --> 00:49:29,180
+انا فعليا في عندي النف موجود فوق في التنتينفي
+
+549
+00:49:29,180 --> 00:49:35,940
+المسألة هان فأصبحت
+
+550
+00:49:35,940 --> 00:49:42,300
+عند بتديني مين؟ بتديني الـQ، قدتني الـQ حسب ال
+
+551
+00:49:42,300 --> 00:49:47,060
+role of inferences، معناه أن هذه وصلت إلى
+
+552
+00:49:47,060 --> 00:49:52,600
+conclusionال rules أو ال hypothesis اللي فوق وصلون
+
+553
+00:49:52,600 --> 00:49:54,600
+إلى ال conclusion باعتماد على ال rule of
+
+554
+00:49:54,600 --> 00:49:58,080
+inferences وال rule of inferences هي عبارة عن
+
+555
+00:49:58,080 --> 00:50:02,300
+valid argument already و تم إثباتها وبالتالي أنا
+
+556
+00:50:02,300 --> 00:50:07,140
+بقدر أتحقق من ال validity من خاصية ال argument هذه
+
+557
+00:50:07,140 --> 00:50:10,840
+هل هي valid ولا invalid لو فعليا قدرت أستغل ال
+
+558
+00:50:10,840 --> 00:50:15,820
+rule of inferences عشان من ال hypothesis أصل لمين
+
+559
+00:50:15,820 --> 00:50:22,270
+لل conclusionاللي موجودة كيف تحلها؟ ما هي نفسها
+
+560
+00:50:22,270 --> 00:50:29,890
+هيها تهيب تحل هام هيك؟ مايب هذه و هذه حسب ال rule
+
+561
+00:50:29,890 --> 00:50:33,230
+of inferences مش موجودات بس بتقدر تعيد ترتيب
+
+562
+00:50:33,230 --> 00:50:37,290
+العناصر تمام بحيث انك تقول و الله انا بدي ارطبهم
+
+563
+00:50:37,290 --> 00:50:43,310
+هيك تصير هيك ب implies ال R نقطة ال R ب oricute
+
+564
+00:50:43,310 --> 00:50:48,330
+ايش افرجت معاك؟ولا إشي بس قعدت الترتيب الآن حليت
+
+565
+00:50:48,330 --> 00:50:55,270
+اللي فوق هذه و طلعت معايا نط ال B صارت عندي نط ال
+
+566
+00:50:55,270 --> 00:51:01,990
+B PRQ معناه تقريبا هتعطيني EQ وبالتالي وصلت لمين
+
+567
+00:51:01,990 --> 00:51:06,750
+لل conclusion اللي موجودة عندي وبالتالي هدول عبارة
+
+568
+00:51:06,750 --> 00:51:10,430
+عن valid argument للمسألة اللي موجودة وبالتالي
+
+569
+00:51:10,430 --> 00:51:14,710
+Gary is a good actor نعم
+
+570
+00:51:15,960 --> 00:51:25,680
+من ضمن
+
+571
+00:51:25,680 --> 00:51:32,800
+ال role of inferences ال
+
+572
+00:51:32,800 --> 00:51:35,660
+role of inferences ممكن أسقطها كمان على مين يا
+
+573
+00:51:35,660 --> 00:51:39,040
+شباب؟ على ال quantifiers و ال predicate function
+
+574
+00:51:39,040 --> 00:51:48,580
+يا رطيف طيب تعالى نشوف for all x بxfor all x بيكس
+
+575
+00:51:48,580 --> 00:51:51,980
+يعني هيك بقول لأي x في ال domain ال بيكس is true
+
+576
+00:51:51,980 --> 00:51:58,960
+معناته اذا بيكس is true ايش من وين ال c هي عبارة
+
+577
+00:51:58,960 --> 00:52:02,400
+عن عنصر في ال domain عنصر في ال domain في ال
+
+578
+00:52:02,400 --> 00:52:06,640
+domain اللي أخدنا منه x يعني هي حالة خاصة من ال x
+
+579
+00:52:06,640 --> 00:52:11,760
+المعرفة اللي فاج لو كان في اندي بيكس for any
+
+580
+00:52:11,760 --> 00:52:16,030
+arbitrary cلو هذا الكلام بتحقق الـ predicate
+
+581
+00:52:16,030 --> 00:52:20,070
+function بتتحقق على أي arbitrary element c في
+
+582
+00:52:20,070 --> 00:52:25,030
+الدمين معناه تجيه هذه تكافئ for all x,b,x نفس
+
+583
+00:52:25,030 --> 00:52:31,090
+المعنى عكس التاني بالضبط there exist b,x معناه بيه
+
+584
+00:52:31,090 --> 00:52:38,720
+c is true for some element c على الأقل واحدBC for
+
+585
+00:52:38,720 --> 00:52:42,300
+some element C معناه تقرأ بقدر أستبدلها الفكرة وين
+
+586
+00:52:42,300 --> 00:52:45,200
+الشباب أثناء الإثبات لو انت وصليت لهذه تقدر
+
+587
+00:52:45,200 --> 00:52:48,020
+تستبدلها بهذه وهذه تقدر تحط مكانها بهذه هذه
+
+588
+00:52:48,020 --> 00:52:51,900
+المفهوم انك انت تقدر تستخدم بعض ال facts بعض
+
+589
+00:52:51,900 --> 00:52:58,180
+الحقائق من أجل تسهيل عملية الإثبات الرياضي every
+
+590
+00:52:58,180 --> 00:53:02,380
+IUG student is genius طلاب الجامعة الإسلامية
+
+591
+00:53:02,380 --> 00:53:12,500
+عذاكرة أيش رأيك يا رامي؟اقرأي 100% أحمد طالب في
+
+592
+00:53:12,500 --> 00:53:19,180
+الجامعة الإسلامية تمام مع ال conclusion therefore
+
+593
+00:53:19,180 --> 00:53:22,900
+أحمد is a genius اذا كل غلاب الجامعة الإسلامية
+
+594
+00:53:22,900 --> 00:53:27,560
+عباقرة و أحمد مسجل في الجامعة الإسلامية كطالب فهو
+
+595
+00:53:27,560 --> 00:53:32,380
+عبقري و ليش رأيك؟ خلصنا فعليا هذا الكلام هي step
+
+596
+00:53:32,380 --> 00:53:39,760
+الأولىfor all x ux ايش ux اللي هو طالب في الجامعة
+
+597
+00:53:39,760 --> 00:53:45,120
+university student implies genius student تمام
+
+598
+00:53:45,120 --> 00:53:51,240
+step 2 for all أحمد أحمد طالب في الجامعة يقعد إلى
+
+599
+00:53:51,240 --> 00:53:54,780
+تلاتة
+
+600
+00:53:54,780 --> 00:53:58,940
+أحمد طالب و أحمد genius وخلصنا من العلاصر الموجودة
+
+601
+00:53:58,940 --> 00:54:06,250
+for all x bc ليه أحمدB of Ahmed if C تنتمي لل
+
+602
+00:54:06,250 --> 00:54:09,110
+domain اللي موجودة اه هو هذا القانون وهذا هو
+
+603
+00:54:09,110 --> 00:54:15,370
+القانون اللي موجود عندنا هنا و سلامتكم هي خلص ال
+
+604
+00:54:15,370 --> 00:54:18,610
+section هذا و بدنا نقول الشبتر الأول الله يعطيه
+
+605
+00:54:18,610 --> 00:54:21,870
+العافية و ضال فيه عنا section مهم جدا طرق الإثبات
+
+606
+00:54:21,870 --> 00:54:25,150
+الرياضة بس هأخره شوية ايه كده عبل ما تتخمروا شوية
+
+607
+00:54:25,150 --> 00:54:28,430
+في الرياضيات معنا اه هناخره ان شاء الله بس لاحقا
+
+608
+00:54:28,430 --> 00:54:31,530
+في اي سؤال الشباب اللي اقرحنا اليوم باشي الله
+
+609
+00:54:31,530 --> 00:54:32,250
+يعطيكوا العافية شباب
+
diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/0uvPY3Nanck.srt b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/0uvPY3Nanck.srt
new file mode 100644
index 0000000000000000000000000000000000000000..006271eeab8c3813fcfa691fd4c11f2e0a15974b
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/0uvPY3Nanck.srt
@@ -0,0 +1,2101 @@
+1
+00:00:20,970 --> 00:00:22,990
+بسم الله والحمد لله والصلاة والسلام على رسول الله
+
+2
+00:00:22,990 --> 00:00:27,370
+اليوم إن شاء الله شباب، هنبدأ بال chapter الثاني من
+
+3
+00:00:27,370 --> 00:00:31,770
+المادة الرياضيات المفصلة، والchapter هذا سيركز على
+
+4
+00:00:31,770 --> 00:00:35,490
+الشغلات أو الـ structures الأساسية أو البنيات
+
+5
+00:00:35,490 --> 00:00:39,210
+الأساسية للرياضيات. سنتكلم على مجموعات
+
+6
+00:00:39,210 --> 00:00:42,730
+سنتكلم على دوال، سنتكلم على series، سنتكلم على
+
+7
+00:00:42,730 --> 00:00:47,750
+relations. سنمشي شوية شوية في الـ chapter هذا، وممكن في
+
+8
+00:00:47,750 --> 00:00:50,170
+لحظة من اللحظات، أجيب section أو اثنين من chapter
+
+9
+00:00:50,170 --> 00:00:53,930
+الثامن، موجودة، كلها related أو على علاقة أو وثيقة
+
+10
+00:00:53,930 --> 00:01:00,290
+الصلة بالـ chapter اللي موجود عندنا. Anyway، على كل حال، نحن
+
+11
+00:01:00,290 --> 00:01:04,370
+سنبدأ اليوم في المجموعات. طبعًا، العناصر التابعة لـ
+
+12
+00:01:04,370 --> 00:01:08,750
+الـ chapter هي: المجموعات، الدوال، الـ sequences،
+
+13
+00:01:08,750 --> 00:01:13,470
+المتتاليات، والمجموعات، الـ cardinalities للمجموعات
+
+14
+00:01:13,470 --> 00:01:17,610
+اللي فوق، والمصفوفات، وممكن زي ما قلت، أروح أجيب الـ
+
+15
+00:01:17,610 --> 00:01:22,270
+relations من chapter الثامن، عشان نخلص الـ related topics
+
+16
+00:01:22,270 --> 00:01:26,390
+اليوم سنتكلم بالدرجة الأولى عن المجموعات، عن الـ
+
+17
+00:01:26,390 --> 00:01:31,250
+section الأول، section المجموعات. طبعًا، لما أنا بأتكلم
+
+18
+00:01:31,250 --> 00:01:35,050
+على مجموعة، بأتكلم على basic
+
+19
+00:01:38,050 --> 00:01:42,570
+بالنسبة للمجموعات مباشرة، يخطر على بالك الـ
+
+20
+00:01:42,570 --> 00:01:47,170
+curly braces، تمام؟ اللي بنرمز بها المجموعات.
+
+21
+00:01:47,170 --> 00:01:52,090
+نحن شفنا قوسين مع الـ intervals، القوسين المربعين، صح؟
+
+22
+00:01:52,090 --> 00:01:55,770
+لـ interval، وهي القوسين،  الـ curly braces
+
+23
+00:01:55,770 --> 00:02:00,880
+من أجل نتكلم على مجموعة. وطبعًا لما أتكلم على
+
+24
+00:02:00,880 --> 00:02:04,080
+المجموعات، هي الـ block الأساسي أو الـ structure الأساسي في
+
+25
+00:02:04,080 --> 00:02:09,100
+الرياضيات، وكل العلوم المبنية عليها. لما بتكلم على
+
+26
+00:02:09,100 --> 00:02:13,200
+العد أو أنظمة العد، أو بدي أعد الأشياء، بحاول أجسمهم
+
+27
+00:02:13,200 --> 00:02:18,200
+لمجموعات، عشان يسهل عملية الحسبة بتجميعهم لمجموعات.
+
+28
+00:02:18,200 --> 00:02:21,580
+يعني هيك، لو أنا جيت بدي أعدكم في القاعة، بقول: هي
+
+29
+00:02:21,580 --> 00:02:25,700
+خمسة، كذا، هي خمسة، وفي عندي أنا عشر، خمسة عشر، وهي
+
+30
+00:02:25,700 --> 00:02:28,180
+عندي أربعة، هي تسعة عشر، فبكون أنا فعليًا، جَسَّمْتُ
+
+31
+00:02:28,180 --> 00:02:32,250
+المجموعات. كانت إيش؟ سهلت عليّ أن أصل للنتيجة اللي
+
+32
+00:02:32,250 --> 00:02:37,350
+أنا بدي إياها، اللي هي موضوع العد. طبعًا، لغات البرمجة لما
+
+33
+00:02:37,350 --> 00:02:40,310
+أنا بأتكلم عليها بشكل عام، برضه بأتكلم على مجموعات.
+
+34
+00:02:40,310 --> 00:02:43,490
+بأتكلم على مجموعات المتغيرات اللي أنت بتعرفها في
+
+35
+00:02:43,490 --> 00:02:46,450
+لغة البرمجة، على الـ scope التابعة لها، وإن هذا الـ
+
+36
+00:02:46,450 --> 00:02:49,730
+variable موجود، فأنت بتتكلم، قاعدين على مجموعات. الـ
+
+37
+00:02:49,730 --> 00:02:52,730
+operations، في عندي عمليات أو مجموعة العمليات
+
+38
+00:02:52,730 --> 00:02:58,730
+الحسابية: الجمع والضرب والطرح والقسمة، صحيح، والـ
+
+39
+00:02:58,730 --> 00:03:02,770
+modulus. وفي عندي مجموعة العمليات المنطقية، اللي هي
+
+40
+00:03:02,770 --> 00:03:07,150
+الـ and، والـ or، والـ not، وهكذا. حتى في داخل الـ loop
+
+41
+00:03:07,150 --> 00:03:10,990
+أو عفواً، في داخل البرنامج الواحد، بتصير كمان عندي
+
+42
+00:03:10,990 --> 00:03:14,270
+مجموعة من الـ blocks: هذا للـ while، هذا للـ condition،
+
+43
+00:03:14,270 --> 00:03:18,970
+للـ if statement. فبقى برضه بأتكلم على مجموعات. في
+
+44
+00:03:18,970 --> 00:03:23,870
+الرياضيات، في علم اسمه نظرية المجموعات، وهذا علم
+
+45
+00:03:23,870 --> 00:03:27,510
+داخل في كثير من التطبيقات اللي موجودة اليوم.
+
+46
+00:03:32,400 --> 00:03:36,340
+نأتي للتعريف اللي بيهمنا نحن بشكل دقيق، شو يعني
+
+47
+00:03:36,340 --> 00:03:43,240
+مجموعة؟ جاي أتكلم على الـ set S، المجموعة هي unordered
+
+48
+00:03:43,240 --> 00:03:52,360
+وهي أول خطوة، collection of objects، مجموعة من العناصر
+
+49
+00:03:53,810 --> 00:03:58,010
+تمام؟ مجموعة من العناصر. Unordered، طبعًا الـ
+
+50
+00:03:58,010 --> 00:04:00,830
+collection بتتكلم عن مجموعة، يعني عنصر أو أكثر ..
+
+51
+00:04:00,830 --> 00:04:04,150
+عنصر أو أكثر .. طب السؤال بيطرح نفسه: ممكن يكون
+
+52
+00:04:04,150 --> 00:04:07,550
+عندي عنصر واحد في المجموعة؟  نعم، ممكن .. وممكن
+
+53
+00:04:07,550 --> 00:04:10,170
+المجموعة تكون فارغة، لأن لحد ما نلاقي، ما نلاقيناش
+
+54
+00:04:10,170 --> 00:04:14,810
+المنبر المناسب، نضعها فيه، مثلاً .. مثلاً لو أنا
+
+55
+00:04:14,810 --> 00:04:17,930
+أجي أقول في لحظة من اللحظات، أنه أنا، شباب، بدي أعمل
+
+56
+00:04:17,930 --> 00:04:24,530
+مجموعة بحيث أنَّها تشتغل زي معيدين في المادة للشباب
+
+57
+00:04:24,530 --> 00:04:28,610
+الثانيين، يحلوا لهم أسئلة، ويشرحوا لهم بعض الأشياء اللي
+
+58
+00:04:28,610 --> 00:04:32,750
+ما قدروش يفهموها منيح .. من في المجموعة الآن يا
+
+59
+00:04:32,750 --> 00:04:38,610
+دكتور؟  مافيش أحد .. ليش؟ لأن مبدئيًا، ما شفتش من
+
+60
+00:04:38,610 --> 00:04:41,690
+الشخص أو من الشخص المناسب اللي يكون موجود في
+
+61
+00:04:41,690 --> 00:04:46,390
+المجموعة. لكن هذه مجموعة قررت أن أعملها، وبالتالي
+
+62
+00:04:46,390 --> 00:04:50,290
+لما بأتكلم على collection، يعني بأتكلم على واحد أو
+
+63
+00:04:50,290 --> 00:04:52,950
+أكثر غالبًا، لكن برضه في استثناء، أن ممكن المجموعة
+
+64
+00:04:52,950 --> 00:04:57,030
+تكون فارغة أو بشكل مؤقت .. Unordered
+
+65
+00:04:59,210 --> 00:05:02,830
+لسه في كمان شغلة في collection، في مفهوم الـ
+
+66
+00:05:02,830 --> 00:05:06,330
+collection. مفهوم الـ collection، يعني التكرار لا يعني
+
+67
+00:05:06,330 --> 00:05:12,150
+شيئًا. ما أجي أقول في المجموعة: أنا عندي أحمد، و
+
+68
+00:05:12,150 --> 00:05:19,370
+أحمد، وكمان أحمد، إذا أنا كنت بأقصد نفس الشخص. أو بين
+
+69
+00:05:19,370 --> 00:05:24,210
+جسيم، ما أجي أقول: أنا سويَّةً، طبعًا أنا عندي
+
+70
+00:05:24,210 --> 00:05:29,960
+خمس سيارات سبارة، وثلاثة وثمانين، وكمان سبارة، ثلاثة
+
+71
+00:05:29,960 --> 00:05:34,440
+وثمانين، وسبارة ثلاثة وثمانين. فأنت بتعدد في نفس الـ
+
+72
+00:05:34,440 --> 00:05:38,000
+object، فأنت دلوقت ما بتتكلمش على collection، أنتَ
+
+73
+00:05:38,000 --> 00:05:42,040
+بتتكلم على element. مافي كلمة collection زي ما كنتَ
+
+74
+00:05:42,040 --> 00:05:46,460
+بتتكلم على واحد أو أكثر. برضه التكرار فيها أو
+
+75
+00:05:46,460 --> 00:05:50,260
+تكرار الشيء، لا يعني شيء، ما لوش قيمة. التكرار في
+
+76
+00:05:50,260 --> 00:05:57,160
+المجموعة هذا، لا يعني شيء. Unordered. كمان الترتيب في
+
+77
+00:05:57,160 --> 00:06:00,820
+المجموعة لا يعني شيء. لو أنا كتبت في داخل
+
+78
+00:06:00,820 --> 00:06:11,480
+الأقواس: A، وM، وH، هذه
+
+79
+00:06:11,480 --> 00:06:19,160
+هي نفس المجموعة: M، وH، وA، الآن.
+
+80
+00:06:19,160 --> 00:06:22,920
+هي نفس المجموعة، نفس المجموعة. من غير صرفهم؟ نفس
+
+81
+00:06:22,920 --> 00:06:26,440
+العناصر، ونفس عددهم، ما تغير فيهم ولا حاجة. كمان مرة،
+
+82
+00:06:26,440 --> 00:06:32,240
+لو أنا جيت كررتها، وقُلتُ الـ A؟ مالوش معنى.
+
+83
+00:06:32,240 --> 00:06:36,100
+التكرار، التكرار مالوش معنى. لأن كلمة connection، الـ
+
+84
+00:06:36,100 --> 00:06:38,780
+connection بتقولي: ما تكررش الـ element اللي موجود.
+
+85
+00:06:38,780 --> 00:06:44,360
+فحتى لو أنت شفته مكتوب، لازم تعمل حسابك أننا بنتكلم
+
+86
+00:06:44,360 --> 00:06:47,040
+عن نفس الـ element. ولما يسألك عدد عناصر المجموعة
+
+87
+00:06:47,040 --> 00:06:50,540
+هي كام شغلة؟  الاجابة بتقولي: ثلاثة، ما تقوليش أربعة، لأن
+
+88
+00:06:50,540 --> 00:06:57,510
+العنصر هذا هو متكرر، هو نفسه، تمام؟ معناته unordered
+
+89
+00:06:57,510 --> 00:07:03,130
+collection. معناته أنا بأتكلم على مجموعة فيها عدد من
+
+90
+00:07:03,130 --> 00:07:08,890
+العناصر، واحد فأكثر، ترتيبهم لا يعني شيء، والتكرار
+
+91
+00:07:08,890 --> 00:07:14,910
+العناصر الموجودة لا يعني شيء. تمام؟ مثلًا، أقول: طلاب
+
+92
+00:07:14,910 --> 00:07:18,800
+المساق، أو الطلاب الموجودين عندي في المحاضرة، سواء
+
+93
+00:07:18,800 --> 00:07:23,900
+قرأت أو نديت على محمد الأدهم، تمام؟ ولا بدأت بعمر
+
+94
+00:07:23,900 --> 00:07:28,420
+مطر؟ مش هتفرق كثير، كلهم موجودين، بس أثناء حضور
+
+95
+00:07:28,420 --> 00:07:31,600
+الغياب، على فرض، لو أنا بدي آخذ حضور وغياب، روح
+
+96
+00:07:31,600 --> 00:07:37,880
+تكرر اسم عمر مطر مرتين. مباشرةً، إذا كان موجود، سأقول
+
+97
+00:07:37,880 --> 00:07:41,560
+للدكتور: إني أزعجته قبل ذلك ولا لا. وإذا لم يكن موجود،
+
+98
+00:07:41,560 --> 00:07:44,040
+الشباب اللي موجودين، سأقول للدكتور: أنتَ ناديته،
+
+99
+00:07:44,040 --> 00:07:48,040
+فبالتالي، هل هو نفس الشخص ولا مختلف؟ فلازم ننتبه أن
+
+100
+00:07:48,040 --> 00:07:51,680
+التكرار في المجموعة لا يعني شيء. تمام؟ الآن، هنوصل
+
+101
+00:07:51,680 --> 00:07:55,500
+للمجموعة. بنقول عنهم الـ objects، اللي هي الأشياء
+
+102
+00:07:55,500 --> 00:07:59,440
+اللي أنا بأذكرها في المجموعة: السيارات، القلاد،
+
+103
+00:07:59,440 --> 00:08:05,060
+الكتب، الأقلام، الكراسي .. المجموعة حسب إيش تركيبتها. لكن
+
+104
+00:08:05,060 --> 00:08:08,140
+عندما أتكلم عن المجموعات، الـ objects هي صارت
+
+105
+00:08:08,140 --> 00:08:11,300
+بالنسبة لي في نظام المجموعة، عبارة عن elements.
+
+106
+00:08:11,300 --> 00:08:14,860
+بأسألك: إيش عناصر المجموعة؟  بأسألك: إيش الـ objects
+
+107
+00:08:14,860 --> 00:08:18,840
+اللي في المجموعة؟  عناصر المجموعة، هتقولي: A، وM، و
+
+108
+00:08:18,840 --> 00:08:24,360
+H، حسب المثال اللي كتبناه قبل شوية. من أعضاء
+
+109
+00:08:24,360 --> 00:08:27,440
+المجموعة، اللي هو المصطلح اللي بعده: member of
+
+110
+00:08:27,440 --> 00:08:32,380
+members. نفس الكلام، لكن اللي بدي أقوله أنا، هنغيب
+
+111
+00:08:32,380 --> 00:08:36,780
+مصطلح الـ objects. سأخبرك من أعضاء المجموعة، أو من
+
+112
+00:08:36,780 --> 00:08:39,100
+العناصر الموجودة في المجموعة. من المصطلحات أو
+
+113
+00:08:39,100 --> 00:08:43,720
+المسميات الموجودة عندنا. وعندما أتكلم عن علاقة
+
+114
+00:08:43,720 --> 00:08:47,180
+العنصر بالمجموعة، العنصر ينتمي إلى المجموعة، هي
+
+115
+00:08:47,180 --> 00:08:52,960
+إشارة: ينتمي، ينتمي.
+
+116
+00:08:52,960 --> 00:08:58,260
+وغالبًا، العنصر نرمز له باسم حرف، واسم المجموعة
+
+117
+00:08:59,340 --> 00:09:01,880
+بنعتمد الـ capital letter. هيك الـ standard في
+
+118
+00:09:01,880 --> 00:09:05,760
+الرياضيات. اسم المجموعة: capital letter، والعناصر
+
+119
+00:09:05,760 --> 00:09:09,560
+اللي فيها: small letter، ما لم تكن أنت فعليًا قاصد أن
+
+120
+00:09:09,560 --> 00:09:15,280
+العناصر تكون capital letter. وهيك بيصير، أنا أقول: الـ
+
+121
+00:09:15,280 --> 00:09:22,100
+A،  بأجراها: A is a member of A، بالمجموعة A، أو A
+
+122
+00:09:22,100 --> 00:09:26,620
+المجموعة contain الـ small a، اللي هي العنصر الـ
+
+123
+00:09:26,620 --> 00:09:31,800
+element اللي موجود عندها. وإذا كان العنصر لا ينتمي،
+
+124
+00:09:31,800 --> 00:09:39,560
+فسأقول: A لا تنتمي لـ A. على نفس القياس بتاعت
+
+125
+00:09:39,560 --> 00:09:48,600
+اليساوي، فسنقول: لا يساوي. تمام؟ الموضوع
+
+126
+00:09:48,600 --> 00:09:53,640
+بشكل عام، اليوم سيكون سهل مقارنة بالذي رأيناه في
+
+127
+00:09:53,640 --> 00:09:56,460
+الفيديو السابق، خصوصًا في الفيديو السابق، قليلًا من
+
+128
+00:09:56,460 --> 00:09:59,890
+الأمور، عندما تلقينا في الـ Logic، لأن الـ logic تبعنا
+
+129
+00:09:59,890 --> 00:10:06,130
+غالبًا، مش سليم. تمام؟ ما بنحسبش المشاكل. تمام؟ معناته
+
+130
+00:10:06,130 --> 00:10:11,850
+نقول: نحن A تنتمي إلى A، A is an element أو is a
+
+131
+00:10:11,850 --> 00:10:17,130
+member. A is not an element. الآن، لو شفتَ مجموعة
+
+132
+00:10:17,130 --> 00:10:22,790
+مكتوبة بالشكل التالي: A تساوي A1، وA2، وA3، لحد Am،
+
+133
+00:10:22,790 --> 00:10:29,620
+هل العناصر هذه، يعني أنهم مرتبة؟ لأ، هذه مجرد رموز
+
+134
+00:10:29,620 --> 00:10:34,060
+عشان أشيل العنصر الأول، العنصر الثاني، العنصر الثالث،
+
+135
+00:10:34,060 --> 00:10:39,400
+الرابع، الخامس، الآن. لكن برضه، كمان مرة، مش بالضرورة
+
+136
+00:10:39,400 --> 00:10:42,400
+الـ value بتاعة العناصر هذه، تكون فعليًا جاية عايشة بـ
+
+137
+00:10:42,400 --> 00:10:45,360
+sequence، أو جاية مرتبة، عندي. لأن اتفقنا أن
+
+138
+00:10:45,360 --> 00:10:50,000
+الترتيب لا يعني شيء. هالشيء مجرد، عشان أقول: العنصر
+
+139
+00:10:50,000 --> 00:10:54,020
+منزلته: العنصر الأول، الثاني، الرابع، الخامس، الآن، إلى
+
+140
+00:10:54,020 --> 00:11:01,290
+آخرهم، العناصر. في وصف المجموعات .. طبعًا، نحن اتفقنا
+
+141
+00:11:01,290 --> 00:11:04,670
+الـ calibrations الأساسية، في كتابة وصف المجموعات.
+
+142
+00:11:04,670 --> 00:11:08,750
+عندي طريقتين: في عندي الـ Roster method، الـ Roster
+
+143
+00:11:08,750 --> 00:11:11,790
+method بيقول: أنا بكتب العناصر التابعة للمجموعة، في
+
+144
+00:11:11,790 --> 00:11:16,710
+داخل الأقواس، بغض النظر عن عددهم. طيب، ممتاز. بأجي بقول:
+
+145
+00:11:16,710 --> 00:11:24,170
+ABCD، مجموعة فيها أربع حروف. بأجي بقول: من صفر لتسعة،
+
+146
+00:11:24,170 --> 00:11:30,410
+اللي هي الـ digits، تمام؟ عشرة. طيب، لو كبرت، كثرت من هيك،
+
+147
+00:11:30,410 --> 00:11:35,450
+بتصير الأمور شوية مزعجة. في الـ roster بيقول: إذا كان
+
+148
+00:11:35,450 --> 00:11:38,910
+الـ sequence هذه، أو الأرقام هذه، familiar معها،
+
+149
+00:11:38,910 --> 00:11:42,870
+بنستخدم الـ ellipses، أو النقاط، عشان أقوله: على نفس
+
+150
+00:11:42,870 --> 00:11:49,410
+السياق هذا، العد بيجي. بقول:  ليه ABC، وحط لي الـ ellipses،
+
+151
+00:11:49,410 --> 00:11:54,350
+ثلاث نقاط هذه، والـ Z. إيش بتفهم منها أنت مباشرة؟ أنه
+
+152
+00:11:54,350 --> 00:11:58,270
+قاعد بتكلم على مجموعة الحروف الأبجدية الإنجليزية.
+
+153
+00:11:58,270 --> 00:12:06,550
+لأ، باجي أقول: أنه في مجموعة: واحد، اثنين، وبحط مئة،
+
+154
+00:12:06,550 --> 00:12:12,490
+مباشرة، مباشرة، هَيَخْطُر في بالك، أو هتفهم: واحد، اثنين،
+
+155
+00:12:12,490 --> 00:12:16,510
+ثلاثة، أربعة، لحد وين؟ المئة. لكن شوف، المجموعة  بتكون
+
+156
+00:12:16,510 --> 00:12:25,060
+شوية، هتختلف الأمور: واحد، ثلاثة .. خمسة .. وحاطط الـ
+
+157
+00:12:25,060 --> 00:12:32,280
+ellipses، لتسعة وتسعين .. الأعداد الفردية الأقل من
+
+158
+00:12:32,280 --> 00:12:35,660
+مائة .. بقى بالسبعة والتسعين منهم .. اه، منهم .. بقى
+
+159
+00:12:35,660 --> 00:12:40,280
+مش مكتوبة ..  حالة  مثل هذه، مين؟ الثلاث نقاط، أو الـ
+
+160
+00:12:40,280 --> 00:12:44,080
+ellipses اللي موجودة قدامي هن .. تمام؟ اللي هي
+
+161
+00:12:44,080 --> 00:12:45,800
+ممكن زي ما يقول زميلكم: جاع قلخ ..
+
+162
+00:12:50,270 --> 00:12:56,550
+المجموعة الـ vowels باللغة الإنجليزية، حروف العلة: A،
+
+163
+00:12:56,550 --> 00:13:07,570
+E، I، O، U.  لسه ما هو حرف العلة؟ لأنها
+
+164
+00:13:07,570 --> 00:13:14,110
+علة في تمييزها عند الكتابة، طبعًا؟ لأنه يجب أن تكون
+
+165
+00:13:14,110 --> 00:13:17,730
+حافظ الـ spelling صح، عشان تقدر أن الكلمة هذه تكتب
+
+166
+00:13:17,730 --> 00:13:22,030
+بالـ O ولا بالـ U؟ والترتيب بتاعتهم؟ طبعًا؟ غير هكذا
+
+167
+00:13:22,030 --> 00:13:31,110
+العلة. لما بتأوي .. أنتَ تخيّل نفسك تقرصهم واحد ورا
+
+168
+00:13:31,110 --> 00:13:34,690
+الثاني، على
+
+223
+00:18:13,040 --> 00:18:19,420
+بدها تساوي B و C؟ هذه لا تساوي لأن هذه مجموعة و
+
+224
+00:18:19,420 --> 00:18:26,510
+هذه عنصر، و الـ B هذه لا تساوي C و X و D لأنها أيضا
+
+225
+00:18:26,510 --> 00:18:32,170
+هذه مجموعة، وبالتالي الـ B لا تنتمي إلى الـ A. طيب
+
+226
+00:18:32,170 --> 00:18:34,530
+يا دكتور، شوية شوية علينا، احنا بنقول إننا لدينا
+
+227
+00:18:34,530 --> 00:18:40,450
+مجموعة كبيرة فيها مجموعتين، فيها مجموعتين، لأن مش
+
+228
+00:18:40,450 --> 00:18:44,750
+المنطق بيقول إن عناصر المجموعتين هادول هما بتنتمي
+
+229
+00:18:44,750 --> 00:18:47,570
+للمجموعة الأكبر. يعني يا دكتور، أنت جاهز؟ بيقول أنا
+
+230
+00:18:47,570 --> 00:18:52,400
+احنا كلاب رياضيات منفصلة، تمام؟ والرياضيات المنفصلة
+
+231
+00:18:52,400 --> 00:18:56,000
+جزء من مساق الـ IT، مساقات الـ IT، ما تحب تقولها
+
+232
+00:18:56,000 --> 00:18:58,420
+بـ IT، ما تقدرش تقولها لا، أنت تقولها بـ رياضيات
+
+233
+00:18:58,420 --> 00:19:05,050
+منفصلة وبس. العلاقة شوية للشباب مختلفة، مختلفة تبع للـ
+
+234
+00:19:05,050 --> 00:19:09,090
+rules اللي احنا عايشين بيبقى مطابقها في غير أو في
+
+235
+00:19:09,090 --> 00:19:11,190
+العلاقة اللي احنا بنوصفها، سواء كانت في الـ members
+
+236
+00:19:11,190 --> 00:19:15,210
+أو في علاقتنا بالمساقات والكلية والجامعة، علاقة
+
+237
+00:19:15,210 --> 00:19:21,150
+subset، مجموعات جزئية، مجموعات جزئية، مش علاقة عضوية
+
+238
+00:19:22,770 --> 00:19:28,750
+أشبه بالتوارث، وعندما أتكلم في مجموعة جزئية، يعني
+
+239
+00:19:28,750 --> 00:19:38,090
+أن كل مجموعة في الجامعة تم تقسيمها لمجموعات مختلفة
+
+240
+00:19:38,090 --> 00:19:42,290
+لكليات، وعناصر الكليات تم تقسيمهم لمجموعات مختلفة
+
+241
+00:19:42,290 --> 00:19:47,720
+لأقسام، وتخصصات، والتخصصات تم تقسيم الطلاب فيهم
+
+242
+00:19:47,720 --> 00:19:51,460
+لمستويات، وكل مستوى له مجموعة من المساقات. لاحظ أن
+
+243
+00:19:51,460 --> 00:19:58,600
+العلاقة subset جزئية من المجموعة، بس هنا لأ، هنا لأ.
+
+244
+00:19:58,600 --> 00:20:02,300
+هنا عضوية، لأن المجموعة هذه بتمثل عنصر واحد.
+
+245
+00:20:02,300 --> 00:20:11,160
+المجموعة هذه بتمثل عنصر واحد. طيب، يعني بينفعش..
+
+246
+00:20:11,160 --> 00:20:24,020
+بينفعش أجي أقول capital X بدها تساوي الـ N و الـ Z و
+
+247
+00:20:24,020 --> 00:20:31,300
+الـ Q و الـ R الآن.
+
+248
+00:20:31,300 --> 00:20:38,700
+لو أنا سألتك جذر الاثنين ينتمي للـ X؟ جذر الاثنين
+
+249
+00:20:38,700 --> 00:20:42,440
+عنصر في المجموعة X؟ لأ.
+
+250
+00:20:44,680 --> 00:20:48,460
+من العناصر، أي واحد من الخمسة هدول، أو من الأربعة
+
+251
+00:20:48,460 --> 00:20:55,260
+هدول. عفوا، كمان مرة، عشان اتكلم، ينتمي، ينتمي لازم
+
+252
+00:20:55,260 --> 00:20:58,960
+أشوف العنصر بنفس صيغته موجود، بنفس العنصر، يعني هيك.
+
+253
+00:20:58,960 --> 00:21:05,470
+لو أنا جيت وقلت لك الـ Y أو الـ I تنتمي للـ X، هذه اللي
+
+254
+00:21:05,470 --> 00:21:09,590
+عرفناها هان، إيش المطلوب منك تساوي؟ تروح تاخد الـ I
+
+255
+00:21:09,590 --> 00:21:12,430
+هذه كما هي، هيك زي ما هي مكتوبة، تجيب الإشارة اللي
+
+256
+00:21:12,430 --> 00:21:16,810
+ينتمي، و تروح تدور عليها وين في عناصر المجموعة هاي.
+
+257
+00:21:16,810 --> 00:21:22,250
+العنصر الأول، هي تساوي الـ I هذه؟ لأ. إيش.. إيش
+
+258
+00:21:22,250 --> 00:21:26,270
+الفاصل ما بين العناصر؟ الكوما. هي العنصر الثاني لا
+
+259
+00:21:26,270 --> 00:21:36,140
+يساوي I، الثالث، الرابع، ما فيه I. لا تنتمي لمين؟ للـ X. هيك
+
+260
+00:21:36,140 --> 00:21:41,360
+بدي يكون قرارك، وهذا الـ rule أو هذا القانون الأول
+
+261
+00:21:41,360 --> 00:21:45,460
+في التعامل مع المجموعة. إذا الـ answer مش مكتوب بشكل
+
+262
+00:21:45,460 --> 00:21:49,700
+مباشر، بقول لك عليه، تعال أورجيك إحنا إيش لما كنا
+
+263
+00:21:49,700 --> 00:21:53,640
+نقصد من وين جيبنا كل integer، أو عفوا كل عدد طبيعي،
+
+264
+00:21:53,640 --> 00:21:59,800
+عدد صحيح، قلنا إنه الآن، أو خلينا نرجع للـ slide
+
+265
+00:21:59,800 --> 00:22:00,220
+الجاي.
+
+266
+00:22:08,520 --> 00:22:11,280
+لما أتينا و كتبنا الـ natural number، كتبنا واحد،
+
+267
+00:22:11,280 --> 00:22:16,200
+اتنين، تلاتة، إلى ما لا نهاية، مظبوط؟ مظبوط؟ ولما
+
+268
+00:22:16,200 --> 00:22:22,480
+أتيت و كتبت الـ Z، إيش كتبناه؟ ما كتبنا الـ cash، كتبنا
+
+269
+00:22:22,480 --> 00:22:28,040
+الـ cash، الـ N، فاصلة، صفر، فاصلة، سالب واحد، سالب اتنين،
+
+270
+00:22:28,040 --> 00:22:31,980
+إلى ما لا نهاية. إيش كتبناه لك؟ كتبناه العناصر، كل
+
+271
+00:22:31,980 --> 00:22:37,680
+هيّاها. الآن، لو أتيت و سألتك، التلاتة
+
+272
+00:22:39,180 --> 00:22:46,740
+تنتمي للـ أعداد الصحيحة؟ true. التلاتة
+
+273
+00:22:46,740 --> 00:22:52,820
+تنتمي للـ Z؟ true، لأن هي مكتوبة، موجودة عندي. لاحظ
+
+274
+00:22:52,820 --> 00:22:55,020
+العلاقة مختلفة تماما عن الأمثلة اللي احنا عايشين
+
+275
+00:22:55,020 --> 00:22:59,900
+حكينا عليها قبل شوية، تمام؟ معناته احنا الآن متفقين،
+
+276
+00:22:59,900 --> 00:23:04,640
+متفقين، إنه الآن لما بتكلم في الـ ينتمي، أو العنصر هذا
+
+277
+00:23:04,640 --> 00:23:09,980
+في المجموعة، لازم أشوف العنصر مثل ما هو في داخل
+
+278
+00:23:09,980 --> 00:23:14,940
+المجموعة. نرجع مرة عشان نرجع من وين دخلنا في
+
+279
+00:23:14,940 --> 00:23:21,900
+التفاصيل الكتيرة. A عبارة عن مجموعة فيها عنصرين، كل
+
+280
+00:23:21,900 --> 00:23:27,040
+عنصر بمثابة مجموعة. X لا تنتمي للـ A.
+
+281
+00:23:34,330 --> 00:23:39,090
+الـ A بدها تساوي المجموعة اللي بتحتوي على عنصر
+
+282
+00:23:39,090 --> 00:23:47,390
+واحد، وهو بمثابة مجموعة {X, Y}. هيّاها ولا لا؟ الآن الـ
+
+283
+00:23:47,390 --> 00:23:51,790
+X و Y هذه اللي داخل الـ curly braces هي عبارة عن
+
+284
+00:23:51,790 --> 00:23:58,210
+عناصر، مظبوط؟ وبالتالي أنا بقدر أقول إن المجموعة هذه
+
+285
+00:23:58,210 --> 00:24:02,510
+تنتمي للـ A، ليش؟ لأن هي زي ما هي هيك، أخذتها منها،
+
+286
+00:24:03,450 --> 00:24:07,130
+ودورت عليها في داخل المجموعة، لقيتها كما هي. فبتكلم عن
+
+287
+00:24:07,130 --> 00:24:14,730
+عنصر. وأنت بقول إن X، المجموعة هذه لا تساوي المجموعة
+
+288
+00:24:14,730 --> 00:24:18,630
+هذه. أيوة.
+
+289
+00:24:18,630 --> 00:24:23,430
+المجموعة هذه فيها عنصرين، المجموعة هذه فيها عنصر
+
+290
+00:24:23,430 --> 00:24:28,630
+واحد، وبالتالي مجموعتين، عدد عناصرهم مختلفين، مستحيل
+
+291
+00:24:28,630 --> 00:24:31,750
+يكونوا متساويتين. نعم.
+
+292
+00:24:45,960 --> 00:24:59,200
+عنصر، الأول، مجموعة {X, Y}. كم
+
+293
+00:24:59,200 --> 00:25:03,260
+عنصر
+
+294
+00:25:03,260 --> 00:25:09,900
+في المجموعة يا شباب؟ حرام عليكم! هذا اسمه تكرار. احنا
+
+295
+00:25:09,900 --> 00:25:13,560
+اتفقنا، إعادة أو ترتيب العناصر لا يعني شيء في
+
+296
+00:25:13,560 --> 00:25:20,460
+المجموعة. يعني هذا العنصر هو عبارة عن {X, Y}، و
+
+297
+00:25:20,460 --> 00:25:24,420
+التكرار
+
+298
+00:25:24,420 --> 00:25:28,680
+في المجموعة لا يعني شيء، مالوش فايدة، وبالتالي
+
+299
+00:25:28,680 --> 00:25:34,300
+المجموعة بتحتوي على عنصر واحد فقط. يمكن كان سؤالك
+
+300
+00:25:34,300 --> 00:25:40,040
+يكون ألطف. لو أنا جيت وقلت إن الـ B.. أو عفوا
+
+301
+00:25:40,040 --> 00:25:47,920
+..{C, B} كمجموعة، تنتمي للـ A؟ صح ولا غلط؟ صح..
+
+302
+00:25:47,920 --> 00:25:52,880
+صح.. صح.. صح.. صح.. صح.. صح.. صح.. صح.. صح
+
+303
+00:25:52,880 --> 00:25:53,860
+.. صح.. صح.. صح.. صح.. صح.. صح.. صح.. صح..
+
+304
+00:25:53,860 --> 00:25:53,920
+صح.. صح.. صح.. صح.. صح.. صح.. صح.. صح..
+
+305
+00:25:53,920 --> 00:25:54,540
+.. صح.. صح.. صح.. صح.. صح.. صح.. صح..
+
+306
+00:25:54,540 --> 00:25:58,360
+صح.. صح.. صح.. صح.. صح.. صح.. صح..
+
+307
+00:25:58,360 --> 00:25:59,000
+.. صح.. صح.. صح.. صح.. صح..
+
+308
+00:25:59,000 --> 00:26:03,220
+صح.. صح.. صح.. صح.. صح..
+
+309
+00:26:06,990 --> 00:26:12,490
+true. ليش؟ لأن المجموعة هذه هي عبارة عن عنصر في
+
+310
+00:26:12,490 --> 00:26:19,030
+المجموعة هيّاها في الـ A، وبالتالي هي member of، تمام؟
+
+311
+00:26:19,030 --> 00:26:27,650
+في أي سؤال حتى اللحظة يا شباب؟ الأمور تمام؟ الصورة
+
+312
+00:26:27,650 --> 00:26:29,710
+الثانية في تعريف المجموعات. احنا الأولى قلنا
+
+313
+00:26:29,710 --> 00:26:33,430
+الـ Roster، تكتب المجموعات، وتذكر العناصر، أو تستخدم
+
+314
+00:26:33,430 --> 00:26:37,130
+الـ ellipses اللي هي النقاط عشان تكمل وصف العناصر
+
+315
+00:26:37,130 --> 00:26:41,110
+اللي معروفة. في أسلوب ثاني اسمه الـ Builder
+
+316
+00:26:41,110 --> 00:26:48,870
+Notation، باستخدام صيغة المجموعة. صيغة المجموعة طبعا
+
+317
+00:26:48,870 --> 00:26:55,210
+الـ curly braces، الأقواس موجودة من البداية، ما فيش
+
+318
+00:26:55,210 --> 00:26:59,270
+عليها خلاف، لكن في داخل الأقواس هذه شو بدك تكتب؟
+
+319
+00:26:59,270 --> 00:27:07,800
+بتكتب expression، يعبر عن عناصر المجموعة، تمام؟ وبعد
+
+320
+00:27:07,800 --> 00:27:12,560
+الـ expression، بتحط الـ properties اللي لازم يحققها
+
+321
+00:27:12,560 --> 00:27:17,920
+كل عناصر المجموعة، وبالتالي
+
+322
+00:27:17,920 --> 00:27:21,500
+لما أنا بتكلم عن الـ builder notation، set builder
+
+323
+00:27:21,500 --> 00:27:24,980
+notation، جاي بتكلم إن هذا الـ builder أو هذا الوصف
+
+324
+00:27:24,980 --> 00:27:30,320
+بدي يوصف وبشكل دقيق العناصر اللي لازم يحققها كل
+
+325
+00:27:30,320 --> 00:27:37,110
+عناصر المجموعة، أو يحقق الصفات، بيحدد الصفات اللي كل
+
+326
+00:27:37,110 --> 00:27:42,590
+عناصر المجموعة لازم تحددها أو تحققها. تمام؟ تعال
+
+327
+00:27:42,590 --> 00:27:51,370
+نشوف مثال. بقول الـ S تساوي، واسم المجموعة {X} اللي هي
+
+328
+00:27:51,370 --> 00:27:57,370
+مثال. الـ expression اللي عندي X، إيش مالها X؟ X is a
+
+329
+00:27:57,370 --> 00:28:04,040
+positive integer less than مئة. إيش بتفهم منها؟ من
+
+330
+00:28:04,040 --> 00:28:11,940
+واحد لتسعة وتسعين. ليه إحنا بنقولها less than، وواحد
+
+331
+00:28:11,940 --> 00:28:20,200
+إلى تسعة وتسعين؟ هو positive integer. يعني بصيغة roster بقول
+
+332
+00:28:20,200 --> 00:28:26,340
+واحد، اتنين، تلاتة، الـ ellipses، والتسعة والتسعين.
+
+333
+00:28:30,310 --> 00:28:34,450
+أنت بتجرب الثانية، ما شاء الله، كويس، إيش بيقول لي؟
+
+334
+00:28:34,450 --> 00:28:39,430
+في الثانية بيقول لي X is an odd positive integer
+
+335
+00:28:39,430 --> 00:28:50,950
+صفتها عدد فردي موجب، عدد فردي موجب أقل من عشرة،
+
+336
+00:28:50,950 --> 00:28:56,750
+واحد، تلاتة، خمسة، سبعة، والتسعة.
+
+337
+00:28:59,390 --> 00:29:04,030
+مبتعد، شوف العدد الفردي كمان مرة، كيف وصفه؟ قال لي X
+
+338
+00:29:04,030 --> 00:29:09,930
+كان ينتمي إلى Z plus. لاحظ صيغة الـ expression شوية
+
+339
+00:29:09,930 --> 00:29:16,590
+اتغيرت هنا ولا لا؟ مش قضية في الآخر، هو عمال يوصف
+
+340
+00:29:16,590 --> 00:29:19,770
+للعناصر اللي بيتكلم عليها، فقال لي إن العنصر تبعي
+
+341
+00:29:19,770 --> 00:29:26,030
+هو عبارة عن عدد صحيح موجب. ممتاز. قال لي إيش؟ X is
+
+342
+00:29:26,030 --> 00:29:34,600
+odd، عدد صحيح موجب أو فردي، and أقل من عشرة. نفس
+
+343
+00:29:34,600 --> 00:29:37,800
+الكلام اللي فوق تماما، بس اختلف في وين؟ في الـ
+
+344
+00:29:37,800 --> 00:29:41,500
+description، أو في صيغة الوصف الدقيقة لكل عناصر
+
+345
+00:29:41,500 --> 00:29:47,560
+المجموعة. لاحظ، لو أخذت أي عنصر في المجموعة، لازم
+
+346
+00:29:47,560 --> 00:29:50,920
+يطبق عليه الوصف اللي موجود هنا، لازم يطبق عليه
+
+347
+00:29:50,920 --> 00:29:52,440
+الوصف اللي موجود بالتمام.
+
+348
+00:29:56,460 --> 00:30:02,560
+الآن، تعال نشوف المثال الأخير. Q plus، Q هي عبارة عن
+
+349
+00:30:02,560 --> 00:30:08,660
+الـ rational number، والـ plus، positive. X تنتمي إلى R،
+
+350
+00:30:08,660 --> 00:30:14,560
+طبيعي. هو X عبارة عن عدد حقيقي. إيه الصفة العدد
+
+351
+00:30:14,560 --> 00:30:23,360
+الحقيقي هذا؟ X تساوي P على Q، يعني العدد الحقيقي هذا
+
+352
+00:30:23,360 --> 00:30:30,560
+نكتبه على صورة كسر، بسط ومقام، for some positive
+
+353
+00:30:30,560 --> 00:30:38,150
+integers P و Q. قلت إياهم. قال لي: أعداد حقيقية بحيث
+
+354
+00:30:38,150 --> 00:30:42,570
+إن P و Q عبارة عن positive integers، positive
+
+355
+00:30:42,570 --> 00:30:47,810
+integers، يعني الصفر مش منهم، تمام؟ ولا السالب منهم.
+
+356
+00:30:47,810 --> 00:30:52,150
+وبالتالي، بصوا، المقام موجبات، فالـ output هيكون موجب.
+
+357
+00:30:52,150 --> 00:30:59,910
+هذا وصف للرقم اللي موجود عندي هان، تمام؟ الـ
+
+358
+00:30:59,910 --> 00:31:05,050
+predicate تذكرها؟ أنا بذكرك فيها. قلنا الـ
+
+359
+00:31:05,050 --> 00:31:09,190
+predicate function في الـ chapter الماضي. P of X
+
+360
+00:31:09,190 --> 00:31:14,910
+denoted by، أن
+
+361
+00:31:14,910 --> 00:31:20,890
+X أكبر من 3، أن P of X هي عبارة عن predicate
+
+362
+00:31:20,890 --> 00:31:26,330
+function، بتشير إلى X أكبر من 3. مين اللي predicated
+
+363
+00:31:26,330 --> 00:31:32,180
+التلاتة؟ قيمة الـ  X. بنقول هذه أنا بقيّمها
+
+364
+00:31:32,180 --> 00:31:37,220
+بناءً على قيمة الـ X. P of خمسة، إيش قيمتها؟ true.
+
+365
+00:31:37,220 --> 00:31:45,540
+P of تلاتة، false. الآن، ممكن تستخدم لـ predicate
+
+366
+00:31:45,540 --> 00:31:51,300
+في الـ set builder notation عشان توصف عناصر
+
+367
+00:31:51,300 --> 00:31:59,830
+المجموعة. X اللي بتحقق عناصر المجموعة. يعني بين قوسين،
+
+368
+00:31:59,830 --> 00:32:08,330
+أنا بقدر أكتبها هيك: {X | X أكبر من 3}. إيه صفة
+
+369
+00:32:08,330 --> 00:32:12,430
+المجموعة اللي هون يا شباب؟ كل الـ positive number،
+
+370
+00:32:12,430 --> 00:32:19,210
+..كل الـ positive real number اللي أكبر من 3؟ 4.
+
+371
+00:32:19,210 --> 00:32:21,050
+ليش قلت real number؟
+
+372
+00:32:23,440 --> 00:32:27,080
+لأنه لم يحدد، ليش الصفة العدد، وبالتالي أنا رحت على
+
+373
+00:32:27,080 --> 00:32:31,060
+أكبر صورة ممكنة، مع الـ real number. و ليش رأيك؟ بدك
+
+374
+00:32:31,060 --> 00:32:37,440
+تقيدها، وتتكلم على integers؟ بتقول: and الـ X تنتمي
+
+375
+00:32:37,440 --> 00:32:42,960
+إلى الـ Z، و
+
+376
+00:32:42,960 --> 00:32:47,360
+هكذا. لاحظ إن أنا بتكلم على predicate من الأمثلة
+
+377
+00:32:47,360 --> 00:32:49,960
+اللي ممكن تكون على الـ predicate. لو أنا عرّفت لك الـ
+
+378
+00:32:49,960 --> 00:32:59,240
+S هي عبارة عن المجموعة، عناصرها X، وبتحقق
+
+379
+00:32:59,240 --> 00:33:06,180
+prime X، أن الـ X is prime، الأعداد الأولية.. إيش
+
+380
+00:33:06,180 --> 00:33:12,210
+الأعداد الأولية يا شباب؟ اتنين. هو عبارة عن كل عدد
+
+381
+00:33:12,210 --> 00:33:20,690
+صحيح موجب، أكبر أو يساوي 2، يقبل القسمة، أو لا يقبل
+
+382
+00:33:20,690 --> 00:33:25,670
+القسمة إلا على نفسه وعلى الواحد. مش هنزعلك. فلو
+
+383
+00:33:25,670 --> 00:33:28,270
+جيبنا أي عدد في الدنيا، بسميه على الواحد، حق.. okay.
+
+384
+00:33:28,270 --> 00:33:38,640
+الآن، نقدر نكتبهم؟ هو يبقى 2، 3، 5، 7، 11، 13،
+
+385
+00:33:38,640 --> 00:33:51,680
+..17، 19، 23، 31، 29، 27، 29، 31، في
+
+386
+00:33:51,680 --> 00:33:57,740
+الآخر مش هتقدر يا صاحبي، مش هتقدر تحط لبس. كمان عرف
+
+387
+00:33:57,740 --> 00:34:02,700
+ليش؟ لأن ما فيش صيغة ثابتة تعتمد عليها عشان تمشي
+
+388
+00:34:03,780 --> 00:34:08,800
+بجهة العناصر. عشان هي كده. لما بنجي نتكلم، نقول
+
+389
+00:34:08,800 --> 00:34:14,720
+مجموعة الأعداد الأولية، وبنسكت، معروفين. خلصنا. هو كل
+
+390
+00:34:14,720 --> 
+
+445
+00:39:49,120 --> 00:39:52,640
+تروح تجيبلها وصف دقيق هي عبارة عن عدد حقيقي، والـ R
+
+446
+00:39:52,640 --> 00:39:57,620
+صفتها عدد حقيقي، وبس. مقدرش أنت فعليا هنا في مجموعة
+
+447
+00:39:57,620 --> 00:40:01,760
+زي الـ universal set تفصلها بالكامل
+
+448
+00:40:05,700 --> 00:40:09,500
+في الـ Intervals ممكن نعبّرها بالـ Set Notation
+
+449
+00:40:09,500 --> 00:40:13,620
+الـ Intervals ممكن نستخدم الـ Notation أو الـ
+
+450
+00:40:13,620 --> 00:40:16,420
+Builder Notation. Set Builder Notation، ونعرف
+
+451
+00:40:16,420 --> 00:40:19,480
+المجموعات، بس باكتب، انتباه كمان مرة، أن الكتاب هنا
+
+452
+00:40:19,480 --> 00:40:24,940
+شوية ممكن يخربط. استخدم في الـ half أو في الـ... في الـ
+
+453
+00:40:24,940 --> 00:40:28,260
+open interval. احنا سابقا اعتمدنا
+
+454
+00:40:30,340 --> 00:40:36,760
+نعكس الابتجاه، هذه فترة مغلقة، وهذه فترة مفتوحة، في
+
+455
+00:40:36,760 --> 00:40:43,320
+الكتاب اعتمد على الـ ] [ تمام؟ على أن الفترة المفتوحة
+
+456
+00:40:43,320 --> 00:40:47,440
+بدل الـ ] [ المربع، استخدم الـ ( ) العادي. نفس الكلام
+
+457
+00:40:47,440 --> 00:40:52,660
+أنت مش هتفرق معاك تمام؟ بس عشان أنا أبقى هيك ما
+
+458
+00:40:52,660 --> 00:40:55,440
+تقوليش أنت وأنا مودينا، واحنا بنعرف شغلات غير هيك
+
+459
+00:40:57,020 --> 00:41:00,120
+Anyway، في الفترة المفتوحة... في الفترة المغلقة
+
+460
+00:41:00,120 --> 00:41:07,080
+اللي فوق A و B هي عبارة عن مجموعة الأرقام، تمام؟ X
+
+461
+00:41:07,080 --> 00:41:12,580
+حيث أن X أكبر أو تساوي A، لأنها مغلقة من عند الـ A
+
+462
+00:41:12,580 --> 00:41:20,420
+and الـ X أقل أو تساوي الـ B، مغلقة من عند الـ B طبعا
+
+463
+00:41:20,420 --> 00:41:28,670
+هذا ممكن تتفصيلها هيك: أداة X حيث أن X أكبر أو
+
+464
+00:41:28,670 --> 00:41:37,810
+تساوي الـ a and الـ x أقل أو تساوي الـ b، مظبوط؟ نفس
+
+465
+00:41:37,810 --> 00:41:43,350
+الكلام اللي هنا، ونفس الكلام بتنسيقه أو بتسقطه على
+
+466
+00:41:43,350 --> 00:41:52,410
+الـ real intervals اللي موجودة عندي هنا. الـ
+
+467
+00:41:52,410 --> 00:41:57,250
+universal set. الـ universal set هي عبارة عن
+
+468
+00:41:57,250 --> 00:42:02,530
+المجموعة اللي بتحتوي على كل...
+
+469
+00:42:02,530 --> 00:42:08,330
+كل شيء ضمن بعض
+
+470
+00:42:08,330 --> 00:42:11,070
+الشروط، أو بعض القيود، لما باجي بقول إيش الـ
+
+471
+00:42:11,070 --> 00:42:15,430
+universal set للأرقام، أو للأعداد الـ real number
+
+472
+00:42:15,430 --> 00:42:21,610
+إيش الـ universal set للأعداد الـ real number؟ وإذا
+
+473
+00:42:21,610 --> 00:42:26,430
+بدك تكبر أكبر شوية، بتقول الـ complex ولا لا؟ اه، لأن
+
+474
+00:42:26,430 --> 00:42:32,310
+أنا جمعت إيش؟ التخيّلي، تمام. لو أنا اجيت قولت إيش
+
+475
+00:42:32,310 --> 00:42:37,610
+الـ universal set لمجموعة الـ vowels، يعني إيش
+
+476
+00:42:37,610 --> 00:42:42,570
+المجموعة اللي أكبر، تمام، من الـ vowels وبتشملها في
+
+477
+00:42:42,570 --> 00:42:48,010
+داخلها. هي مجموعة الـ alphabetical characters، مظبوط؟
+
+478
+00:42:49,170 --> 00:42:52,930
+وبالتالي، لما أنا بتكلم على universal set، أنا بتكلم
+
+479
+00:42:52,930 --> 00:42:56,870
+على مجموعة بتشمل كل شيء... بتشمل كل شيء، وغالبا
+
+480
+00:42:56,870 --> 00:43:01,370
+هلاقي في بعض الصعوبة في أي شيء في وصف، أو في وصف
+
+481
+00:43:01,370 --> 00:43:05,710
+المجموعة اللي موجودة عندها، في مقابل الـ universal
+
+482
+00:43:05,710 --> 00:43:10,750
+احنا شايفين الـ Φ الـ empty، يعني هيك الـ universal
+
+483
+00:43:10,750 --> 00:43:14,210
+set هي المجموعة اللي بتشمل كل شيء، والـ empty set
+
+484
+00:43:15,240 --> 00:43:26,340
+التي لا تحتوي أو لا تتضمن على أي شيء، تمام. الآن
+
+485
+00:43:26,340 --> 00:43:31,460
+هرجع على... لأ، ما رجعناش. اه، جزاك الله خير. الـ definition هدول
+
+486
+00:43:31,460 --> 00:43:34,960
+الـ quantifiers. اه، خلاص. يعني برضه، برضه استخدامهم
+
+487
+00:43:34,960 --> 00:43:41,400
+بسيط. الآن، عشان أقول عن مجموعتين متساويتين، عشان أقول
+
+488
+00:43:41,400 --> 00:43:47,220
+عن مجموعتين متساويتين، لازم يكونوا كل العناصر أو
+
+489
+00:43:47,220 --> 00:43:52,540
+الـ اتنين بيعتمدوا على نفس العناصر. يعني باجي بقول A
+
+490
+00:43:52,540 --> 00:43:59,820
+بدها تساوي واحد، واتنين، وتلاتة، و B بدها تساوي
+
+491
+00:43:59,820 --> 00:44:06,730
+تلاتة، وواحد، واتنين. هل الـ A تساوي B؟ هل إيه تساوي
+
+492
+00:44:06,730 --> 00:44:10,810
+بيه؟ تساويها، لأنهم لازم يحتويا الاتنين، لازم يكونوا
+
+493
+00:44:10,810 --> 00:44:14,510
+بيشتملوا على نفس العناصر. ولما نقول بيشتملوا على
+
+494
+00:44:14,510 --> 00:44:18,410
+نفس العناصر، أول شغل اللي لازم تخطر في بالي أن عدد
+
+495
+00:44:18,410 --> 00:44:23,850
+العناصر في المجموعتين متساوي. عدد العناصر في
+
+496
+00:44:23,850 --> 00:44:28,550
+المجموعتين متساوي. يعني لو شوفت مجموعة فيها عدد
+
+497
+00:44:28,550 --> 00:44:33,590
+عناصرها أكبر من عناصر المجموعة التالية مباشرة، بغير
+
+498
+00:44:33,590 --> 00:44:41,780
+متساويات، تمام؟ يعني هيك لو في عندي هنا أربعة، هل هي
+
+499
+00:44:41,780 --> 00:44:46,900
+تساوي بيه؟ لأ، طبعا ليش؟ لأنه صارت عندي الأربعة هذه
+
+500
+00:44:46,900 --> 00:44:51,120
+أو الـ B فيها أربع عناصر، والـ A فيها تلات عناصر
+
+501
+00:44:51,120 --> 00:44:57,380
+فبالتالي حتما في فرق بين الاتنين، بس إياك تنسى في
+
+502
+00:44:57,380 --> 00:45:02,300
+المطابقة نفسه يا أحمد، ونروح نقول إيش؟ هي
+
+503
+00:45:02,300 --> 00:45:02,840
+التلاتة
+
+504
+00:45:06,060 --> 00:45:10,400
+تكراره بتلغيه، هذا مش موجود، مالوش قيمة عندي هنا
+
+505
+00:45:10,400 --> 00:45:15,440
+فالاثنين متساويتين، فالاتنين بيكونوا متساويتين، تمام
+
+506
+00:45:15,440 --> 00:45:20,760
+صيغة أهل الرياضيات: بنقول المجموعتين متساويتين لما
+
+507
+00:45:20,760 --> 00:45:28,240
+بيكون for all X، لأي X، X بتنتمي للمجموعة الأولى،
+
+508
+00:45:29,260 --> 00:45:34,620
+هتلاقي X موجودة في المجموعة التانية، ونفس الـ
+
+509
+00:45:34,620 --> 00:45:37,940
+element أكيد، لأنها نفس الـ element، والـ X اللي
+
+510
+00:45:37,940 --> 00:45:41,700
+بتنتمي في المجموعة التانية، هتلاقيها بتنتمي لمين؟
+
+511
+00:45:41,700 --> 00:45:44,560
+للمجموعة الأولى، لإن هو by conditional: if and only
+
+512
+00:45:44,560 --> 00:45:53,720
+if. تمام. هاي مثال على المجموعات المتساوية: واحد،
+
+513
+00:45:53,720 --> 00:45:58,650
+تلاتة، خمسة. تلاتة، خمسة، واحد. equal. الترتيب لا يعني
+
+514
+00:45:58,650 --> 00:46:05,210
+شيء. واحد، خمسة، خمسة، خمسة، تلاتة، تلاتة، واحد. التكرار
+
+515
+00:46:05,210 --> 00:46:09,670
+هذا بدك تطيره. صفة المجموعة: واحد، خمسة، تلاتة، واحد
+
+516
+00:46:09,670 --> 00:46:15,310
+والآخر واحد كمان مكرر، صار عندي واحد، خمسة، تلاتة
+
+517
+00:46:15,310 --> 00:46:19,590
+واحد، تلاتة، خمسة. في بينهم تساوي
+
+518
+00:46:26,530 --> 00:46:30,490
+شوفك في المجموعات اللي قدامنا هنا كـ groups: تسعة،
+
+519
+00:46:30,490 --> 00:46:34,410
+سبعة، تسعة، اتنين، سبعة، سالب تلاتة. الأولى
+
+520
+00:46:34,410 --> 00:46:41,250
+متساويات. التانية لأ، لأن السنجاب مش موجود في
+
+521
+00:46:41,250 --> 00:46:46,930
+المجموعة الأولى، بقى غير متساوية. التالتة، الحصار
+
+522
+00:46:46,930 --> 00:46:51,900
+موجود، أيوة، بس في عندي تكرار في الـ cat، بنشيله، و
+
+523
+00:46:51,900 --> 00:46:55,440
+بنلغيه، ومقابلته في عندي هنا تساوي ما بين العناصر
+
+524
+00:46:55,440 --> 00:47:04,420
+اللي موجودة عندي.ها. subset
+
+525
+00:47:04,420 --> 00:47:11,520
+إيش يعني subset؟ مجموعة جزئية. بنقول لو كان في عندي
+
+526
+00:47:11,520 --> 00:47:19,130
+مجموعتين A و B، أن الـ A subset من الـ B. الـ A is a
+
+527
+00:47:19,130 --> 00:47:24,950
+subset من الـ B، مجموعة جزئية من الـ B، if and only if
+
+528
+00:47:24,950 --> 00:47:34,750
+فقط إذا تحقق هذا الشرط فقط: every element in A is
+
+529
+00:47:34,750 --> 00:47:43,690
+also an element of B. برياضيات: for all X، X تنتمي
+
+530
+00:47:43,690 --> 00:47:50,190
+إلى A، يؤدي إلى X تنتمي إلى B. ولو كانت في المثال
+
+531
+00:47:50,190 --> 00:47:53,910
+اللي تابعت قبل شوية، by conditional، صارت فيها تساوي
+
+532
+00:47:53,910 --> 00:47:59,290
+طبعا، صرت أنا باتجاه واحد فقط، باتجاه واحد فقط، طبعا
+
+533
+00:47:59,290 --> 00:48:06,870
+يعني يعني بفهم من الكلام هذا أن عناصر أو عدد عناصر
+
+534
+00:48:07,610 --> 00:48:13,230
+الـ B أكبر أو يساوي عدد عناصر الـ A. هذا أول شرط
+
+535
+00:48:13,230 --> 00:48:18,570
+عدد عناصر الـ B أكبر أو يساوي عدد عناصر الـ A.
+
+536
+00:48:18,570 --> 00:48:24,310
+بعدين، كل عناصر الـ A موجودة في الـ B. كل عناصر الـ
+
+537
+00:48:24,310 --> 00:48:28,970
+A موجودة في الـ B. بنستخدم الرمز هذا عشان نقول
+
+538
+00:48:28,970 --> 00:48:33,550
+subset، مجموعة جزئية، مجموعة جزئية
+
+539
+00:48:37,270 --> 00:48:41,850
+الآن، في الأمثلة السابقة، لو أنا جيت قولت أن الـ B
+
+540
+00:48:41,850 --> 00:48:48,670
+بدها تساوي واحد، واتنين، وتلاتة، وقولت أن الـ A
+
+541
+00:48:48,670 --> 00:48:56,910
+بدها تساوي واحد، واتنين. هل الـ A subset من B؟ صحيح
+
+542
+00:48:56,910 --> 00:49:02,830
+الآن بدك تاخد كل عنصر في A، وتروح تشوف هل هو موجود
+
+543
+00:49:02,830 --> 00:49:10,800
+في B ولا لأ، تمام. موجود، تمام. معناته الـ A subset من
+
+544
+00:49:10,800 --> 00:49:14,960
+الـ B. طب لو التلاتة ما كانتش موجودة، تبقى العملية عشان
+
+545
+00:49:14,960 --> 00:49:19,660
+صحيحة، لأنه أنا بهمني أن العناصر نفسها موجودة في
+
+546
+00:49:19,660 --> 00:49:24,140
+المجموعة في المجموعتين. بس أدق يساوي كيف؟ يساوي أدق
+
+547
+00:49:24,140 --> 00:49:27,800
+كيف يساوي أدق؟ اه، just like in an equivalent. احنا
+
+548
+00:49:27,800 --> 00:49:30,500
+ما سألناش في الـ equivalent، خلصنا. أنا بسألك الآن: هذي
+
+549
+00:49:30,500 --> 00:49:31,920
+true ولا false؟ true
+
+550
+00:49:36,380 --> 00:49:40,660
+A equal B، true
+
+551
+00:49:40,660 --> 00:49:46,920
+بالمناسبة، subset هذه فيها احتمالية المساواة، فيها
+
+552
+00:49:46,920 --> 00:49:50,320
+احتمالية المساواة، عشان هيك أنا قلت لك أول
+
+553
+00:49:50,320 --> 00:49:55,600
+indication أن عدد عناصر الـ B أكبر أو يساوي عناصر
+
+554
+00:49:55,600 --> 00:49:58,980
+الـ A، وكل عناصر الـ A موجودة في الـ B. بل لو كانوا
+
+555
+00:49:58,980 --> 00:50:03,940
+يساويها مع بعضها، تبقى كلها على نفس المجموعة. الـ A كان
+
+556
+00:50:03,940 --> 00:50:04,760
+ثاني إلى الـ Φ
+
+557
+00:50:08,170 --> 00:50:15,270
+الـ A تنتمي إلى الـ Φ. ماهو الـ Φ؟
+
+558
+00:50:15,270 --> 00:50:20,090
+Empty، المجموعة
+
+559
+00:50:20,090 --> 00:50:24,170
+الفارغة. الـ A تنتمي إلى المجموعة الفارغة؟ False
+
+560
+00:50:24,170 --> 00:50:28,810
+وهذا دائما False، لأن الـ Φ مافيش فيها عناصر. الـ
+
+561
+00:50:28,810 --> 00:50:33,790
+Φ subset من الـ S، أو أفضل: الـ Φ subset من الـ S
+
+562
+00:50:35,370 --> 00:50:40,270
+الـ Φ مجموعة جزئية من أي مجموعة أخرى. المجموعة
+
+563
+00:50:40,270 --> 00:50:44,590
+الفارغة مجموعة جزئية من أي مجموعة فارغة، من أي
+
+564
+00:50:44,590 --> 00:50:48,670
+مجموعة أخرى. يعني لو أتينا وقلنا هنا: Φ subset
+
+565
+00:50:48,670 --> 00:50:58,130
+من الـ A، هذا true. ليش؟ لأن حسب القانون، حسب القانون
+
+566
+00:50:58,130 --> 00:51:03,250
+عدد عناصر الـ Φ لازم يكون أقل أو يساوي عدد عناصر
+
+567
+00:51:03,250 --> 00:51:08,210
+الـ A. أقل منها، عدد عناصرها صفر. هذه واحدة. كل
+
+568
+00:51:08,210 --> 00:51:12,150
+العناصر اللي في الـ Φ موجودة في الـ A. طب الـ Φ
+
+569
+00:51:12,150 --> 00:51:16,210
+مافيش فيها ولا عنصر، فاضية، مافيش فيها عناصر، already
+
+570
+00:51:16,210 --> 00:51:26,920
+حققت الشرط، وبالتالي هي true دائما. كل مجموعة جزئية
+
+571
+00:51:26,920 --> 00:51:33,600
+من نفسها true. true. تمام، لأن فيها إيش؟ مساواة، وكل
+
+572
+00:51:33,600 --> 00:51:41,460
+العناصر موجودة. هذه
+
+573
+00:51:41,460 --> 00:51:44,480
+الكلام اللي قلناه سابقا في الـ slide الماضي، قررناه
+
+574
+00:51:44,480 --> 00:51:52,040
+كمان مرة، بنفس الصيغة السابقة. الـ proper subset
+
+575
+00:51:54,200 --> 00:52:02,080
+Proper subset، مجموعة جزئية غير مساوية. مجموعة جزئية
+
+576
+00:52:02,080 --> 00:52:07,580
+غير مساوية. ولاحظ الرمز الآن، بيقول: لو كانت الـ A
+
+577
+00:52:07,580 --> 00:52:14,840
+subset من الـ B، والـ A لا تساوي الـ B، بنكتب أن هذا
+
+578
+00:52:14,840 --> 00:52:19,140
+مجموعة proper subset. إيش proper subset؟ يعني مجموعة
+
+579
+00:52:19,140 --> 00:52:25,490
+جزئية لا تساوي الـ B. يعني ببساطة: عدد عناصر الـ A
+
+580
+00:52:25,490 --> 00:52:29,670
+أقل من عدد عناصر الـ B، لو ب عنصر واحد أقل منه في
+
+581
+00:52:29,670 --> 00:52:39,910
+الآخر، المساواة بطلت موجودة. for
+
+582
+00:52:39,910 --> 00:52:44,590
+all، if الـ A proper subset، proper subset من الـ B،
+
+583
+00:52:44,590 --> 00:52:52,910
+معناته for all x، X تنتمي إلى A، يؤدي إلى X تنتمي إلى B،
+
+584
+00:52:52,910 --> 00:52:59,550
+and there exist على الأقل هناك عنصر واحد X تنتمي
+
+585
+00:52:59,550 --> 00:53:05,930
+إلى B and X لا تنتمي إلى A. إذا كان الـ X ممكن تخربط
+
+586
+00:53:05,930 --> 00:53:10,590
+الذكاء، أما الـ Y مش هتفرق كتير ولا شوية؟ بس في الآخر
+
+587
+00:53:10,590 --> 00:53:15,710
+لكل عناصر المجموعة A، هتلاقيها موجودة في المجموعة B،
+
+588
+00:53:15,710 --> 00:53:20,890
+وهناك عنصر واحد على الأقل في B مش موجود في A، عشان
+
+589
+00:53:20,890 --> 00:53:26,710
+نحقق الـ proper subset. كيف؟
+
+590
+00:53:26,710 --> 00:53:33,950
+الـ B أكبر من A. طيب
+
+591
+00:53:33,950 --> 00:53:38,310
+كمان مرة الآن بنقول
+
+592
+00:53:40,150 --> 00:53:46,030
+الـ A is a proper subset of B، أن الـ A مجموعة
+
+593
+00:53:46,030 --> 00:53:51,790
+جزئية من الـ B ولا تساويها، تمام؟ هذا الكلام بيكون
+
+594
+00:53:51,790 --> 00:53:58,730
+صحيح if and only if، لكل X في A، X تنتمي إلى A، حاليا
+
+595
+00:53:58,730 --> 00:54:04,930
+X تنتمي لمين؟ لـ B، and بالإضافة للشرط هذا، there
+
+596
+00:54:04,930 --> 00:54:11,190
+exist at least one X أو one Y. one X موجودة، X موجودة
+
+597
+00:54:11,190 --> 00:54:16,470
+في B، ومش موجودة... يعني لو احنا بالمثال اللي شفناه
+
+598
+00:54:16,470 --> 00:54:22,390
+قبل شوية، A بدها تساوي واحد، واتنين، وتلاتة، والـ A
+
+599
+00:54:22,390 --> 00:54:28,110
+... والـ B عفوا، بدها تساوي واحد، واتنين، وتلاتة، و
+
+600
+00:54:28,110 --> 00:54:38,460
+أربعة. الـ A proper subset من الـ B. الـ A proper subset
+
+601
+00:54:38,460 --> 00:54:44,540
+من الـ B؟ لأ
+
+602
+00:54:44,540 --> 00:54:51,580
+لأ. في الـ subset قلنا أن عدد عناصر الـ A أقل أو
+
+603
+00:54:51,580 --> 00:54:57,580
+تساوي عدد عناصر الـ B، تمام. بس هنا عندي sharp and
+
+604
+00:54:57,580 --> 00:55:04,980
+تمام، أن العنصر في، عدد عناصر الـ B أكبر من عناصر الـ
+
+605
+00:55:04,980 --> 00:55:16,420
+A. طيب، في عندي قانونين مهمات بقول
+
+606
+00:55:16,420 --> 00:55:22,780
+لو كانت الـ A تساوي B، معناته ده أنا باخد منه أو
+
+607
+00:55:22,780 --> 00:55:28,700
+بفهم منه أن الـ A subset من الـ B، والـ B subset من
+
+608
+00:55:28,700 --> 00:55:32,780
+الـ A، لو
+
+609
+00:55:32,780 --> 00:55:36,720
+كانت الـ A تساوي الـ B. معناته الاتنين اللي هم نفس عدد
+
+610
+00:55:36,720 --> 00:55:42,620
+العناصر، مظبوط، وكل عنصر في A موجود في B. وهذه عنوان
+
+611
+00:55:42,620 --> 00:55:46,520
+إيش؟ عنوان الـ subset، يعني A subset من الـ B، وبما أن
+
+612
+00:55:46,520 --> 00:55:51,320
+العلاقة بينهم equal، معناته كل عنصر في B موجود في A،
+
+613
+00:55:51,320 --> 0
+
+667
+01:01:01,390 --> 01:01:05,290
+موجودات بدي آخذ الـ element اللي جواتهم هل هو
+
+668
+01:01:05,290 --> 01:01:12,790
+موجود؟ False. الـ Y Subset
+
+669
+01:01:12,790 --> 01:01:16,170
+احفظ المباراة، احتاجها. عيني هتبقى جامدة إذا بتنجح.
+
+670
+01:01:16,170 --> 01:01:19,990
+إذا بتقدر تحلهم بالحفظ، بمشي الحفظ وهيك أمور يا
+
+671
+01:01:19,990 --> 01:01:28,120
+شباب، الآن الـ Y Subset من .. هي الـ Y هل الأواعي
+
+672
+01:01:28,120 --> 01:01:35,020
+موجودة as an element في الـ A؟ لأ، خلصنا؟
+
+673
+01:01:35,020 --> 01:01:42,800
+تمام؟ الحمد لله. subset
+
+674
+01:01:42,800 --> 01:01:51,820
+على العناصر اللي موجودة عندي هان الأولى
+
+675
+01:01:51,820 --> 01:01:56,960
+subset؟ ايه الـ subset من الـ B؟ true. الثانية، ايه الـ
+
+676
+01:01:56,960 --> 01:02:02,860
+subset من الـ B؟ true.  لكي
+
+677
+01:02:02,860 --> 01:02:09,240
+أطيّرهم. تالتة false لأن العنصر الواحد موجود في الـ
+
+678
+01:02:09,240 --> 01:02:18,360
+A مش موجود في الـ B. proper؟ غلط يا صاحبي، ولا proper
+
+679
+01:02:18,360 --> 01:02:22,460
+كمان ولا
+
+680
+01:02:22,460 --> 01:02:23,040
+الـ B subset
+
+681
+01:02:33,650 --> 01:02:38,090
+false. false. إذا
+
+682
+01:02:38,090 --> 01:02:42,770
+هي ماكنتش proper subset فهي مستحيل تكون subset. طيب
+
+683
+01:02:42,770 --> 01:02:45,030
+على هيك يا شباب، هنجي في اليوم إن شاء الله، و
+
+684
+01:02:45,030 --> 01:02:47,330
+تعالى والمحاضرة اللي جايه بنبدأ من عند الـ
+
+685
+01:02:47,330 --> 01:02:52,170
+cardinality والمقصود فيها عدد عناصر المجموعة. عدد
+
+686
+01:02:52,170 --> 01:02:54,890
+عناصر المجموعة. في أي سؤال يا شباب؟ الله يعطيكوا
+
+687
+01:02:54,890 --> 01:02:55,230
+العافية
diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/0uvPY3Nanck_postprocess.srt b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/0uvPY3Nanck_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..8d4d37b3ba9436495e8698ad55c062ba0495fff9
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/0uvPY3Nanck_postprocess.srt
@@ -0,0 +1,2748 @@
+1
+00:00:20,970 --> 00:00:22,990
+بسم الله والحمد لله والصلاة والسلام على رسول الله
+
+2
+00:00:22,990 --> 00:00:27,370
+اليوم ان شاء الله شباب هنبدأ بال chapter التانيمن
+
+3
+00:00:27,370 --> 00:00:31,770
+المادة الرياضة المفصلة والشبتر هذا هيركز على
+
+4
+00:00:31,770 --> 00:00:35,490
+الشغلات أو ال structures الأساسية أو البنيات
+
+5
+00:00:35,490 --> 00:00:39,210
+البنية الأساسية للرياضيات هنتكلم على مجموعات
+
+6
+00:00:39,210 --> 00:00:42,730
+هنتكلم على دوال هنتكلم على series هنتكلم على
+
+7
+00:00:42,730 --> 00:00:47,750
+relations هنمشي شوية شوية في الشبتر هذا وممكن في
+
+8
+00:00:47,750 --> 00:00:50,170
+لحظة من اللحظات اجيب section او اتنين من شبتر
+
+9
+00:00:50,170 --> 00:00:53,930
+تمانية موجودة كلهم related او على علاقة أو وثيقة
+
+10
+00:00:53,930 --> 00:01:00,290
+فيش بالشبتر اللي موجود عندهاAnyway انا كل حال احنا
+
+11
+00:01:00,290 --> 00:01:04,370
+هنبلش اليوم في المجموعات طبعا العناصر تبعت ال
+
+12
+00:01:04,370 --> 00:01:08,750
+chapter اللي انها المجموعاتالدوال الـ sequences
+
+13
+00:01:08,750 --> 00:01:13,470
+المتتاليات والمجميع ال cardinalities للمجموعات
+
+14
+00:01:13,470 --> 00:01:17,610
+اللي فوق والمصفوفات وممكن زي ما قلت اروح اجيب ال
+
+15
+00:01:17,610 --> 00:01:22,270
+relation من chapter 8 عشان نخلص ال related topics
+
+16
+00:01:22,270 --> 00:01:26,390
+اليوم هنتكلم بالدرجة الأولى عن المجموعات عن ال
+
+17
+00:01:26,390 --> 00:01:31,250
+section الأول section المجموعات طبعا لما أنا بتكلم
+
+18
+00:01:31,250 --> 00:01:35,050
+على مجموعة بتكلم على basic
+
+19
+00:01:38,050 --> 00:01:42,570
+بالنسبة للمجموعات المباشرة يخطر على بالك القواص
+
+20
+00:01:42,570 --> 00:01:47,170
+high الـ curly braces تمام؟ اللي بنرمز المجموعات
+
+21
+00:01:47,170 --> 00:01:52,090
+احنا شفنا قواص مع ال intervals القواص المربع صح؟
+
+22
+00:01:52,090 --> 00:01:55,770
+لل interval وهي القواص عينيه ال curly high braces
+
+23
+00:01:55,770 --> 00:02:00,880
+من أجل نتكلم على مجموعةوطبعا لما أتكلم على
+
+24
+00:02:00,880 --> 00:02:04,080
+المجموعات هي block أساسي أو structure أساسي في
+
+25
+00:02:04,080 --> 00:02:09,100
+الرياضيات وكل العلوم المبنية عليها لما بتكلم على
+
+26
+00:02:09,100 --> 00:02:13,200
+العد أو أنظمة العد أو بدي أعد الشغلات بحاول أجسمهم
+
+27
+00:02:13,200 --> 00:02:18,200
+لمجموعات عشان يسهل مجموع الحسبة بمزعهم لمجموعات
+
+28
+00:02:18,200 --> 00:02:21,580
+يعني هيك لو أنا جيت بدي أعدكوا في القاعة بقولت هي
+
+29
+00:02:21,580 --> 00:02:25,700
+خمسة كذا هي خمسة وهي في عندي انا عشر خمستاش وهي
+
+30
+00:02:25,700 --> 00:02:28,180
+عندي اربعة هي تسعتاش فبكون انا فعليا تجسمتي
+
+31
+00:02:28,180 --> 00:02:32,250
+للمجموعات كانت ايش؟سهلت علي أن أصل للنتيجة اللي
+
+32
+00:02:32,250 --> 00:02:37,350
+أنا بديها اللي هي موضوع العد طبعا لغات البرمجة لما
+
+33
+00:02:37,350 --> 00:02:40,310
+أنا بتكلم عليها بشكل عام برضه بتكلم على مجموعات
+
+34
+00:02:40,310 --> 00:02:43,490
+بتكلم على مجموعات المتغيرات اللي أنت بتعرفها في
+
+35
+00:02:43,490 --> 00:02:46,450
+لغة البرمجة على ال scope تبعتها وإن هذا ال
+
+36
+00:02:46,450 --> 00:02:49,730
+variable موجود فانت بتتكلم قاعدين على مجموعات ال
+
+37
+00:02:49,730 --> 00:02:52,730
+operations في عندي عمليات أو مجموعة العمليات
+
+38
+00:02:52,730 --> 00:02:58,730
+الحسابية الجمع والضرب والطرح والقسمة مصبوط وال
+
+39
+00:02:58,730 --> 00:03:02,770
+modulusو في عندى مجموعة العمليات المنطقية اللى هى
+
+40
+00:03:02,770 --> 00:03:07,150
+ال and و ال or و ال not و هكذا حتى فى داخل ال loop
+
+41
+00:03:07,150 --> 00:03:10,990
+او عفوا فى داخل البرنامج الواحد بتصير كمان عندى
+
+42
+00:03:10,990 --> 00:03:14,270
+مجموعة من ال blocks هذا لل while هذا لل condition
+
+43
+00:03:14,270 --> 00:03:18,970
+لل if statement فبقى برضه بتكلم على مجموعات فى
+
+44
+00:03:18,970 --> 00:03:23,870
+الرياضيات فى علم اسمه نظرية المجموعات و هذا علم
+
+45
+00:03:23,870 --> 00:03:27,510
+داخل فى كثير من التطبيقات اللى موجودة اليوم
+
+46
+00:03:32,400 --> 00:03:36,340
+نجي للتعريف اللي بيهمنا احنا بشكل دقيق شو يعني
+
+47
+00:03:36,340 --> 00:03:43,240
+مجموعة جاي بتكلم ال set S المجموعة هي unordered
+
+48
+00:03:43,240 --> 00:03:52,360
+وهي أول خط collection of objects مجموعة من العناصر
+
+49
+00:03:53,810 --> 00:03:58,010
+تمام؟ مجموعة من العناصر Unordered طبعا الـ
+
+50
+00:03:58,010 --> 00:04:00,830
+Collection بتتكلم عن مجموعة يعني عنصر أو أكتر ..
+
+51
+00:04:00,830 --> 00:04:04,150
+عنصر أو أكتر .. طب السؤال بيطرح نفسه ممكن يكون
+
+52
+00:04:04,150 --> 00:04:07,550
+عندي عنصر واحد في المجموعة؟ أه ممكن .. و ممكن
+
+53
+00:04:07,550 --> 00:04:10,170
+المجموعة تكون فاضية لأنه لحد تلقاه مالاقيناش
+
+54
+00:04:10,170 --> 00:04:14,810
+المنبر المناسب ان نحطه فيها مثلا .. مثلا لو أنا
+
+55
+00:04:14,810 --> 00:04:17,930
+أجي لقول في لحظة من اللحظات أنه أنا شباب بدي أعمل
+
+56
+00:04:17,930 --> 00:04:24,530
+مجموعةبحيث انها تشتغل زي معيدين في المادة للشباب
+
+57
+00:04:24,530 --> 00:04:28,610
+التانين يحلولهم أسئلة و يشرحولهم بعض الشغلات اللي
+
+58
+00:04:28,610 --> 00:04:32,750
+ماقدروش يفهموها منيكويس .. من في المجموعة الآن يا
+
+59
+00:04:32,750 --> 00:04:38,610
+دكتور؟ مافيش حد .. ليش؟ لأن مبدأيا ماشوفتش من
+
+60
+00:04:38,610 --> 00:04:41,690
+الشخص أو من الشخص المناسب اللي يكون موجود في
+
+61
+00:04:41,690 --> 00:04:46,390
+المجموعة لكن هذه مجموعة قررت أن أعملها وبالتالي
+
+62
+00:04:46,390 --> 00:04:50,290
+لما بتكلم على collection يعني بتكلم على واحد أو
+
+63
+00:04:50,290 --> 00:04:52,950
+أكتر غالبا لكن برضه في استثناء أن ممكن المجموعة
+
+64
+00:04:52,950 --> 00:04:57,030
+تكون فاضية أو بشكل مؤقت .. Unordered
+
+65
+00:04:59,210 --> 00:05:02,830
+لسه افن في كمان شغلة في collection في مفهوم ال
+
+66
+00:05:02,830 --> 00:05:06,330
+collection مفهوم collection يعني اتكرار بيعنيش
+
+67
+00:05:06,330 --> 00:05:12,150
+حاجة بنفهش اجي اقول في المجموعة انا عندي احمد و
+
+68
+00:05:12,150 --> 00:05:19,370
+احمد و كمان احمد اذا انا كنت بقصد نفس الشخص او بين
+
+69
+00:05:19,370 --> 00:05:24,210
+جسيم بنفهش اجي اقول انا سوي الطرفة طبعا انا عندي
+
+70
+00:05:24,210 --> 00:05:29,960
+خمس سيارات سبارة و تلاتة و تمانينوكمان سبارة تلاتة
+
+71
+00:05:29,960 --> 00:05:34,440
+وتمانين و سبارة تلاتة وتمانين فانت بتعدد في نفس ال
+
+72
+00:05:34,440 --> 00:05:38,000
+object فانت دلوقتي ما بتتكلمش على collection انت
+
+73
+00:05:38,000 --> 00:05:42,040
+بتتكلم على element مافي كلمة collection زي ما كنت
+
+74
+00:05:42,040 --> 00:05:46,460
+بتتكلم على أكثر واحد أو أكثر برضه التكرار فيها أو
+
+75
+00:05:46,460 --> 00:05:50,260
+تكرار الشيء لا يعني شيء مالوش قيمة التكرار في
+
+76
+00:05:50,260 --> 00:05:57,160
+المجموعة هذا لا يعني شيء Unorderedكمان الترتيب في
+
+77
+00:05:57,160 --> 00:06:00,820
+المجموعة لا يعني شيء، لو أنا اجهزة كتبت في داخل
+
+78
+00:06:00,820 --> 00:06:11,480
+الأقواس A و M و H هذه
+
+79
+00:06:11,480 --> 00:06:19,160
+هي نفس المجموعة M و H و A الآن
+
+80
+00:06:19,160 --> 00:06:22,920
+هي نفس المجموعة نفس المجموعة، من على صرفهم؟نفس
+
+81
+00:06:22,920 --> 00:06:26,440
+العناصر و نفس عددهم ماتغيرش فيهم ولا حاجة كمان مرة
+
+82
+00:06:26,440 --> 00:06:32,240
+لو انا اتيت كرارتها و قولت ال ايه؟ مالوش معنى
+
+83
+00:06:32,240 --> 00:06:36,100
+اتكرار اتكرار مالوشش معنى لأن كلمة connection ال
+
+84
+00:06:36,100 --> 00:06:38,780
+connection بتقولي ماتكررش ال element اللي موجود
+
+85
+00:06:38,780 --> 00:06:44,360
+فحتى لو انت شفته مكتوب لازم تعمل حسابك اننا بنتكلم
+
+86
+00:06:44,360 --> 00:06:47,040
+عن نفس ال element و لما يسألك عدد عناصر المجموعة
+
+87
+00:06:47,040 --> 00:06:50,540
+هي كام شبال؟ العصر بتقولي تلاتة ماتقوليش أربعة لأن
+
+88
+00:06:50,540 --> 00:06:57,510
+العصر هذا هومتكرر هو نفسه تمام معناته unordered
+
+89
+00:06:57,510 --> 00:07:03,130
+collection معناته انا بتكلم على مجموعة فيها عدد من
+
+90
+00:07:03,130 --> 00:07:08,890
+العناصر واحد فاكثر ترتيبهم لا يعني شيء والتكرار
+
+91
+00:07:08,890 --> 00:07:14,910
+العناصر الموجودة لا يعني شيء تمام مثل اش اقول طلاب
+
+92
+00:07:14,910 --> 00:07:18,800
+المساقها او الطلاب الموجودين عندى في المحاضرةسواء
+
+93
+00:07:18,800 --> 00:07:23,900
+قرأت أو نديت على محمد الأدهم، تمام؟ ولا بدأت بعمر
+
+94
+00:07:23,900 --> 00:07:28,420
+مطر؟ مش هتفرج كتير، كلهم موجودين، بس أثناء حضوره
+
+95
+00:07:28,420 --> 00:07:31,600
+الغياب، على فرض، لو أنا بدي أخد حضوره غياب، روح
+
+96
+00:07:31,600 --> 00:07:37,880
+اتكررت اسم عمر مطر مرتينمباشرة إذا كان موجود سأقول
+
+97
+00:07:37,880 --> 00:07:41,560
+لدكتور أني أزعجته قبل ذلك ولا لا وإذا لم يكن موجود
+
+98
+00:07:41,560 --> 00:07:44,040
+الشباب اللي موجودين سأقول لدكتور أنت ناديته
+
+99
+00:07:44,040 --> 00:07:48,040
+فبالتالي هل هو نفس الشخص ولا مختلف فلازم ننتبه أن
+
+100
+00:07:48,040 --> 00:07:51,680
+التكرار في المجموعة لا يعني شيء تمام الآن هنوصل
+
+101
+00:07:51,680 --> 00:07:55,500
+للمجموعة بنقول عنهم ال objects اللي هي الشغلات
+
+102
+00:07:55,500 --> 00:07:59,440
+اللي أنعنالي بأذكرها في المجموعة السيارات القلاد
+
+103
+00:07:59,440 --> 00:08:05,060
+الكتب الجلام الكراسي المجموعة حسب إيش تركبتهالكن
+
+104
+00:08:05,060 --> 00:08:08,140
+عندما أتكلم عن المجموعات الـ object هي صارت
+
+105
+00:08:08,140 --> 00:08:11,300
+بالنسبة لي في نظام المجموعة عبارة عن elements
+
+106
+00:08:11,300 --> 00:08:14,860
+بقولك إيش عناصر المجموعة بسألكاش إيش ال object
+
+107
+00:08:14,860 --> 00:08:18,840
+اللي في المجموعة من عناصر المجموعة هتقولي a و m و
+
+108
+00:08:18,840 --> 00:08:24,360
+h حسب المثال اللي كتبناها قبل شوية من أعضاء
+
+109
+00:08:24,360 --> 00:08:27,440
+المجموعة اللي هو المصطلح اللي بعدي member of
+
+110
+00:08:27,440 --> 00:08:32,380
+members نفس الكلام لكن اللي بدي أقوله أنا هنغيب
+
+111
+00:08:32,380 --> 00:08:36,780
+مصطلح ال objectسأخبرك من أعضاء المجموعة أو من
+
+112
+00:08:36,780 --> 00:08:39,100
+العناصر الموجودة في المجموعة من المصطلحات أو
+
+113
+00:08:39,100 --> 00:08:43,720
+المسميات الموجودة عندهم وعندما أتكلم عن علاقة
+
+114
+00:08:43,720 --> 00:08:47,180
+العنصر بالمجموعة العنصر ينتمي إلى المجموعة هي
+
+115
+00:08:47,180 --> 00:08:52,960
+إشارات ينتمي ينتمي
+
+116
+00:08:52,960 --> 00:08:58,260
+وغالبا العنصر نرمزه باسم letter واسم المجموعة
+
+117
+00:08:59,340 --> 00:09:01,880
+بنعتمد الـ capital letter هيك ال standard في
+
+118
+00:09:01,880 --> 00:09:05,760
+الرياضيات اسم المجموعة capital letter والعناصر
+
+119
+00:09:05,760 --> 00:09:09,560
+اللي فيها small letter ما لم تكن انت فعليا قاصد ان
+
+120
+00:09:09,560 --> 00:09:15,280
+العناصر كوناش capital letter وهك بيصير انا اقول ال
+
+121
+00:09:15,280 --> 00:09:22,100
+a بجراها a is a member of a بالمجموعة a او a
+
+122
+00:09:22,100 --> 00:09:26,620
+المجموعة contains small a اللي هي العنصر ال
+
+123
+00:09:26,620 --> 00:09:31,800
+element اللي موجود عندهاوإذا كان العنصر لا ينتمي ،
+
+124
+00:09:31,800 --> 00:09:39,560
+فسأقول A لا تنتمي للـ A على نفس القياس تبعت
+
+125
+00:09:39,560 --> 00:09:48,600
+اليساوي ، فسنقول لا يساوي تمام؟ الموضوع
+
+126
+00:09:48,600 --> 00:09:53,640
+بشكل عام اليوم سيكون سهل مقارنة بالذي رأيناه في
+
+127
+00:09:53,640 --> 00:09:56,460
+الفيديو السابق خصوصا في الفيديو السابق قليلا أو
+
+128
+00:09:56,460 --> 00:09:59,890
+الأمور عندما تلقوا في الـ Logicلأن ال logic تبعنا
+
+129
+00:09:59,890 --> 00:10:06,130
+غالبا مش سليم تمام؟ مابنبنحسب المشاكل تمام معناته
+
+130
+00:10:06,130 --> 00:10:11,850
+نقول احنا a تنتمي إلى a a is an element او is a
+
+131
+00:10:11,850 --> 00:10:17,130
+member a is not an element الآن لو تشوفت مجموعة
+
+132
+00:10:17,130 --> 00:10:22,790
+مكتوبة بالشكل التالي a تساوي a1 و a2 و a3 لحد am
+
+133
+00:10:22,790 --> 00:10:29,620
+هل العناصر هذه يعني انهم مرتبات؟ لأهذه مجرد رموز
+
+134
+00:10:29,620 --> 00:10:34,060
+عشان أشيل العنصر الأول العنصر التاني العنصر التالت
+
+135
+00:10:34,060 --> 00:10:39,400
+الرابع الخامس الان لكن برضه كمان مرة مش بالضرورة
+
+136
+00:10:39,400 --> 00:10:42,400
+ال value تبعت العناصر هذه تكون فعليا جاي عيشت ب
+
+137
+00:10:42,400 --> 00:10:45,360
+sequence أو جاية مرتبة فالعندي لإن اتفقنا أن
+
+138
+00:10:45,360 --> 00:10:50,000
+الترتيب لا يعني شيء هال مجرد عشان أقول العنصر
+
+139
+00:10:50,000 --> 00:10:54,020
+منزلة في العنصر جديش التاني الرابع الخامس الان إلى
+
+140
+00:10:54,020 --> 00:11:01,290
+آخرهم العناصرفي وصف المجموعات .. طبعا احنا اتفقنا
+
+141
+00:11:01,290 --> 00:11:04,670
+الـ Calibrations أساسية في كتبتها في وصف المجموعات
+
+142
+00:11:04,670 --> 00:11:08,750
+عندي قوراكتين في عند الـ Roster method الـ Roster
+
+143
+00:11:08,750 --> 00:11:11,790
+method بيقول أنا بكتب العناصر تابعة المجموعة في
+
+144
+00:11:11,790 --> 00:11:16,710
+داخل الأقلاص بغض النظر عن عددهم طب ممتاز باجي بقول
+
+145
+00:11:16,710 --> 00:11:24,170
+ABCD مجموعة فيها أربع حروف باجي بقول من صفر لتسعة
+
+146
+00:11:24,170 --> 00:11:30,410
+اللي هي ال digitتمام عشرة طيب لو كبرى تكتر من هيك
+
+147
+00:11:30,410 --> 00:11:35,450
+بتصير الأمور شوية مزعجة في ال roster بيقول إذا كان
+
+148
+00:11:35,450 --> 00:11:38,910
+ال sequence هذه أو الأرقام هذه familiar معاها
+
+149
+00:11:38,910 --> 00:11:42,870
+بنستخدم ال ellipses أو النقاط عشان أقوله على نفس
+
+150
+00:11:42,870 --> 00:11:49,410
+السياق هذا عد بيجي بقول ليه ABC وحطيلي ال ellipses
+
+151
+00:11:49,410 --> 00:11:54,350
+تلت نقاط هذهوالـ Z ايش بتفهم منها انت مباشرة؟ انه
+
+152
+00:11:54,350 --> 00:11:58,270
+قاعد بتكلم على مجموعة الحروف الأبجدية الإنجليزية
+
+153
+00:11:58,270 --> 00:12:06,550
+لأ باجب اقول انه في مجموعة واحد اتنين و بحط مية
+
+154
+00:12:06,550 --> 00:12:12,490
+مباشرة مباشرة هخطر في بالك او هتفهم ان واحد اتنين
+
+155
+00:12:12,490 --> 00:12:16,510
+تلاتة اربعة لحد وين؟ المية لكن شوف المجموعة داني
+
+156
+00:12:16,510 --> 00:12:25,060
+شويه هتختلف الأمور واحدتلاتة .. خمسة .. وحقية الـ
+
+157
+00:12:25,060 --> 00:12:32,280
+ellipses لتسعة وتسعين .. الأعداد الفردية الأقل من
+
+158
+00:12:32,280 --> 00:12:35,660
+مائة .. بقى بالسبعة وسبعين منهم .. اه منهم .. بقى
+
+159
+00:12:35,660 --> 00:12:40,280
+مش مكتوبة .. حالة محالها مين؟ التلات نقاط أو ال
+
+160
+00:12:40,280 --> 00:12:44,080
+ellipses اللي موجودة جدامي هن .. تمام؟ اللي هي
+
+161
+00:12:44,080 --> 00:12:45,800
+ممكن زي ما يقول زميلكم جاعة قلخ ..
+
+162
+00:12:50,270 --> 00:12:56,550
+المجموعة الـ vowels باللغة الإنجليزية حروف العلة A
+
+163
+00:12:56,550 --> 00:13:07,570
+-U-I-O-U لسه ما هو حرف العلة لأنها
+
+164
+00:13:07,570 --> 00:13:14,110
+علة في تمييزها عند الكتابةطبعا؟ لأنه يجب أن تكون
+
+165
+00:13:14,110 --> 00:13:17,730
+حافظ ال spelling صح عشان تقدر أن الكلمة هذه تكتب
+
+166
+00:13:17,730 --> 00:13:22,030
+بال O ولا بال U؟ و الترتيب تبعتهم؟ طبعا؟ غير هكذا
+
+167
+00:13:22,030 --> 00:13:31,110
+العليل لما بتأوه .. انت تخيل نفسك تقفضهم واحد ورا
+
+168
+00:13:31,110 --> 00:13:34,690
+التاني على رأي زميلنا جينا للشلاليت
+
+169
+00:13:37,780 --> 00:13:42,740
+مجموعة الـ odd positive integer less than عشرة
+
+170
+00:13:42,740 --> 00:13:50,160
+واحد اتنين واحد تلاتة خمسة سبعة تسعة مجموعة ال
+
+171
+00:13:50,160 --> 00:13:55,720
+positive integer الاقل من مية فانت ممكن تصيغ ..
+
+172
+00:13:55,720 --> 00:13:59,280
+كيف ما تصيغ الأقام اللي موجودة عندك فبتكون الأمور
+
+173
+00:13:59,280 --> 00:14:06,610
+تمام من المجموعات اللي احنا بنعرفها بشكل كويسالـ
+
+174
+00:14:06,610 --> 00:14:10,230
+Natural number، مجموعة الأعداد الطبيعية، واحد،
+
+175
+00:14:10,230 --> 00:14:14,330
+اتنين، تلاتة، أربع، بس ملاحظة، كتابنا تبع الـ
+
+176
+00:14:14,330 --> 00:14:17,730
+Discrete Mathematics تبع الفصل هذا، بقول إن الـ
+
+177
+00:14:17,730 --> 00:14:24,250
+Natural number بتبدأ من وين؟ من صفر طب احنا مع مين
+
+178
+00:14:24,250 --> 00:14:28,780
+بدنا نشتغل؟نشتغل مع الكتاب؟ مع الكتاب مش قضوية
+
+179
+00:14:28,780 --> 00:14:31,920
+كتير أنا بالنسبة لو عدلت المثال و كتبته زي ما احنا
+
+180
+00:14:31,920 --> 00:14:36,000
+ياش متفق انه زي ما احنا بنتعامل مع المجموعة طب يا
+
+181
+00:14:36,000 --> 00:14:38,580
+أستاذ لو انت بقى تجيبلنا مثال أو سؤال فنحله في
+
+182
+00:14:38,580 --> 00:14:41,780
+الكتاب فنحله على صفر ولا بدون مش هتفرج كتير معايا
+
+183
+00:14:41,780 --> 00:14:45,760
+هذه الساعة مش هندج عليك او بدي مجموعة .. في
+
+184
+00:14:45,760 --> 00:14:49,520
+مجموعات تانية في زبد و في Q و في R ماتجلجش
+
+185
+00:14:49,520 --> 00:14:53,780
+فنستمعنها من الأسئلة و برا أيه راسنا عشان نخلكاش
+
+186
+00:14:53,780 --> 00:14:58,140
+أياش تغلط فيها و تلطخمبس انا حبيت اناوحلك ان
+
+187
+00:14:58,140 --> 00:15:03,680
+الكتاب فعليا هذا من الناس اللي بتعد الصفر من ضمن
+
+188
+00:15:03,680 --> 00:15:07,460
+ال natural number و احنا اتفقنا أساسا ان الصفر مش
+
+189
+00:15:07,460 --> 00:15:10,960
+من ال natural number لأنه أساس وجودها من أجل العد
+
+190
+00:15:10,960 --> 00:15:15,600
+والترتيب مابجيش اقول أن العنصر رقم صفر او العنصر
+
+191
+00:15:15,600 --> 00:15:20,620
+لما بتبدأ تعد بتبدأ تعد صفر من واحد وبالتالي هذا
+
+192
+00:15:20,620 --> 00:15:26,700
+كان أساس ال natural number anyway ال ZZ Plus مش Z
+
+193
+00:15:26,700 --> 00:15:31,860
+Star Z Plus يعني مجموعة الأعداد الموجبة اللي بتبدأ
+
+194
+00:15:31,860 --> 00:15:34,560
+واحد اتنين تلاتة اللي المفروض تساوي ال natural
+
+195
+00:15:34,560 --> 00:15:39,420
+number حسب ال definition اللي فوق Q مجموعة الأعداد
+
+196
+00:15:39,420 --> 00:15:47,300
+المسبية وال R مجموعة الأعداد الحقيقية من
+
+197
+00:15:47,300 --> 00:15:51,380
+المجموعات المشهورة كذلك ال Phi المجموعة الفارغة
+
+198
+00:15:55,140 --> 00:15:57,780
+مافيش فيها ولا عنصر زي ما قلنا قبل شوية أنا في
+
+199
+00:15:57,780 --> 00:16:01,640
+عندي مجموعة إلها إسم وفي العناصر تبعونها إلهم صفة
+
+200
+00:16:01,640 --> 00:16:07,720
+لكن ولا حد لسه في داخل المجموعة هذه ماحدش حقق
+
+201
+00:16:07,720 --> 00:16:12,420
+الخصية أو الصفة المطلوبة حاليًا الـ A تساوي
+
+202
+00:16:12,420 --> 00:16:19,480
+المجموعة Z أو تساوي المجموعة اللي فيها عنصر واحد
+
+203
+00:16:19,480 --> 00:16:28,190
+اللي هو الـ Z الأن لاحظ الـ Z تنتميللـ A لكن الـ Z
+
+204
+00:16:28,190 --> 00:16:33,130
+كأنصر هنا ليه تساوي الـ Z كمجموعة؟ لأن أحنا الأن
+
+205
+00:16:33,130 --> 00:16:38,690
+بدنا نفرق بين عنصر وبين مجموعة إيش الحكل بينهم؟
+
+206
+00:16:38,690 --> 00:16:42,010
+الأقواص .. الأقواص .. إذا الـ curly braces هذه
+
+207
+00:16:42,010 --> 00:16:45,290
+الموجودة معاك .. أنا بتكلم على مجموعة .. بتكلم على
+
+208
+00:16:45,290 --> 00:16:54,310
+مجموعة .. تمام الـ A هي عبارة عن مجموعةعاصرها ..
+
+209
+00:16:54,310 --> 00:17:00,030
+كم عنصر في الـ A يا شباب؟ كم عنصر في الـ A؟ عنصرين
+
+210
+00:17:00,030 --> 00:17:05,530
+.. المجموعة الأولى .. عنصرين .. كل عنصر عبارة عن
+
+211
+00:17:05,530 --> 00:17:11,610
+مجموعة بي و سي .. والمجموعة التانية أو العنصر
+
+212
+00:17:11,610 --> 00:17:16,950
+التاني في المجموعة عبارة عن مجموعة فيها C و X و D
+
+213
+00:17:16,950 --> 00:17:24,100
+وبدى منك شغلة انتبه وما تحاولش تسقطاللي بنعرفه عن
+
+214
+00:17:24,100 --> 00:17:28,500
+الأعداد أن كل عدد طبيعي
+
+215
+00:17:28,500 --> 00:17:32,820
+هو عبارة عن عدد صحيح وكل عدد صحيح عبارة عن عدد
+
+216
+00:17:32,820 --> 00:17:37,220
+نسبي وكل عدد نسبي عبارة عن عدد حقيقي العلاقة هذه
+
+217
+00:17:37,220 --> 00:17:42,060
+شويه لسالي إياها يعني لو أنا جيت سألتك بقولتلك ال
+
+218
+00:17:42,060 --> 00:17:50,180
+B في المثال هذا كان تميء لل A إيش
+
+219
+00:17:50,180 --> 00:17:51,220
+هترد عليا؟
+
+220
+00:17:54,800 --> 00:18:00,400
+false ليش؟ لأن احنا متفقين لما سألتك كم عنصر في
+
+221
+00:18:00,400 --> 00:18:07,800
+المجموعة ايش قلت ليه؟ اثنين فيها عنصرين هل ال B ها
+
+222
+00:18:07,800 --> 00:18:13,040
+دي تساوي احد العنصرين؟ يعني بين جسين هل ال B هك
+
+223
+00:18:13,040 --> 00:18:19,420
+بدها تساوي B و C؟ هذه لا تساوي لأن هذه مجموعة و
+
+224
+00:18:19,420 --> 00:18:26,510
+هذه عنصر و ال B ها دي لا تساويC و X و D لأنها أيضا
+
+225
+00:18:26,510 --> 00:18:32,170
+هذه مجموعة وبالتالي الـ B لا تنتمي إلى الـ A طيب
+
+226
+00:18:32,170 --> 00:18:34,530
+يا دكتور شوية شوية علينا احنا بنقول اننا لدينا
+
+227
+00:18:34,530 --> 00:18:40,450
+مجموعة كبيرة فيها مجموعتين فيها مجموعتين لأن مش
+
+228
+00:18:40,450 --> 00:18:44,750
+المنطق بيقول ان علاصر المجموعتين هدولة هما بنتمل
+
+229
+00:18:44,750 --> 00:18:47,570
+المجموعة الأكبر يعني يا دكتور انت جاهز بيقول انا
+
+230
+00:18:47,570 --> 00:18:52,400
+احنا كلاب رياضيات منفصلةتمام؟ والرياضيات منفصلة
+
+231
+00:18:52,400 --> 00:18:56,000
+جزء من مساق الـ IT، مساقات الـ IT، ما تحب تقولها
+
+232
+00:18:56,000 --> 00:18:58,420
+بـ IT، ما تقدرش تقولها لا، انت تقولها بريبات
+
+233
+00:18:58,420 --> 00:19:05,050
+منفصلة وبسالعلاقة شويهة لشباب مختلفة مختلفة تبع لل
+
+234
+00:19:05,050 --> 00:19:09,090
+rules اللي احنا عايش بيبقى مطابقها في غير او في
+
+235
+00:19:09,090 --> 00:19:11,190
+العلاقة اللي احنا بنوصفها سواء كانت في ال members
+
+236
+00:19:11,190 --> 00:19:15,210
+او في علاقتنا بالمساقات والكلية والجامعة علاقة
+
+237
+00:19:15,210 --> 00:19:21,150
+subset مجموعات جزئية مجموعات جزئية مش علاقة عضوية
+
+238
+00:19:22,770 --> 00:19:28,750
+أشبه بالتوارث، وعندما أتكلم في مجموعة جزئية، يعني
+
+239
+00:19:28,750 --> 00:19:38,090
+أن كل مجموعة في الجامعة تم تقسيمها لمجموعات مختلفة
+
+240
+00:19:38,090 --> 00:19:42,290
+لكليات، وعناصر الكليات تم تقسيمهم لمجموعات مختلفة
+
+241
+00:19:42,290 --> 00:19:47,720
+لإقسامتقوى التخصصات والتخصصات تم تقسيم الطلاب فيهم
+
+242
+00:19:47,720 --> 00:19:51,460
+لمستويات وكل مستوى له مجموعة من المساقات لاحظ ان
+
+243
+00:19:51,460 --> 00:19:58,600
+العلاقة subset دزئية من المجموعة بس هنا لأ هنا لأ
+
+244
+00:19:58,600 --> 00:20:02,300
+هنا عضوية لأن المجموعة هذه بتمثل عنصر واحد
+
+245
+00:20:02,300 --> 00:20:11,160
+المجموعة هذه بتمثل عنصر واحد طيب يعني بينفعش ..
+
+246
+00:20:11,160 --> 00:20:24,020
+بينفعشأجي أقول capital X بدها تساوي ال N و ال Z و
+
+247
+00:20:24,020 --> 00:20:31,300
+ال Q و ال R الآن
+
+248
+00:20:31,300 --> 00:20:38,700
+لو أنا سألتك جذر التنين تنتمي لل X؟ جذر التنين
+
+249
+00:20:38,700 --> 00:20:42,440
+عنصر في المجموعة X؟ لأ
+
+250
+00:20:44,680 --> 00:20:48,460
+من العناصر اي واحد من الخمسة هدول او من الأربعة
+
+251
+00:20:48,460 --> 00:20:55,260
+هدول عفوا كمان مرة عشان اتكلم ينتمي ينتمي لازم
+
+252
+00:20:55,260 --> 00:20:58,960
+اشوف العنصر بنفس صيغته موجود بنفس العنصر يعني هيك
+
+253
+00:20:58,960 --> 00:21:05,470
+لو انا جيت وقلتلك ال Y او ال I تنتميللـ X هذه اللي
+
+254
+00:21:05,470 --> 00:21:09,590
+عرفناها هان ايش المطلوب منك تساوي تروح تاخد الـ I
+
+255
+00:21:09,590 --> 00:21:12,430
+هذه كما هي هيك زي ما هي مكتوبة جاب الإشارة اللي
+
+256
+00:21:12,430 --> 00:21:16,810
+ينتمي و تروح تدور عليها وين في عناصر المجموعة هاي
+
+257
+00:21:16,810 --> 00:21:22,250
+الأنصار الأول هى يساوي الـ I هذه؟ لأ ايش .. ايش
+
+258
+00:21:22,250 --> 00:21:26,270
+الفاصل ما بين العناصر؟ الكمة هى الأنصار التاني لا
+
+259
+00:21:26,270 --> 00:21:36,140
+يساوي I التالت الرابع ماته I لا تمتمي لمين؟ لل Xهك
+
+260
+00:21:36,140 --> 00:21:41,360
+بدي يكون قرارك وهذا ال role أو هذا القانون الأول
+
+261
+00:21:41,360 --> 00:21:45,460
+في التعامل مع المجموعة إذا ال answer مش مكتوب بشكل
+
+262
+00:21:45,460 --> 00:21:49,700
+مباشر بقولش عليه تعالى أورجيك إحنا إيش لما كنا
+
+263
+00:21:49,700 --> 00:21:53,640
+نقصد من وين جيبنا كل integer أو عفوا كل عدد طبيعي
+
+264
+00:21:53,640 --> 00:21:59,800
+عدد صحيح قلنا إنه الآن أو خلينا نرجع لل slide
+
+265
+00:21:59,800 --> 00:22:00,220
+الجابر
+
+266
+00:22:08,520 --> 00:22:11,280
+لما اتينا و كتبنا الـ natural number كتبنا واحد
+
+267
+00:22:11,280 --> 00:22:16,200
+اتنين تلاتة إلى ما لا نهاية مظبوط؟ مظبوط؟ و لما
+
+268
+00:22:16,200 --> 00:22:22,480
+اتيت و كتبت ال Z ايش كتبناه؟ مكتبت ال cash مكتبت
+
+269
+00:22:22,480 --> 00:22:28,040
+ال cash ال N فاصلة صفر فاصلة سالب واحد سالب اتنين
+
+270
+00:22:28,040 --> 00:22:31,980
+إلى ما لا نهاية ايش كتبناه لك؟ كتبناه العناصر كل
+
+271
+00:22:31,980 --> 00:22:37,680
+هياتها الان لو اتيت و سألتك التلاتة
+
+272
+00:22:39,180 --> 00:22:46,740
+تنتمي للأن صحيح true التلاتة
+
+273
+00:22:46,740 --> 00:22:52,820
+تنتمي للزد true لأن هي مكتوبة موجودة عندي لاحظ
+
+274
+00:22:52,820 --> 00:22:55,020
+العلاقة مختلفة تماما على الأمثل اللي احنا عايش
+
+275
+00:22:55,020 --> 00:22:59,900
+حكينا عليها قبل شوية تمام معناته احنا الآن متفقين
+
+276
+00:22:59,900 --> 00:23:04,640
+متفقين انه الآن لما بتكلم في الينتمي او العنصر هذا
+
+277
+00:23:04,640 --> 00:23:09,980
+في المجموعة لازم اشوف العنصر مثل ما هو في داخلقاس
+
+278
+00:23:09,980 --> 00:23:14,940
+المجموعة نرجح مرة عشان نرجح من وين بدخلنا في
+
+279
+00:23:14,940 --> 00:23:21,900
+التفاصيل الكتيرة A عبارة عن مجموعة فيها عنصرين كل
+
+280
+00:23:21,900 --> 00:23:27,040
+عنصر بمثابة مجموعة X لا تنتمي لل A
+
+281
+00:23:34,330 --> 00:23:39,090
+الـ A بدها تساوي المجموعة اللي بتحتوي على أنصر
+
+282
+00:23:39,090 --> 00:23:47,390
+واحد و هو مثابت مجموعة X و Y هيها ولا لا؟ الآن الـ
+
+283
+00:23:47,390 --> 00:23:51,790
+X و Y هذه اللي داخل الـ curly braces هي عبارة عن
+
+284
+00:23:51,790 --> 00:23:58,210
+أنصر مصبوط؟ وبالتالي أنا بقدر أقول إن المجموعة هذه
+
+285
+00:23:58,210 --> 00:24:02,510
+تنتمي للـ A ليش؟ لأن هي زي ما هي هيك أخدت منها
+
+286
+00:24:03,450 --> 00:24:07,130
+ودورت عليها في داخل المجموعة فلجت كما هي فبتكلم عن
+
+287
+00:24:07,130 --> 00:24:14,730
+عنصر وانت بيه ان X المجموعة هذه لا تساوي المجموعة
+
+288
+00:24:14,730 --> 00:24:18,630
+هذه ايوة
+
+289
+00:24:18,630 --> 00:24:23,430
+المجموعة هذه فيها عنصرين المجموعة هذه فيها عنصر
+
+290
+00:24:23,430 --> 00:24:28,630
+واحد وبالتالي مجموعتين عدم على صرهم مختلفين مستحيل
+
+291
+00:24:28,630 --> 00:24:31,750
+يكونوا متساويتين نعم
+
+292
+00:24:45,960 --> 00:24:59,200
+عنصر الأول مجموعة X وY كم
+
+293
+00:24:59,200 --> 00:25:03,260
+عنصر
+
+294
+00:25:03,260 --> 00:25:09,900
+في المجموعة يا شباب؟ حرام عليكمهذا اسمه تكرار احنا
+
+295
+00:25:09,900 --> 00:25:13,560
+اتفقنا اعادة او ترتيب العناصر لا يعني شيء في
+
+296
+00:25:13,560 --> 00:25:20,460
+المجموعة يعني هذا العنصر هو عبارة عن X و Y و
+
+297
+00:25:20,460 --> 00:25:24,420
+التكرار
+
+298
+00:25:24,420 --> 00:25:28,680
+في المجموعة لا يعني شيء مالوش فايدة وبالتالي
+
+299
+00:25:28,680 --> 00:25:34,300
+المجموعة بتحتوي على عنصر واحد فقط يمكن كان سؤالك
+
+300
+00:25:34,300 --> 00:25:40,040
+يكون ألطفلو انا اجيتها و قلت ان الـ B .. او عفوا
+
+301
+00:25:40,040 --> 00:25:47,920
+.. C و الـ B كمجموعة تنتمي للـ A صح ولا غلط؟ صح ..
+
+302
+00:25:47,920 --> 00:25:52,880
+صح .. صح .. صح .. صح .. صح .. صح .. صح .. صح .. صح
+
+303
+00:25:52,880 --> 00:25:53,860
+.. صح .. صح .. صح .. صح .. صح .. صح .. صح .. صح ..
+
+304
+00:25:53,860 --> 00:25:53,920
+صح .. صح .. صح .. صح .. صح .. صح .. صح .. صح .. صح
+
+305
+00:25:53,920 --> 00:25:54,540
+.. صح .. صح .. صح .. صح .. صح .. صح .. صح .. صح ..
+
+306
+00:25:54,540 --> 00:25:58,360
+صح .. صح .. صح .. صح .. صح .. صح .. صح .. صح .. صح
+
+307
+00:25:58,360 --> 00:25:59,000
+.. صح .. صح .. صح .. صح .. صح .. صح .. صح .. صح ..
+
+308
+00:25:59,000 --> 00:26:03,220
+صح .. صح .. صح .. صح .. صح .. صح .. صح
+
+309
+00:26:06,990 --> 00:26:12,490
+true ليش؟ لأن المجموعة هذه هي عبارة عن عنصر في
+
+310
+00:26:12,490 --> 00:26:19,030
+المجموعة هيها في الـA وبالتالي هي member of تمام؟
+
+311
+00:26:19,030 --> 00:26:27,650
+في أي سؤال حتى اللحظة يا شباب؟ الأمور تمام؟ الصورة
+
+312
+00:26:27,650 --> 00:26:29,710
+التانية في تعريف المجموعات احنا الأولى قلنا
+
+313
+00:26:29,710 --> 00:26:33,430
+الـRosterتكتب المجموعات وتذكر العناصر أو تستخدم
+
+314
+00:26:33,430 --> 00:26:37,130
+الـ ellipses اللي هي النقاط عشان تكمل وصف العناصر
+
+315
+00:26:37,130 --> 00:26:41,110
+اللي معروفة في أين دي شغل اسمها الـ Builder
+
+316
+00:26:41,110 --> 00:26:48,870
+Notation باستخدام صيغة المجموعة صيغة المجموعة طبعا
+
+317
+00:26:48,870 --> 00:26:55,210
+الـ curly braces الأقواص موجودة من البداية مافيش
+
+318
+00:26:55,210 --> 00:26:59,270
+عليها خلاف لكن في داخل الأقواص هذه شو بدك تكتب؟
+
+319
+00:26:59,270 --> 00:27:07,800
+بتكتب Exhibitionيعبر عن عناصر المجموعة تمام؟ وبعد
+
+320
+00:27:07,800 --> 00:27:12,560
+الـ expression بتحط ال properties اللي لازم يحققها
+
+321
+00:27:12,560 --> 00:27:17,920
+كل عناصر المجموعة وبالتالي
+
+322
+00:27:17,920 --> 00:27:21,500
+لما أنا بتكلم عن ال builder notation set builder
+
+323
+00:27:21,500 --> 00:27:24,980
+notation جاعت بتكلم أن هذا ال builder أو هذا الوصف
+
+324
+00:27:24,980 --> 00:27:30,320
+بدي يوصف وبشكل دقيق العناصر اللي لازم يحققها كل
+
+325
+00:27:30,320 --> 00:27:37,110
+عناصرالمجموعة او يحقق الصفات بيحدد الصفات اللي كل
+
+326
+00:27:37,110 --> 00:27:42,590
+عناصر المجموعة لازم اتحددها او اتحققها تمام تعالى
+
+327
+00:27:42,590 --> 00:27:51,370
+نشوف مثال بقول ال S تساوي واسم جموعة X اللي هي
+
+328
+00:27:51,370 --> 00:27:57,370
+مثال ال expression اللي عندي X ايش مالها X X is a
+
+329
+00:27:57,370 --> 00:28:04,040
+positive integer less thanمية ايش بتفهم منها؟ من
+
+330
+00:28:04,040 --> 00:28:11,940
+واحد لتسعة وتسعين ليه اشنا بقولها less than وواحد
+
+331
+00:28:11,940 --> 00:28:20,200
+اش جالي هو positive integer يعني بصيغة roster بقول
+
+332
+00:28:20,200 --> 00:28:26,340
+واحد اتنين تلاتة ال ellipses والتسعة وتسعين
+
+333
+00:28:30,310 --> 00:28:34,450
+انت بتجرب التانية، ما شاء الله، كويس، إيش بيقوللي؟
+
+334
+00:28:34,450 --> 00:28:39,430
+في التانية بيقوللي X is an odd positive integer
+
+335
+00:28:39,430 --> 00:28:50,950
+الصفته عدد فردي موجب، عدد فردي موجب أقل من عشرة،
+
+336
+00:28:50,950 --> 00:28:56,750
+واحد، تلاتة، خمسة، سبعة والتسعة
+
+337
+00:28:59,390 --> 00:29:04,030
+مبتعد شوف العدد الفردي كمان مرة كيف وصفه قال لي X
+
+338
+00:29:04,030 --> 00:29:09,930
+كان تميء إلى Z plus لاحظ صيغة ال expression شوية
+
+339
+00:29:09,930 --> 00:29:16,590
+اتغيرت هنا ولا لا مش قضية في الآخر هو عمال يوصف
+
+340
+00:29:16,590 --> 00:29:19,770
+للعراصر اللي بيتكلم عليها فقال لي ان العنصر تبعي
+
+341
+00:29:19,770 --> 00:29:26,030
+هو عبارة عن عدد صحيح موجب ممتاز قال لي ايش X is
+
+342
+00:29:26,030 --> 00:29:34,600
+oddعدد صحيح موجب أو فردي and أقل من عشرة نفس
+
+343
+00:29:34,600 --> 00:29:37,800
+الكلام اللي فوق تماما، بس اختلف في وين؟ في ال
+
+344
+00:29:37,800 --> 00:29:41,500
+description أو في صيغة الوصف الدقيقة لكل عناصر
+
+345
+00:29:41,500 --> 00:29:47,560
+المجموعة لاحظ، لو أخدت أي عنصر في المجموعة، لازم
+
+346
+00:29:47,560 --> 00:29:50,920
+يطبق عليه الوصف اللي موجود هنا لازم يطبق عليه
+
+347
+00:29:50,920 --> 00:29:52,440
+الوصف اللي موجود بالتمام
+
+348
+00:29:56,460 --> 00:30:02,560
+الآن تعالى نشوف المثال الأخير Q plus Q هي عبارة عن
+
+349
+00:30:02,560 --> 00:30:08,660
+ال rational number وال plus positive X تنتمي إلى R
+
+350
+00:30:08,660 --> 00:30:14,560
+طبيعي هو X عبارة عن عدد حقيقي ايه الصفة العدد
+
+351
+00:30:14,560 --> 00:30:23,360
+الحقيقي هذا؟X تساوي P على Q يعني العدل الحقيقي هذا
+
+352
+00:30:23,360 --> 00:30:30,560
+نكتبه على صورة كسر بسط و مقام for some positive
+
+353
+00:30:30,560 --> 00:30:38,150
+integers P و Q قصصت إياهمقال لي لأعداد حقيقية بحيث
+
+354
+00:30:38,150 --> 00:30:42,570
+ان بي و كيو عبارة عن positive integers positive
+
+355
+00:30:42,570 --> 00:30:47,810
+integers يعني الصفر مش منهم تمام ولا السلب منهم
+
+356
+00:30:47,810 --> 00:30:52,150
+وبالتالي بصتوا المقام موجبات فال output هيكون موجب
+
+357
+00:30:52,150 --> 00:30:59,910
+هايوصف للرقم اللي موجود عندي هان تمام ال
+
+358
+00:30:59,910 --> 00:31:05,050
+predicateتذكرها؟ أنا بذكرك فيها قولنا الـ
+
+359
+00:31:05,050 --> 00:31:09,190
+predicate function في الـ chapter الماضي P of X
+
+360
+00:31:09,190 --> 00:31:14,910
+denoted by أن
+
+361
+00:31:14,910 --> 00:31:20,890
+X أكبر من 3 أن P of X هي عبارة عن predicate
+
+362
+00:31:20,890 --> 00:31:26,330
+function بتشير إلى X أكبر من 3 مين اللي predicated
+
+363
+00:31:26,330 --> 00:31:32,180
+التلاتة؟ قيمة المصندق إليهاقول هذه أنا بقيّمهم
+
+364
+00:31:32,180 --> 00:31:37,220
+بناءً على قيمة الـ X بي أوف خمسة إيش قيمتها؟ true
+
+365
+00:31:37,220 --> 00:31:45,540
+بي أوف تلاتة fourth الآن ممكن تستخدم لـ predicate
+
+366
+00:31:45,540 --> 00:31:51,300
+في الـ set builder notation عشان توصف عراصر
+
+367
+00:31:51,300 --> 00:31:59,830
+المجموعة X اللي بتحقق عراصر المجموعةيعني بين قسين
+
+368
+00:31:59,830 --> 00:32:08,330
+انا بقدر اكتبها هيك X حيث X أكبر من 3 ايه شرصة
+
+369
+00:32:08,330 --> 00:32:12,430
+المجموعة اللي هون يا شباب؟ كل ال positive number
+
+370
+00:32:12,430 --> 00:32:19,210
+.. كل ال positive real number اللي أكبر من 3؟ 4
+
+371
+00:32:19,210 --> 00:32:21,050
+ليش قلت real number؟
+
+372
+00:32:23,440 --> 00:32:27,080
+لأنه لم يحدد ليش الصفة العدد وبالتالي انا روحت على
+
+373
+00:32:27,080 --> 00:32:31,060
+أكبر صورة ممكنة مع الـ real number وليش رأيك؟ بدك
+
+374
+00:32:31,060 --> 00:32:37,440
+تقيدها و تتكلم على integers بتقولوا and ال X تنتمي
+
+375
+00:32:37,440 --> 00:32:42,960
+إلى ال Z و
+
+376
+00:32:42,960 --> 00:32:47,360
+هكذا لاحظ ان انا بتكلم على predicate من الأمثلة
+
+377
+00:32:47,360 --> 00:32:49,960
+اللي ممكن تكون على ال predicate لو انا أعرفتلك ال
+
+378
+00:32:49,960 --> 00:32:59,240
+Sهي عبارة عن المجموعة لعناصرها X واتحقق
+
+379
+00:32:59,240 --> 00:33:06,180
+prime X ان ال X is prime الأعداد الأولية .. إيش
+
+380
+00:33:06,180 --> 00:33:12,210
+الأعداد الأولية يا شباب؟تنين هو عبارة عن كل هدد
+
+381
+00:33:12,210 --> 00:33:20,690
+صحيح موجب أكبر أو يساوي 2 يقبل القسمة أو لا يقبل
+
+382
+00:33:20,690 --> 00:33:25,670
+القسمة إلا على نفسه هو على الواحد مش هنزعلك فلو
+
+383
+00:33:25,670 --> 00:33:28,270
+جيبنا أي عدد في الدنيا بسميه على الواحد حق .. okay
+
+384
+00:33:28,270 --> 00:33:38,640
+الآن نقدر نكتبهم؟ هو يبقى 23 .. 5 .. 7 .. 11 .. 13
+
+385
+00:33:38,640 --> 00:33:51,680
+.. 17 .. 19 .. 23 .. 31 .. 29 .. 27 .. 29 .. 31 في
+
+386
+00:33:51,680 --> 00:33:57,740
+الآخر مش هتقدر يا صاحبي مش هتقدر تحط لبس كمان عرف
+
+387
+00:33:57,740 --> 00:34:02,700
+ليش؟ لإن مافيش صيغة ثابتة تعتمد عليها عشان تمشي
+
+388
+00:34:03,780 --> 00:34:08,800
+بجيهة العناصر عشان هي كد لما بنجي نتكلم نقول
+
+389
+00:34:08,800 --> 00:34:14,720
+مجموعة الأعداد الأولية وبنسكت معروفين خلصنا هو كل
+
+390
+00:34:14,720 --> 00:34:18,340
+عدد لا يقبل قسم عدد صحيح موجب لا يقبل قسم اللي على
+
+391
+00:34:18,340 --> 00:34:25,800
+نفسه خلصنا وبالتالي هي العدد الأولية تعالى نشوف
+
+392
+00:34:25,800 --> 00:34:31,060
+المثال اللي بعده جالي X او المجموعة A تعرف ب X
+
+393
+00:34:31,060 --> 00:34:39,420
+بالعناصر Xوال X تنتمي إلى N و X أكبر من 7 ماذا
+
+394
+00:34:39,420 --> 00:34:48,500
+يعني؟ مجموعة الأعداد الطبيعية الأكبر من 7 الأخيرة
+
+395
+00:34:48,500 --> 00:34:55,520
+.. الآن هذه معناتها أن عراسر المجموعة تنتمي إلى N
+
+396
+00:34:57,290 --> 00:35:01,170
+الـ Natural number هو عبارة عن عدد صحيح موجب أكبر
+
+397
+00:35:01,170 --> 00:35:06,810
+من واحد Natural number أكبر من واحد تمام؟ بحيث أن
+
+398
+00:35:06,810 --> 00:35:13,250
+صفة الـ N هذه لو ربعتها زائد واحد تساوي صفر مين
+
+399
+00:35:13,250 --> 00:35:17,390
+بيحقق المعادلة هذه؟ تربيع الرقم زائد واحد يساوي
+
+400
+00:35:17,390 --> 00:35:22,610
+صفر أساسا التربيع يضمن اليهم كلهم موجب بصبوط؟ وزيد
+
+401
+00:35:22,610 --> 00:35:27,480
+عليهم واحدبما أن هي أساساً الأعداد اللي عندى
+
+402
+00:35:27,480 --> 00:35:31,740
+natural number يعني ماعنديش سالب فاجلش واحد فواحد
+
+403
+00:35:31,740 --> 00:35:36,420
+زائد واحد اتنين واتنين لا تساوي الصفر ولو على رأي
+
+404
+00:35:36,420 --> 00:35:40,080
+الكتاب بدي اعتمد الصفر من ال natural number صفر
+
+405
+00:35:40,080 --> 00:35:44,620
+تربيع صفر زائد واحد واحد واحد لا تساوي صفر
+
+406
+00:35:44,620 --> 00:35:48,980
+وبالتالي مافيش ولا element في ال natural number
+
+407
+00:35:48,980 --> 00:35:56,380
+بيحقق ال property هاي وبالتالي أنا بروحباتجاهها
+
+408
+00:35:56,380 --> 00:36:00,660
+تمام okay
+
+409
+00:36:00,660 --> 00:36:08,060
+كيف ممكن نعبر عن مجموعة الأعداد النسبية كيف ممكن
+
+410
+00:36:08,060 --> 00:36:14,540
+نعبر عن مجموعة الأعداد النسبية Q بدها تساوي across
+
+411
+00:36:14,540 --> 00:36:22,550
+و Xمباشرة notation builder بتشتغل بالشكل هذا هي
+
+412
+00:36:22,550 --> 00:36:27,310
+عبارة عن X ال X لصفتها واحد اتنين تلفت بتفصل فيها
+
+413
+00:36:27,310 --> 00:36:38,850
+الآن ايه صفة ال X؟ X بتتساوي A على B بس بس
+
+414
+00:36:38,850 --> 00:36:46,310
+لسه أنت A و B ينتمي لإيش؟
+
+415
+00:36:48,230 --> 00:37:02,270
+للـ Z عداد صحيحة and ال B لا تساوي الصفر خلصت خلصت
+
+416
+00:37:02,270 --> 00:37:06,070
+مش بالزيادة انت اشتغلت بس عينينا مقلوب ماتتجملش
+
+417
+00:37:06,070 --> 00:37:09,650
+عينينا ولا بحاجة لان هيك المقلوب منك كان ممكن تكتب
+
+418
+00:37:09,650 --> 00:37:12,650
+موسيقى تانية Q
+
+419
+00:37:18,480 --> 00:37:30,080
+هي عبارة عن كل الكثور اللي فيها A تنتمي إلى Z و B
+
+420
+00:37:30,080 --> 00:37:39,480
+تنتمي إلى Z Plus بصيغة لا مصيرش وهي بصيغة أبسط من
+
+421
+00:37:39,480 --> 00:37:43,380
+أو خلّيني أقول التفصيل تبعها نفس التفصيل السابق
+
+422
+00:37:43,380 --> 00:37:48,860
+لكنه أسهل اعتمد فقط على two conditionsولا لأ؟ هذه
+
+423
+00:37:48,860 --> 00:37:54,120
+صح و هذه صح أي صيغة تكتبها انت الفكرة بتحدد ال
+
+424
+00:37:54,120 --> 00:37:58,480
+expression من العنصر اللي هان عشان بعد الفاصلة هذه
+
+425
+00:37:58,480 --> 00:38:02,700
+الجزء التاني تروح توصف ليها بشكل واضح ايش يكون
+
+426
+00:38:02,700 --> 00:38:09,760
+احنا قلنا هان هي عبارة عن الكسور البسط و مقام بحيث
+
+427
+00:38:09,760 --> 00:38:15,130
+انها تحقق كالتالي ان ال a تنتمي لل zعدد صحيحة
+
+428
+00:38:15,130 --> 00:38:21,130
+سالبة موجبة وصفر and الـ B فقط أعداد صحيحة موجبة
+
+429
+00:38:21,130 --> 00:38:25,450
+استخدمت منها الصفر وبالتالي تبقى العملية معرفة ولو
+
+430
+00:38:25,450 --> 00:38:29,190
+انا بدي .. أستاذ بدي سالب .. بدي سالب نص عدد نسلي
+
+431
+00:38:29,190 --> 00:38:34,710
+ماهي سالب واحد تنتمي إلى Z والتانين تنتمي إلى Z
+
+432
+00:38:34,710 --> 00:38:37,370
+plus مش بالضرورة السالب يكون للمقام
+
+433
+00:38:40,130 --> 00:38:44,710
+ممكن تحط N بدل ال Z بمشي الحل كمان يا شباب السؤال
+
+434
+00:38:44,710 --> 00:38:50,890
+اللي بيقرح نفسه هل ممكن تعطيني وصف لمجموعة الأعداد
+
+435
+00:38:50,890 --> 00:38:56,490
+الحقيقية اللي
+
+436
+00:38:56,490 --> 00:39:00,550
+هي ال R اديني وصف إلها كمجموعة أيه يا أحمد ماعلك
+
+437
+00:39:00,550 --> 00:39:05,170
+ساكت اليوم او
+
+438
+00:39:05,170 --> 00:39:15,800
+X طيب إيه صفة ال Rأيوة؟ ينتمي لإيش؟ الـQ أو العدد
+
+439
+00:39:15,800 --> 00:39:20,420
+الغير نسبية يعني
+
+440
+00:39:20,420 --> 00:39:29,020
+أصدركوا بقول والـR تنتمي لـQ أو الـR تنتمي للـI لا
+
+441
+00:39:29,020 --> 00:39:34,820
+irrational على فرض أنها عدد غير نسبية بس
+
+442
+00:39:34,820 --> 00:39:41,020
+يعني في الآخر ما .. ماديبتش معنى جديدماشي هالاشياء
+
+443
+00:39:41,020 --> 00:39:44,500
+بتقدر تجيلها وصف لأن المجموعة فعليا هذه بنسميها
+
+444
+00:39:44,500 --> 00:39:49,120
+universal set المجموعة اللي بتشمل كل شيء فصعب أنك
+
+445
+00:39:49,120 --> 00:39:52,640
+تروح تجيبلها وصف دقيق هي عبارة عن عدد حقيقي والـR
+
+446
+00:39:52,640 --> 00:39:57,620
+صفتها عدد حقيقي و بس مقدرش أنت فعليا هنا في مجموعة
+
+447
+00:39:57,620 --> 00:40:01,760
+زي ال universal set تفصلها بالكامل
+
+448
+00:40:05,700 --> 00:40:09,500
+في الـ Intervals ممكن نعبّرها بالـ Set Notation
+
+449
+00:40:09,500 --> 00:40:13,620
+الـ Intervals ممكن نستخدم الـ Notation أو ال
+
+450
+00:40:13,620 --> 00:40:16,420
+Builder Notation Set Builder Notation و نعرف
+
+451
+00:40:16,420 --> 00:40:19,480
+المجموعات بس باكتب انتباه كمان مرة ان الكتاب هنا
+
+452
+00:40:19,480 --> 00:40:24,940
+شوية ممكن يخربط استخدم في ال half او في ال .. في
+
+453
+00:40:24,940 --> 00:40:28,260
+ال open interval احنا سابقا اعتمدنا
+
+454
+00:40:30,340 --> 00:40:36,760
+نعكس الابتجاه، هذه فترة مغلقة وهذه فترة مفتوحة في
+
+455
+00:40:36,760 --> 00:40:43,320
+الكتاب اتمد على الجوس تمام؟ على ان الفترة المفتوحة
+
+456
+00:40:43,320 --> 00:40:47,440
+بدل الجوس المربع استخدم الجوس العادي نفس الكلام
+
+457
+00:40:47,440 --> 00:40:52,660
+انت مش هتفرج معاك تمام؟ بس عشان انا ابقى هك ما
+
+458
+00:40:52,660 --> 00:40:55,440
+تقوليش انت واني مودينا واحنا بنعرف شغلات غير هيك
+
+459
+00:40:57,020 --> 00:41:00,120
+Anyway في الفترة المفتوحة .. في الفترة المغلقة
+
+460
+00:41:00,120 --> 00:41:07,080
+اللي فوق A و B هي عبارة عن مجموعة الأرقام تمام؟ X
+
+461
+00:41:07,080 --> 00:41:12,580
+حيث أن X أكبر أو تساوي A لأنها مغلقة من عند ال A
+
+462
+00:41:12,580 --> 00:41:20,420
+and ال X أقل أو تساوي ال B مغلقة من عند ال B طبعا
+
+463
+00:41:20,420 --> 00:41:28,670
+هذا ممكن تتفصيلها هيك ادهارك X حيث ان ال Xأكبر أو
+
+464
+00:41:28,670 --> 00:41:37,810
+تساوي ال a and ال x أقل أو تساوي ال b مظبوط؟ نفس
+
+465
+00:41:37,810 --> 00:41:43,350
+الكلام اللي هنا و نفس الكلام بتنسيقه أو بتسقطه على
+
+466
+00:41:43,350 --> 00:41:52,410
+ال bagel intervals اللي موجودة عندي هنا ال
+
+467
+00:41:52,410 --> 00:41:57,250
+universal setالـ universal set هي عبارة عن
+
+468
+00:41:57,250 --> 00:42:02,530
+المجموعة اللي بتحتوي على كل ..
+
+469
+00:42:02,530 --> 00:42:08,330
+كل شيء ضمن بعض
+
+470
+00:42:08,330 --> 00:42:11,070
+الشروط أو بعض القيود لما باجي بقول إيش ال
+
+471
+00:42:11,070 --> 00:42:15,430
+universal set للأرقام أو للأعداد ال real number
+
+472
+00:42:15,430 --> 00:42:21,610
+إيش ال universal set للأعداد ال real number وإذا
+
+473
+00:42:21,610 --> 00:42:26,430
+بدك تكبر أكبر شوية بتقول ال complexولا لا؟ اه لان
+
+474
+00:42:26,430 --> 00:42:32,310
+انا جمعت ايش؟ التخيّلي تمام لو انا اجيت قولت ايش
+
+475
+00:42:32,310 --> 00:42:37,610
+ال universal set لمجموعة ال vowels يعني ايش
+
+476
+00:42:37,610 --> 00:42:42,570
+المجموعة اللي اكبر تمام من ال vowels و بتشملها في
+
+477
+00:42:42,570 --> 00:42:48,010
+داخلها هي مجموعة ال alphabetical مصبوط؟ characters
+
+478
+00:42:49,170 --> 00:42:52,930
+وبالتالي لما انا بتكلم على universal set انا بتكلم
+
+479
+00:42:52,930 --> 00:42:56,870
+على مجموعة بتشمل كل شيء .. بتشمل كل شيء و غالبا
+
+480
+00:42:56,870 --> 00:43:01,370
+هلاجي في بعض الصعوبة في أي شيء في وصف أو في وصف
+
+481
+00:43:01,370 --> 00:43:05,710
+المنموعة اللي موجودة عندها في مقابل ال universal
+
+482
+00:43:05,710 --> 00:43:10,750
+احنا شاكاش الفاي ال empty يعني هيك ال universal
+
+483
+00:43:10,750 --> 00:43:14,210
+set هي المجموعة اللي بتشمل كل شيء و ال empty set
+
+484
+00:43:15,240 --> 00:43:26,340
+التي لا تحتوي أو لا تجتمل على أي شيء تمام الآن
+
+485
+00:43:26,340 --> 00:43:31,460
+هروح على .. لأ مارجعناش اه جزاك ال definition هدول
+
+486
+00:43:31,460 --> 00:43:34,960
+ال quantifiers اه خلاص يعني برضه برضه استخدامهم
+
+487
+00:43:34,960 --> 00:43:41,400
+بسيط الآن عشان اقول عن مجموعتين متساويتينعشان اقول
+
+488
+00:43:41,400 --> 00:43:47,220
+عن مجموعتين متساويتين لازم يكونوا كل العناصر او
+
+489
+00:43:47,220 --> 00:43:52,540
+بالتنتين بيعتمنوا على نفس العناصر يعني باجي بقول A
+
+490
+00:43:52,540 --> 00:43:59,820
+بدها تساوي واحد و اتنين و تلاتة و B بدها تساوي
+
+491
+00:43:59,820 --> 00:44:06,730
+تلاتة و واحد و اتنين هل ال A تساوي B؟هل إيه تساوي
+
+492
+00:44:06,730 --> 00:44:10,810
+بيه؟ تساويها لأنهم لازم يحتويوا تلتين لازم يكونوا
+
+493
+00:44:10,810 --> 00:44:14,510
+بيشتملوا على نفس العناصر ولما نقول بيشتملوا على
+
+494
+00:44:14,510 --> 00:44:18,410
+نفس العناصر أول شغل اللي لازم تخطر في بالي أن عدد
+
+495
+00:44:18,410 --> 00:44:23,850
+العناصر في المجموعتين متساوي عدد العناصر في
+
+496
+00:44:23,850 --> 00:44:28,550
+المجموعتين متساوي يعني لو شوفت مجموعة فيها عدد
+
+497
+00:44:28,550 --> 00:44:33,590
+عناصرها أكبر من عناصر المجموعة التالية مباشرة بغير
+
+498
+00:44:33,590 --> 00:44:41,780
+متساوياتتمام؟ يعني هيك لو في عندي هان أربعة هل هي
+
+499
+00:44:41,780 --> 00:44:46,900
+تساوي بيه؟ لأ باشر ليش؟ لأنه صارت عندي الأربعة هذه
+
+500
+00:44:46,900 --> 00:44:51,120
+أو ال بي فيها أربع عناصر والإيه فيها تلت عناصر
+
+501
+00:44:51,120 --> 00:44:57,380
+فبالتالي حتما في فرق بين التنتين بس إياك تجع في
+
+502
+00:44:57,380 --> 00:45:02,300
+المطاب نفسه يا أحمد ونروح نقولك احنا أيش؟ هي
+
+503
+00:45:02,300 --> 00:45:02,840
+التلاتة
+
+504
+00:45:06,060 --> 00:45:10,400
+تكراره بتلغيه هذا مش موجود مالوش قيمة عندي هنا
+
+505
+00:45:10,400 --> 00:45:15,440
+فالتنتين متساويه فالتنتين بيكونوا متساويه تمام
+
+506
+00:45:15,440 --> 00:45:20,760
+صيغة أهل الرياضيات بنقول المجموعتين متساويه لما
+
+507
+00:45:20,760 --> 00:45:28,240
+بيكون for all X لأي X X بتنتمي للمجموعة الأولى
+
+508
+00:45:29,260 --> 00:45:34,620
+هتلاقي X موجودة في المجموعة التانية و نفس ال
+
+509
+00:45:34,620 --> 00:45:37,940
+element أكيد لأنها نفس ال element و ال X اللي
+
+510
+00:45:37,940 --> 00:45:41,700
+بتنتمي في المجموعة التانية هتلاقيها متتمية لمين؟
+
+511
+00:45:41,700 --> 00:45:44,560
+للمجموعة الأولى لإن هو by conditional if and only
+
+512
+00:45:44,560 --> 00:45:53,720
+if تمام هاي مثال على المجموعات المتساوية واحد،
+
+513
+00:45:53,720 --> 00:45:58,650
+تلاتة، خمسةتلاتة خمسة واحد equal الترتيب لا يعني
+
+514
+00:45:58,650 --> 00:46:05,210
+شيء واحد خمسة خمسة خمسة تلاتة تلاتة واحد التكرار
+
+515
+00:46:05,210 --> 00:46:09,670
+هذا بدك تطيره صفة المجموعة واحد خمسة تلاتة واحد
+
+516
+00:46:09,670 --> 00:46:15,310
+والاخر واحد كمان مكرر صار عندي واحد خمسة تلاتة
+
+517
+00:46:15,310 --> 00:46:19,590
+واحد تلاتة خمسة في بينهم تساوي
+
+518
+00:46:26,530 --> 00:46:30,490
+شوفك في المجموعات اللي قدامنا هنا ك groups تسعة
+
+519
+00:46:30,490 --> 00:46:34,410
+سبعة تسعة اتنين سبعة سالب ثلاثة سبعة الأولى
+
+520
+00:46:34,410 --> 00:46:41,250
+متساويات التانية لأ لأن السنجاب مش موجود في
+
+521
+00:46:41,250 --> 00:46:46,930
+المجموعة الأولى بقى تغير متساوية التالتة الحصار
+
+522
+00:46:46,930 --> 00:46:51,900
+موجود أيوةبس فى عندى تكرار فى الـ cat بنشيله و
+
+523
+00:46:51,900 --> 00:46:55,440
+بنلغيه و مقاتله فى عندي هانش تساوي ما بين العناصر
+
+524
+00:46:55,440 --> 00:47:04,420
+اللى موجودة عنديها subset
+
+525
+00:47:04,420 --> 00:47:11,520
+ايش يعني subset مجموعة جزئية بنقول لو كان في عندي
+
+526
+00:47:11,520 --> 00:47:19,130
+مجموعتين A و B ان ال A subset من ال Bالـ A is a
+
+527
+00:47:19,130 --> 00:47:24,950
+subset من ال B مجموعة جزئية من ال B if and only if
+
+528
+00:47:24,950 --> 00:47:34,750
+فقط إذا تحقق هذا الشروط فقط every element in A is
+
+529
+00:47:34,750 --> 00:47:43,690
+also an element of B برياضيات for all X X تنتمي
+
+530
+00:47:43,690 --> 00:47:50,190
+إلى A يؤدي إلى X تنتمي إلىإلى B ولو كانت في المثال
+
+531
+00:47:50,190 --> 00:47:53,910
+اللي بتابعت قبل شوية by conditional صارت فيها ساوي
+
+532
+00:47:53,910 --> 00:47:59,290
+طبعا صرت أنا باتجاه واحد فقط باتجاه واحد فقط طبعا
+
+533
+00:47:59,290 --> 00:48:06,870
+يعني يعني بفهم من الكلام هذا أن عناصر أو عدد عناصر
+
+534
+00:48:07,610 --> 00:48:13,230
+الـ B أكبر أو يساوي عدد عناصر الـ A هذا أول شرط
+
+535
+00:48:13,230 --> 00:48:18,570
+عدد عناصر الـ B أكبر أو يساوي عدد عناصر الـ A
+
+536
+00:48:18,570 --> 00:48:24,310
+بعدين كل عناصر الـ A موجودة في الـ B كل عناصر الـ
+
+537
+00:48:24,310 --> 00:48:28,970
+A موجودة في الـ B بنستخدم الرمز هذا عشان نقول
+
+538
+00:48:28,970 --> 00:48:33,550
+subset مجموعة جزئية مجموعة جزئية
+
+539
+00:48:37,270 --> 00:48:41,850
+الان في الأمثلة السابقة لو انا جيت قولت ان ال B
+
+540
+00:48:41,850 --> 00:48:48,670
+بدها تساوي واحد و اتنين و تلاتة و قولت ان ال A
+
+541
+00:48:48,670 --> 00:48:56,910
+بدها تساوي واحد و اتنين هل ال A subset من B؟ صحيح
+
+542
+00:48:56,910 --> 00:49:02,830
+الان بدك تاخد كل عنصر في A و تروح تشوف هل هو موجود
+
+543
+00:49:02,830 --> 00:49:10,800
+في V ولا لأ تمامموجود تمام معناته الـA subset من
+
+544
+00:49:10,800 --> 00:49:14,960
+الـB طب لو التلاتة ماكنتش موجودة تبقى العملية عشان
+
+545
+00:49:14,960 --> 00:49:19,660
+صحيحة لأنه أنا بهمني أن العراصر نفسها موجودة في
+
+546
+00:49:19,660 --> 00:49:24,140
+المجموعة في المجموعتين بس أدق يساوي كيف؟ يساوي أدق
+
+547
+00:49:24,140 --> 00:49:27,800
+كيف يساوي أدق؟ اه just like in a equivalent احنا
+
+548
+00:49:27,800 --> 00:49:30,500
+ماسألاش في ال equivalent خلصنا أنا بسألك الآن هذي
+
+549
+00:49:30,500 --> 00:49:31,920
+true ولا خالص؟ true
+
+550
+00:49:36,380 --> 00:49:40,660
+A equal B true
+
+551
+00:49:40,660 --> 00:49:46,920
+بالمناسبة subset هذه فيها احتمالية المساواة فيها
+
+552
+00:49:46,920 --> 00:49:50,320
+احتمالية المساواة عشان هيك انا قلتلك اول
+
+553
+00:49:50,320 --> 00:49:55,600
+indication ان عدد عناصر الـB اكبر او يساوي عناصر
+
+554
+00:49:55,600 --> 00:49:58,980
+الـA وكل عناصر الـA موجودة في الـB بل لو كانوا
+
+555
+00:49:58,980 --> 00:50:03,940
+يساويها معاها تبقى كلها على نفس المجموعة الـA كان
+
+556
+00:50:03,940 --> 00:50:04,760
+ثاني الى الـPhi
+
+557
+00:50:08,170 --> 00:50:15,270
+الـ A تنتمي إلى الـ Phi ماهو الـ Phi؟
+
+558
+00:50:15,270 --> 00:50:20,090
+Empty المجموعة
+
+559
+00:50:20,090 --> 00:50:24,170
+الفارغة الـ A تنتمي إلى المجموعة الفارغة؟ False
+
+560
+00:50:24,170 --> 00:50:28,810
+وهذا دائما False لأن الـ Phi مافيش فيها عناصر الـ
+
+561
+00:50:28,810 --> 00:50:33,790
+Q subset من الـ S أو أفضل الـ Phi subset من الـ S
+
+562
+00:50:35,370 --> 00:50:40,270
+الـ Phi مجموعة جزئية من أي مجموعة أخرى المجموعة
+
+563
+00:50:40,270 --> 00:50:44,590
+الفارغة مجموعة جزئية من أي مجموعة فارغة من أي
+
+564
+00:50:44,590 --> 00:50:48,670
+مجموعة أخرى يعني لو أتينا و أقولنا هنا Phi subset
+
+565
+00:50:48,670 --> 00:50:58,130
+من الـ A هذا true ليش؟ لأن حسب القانونحسب القانون
+
+566
+00:50:58,130 --> 00:51:03,250
+عدد عناصر الـ Phi لازم يكون اقل او يسوى عدد عناصر
+
+567
+00:51:03,250 --> 00:51:08,210
+الـ A اقل منها عدد عناصرها صفر هذه واحدة كل
+
+568
+00:51:08,210 --> 00:51:12,150
+العناصر اللي في الـ Phi موجودة في الـ A طب الفي
+
+569
+00:51:12,150 --> 00:51:16,210
+مافيش فيها ولا عنصر فاضية مافيش فيها عناصر already
+
+570
+00:51:16,210 --> 00:51:26,920
+حققتش الشرط وبالتالي هي true دائما كل مجموعةجزئية
+
+571
+00:51:26,920 --> 00:51:33,600
+من نفسها true true تمام لإن فيها أيش مساواة وكل
+
+572
+00:51:33,600 --> 00:51:41,460
+العناصر موجودة هذه
+
+573
+00:51:41,460 --> 00:51:44,480
+الكلام اللي قلناه سابقا في ال slide الماضي قررناه
+
+574
+00:51:44,480 --> 00:51:52,040
+كمان مرة بنفس الصيغة السابقة ال proper subset
+
+575
+00:51:54,200 --> 00:52:02,080
+Proper subset مجموعة جزئية غير مساوية مجموعة جزئية
+
+576
+00:52:02,080 --> 00:52:07,580
+غير مساوية و لاحظ الرمز الان بيقول لو كانت ال a
+
+577
+00:52:07,580 --> 00:52:14,840
+subset من ال b و ال a لا تساوي ال b بنكتب ان هذا
+
+578
+00:52:14,840 --> 00:52:19,140
+مجموعة proper subset ايش proper subset يعني مجموعة
+
+579
+00:52:19,140 --> 00:52:25,490
+جزئية لا تساوي ال bيعني بين جثين عدد عناصر ال a
+
+580
+00:52:25,490 --> 00:52:29,670
+أقل من عدد عناصر ال b لو بأنصر واحد أقل منه في
+
+581
+00:52:29,670 --> 00:52:39,910
+الآخر المساواة بطلت موجودة for
+
+582
+00:52:39,910 --> 00:52:44,590
+all if ال a proper subset proper subset من ال b
+
+583
+00:52:44,590 --> 00:52:52,910
+معناته for all xX تنتمي إلى A يقد أن X تنتمي إلى B
+
+584
+00:52:52,910 --> 00:52:59,550
+and they exist على الأقل هناك عنصر واحد X تنتمي
+
+585
+00:52:59,550 --> 00:53:05,930
+إلى B and X لا تنتمي إلى A إذا كان ال X ممكن تخرب
+
+586
+00:53:05,930 --> 00:53:10,590
+الذكاء أما ال Y مش هتفرج كتير ولا شريك؟بس في الآخر
+
+587
+00:53:10,590 --> 00:53:15,710
+لكل عناصر المجموعة A هتلاقيها موجودة في المجموعة B
+
+588
+00:53:15,710 --> 00:53:20,890
+وهناك عنصر واحد على الأقل في B مش موجود في A عشان
+
+589
+00:53:20,890 --> 00:53:26,710
+نحقق البروبر subset كيف
+
+590
+00:53:26,710 --> 00:53:33,950
+ال B أكبر من A طيب
+
+591
+00:53:33,950 --> 00:53:38,310
+كمان مرة الآن بنقول
+
+592
+00:53:40,150 --> 00:53:46,030
+الـ A is a proper subset of B ان الـ A مجموعة
+
+593
+00:53:46,030 --> 00:53:51,790
+جزئية من الـ B ولا تساويها تمام؟ هذا الكلام بيكون
+
+594
+00:53:51,790 --> 00:53:58,730
+صحيح if and only if لكل X في A X تنتمي إلى A حاليا
+
+595
+00:53:58,730 --> 00:54:04,930
+X تنتمي لمين؟ لـ B and بالإضافة للشرق هذا there
+
+596
+00:54:04,930 --> 00:54:11,190
+exist at least one X أو one Yone X موجودة X موجودة
+
+597
+00:54:11,190 --> 00:54:16,470
+في B و مش موجودة يعني لو احنا بالمثال اللي شوفناه
+
+598
+00:54:16,470 --> 00:54:22,390
+قبل شوية A بدها تساوي واحد و اتنين و تلاتة و ال A
+
+599
+00:54:22,390 --> 00:54:28,110
+.. و ال B عفوا بدها تساوي واحد و اتنين و تلاتة و
+
+600
+00:54:28,110 --> 00:54:38,460
+أربعة ال A proper subset من ال B ال AProper subset
+
+601
+00:54:38,460 --> 00:54:44,540
+من الـ B لأ
+
+602
+00:54:44,540 --> 00:54:51,580
+لأ في ال subset قلنا ان عدد عناصر ال X أقل او
+
+603
+00:54:51,580 --> 00:54:57,580
+تساوي عدد عناصر ال B تمام بس هنا عندي sharp and
+
+604
+00:54:57,580 --> 00:55:04,980
+تمام ان العنصر في عدد عناصر ال B أكبر من عناصر ال
+
+605
+00:55:04,980 --> 00:55:16,420
+Aطيب في عندي قانونين مهمات بقول
+
+606
+00:55:16,420 --> 00:55:22,780
+لو كانت ال a تساوي b معناته ده انا باخد منه او
+
+607
+00:55:22,780 --> 00:55:28,700
+بفهم منه ان ال a subset من ال b و ال b subset من
+
+608
+00:55:28,700 --> 00:55:32,780
+ال a لو
+
+609
+00:55:32,780 --> 00:55:36,720
+كانت ال a تساوي ال bمعناته التنتين اللي هم نفس عدد
+
+610
+00:55:36,720 --> 00:55:42,620
+العناصر مظبوط وكل عنصر في A موجود في B وهذه عنوان
+
+611
+00:55:42,620 --> 00:55:46,520
+إيش؟ عنوان ال subset يعني A subset من ال B وبما أن
+
+612
+00:55:46,520 --> 00:55:51,320
+العلاقة بينهم equal معناته كل عنصر في B موجود في A
+
+613
+00:55:51,320 --> 00:55:55,480
+وبهذا اللي برضه ال subset معناته A subset من B and
+
+614
+00:55:55,480 --> 00:55:57,660
+ال B subset من A
+
+615
+00:56:01,820 --> 00:56:05,520
+والعلاقة اللى موجودة ما بين الأرقام اللى احنا قلنا
+
+616
+00:56:05,520 --> 00:56:09,380
+لك أجيلها كمان شوية بين الأعداد مجموعات الأعداد هي
+
+617
+00:56:09,380 --> 00:56:14,460
+عبارة عن subset عبارة عن subset لما تكون ال a
+
+618
+00:56:14,460 --> 00:56:21,340
+subset من ال b and ال b subset من ال c معناته ال a
+
+619
+00:56:21,340 --> 00:56:28,300
+subset من ال c ال natural subset من ال zip من ال
+
+620
+00:56:28,300 --> 00:56:34,070
+integer ولا لا؟طب وال integer subset من ال real
+
+621
+00:56:34,070 --> 00:56:40,030
+number معناته natural subset طيب عشان نريحك في
+
+622
+00:56:40,030 --> 00:56:44,390
+الموضوع ال subset خلينا نشوف هيك على السريع واحد
+
+623
+00:56:44,390 --> 00:56:51,670
+اتنين تلاتة اربعة عشان تعمل subset صحيحة على فرض
+
+624
+00:56:51,670 --> 00:56:56,910
+ان هذه هي المجموعة B هي subset من ال B ده يفتح
+
+625
+00:56:56,910 --> 00:57:03,900
+أجواسأخد أي عدد من الـ element من داخل الـ B حطهم
+
+626
+00:57:03,900 --> 00:57:10,120
+وين؟ جوا الأقواس إيش ممكن تاخد؟ لو أخدت الواحد
+
+627
+00:57:10,120 --> 00:57:17,500
+لحالها، صح؟ أخدت التنين، صح؟ أخدت الواحد والتنين؟
+
+628
+00:57:17,500 --> 00:57:22,820
+خدتهم كلهم، صح؟ مافي مشكلة عندك هذه مفهوم الـ
+
+629
+00:57:22,820 --> 00:57:29,030
+subset إن أخد عناصر المجموعة وحطهمأو جزء من عناصر
+
+630
+00:57:29,030 --> 00:57:33,250
+المجموعة بيحطهم في الداخل مجموعة بالمثال اللي
+
+631
+00:57:33,250 --> 00:57:38,670
+شفناه قبل شوية لما كان بيقولني ان ال A بدها تساوي
+
+632
+00:57:38,670 --> 00:57:41,950
+X
+
+633
+00:57:41,950 --> 00:57:45,930
+و Y و
+
+634
+00:57:45,930 --> 00:57:51,830
+X و Y و Z لو
+
+635
+00:57:51,830 --> 00:57:59,640
+أنا قد قلتلك كتاني X و Yمجموعة جزئية من الـ A صح؟
+
+636
+00:57:59,640 --> 00:58:06,240
+كم واحد بيقول صح؟ X و Y مجموعة جزئية من الـ A كم
+
+637
+00:58:06,240 --> 00:58:12,260
+واحد بيقول صح رفع يده؟ غلط ايش
+
+638
+00:58:12,260 --> 00:58:15,540
+احنا اتفقنا يا شباب عشان نقول مجموعة جزئية؟ قولت
+
+639
+00:58:15,540 --> 00:58:21,160
+بدك تاخد الجثين هدول هيك وتاخد ال element وتحطه
+
+640
+00:58:21,160 --> 00:58:25,080
+جوا الجثين مين ال element اللي جوا الجثين؟ هيه
+
+641
+00:58:31,290 --> 00:58:37,210
+هيو ايوة فانت بدك تنتبه .. تنتبه لوضع العناصر اللي
+
+642
+00:58:37,210 --> 00:58:44,510
+موجودة عندك اعيد تاني ال a بتتساوح اضربها x و x
+
+643
+00:58:44,510 --> 00:58:50,670
+بالشكل هذا المجموعة
+
+644
+00:58:50,670 --> 00:58:56,840
+اللي عندي a كم عنصر فيها؟ عنصرينالأصل الأول X
+
+645
+00:58:56,840 --> 00:59:05,000
+والأصل التاني مجموعة فيها X تمام ال X تنتمي إلى A
+
+646
+00:59:05,000 --> 00:59:09,260
+صحيحة
+
+647
+00:59:09,260 --> 00:59:13,140
+و
+
+648
+00:59:13,140 --> 00:59:22,420
+المجموعة X تنتمي إلى A صحيحة المجموعة X subset من
+
+649
+00:59:22,420 --> 00:59:22,760
+ال A
+
+650
+00:59:26,420 --> 00:59:29,980
+أيوة اختلف الفقه اهلا جدا احنا ايش جونا شباب
+
+651
+00:59:29,980 --> 00:59:34,900
+subset معناته بدي اخد ال element اللي هان و اروح
+
+652
+00:59:34,900 --> 00:59:39,160
+اشوف هو element in A ولا لأ ال X موجودة في A
+
+653
+00:59:39,160 --> 00:59:46,720
+لحالها بدون اقواس تمام معناته دي subset و المجموعة
+
+654
+00:59:46,720 --> 00:59:54,620
+ها دي برضه subset في ال A ليش؟ بدي اخد ال element
+
+655
+00:59:54,620 --> 00:59:59,410
+اللي جواتهاو انا هاناول هاي موجود كما هو وبالتالي
+
+656
+00:59:59,410 --> 01:00:03,970
+انتبه .. انتبه لل details هاي لما اقول subset او
+
+657
+01:00:03,970 --> 01:00:08,370
+لام تمي هل العنصر موجود تمام او لأ بمجرد اقولك
+
+658
+01:00:08,370 --> 01:00:12,090
+subset ماتحطه لجواس و لازم العنصر اللي كونها
+
+659
+01:00:12,090 --> 01:00:16,690
+العناصر اللي كونها تكون موجودة as elements as
+
+660
+01:00:16,690 --> 01:00:24,150
+elements يعني لو انا بدى اغير بالمثال التالي احنا
+
+661
+01:00:24,150 --> 01:00:24,990
+رجعنا للجلم هذا
+
+662
+01:00:31,940 --> 01:00:39,000
+طيب لو اتينا يقولنا ال A بدها تساوي X
+
+663
+01:00:39,000 --> 01:00:47,760
+و X و Y الآن
+
+664
+01:00:47,760 --> 01:00:50,900
+ال
+
+665
+01:00:50,900 --> 01:00:54,660
+X subset من ال A
+
+666
+01:00:58,090 --> 01:01:01,390
+X Subset يعني أنا بدي الأقواس اللي برا يظلوا
+
+667
+01:01:01,390 --> 01:01:05,290
+موجودات بدي أاخد ال element اللي جواتهم هل هو
+
+668
+01:01:05,290 --> 01:01:12,790
+موجود؟ False E الفرمية ال Y Subset
+
+669
+01:01:12,790 --> 01:01:16,170
+احفظ المباراة احتاجها عيني هتبقى جاملة إذا بتنجح
+
+670
+01:01:16,170 --> 01:01:19,990
+إذا بتقدر تحلهم بالحفظ بمشيش الحفظ و هيك أمور يا
+
+671
+01:01:19,990 --> 01:01:28,120
+شباب الآن ال Y Subset من .. هي ال Yهل الأواعي
+
+672
+01:01:28,120 --> 01:01:35,020
+موجودة as element في الـ A؟ لأ خلصنا؟
+
+673
+01:01:35,020 --> 01:01:42,800
+تمام؟ الحمد لله subset
+
+674
+01:01:42,800 --> 01:01:51,820
+على العناصر اللي موجودة عندي هان الأولى
+
+675
+01:01:51,820 --> 01:01:56,960
+subset؟ ايه ال subset من ال B؟ trueتانية ايه ال
+
+676
+01:01:56,960 --> 01:02:02,860
+subset من ال B؟ true لكي
+
+677
+01:02:02,860 --> 01:02:09,240
+أطيّرهم تالتة false لأن التلائم الواحد موجود في ال
+
+678
+01:02:09,240 --> 01:02:18,360
+A مش موجود في ال B proper؟ غلط يا صاحبي ولا proper
+
+679
+01:02:18,360 --> 01:02:22,460
+كمان ولا
+
+680
+01:02:22,460 --> 01:02:23,040
+ال B subset
+
+681
+01:02:33,650 --> 01:02:38,090
+false false إذا
+
+682
+01:02:38,090 --> 01:02:42,770
+هي ماكنتش proper subset فهي مستحيل تكون subset طيب
+
+683
+01:02:42,770 --> 01:02:45,030
+على هيك يا شباب هنجي في اليوم ان شاء الله تورج و
+
+684
+01:02:45,030 --> 01:02:47,330
+تعالى و المحاضرة اللي جايه بنبدأ من عند ال
+
+685
+01:02:47,330 --> 01:02:52,170
+cardinality و المقصود فيها عدد عناصر المجموعة عدد
+
+686
+01:02:52,170 --> 01:02:54,890
+عناصر المجموعة في أي سؤال يا شباب الله يعطيكوا
+
+687
+01:02:54,890 --> 01:02:55,230
+العافية
+
diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/0uvPY3Nanck_raw.srt b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/0uvPY3Nanck_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..8d4d37b3ba9436495e8698ad55c062ba0495fff9
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/0uvPY3Nanck_raw.srt
@@ -0,0 +1,2748 @@
+1
+00:00:20,970 --> 00:00:22,990
+بسم الله والحمد لله والصلاة والسلام على رسول الله
+
+2
+00:00:22,990 --> 00:00:27,370
+اليوم ان شاء الله شباب هنبدأ بال chapter التانيمن
+
+3
+00:00:27,370 --> 00:00:31,770
+المادة الرياضة المفصلة والشبتر هذا هيركز على
+
+4
+00:00:31,770 --> 00:00:35,490
+الشغلات أو ال structures الأساسية أو البنيات
+
+5
+00:00:35,490 --> 00:00:39,210
+البنية الأساسية للرياضيات هنتكلم على مجموعات
+
+6
+00:00:39,210 --> 00:00:42,730
+هنتكلم على دوال هنتكلم على series هنتكلم على
+
+7
+00:00:42,730 --> 00:00:47,750
+relations هنمشي شوية شوية في الشبتر هذا وممكن في
+
+8
+00:00:47,750 --> 00:00:50,170
+لحظة من اللحظات اجيب section او اتنين من شبتر
+
+9
+00:00:50,170 --> 00:00:53,930
+تمانية موجودة كلهم related او على علاقة أو وثيقة
+
+10
+00:00:53,930 --> 00:01:00,290
+فيش بالشبتر اللي موجود عندهاAnyway انا كل حال احنا
+
+11
+00:01:00,290 --> 00:01:04,370
+هنبلش اليوم في المجموعات طبعا العناصر تبعت ال
+
+12
+00:01:04,370 --> 00:01:08,750
+chapter اللي انها المجموعاتالدوال الـ sequences
+
+13
+00:01:08,750 --> 00:01:13,470
+المتتاليات والمجميع ال cardinalities للمجموعات
+
+14
+00:01:13,470 --> 00:01:17,610
+اللي فوق والمصفوفات وممكن زي ما قلت اروح اجيب ال
+
+15
+00:01:17,610 --> 00:01:22,270
+relation من chapter 8 عشان نخلص ال related topics
+
+16
+00:01:22,270 --> 00:01:26,390
+اليوم هنتكلم بالدرجة الأولى عن المجموعات عن ال
+
+17
+00:01:26,390 --> 00:01:31,250
+section الأول section المجموعات طبعا لما أنا بتكلم
+
+18
+00:01:31,250 --> 00:01:35,050
+على مجموعة بتكلم على basic
+
+19
+00:01:38,050 --> 00:01:42,570
+بالنسبة للمجموعات المباشرة يخطر على بالك القواص
+
+20
+00:01:42,570 --> 00:01:47,170
+high الـ curly braces تمام؟ اللي بنرمز المجموعات
+
+21
+00:01:47,170 --> 00:01:52,090
+احنا شفنا قواص مع ال intervals القواص المربع صح؟
+
+22
+00:01:52,090 --> 00:01:55,770
+لل interval وهي القواص عينيه ال curly high braces
+
+23
+00:01:55,770 --> 00:02:00,880
+من أجل نتكلم على مجموعةوطبعا لما أتكلم على
+
+24
+00:02:00,880 --> 00:02:04,080
+المجموعات هي block أساسي أو structure أساسي في
+
+25
+00:02:04,080 --> 00:02:09,100
+الرياضيات وكل العلوم المبنية عليها لما بتكلم على
+
+26
+00:02:09,100 --> 00:02:13,200
+العد أو أنظمة العد أو بدي أعد الشغلات بحاول أجسمهم
+
+27
+00:02:13,200 --> 00:02:18,200
+لمجموعات عشان يسهل مجموع الحسبة بمزعهم لمجموعات
+
+28
+00:02:18,200 --> 00:02:21,580
+يعني هيك لو أنا جيت بدي أعدكوا في القاعة بقولت هي
+
+29
+00:02:21,580 --> 00:02:25,700
+خمسة كذا هي خمسة وهي في عندي انا عشر خمستاش وهي
+
+30
+00:02:25,700 --> 00:02:28,180
+عندي اربعة هي تسعتاش فبكون انا فعليا تجسمتي
+
+31
+00:02:28,180 --> 00:02:32,250
+للمجموعات كانت ايش؟سهلت علي أن أصل للنتيجة اللي
+
+32
+00:02:32,250 --> 00:02:37,350
+أنا بديها اللي هي موضوع العد طبعا لغات البرمجة لما
+
+33
+00:02:37,350 --> 00:02:40,310
+أنا بتكلم عليها بشكل عام برضه بتكلم على مجموعات
+
+34
+00:02:40,310 --> 00:02:43,490
+بتكلم على مجموعات المتغيرات اللي أنت بتعرفها في
+
+35
+00:02:43,490 --> 00:02:46,450
+لغة البرمجة على ال scope تبعتها وإن هذا ال
+
+36
+00:02:46,450 --> 00:02:49,730
+variable موجود فانت بتتكلم قاعدين على مجموعات ال
+
+37
+00:02:49,730 --> 00:02:52,730
+operations في عندي عمليات أو مجموعة العمليات
+
+38
+00:02:52,730 --> 00:02:58,730
+الحسابية الجمع والضرب والطرح والقسمة مصبوط وال
+
+39
+00:02:58,730 --> 00:03:02,770
+modulusو في عندى مجموعة العمليات المنطقية اللى هى
+
+40
+00:03:02,770 --> 00:03:07,150
+ال and و ال or و ال not و هكذا حتى فى داخل ال loop
+
+41
+00:03:07,150 --> 00:03:10,990
+او عفوا فى داخل البرنامج الواحد بتصير كمان عندى
+
+42
+00:03:10,990 --> 00:03:14,270
+مجموعة من ال blocks هذا لل while هذا لل condition
+
+43
+00:03:14,270 --> 00:03:18,970
+لل if statement فبقى برضه بتكلم على مجموعات فى
+
+44
+00:03:18,970 --> 00:03:23,870
+الرياضيات فى علم اسمه نظرية المجموعات و هذا علم
+
+45
+00:03:23,870 --> 00:03:27,510
+داخل فى كثير من التطبيقات اللى موجودة اليوم
+
+46
+00:03:32,400 --> 00:03:36,340
+نجي للتعريف اللي بيهمنا احنا بشكل دقيق شو يعني
+
+47
+00:03:36,340 --> 00:03:43,240
+مجموعة جاي بتكلم ال set S المجموعة هي unordered
+
+48
+00:03:43,240 --> 00:03:52,360
+وهي أول خط collection of objects مجموعة من العناصر
+
+49
+00:03:53,810 --> 00:03:58,010
+تمام؟ مجموعة من العناصر Unordered طبعا الـ
+
+50
+00:03:58,010 --> 00:04:00,830
+Collection بتتكلم عن مجموعة يعني عنصر أو أكتر ..
+
+51
+00:04:00,830 --> 00:04:04,150
+عنصر أو أكتر .. طب السؤال بيطرح نفسه ممكن يكون
+
+52
+00:04:04,150 --> 00:04:07,550
+عندي عنصر واحد في المجموعة؟ أه ممكن .. و ممكن
+
+53
+00:04:07,550 --> 00:04:10,170
+المجموعة تكون فاضية لأنه لحد تلقاه مالاقيناش
+
+54
+00:04:10,170 --> 00:04:14,810
+المنبر المناسب ان نحطه فيها مثلا .. مثلا لو أنا
+
+55
+00:04:14,810 --> 00:04:17,930
+أجي لقول في لحظة من اللحظات أنه أنا شباب بدي أعمل
+
+56
+00:04:17,930 --> 00:04:24,530
+مجموعةبحيث انها تشتغل زي معيدين في المادة للشباب
+
+57
+00:04:24,530 --> 00:04:28,610
+التانين يحلولهم أسئلة و يشرحولهم بعض الشغلات اللي
+
+58
+00:04:28,610 --> 00:04:32,750
+ماقدروش يفهموها منيكويس .. من في المجموعة الآن يا
+
+59
+00:04:32,750 --> 00:04:38,610
+دكتور؟ مافيش حد .. ليش؟ لأن مبدأيا ماشوفتش من
+
+60
+00:04:38,610 --> 00:04:41,690
+الشخص أو من الشخص المناسب اللي يكون موجود في
+
+61
+00:04:41,690 --> 00:04:46,390
+المجموعة لكن هذه مجموعة قررت أن أعملها وبالتالي
+
+62
+00:04:46,390 --> 00:04:50,290
+لما بتكلم على collection يعني بتكلم على واحد أو
+
+63
+00:04:50,290 --> 00:04:52,950
+أكتر غالبا لكن برضه في استثناء أن ممكن المجموعة
+
+64
+00:04:52,950 --> 00:04:57,030
+تكون فاضية أو بشكل مؤقت .. Unordered
+
+65
+00:04:59,210 --> 00:05:02,830
+لسه افن في كمان شغلة في collection في مفهوم ال
+
+66
+00:05:02,830 --> 00:05:06,330
+collection مفهوم collection يعني اتكرار بيعنيش
+
+67
+00:05:06,330 --> 00:05:12,150
+حاجة بنفهش اجي اقول في المجموعة انا عندي احمد و
+
+68
+00:05:12,150 --> 00:05:19,370
+احمد و كمان احمد اذا انا كنت بقصد نفس الشخص او بين
+
+69
+00:05:19,370 --> 00:05:24,210
+جسيم بنفهش اجي اقول انا سوي الطرفة طبعا انا عندي
+
+70
+00:05:24,210 --> 00:05:29,960
+خمس سيارات سبارة و تلاتة و تمانينوكمان سبارة تلاتة
+
+71
+00:05:29,960 --> 00:05:34,440
+وتمانين و سبارة تلاتة وتمانين فانت بتعدد في نفس ال
+
+72
+00:05:34,440 --> 00:05:38,000
+object فانت دلوقتي ما بتتكلمش على collection انت
+
+73
+00:05:38,000 --> 00:05:42,040
+بتتكلم على element مافي كلمة collection زي ما كنت
+
+74
+00:05:42,040 --> 00:05:46,460
+بتتكلم على أكثر واحد أو أكثر برضه التكرار فيها أو
+
+75
+00:05:46,460 --> 00:05:50,260
+تكرار الشيء لا يعني شيء مالوش قيمة التكرار في
+
+76
+00:05:50,260 --> 00:05:57,160
+المجموعة هذا لا يعني شيء Unorderedكمان الترتيب في
+
+77
+00:05:57,160 --> 00:06:00,820
+المجموعة لا يعني شيء، لو أنا اجهزة كتبت في داخل
+
+78
+00:06:00,820 --> 00:06:11,480
+الأقواس A و M و H هذه
+
+79
+00:06:11,480 --> 00:06:19,160
+هي نفس المجموعة M و H و A الآن
+
+80
+00:06:19,160 --> 00:06:22,920
+هي نفس المجموعة نفس المجموعة، من على صرفهم؟نفس
+
+81
+00:06:22,920 --> 00:06:26,440
+العناصر و نفس عددهم ماتغيرش فيهم ولا حاجة كمان مرة
+
+82
+00:06:26,440 --> 00:06:32,240
+لو انا اتيت كرارتها و قولت ال ايه؟ مالوش معنى
+
+83
+00:06:32,240 --> 00:06:36,100
+اتكرار اتكرار مالوشش معنى لأن كلمة connection ال
+
+84
+00:06:36,100 --> 00:06:38,780
+connection بتقولي ماتكررش ال element اللي موجود
+
+85
+00:06:38,780 --> 00:06:44,360
+فحتى لو انت شفته مكتوب لازم تعمل حسابك اننا بنتكلم
+
+86
+00:06:44,360 --> 00:06:47,040
+عن نفس ال element و لما يسألك عدد عناصر المجموعة
+
+87
+00:06:47,040 --> 00:06:50,540
+هي كام شبال؟ العصر بتقولي تلاتة ماتقوليش أربعة لأن
+
+88
+00:06:50,540 --> 00:06:57,510
+العصر هذا هومتكرر هو نفسه تمام معناته unordered
+
+89
+00:06:57,510 --> 00:07:03,130
+collection معناته انا بتكلم على مجموعة فيها عدد من
+
+90
+00:07:03,130 --> 00:07:08,890
+العناصر واحد فاكثر ترتيبهم لا يعني شيء والتكرار
+
+91
+00:07:08,890 --> 00:07:14,910
+العناصر الموجودة لا يعني شيء تمام مثل اش اقول طلاب
+
+92
+00:07:14,910 --> 00:07:18,800
+المساقها او الطلاب الموجودين عندى في المحاضرةسواء
+
+93
+00:07:18,800 --> 00:07:23,900
+قرأت أو نديت على محمد الأدهم، تمام؟ ولا بدأت بعمر
+
+94
+00:07:23,900 --> 00:07:28,420
+مطر؟ مش هتفرج كتير، كلهم موجودين، بس أثناء حضوره
+
+95
+00:07:28,420 --> 00:07:31,600
+الغياب، على فرض، لو أنا بدي أخد حضوره غياب، روح
+
+96
+00:07:31,600 --> 00:07:37,880
+اتكررت اسم عمر مطر مرتينمباشرة إذا كان موجود سأقول
+
+97
+00:07:37,880 --> 00:07:41,560
+لدكتور أني أزعجته قبل ذلك ولا لا وإذا لم يكن موجود
+
+98
+00:07:41,560 --> 00:07:44,040
+الشباب اللي موجودين سأقول لدكتور أنت ناديته
+
+99
+00:07:44,040 --> 00:07:48,040
+فبالتالي هل هو نفس الشخص ولا مختلف فلازم ننتبه أن
+
+100
+00:07:48,040 --> 00:07:51,680
+التكرار في المجموعة لا يعني شيء تمام الآن هنوصل
+
+101
+00:07:51,680 --> 00:07:55,500
+للمجموعة بنقول عنهم ال objects اللي هي الشغلات
+
+102
+00:07:55,500 --> 00:07:59,440
+اللي أنعنالي بأذكرها في المجموعة السيارات القلاد
+
+103
+00:07:59,440 --> 00:08:05,060
+الكتب الجلام الكراسي المجموعة حسب إيش تركبتهالكن
+
+104
+00:08:05,060 --> 00:08:08,140
+عندما أتكلم عن المجموعات الـ object هي صارت
+
+105
+00:08:08,140 --> 00:08:11,300
+بالنسبة لي في نظام المجموعة عبارة عن elements
+
+106
+00:08:11,300 --> 00:08:14,860
+بقولك إيش عناصر المجموعة بسألكاش إيش ال object
+
+107
+00:08:14,860 --> 00:08:18,840
+اللي في المجموعة من عناصر المجموعة هتقولي a و m و
+
+108
+00:08:18,840 --> 00:08:24,360
+h حسب المثال اللي كتبناها قبل شوية من أعضاء
+
+109
+00:08:24,360 --> 00:08:27,440
+المجموعة اللي هو المصطلح اللي بعدي member of
+
+110
+00:08:27,440 --> 00:08:32,380
+members نفس الكلام لكن اللي بدي أقوله أنا هنغيب
+
+111
+00:08:32,380 --> 00:08:36,780
+مصطلح ال objectسأخبرك من أعضاء المجموعة أو من
+
+112
+00:08:36,780 --> 00:08:39,100
+العناصر الموجودة في المجموعة من المصطلحات أو
+
+113
+00:08:39,100 --> 00:08:43,720
+المسميات الموجودة عندهم وعندما أتكلم عن علاقة
+
+114
+00:08:43,720 --> 00:08:47,180
+العنصر بالمجموعة العنصر ينتمي إلى المجموعة هي
+
+115
+00:08:47,180 --> 00:08:52,960
+إشارات ينتمي ينتمي
+
+116
+00:08:52,960 --> 00:08:58,260
+وغالبا العنصر نرمزه باسم letter واسم المجموعة
+
+117
+00:08:59,340 --> 00:09:01,880
+بنعتمد الـ capital letter هيك ال standard في
+
+118
+00:09:01,880 --> 00:09:05,760
+الرياضيات اسم المجموعة capital letter والعناصر
+
+119
+00:09:05,760 --> 00:09:09,560
+اللي فيها small letter ما لم تكن انت فعليا قاصد ان
+
+120
+00:09:09,560 --> 00:09:15,280
+العناصر كوناش capital letter وهك بيصير انا اقول ال
+
+121
+00:09:15,280 --> 00:09:22,100
+a بجراها a is a member of a بالمجموعة a او a
+
+122
+00:09:22,100 --> 00:09:26,620
+المجموعة contains small a اللي هي العنصر ال
+
+123
+00:09:26,620 --> 00:09:31,800
+element اللي موجود عندهاوإذا كان العنصر لا ينتمي ،
+
+124
+00:09:31,800 --> 00:09:39,560
+فسأقول A لا تنتمي للـ A على نفس القياس تبعت
+
+125
+00:09:39,560 --> 00:09:48,600
+اليساوي ، فسنقول لا يساوي تمام؟ الموضوع
+
+126
+00:09:48,600 --> 00:09:53,640
+بشكل عام اليوم سيكون سهل مقارنة بالذي رأيناه في
+
+127
+00:09:53,640 --> 00:09:56,460
+الفيديو السابق خصوصا في الفيديو السابق قليلا أو
+
+128
+00:09:56,460 --> 00:09:59,890
+الأمور عندما تلقوا في الـ Logicلأن ال logic تبعنا
+
+129
+00:09:59,890 --> 00:10:06,130
+غالبا مش سليم تمام؟ مابنبنحسب المشاكل تمام معناته
+
+130
+00:10:06,130 --> 00:10:11,850
+نقول احنا a تنتمي إلى a a is an element او is a
+
+131
+00:10:11,850 --> 00:10:17,130
+member a is not an element الآن لو تشوفت مجموعة
+
+132
+00:10:17,130 --> 00:10:22,790
+مكتوبة بالشكل التالي a تساوي a1 و a2 و a3 لحد am
+
+133
+00:10:22,790 --> 00:10:29,620
+هل العناصر هذه يعني انهم مرتبات؟ لأهذه مجرد رموز
+
+134
+00:10:29,620 --> 00:10:34,060
+عشان أشيل العنصر الأول العنصر التاني العنصر التالت
+
+135
+00:10:34,060 --> 00:10:39,400
+الرابع الخامس الان لكن برضه كمان مرة مش بالضرورة
+
+136
+00:10:39,400 --> 00:10:42,400
+ال value تبعت العناصر هذه تكون فعليا جاي عيشت ب
+
+137
+00:10:42,400 --> 00:10:45,360
+sequence أو جاية مرتبة فالعندي لإن اتفقنا أن
+
+138
+00:10:45,360 --> 00:10:50,000
+الترتيب لا يعني شيء هال مجرد عشان أقول العنصر
+
+139
+00:10:50,000 --> 00:10:54,020
+منزلة في العنصر جديش التاني الرابع الخامس الان إلى
+
+140
+00:10:54,020 --> 00:11:01,290
+آخرهم العناصرفي وصف المجموعات .. طبعا احنا اتفقنا
+
+141
+00:11:01,290 --> 00:11:04,670
+الـ Calibrations أساسية في كتبتها في وصف المجموعات
+
+142
+00:11:04,670 --> 00:11:08,750
+عندي قوراكتين في عند الـ Roster method الـ Roster
+
+143
+00:11:08,750 --> 00:11:11,790
+method بيقول أنا بكتب العناصر تابعة المجموعة في
+
+144
+00:11:11,790 --> 00:11:16,710
+داخل الأقلاص بغض النظر عن عددهم طب ممتاز باجي بقول
+
+145
+00:11:16,710 --> 00:11:24,170
+ABCD مجموعة فيها أربع حروف باجي بقول من صفر لتسعة
+
+146
+00:11:24,170 --> 00:11:30,410
+اللي هي ال digitتمام عشرة طيب لو كبرى تكتر من هيك
+
+147
+00:11:30,410 --> 00:11:35,450
+بتصير الأمور شوية مزعجة في ال roster بيقول إذا كان
+
+148
+00:11:35,450 --> 00:11:38,910
+ال sequence هذه أو الأرقام هذه familiar معاها
+
+149
+00:11:38,910 --> 00:11:42,870
+بنستخدم ال ellipses أو النقاط عشان أقوله على نفس
+
+150
+00:11:42,870 --> 00:11:49,410
+السياق هذا عد بيجي بقول ليه ABC وحطيلي ال ellipses
+
+151
+00:11:49,410 --> 00:11:54,350
+تلت نقاط هذهوالـ Z ايش بتفهم منها انت مباشرة؟ انه
+
+152
+00:11:54,350 --> 00:11:58,270
+قاعد بتكلم على مجموعة الحروف الأبجدية الإنجليزية
+
+153
+00:11:58,270 --> 00:12:06,550
+لأ باجب اقول انه في مجموعة واحد اتنين و بحط مية
+
+154
+00:12:06,550 --> 00:12:12,490
+مباشرة مباشرة هخطر في بالك او هتفهم ان واحد اتنين
+
+155
+00:12:12,490 --> 00:12:16,510
+تلاتة اربعة لحد وين؟ المية لكن شوف المجموعة داني
+
+156
+00:12:16,510 --> 00:12:25,060
+شويه هتختلف الأمور واحدتلاتة .. خمسة .. وحقية الـ
+
+157
+00:12:25,060 --> 00:12:32,280
+ellipses لتسعة وتسعين .. الأعداد الفردية الأقل من
+
+158
+00:12:32,280 --> 00:12:35,660
+مائة .. بقى بالسبعة وسبعين منهم .. اه منهم .. بقى
+
+159
+00:12:35,660 --> 00:12:40,280
+مش مكتوبة .. حالة محالها مين؟ التلات نقاط أو ال
+
+160
+00:12:40,280 --> 00:12:44,080
+ellipses اللي موجودة جدامي هن .. تمام؟ اللي هي
+
+161
+00:12:44,080 --> 00:12:45,800
+ممكن زي ما يقول زميلكم جاعة قلخ ..
+
+162
+00:12:50,270 --> 00:12:56,550
+المجموعة الـ vowels باللغة الإنجليزية حروف العلة A
+
+163
+00:12:56,550 --> 00:13:07,570
+-U-I-O-U لسه ما هو حرف العلة لأنها
+
+164
+00:13:07,570 --> 00:13:14,110
+علة في تمييزها عند الكتابةطبعا؟ لأنه يجب أن تكون
+
+165
+00:13:14,110 --> 00:13:17,730
+حافظ ال spelling صح عشان تقدر أن الكلمة هذه تكتب
+
+166
+00:13:17,730 --> 00:13:22,030
+بال O ولا بال U؟ و الترتيب تبعتهم؟ طبعا؟ غير هكذا
+
+167
+00:13:22,030 --> 00:13:31,110
+العليل لما بتأوه .. انت تخيل نفسك تقفضهم واحد ورا
+
+168
+00:13:31,110 --> 00:13:34,690
+التاني على رأي زميلنا جينا للشلاليت
+
+169
+00:13:37,780 --> 00:13:42,740
+مجموعة الـ odd positive integer less than عشرة
+
+170
+00:13:42,740 --> 00:13:50,160
+واحد اتنين واحد تلاتة خمسة سبعة تسعة مجموعة ال
+
+171
+00:13:50,160 --> 00:13:55,720
+positive integer الاقل من مية فانت ممكن تصيغ ..
+
+172
+00:13:55,720 --> 00:13:59,280
+كيف ما تصيغ الأقام اللي موجودة عندك فبتكون الأمور
+
+173
+00:13:59,280 --> 00:14:06,610
+تمام من المجموعات اللي احنا بنعرفها بشكل كويسالـ
+
+174
+00:14:06,610 --> 00:14:10,230
+Natural number، مجموعة الأعداد الطبيعية، واحد،
+
+175
+00:14:10,230 --> 00:14:14,330
+اتنين، تلاتة، أربع، بس ملاحظة، كتابنا تبع الـ
+
+176
+00:14:14,330 --> 00:14:17,730
+Discrete Mathematics تبع الفصل هذا، بقول إن الـ
+
+177
+00:14:17,730 --> 00:14:24,250
+Natural number بتبدأ من وين؟ من صفر طب احنا مع مين
+
+178
+00:14:24,250 --> 00:14:28,780
+بدنا نشتغل؟نشتغل مع الكتاب؟ مع الكتاب مش قضوية
+
+179
+00:14:28,780 --> 00:14:31,920
+كتير أنا بالنسبة لو عدلت المثال و كتبته زي ما احنا
+
+180
+00:14:31,920 --> 00:14:36,000
+ياش متفق انه زي ما احنا بنتعامل مع المجموعة طب يا
+
+181
+00:14:36,000 --> 00:14:38,580
+أستاذ لو انت بقى تجيبلنا مثال أو سؤال فنحله في
+
+182
+00:14:38,580 --> 00:14:41,780
+الكتاب فنحله على صفر ولا بدون مش هتفرج كتير معايا
+
+183
+00:14:41,780 --> 00:14:45,760
+هذه الساعة مش هندج عليك او بدي مجموعة .. في
+
+184
+00:14:45,760 --> 00:14:49,520
+مجموعات تانية في زبد و في Q و في R ماتجلجش
+
+185
+00:14:49,520 --> 00:14:53,780
+فنستمعنها من الأسئلة و برا أيه راسنا عشان نخلكاش
+
+186
+00:14:53,780 --> 00:14:58,140
+أياش تغلط فيها و تلطخمبس انا حبيت اناوحلك ان
+
+187
+00:14:58,140 --> 00:15:03,680
+الكتاب فعليا هذا من الناس اللي بتعد الصفر من ضمن
+
+188
+00:15:03,680 --> 00:15:07,460
+ال natural number و احنا اتفقنا أساسا ان الصفر مش
+
+189
+00:15:07,460 --> 00:15:10,960
+من ال natural number لأنه أساس وجودها من أجل العد
+
+190
+00:15:10,960 --> 00:15:15,600
+والترتيب مابجيش اقول أن العنصر رقم صفر او العنصر
+
+191
+00:15:15,600 --> 00:15:20,620
+لما بتبدأ تعد بتبدأ تعد صفر من واحد وبالتالي هذا
+
+192
+00:15:20,620 --> 00:15:26,700
+كان أساس ال natural number anyway ال ZZ Plus مش Z
+
+193
+00:15:26,700 --> 00:15:31,860
+Star Z Plus يعني مجموعة الأعداد الموجبة اللي بتبدأ
+
+194
+00:15:31,860 --> 00:15:34,560
+واحد اتنين تلاتة اللي المفروض تساوي ال natural
+
+195
+00:15:34,560 --> 00:15:39,420
+number حسب ال definition اللي فوق Q مجموعة الأعداد
+
+196
+00:15:39,420 --> 00:15:47,300
+المسبية وال R مجموعة الأعداد الحقيقية من
+
+197
+00:15:47,300 --> 00:15:51,380
+المجموعات المشهورة كذلك ال Phi المجموعة الفارغة
+
+198
+00:15:55,140 --> 00:15:57,780
+مافيش فيها ولا عنصر زي ما قلنا قبل شوية أنا في
+
+199
+00:15:57,780 --> 00:16:01,640
+عندي مجموعة إلها إسم وفي العناصر تبعونها إلهم صفة
+
+200
+00:16:01,640 --> 00:16:07,720
+لكن ولا حد لسه في داخل المجموعة هذه ماحدش حقق
+
+201
+00:16:07,720 --> 00:16:12,420
+الخصية أو الصفة المطلوبة حاليًا الـ A تساوي
+
+202
+00:16:12,420 --> 00:16:19,480
+المجموعة Z أو تساوي المجموعة اللي فيها عنصر واحد
+
+203
+00:16:19,480 --> 00:16:28,190
+اللي هو الـ Z الأن لاحظ الـ Z تنتميللـ A لكن الـ Z
+
+204
+00:16:28,190 --> 00:16:33,130
+كأنصر هنا ليه تساوي الـ Z كمجموعة؟ لأن أحنا الأن
+
+205
+00:16:33,130 --> 00:16:38,690
+بدنا نفرق بين عنصر وبين مجموعة إيش الحكل بينهم؟
+
+206
+00:16:38,690 --> 00:16:42,010
+الأقواص .. الأقواص .. إذا الـ curly braces هذه
+
+207
+00:16:42,010 --> 00:16:45,290
+الموجودة معاك .. أنا بتكلم على مجموعة .. بتكلم على
+
+208
+00:16:45,290 --> 00:16:54,310
+مجموعة .. تمام الـ A هي عبارة عن مجموعةعاصرها ..
+
+209
+00:16:54,310 --> 00:17:00,030
+كم عنصر في الـ A يا شباب؟ كم عنصر في الـ A؟ عنصرين
+
+210
+00:17:00,030 --> 00:17:05,530
+.. المجموعة الأولى .. عنصرين .. كل عنصر عبارة عن
+
+211
+00:17:05,530 --> 00:17:11,610
+مجموعة بي و سي .. والمجموعة التانية أو العنصر
+
+212
+00:17:11,610 --> 00:17:16,950
+التاني في المجموعة عبارة عن مجموعة فيها C و X و D
+
+213
+00:17:16,950 --> 00:17:24,100
+وبدى منك شغلة انتبه وما تحاولش تسقطاللي بنعرفه عن
+
+214
+00:17:24,100 --> 00:17:28,500
+الأعداد أن كل عدد طبيعي
+
+215
+00:17:28,500 --> 00:17:32,820
+هو عبارة عن عدد صحيح وكل عدد صحيح عبارة عن عدد
+
+216
+00:17:32,820 --> 00:17:37,220
+نسبي وكل عدد نسبي عبارة عن عدد حقيقي العلاقة هذه
+
+217
+00:17:37,220 --> 00:17:42,060
+شويه لسالي إياها يعني لو أنا جيت سألتك بقولتلك ال
+
+218
+00:17:42,060 --> 00:17:50,180
+B في المثال هذا كان تميء لل A إيش
+
+219
+00:17:50,180 --> 00:17:51,220
+هترد عليا؟
+
+220
+00:17:54,800 --> 00:18:00,400
+false ليش؟ لأن احنا متفقين لما سألتك كم عنصر في
+
+221
+00:18:00,400 --> 00:18:07,800
+المجموعة ايش قلت ليه؟ اثنين فيها عنصرين هل ال B ها
+
+222
+00:18:07,800 --> 00:18:13,040
+دي تساوي احد العنصرين؟ يعني بين جسين هل ال B هك
+
+223
+00:18:13,040 --> 00:18:19,420
+بدها تساوي B و C؟ هذه لا تساوي لأن هذه مجموعة و
+
+224
+00:18:19,420 --> 00:18:26,510
+هذه عنصر و ال B ها دي لا تساويC و X و D لأنها أيضا
+
+225
+00:18:26,510 --> 00:18:32,170
+هذه مجموعة وبالتالي الـ B لا تنتمي إلى الـ A طيب
+
+226
+00:18:32,170 --> 00:18:34,530
+يا دكتور شوية شوية علينا احنا بنقول اننا لدينا
+
+227
+00:18:34,530 --> 00:18:40,450
+مجموعة كبيرة فيها مجموعتين فيها مجموعتين لأن مش
+
+228
+00:18:40,450 --> 00:18:44,750
+المنطق بيقول ان علاصر المجموعتين هدولة هما بنتمل
+
+229
+00:18:44,750 --> 00:18:47,570
+المجموعة الأكبر يعني يا دكتور انت جاهز بيقول انا
+
+230
+00:18:47,570 --> 00:18:52,400
+احنا كلاب رياضيات منفصلةتمام؟ والرياضيات منفصلة
+
+231
+00:18:52,400 --> 00:18:56,000
+جزء من مساق الـ IT، مساقات الـ IT، ما تحب تقولها
+
+232
+00:18:56,000 --> 00:18:58,420
+بـ IT، ما تقدرش تقولها لا، انت تقولها بريبات
+
+233
+00:18:58,420 --> 00:19:05,050
+منفصلة وبسالعلاقة شويهة لشباب مختلفة مختلفة تبع لل
+
+234
+00:19:05,050 --> 00:19:09,090
+rules اللي احنا عايش بيبقى مطابقها في غير او في
+
+235
+00:19:09,090 --> 00:19:11,190
+العلاقة اللي احنا بنوصفها سواء كانت في ال members
+
+236
+00:19:11,190 --> 00:19:15,210
+او في علاقتنا بالمساقات والكلية والجامعة علاقة
+
+237
+00:19:15,210 --> 00:19:21,150
+subset مجموعات جزئية مجموعات جزئية مش علاقة عضوية
+
+238
+00:19:22,770 --> 00:19:28,750
+أشبه بالتوارث، وعندما أتكلم في مجموعة جزئية، يعني
+
+239
+00:19:28,750 --> 00:19:38,090
+أن كل مجموعة في الجامعة تم تقسيمها لمجموعات مختلفة
+
+240
+00:19:38,090 --> 00:19:42,290
+لكليات، وعناصر الكليات تم تقسيمهم لمجموعات مختلفة
+
+241
+00:19:42,290 --> 00:19:47,720
+لإقسامتقوى التخصصات والتخصصات تم تقسيم الطلاب فيهم
+
+242
+00:19:47,720 --> 00:19:51,460
+لمستويات وكل مستوى له مجموعة من المساقات لاحظ ان
+
+243
+00:19:51,460 --> 00:19:58,600
+العلاقة subset دزئية من المجموعة بس هنا لأ هنا لأ
+
+244
+00:19:58,600 --> 00:20:02,300
+هنا عضوية لأن المجموعة هذه بتمثل عنصر واحد
+
+245
+00:20:02,300 --> 00:20:11,160
+المجموعة هذه بتمثل عنصر واحد طيب يعني بينفعش ..
+
+246
+00:20:11,160 --> 00:20:24,020
+بينفعشأجي أقول capital X بدها تساوي ال N و ال Z و
+
+247
+00:20:24,020 --> 00:20:31,300
+ال Q و ال R الآن
+
+248
+00:20:31,300 --> 00:20:38,700
+لو أنا سألتك جذر التنين تنتمي لل X؟ جذر التنين
+
+249
+00:20:38,700 --> 00:20:42,440
+عنصر في المجموعة X؟ لأ
+
+250
+00:20:44,680 --> 00:20:48,460
+من العناصر اي واحد من الخمسة هدول او من الأربعة
+
+251
+00:20:48,460 --> 00:20:55,260
+هدول عفوا كمان مرة عشان اتكلم ينتمي ينتمي لازم
+
+252
+00:20:55,260 --> 00:20:58,960
+اشوف العنصر بنفس صيغته موجود بنفس العنصر يعني هيك
+
+253
+00:20:58,960 --> 00:21:05,470
+لو انا جيت وقلتلك ال Y او ال I تنتميللـ X هذه اللي
+
+254
+00:21:05,470 --> 00:21:09,590
+عرفناها هان ايش المطلوب منك تساوي تروح تاخد الـ I
+
+255
+00:21:09,590 --> 00:21:12,430
+هذه كما هي هيك زي ما هي مكتوبة جاب الإشارة اللي
+
+256
+00:21:12,430 --> 00:21:16,810
+ينتمي و تروح تدور عليها وين في عناصر المجموعة هاي
+
+257
+00:21:16,810 --> 00:21:22,250
+الأنصار الأول هى يساوي الـ I هذه؟ لأ ايش .. ايش
+
+258
+00:21:22,250 --> 00:21:26,270
+الفاصل ما بين العناصر؟ الكمة هى الأنصار التاني لا
+
+259
+00:21:26,270 --> 00:21:36,140
+يساوي I التالت الرابع ماته I لا تمتمي لمين؟ لل Xهك
+
+260
+00:21:36,140 --> 00:21:41,360
+بدي يكون قرارك وهذا ال role أو هذا القانون الأول
+
+261
+00:21:41,360 --> 00:21:45,460
+في التعامل مع المجموعة إذا ال answer مش مكتوب بشكل
+
+262
+00:21:45,460 --> 00:21:49,700
+مباشر بقولش عليه تعالى أورجيك إحنا إيش لما كنا
+
+263
+00:21:49,700 --> 00:21:53,640
+نقصد من وين جيبنا كل integer أو عفوا كل عدد طبيعي
+
+264
+00:21:53,640 --> 00:21:59,800
+عدد صحيح قلنا إنه الآن أو خلينا نرجع لل slide
+
+265
+00:21:59,800 --> 00:22:00,220
+الجابر
+
+266
+00:22:08,520 --> 00:22:11,280
+لما اتينا و كتبنا الـ natural number كتبنا واحد
+
+267
+00:22:11,280 --> 00:22:16,200
+اتنين تلاتة إلى ما لا نهاية مظبوط؟ مظبوط؟ و لما
+
+268
+00:22:16,200 --> 00:22:22,480
+اتيت و كتبت ال Z ايش كتبناه؟ مكتبت ال cash مكتبت
+
+269
+00:22:22,480 --> 00:22:28,040
+ال cash ال N فاصلة صفر فاصلة سالب واحد سالب اتنين
+
+270
+00:22:28,040 --> 00:22:31,980
+إلى ما لا نهاية ايش كتبناه لك؟ كتبناه العناصر كل
+
+271
+00:22:31,980 --> 00:22:37,680
+هياتها الان لو اتيت و سألتك التلاتة
+
+272
+00:22:39,180 --> 00:22:46,740
+تنتمي للأن صحيح true التلاتة
+
+273
+00:22:46,740 --> 00:22:52,820
+تنتمي للزد true لأن هي مكتوبة موجودة عندي لاحظ
+
+274
+00:22:52,820 --> 00:22:55,020
+العلاقة مختلفة تماما على الأمثل اللي احنا عايش
+
+275
+00:22:55,020 --> 00:22:59,900
+حكينا عليها قبل شوية تمام معناته احنا الآن متفقين
+
+276
+00:22:59,900 --> 00:23:04,640
+متفقين انه الآن لما بتكلم في الينتمي او العنصر هذا
+
+277
+00:23:04,640 --> 00:23:09,980
+في المجموعة لازم اشوف العنصر مثل ما هو في داخلقاس
+
+278
+00:23:09,980 --> 00:23:14,940
+المجموعة نرجح مرة عشان نرجح من وين بدخلنا في
+
+279
+00:23:14,940 --> 00:23:21,900
+التفاصيل الكتيرة A عبارة عن مجموعة فيها عنصرين كل
+
+280
+00:23:21,900 --> 00:23:27,040
+عنصر بمثابة مجموعة X لا تنتمي لل A
+
+281
+00:23:34,330 --> 00:23:39,090
+الـ A بدها تساوي المجموعة اللي بتحتوي على أنصر
+
+282
+00:23:39,090 --> 00:23:47,390
+واحد و هو مثابت مجموعة X و Y هيها ولا لا؟ الآن الـ
+
+283
+00:23:47,390 --> 00:23:51,790
+X و Y هذه اللي داخل الـ curly braces هي عبارة عن
+
+284
+00:23:51,790 --> 00:23:58,210
+أنصر مصبوط؟ وبالتالي أنا بقدر أقول إن المجموعة هذه
+
+285
+00:23:58,210 --> 00:24:02,510
+تنتمي للـ A ليش؟ لأن هي زي ما هي هيك أخدت منها
+
+286
+00:24:03,450 --> 00:24:07,130
+ودورت عليها في داخل المجموعة فلجت كما هي فبتكلم عن
+
+287
+00:24:07,130 --> 00:24:14,730
+عنصر وانت بيه ان X المجموعة هذه لا تساوي المجموعة
+
+288
+00:24:14,730 --> 00:24:18,630
+هذه ايوة
+
+289
+00:24:18,630 --> 00:24:23,430
+المجموعة هذه فيها عنصرين المجموعة هذه فيها عنصر
+
+290
+00:24:23,430 --> 00:24:28,630
+واحد وبالتالي مجموعتين عدم على صرهم مختلفين مستحيل
+
+291
+00:24:28,630 --> 00:24:31,750
+يكونوا متساويتين نعم
+
+292
+00:24:45,960 --> 00:24:59,200
+عنصر الأول مجموعة X وY كم
+
+293
+00:24:59,200 --> 00:25:03,260
+عنصر
+
+294
+00:25:03,260 --> 00:25:09,900
+في المجموعة يا شباب؟ حرام عليكمهذا اسمه تكرار احنا
+
+295
+00:25:09,900 --> 00:25:13,560
+اتفقنا اعادة او ترتيب العناصر لا يعني شيء في
+
+296
+00:25:13,560 --> 00:25:20,460
+المجموعة يعني هذا العنصر هو عبارة عن X و Y و
+
+297
+00:25:20,460 --> 00:25:24,420
+التكرار
+
+298
+00:25:24,420 --> 00:25:28,680
+في المجموعة لا يعني شيء مالوش فايدة وبالتالي
+
+299
+00:25:28,680 --> 00:25:34,300
+المجموعة بتحتوي على عنصر واحد فقط يمكن كان سؤالك
+
+300
+00:25:34,300 --> 00:25:40,040
+يكون ألطفلو انا اجيتها و قلت ان الـ B .. او عفوا
+
+301
+00:25:40,040 --> 00:25:47,920
+.. C و الـ B كمجموعة تنتمي للـ A صح ولا غلط؟ صح ..
+
+302
+00:25:47,920 --> 00:25:52,880
+صح .. صح .. صح .. صح .. صح .. صح .. صح .. صح .. صح
+
+303
+00:25:52,880 --> 00:25:53,860
+.. صح .. صح .. صح .. صح .. صح .. صح .. صح .. صح ..
+
+304
+00:25:53,860 --> 00:25:53,920
+صح .. صح .. صح .. صح .. صح .. صح .. صح .. صح .. صح
+
+305
+00:25:53,920 --> 00:25:54,540
+.. صح .. صح .. صح .. صح .. صح .. صح .. صح .. صح ..
+
+306
+00:25:54,540 --> 00:25:58,360
+صح .. صح .. صح .. صح .. صح .. صح .. صح .. صح .. صح
+
+307
+00:25:58,360 --> 00:25:59,000
+.. صح .. صح .. صح .. صح .. صح .. صح .. صح .. صح ..
+
+308
+00:25:59,000 --> 00:26:03,220
+صح .. صح .. صح .. صح .. صح .. صح .. صح
+
+309
+00:26:06,990 --> 00:26:12,490
+true ليش؟ لأن المجموعة هذه هي عبارة عن عنصر في
+
+310
+00:26:12,490 --> 00:26:19,030
+المجموعة هيها في الـA وبالتالي هي member of تمام؟
+
+311
+00:26:19,030 --> 00:26:27,650
+في أي سؤال حتى اللحظة يا شباب؟ الأمور تمام؟ الصورة
+
+312
+00:26:27,650 --> 00:26:29,710
+التانية في تعريف المجموعات احنا الأولى قلنا
+
+313
+00:26:29,710 --> 00:26:33,430
+الـRosterتكتب المجموعات وتذكر العناصر أو تستخدم
+
+314
+00:26:33,430 --> 00:26:37,130
+الـ ellipses اللي هي النقاط عشان تكمل وصف العناصر
+
+315
+00:26:37,130 --> 00:26:41,110
+اللي معروفة في أين دي شغل اسمها الـ Builder
+
+316
+00:26:41,110 --> 00:26:48,870
+Notation باستخدام صيغة المجموعة صيغة المجموعة طبعا
+
+317
+00:26:48,870 --> 00:26:55,210
+الـ curly braces الأقواص موجودة من البداية مافيش
+
+318
+00:26:55,210 --> 00:26:59,270
+عليها خلاف لكن في داخل الأقواص هذه شو بدك تكتب؟
+
+319
+00:26:59,270 --> 00:27:07,800
+بتكتب Exhibitionيعبر عن عناصر المجموعة تمام؟ وبعد
+
+320
+00:27:07,800 --> 00:27:12,560
+الـ expression بتحط ال properties اللي لازم يحققها
+
+321
+00:27:12,560 --> 00:27:17,920
+كل عناصر المجموعة وبالتالي
+
+322
+00:27:17,920 --> 00:27:21,500
+لما أنا بتكلم عن ال builder notation set builder
+
+323
+00:27:21,500 --> 00:27:24,980
+notation جاعت بتكلم أن هذا ال builder أو هذا الوصف
+
+324
+00:27:24,980 --> 00:27:30,320
+بدي يوصف وبشكل دقيق العناصر اللي لازم يحققها كل
+
+325
+00:27:30,320 --> 00:27:37,110
+عناصرالمجموعة او يحقق الصفات بيحدد الصفات اللي كل
+
+326
+00:27:37,110 --> 00:27:42,590
+عناصر المجموعة لازم اتحددها او اتحققها تمام تعالى
+
+327
+00:27:42,590 --> 00:27:51,370
+نشوف مثال بقول ال S تساوي واسم جموعة X اللي هي
+
+328
+00:27:51,370 --> 00:27:57,370
+مثال ال expression اللي عندي X ايش مالها X X is a
+
+329
+00:27:57,370 --> 00:28:04,040
+positive integer less thanمية ايش بتفهم منها؟ من
+
+330
+00:28:04,040 --> 00:28:11,940
+واحد لتسعة وتسعين ليه اشنا بقولها less than وواحد
+
+331
+00:28:11,940 --> 00:28:20,200
+اش جالي هو positive integer يعني بصيغة roster بقول
+
+332
+00:28:20,200 --> 00:28:26,340
+واحد اتنين تلاتة ال ellipses والتسعة وتسعين
+
+333
+00:28:30,310 --> 00:28:34,450
+انت بتجرب التانية، ما شاء الله، كويس، إيش بيقوللي؟
+
+334
+00:28:34,450 --> 00:28:39,430
+في التانية بيقوللي X is an odd positive integer
+
+335
+00:28:39,430 --> 00:28:50,950
+الصفته عدد فردي موجب، عدد فردي موجب أقل من عشرة،
+
+336
+00:28:50,950 --> 00:28:56,750
+واحد، تلاتة، خمسة، سبعة والتسعة
+
+337
+00:28:59,390 --> 00:29:04,030
+مبتعد شوف العدد الفردي كمان مرة كيف وصفه قال لي X
+
+338
+00:29:04,030 --> 00:29:09,930
+كان تميء إلى Z plus لاحظ صيغة ال expression شوية
+
+339
+00:29:09,930 --> 00:29:16,590
+اتغيرت هنا ولا لا مش قضية في الآخر هو عمال يوصف
+
+340
+00:29:16,590 --> 00:29:19,770
+للعراصر اللي بيتكلم عليها فقال لي ان العنصر تبعي
+
+341
+00:29:19,770 --> 00:29:26,030
+هو عبارة عن عدد صحيح موجب ممتاز قال لي ايش X is
+
+342
+00:29:26,030 --> 00:29:34,600
+oddعدد صحيح موجب أو فردي and أقل من عشرة نفس
+
+343
+00:29:34,600 --> 00:29:37,800
+الكلام اللي فوق تماما، بس اختلف في وين؟ في ال
+
+344
+00:29:37,800 --> 00:29:41,500
+description أو في صيغة الوصف الدقيقة لكل عناصر
+
+345
+00:29:41,500 --> 00:29:47,560
+المجموعة لاحظ، لو أخدت أي عنصر في المجموعة، لازم
+
+346
+00:29:47,560 --> 00:29:50,920
+يطبق عليه الوصف اللي موجود هنا لازم يطبق عليه
+
+347
+00:29:50,920 --> 00:29:52,440
+الوصف اللي موجود بالتمام
+
+348
+00:29:56,460 --> 00:30:02,560
+الآن تعالى نشوف المثال الأخير Q plus Q هي عبارة عن
+
+349
+00:30:02,560 --> 00:30:08,660
+ال rational number وال plus positive X تنتمي إلى R
+
+350
+00:30:08,660 --> 00:30:14,560
+طبيعي هو X عبارة عن عدد حقيقي ايه الصفة العدد
+
+351
+00:30:14,560 --> 00:30:23,360
+الحقيقي هذا؟X تساوي P على Q يعني العدل الحقيقي هذا
+
+352
+00:30:23,360 --> 00:30:30,560
+نكتبه على صورة كسر بسط و مقام for some positive
+
+353
+00:30:30,560 --> 00:30:38,150
+integers P و Q قصصت إياهمقال لي لأعداد حقيقية بحيث
+
+354
+00:30:38,150 --> 00:30:42,570
+ان بي و كيو عبارة عن positive integers positive
+
+355
+00:30:42,570 --> 00:30:47,810
+integers يعني الصفر مش منهم تمام ولا السلب منهم
+
+356
+00:30:47,810 --> 00:30:52,150
+وبالتالي بصتوا المقام موجبات فال output هيكون موجب
+
+357
+00:30:52,150 --> 00:30:59,910
+هايوصف للرقم اللي موجود عندي هان تمام ال
+
+358
+00:30:59,910 --> 00:31:05,050
+predicateتذكرها؟ أنا بذكرك فيها قولنا الـ
+
+359
+00:31:05,050 --> 00:31:09,190
+predicate function في الـ chapter الماضي P of X
+
+360
+00:31:09,190 --> 00:31:14,910
+denoted by أن
+
+361
+00:31:14,910 --> 00:31:20,890
+X أكبر من 3 أن P of X هي عبارة عن predicate
+
+362
+00:31:20,890 --> 00:31:26,330
+function بتشير إلى X أكبر من 3 مين اللي predicated
+
+363
+00:31:26,330 --> 00:31:32,180
+التلاتة؟ قيمة المصندق إليهاقول هذه أنا بقيّمهم
+
+364
+00:31:32,180 --> 00:31:37,220
+بناءً على قيمة الـ X بي أوف خمسة إيش قيمتها؟ true
+
+365
+00:31:37,220 --> 00:31:45,540
+بي أوف تلاتة fourth الآن ممكن تستخدم لـ predicate
+
+366
+00:31:45,540 --> 00:31:51,300
+في الـ set builder notation عشان توصف عراصر
+
+367
+00:31:51,300 --> 00:31:59,830
+المجموعة X اللي بتحقق عراصر المجموعةيعني بين قسين
+
+368
+00:31:59,830 --> 00:32:08,330
+انا بقدر اكتبها هيك X حيث X أكبر من 3 ايه شرصة
+
+369
+00:32:08,330 --> 00:32:12,430
+المجموعة اللي هون يا شباب؟ كل ال positive number
+
+370
+00:32:12,430 --> 00:32:19,210
+.. كل ال positive real number اللي أكبر من 3؟ 4
+
+371
+00:32:19,210 --> 00:32:21,050
+ليش قلت real number؟
+
+372
+00:32:23,440 --> 00:32:27,080
+لأنه لم يحدد ليش الصفة العدد وبالتالي انا روحت على
+
+373
+00:32:27,080 --> 00:32:31,060
+أكبر صورة ممكنة مع الـ real number وليش رأيك؟ بدك
+
+374
+00:32:31,060 --> 00:32:37,440
+تقيدها و تتكلم على integers بتقولوا and ال X تنتمي
+
+375
+00:32:37,440 --> 00:32:42,960
+إلى ال Z و
+
+376
+00:32:42,960 --> 00:32:47,360
+هكذا لاحظ ان انا بتكلم على predicate من الأمثلة
+
+377
+00:32:47,360 --> 00:32:49,960
+اللي ممكن تكون على ال predicate لو انا أعرفتلك ال
+
+378
+00:32:49,960 --> 00:32:59,240
+Sهي عبارة عن المجموعة لعناصرها X واتحقق
+
+379
+00:32:59,240 --> 00:33:06,180
+prime X ان ال X is prime الأعداد الأولية .. إيش
+
+380
+00:33:06,180 --> 00:33:12,210
+الأعداد الأولية يا شباب؟تنين هو عبارة عن كل هدد
+
+381
+00:33:12,210 --> 00:33:20,690
+صحيح موجب أكبر أو يساوي 2 يقبل القسمة أو لا يقبل
+
+382
+00:33:20,690 --> 00:33:25,670
+القسمة إلا على نفسه هو على الواحد مش هنزعلك فلو
+
+383
+00:33:25,670 --> 00:33:28,270
+جيبنا أي عدد في الدنيا بسميه على الواحد حق .. okay
+
+384
+00:33:28,270 --> 00:33:38,640
+الآن نقدر نكتبهم؟ هو يبقى 23 .. 5 .. 7 .. 11 .. 13
+
+385
+00:33:38,640 --> 00:33:51,680
+.. 17 .. 19 .. 23 .. 31 .. 29 .. 27 .. 29 .. 31 في
+
+386
+00:33:51,680 --> 00:33:57,740
+الآخر مش هتقدر يا صاحبي مش هتقدر تحط لبس كمان عرف
+
+387
+00:33:57,740 --> 00:34:02,700
+ليش؟ لإن مافيش صيغة ثابتة تعتمد عليها عشان تمشي
+
+388
+00:34:03,780 --> 00:34:08,800
+بجيهة العناصر عشان هي كد لما بنجي نتكلم نقول
+
+389
+00:34:08,800 --> 00:34:14,720
+مجموعة الأعداد الأولية وبنسكت معروفين خلصنا هو كل
+
+390
+00:34:14,720 --> 00:34:18,340
+عدد لا يقبل قسم عدد صحيح موجب لا يقبل قسم اللي على
+
+391
+00:34:18,340 --> 00:34:25,800
+نفسه خلصنا وبالتالي هي العدد الأولية تعالى نشوف
+
+392
+00:34:25,800 --> 00:34:31,060
+المثال اللي بعده جالي X او المجموعة A تعرف ب X
+
+393
+00:34:31,060 --> 00:34:39,420
+بالعناصر Xوال X تنتمي إلى N و X أكبر من 7 ماذا
+
+394
+00:34:39,420 --> 00:34:48,500
+يعني؟ مجموعة الأعداد الطبيعية الأكبر من 7 الأخيرة
+
+395
+00:34:48,500 --> 00:34:55,520
+.. الآن هذه معناتها أن عراسر المجموعة تنتمي إلى N
+
+396
+00:34:57,290 --> 00:35:01,170
+الـ Natural number هو عبارة عن عدد صحيح موجب أكبر
+
+397
+00:35:01,170 --> 00:35:06,810
+من واحد Natural number أكبر من واحد تمام؟ بحيث أن
+
+398
+00:35:06,810 --> 00:35:13,250
+صفة الـ N هذه لو ربعتها زائد واحد تساوي صفر مين
+
+399
+00:35:13,250 --> 00:35:17,390
+بيحقق المعادلة هذه؟ تربيع الرقم زائد واحد يساوي
+
+400
+00:35:17,390 --> 00:35:22,610
+صفر أساسا التربيع يضمن اليهم كلهم موجب بصبوط؟ وزيد
+
+401
+00:35:22,610 --> 00:35:27,480
+عليهم واحدبما أن هي أساساً الأعداد اللي عندى
+
+402
+00:35:27,480 --> 00:35:31,740
+natural number يعني ماعنديش سالب فاجلش واحد فواحد
+
+403
+00:35:31,740 --> 00:35:36,420
+زائد واحد اتنين واتنين لا تساوي الصفر ولو على رأي
+
+404
+00:35:36,420 --> 00:35:40,080
+الكتاب بدي اعتمد الصفر من ال natural number صفر
+
+405
+00:35:40,080 --> 00:35:44,620
+تربيع صفر زائد واحد واحد واحد لا تساوي صفر
+
+406
+00:35:44,620 --> 00:35:48,980
+وبالتالي مافيش ولا element في ال natural number
+
+407
+00:35:48,980 --> 00:35:56,380
+بيحقق ال property هاي وبالتالي أنا بروحباتجاهها
+
+408
+00:35:56,380 --> 00:36:00,660
+تمام okay
+
+409
+00:36:00,660 --> 00:36:08,060
+كيف ممكن نعبر عن مجموعة الأعداد النسبية كيف ممكن
+
+410
+00:36:08,060 --> 00:36:14,540
+نعبر عن مجموعة الأعداد النسبية Q بدها تساوي across
+
+411
+00:36:14,540 --> 00:36:22,550
+و Xمباشرة notation builder بتشتغل بالشكل هذا هي
+
+412
+00:36:22,550 --> 00:36:27,310
+عبارة عن X ال X لصفتها واحد اتنين تلفت بتفصل فيها
+
+413
+00:36:27,310 --> 00:36:38,850
+الآن ايه صفة ال X؟ X بتتساوي A على B بس بس
+
+414
+00:36:38,850 --> 00:36:46,310
+لسه أنت A و B ينتمي لإيش؟
+
+415
+00:36:48,230 --> 00:37:02,270
+للـ Z عداد صحيحة and ال B لا تساوي الصفر خلصت خلصت
+
+416
+00:37:02,270 --> 00:37:06,070
+مش بالزيادة انت اشتغلت بس عينينا مقلوب ماتتجملش
+
+417
+00:37:06,070 --> 00:37:09,650
+عينينا ولا بحاجة لان هيك المقلوب منك كان ممكن تكتب
+
+418
+00:37:09,650 --> 00:37:12,650
+موسيقى تانية Q
+
+419
+00:37:18,480 --> 00:37:30,080
+هي عبارة عن كل الكثور اللي فيها A تنتمي إلى Z و B
+
+420
+00:37:30,080 --> 00:37:39,480
+تنتمي إلى Z Plus بصيغة لا مصيرش وهي بصيغة أبسط من
+
+421
+00:37:39,480 --> 00:37:43,380
+أو خلّيني أقول التفصيل تبعها نفس التفصيل السابق
+
+422
+00:37:43,380 --> 00:37:48,860
+لكنه أسهل اعتمد فقط على two conditionsولا لأ؟ هذه
+
+423
+00:37:48,860 --> 00:37:54,120
+صح و هذه صح أي صيغة تكتبها انت الفكرة بتحدد ال
+
+424
+00:37:54,120 --> 00:37:58,480
+expression من العنصر اللي هان عشان بعد الفاصلة هذه
+
+425
+00:37:58,480 --> 00:38:02,700
+الجزء التاني تروح توصف ليها بشكل واضح ايش يكون
+
+426
+00:38:02,700 --> 00:38:09,760
+احنا قلنا هان هي عبارة عن الكسور البسط و مقام بحيث
+
+427
+00:38:09,760 --> 00:38:15,130
+انها تحقق كالتالي ان ال a تنتمي لل zعدد صحيحة
+
+428
+00:38:15,130 --> 00:38:21,130
+سالبة موجبة وصفر and الـ B فقط أعداد صحيحة موجبة
+
+429
+00:38:21,130 --> 00:38:25,450
+استخدمت منها الصفر وبالتالي تبقى العملية معرفة ولو
+
+430
+00:38:25,450 --> 00:38:29,190
+انا بدي .. أستاذ بدي سالب .. بدي سالب نص عدد نسلي
+
+431
+00:38:29,190 --> 00:38:34,710
+ماهي سالب واحد تنتمي إلى Z والتانين تنتمي إلى Z
+
+432
+00:38:34,710 --> 00:38:37,370
+plus مش بالضرورة السالب يكون للمقام
+
+433
+00:38:40,130 --> 00:38:44,710
+ممكن تحط N بدل ال Z بمشي الحل كمان يا شباب السؤال
+
+434
+00:38:44,710 --> 00:38:50,890
+اللي بيقرح نفسه هل ممكن تعطيني وصف لمجموعة الأعداد
+
+435
+00:38:50,890 --> 00:38:56,490
+الحقيقية اللي
+
+436
+00:38:56,490 --> 00:39:00,550
+هي ال R اديني وصف إلها كمجموعة أيه يا أحمد ماعلك
+
+437
+00:39:00,550 --> 00:39:05,170
+ساكت اليوم او
+
+438
+00:39:05,170 --> 00:39:15,800
+X طيب إيه صفة ال Rأيوة؟ ينتمي لإيش؟ الـQ أو العدد
+
+439
+00:39:15,800 --> 00:39:20,420
+الغير نسبية يعني
+
+440
+00:39:20,420 --> 00:39:29,020
+أصدركوا بقول والـR تنتمي لـQ أو الـR تنتمي للـI لا
+
+441
+00:39:29,020 --> 00:39:34,820
+irrational على فرض أنها عدد غير نسبية بس
+
+442
+00:39:34,820 --> 00:39:41,020
+يعني في الآخر ما .. ماديبتش معنى جديدماشي هالاشياء
+
+443
+00:39:41,020 --> 00:39:44,500
+بتقدر تجيلها وصف لأن المجموعة فعليا هذه بنسميها
+
+444
+00:39:44,500 --> 00:39:49,120
+universal set المجموعة اللي بتشمل كل شيء فصعب أنك
+
+445
+00:39:49,120 --> 00:39:52,640
+تروح تجيبلها وصف دقيق هي عبارة عن عدد حقيقي والـR
+
+446
+00:39:52,640 --> 00:39:57,620
+صفتها عدد حقيقي و بس مقدرش أنت فعليا هنا في مجموعة
+
+447
+00:39:57,620 --> 00:40:01,760
+زي ال universal set تفصلها بالكامل
+
+448
+00:40:05,700 --> 00:40:09,500
+في الـ Intervals ممكن نعبّرها بالـ Set Notation
+
+449
+00:40:09,500 --> 00:40:13,620
+الـ Intervals ممكن نستخدم الـ Notation أو ال
+
+450
+00:40:13,620 --> 00:40:16,420
+Builder Notation Set Builder Notation و نعرف
+
+451
+00:40:16,420 --> 00:40:19,480
+المجموعات بس باكتب انتباه كمان مرة ان الكتاب هنا
+
+452
+00:40:19,480 --> 00:40:24,940
+شوية ممكن يخربط استخدم في ال half او في ال .. في
+
+453
+00:40:24,940 --> 00:40:28,260
+ال open interval احنا سابقا اعتمدنا
+
+454
+00:40:30,340 --> 00:40:36,760
+نعكس الابتجاه، هذه فترة مغلقة وهذه فترة مفتوحة في
+
+455
+00:40:36,760 --> 00:40:43,320
+الكتاب اتمد على الجوس تمام؟ على ان الفترة المفتوحة
+
+456
+00:40:43,320 --> 00:40:47,440
+بدل الجوس المربع استخدم الجوس العادي نفس الكلام
+
+457
+00:40:47,440 --> 00:40:52,660
+انت مش هتفرج معاك تمام؟ بس عشان انا ابقى هك ما
+
+458
+00:40:52,660 --> 00:40:55,440
+تقوليش انت واني مودينا واحنا بنعرف شغلات غير هيك
+
+459
+00:40:57,020 --> 00:41:00,120
+Anyway في الفترة المفتوحة .. في الفترة المغلقة
+
+460
+00:41:00,120 --> 00:41:07,080
+اللي فوق A و B هي عبارة عن مجموعة الأرقام تمام؟ X
+
+461
+00:41:07,080 --> 00:41:12,580
+حيث أن X أكبر أو تساوي A لأنها مغلقة من عند ال A
+
+462
+00:41:12,580 --> 00:41:20,420
+and ال X أقل أو تساوي ال B مغلقة من عند ال B طبعا
+
+463
+00:41:20,420 --> 00:41:28,670
+هذا ممكن تتفصيلها هيك ادهارك X حيث ان ال Xأكبر أو
+
+464
+00:41:28,670 --> 00:41:37,810
+تساوي ال a and ال x أقل أو تساوي ال b مظبوط؟ نفس
+
+465
+00:41:37,810 --> 00:41:43,350
+الكلام اللي هنا و نفس الكلام بتنسيقه أو بتسقطه على
+
+466
+00:41:43,350 --> 00:41:52,410
+ال bagel intervals اللي موجودة عندي هنا ال
+
+467
+00:41:52,410 --> 00:41:57,250
+universal setالـ universal set هي عبارة عن
+
+468
+00:41:57,250 --> 00:42:02,530
+المجموعة اللي بتحتوي على كل ..
+
+469
+00:42:02,530 --> 00:42:08,330
+كل شيء ضمن بعض
+
+470
+00:42:08,330 --> 00:42:11,070
+الشروط أو بعض القيود لما باجي بقول إيش ال
+
+471
+00:42:11,070 --> 00:42:15,430
+universal set للأرقام أو للأعداد ال real number
+
+472
+00:42:15,430 --> 00:42:21,610
+إيش ال universal set للأعداد ال real number وإذا
+
+473
+00:42:21,610 --> 00:42:26,430
+بدك تكبر أكبر شوية بتقول ال complexولا لا؟ اه لان
+
+474
+00:42:26,430 --> 00:42:32,310
+انا جمعت ايش؟ التخيّلي تمام لو انا اجيت قولت ايش
+
+475
+00:42:32,310 --> 00:42:37,610
+ال universal set لمجموعة ال vowels يعني ايش
+
+476
+00:42:37,610 --> 00:42:42,570
+المجموعة اللي اكبر تمام من ال vowels و بتشملها في
+
+477
+00:42:42,570 --> 00:42:48,010
+داخلها هي مجموعة ال alphabetical مصبوط؟ characters
+
+478
+00:42:49,170 --> 00:42:52,930
+وبالتالي لما انا بتكلم على universal set انا بتكلم
+
+479
+00:42:52,930 --> 00:42:56,870
+على مجموعة بتشمل كل شيء .. بتشمل كل شيء و غالبا
+
+480
+00:42:56,870 --> 00:43:01,370
+هلاجي في بعض الصعوبة في أي شيء في وصف أو في وصف
+
+481
+00:43:01,370 --> 00:43:05,710
+المنموعة اللي موجودة عندها في مقابل ال universal
+
+482
+00:43:05,710 --> 00:43:10,750
+احنا شاكاش الفاي ال empty يعني هيك ال universal
+
+483
+00:43:10,750 --> 00:43:14,210
+set هي المجموعة اللي بتشمل كل شيء و ال empty set
+
+484
+00:43:15,240 --> 00:43:26,340
+التي لا تحتوي أو لا تجتمل على أي شيء تمام الآن
+
+485
+00:43:26,340 --> 00:43:31,460
+هروح على .. لأ مارجعناش اه جزاك ال definition هدول
+
+486
+00:43:31,460 --> 00:43:34,960
+ال quantifiers اه خلاص يعني برضه برضه استخدامهم
+
+487
+00:43:34,960 --> 00:43:41,400
+بسيط الآن عشان اقول عن مجموعتين متساويتينعشان اقول
+
+488
+00:43:41,400 --> 00:43:47,220
+عن مجموعتين متساويتين لازم يكونوا كل العناصر او
+
+489
+00:43:47,220 --> 00:43:52,540
+بالتنتين بيعتمنوا على نفس العناصر يعني باجي بقول A
+
+490
+00:43:52,540 --> 00:43:59,820
+بدها تساوي واحد و اتنين و تلاتة و B بدها تساوي
+
+491
+00:43:59,820 --> 00:44:06,730
+تلاتة و واحد و اتنين هل ال A تساوي B؟هل إيه تساوي
+
+492
+00:44:06,730 --> 00:44:10,810
+بيه؟ تساويها لأنهم لازم يحتويوا تلتين لازم يكونوا
+
+493
+00:44:10,810 --> 00:44:14,510
+بيشتملوا على نفس العناصر ولما نقول بيشتملوا على
+
+494
+00:44:14,510 --> 00:44:18,410
+نفس العناصر أول شغل اللي لازم تخطر في بالي أن عدد
+
+495
+00:44:18,410 --> 00:44:23,850
+العناصر في المجموعتين متساوي عدد العناصر في
+
+496
+00:44:23,850 --> 00:44:28,550
+المجموعتين متساوي يعني لو شوفت مجموعة فيها عدد
+
+497
+00:44:28,550 --> 00:44:33,590
+عناصرها أكبر من عناصر المجموعة التالية مباشرة بغير
+
+498
+00:44:33,590 --> 00:44:41,780
+متساوياتتمام؟ يعني هيك لو في عندي هان أربعة هل هي
+
+499
+00:44:41,780 --> 00:44:46,900
+تساوي بيه؟ لأ باشر ليش؟ لأنه صارت عندي الأربعة هذه
+
+500
+00:44:46,900 --> 00:44:51,120
+أو ال بي فيها أربع عناصر والإيه فيها تلت عناصر
+
+501
+00:44:51,120 --> 00:44:57,380
+فبالتالي حتما في فرق بين التنتين بس إياك تجع في
+
+502
+00:44:57,380 --> 00:45:02,300
+المطاب نفسه يا أحمد ونروح نقولك احنا أيش؟ هي
+
+503
+00:45:02,300 --> 00:45:02,840
+التلاتة
+
+504
+00:45:06,060 --> 00:45:10,400
+تكراره بتلغيه هذا مش موجود مالوش قيمة عندي هنا
+
+505
+00:45:10,400 --> 00:45:15,440
+فالتنتين متساويه فالتنتين بيكونوا متساويه تمام
+
+506
+00:45:15,440 --> 00:45:20,760
+صيغة أهل الرياضيات بنقول المجموعتين متساويه لما
+
+507
+00:45:20,760 --> 00:45:28,240
+بيكون for all X لأي X X بتنتمي للمجموعة الأولى
+
+508
+00:45:29,260 --> 00:45:34,620
+هتلاقي X موجودة في المجموعة التانية و نفس ال
+
+509
+00:45:34,620 --> 00:45:37,940
+element أكيد لأنها نفس ال element و ال X اللي
+
+510
+00:45:37,940 --> 00:45:41,700
+بتنتمي في المجموعة التانية هتلاقيها متتمية لمين؟
+
+511
+00:45:41,700 --> 00:45:44,560
+للمجموعة الأولى لإن هو by conditional if and only
+
+512
+00:45:44,560 --> 00:45:53,720
+if تمام هاي مثال على المجموعات المتساوية واحد،
+
+513
+00:45:53,720 --> 00:45:58,650
+تلاتة، خمسةتلاتة خمسة واحد equal الترتيب لا يعني
+
+514
+00:45:58,650 --> 00:46:05,210
+شيء واحد خمسة خمسة خمسة تلاتة تلاتة واحد التكرار
+
+515
+00:46:05,210 --> 00:46:09,670
+هذا بدك تطيره صفة المجموعة واحد خمسة تلاتة واحد
+
+516
+00:46:09,670 --> 00:46:15,310
+والاخر واحد كمان مكرر صار عندي واحد خمسة تلاتة
+
+517
+00:46:15,310 --> 00:46:19,590
+واحد تلاتة خمسة في بينهم تساوي
+
+518
+00:46:26,530 --> 00:46:30,490
+شوفك في المجموعات اللي قدامنا هنا ك groups تسعة
+
+519
+00:46:30,490 --> 00:46:34,410
+سبعة تسعة اتنين سبعة سالب ثلاثة سبعة الأولى
+
+520
+00:46:34,410 --> 00:46:41,250
+متساويات التانية لأ لأن السنجاب مش موجود في
+
+521
+00:46:41,250 --> 00:46:46,930
+المجموعة الأولى بقى تغير متساوية التالتة الحصار
+
+522
+00:46:46,930 --> 00:46:51,900
+موجود أيوةبس فى عندى تكرار فى الـ cat بنشيله و
+
+523
+00:46:51,900 --> 00:46:55,440
+بنلغيه و مقاتله فى عندي هانش تساوي ما بين العناصر
+
+524
+00:46:55,440 --> 00:47:04,420
+اللى موجودة عنديها subset
+
+525
+00:47:04,420 --> 00:47:11,520
+ايش يعني subset مجموعة جزئية بنقول لو كان في عندي
+
+526
+00:47:11,520 --> 00:47:19,130
+مجموعتين A و B ان ال A subset من ال Bالـ A is a
+
+527
+00:47:19,130 --> 00:47:24,950
+subset من ال B مجموعة جزئية من ال B if and only if
+
+528
+00:47:24,950 --> 00:47:34,750
+فقط إذا تحقق هذا الشروط فقط every element in A is
+
+529
+00:47:34,750 --> 00:47:43,690
+also an element of B برياضيات for all X X تنتمي
+
+530
+00:47:43,690 --> 00:47:50,190
+إلى A يؤدي إلى X تنتمي إلىإلى B ولو كانت في المثال
+
+531
+00:47:50,190 --> 00:47:53,910
+اللي بتابعت قبل شوية by conditional صارت فيها ساوي
+
+532
+00:47:53,910 --> 00:47:59,290
+طبعا صرت أنا باتجاه واحد فقط باتجاه واحد فقط طبعا
+
+533
+00:47:59,290 --> 00:48:06,870
+يعني يعني بفهم من الكلام هذا أن عناصر أو عدد عناصر
+
+534
+00:48:07,610 --> 00:48:13,230
+الـ B أكبر أو يساوي عدد عناصر الـ A هذا أول شرط
+
+535
+00:48:13,230 --> 00:48:18,570
+عدد عناصر الـ B أكبر أو يساوي عدد عناصر الـ A
+
+536
+00:48:18,570 --> 00:48:24,310
+بعدين كل عناصر الـ A موجودة في الـ B كل عناصر الـ
+
+537
+00:48:24,310 --> 00:48:28,970
+A موجودة في الـ B بنستخدم الرمز هذا عشان نقول
+
+538
+00:48:28,970 --> 00:48:33,550
+subset مجموعة جزئية مجموعة جزئية
+
+539
+00:48:37,270 --> 00:48:41,850
+الان في الأمثلة السابقة لو انا جيت قولت ان ال B
+
+540
+00:48:41,850 --> 00:48:48,670
+بدها تساوي واحد و اتنين و تلاتة و قولت ان ال A
+
+541
+00:48:48,670 --> 00:48:56,910
+بدها تساوي واحد و اتنين هل ال A subset من B؟ صحيح
+
+542
+00:48:56,910 --> 00:49:02,830
+الان بدك تاخد كل عنصر في A و تروح تشوف هل هو موجود
+
+543
+00:49:02,830 --> 00:49:10,800
+في V ولا لأ تمامموجود تمام معناته الـA subset من
+
+544
+00:49:10,800 --> 00:49:14,960
+الـB طب لو التلاتة ماكنتش موجودة تبقى العملية عشان
+
+545
+00:49:14,960 --> 00:49:19,660
+صحيحة لأنه أنا بهمني أن العراصر نفسها موجودة في
+
+546
+00:49:19,660 --> 00:49:24,140
+المجموعة في المجموعتين بس أدق يساوي كيف؟ يساوي أدق
+
+547
+00:49:24,140 --> 00:49:27,800
+كيف يساوي أدق؟ اه just like in a equivalent احنا
+
+548
+00:49:27,800 --> 00:49:30,500
+ماسألاش في ال equivalent خلصنا أنا بسألك الآن هذي
+
+549
+00:49:30,500 --> 00:49:31,920
+true ولا خالص؟ true
+
+550
+00:49:36,380 --> 00:49:40,660
+A equal B true
+
+551
+00:49:40,660 --> 00:49:46,920
+بالمناسبة subset هذه فيها احتمالية المساواة فيها
+
+552
+00:49:46,920 --> 00:49:50,320
+احتمالية المساواة عشان هيك انا قلتلك اول
+
+553
+00:49:50,320 --> 00:49:55,600
+indication ان عدد عناصر الـB اكبر او يساوي عناصر
+
+554
+00:49:55,600 --> 00:49:58,980
+الـA وكل عناصر الـA موجودة في الـB بل لو كانوا
+
+555
+00:49:58,980 --> 00:50:03,940
+يساويها معاها تبقى كلها على نفس المجموعة الـA كان
+
+556
+00:50:03,940 --> 00:50:04,760
+ثاني الى الـPhi
+
+557
+00:50:08,170 --> 00:50:15,270
+الـ A تنتمي إلى الـ Phi ماهو الـ Phi؟
+
+558
+00:50:15,270 --> 00:50:20,090
+Empty المجموعة
+
+559
+00:50:20,090 --> 00:50:24,170
+الفارغة الـ A تنتمي إلى المجموعة الفارغة؟ False
+
+560
+00:50:24,170 --> 00:50:28,810
+وهذا دائما False لأن الـ Phi مافيش فيها عناصر الـ
+
+561
+00:50:28,810 --> 00:50:33,790
+Q subset من الـ S أو أفضل الـ Phi subset من الـ S
+
+562
+00:50:35,370 --> 00:50:40,270
+الـ Phi مجموعة جزئية من أي مجموعة أخرى المجموعة
+
+563
+00:50:40,270 --> 00:50:44,590
+الفارغة مجموعة جزئية من أي مجموعة فارغة من أي
+
+564
+00:50:44,590 --> 00:50:48,670
+مجموعة أخرى يعني لو أتينا و أقولنا هنا Phi subset
+
+565
+00:50:48,670 --> 00:50:58,130
+من الـ A هذا true ليش؟ لأن حسب القانونحسب القانون
+
+566
+00:50:58,130 --> 00:51:03,250
+عدد عناصر الـ Phi لازم يكون اقل او يسوى عدد عناصر
+
+567
+00:51:03,250 --> 00:51:08,210
+الـ A اقل منها عدد عناصرها صفر هذه واحدة كل
+
+568
+00:51:08,210 --> 00:51:12,150
+العناصر اللي في الـ Phi موجودة في الـ A طب الفي
+
+569
+00:51:12,150 --> 00:51:16,210
+مافيش فيها ولا عنصر فاضية مافيش فيها عناصر already
+
+570
+00:51:16,210 --> 00:51:26,920
+حققتش الشرط وبالتالي هي true دائما كل مجموعةجزئية
+
+571
+00:51:26,920 --> 00:51:33,600
+من نفسها true true تمام لإن فيها أيش مساواة وكل
+
+572
+00:51:33,600 --> 00:51:41,460
+العناصر موجودة هذه
+
+573
+00:51:41,460 --> 00:51:44,480
+الكلام اللي قلناه سابقا في ال slide الماضي قررناه
+
+574
+00:51:44,480 --> 00:51:52,040
+كمان مرة بنفس الصيغة السابقة ال proper subset
+
+575
+00:51:54,200 --> 00:52:02,080
+Proper subset مجموعة جزئية غير مساوية مجموعة جزئية
+
+576
+00:52:02,080 --> 00:52:07,580
+غير مساوية و لاحظ الرمز الان بيقول لو كانت ال a
+
+577
+00:52:07,580 --> 00:52:14,840
+subset من ال b و ال a لا تساوي ال b بنكتب ان هذا
+
+578
+00:52:14,840 --> 00:52:19,140
+مجموعة proper subset ايش proper subset يعني مجموعة
+
+579
+00:52:19,140 --> 00:52:25,490
+جزئية لا تساوي ال bيعني بين جثين عدد عناصر ال a
+
+580
+00:52:25,490 --> 00:52:29,670
+أقل من عدد عناصر ال b لو بأنصر واحد أقل منه في
+
+581
+00:52:29,670 --> 00:52:39,910
+الآخر المساواة بطلت موجودة for
+
+582
+00:52:39,910 --> 00:52:44,590
+all if ال a proper subset proper subset من ال b
+
+583
+00:52:44,590 --> 00:52:52,910
+معناته for all xX تنتمي إلى A يقد أن X تنتمي إلى B
+
+584
+00:52:52,910 --> 00:52:59,550
+and they exist على الأقل هناك عنصر واحد X تنتمي
+
+585
+00:52:59,550 --> 00:53:05,930
+إلى B and X لا تنتمي إلى A إذا كان ال X ممكن تخرب
+
+586
+00:53:05,930 --> 00:53:10,590
+الذكاء أما ال Y مش هتفرج كتير ولا شريك؟بس في الآخر
+
+587
+00:53:10,590 --> 00:53:15,710
+لكل عناصر المجموعة A هتلاقيها موجودة في المجموعة B
+
+588
+00:53:15,710 --> 00:53:20,890
+وهناك عنصر واحد على الأقل في B مش موجود في A عشان
+
+589
+00:53:20,890 --> 00:53:26,710
+نحقق البروبر subset كيف
+
+590
+00:53:26,710 --> 00:53:33,950
+ال B أكبر من A طيب
+
+591
+00:53:33,950 --> 00:53:38,310
+كمان مرة الآن بنقول
+
+592
+00:53:40,150 --> 00:53:46,030
+الـ A is a proper subset of B ان الـ A مجموعة
+
+593
+00:53:46,030 --> 00:53:51,790
+جزئية من الـ B ولا تساويها تمام؟ هذا الكلام بيكون
+
+594
+00:53:51,790 --> 00:53:58,730
+صحيح if and only if لكل X في A X تنتمي إلى A حاليا
+
+595
+00:53:58,730 --> 00:54:04,930
+X تنتمي لمين؟ لـ B and بالإضافة للشرق هذا there
+
+596
+00:54:04,930 --> 00:54:11,190
+exist at least one X أو one Yone X موجودة X موجودة
+
+597
+00:54:11,190 --> 00:54:16,470
+في B و مش موجودة يعني لو احنا بالمثال اللي شوفناه
+
+598
+00:54:16,470 --> 00:54:22,390
+قبل شوية A بدها تساوي واحد و اتنين و تلاتة و ال A
+
+599
+00:54:22,390 --> 00:54:28,110
+.. و ال B عفوا بدها تساوي واحد و اتنين و تلاتة و
+
+600
+00:54:28,110 --> 00:54:38,460
+أربعة ال A proper subset من ال B ال AProper subset
+
+601
+00:54:38,460 --> 00:54:44,540
+من الـ B لأ
+
+602
+00:54:44,540 --> 00:54:51,580
+لأ في ال subset قلنا ان عدد عناصر ال X أقل او
+
+603
+00:54:51,580 --> 00:54:57,580
+تساوي عدد عناصر ال B تمام بس هنا عندي sharp and
+
+604
+00:54:57,580 --> 00:55:04,980
+تمام ان العنصر في عدد عناصر ال B أكبر من عناصر ال
+
+605
+00:55:04,980 --> 00:55:16,420
+Aطيب في عندي قانونين مهمات بقول
+
+606
+00:55:16,420 --> 00:55:22,780
+لو كانت ال a تساوي b معناته ده انا باخد منه او
+
+607
+00:55:22,780 --> 00:55:28,700
+بفهم منه ان ال a subset من ال b و ال b subset من
+
+608
+00:55:28,700 --> 00:55:32,780
+ال a لو
+
+609
+00:55:32,780 --> 00:55:36,720
+كانت ال a تساوي ال bمعناته التنتين اللي هم نفس عدد
+
+610
+00:55:36,720 --> 00:55:42,620
+العناصر مظبوط وكل عنصر في A موجود في B وهذه عنوان
+
+611
+00:55:42,620 --> 00:55:46,520
+إيش؟ عنوان ال subset يعني A subset من ال B وبما أن
+
+612
+00:55:46,520 --> 00:55:51,320
+العلاقة بينهم equal معناته كل عنصر في B موجود في A
+
+613
+00:55:51,320 --> 00:55:55,480
+وبهذا اللي برضه ال subset معناته A subset من B and
+
+614
+00:55:55,480 --> 00:55:57,660
+ال B subset من A
+
+615
+00:56:01,820 --> 00:56:05,520
+والعلاقة اللى موجودة ما بين الأرقام اللى احنا قلنا
+
+616
+00:56:05,520 --> 00:56:09,380
+لك أجيلها كمان شوية بين الأعداد مجموعات الأعداد هي
+
+617
+00:56:09,380 --> 00:56:14,460
+عبارة عن subset عبارة عن subset لما تكون ال a
+
+618
+00:56:14,460 --> 00:56:21,340
+subset من ال b and ال b subset من ال c معناته ال a
+
+619
+00:56:21,340 --> 00:56:28,300
+subset من ال c ال natural subset من ال zip من ال
+
+620
+00:56:28,300 --> 00:56:34,070
+integer ولا لا؟طب وال integer subset من ال real
+
+621
+00:56:34,070 --> 00:56:40,030
+number معناته natural subset طيب عشان نريحك في
+
+622
+00:56:40,030 --> 00:56:44,390
+الموضوع ال subset خلينا نشوف هيك على السريع واحد
+
+623
+00:56:44,390 --> 00:56:51,670
+اتنين تلاتة اربعة عشان تعمل subset صحيحة على فرض
+
+624
+00:56:51,670 --> 00:56:56,910
+ان هذه هي المجموعة B هي subset من ال B ده يفتح
+
+625
+00:56:56,910 --> 00:57:03,900
+أجواسأخد أي عدد من الـ element من داخل الـ B حطهم
+
+626
+00:57:03,900 --> 00:57:10,120
+وين؟ جوا الأقواس إيش ممكن تاخد؟ لو أخدت الواحد
+
+627
+00:57:10,120 --> 00:57:17,500
+لحالها، صح؟ أخدت التنين، صح؟ أخدت الواحد والتنين؟
+
+628
+00:57:17,500 --> 00:57:22,820
+خدتهم كلهم، صح؟ مافي مشكلة عندك هذه مفهوم الـ
+
+629
+00:57:22,820 --> 00:57:29,030
+subset إن أخد عناصر المجموعة وحطهمأو جزء من عناصر
+
+630
+00:57:29,030 --> 00:57:33,250
+المجموعة بيحطهم في الداخل مجموعة بالمثال اللي
+
+631
+00:57:33,250 --> 00:57:38,670
+شفناه قبل شوية لما كان بيقولني ان ال A بدها تساوي
+
+632
+00:57:38,670 --> 00:57:41,950
+X
+
+633
+00:57:41,950 --> 00:57:45,930
+و Y و
+
+634
+00:57:45,930 --> 00:57:51,830
+X و Y و Z لو
+
+635
+00:57:51,830 --> 00:57:59,640
+أنا قد قلتلك كتاني X و Yمجموعة جزئية من الـ A صح؟
+
+636
+00:57:59,640 --> 00:58:06,240
+كم واحد بيقول صح؟ X و Y مجموعة جزئية من الـ A كم
+
+637
+00:58:06,240 --> 00:58:12,260
+واحد بيقول صح رفع يده؟ غلط ايش
+
+638
+00:58:12,260 --> 00:58:15,540
+احنا اتفقنا يا شباب عشان نقول مجموعة جزئية؟ قولت
+
+639
+00:58:15,540 --> 00:58:21,160
+بدك تاخد الجثين هدول هيك وتاخد ال element وتحطه
+
+640
+00:58:21,160 --> 00:58:25,080
+جوا الجثين مين ال element اللي جوا الجثين؟ هيه
+
+641
+00:58:31,290 --> 00:58:37,210
+هيو ايوة فانت بدك تنتبه .. تنتبه لوضع العناصر اللي
+
+642
+00:58:37,210 --> 00:58:44,510
+موجودة عندك اعيد تاني ال a بتتساوح اضربها x و x
+
+643
+00:58:44,510 --> 00:58:50,670
+بالشكل هذا المجموعة
+
+644
+00:58:50,670 --> 00:58:56,840
+اللي عندي a كم عنصر فيها؟ عنصرينالأصل الأول X
+
+645
+00:58:56,840 --> 00:59:05,000
+والأصل التاني مجموعة فيها X تمام ال X تنتمي إلى A
+
+646
+00:59:05,000 --> 00:59:09,260
+صحيحة
+
+647
+00:59:09,260 --> 00:59:13,140
+و
+
+648
+00:59:13,140 --> 00:59:22,420
+المجموعة X تنتمي إلى A صحيحة المجموعة X subset من
+
+649
+00:59:22,420 --> 00:59:22,760
+ال A
+
+650
+00:59:26,420 --> 00:59:29,980
+أيوة اختلف الفقه اهلا جدا احنا ايش جونا شباب
+
+651
+00:59:29,980 --> 00:59:34,900
+subset معناته بدي اخد ال element اللي هان و اروح
+
+652
+00:59:34,900 --> 00:59:39,160
+اشوف هو element in A ولا لأ ال X موجودة في A
+
+653
+00:59:39,160 --> 00:59:46,720
+لحالها بدون اقواس تمام معناته دي subset و المجموعة
+
+654
+00:59:46,720 --> 00:59:54,620
+ها دي برضه subset في ال A ليش؟ بدي اخد ال element
+
+655
+00:59:54,620 --> 00:59:59,410
+اللي جواتهاو انا هاناول هاي موجود كما هو وبالتالي
+
+656
+00:59:59,410 --> 01:00:03,970
+انتبه .. انتبه لل details هاي لما اقول subset او
+
+657
+01:00:03,970 --> 01:00:08,370
+لام تمي هل العنصر موجود تمام او لأ بمجرد اقولك
+
+658
+01:00:08,370 --> 01:00:12,090
+subset ماتحطه لجواس و لازم العنصر اللي كونها
+
+659
+01:00:12,090 --> 01:00:16,690
+العناصر اللي كونها تكون موجودة as elements as
+
+660
+01:00:16,690 --> 01:00:24,150
+elements يعني لو انا بدى اغير بالمثال التالي احنا
+
+661
+01:00:24,150 --> 01:00:24,990
+رجعنا للجلم هذا
+
+662
+01:00:31,940 --> 01:00:39,000
+طيب لو اتينا يقولنا ال A بدها تساوي X
+
+663
+01:00:39,000 --> 01:00:47,760
+و X و Y الآن
+
+664
+01:00:47,760 --> 01:00:50,900
+ال
+
+665
+01:00:50,900 --> 01:00:54,660
+X subset من ال A
+
+666
+01:00:58,090 --> 01:01:01,390
+X Subset يعني أنا بدي الأقواس اللي برا يظلوا
+
+667
+01:01:01,390 --> 01:01:05,290
+موجودات بدي أاخد ال element اللي جواتهم هل هو
+
+668
+01:01:05,290 --> 01:01:12,790
+موجود؟ False E الفرمية ال Y Subset
+
+669
+01:01:12,790 --> 01:01:16,170
+احفظ المباراة احتاجها عيني هتبقى جاملة إذا بتنجح
+
+670
+01:01:16,170 --> 01:01:19,990
+إذا بتقدر تحلهم بالحفظ بمشيش الحفظ و هيك أمور يا
+
+671
+01:01:19,990 --> 01:01:28,120
+شباب الآن ال Y Subset من .. هي ال Yهل الأواعي
+
+672
+01:01:28,120 --> 01:01:35,020
+موجودة as element في الـ A؟ لأ خلصنا؟
+
+673
+01:01:35,020 --> 01:01:42,800
+تمام؟ الحمد لله subset
+
+674
+01:01:42,800 --> 01:01:51,820
+على العناصر اللي موجودة عندي هان الأولى
+
+675
+01:01:51,820 --> 01:01:56,960
+subset؟ ايه ال subset من ال B؟ trueتانية ايه ال
+
+676
+01:01:56,960 --> 01:02:02,860
+subset من ال B؟ true لكي
+
+677
+01:02:02,860 --> 01:02:09,240
+أطيّرهم تالتة false لأن التلائم الواحد موجود في ال
+
+678
+01:02:09,240 --> 01:02:18,360
+A مش موجود في ال B proper؟ غلط يا صاحبي ولا proper
+
+679
+01:02:18,360 --> 01:02:22,460
+كمان ولا
+
+680
+01:02:22,460 --> 01:02:23,040
+ال B subset
+
+681
+01:02:33,650 --> 01:02:38,090
+false false إذا
+
+682
+01:02:38,090 --> 01:02:42,770
+هي ماكنتش proper subset فهي مستحيل تكون subset طيب
+
+683
+01:02:42,770 --> 01:02:45,030
+على هيك يا شباب هنجي في اليوم ان شاء الله تورج و
+
+684
+01:02:45,030 --> 01:02:47,330
+تعالى و المحاضرة اللي جايه بنبدأ من عند ال
+
+685
+01:02:47,330 --> 01:02:52,170
+cardinality و المقصود فيها عدد عناصر المجموعة عدد
+
+686
+01:02:52,170 --> 01:02:54,890
+عناصر المجموعة في أي سؤال يا شباب الله يعطيكوا
+
+687
+01:02:54,890 --> 01:02:55,230
+العافية
+
diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/AGhpvbdD4Ug.srt b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/AGhpvbdD4Ug.srt
new file mode 100644
index 0000000000000000000000000000000000000000..d1dee2aed65510babe3f742729f2ddec7dfd2297
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/AGhpvbdD4Ug.srt
@@ -0,0 +1,1670 @@
+1
+00:00:21,500 --> 00:00:23,400
+بسم الله الحمد لله والصلاة والسلام على رسول الله
+
+2
+00:00:23,400 --> 00:00:26,440
+طيب شباب أهلا وسهلا بكم في اللقاء الثاني في ال
+
+3
+00:00:26,440 --> 00:00:29,640
+chapter الـ .. أو الثالث في الـ chapter الذي قتل الـ
+
+4
+00:00:29,640 --> 00:00:32,900
+logical propositional logic واليوم إن شاء الله
+
+5
+00:00:32,900 --> 00:00:38,460
+محاضرتنا قصيرة سنخلص فيها فقط الـ section الذي هو
+
+6
+00:00:38,460 --> 00:00:43,100
+متعلق بـ propositional equivalence نعم بدأتُ بس
+
+7
+00:00:43,100 --> 00:00:46,220
+فيها سؤال: جئتُ لما مثلاً  اثنان زائد اثنان
+
+8
+00:00:46,220 --> 00:00:47,960
+بتساوي أربعة، كيف بتقع فيها؟
+
+9
+00:00:57,150 --> 00:01:02,710
+آه، بس it's not equal طيب
+
+10
+00:01:02,710 --> 00:01:05,530
+الـ .. كنا نحن بدأنا فعلياً المحاضرة الماضية
+
+11
+00:01:05,530 --> 00:01:08,190
+تكلّمنا على الـ logical equivalence أو proposition
+
+12
+00:01:08,190 --> 00:01:12,210
+equivalence وقلنا فيها أن مجموعة من الـ terms أو
+
+13
+00:01:12,210 --> 00:01:16,530
+مجموعة من المصطلحات، يجب أن نفهمها ونحفظها جيداً لما
+
+14
+00:01:16,530 --> 00:01:20,010
+بتكون في عندي compound proposition ودائماً الـ
+
+15
+00:01:20,010 --> 00:01:25,760
+result تبعه true معناته هو Tautology يعني لو أنا
+
+16
+00:01:25,760 --> 00:01:34,220
+أتيتُ بكل بساطة وقلت لك: أنا في عندي B نقطة B وفي
+
+17
+00:01:34,220 --> 00:01:39,940
+بينهما R تمام
+
+18
+00:01:39,940 --> 00:01:46,160
+الآن بما أنهُ اتكلم على one preposition تمام
+
+19
+00:01:46,160 --> 00:01:51,280
+معناته true و false نفيها false، between true true
+
+20
+00:01:51,280 --> 00:01:56,910
+or false true False or True؟ True هذا الآن الـ
+
+21
+00:01:56,910 --> 00:02:01,590
+compound proposition هو عبارة عن Tautology لأنه
+
+22
+00:02:01,590 --> 00:02:06,390
+قيمة الـ True مع كل صفوف جدول الاحتمالات التي
+
+23
+00:02:06,390 --> 00:02:08,830
+موجودة لدينا بغض النظر عن حجم الجدول، صغير أم كبير
+
+24
+00:02:08,830 --> 00:02:13,470
+نفس المنطقة تمام؟ الآن لو الجدول كله من تمام مثلاً
+
+25
+00:02:13,470 --> 00:02:17,510
+الخانات عفواً أو تمام صفوف  في خانة واحدة فقط
+
+26
+00:02:17,510 --> 00:02:21,420
+False لا أستطيع أن أقول عنه Tautology لا أستطيع أن أقول عنه
+
+27
+00:02:21,420 --> 00:02:28,960
+tautology فلازم يكون هو دائماً في كل الأوقات  لازم
+
+28
+00:02:28,960 --> 00:02:35,960
+يكون true، كذلك لو كانت القيمة في أي وقت تساوي
+
+29
+00:02:35,960 --> 00:02:45,280
+false نقول عنه contradiction، تعامل تبديل الـ b و
+
+30
+00:02:45,280 --> 00:02:45,920
+نقطة الـ b
+
+31
+00:02:49,140 --> 00:02:56,020
+true and false false، false and true false لاحظ أنه
+
+32
+00:02:56,020 --> 00:03:00,100
+فعلياً أن كل صفوف جدول الاحتمالات كانت نتيجتها
+
+33
+00:03:00,100 --> 00:03:04,320
+false، هذان التعريفان الأسهل، two definition
+
+34
+00:03:04,320 --> 00:03:09,940
+ممكن أن يكونا موجودين معنا بكل بساطة، الآن تريد أن ترى
+
+35
+00:03:09,940 --> 00:03:15,180
+الجملة التالية، ستستخدم جدول الاحتمالات لـ
+
+36
+00:03:15,180 --> 00:03:22,900
+تحليلها، واتفقنا أننا سنعتمد الإشارة هذه على أنها
+
+37
+00:03:22,900 --> 00:03:26,340
+إشارة الـ equivalence بين الـ proposition  يجب أن
+
+38
+00:03:26,340 --> 00:03:29,980
+نعتمد الإشارة هذه as equivalence بين الـ
+
+39
+00:03:29,980 --> 00:03:37,020
+proposition الموجودة لدي، يجيب ويقول لي: شوف لي
+
+40
+00:03:37,020 --> 00:03:48,580
+نفي الـ D R أو نفي P or Q، نفي P or Q أو نقطة P ونقطة Q
+
+41
+00:03:48,580 --> 00:03:54,880
+نقطة P ونقطة Q، نقطة P ونقطة Q، نقطة P ونقطة Q
+
+42
+00:03:54,880 --> 00:03:59,060
+نقطة P ونقطة Q، نقطة P ونقطة Q، نقطة P ونقطة Q
+
+43
+00:03:59,060 --> 00:04:00,360
+نقطة P ونقطة P ونقطة Q، نقطة P ونقطة P ونقطة P
+
+44
+00:04:00,360 --> 00:04:00,380
+ونقطة P ونقطة P ونقطة P ونقطة P ونقطة P و
+
+45
+00:04:00,380 --> 00:04:00,860
+نقطة P ونقطة P ونقطة P ونقطة P ونقطة P ونقطة
+
+46
+00:04:00,860 --> 00:04:03,340
+P ونقطة P ونقطة P ونقطة P ونقطة P ونقطة P و
+
+47
+00:04:03,340 --> 00:04:14,960
+P ونقطة P ونقطة P ونقطة P ونقطة P و
+
+48
+00:04:15,080 --> 00:04:19,100
+و اثنين false، العمود الذي بعده واحدة true واحدة
+
+49
+00:04:19,100 --> 00:04:25,600
+false وبدأنا نطبق المسألة بكل بساطة، نفي نقطة B هي
+
+50
+00:04:25,600 --> 00:04:33,460
+نقطة Q، P or Q هي P or Q، true or true true
+
+51
+00:04:33,460 --> 00:04:38,920
+نفيها false، true or false true، نفيها false، false
+
+52
+00:04:38,920 --> 00:04:43,040
+or true true، نفيها false، false or false false
+
+53
+00:04:43,040 --> 00:04:46,500
+نفيها true، وبعدين نذهب، طبعاً هنا في خطأ بسيط
+
+54
+00:04:46,500 --> 00:04:54,980
+يجب أن نفي Q، وبالتالي بدأت أحسب نفي الـ B and نفي الـ
+
+55
+00:04:54,980 --> 00:04:58,640
+Q، false and false false، and true true and false
+
+56
+00:04:58,640 --> 00:05:04,130
+true and true، لاحظ في النهاية أنني وصلت إلى أن في عندي
+
+57
+00:05:04,130 --> 00:05:08,390
+تكافؤ بين الـ two proposition الموجودة أمامي
+
+58
+00:05:08,390 --> 00:05:12,210
+وهذا الأمر حتى الآن بسيط، إنشاء جدول الاحتمالات
+
+59
+00:05:12,210 --> 00:05:16,090
+وحسابه، الأمر بسيط وسهل، ليس فيه أي مشكلة، الأمر
+
+60
+00:05:16,090 --> 00:05:20,730
+هو بشكل عام بسيط، لكن قد يسبب صعوبة أو تعقيداً نوعاً
+
+61
+00:05:20,730 --> 00:05:25,210
+ما حسب المسألة المعروضة أمامك، بدايةً على الـ
+
+62
+00:05:25,210 --> 00:05:28,670
+equivalence، صار في عندنا مجموعة من القوانين ممكن
+
+63
+00:05:28,670 --> 00:05:32,730
+أن تكون موجودة، لأن الشباب لو جاءت تتحدث عن compound
+
+64
+00:05:32,730 --> 00:05:41,330
+proposition مع five simple propositions، ماذا
+
+65
+00:05:41,330 --> 00:05:46,130
+يصل إليه في المسألة التي لديه؟ عدد جداول الاحتمالات
+
+66
+00:05:46,130 --> 00:05:51,030
+التابعة؟ اثنان واثنان، خمسة، اثنان وثلاثون، اثنان و
+
+67
+00:05:51,030 --> 00:05:56,190
+ثلاثون، فتخيّل  كم سيكون الأمر معقداً مثل المثال
+
+68
+00:05:56,190 --> 00:06:01,750
+هذا على سبيل المثال، مثل
+
+69
+00:06:01,750 --> 00:06:08,290
+هكذا بخمسة متغيرات أو ستة، ستحتاج ساعة لعمل جدول
+
+70
+00:06:08,290 --> 00:06:11,070
+الاحتمالات، أنت تعمل فيه، لن يكون كافياً
+
+71
+00:06:11,070 --> 00:06:16,510
+بالنسبة لك، الحل: أن نحاول أن نعتمد على مجموعة من القوانين
+
+72
+00:06:16,510 --> 00:06:20,210
+بحيث أننا نختصر أو نختزل هذه المسائل، وفعلياً نقدر
+
+73
+00:06:20,210 --> 00:06:24,810
+أن نرى إلى أين تقودنا هذه المسائل، بشكل بسيط نقول
+
+74
+00:06:24,810 --> 00:06:29,150
+هذه المسائل يا شباب، وهي أشياء سهلة، يجب أن نحفظها و
+
+75
+00:06:29,150 --> 00:06:33,110
+نتمعن فيها، حتى الآن كل كلامنا Logical Gates أو
+
+76
+00:06:33,110 --> 00:06:39,390
+Boolean ألجبر، true and true true، and false false
+
+77
+00:06:39,390 --> 00:06:45,280
+true or true true، true or false true، مصدر أو لا، و
+
+78
+00:06:45,280 --> 00:06:48,740
+تعالَ لنرَها، وبالتالي لو أنا، ما مكانة في القانون
+
+79
+00:06:48,740 --> 00:06:52,940
+الأول؟ هذا قانون الوحدة، يعني ماذا هو العنصر المحايد
+
+80
+00:06:52,940 --> 00:06:56,200
+الضربي في عملية الضرب؟ الواحد، والمحايد الجمعي
+
+81
+00:06:56,200 --> 00:07:02,080
+الصفر، وليس هناك محايد مع عملية الـ and، الـ true الذي
+
+82
+00:07:02,080 --> 00:07:08,220
+لا يؤثر، لو أضفته لن يؤثر، لأن true and true لأن
+
+83
+00:07:08,220 --> 00:07:11,670
+لو كانت قيمته true ستكون true، ولو كانت قيمته
+
+84
+00:07:11,670 --> 00:07:16,750
+false ستكون false، كذلك الـ false هي المحايد مع الـ
+
+85
+00:07:16,750 --> 00:07:22,450
+or الآن
+
+86
+00:07:22,450 --> 00:07:27,970
+كذلك في قانون الـ domination، بمجرد أن تجد true مع الـ
+
+87
+00:07:27,970 --> 00:07:32,010
+or النتيجة true بناءً على التعريف، تكون واحدة
+
+88
+00:07:32,010 --> 00:07:34,710
+من المتطلبات، على الأقل الـ true، فأنت تضمن الـ
+
+89
+00:07:34,710 --> 00:07:39,800
+true، في حالة الـ false مع الـ and، واحدة على الأقل
+
+90
+00:07:39,800 --> 00:07:47,660
+false معناته ماذا الاختزال؟
+
+91
+00:07:47,660 --> 00:07:54,440
+الآن P and P، بما أنه نفس المتغير، معناته هي نفس
+
+92
+00:07:54,440 --> 00:07:58,600
+قيمة truth value، إما أن تكون true أو أن تكون false
+
+93
+00:07:58,600 --> 00:08:07,500
+وهذه ستساوي false وهذه ستساوي true، وبالتالي تكافئ
+
+94
+00:08:08,560 --> 00:08:12,580
+الـ P، وعند الـ or كذلك، لأنها نفس القيمة التي
+
+95
+00:08:12,580 --> 00:08:18,940
+موجودة لدي في الموضوع الذي فيه P and not الـ B
+
+96
+00:08:18,940 --> 00:08:24,140
+false، لأن إذا كانت true ستكون false ... false، ولو
+
+97
+00:08:24,140 --> 00:08:28,040
+كانت هذه false فهي already خلاص لا نبحث عن التي بعدها
+
+98
+00:08:28,040 --> 00:08:33,280
+true or not الـ B، عفواً P or not الـ B، true لأن لو
+
+99
+00:08:33,280 --> 00:08:35,600
+كانت هذه false ستكون الثانية true، ولو كانت true
+
+100
+00:08:35,600 --> 00:08:42,740
+already بمفردها، في النفي، نفي النفي إثبات، commutative
+
+101
+00:08:42,740 --> 00:08:48,400
+أو الإبدال، P and Q تساوي Q and P، وهذه العملية
+
+102
+00:08:48,400 --> 00:08:56,140
+قلنا إبدالية، وكذلك هي عند الـ or، قانون التجميع P and
+
+103
+00:08:56,140 --> 00:09:02,590
+Q and R نحن نجد أن العملية عملية تجميعية و
+
+104
+00:09:02,590 --> 00:09:06,670
+ثنائية، في نفس الوقت تعني تساوي P and Q الكل and R
+
+105
+00:09:06,670 --> 00:09:14,670
+كذلك تساوي P and افتح قوس Q and الـ R، كذلك عملية
+
+106
+00:09:14,670 --> 00:09:21,130
+الجمع أو عفواً عملية الـ or هي عبارة عن عملية كذلك
+
+107
+00:09:21,130 --> 00:09:28,710
+عملية تجميعية، من ناحية التوزيع، تستطيع أن توزع الـ and
+
+108
+00:09:29,560 --> 00:09:35,200
+على الـ or، وتوزع الـ or على الـ and، بحيث أن P or
+
+109
+00:09:35,200 --> 00:09:40,960
+لكي لا تنسى، دائماً خذ الـ proposition والإشارة
+
+110
+00:09:40,960 --> 00:09:47,580
+معها وبالتالي
+
+111
+00:09:47,580 --> 00:09:55,680
+P and q or الـ r تساوي P and q or P and الـ r، كذلك
+
+112
+00:09:55,680 --> 00:10:00,400
+عند الـ or لما نوزعها على الـ and، P or q and P or
+
+113
+00:10:00,400 --> 00:10:07,140
+الـ r، دي مورجان،  قانون دي مورجان، لو أثبت من خلال
+
+114
+00:10:07,140 --> 00:10:11,260
+جدول الاحتمالات أنه لو دخلنا النفي على الـ and والـ
+
+115
+00:10:11,260 --> 00:10:14,460
+or، ليس فقط قيمة truth value التابعة للـ proposition هي التي
+
+116
+00:10:14,460 --> 00:10:21,160
+تتغير، بل حتى العملية، تصبح الـ and تصبح or، وبالتالي
+
+117
+00:10:21,160 --> 00:10:28,520
+not a and b تساوي not a or not b، نقطة P أو نقطة Q، نقطة P
+
+118
+00:10:28,520 --> 00:10:38,580
+أو نقطة Q، نقطة P أو نقطة Q، نقطة P أو نقطة Q، نقطة P
+
+119
+00:10:38,580 --> 00:10:47,420
+أو نقطة Q، نقطة Q أو نقطة P أو نقطة Q، نقطة P أو
+
+120
+00:10:47,420 --> 00:10:54,280
+نقطة Q أو نقطة P أو نقطة P أو نقطة P أو نقطة P أو
+
+121
+00:10:54,280 --> 00:10:55,080
+نقطة P أو نقطة P أو نقطة P أو نقطة P أو نقطة P أو
+
+122
+00:10:55,080 --> 00:11:01,190
+نقطة P أو نقطة P أو B implies Q and B implies R
+
+123
+00:11:01,190 --> 00:11:07,330
+يؤدي إلى تكافؤ B implies وكأنه ما كنت أقوله؟
+
+124
+00:11:07,330 --> 00:11:11,270
+أخذناه
+
+125
+00:11:11,270 --> 00:11:22,390
+معامل مشترك، أيضاً الـ implies B
+
+126
+00:11:22,390 --> 00:11:30,250
+implies R or Q implies R، كذلك سأجمع الـ implication
+
+127
+00:11:30,250 --> 00:11:39,910
+B and Q implies R، وأريك أن تنتبه للأخطاء كيف
+
+128
+00:11:39,910 --> 00:11:43,730
+أصبحت في المسألة الثانية، لماذا؟ لأنه لا تنسى أن
+
+129
+00:11:43,730 --> 00:11:50,150
+هذا القانون الأساسي، موضوع الإشارة، نثبت أنفسنا أو
+
+130
+00:11:50,150 --> 00:11:56,880
+نشوف كيف نثبت هذا الكلام، طيب في الـ biconditional B
+
+131
+00:11:56,880 --> 00:12:04,300
+biconditional of Q B، biconditional of Q B
+
+132
+00:12:04,300 --> 00:12:13,660
+biconditional of Q B، biconditional of Q B، by
+
+133
+00:12:13,660 --> 00:12:14,580
+conditional of Q B، biconditional of Q B، by
+
+134
+00:12:14,580 --> 00:12:19,560
+conditional of Q B، biconditional of Q B، by
+
+135
+00:12:19,560 --> 00:12:21,920
+conditional of Q B، biconditional of Q
+
+136
+00:12:25,330 --> 00:12:28,650
+بالنسبة، ماذا يحدث للمسلّمات؟ يجب أن تحفظها؟ نعم،
+
+137
+00:12:28,650 --> 00:12:32,670
+يجب أن تحفظها، ولكن قبل أن تحفظها يجب أن تحاول أو
+
+138
+00:12:32,670 --> 00:12:36,070
+نحاول معاً أن نعرف أن هذه القوانين من أين أتت، بناءً
+
+139
+00:12:36,070 --> 00:12:41,150
+على ماذا كُتبت وأصبحت تساوي هذا، موجود الآن في
+
+140
+00:12:41,150 --> 00:12:43,550
+الحالة، تعالَ لنرى الحالة الأولى الموجودة لدينا
+
+141
+00:12:43,550 --> 00:12:48,490
+أو دعنا لا نأخذ أكثر من حالة، نعود مثلاً لدي مورجان
+
+142
+00:12:48,490 --> 00:12:52,670
+مثلاً
+
+143
+00:12:52,670 --> 00:12:56,330
+نأخذ واحدة من دي مورجان والتوزيع، لأثبت أن
+
+144
+00:12:56,330 --> 00:13:01,470
+هذان متكافئان، هذه القوانين يا شباب، مرة أخرى هي
+
+145
+00:13:01,470 --> 00:13:05,230
+التي ستفيدني عندما يكون عدد الـ proposition كبير
+
+146
+00:13:05,230 --> 00:13:08,870
+لا أستطيع أن أُشكل جدول الاحتمالات، وبالتالي سأذهب للقوانين
+
+147
+00:13:08,870 --> 00:13:11,950
+في الحالة التي مثل هذه، ماذا المطلوب فعله يا شباب؟
+
+148
+00:13:11,950 --> 00:13:16,150
+المفروض أن أُعمل جدول الاحتمالات لكل عنصر من العناصر
+
+149
+00:13:16,150 --> 00:13:19,790
+أو الأقواس هذين، وأرى هل هما متساويان أم لا؟
+
+150
+00:13:25,490 --> 00:13:29,450
+false, false true,
+
+151
+00:13:29,610 --> 00:13:40,610
+false true, false الآن P or Q ونفيها، أصبحت لأن
+
+152
+00:13:40,610 --> 00:13:47,630
+true or true true ونفيها false، true or false true
+
+153
+00:13:47,630 --> 00:13:51,850
+ونفيها false، false or true true ونفيها false
+
+154
+00:13:51,850 --> 00:13:57,780
+false or false false وtrue ونفيها true، طيب الطرف
+
+155
+00:13:57,780 --> 00:14:05,060
+الثاني نقطة B ونقطة Q، false
+
+156
+00:14:05,060 --> 00:14:10,140
+and false false، طيب لماذا أقول false وأشرح على
+
+157
+00:14:10,140 --> 00:14:14,000
+true؟ لأني أعمل المسألة التي أُريدها بالنفي false
+
+158
+00:14:14,000 --> 00:14:21,240
+and true false، true and false false، true and true
+
+159
+00:14:21,240 --> 00:14:26,820
+true، وبالتالي المعادلتان أو two compound
+
+160
+00:14:26,820 --> 00:14:32,800
+proposition equivalent، متكافئتان لأن عند كل صفوف
+
+161
+00:14:32,800 --> 00:14:38,440
+جدول الاحتمالات لهما نفس النتيجة، يعني ماذا؟ مهما أخذت
+
+162
+00:14:38,440 --> 00:14:43,680
+قيمة لـ P و Q، المعادلتان ستعطيان نفس النتيجة، وبالتالي
+
+163
+00:14:43,680 --> 00:14:47,520
+نحن نتكلم عن تساوي أو تكافؤ بين العناصر التي
+
+164
+00:14:47,520 --> 00:14:48,160
+موجودة لدينا
+
+165
+00:14:51,570 --> 00:14:54,970
+كذلك في حالة الـ implication، لو أنا أريد أن أثبتها
+
+166
+00:14:54,970 --> 00:15:02,610
+كذلك نفس الموضوع، جدول الاحتمالات، وأعمل عليه، طيب
+
+167
+00:15:02,610 --> 00:15:07,910
+لنرى
+
+168
+00:15:07,910 --> 00:15:12,710
+الأخيرة من العناصر الموجودة لدينا في القيمة
+
+169
+00:15:12,710 --> 00:15:15,050
+التي لديك، كم متغير؟ ثلاثة
+
+170
+00:15:21,630 --> 00:15:30,290
+True True True True False False False False True
+
+171
+00:15:30,290 --> 00:15:37,850
+True False False True True False False True False
+
+172
+00:15:37,850 --> 00:15:41,550
+True False True False False True False False True
+
+173
+00:15:41,550 --> 00:15:41,570
+False True False True False True False True False
+
+174
+00:15:41,570 --> 00:15:43,940
+true true true true true true true false، هذا جدول
+
+175
+00:15:43,940 --> 00:15:46,560
+الاحتمالات، الصفوف التي ممكن أن تكون موجودة
+
+176
+00:15:46,560 --> 00:15:56,360
+لدينا، بعد ذلك B implies Q أو B implies الـ R، true
+
+177
+00:15:56,360
+
+223
+00:19:49,230 --> 00:19:54,070
+دائما، دائما، حاول خذ نظرة على الطرف الثاني من
+
+224
+00:19:54,070 --> 00:19:57,390
+المسألة، وحاول إذا كان فيه صورة ثانية ممكن تكون
+
+225
+00:19:57,390 --> 00:20:02,710
+عليها، عشان تفهم إيش هو ممكن، إيه يكون هذا المثال
+
+226
+00:20:02,710 --> 00:20:07,070
+اللي عندنا مباشرة، ومافيهِش فيها عبارة عن جُثّة بينهم
+
+227
+00:20:07,070 --> 00:20:09,810
+والإشارات ده فيه يعني بدك تفهم الجُثّة اللي
+
+228
+00:20:09,810 --> 00:20:13,450
+موجودة عندك كويسة، هان هذه المسألة هي عبارة عن B
+
+229
+00:20:13,450 --> 00:20:20,590
+implies Q and Q implies R حسب القانون 1 هان، ولا
+
+230
+00:20:20,590 --> 00:20:21,190
+لأ؟
+
+231
+00:20:26,600 --> 00:20:37,680
+مصبوط؟ اه، حط اه P، تمام، هاي الخطوة رقم واحد اللي
+
+232
+00:20:37,680 --> 00:20:40,960
+ابتدي أشغلها، الخطوة الثانية، الـ implication هذه
+
+233
+00:20:40,960 --> 00:20:44,960
+لازم أنا أخلص منها، عشان أنا في الآخر بدي أصف فقط
+
+234
+00:20:44,960 --> 00:20:48,800
+and و or في المسألة، مين بيخدمني فيها؟ بيخدمني فيها
+
+235
+00:20:48,800 --> 00:20:53,230
+القانون الأول، معناته بتصير في عندي not B
+
+236
+00:20:53,230 --> 00:21:09,730
+or Q and not Q or B، مظبوط هيك لحد ما تلقاه ما فيهِش
+
+237
+00:21:09,730 --> 00:21:17,180
+مشكلة، والأمور تحت السيطرة، الخطوة اللي بعد هيك إحنا
+
+238
+00:21:17,180 --> 00:21:20,940
+كان فينا توزيع وتجميع، ولا لأ؟ الآن في حالة، في حالة
+
+239
+00:21:20,940 --> 00:21:23,620
+زي هذه، شو بقى تساوي، تفكر فيها يا شباب؟ بدك تأخذ
+
+240
+00:21:23,620 --> 00:21:28,180
+الجُزء بالكامل، وتوزعه وكأنه single element، يعني بقى
+
+241
+00:21:28,180 --> 00:21:32,440
+تفترض أن هذه لحالها X أو B، وبقى تدخلها على الجُزء
+
+242
+00:21:32,440 --> 00:21:38,520
+اللي موجود، ليش؟ عشان أنا في الآخر محتاج أن أصفي
+
+243
+00:21:38,520 --> 00:21:45,210
+أنّه B لحالها أو المُثبتات على الطرف والمُثبتات على
+
+244
+00:21:45,210 --> 00:21:51,410
+الطرف الثاني، أو مع بعضهم، معناته دي بقدي not B or
+
+245
+00:21:51,410 --> 00:22:07,990
+Q and not Q، صح؟ مظبوط؟ طيب، or خذ الجُثّة نفسه، not
+
+246
+00:22:07,990 --> 00:22:12,110
+B or Q and
+
+247
+00:22:14,460 --> 00:22:19,180
+الـ B، تمام؟
+
+248
+00:22:19,180 --> 00:22:27,500
+لم تفعل شيء، إحنا في عندنا كمان مرة B and Q or R
+
+249
+00:22:27,500 --> 00:22:36,440
+تكافئ B and Q or B and R، صح؟ لما قلت لك خذ هدول
+
+250
+00:22:36,440 --> 00:22:41,890
+ووزعهم على عناصر الجُزء، بس الـ B اللي عندي الآن مش
+
+251
+00:22:41,890 --> 00:22:44,950
+single event، مش single proposition، come down
+
+252
+00:22:44,950 --> 00:22:50,370
+proposition، فنجلّتها، تمام، كمان مرة بدي أروح أوزع
+
+253
+00:22:50,370 --> 00:23:04,550
+مين الـ Q، بدي أوزع الـ Q، طيب تعالَ خذ الـ Q، إيه
+
+254
+00:23:04,550 --> 00:23:05,410
+بتصير في عندي هان
+
+255
+00:23:08,510 --> 00:23:18,370
+not B and not Q or، لاحظ هذا الـ term عمال
+
+256
+00:23:18,370 --> 00:23:28,770
+وصلته أنا بدي إياه، كمّل، or Q and not Q، خلّصت من
+
+257
+00:23:28,770 --> 00:23:35,130
+الجُزء الأول، صح؟ or not
+
+258
+00:23:35,130 --> 00:23:37,250
+B and B
+
+259
+00:23:42,320 --> 00:23:54,160
+R Q and، بيه، إيش اللي أنا بسوي، الـ guide، بوزع النقطة
+
+260
+00:23:54,160 --> 00:23:59,200
+Q هذه على الجُثّة هذا، والـ and بيه هذه، ووزعتها على
+
+261
+00:23:59,200 --> 00:24:06,460
+الجُثّة هذا، كمان مرة، فلما بدأت أوزع الآن، صفة المسألة
+
+262
+00:24:06,460 --> 00:24:16,750
+عندي، بيه، عفوا، نقطة B and نقطة Q or Q and نقطة Q
+
+263
+00:24:16,750 --> 00:24:27,190
+الجواص الثاني بنفس الكيفية، نقطة B and B or Q and
+
+264
+00:24:27,190 --> 00:24:33,340
+B، الأقواس اللي عندي، لاحظوا يا شباب، هذه فكت الجُثّة
+
+265
+00:24:33,340 --> 00:24:37,720
+الأولى، وهذه، وهذه الجُثّة الثانية اللي عندك، واضح أن
+
+266
+00:24:37,720 --> 00:24:42,840
+المسألة كلها يدها إيش المستخدم فيها، or، يعني كلها
+
+267
+00:24:42,840 --> 00:24:46,560
+هي نفس المسألة، معناته أنا بقدر أجمع، أختزل بالأقواس
+
+268
+00:24:46,560 --> 00:24:51,180
+زي ما بدي، هذي واحد، اثنين، أنا في عندي بعض المسائل
+
+269
+00:24:51,180 --> 00:24:58,480
+عمالها راحت وين، باتجاه وين، Q and نقطة Q، false ولا
+
+270
+00:24:58,480 --> 00:25:08,350
+لا، P and نقطة P، false، في عندنا قانون بيقول بي or
+
+271
+00:25:08,350 --> 00:25:14,630
+false equivalent to إيش؟ to P ولا بقى؟ ممتاز، عند
+
+272
+00:25:14,630 --> 00:25:22,650
+الجُزء هذا or false، معناته الجُزء نقطة P ونقطة
+
+273
+00:25:22,650 --> 00:25:26,770
+Q، إيش بينهم؟
+
+274
+00:25:26,770 --> 00:25:30,790
+or false or Q and B
+
+275
+00:25:36,970 --> 00:25:41,810
+بس شوية يا شباب، نجمّلها ونعيد ترتيب العناصر، الـ or
+
+276
+00:25:41,810 --> 00:25:46,310
+إبدالية، والـ and إبدالية، مظبوط لأ؟ وهذه بدها تساوي
+
+277
+00:25:46,310 --> 00:25:55,250
+B and Q، يعني بدّلت الجُزء هذا، وبدّلته على ناحية
+
+278
+00:25:55,250 --> 00:26:04,050
+ثانية، or نقطة الـ B and نقطة الـ Q، صعب
+
+279
+00:26:04,050 --> 00:26:04,310
+الأمر
+
+280
+00:26:08,470 --> 00:26:14,130
+الجدول أحسن وأقوم، بس الجدول في لحظة من اللحظات
+
+281
+00:26:14,130 --> 00:26:19,210
+ممكن يكلفك الصفحة كلها، وما توصلهاش، تمام؟ فبالتالي
+
+282
+00:26:19,210 --> 00:26:23,730
+إحنا أخذنا الجدول وبنينا على الجدول، عشان نصل للشغل
+
+283
+00:26:23,730 --> 00:26:28,510
+بالشكل هذا، طيب، نأخذ كمان عناصر أو كمان مسائل، ما هيك؟
+
+284
+00:26:28,510 --> 00:26:31,730
+أنت لو طلعت مسائل الكتاب، إيش بيقول لك، هتلاقي في
+
+285
+00:26:31,730 --> 00:26:35,070
+السؤال بيقول لك باعتمادك على جدول الاحتمالات، يعني
+
+286
+00:26:35,070 --> 00:26:38,270
+أنا بطلب منك تستخدم جدول الاحتمالات، ومرات ثانية
+
+287
+00:26:38,270 --> 00:26:42,410
+بيقول لك باستخدام الخطوات المنطقية أو رياضيات
+
+288
+00:26:42,410 --> 00:26:48,950
+الخطوات المنطقية، اثبت أنّه كذا، من أول لحظة يجب أن
+
+289
+00:26:48,950 --> 00:26:53,690
+تحفظهم، و ليش إحنا حطيناهم equivalent، أو كيف أثبتنا
+
+290
+00:26:53,690 --> 00:26:58,470
+أنّهم equivalent؟ من يحفظهم؟ أنت
+
+291
+00:27:05,720 --> 00:27:10,060
+وأنا بأنصحك يا شباب، يعني ما تحاولش.. ما تحاولش في
+
+292
+00:27:10,060 --> 00:27:13,700
+المادة، تأجّل شغلها بعدين، أنت لسه في أول الفصل، إحنا
+
+293
+00:27:13,700 --> 00:27:16,920
+في الأسبوع الثاني، تمام؟ المسائل اللي بقول لك في
+
+294
+00:27:16,920 --> 00:27:21,640
+الكتاب، حلّها، حلّ منها قدش بتقدر، ومعفن ما تحلّ.. ما
+
+295
+00:27:21,640 --> 00:27:28,890
+تحلّش على ورق وترميه، شوف لك دفتر، تمام؟ أبو المئة أو
+
+296
+00:27:28,890 --> 00:27:32,930
+مجموعة ورق وبتدبسهم مع بعض، وأنت حر، بس في الآخر كل
+
+297
+00:27:32,930 --> 00:27:36,750
+ورقة.. كل حرف بتكتبه، إحتفظ فيه، لإنه عند
+
+298
+00:27:36,750 --> 00:27:41,550
+المراجعة، تمام؟ بتتثبت.. بتلاقي الأمور أفضل
+
+299
+00:27:41,550 --> 00:27:45,070
+بقول لك إيش؟ إنّه هذا الدفتر هتسلّمني إياه في الآخر، وليه
+
+300
+00:27:45,070 --> 00:27:51,110
+علامات زي المدارس؟ لا يا أستاذي، تمام؟ بالمناسبة
+
+301
+00:27:51,110 --> 00:27:55,770
+لا بدّوش، نحلّ، بلاش الأمر، ما تتركه تماما، إيش بيقول لي في
+
+302
+00:27:55,770 --> 00:28:05,630
+المسألة هذه؟ بيقول اثبت أن نفي الجُزء هذا (P and Q)
+
+303
+00:28:05,630 --> 00:28:15,830
+equivalent to (not P and not Q)، باعتمادك على series
+
+304
+00:28:15,830 --> 00:28:21,450
+of logical equivalence، على سلسلة من الـ logical
+
+305
+00:28:21,450 --> 00:28:23,870
+equivalence اللي بدك تتبعها، يعني لو حلّيته بجدول
+
+306
+00:28:23,870 --> 00:28:25,690
+الاحتمالات، غلط
+
+307
+00:28:28,170 --> 00:28:33,110
+تمام؟ أما الصعب هيك، صح؟ على الآخر، طيب الآن أنا
+
+308
+00:28:33,110 --> 00:28:37,070
+بقول لك أثبت أن الطرف هذا يساوي هذا، قلت لك، أو نصحتك
+
+309
+00:28:37,070 --> 00:28:40,330
+أنا دائما، خذ نظرة على الطرف الثاني، على الطرف
+
+310
+00:28:40,330 --> 00:28:44,990
+الأسهل اللي أنت بدك تروح له، هل هذا ممكن يكتب على
+
+311
+00:28:44,990 --> 00:28:49,710
+صورة ثانية؟ لأ، استعجل، أزمّلّك وقال لأ، بس أنا بقول
+
+312
+00:28:49,710 --> 00:28:55,470
+لأ، ممكن يكتب  باستخدام دي مورغان، لو ممكن
+
+313
+00:28:55,470 --> 00:28:59,270
+تكون الصورة هي، إيش أنا قاعد بقول لك؟ شوف الصورة، هل
+
+314
+00:28:59,270 --> 00:29:03,110
+ممكن يكتب على صورة ثانية ولا لأ؟ لأن أثناء البحث
+
+315
+00:29:03,110 --> 00:29:07,030
+.. أثناء.. أثناء ما أنت مركز في الخطوات، ممكن تصل
+
+316
+00:29:07,030 --> 00:29:12,470
+للصورة المكافئة، وأنت فعليا.. لأن خلاص هذه اللي في
+
+317
+00:29:12,470 --> 00:29:19,670
+دماغك، مش شايف إنك أنت خلصت، طيب تعالَ نحلّ المسألة
+
+318
+00:29:19,670 --> 00:29:27,500
+اللي عندي، هيو، بيقول لي not (P and Q)، وهي
+
+319
+00:29:27,500 --> 00:29:34,700
+الأقواس، لاحظ.. لاحظ أن النفي لو بقى خارج، يمكن أن
+
+320
+00:29:34,700 --> 00:29:38,520
+يخدمني أو لا.. فممكن أن أعتبره منهجي، وأتركه
+
+321
+00:29:38,520 --> 00:29:42,940
+عنده.. أو عفوا، أعتبره خطوة وأتركه، وأصير أشغل
+
+322
+00:29:42,940 --> 00:29:50,140
+وين؟ على الجُزء والجُزء، وهذه كافة.. بدي أ.. بالضبط
+
+323
+00:29:50,140 --> 00:29:51,280
+.. بدي أوزع الآن
+
+324
+00:29:54,220 --> 00:29:59,720
+على العنصر اللي عندي، تمام، ما هي تهيئتنا فيه، هتصير
+
+325
+00:29:59,720 --> 00:30:10,680
+الـ P عندي، (P or P) and  مرة ثانية (P or Q)، ممتاز
+
+326
+00:30:10,680 --> 00:30:19,440
+الأولى حرام عليك يا شيخ، true، لأنّ بينهم or، لأن
+
+327
+00:30:19,440 --> 00:30:24,540
+اسمّيته false، واحد قال الأولى false، true، true and x
+
+328
+00:30:24,540 --> 00:30:33,160
+true، ميزة، equivalent to نفي الـ B or الـ Q، خلّصنا، بدك
+
+329
+00:30:33,160 --> 00:30:39,020
+تجيب الخطوة الثالثة الآن اللي هي not B and not
+
+330
+00:30:39,020 --> 00:30:44,860
+Q، وبتكون أنت وصلت للحل المطلوب، يا سلام، هي هيك
+
+331
+00:30:44,860 --> 00:30:49,380
+الآن كمان مرة، بينفعش في لحظة من اللحظات، وبيقول لي
+
+332
+00:30:49,380 --> 00:30:53,410
+ما تستخدمش جدول الاحتمالات، وطبعا تستخدم جد ولا
+
+333
+00:30:53,410 --> 00:31:00,350
+احتمالات، طبعا، حاولت أفصّلك في الخطوات أكثر طبعا
+
+334
+00:31:00,350 --> 00:31:06,530
+شوف أنا إيش سويت في الأول يعني
+
+335
+00:31:06,530 --> 00:31:12,490
+إحنا أخذنا حلّ، وقلنا خَلّ النفي برا، فبالحل الثاني
+
+336
+00:31:12,490 --> 00:31:18,600
+اللي ممكن أنا أشعر أني أبقى فيه، أدخلت النفي جوا، في
+
+337
+00:31:18,600 --> 00:31:23,840
+معناته not (B and) نفي الجُزء هذا، الخطوة التالية
+
+338
+00:31:23,840 --> 00:31:31,320
+صارت نفي نفي، بتدخل الجُزء، نفي كمان مرة كمان
+
+339
+00:31:31,320 --> 00:31:38,280
+مرة، في الآخر هتصل لنفس الحل، هتصل لنفس الحل، لكنه مع
+
+340
+00:31:38,280 --> 00:31:45,000
+خطوات.. شوف، طالما خطواتك منطقية، تمام، غالبا هتصل
+
+341
+00:31:45,000 --> 00:31:50,490
+لحلّ، الحلّ هيكون تبعك صحيح، طالما أنك بتقلفش، يعني
+
+342
+00:31:50,490 --> 00:31:54,190
+أنك في الـ Pseuocyte، طالما أنك بتقلفش، يعني أنك
+
+343
+00:31:54,190 --> 00:32:00,450
+في السليم، تعالَ نشوف المسألة هذه، بيقول اثبت أن
+
+344
+00:32:00,450 --> 00:32:05,210
+هذه توتولوجيا، شو يعني توتولوجيا؟ أن قيمتها true
+
+345
+00:32:05,210 --> 00:32:08,210
+and cruel، جدول الاحتمالات، بس اللي أنا ما بديش جدول
+
+346
+00:32:08,210 --> 00:32:12,860
+الاحتمالات، معناته أنا بدي أختصر بنفس الكيفية، وإذا
+
+347
+00:32:12,860 --> 00:32:18,580
+وصلت لـ true، أن هذه هيك تكافئ true، خلّصنا، ما هي
+
+348
+00:32:18,580 --> 00:32:22,560
+توتولوجيا بدون جدول احتمالات، تمام، تعالَ نشوف كيف ما
+
+349
+00:32:22,560 --> 00:32:26,960
+ممكن نشتغل فيها، كمان مرة، طب هنقول لأ، مئة مرة
+
+350
+00:32:26,960 --> 00:32:32,820
+الأولوية دائما لمين؟ للأقواس، تمام؟ معناته هقول له
+
+351
+00:32:32,820 --> 00:32:38,080
+هذا equivalent to P or، بدي أدخل النفي الأول، نقطة
+
+352
+00:32:38,080 --> 00:32:45,310
+P or Q، بنأخذها عادي، مظبوط، الخطوة الثانية
+
+353
+00:32:45,310 --> 00:32:53,030
+بدي آخذ الـ P وأدخله على الجُثث، وهذه تكافئ P or
+
+354
+00:32:53,030 --> 00:33:00,550
+P or Q، ليش بدون أقواس؟ خلاص أنا بدأت معاهم، فمش
+
+355
+00:33:00,550 --> 00:33:12,410
+مشكلة، P or P or Q، الأولى هذه جداش قيمتها true
+
+356
+00:33:12,410 --> 00:33:18,250
+الثانية true، حرام عليك، P and Q هدول، إيوة، فالآن
+
+357
+00:33:18,250 --> 00:33:21,950
+أصبحت أنا على قانون السيطرة، تبقى لي true مع الـ R
+
+358
+00:33:21,950 --> 00:33:31,170
+true or P or not Q، يكافئ true، معناته أنا بتكلم أن
+
+359
+00:33:31,170 --> 00:33:34,110
+الـ compound proposition اللي قلت معايا هذا عبارة
+
+360
+00:33:34,110 --> 00:33:39,130
+عن tetralogy، كيف أجت؟ مش إحنا في عندنا P أو الـ true
+
+361
+00:33:39,130 --> 00:33:50,310
+true، صح، هي الـ true وهي الـ P مع بعض، وبينهم or، و
+
+362
+00:33:50,310 --> 00:33:52,890
+بينهم or، وأنا ضمنت واحدة من الـ true في الـ output
+
+363
+00:33:52,890 --> 00:33:56,150
+هو محصلة true على القانون
+
+364
+00:34:15,600 --> 00:34:23,080
+لأ لأ، شوية إيش، فل حقا، okay، طيب، هان هذه الأسئلة، خلاص
+
+365
+00:34:23,080 --> 00:34:25,680
+طبعا إحنا الـ section هذه، الأسئلة أخذتها عشوائية من
+
+366
+00:34:25,680 --> 00:34:34,780
+الكتاب، وتعمدنا أرقام، همشي أرقام زوجية، طبعا بدنا
+
+367
+00:34:34,780 --> 00:34:37,700
+الحلّ، أو بدنا المحاضرة بحلّ هذا، دي مورغان
+
+368
+00:34:37,700 --> 00:34:42,380
+أثبتناها، عمال يقول استخدم الـ truth table في المسألة
+
+369
+00:34:42,380 --> 00:34:46,560
+الثانية يا شباب، المسألة الثانية، طلعش تقول لي عمّاله
+
+370
+00:34:46,560 --> 00:34:49,780
+determine
+
+371
+00:34:49,780 --> 00:34:55,920
+whether، يعني حدّد إذا كانت هذه المسألة tautology ولا
+
+372
+00:34:55,920 --> 00:35:04,280
+لأ، تخيّل في لحظة من اللحظات كانت مكتوبة هنا، دي show
+
+373
+00:35:04,280 --> 00:35:11,360
+that it is a tautology، إيش بتساوي؟ هتبدا تشتغل؟
+
+374
+00:35:14,490 --> 00:35:18,810
+المسألة مختلفة تماما، بالمناسبة، determined حد ما
+
+375
+00:35:18,810 --> 00:35:24,340
+إذا كانت tautology أو لأ، غير أنّها اثبت أنّها tautology
+
+376
+00:35:24,340 --> 00:35:29,000
+طبعا، ليش أنا قاعد بقول الكلام هذا؟ عشان أكّد على
+
+377
+00:35:29,000 --> 00:35:34,060
+مبدأ أن فهم السؤال مهم جدا.. فهم السؤال مهم جدا
+
+378
+00:35:34,060 --> 00:35:37,900
+خلينا نتكلم بنظرة إن والله أنا فهمت السؤال
+
+379
+00:35:37,900 --> 00:35:42,320
+أثبت لي إياها، لو أما هتروح معايا المسألة، هتصل لمرحلة
+
+380
+00:35:42,320 --> 00:35:47,820
+..هتصل لمرحلة، والمسألة عايشة، بتجفل معاك على الرغم
+
+381
+00:35:47,820 --> 00:35:51,960
+أن كل خطواتك اللي كتبتها صح، تعالى جرب بس، أو أورّيك
+
+382
+00:35:51,960 --> 00:35:55,780
+أنّها بتجفل ولا بتجفش، لأن في الآخر، في الآخر لازم لو
+
+383
+00:35:55,780 --> 00:36:02,440
+كانت خطواتك منطقية، متسلسلة، خلاص، طيب الآن حسب
+
+384
+00:36:02,440 --> 00:36:06,100
+المعادلة اللي عندي، تعالَ أكتبها يعني بشكل كويس في
+
+385
+00:36:06,100 --> 00:36:14,720
+عندي not B and (P implies Q) الكل
+
+386
+00:36:16,500 --> 00:36:21,640
+implies not Q، الوزع
+
+387
+00:36:21,640 --> 00:36:27,080
+طيب، اللي بدك إياه، بنمشي الحلّ، و ليش ما تف
+
+445
+00:41:39,710 --> 00:41:47,430
+المسألة بيحصل false، متى المسألة هذه بتصير false؟ لو
+
+446
+00:41:47,430 --> 00:41:54,850
+كانت هذه false وهذه true، فح؟ متى ممكن تكون false؟
+
+447
+00:41:54,850 --> 00:42:01,910
+أيه، معناته الـQ بدها تساوي true عشان تكون هذه
+
+448
+00:42:01,910 --> 00:42:09,150
+false والـB هذه بدها تكون true، والـB equal true
+
+449
+00:42:11,210 --> 00:42:18,010
+بتصير، لا فيها false بتكون
+
+450
+00:42:18,010 --> 00:42:25,730
+false وهذه بدها تكون true، هذه عشان تكون true false
+
+451
+00:42:25,730 --> 00:42:30,810
+false ما تهزر، في عندي حالة إن المسألة تقول فيها
+
+452
+00:42:30,810 --> 00:42:38,500
+لمين؟ للـ false بي equal true و Q equal false، بطبقها
+
+453
+00:42:38,500 --> 00:42:41,720
+في المسألة هذه، حتلاقيها تقول إلى false وبالتالي
+
+454
+00:42:41,720 --> 00:42:45,500
+المسألة هذه not tautology، الأسهل أني أرسم جدول
+
+455
+00:42:45,500 --> 00:42:48,640
+الاحتمالات على السريع، خصوصًا أنه أربع أعمدة، أربع صفوف
+
+456
+00:42:48,640 --> 00:42:53,120
+وبقدر أحدد من القيم اللي ممكن إيش تأثر في المسألة
+
+457
+00:42:53,120 --> 00:43:01,000
+اللي موجودة عندي، طيب بعديها عمالة جاية بتقول لي
+
+458
+00:43:01,000 --> 00:43:09,580
+show that يعني اثبت B and Q implies R، and B implies
+
+459
+00:43:09,580 --> 00:43:16,660
+R، and Q implies R are not tautology
+
+460
+00:43:16,660 --> 00:43:21,110
+يعني ما في، اثبتوا إنهم غير متساويات، عشان تثبت إنهم
+
+461
+00:43:21,110 --> 00:43:25,630
+غير متساويات، إياك تستخدم القوانين، القوانين هتوصل لك
+
+462
+00:43:25,630 --> 00:43:31,870
+لطريق مسدودة، الحل جدول الاحتمالات أو تحاول ترسم
+
+463
+00:43:31,870 --> 00:43:36,250
+جدول الاحتمالات على جانب، وتشوف إيش الصف اللي بيخلي
+
+464
+00:43:36,250 --> 00:43:43,450
+الجمالتين هدول مش متكافئات، أكيد لو عند أول صف في
+
+465
+00:43:43,450 --> 00:43:47,730
+بتمسكو بحق، خلاص معناته هدول الاثنين صار فيه إنه
+
+466
+00:43:47,730 --> 00:43:53,580
+مختلف، بالتالي عندنا كم قيمة يا شباب؟ عندنا ثلاث
+
+467
+00:43:53,580 --> 00:44:02,740
+متغيرات BQR: true true true، true false false، false true true
+
+468
+00:44:02,740 --> 00:44:11,460
+true true false، false true true، false true false، true false true
+
+469
+00:44:11,460 --> 00:44:18,380
+false true false، true false false،  أصبت؟ طيب
+
+470
+00:44:18,670 --> 00:44:26,350
+الآن دعنا على السريع الصف الأول: true and true true
+
+471
+00:44:26,350 --> 00:44:31,290
+implies true، true true true true true true true
+
+472
+00:44:31,290 --> 00:44:31,930
+true true true true true true true true true true
+
+473
+00:44:31,930 --> 00:44:33,190
+true true true true true true true true true true
+
+474
+00:44:33,190 --> 00:44:41,290
+true true true
+
+475
+00:44:41,290 --> 00:44:44,090
+true true true true true true true true true true
+
+476
+00:44:44,090 --> 00:44:44,330
+true true true true true true true true true true
+
+477
+00:44:44,330 --> 00:44:47,260
+true true true true true true false implies false
+
+478
+00:44:47,260 --> 00:44:51,880
+true true and true true، برضه الصف الأخير، لأ اللي
+
+479
+00:44:51,880 --> 00:45:00,200
+بعده: true true false true و true و false false
+
+480
+00:45:00,200 --> 00:45:05,320
+implies true، أو عفوا true implies false false، يعني
+
+481
+00:45:05,320 --> 00:45:11,160
+true implies false، true implies false، وبينهم and
+
+482
+00:45:11,160 --> 00:45:15,430
+false، معناته false، و false برضه، الثاني، بارا نشوف
+
+483
+00:45:15,430 --> 00:45:19,510
+الثالث، لاحظ
+
+484
+00:45:19,510 --> 00:45:23,490
+إن أنت بتحسب على المعادلة نفسها ووحدها بس، عشان
+
+485
+00:45:23,490 --> 00:45:29,610
+تتأكد إن أنت خدت الصفوف واحد واحد، الآن true false
+
+486
+00:45:29,610 --> 00:45:34,670
+true false
+
+487
+00:45:34,670 --> 00:45:36,630
+implies true true
+
+488
+00:45:40,700 --> 00:45:45,980
+true implies true، true false implies true، true and
+
+489
+00:45:45,980 --> 00:45:54,020
+true true، برضه متكافئات، الصف الأخير true false
+
+490
+00:45:54,020 --> 00:46:02,740
+false true false false false implies true false
+
+491
+00:46:02,740 --> 00:46:04,420
+implies false true
+
+492
+00:46:11,830 --> 00:46:19,710
+الآن هذه true وهذه false وهذه false وهذه false
+
+493
+00:46:19,710 --> 00:46:25,270
+true implies false and false implies false true
+
+494
+00:46:25,270 --> 00:46:32,770
+true and false، القيمتين هي هم اختلفوا، وبالتالي هدول
+
+495
+00:46:32,770 --> 00:46:36,010
+القيمتين is not logically equivalent، وبالذنب
+
+496
+00:46:36,010 --> 00:46:44,590
+أقوله عند القيمة B equal true, Q equal false، وR
+
+497
+00:46:44,590 --> 00:46:49,090
+equal false، هدول اللي بيثبتوا إن القيم اللي عندي is
+
+498
+00:46:49,090 --> 00:46:53,200
+not equivalent، واضح الأمور يا شباب؟ قبل ما أطلع
+
+499
+00:46:53,200 --> 00:46:56,260
+خلينا نشوف بس أسئلة الكتاب، أنا هأقول الأسئلة دي
+
+500
+00:46:56,260 --> 00:46:58,780
+أجيبتهم من الكتاب طبعًا، وزي ما قلت لك اخترتهم بشكل
+
+501
+00:46:58,780 --> 00:47:01,400
+عشوائي، لأ لسه ما خلصنا الشابتر واحد، خلصنا section
+
+502
+00:47:01,400 --> 00:47:06,140
+واحد ثلاثة،  دال فيه تقريبًا اثنين
+
+503
+00:47:11,350 --> 00:47:16,490
+الآن آخر شغلة قبل ما نطلع، لازم تاخد نظرة على أسئلة
+
+504
+00:47:16,490 --> 00:47:21,470
+الكتاب، وأنا حددت لك في الـ slides السؤال من 1 لـ 33
+
+505
+00:47:21,470 --> 00:47:25,250
+حاول تحلهم، الأسئلة الفردية موجود حلولها في نهاية
+
+506
+00:47:25,250 --> 00:47:27,910
+الكتاب، زي ما قلت لك المرة الماضية، وأنا جبت لك
+
+507
+00:47:27,910 --> 00:47:31,030
+مجموعة من الأسئلة الزوجية، تعالَ عما لا بقول لك use
+
+508
+00:47:31,030 --> 00:47:36,470
+the truth table، عشان تتأكد من الـ equivalence، الآن
+
+509
+00:47:36,470 --> 00:47:41,610
+هذه المعادلة، الـ truth table تبعها من كام صفحة؟ عام
+
+510
+00:47:41,610 --> 00:47:45,830
+عليكوا اثنين، لأن في عندك one variable، اثنين أُس
+
+511
+00:47:45,830 --> 00:47:51,330
+واحد اثنين، طيب في المسألة في رقم ثلاثة، لما بيجي
+
+512
+00:47:51,330 --> 00:47:54,850
+بيقول لك اثبت الشغلات هذه، وأربعة في أربعة جدول
+
+513
+00:47:54,850 --> 00:47:58,350
+الاحتمالات، لاحظ يا شباب لما بيقول لك استخدم جدول
+
+514
+00:47:58,350 --> 00:48:02,670
+الاحتمالات، بيقول لك استخدم الـ truth table، شوف مسألة
+
+515
+00:48:02,670 --> 00:48:06,890
+اثنا عشر، سؤال اثنا عشر، إيش بيقول لك؟ show that each
+
+516
+00:48:06,890 --> 00:48:11,610
+conditional statement in exercise عشر اللي فوق is a
+
+517
+00:48:11,610 --> 00:48:18,070
+tautology without using truth table، معناته أنت
+
+518
+00:48:18,070 --> 00:48:22,790
+الآن ما شبكة تساوي، بتكاشي تستخدم جدول الاحتمالات،
+
+519
+00:48:22,790 --> 00:48:28,270
+بتكاشي تستخدم القوانين، صعبة؟ بهيك نكون أنهينا
+
+520
+00:48:28,270 --> 00:48:30,830
+المحاضرة، الله يعطيكم العافية
diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/AGhpvbdD4Ug_raw.json b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/AGhpvbdD4Ug_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..523b2e8e3c5b08776683d858fab48fc819f05e74
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/AGhpvbdD4Ug_raw.json
@@ -0,0 +1 @@
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"start": 2740.7, "end": 2764.42, "text": "true implies true true false implies true true and true true برضه متكافئات الصف الأخير true false false true false false false implies true false implies false true", "tokens": [6903, 622, 18779, 2074, 2074, 7908, 18779, 2074, 2074, 293, 2074, 2074, 4724, 43042, 3224, 44650, 4117, 31845, 19986, 9307, 31767, 5172, 16247, 9778, 13546, 2074, 7908, 7908, 2074, 7908, 7908, 7908, 18779, 2074, 7908, 18779, 7908, 2074], "avg_logprob": -0.32932691543530196, "compression_ratio": 2.0, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 2740.7, "end": 2740.98, "word": "true", "probability": 0.6802978515625}, {"start": 2740.98, "end": 2741.24, "word": " implies", "probability": 0.260986328125}, {"start": 2741.24, "end": 2741.66, "word": " true", "probability": 0.96484375}, {"start": 2741.66, "end": 2742.92, "word": " true", "probability": 0.2186279296875}, {"start": 2742.92, "end": 2744.06, "word": " false", "probability": 0.6328125}, {"start": 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2754.02, "end": 2754.52, "word": " false", "probability": 0.81787109375}, {"start": 2754.52, "end": 2757.24, "word": " true", "probability": 0.71533203125}, {"start": 2757.24, "end": 2757.98, "word": " false", "probability": 0.8916015625}, {"start": 2757.98, "end": 2758.78, "word": " false", "probability": 0.91064453125}, {"start": 2758.78, "end": 2759.6, "word": " false", "probability": 0.873046875}, {"start": 2759.6, "end": 2759.9, "word": " implies", "probability": 0.9248046875}, {"start": 2759.9, "end": 2760.4, "word": " true", "probability": 0.96484375}, {"start": 2760.4, "end": 2762.74, "word": " false", "probability": 0.8330078125}, {"start": 2762.74, "end": 2763.06, "word": " implies", "probability": 0.92236328125}, {"start": 2763.06, "end": 2763.54, "word": " false", "probability": 0.86279296875}, {"start": 2763.54, "end": 2764.42, "word": " true", "probability": 0.97509765625}], "temperature": 1.0}, {"id": 100, "seek": 278619, "start": 2771.83, "end": 2786.19, "text": "الأن هذه true وهذه false وهذه false وهذه false true implies false and false implies false true true and false", "tokens": [6027, 33456, 29538, 2074, 37037, 24192, 7908, 37037, 24192, 7908, 37037, 24192, 7908, 2074, 18779, 7908, 293, 7908, 18779, 7908, 2074, 2074, 293, 7908], "avg_logprob": -0.4734375, "compression_ratio": 2.0317460317460316, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2771.83, "end": 2772.91, "word": "الأن", "probability": 0.2083740234375}, {"start": 2772.91, "end": 2773.15, "word": " هذه", "probability": 0.29638671875}, {"start": 2773.15, "end": 2773.51, "word": " true", "probability": 0.86669921875}, {"start": 2773.51, "end": 2774.51, "word": " وهذه", "probability": 0.8642578125}, {"start": 2774.51, "end": 2775.03, "word": " false", "probability": 0.84912109375}, {"start": 2775.03, "end": 2776.03, "word": " وهذه", "probability": 0.8076171875}, {"start": 2776.03, "end": 2777.35, "word": " false", "probability": 0.779296875}, {"start": 2777.35, "end": 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"word": " بالذنب", "probability": 0.69757080078125}, {"start": 2796.01, "end": 2796.67, "word": " اقوله", "probability": 0.5260416666666666}, {"start": 2796.67, "end": 2797.29, "word": " عند", "probability": 0.87353515625}, {"start": 2797.29, "end": 2798.33, "word": " القيمة", "probability": 0.9358723958333334}, {"start": 2798.33, "end": 2799.35, "word": " B", "probability": 0.203369140625}, {"start": 2799.35, "end": 2800.43, "word": " equal", "probability": 0.053192138671875}, {"start": 2800.43, "end": 2800.91, "word": " true,", "probability": 0.70263671875}, {"start": 2801.75, "end": 2802.19, "word": " Q", "probability": 0.7373046875}, {"start": 2802.19, "end": 2802.65, "word": " equal", "probability": 0.77587890625}, {"start": 2802.65, "end": 2803.23, "word": " false", "probability": 0.81591796875}, {"start": 2803.23, "end": 2804.59, "word": " وR", "probability": 0.640380859375}, {"start": 2804.59, "end": 2805.17, "word": " equal", "probability": 0.890625}, {"start": 2805.17, "end": 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الأمور يا شباب؟ قبل ما أطلع خلينا نشوف بس الأسئلة الكتاب انا هدقول الأسئلة دي أجيبتهم من الكتاب طبعا وزي ما قلت لك اختارتهم بشكل عشوائي لأ لسه ما خلصنا الشابتر واحد خلصنا section واحد تلاتة دال فيه تقريبا اتنين", "tokens": [2407, 46958, 5016, 16247, 2304, 13063, 35186, 13412, 3555, 16758, 22807, 12174, 36150, 19446, 5551, 9566, 1211, 3615, 16490, 20292, 8315, 8717, 8592, 38688, 4724, 3794, 16247, 3794, 19986, 37977, 33251, 2655, 16758, 1975, 8315, 8032, 3215, 39648, 16247, 3794, 19986, 37977, 11778, 1829, 5551, 7435, 1829, 3555, 2655, 16095, 9154, 33251, 2655, 16758, 23032, 3555, 3615, 995, 4032, 11622, 1829, 19446, 12174, 1211, 2655, 5296, 4117, 1975, 46456, 9640, 2655, 16095, 4724, 8592, 28820, 6225, 8592, 2407, 16373, 1829, 5296, 10721, 5296, 3794, 3224, 19446, 16490, 1211, 9381, 8315, 25124, 16758, 2655, 2288, 36764, 24401, 16490, 1211, 9381, 8315, 3541, 36764, 24401, 6055, 1211, 9307, 3660, 11778, 6027, 8978, 3224, 6055, 4587, 16572, 3555, 995, 1975, 2655, 1863, 9957], 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بيقولك اثبت الشغلات هدا واربعة فاربعة جدول الاحتمالات لاحظ يا شباب لما بيقولك استخدم جدول الاحتمالات بيقولك استخدم ال truth table شوف مسألة اتناشه سؤال اتناشه ايش بيقولك show that each conditional statement in exercise عشر اللي فوق", "tokens": [5016, 2288, 10943, 25894, 4117, 14407, 1975, 2655, 1863, 9957, 5296, 7649, 8978, 43242, 4117, 472, 7006, 1975, 2655, 1863, 9957, 1975, 9381, 36764, 24401, 1975, 2655, 1863, 9957, 23032, 1829, 3555, 8978, 9673, 3794, 10721, 37977, 8978, 5296, 4587, 2304, 6055, 1211, 9307, 3660, 5296, 15042, 4724, 1829, 7435, 1829, 4724, 1829, 39648, 4117, 1975, 12984, 3555, 2655, 25124, 17082, 1211, 9307, 8032, 28259, 4032, 9640, 3555, 27884, 6156, 9640, 3555, 27884, 10874, 3215, 12610, 42963, 33753, 2304, 6027, 9307, 20193, 5016, 19913, 35186, 13412, 3555, 16758, 5296, 15042, 4724, 1829, 39648, 4117, 44713, 9778, 40448, 10874, 3215, 12610, 42963, 33753, 2304, 6027, 9307, 4724, 1829, 39648, 4117, 44713, 9778, 40448, 2423, 3494, 3199, 13412, 38688, 47524, 10721, 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{"start": 2898.27, "end": 2898.45, "word": " شبك", "probability": 0.6871744791666666}, {"start": 2898.45, "end": 2898.85, "word": " تساوي", "probability": 0.816162109375}, {"start": 2898.85, "end": 2900.01, "word": " بتكاشي", "probability": 0.67340087890625}, {"start": 2900.01, "end": 2900.61, "word": " تستخدم", "probability": 0.989990234375}, {"start": 2900.61, "end": 2901.93, "word": " جدول", "probability": 0.9505208333333334}, {"start": 2901.93, "end": 2902.79, "word": " الاحتمالات،", "probability": 0.8953043619791666}, {"start": 2902.79, "end": 2903.11, "word": " بتكاشي", "probability": 0.9471435546875}, {"start": 2903.11, "end": 2904.49, "word": " تستخدم", "probability": 0.9921875}, {"start": 2904.49, "end": 2906.39, "word": " القوانين،", "probability": 0.820263671875}, {"start": 2906.39, "end": 2907.51, "word": " صعبة؟", "probability": 0.85791015625}, {"start": 2907.51, "end": 2907.95, "word": " بهيكة", "probability": 0.46734619140625}, {"start": 2907.95, "end": 2908.27, "word": " نتيجة", "probability": 0.72265625}, {"start": 2908.27, "end": 2909.97, "word": " المحاضرة،", "probability": 0.884814453125}, {"start": 2909.97, "end": 2910.17, "word": " الله", "probability": 0.837890625}, {"start": 2910.17, "end": 2910.41, "word": " يعطيكم", "probability": 0.7857666015625}, {"start": 2910.41, "end": 2910.83, "word": " العافية", "probability": 0.8966471354166666}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2911.341125, "duration_after_vad": 2765.1149999999907}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/AGhpvbdD4Ug_raw.srt b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/AGhpvbdD4Ug_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..30a7ef6862f6b81ebe172e74a7bf75e1e3fce939
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/AGhpvbdD4Ug_raw.srt
@@ -0,0 +1,2256 @@
+1
+00:00:21,500 --> 00:00:23,400
+بسم الله الحمد لله والصلاة والسلام على رسول الله
+
+2
+00:00:23,400 --> 00:00:26,440
+طيب شباب أهلا وسهلا فيكوا في اللقاء التاني في ال
+
+3
+00:00:26,440 --> 00:00:29,640
+chapter ال .. أو التالت في ال chapter اللي قتل ال
+
+4
+00:00:29,640 --> 00:00:32,900
+logical propositional logic واليوم ان شاء الله
+
+5
+00:00:32,900 --> 00:00:38,460
+محاضرتنا قصيرة هنخلص فيها بفقط ال section اللي هو
+
+6
+00:00:38,460 --> 00:00:43,100
+متعلق ال propositional equivalence نعم بديت بس
+
+7
+00:00:43,100 --> 00:00:46,220
+فيها سؤالة جيت لما مثلا الدين اتنين زاد اتنين
+
+8
+00:00:46,220 --> 00:00:47,960
+بتسوا أربع كيه بتقع فيها؟
+
+9
+00:00:57,150 --> 00:01:02,710
+أه بس it's not equal طيب
+
+10
+00:01:02,710 --> 00:01:05,530
+.. ال .. كنا احنا بدأنا فعليا المحاضرة الماضية
+
+11
+00:01:05,530 --> 00:01:08,190
+تكلمنا على ال logical equivalence او proposition
+
+12
+00:01:08,190 --> 00:01:12,210
+equivalence وقولنا فيها ان مجموعة من ال terms او
+
+13
+00:01:12,210 --> 00:01:16,530
+مجموعة من المصطلحات بدنا نفهمهم و نحفظهم كويس لما
+
+14
+00:01:16,530 --> 00:01:20,010
+بتكون في عندي compound و proposition و دائما ال
+
+15
+00:01:20,010 --> 00:01:25,760
+result تبعته true معناته هوTautology يعني لو انا
+
+16
+00:01:25,760 --> 00:01:34,220
+اتيت بكل بساطة قولتلك انا في عندى B نقطة B وفي
+
+17
+00:01:34,220 --> 00:01:39,940
+بينهم R تمام
+
+18
+00:01:39,940 --> 00:01:46,160
+الان بما ان هو اتكلم على one preposition تمام
+
+19
+00:01:46,160 --> 00:01:51,280
+معناته true و false نفيها false between true true
+
+20
+00:01:51,280 --> 00:01:56,910
+or false trueFalse or True؟ True هذا الآن الـ
+
+21
+00:01:56,910 --> 00:02:01,590
+compound proposition هو عبارة عن Totology لأنه
+
+22
+00:02:01,590 --> 00:02:06,390
+قيمة الـ True مع كل صفوف جدول الاحتمالات اللي
+
+23
+00:02:06,390 --> 00:02:08,830
+موجودة عندنا بغض النظر الجدول كان صغير ولا كبير
+
+24
+00:02:08,830 --> 00:02:13,470
+نفس المنطقة تمام؟ الآن لو الجدول كله من تمام مثلا
+
+25
+00:02:13,470 --> 00:02:17,510
+الخنات عفوا او تمام صفوف لجد في خانة واحدة فقط
+
+26
+00:02:17,510 --> 00:02:21,420
+False ماقدرش اقول عنه Totologyماقدرش اقول عنه
+
+27
+00:02:21,420 --> 00:02:28,960
+tautology فلازم يكون هو دائما في كل الأوقات لازم
+
+28
+00:02:28,960 --> 00:02:35,960
+يكون true كذلك لو كان القيمة في أي وقت تقول الى
+
+29
+00:02:35,960 --> 00:02:45,280
+false بنقول عنه contradiction تعامل تبدل ال b and
+
+30
+00:02:45,280 --> 00:02:45,920
+نقطة ال b
+
+31
+00:02:49,140 --> 00:02:56,020
+true and false false false and true false لاحظ انه
+
+32
+00:02:56,020 --> 00:03:00,100
+فعليا ان كل صفوف جدول الاحتمالات كانت عند النتيجة
+
+33
+00:03:00,100 --> 00:03:04,320
+false هدول ال two definition أسهل two definition
+
+34
+00:03:04,320 --> 00:03:09,940
+ممكن يكونوا موجودات معانا بكل بساطة الآن بدك تشوف
+
+35
+00:03:09,940 --> 00:03:15,180
+الجملة التالية بدك تستخدم جدول الاحتمالات عشان
+
+36
+00:03:15,180 --> 00:03:22,900
+تحللهاواتفقنا إنه هنعتمد الإشارة هذه على إنها
+
+37
+00:03:22,900 --> 00:03:26,340
+إشارة الـ equivalence ما بين ال proposition بدنا
+
+38
+00:03:26,340 --> 00:03:29,980
+نعتمد الإشارة هذه as equivalence بين ال
+
+39
+00:03:29,980 --> 00:03:37,020
+proposition اللي موجودة عندي بيجيب ويقول لي شوف لي
+
+40
+00:03:37,020 --> 00:03:48,580
+نط ال D R أو نط P or Q نط P or Qأو نقطة P و نقطة Q
+
+41
+00:03:48,580 --> 00:03:54,880
+نقطة P و نقطة Q نقطة P و نقطة Q نقطة P و نقطة Q
+
+42
+00:03:54,880 --> 00:03:59,060
+نقطة P و نقطة Q نقطة P و نقطة Q نقطة P و نقطة Q
+
+43
+00:03:59,060 --> 00:04:00,360
+نقطة P و نقطة P و نقطة Q نقطة P و نقطة P و نقطة P
+
+44
+00:04:00,360 --> 00:04:00,380
+و نقطة P و نقطة P و نقطة P و نقطة P و نقطة P و
+
+45
+00:04:00,380 --> 00:04:00,860
+نقطة P و نقطة P و نقطة P و نقطة P و نقطة P و نقطة
+
+46
+00:04:00,860 --> 00:04:03,340
+P و نقطة P و نقطة P و نقطة P و نقطة P و نقطة P و
+
+47
+00:04:03,340 --> 00:04:03,340
+نقطة P و نقطة P و نقطة P و نقطة P و نقطة P و نقطة
+
+48
+00:04:03,340 --> 00:04:14,960
+P و نقطة P و نقطة P و نقطة P و نقطة P و
+
+49
+00:04:15,080 --> 00:04:19,100
+و اتنين false العمود اللي بعده واحدة true واحدة
+
+50
+00:04:19,100 --> 00:04:25,600
+false وبدينا نطبق المسألة بكل بصابة نفت نقطة B هي
+
+51
+00:04:25,600 --> 00:04:33,460
+نقطة Q نقطة P or Q هي P or Q true or truetrue
+
+52
+00:04:33,460 --> 00:04:38,920
+نفيها false true or false true نفيها false false
+
+53
+00:04:38,920 --> 00:04:43,040
+or true true نفيها false false or false false
+
+54
+00:04:43,040 --> 00:04:46,500
+نفيها true و بعدين روح نجيب طبعا هنا في خطأ بسيط
+
+55
+00:04:46,500 --> 00:04:54,980
+بدك نط Q و بالتالي روح بدت أحسب نط ال B and نط ال
+
+56
+00:04:54,980 --> 00:04:58,640
+Q false and false false and true true and false
+
+57
+00:04:58,640 --> 00:05:04,130
+true and true لاحظ في النهايةإن وصلت إنه في عندي
+
+58
+00:05:04,130 --> 00:05:08,390
+تكافؤ ما بين ال two proposition اللي موجودات قدامي
+
+59
+00:05:08,390 --> 00:05:12,210
+وهذا الأمر لحد اللحظة بسيط إن أشكل جدول الاحتمالات
+
+60
+00:05:12,210 --> 00:05:16,090
+و أحسبه الأمر بسيط وهين مافيش فيه أي مشكلة الأمر
+
+61
+00:05:16,090 --> 00:05:20,730
+هو بشكل عام بسيط لكن قد يسداد صعوبة أو تعقيد نوعا
+
+62
+00:05:20,730 --> 00:05:25,210
+ما حسب المسألة اللي مقروحة قدامكبداية على الـ
+
+63
+00:05:25,210 --> 00:05:28,670
+equivalence صار في عندنا مجموعة من القوانين ممكن
+
+64
+00:05:28,670 --> 00:05:32,730
+تكون موجودة لأن الشباب لو جاءت تتكلمت على compound
+
+65
+00:05:32,730 --> 00:05:41,330
+proposition مع five simple propositions ايش
+
+66
+00:05:41,330 --> 00:05:46,130
+بيوصل في المسألة اللي عندك؟ ردد جد ولا احتمالات
+
+67
+00:05:46,130 --> 00:05:51,030
+تبعتها؟ اتنين و اص خمسة اتنين و تلاتين اتنين و
+
+68
+00:05:51,030 --> 00:05:56,190
+تلاتين فتخيل كمان يكونقولوا شويه معقد زي المثال
+
+69
+00:05:56,190 --> 00:06:01,750
+هذا على سبيل المثال زي
+
+70
+00:06:01,750 --> 00:06:08,290
+هيك بخمس متغيرات او ستة معناته ساعة عشان تعمل جد
+
+71
+00:06:08,290 --> 00:06:11,070
+ولا احتمالاته انت بتشتغل فيه مش هتكون كافية
+
+72
+00:06:11,070 --> 00:06:16,510
+بالنسبة لكالحل نحاول نعتمد على مجموعة من القوانين
+
+73
+00:06:16,510 --> 00:06:20,210
+بحيث أننا نختصر أو نختزل المسائل هذه وفعليا نقدر
+
+74
+00:06:20,210 --> 00:06:24,810
+نشوف إلى أين بتقول المسائل هذه بشكل بسيط نقول
+
+75
+00:06:24,810 --> 00:06:29,150
+المسائل هذه يا شباب و هي شغلات سهلة لازم نحفظها و
+
+76
+00:06:29,150 --> 00:06:33,110
+نتمهلها لحد اللحظة كل كلامنا Logical Gates أو
+
+77
+00:06:33,110 --> 00:06:39,390
+Boolean ألجيبرا true and true true and false false
+
+78
+00:06:39,390 --> 00:06:45,280
+true or truetrue true or false true مصدر او لا و
+
+79
+00:06:45,280 --> 00:06:48,740
+تعالى نشوفها و بالتالي لو انا ايش مكانة في القانون
+
+80
+00:06:48,740 --> 00:06:52,940
+الاول هذا القانون الوحدة يعني ايش المعامل المحايد
+
+81
+00:06:52,940 --> 00:06:56,200
+الضربي في عملية الضرب الواحد والمحايد الجامعي
+
+82
+00:06:56,200 --> 00:07:02,080
+الصفر ومافيش المحايد مع عملية ال and ل true اللي
+
+83
+00:07:02,080 --> 00:07:08,220
+بيأثرش لو انت اضافته مش هيأثر بي and true بي لان
+
+84
+00:07:08,220 --> 00:07:11,670
+لو كانت قيمتها trueهتكون true و لو كان قيمتها
+
+85
+00:07:11,670 --> 00:07:16,750
+false هتكون false كذلك ال false هي المحادث مع ال
+
+86
+00:07:16,750 --> 00:07:22,450
+or الآن
+
+87
+00:07:22,450 --> 00:07:27,970
+كذلك في قانون ال domination بمجرد تلاقي true مع ال
+
+88
+00:07:27,970 --> 00:07:32,010
+or فالنتيجة true بناء على ال definition تكون واحدة
+
+89
+00:07:32,010 --> 00:07:34,710
+من المتخلقة على الأقل ال true فانت عايش تضمن ال
+
+90
+00:07:34,710 --> 00:07:39,800
+true في حالة ال false مع ال andواحدة على الأقل
+
+91
+00:07:39,800 --> 00:07:47,660
+false معناته ايش الاختزال
+
+92
+00:07:47,660 --> 00:07:54,440
+الان P and P بما ان هو نفس المتغير معناته هي نفس
+
+93
+00:07:54,440 --> 00:07:58,600
+قيمة truth value اما هتكون true او هتكون false
+
+94
+00:07:58,600 --> 00:08:07,500
+وهذه هتقابل false وهذه هتقابل true وبالتالي تكافئ
+
+95
+00:08:08,560 --> 00:08:12,580
+الـ B و عند ال or كذلك لأن هي نفس القيمة اللى
+
+96
+00:08:12,580 --> 00:08:18,940
+موجودة عندى فى الموضوع اللى فيه P and not ال B
+
+97
+00:08:18,940 --> 00:08:24,140
+false لإن إذا كانت true هتكون false .. false و لو
+
+98
+00:08:24,140 --> 00:08:28,040
+كانت هذه false فهي already خلاص ماتدورش اللى بعدها
+
+99
+00:08:28,040 --> 00:08:33,280
+true or not ال B عفوا بي or not ال B true لإن لو
+
+100
+00:08:33,280 --> 00:08:35,600
+كانت هذه false هتكون التانية true و لو كانت true
+
+101
+00:08:35,600 --> 00:08:42,740
+already بمناهافي النفي نفي النفي اثبات commutative
+
+102
+00:08:42,740 --> 00:08:48,400
+او الإبدال P and Q نبط P وQ نبط P وهذه العملية
+
+103
+00:08:48,400 --> 00:08:56,140
+قلنا إبدالية وكذلك هي عند ال R قانون التجميع P and
+
+104
+00:08:56,140 --> 00:09:02,590
+Q and Rأحنا بتفقد أن العملية عملية تجميعية و
+
+105
+00:09:02,590 --> 00:09:06,670
+اثنائية في نفس الوجد بيعني تسوى P and Q الكل and R
+
+106
+00:09:06,670 --> 00:09:14,670
+كذلك بتسوى P and افتح جوز Q and ال R كذلك عملية
+
+107
+00:09:14,670 --> 00:09:21,130
+الجمع او عفوا عملية ال R هي عبارة عن عملية كذلك
+
+108
+00:09:21,130 --> 00:09:28,710
+عملية تجميعية من ناحية التوزيع بتقدر توزع ال and
+
+109
+00:09:29,560 --> 00:09:35,200
+على ال or و توزع ال or على ال and بحيث ان بي or
+
+110
+00:09:35,200 --> 00:09:40,960
+عشان ما تنساش دائما خد ال proposition و الإشارة
+
+111
+00:09:40,960 --> 00:09:47,580
+معاه وبالتالي
+
+112
+00:09:47,580 --> 00:09:55,680
+بي and q or ال r نتكلم بي and q or بي and ال rكذلك
+
+113
+00:09:55,680 --> 00:10:00,400
+عند الـ R لما وزّيها على ال end بيوركيو and بيور
+
+114
+00:10:00,400 --> 00:10:07,140
+ال R دي مورجان لاو بقول دي مورجان لو أثبت من خلال
+
+115
+00:10:07,140 --> 00:10:11,260
+جدول الإحتمالات أنه لو دخلنا النفي على ال end و ال
+
+116
+00:10:11,260 --> 00:10:14,460
+R مش بس ال truth value تبعت ال proposition هي اللي
+
+117
+00:10:14,460 --> 00:10:21,160
+تنجلب لأ حتى العملية بتصير ال end بتصير R وبالتالي
+
+118
+00:10:21,160 --> 00:10:28,520
+not a and b أو not p and qنقطة P أو نقطة Q نقطة P
+
+119
+00:10:28,520 --> 00:10:38,580
+أو نقطة Q نقطة P أو نقطة Q نقطة P أو نقطة Q نقطة P
+
+120
+00:10:38,580 --> 00:10:47,420
+أو نقطة Q نقطة Q أو نقطة P أو نقطة Q نقطة P أو
+
+121
+00:10:47,420 --> 00:10:54,280
+نقطة Q أو نقطة P أو نقطة P أو نقطة P أو نقطة P أو
+
+122
+00:10:54,280 --> 00:10:55,080
+نقطة P أو نقطة P أو نقطة P أو نقطة P أو نقطة P أو
+
+123
+00:10:55,080 --> 00:10:55,080
+نقطة P أو نقطة P أو نقطة P أو نقطة P أو نقطة P أو
+
+124
+00:10:55,080 --> 00:10:55,080
+نقطة P أو نقطة P أو نقطة P أو نقطة P أو نقطة P أو
+
+125
+00:10:55,080 --> 00:10:55,080
+نقطة P أو نقطة P أو نقطة P أو نقطة P أو نقطة P أو
+
+126
+00:10:55,080 --> 00:10:55,080
+نقطة P أو نقطة P أو نقطة P أو نقطة P أو نقطة P أو
+
+127
+00:10:55,080 --> 00:11:01,190
+نقطة P أو نقطة P أوB implies Q and B implies R
+
+128
+00:11:01,190 --> 00:11:07,330
+يؤدي إلى تكافئة B implies وكأنه ما كنت أقوله؟
+
+129
+00:11:07,330 --> 00:11:11,270
+خدناه
+
+130
+00:11:11,270 --> 00:11:22,390
+معامل مشترك كمان ال implies B
+
+131
+00:11:22,390 --> 00:11:30,250
+implies R or Q implies Rكذلك سأجمع الـ implication
+
+132
+00:11:30,250 --> 00:11:39,910
+B and Q implies R و أريك أن تنتبه الأورهام كيف
+
+133
+00:11:39,910 --> 00:11:43,730
+أصبحت في المسألة التانية لماذا؟ لأنه لا تنسى أن
+
+134
+00:11:43,730 --> 00:11:50,150
+هذه القانون الأساسي موضوع الإشارة نثبت نفسنا أو
+
+135
+00:11:50,150 --> 00:11:56,880
+نشوف كيف نثبت هذا الكلام طيب في الـ biconditionalB
+
+136
+00:11:56,880 --> 00:12:04,300
+by conditional of Q B by conditional of Q B
+
+137
+00:12:04,300 --> 00:12:13,660
+by conditional of Q B by conditional of Q B by
+
+138
+00:12:13,660 --> 00:12:14,580
+conditional of Q B by conditional of Q B by
+
+139
+00:12:14,580 --> 00:12:19,560
+conditional of Q B by conditional of Q B by
+
+140
+00:12:19,560 --> 00:12:21,920
+conditional of Q B by conditional of Q
+
+141
+00:12:25,330 --> 00:12:28,650
+بالنسبة إيه اللي بتصير المسلمات؟ بدك تحفظها؟ أه
+
+142
+00:12:28,650 --> 00:12:32,670
+بدك تحفظها بس قبل ما بدك تحفظها بدك تحاول أو
+
+143
+00:12:32,670 --> 00:12:36,070
+بنحاول مع بعض نعرف إن هذه القولين من وين إجت بالإن
+
+144
+00:12:36,070 --> 00:12:41,150
+على إيش انكتبت وصارت تساوي هذا موجود الآن في
+
+145
+00:12:41,150 --> 00:12:43,550
+الحالة تعالى نشوف الحالة الأولى اللي موجودة عندها
+
+146
+00:12:43,550 --> 00:12:48,490
+أو بلاش ناخد أكتر من حالة نرجع مثلا للدي مورجان
+
+147
+00:12:48,490 --> 00:12:52,670
+مثلا
+
+148
+00:12:52,670 --> 00:12:56,330
+ناخد واحدة من الدي مورجان الوزعشان انا اثبت ان
+
+149
+00:12:56,330 --> 00:13:01,470
+هدول equivalent هاد القوانين يا شباب كمان مرة هي
+
+150
+00:13:01,470 --> 00:13:05,230
+اللي هتخدمني لما يكون عدد ال proposition كبير
+
+151
+00:13:05,230 --> 00:13:08,870
+بقدرش اشكل جدول الاحتمالات وبالتالي هتجه للقوانين
+
+152
+00:13:08,870 --> 00:13:11,950
+في الحالة اللي زي هذه ايش المطلوب اساوي يا شباب
+
+153
+00:13:11,950 --> 00:13:16,150
+المفروض اعمل جدول الاحتمالات لكل واحدة من العناصر
+
+154
+00:13:16,150 --> 00:13:19,790
+او القرفين هدولة واشوف هم هل هم متساويات ولا لأ
+
+155
+00:13:25,490 --> 00:13:29,450
+false, false true,
+
+156
+00:13:29,610 --> 00:13:40,610
+false true, false الان P or Q و نفيها أصبت لأن
+
+157
+00:13:40,610 --> 00:13:47,630
+true or true true و نفيها false true or false true
+
+158
+00:13:47,630 --> 00:13:51,850
+و نفيها false false or true true و نفيها false
+
+159
+00:13:51,850 --> 00:13:57,780
+false or false false و trueأو نفيها true طيب الطرف
+
+160
+00:13:57,780 --> 00:14:05,060
+التاني نقطة B و نقطة Q false
+
+161
+00:14:05,060 --> 00:14:10,140
+and false false طب ليش أنا بقول false و بشرح على
+
+162
+00:14:10,140 --> 00:14:14,000
+true لإن أنا أعمل المسألة اللي بديها بالنفي false
+
+163
+00:14:14,000 --> 00:14:21,240
+and true false true and false false true and true
+
+164
+00:14:21,240 --> 00:14:26,820
+trueوبالتالي المعادلتين او two compound
+
+165
+00:14:26,820 --> 00:14:32,800
+proposition equivalent متكافئين لأن عند كل صفوف
+
+166
+00:14:32,800 --> 00:14:38,440
+الجدول الاحتمالات دون نفس النتيجة يعني أيش ما تاخد
+
+167
+00:14:38,440 --> 00:14:43,680
+قيمة ل P و Q المعادلتين هيدوك نفس النتيجة وبالتالي
+
+168
+00:14:43,680 --> 00:14:47,520
+احنا بنتكلم على تساوي او تكافئ ما بين العناصر اللي
+
+169
+00:14:47,520 --> 00:14:48,160
+موجودة عندها
+
+170
+00:14:51,570 --> 00:14:54,970
+كذلك في حالة الـ implication لو انا بدي اثبتها
+
+171
+00:14:54,970 --> 00:15:02,610
+كمان نفس الموضوع بجدوا الاحتمالات و اشتغل عليه طيب
+
+172
+00:15:02,610 --> 00:15:07,910
+نشوف
+
+173
+00:15:07,910 --> 00:15:12,710
+الأخيرة من العناصر اللي موجودة عندها في القيمة
+
+174
+00:15:12,710 --> 00:15:15,050
+اللي عندك كم متغير تلاتة
+
+175
+00:15:21,630 --> 00:15:30,290
+True True True True False False False False True
+
+176
+00:15:30,290 --> 00:15:37,850
+True False False True True False False True False
+
+177
+00:15:37,850 --> 00:15:41,550
+True False True False False True False False True
+
+178
+00:15:41,550 --> 00:15:41,550
+False False True False False True False True False
+
+179
+00:15:41,550 --> 00:15:41,550
+True False True False True False True False True
+
+180
+00:15:41,550 --> 00:15:41,570
+False True False True False True False True False
+
+181
+00:15:41,570 --> 00:15:41,570
+True False True False True False True False True
+
+182
+00:15:41,570 --> 00:15:41,570
+True True True True True True True True True True
+
+183
+00:15:41,570 --> 00:15:41,570
+True True True True True True True True True True
+
+184
+00:15:41,570 --> 00:15:41,570
+True True True True True True True True True True
+
+185
+00:15:41,570 --> 00:15:41,570
+True True True True True True True True True True
+
+186
+00:15:41,570 --> 00:15:41,570
+True True True True True True True True True True
+
+187
+00:15:41,570 --> 00:15:41,570
+True True True True True True True True True True
+
+188
+00:15:41,570 --> 00:15:41,570
+True True True True True True True True True True
+
+189
+00:15:41,570 --> 00:15:41,570
+True True True True True true true true true true
+
+190
+00:15:41,570 --> 00:15:43,940
+true true true true true truetrue false هاي جدول
+
+191
+00:15:43,940 --> 00:15:46,560
+الاحتمالات بتاعة الصحوف اللى ممكن تكون موجودة
+
+192
+00:15:46,560 --> 00:15:56,360
+عندها بعد هيك B implies Q او B implies ال R true
+
+193
+00:15:56,360 --> 00:16:01,220
+implies true true true implies false false true
+
+194
+00:16:01,220 --> 00:16:08,660
+true false false implies true true false implies
+
+195
+00:16:08,660 --> 00:16:15,400
+falsetrue false implies false true بس هي هذه
+
+196
+00:16:15,400 --> 00:16:17,420
+الحالة اللي ممكن تصير فيها true implies لا false
+
+197
+00:16:17,420 --> 00:16:23,100
+قولنا false implies true true true Q implies ال R
+
+198
+00:16:23,100 --> 00:16:28,960
+true
+
+199
+00:16:28,960 --> 00:16:39,940
+false true true true false true trueمش فاهمين؟ و
+
+200
+00:16:39,940 --> 00:16:44,700
+لا مش شايفين؟ مش شايفين ماشي الحال الآن كمان مرة
+
+201
+00:16:44,700 --> 00:16:49,380
+هاي ال Q و هاي ال R أعمل implication بينهم true
+
+202
+00:16:49,380 --> 00:16:53,320
+implies true true implies false false false
+
+203
+00:16:53,320 --> 00:16:57,340
+implies true وكملنا الجدول طيب الآن بدي أجمع ما
+
+204
+00:16:57,340 --> 00:17:04,260
+بينهم بال or تبقى في الجثت طرف الأول هذي بصبوط؟
+
+205
+00:17:04,260 --> 00:17:09,680
+طيب تعالي مع الطرف الأول and بينهم or عفواtrue
+
+206
+00:17:09,680 --> 00:17:17,720
+false true true true true true true true true true
+
+207
+00:17:17,720 --> 00:17:22,840
+true true true true true true true true true true
+
+208
+00:17:22,840 --> 00:17:25,660
+true true true true true true true true true true
+
+209
+00:17:25,660 --> 00:17:25,660
+true true true true true true true true true true
+
+210
+00:17:25,660 --> 00:17:30,900
+true true true true true true true true true true
+
+211
+00:17:30,900 --> 00:17:31,520
+true true true true true true true true true true
+
+212
+00:17:31,520 --> 00:17:35,140
+true true true true true true true true true true
+
+213
+00:17:35,140 --> 00:17:35,140
+true true true true true true true true true true
+
+214
+00:17:35,140 --> 00:17:35,160
+true true true true true true true true true true
+
+215
+00:17:35,160 --> 00:17:35,240
+true true true true true true true true true true
+
+216
+00:17:35,240 --> 00:17:35,300
+true true true true true true true true true true
+
+217
+00:17:35,300 --> 00:17:35,300
+true true true true true true true true true true
+
+218
+00:17:35,300 --> 00:17:35,300
+true true true true true true true true true true
+
+219
+00:17:35,300 --> 00:17:35,300
+true true true true true true true true true true
+
+220
+00:17:35,300 --> 00:17:35,300
+true true true true true true true true true true
+
+221
+00:17:35,300 --> 00:17:35,300
+true true true true true true true true true true
+
+222
+00:17:35,300 --> 00:17:35,300
+true true true true true true true true true true
+
+223
+00:17:35,300 --> 00:17:35,300
+true true true true true true true true true true
+
+224
+00:17:35,300 --> 00:17:35,300
+true true true true true true true true true true
+
+225
+00:17:35,300 --> 00:17:35,300
+true true true true true true true true true true
+
+226
+00:17:35,300 --> 00:17:35,300
+true true true true true true true true true true
+
+227
+00:17:35,300 --> 00:17:35,300
+true true true true true true true true true true
+
+228
+00:17:35,300 --> 00:17:41,240
+true trueimplies ال R اذا انت مش قادر تحلها بشكل
+
+229
+00:17:41,240 --> 00:17:45,360
+سريع اعملها عمود مستقل و ريح راسك عشان تكبر في
+
+230
+00:17:45,360 --> 00:17:49,440
+المضمون لان تعالي نفسي نسوي P and Q مش هيك عندي
+
+231
+00:17:49,440 --> 00:17:55,220
+true and true implies true true true and true true
+
+232
+00:17:55,220 --> 00:18:00,340
+implies false false true and false false implies
+
+233
+00:18:00,340 --> 00:18:07,710
+true true true implies falsefalse true and false
+
+234
+00:18:07,710 --> 00:18:13,890
+.. false implies true .. true true and false ..
+
+235
+00:18:13,890 --> 00:18:19,570
+false implies false .. true false and true ..
+
+236
+00:18:19,570 --> 00:18:23,950
+false implies true .. false
+
+237
+00:18:23,950 --> 00:18:31,710
+and true .. false implies false .. true خلاص كل
+
+238
+00:18:31,710 --> 00:18:35,820
+الباقي true؟اقتنعته فبالتالي هذه equivalent لهذه
+
+239
+00:18:35,820 --> 00:18:39,880
+وبالتالي انا ممكن في لحظة من اللحظات استبدل term
+
+240
+00:18:39,880 --> 00:18:44,020
+زي هذا بterm اخر اثناء المعادلة عشان اختصر او عشان
+
+241
+00:18:44,020 --> 00:18:47,940
+اوصل لحل اسرع ماكنت انا ممكن افكر فيه في المسألة
+
+242
+00:18:47,940 --> 00:19:02,080
+اللي موجودة عندي تعالى
+
+243
+00:19:02,080 --> 00:19:08,100
+نشوفالمسألة الأخيرة هاي
+
+244
+00:19:08,100 --> 00:19:18,400
+بقول ايه بي by conditional q equivalent to b and q
+
+245
+00:19:18,400 --> 00:19:21,600
+are
+
+246
+00:19:21,600 --> 00:19:28,040
+نط ال b and نط ال q بس المرة ها دي مابديش اشتغلها
+
+247
+00:19:28,040 --> 00:19:30,580
+بالجدول الاحتمالات خلاص
+
+248
+00:19:33,050 --> 00:19:36,830
+أكبرنا، الآن بدي أبدأ أشتغل، أشتغل بحيث أني أستفيد
+
+249
+00:19:36,830 --> 00:19:40,330
+من القوانين السابقة، طيب، إيش أول قانون أنا موجود
+
+250
+00:19:40,330 --> 00:19:44,270
+عندي هان؟
+
+251
+00:19:44,270 --> 00:19:49,230
+هاين، مظبوط؟ طيب، بيجي يقوللي هان، طبعا يا شباب،
+
+252
+00:19:49,230 --> 00:19:54,070
+دائما، دائما، حاول خد نظرة علىالطرف التاني من
+
+253
+00:19:54,070 --> 00:19:57,390
+المسألة و حاول إذا كان فيه صورة تانية ممكن تكون
+
+254
+00:19:57,390 --> 00:20:02,710
+عليها عشان تفهمه إيش هو ممكن ايه يكون هذا المثال
+
+255
+00:20:02,710 --> 00:20:07,070
+اللي عندنا مباشرة و مافيش فيها عبارة عن جثين بينهم
+
+256
+00:20:07,070 --> 00:20:09,810
+and والإشارات ده فيه يعني بدك تفهم الجثة اللي
+
+257
+00:20:09,810 --> 00:20:13,450
+موجودة عندك كويسة هان هذه المسألة هي عبارة عن B
+
+258
+00:20:13,450 --> 00:20:20,590
+implies Q and Q implies ال R حسب القانون 1 هان ولا
+
+259
+00:20:20,590 --> 00:20:21,190
+لأ؟
+
+260
+00:20:26,600 --> 00:20:37,680
+مصبوط؟ اه حط اه P تمام هاي الخطوة رقم واحد اللي
+
+261
+00:20:37,680 --> 00:20:40,960
+ابتدي أشغلها الخطوة التانية ال implication هذه
+
+262
+00:20:40,960 --> 00:20:44,960
+لازم انا أخلص منها عشان انا في الآخره بدي أصف فقط
+
+263
+00:20:44,960 --> 00:20:48,800
+and و or في المسألة مين بيخدمني فيها؟ بيخدمني فيها
+
+264
+00:20:48,800 --> 00:20:53,230
+القانون الأول handمعناته بتصير في عندي hand not b
+
+265
+00:20:53,230 --> 00:21:09,730
+or q and not q or ال b مظبوط هيك لحد تلقاه مافيش
+
+266
+00:21:09,730 --> 00:21:17,180
+مشكلة و الأمور تحت السيطرة الخطوة اللي بعد هيكأحنا
+
+267
+00:21:17,180 --> 00:21:20,940
+كان فينا توزيع وتجميع ولا لأ؟ الآن في حالة في حالة
+
+268
+00:21:20,940 --> 00:21:23,620
+زي هذه شو بقى تساوي تفكر فيها يا شباب؟ بدك تاخد
+
+269
+00:21:23,620 --> 00:21:28,180
+الجوس بالكامل وتوزعه وكأنه single element يعني بقى
+
+270
+00:21:28,180 --> 00:21:32,440
+تفترض أن هذه لحالها X أو B و بقى تدخلها على الجوس
+
+271
+00:21:32,440 --> 00:21:38,520
+اللي موجود ليش؟ عشان أنا في الآخر محتاج أن أصفي
+
+272
+00:21:38,520 --> 00:21:45,210
+أنه B لحال أو الملفيات على الطرفوالمثبتات على
+
+273
+00:21:45,210 --> 00:21:51,410
+الطرف التاني او مع بعضهم معناته دي بقدي نط ال B or
+
+274
+00:21:51,410 --> 00:22:07,990
+Q and نط ال Q صح؟ مظبوط؟ طيب or خد الجث نفسه نط ال
+
+275
+00:22:07,990 --> 00:22:12,110
+B or Q and
+
+276
+00:22:14,460 --> 00:22:19,180
+الـ B تمام؟
+
+277
+00:22:19,180 --> 00:22:27,500
+لم تفعل شيء احنا في عندنا كمان مرة B and Q or ال R
+
+278
+00:22:27,500 --> 00:22:36,440
+تكافئ B and Q or B and ال R صح؟ لما قلت لك خد هدول
+
+279
+00:22:36,440 --> 00:22:41,890
+و بوزعهمعلى عناصر الجوز بس ال B اللي عندي الان مش
+
+280
+00:22:41,890 --> 00:22:44,950
+single event مش single proposition come down
+
+281
+00:22:44,950 --> 00:22:50,370
+proposition فنجلتها تمام كمان مرة بدي اروح اوزع
+
+282
+00:22:50,370 --> 00:23:04,550
+مين ال Q بدي اوزع ال Q طيب تعالي اخد ال Q ايه
+
+283
+00:23:04,550 --> 00:23:05,410
+بتصير في عندي هان
+
+284
+00:23:08,510 --> 00:23:18,370
+not ال B and not ال Q or لاحظ هذا ال term عمّال
+
+285
+00:23:18,370 --> 00:23:28,770
+وصلته أنا بدي إياه كمّر or Q and not ال Q خلّصت من
+
+286
+00:23:28,770 --> 00:23:35,130
+الجرس الأول صح؟ or not
+
+287
+00:23:35,130 --> 00:23:37,250
+ال B and ال B
+
+288
+00:23:42,320 --> 00:23:54,160
+R Q and بيه اش اللي انا بسوي ال guide بوزع النقطة
+
+289
+00:23:54,160 --> 00:23:59,200
+Q هذه على الجثة هذا و ال and بيه هذه و وزعتها على
+
+290
+00:23:59,200 --> 00:24:06,460
+الجثة هذا كمان مرة فلما بدأت اوزع الان صفة المسألة
+
+291
+00:24:06,460 --> 00:24:16,750
+عندي بيهعفوا نقطة B and نقطة Q or Q and نقطة Q
+
+292
+00:24:16,750 --> 00:24:27,190
+الجواص التاني بنفس الكيفية نقطة B and B or Q and
+
+293
+00:24:27,190 --> 00:24:33,340
+B الأقواس اللي عندي لاحظوا يا شبابهذه فكت الجثة
+
+294
+00:24:33,340 --> 00:24:37,720
+الأول وهذه وهذه الجثة التانية اللي عندك واضح ان
+
+295
+00:24:37,720 --> 00:24:42,840
+المسألة كلها يدها ايش المستخدم فيها or يعني كلها
+
+296
+00:24:42,840 --> 00:24:46,560
+هي نفس المسألة معناته انا بقدر اجمع اختزل بالاقواص
+
+297
+00:24:46,560 --> 00:24:51,180
+زي ما بدي هذي واحد اتنين انا في عندي بعض المسائل
+
+298
+00:24:51,180 --> 00:24:58,480
+عمالها راحت وين باتجاه وين Q and نقطة Q false ولا
+
+299
+00:24:58,480 --> 00:25:08,350
+لا P and نقطة Pfalse في عند القانون بيقول بي او
+
+300
+00:25:08,350 --> 00:25:14,630
+فالس equivalent to ايش؟ to بي ولا بقى؟ ممتاز عند
+
+301
+00:25:14,630 --> 00:25:22,650
+الجوص هذا or ال false معناته الجوص نقطة بي و نقطة
+
+302
+00:25:22,650 --> 00:25:26,770
+كيو ايش بينهم؟
+
+303
+00:25:26,770 --> 00:25:30,790
+or false or q and b
+
+304
+00:25:36,970 --> 00:25:41,810
+بس شوية يا شبايل نجملها و نعيد ترتيب العناصر ال or
+
+305
+00:25:41,810 --> 00:25:46,310
+إبدالية و ال and إبدالية مظلومة لأ و هذه بدو يساوي
+
+306
+00:25:46,310 --> 00:25:55,250
+B and Q يعني بدلت الجوس هذا و بدلته على ناحية
+
+307
+00:25:55,250 --> 00:26:04,050
+تانية or نقطة ال B and نقطة ال Q صعب
+
+308
+00:26:04,050 --> 00:26:04,310
+الأمر
+
+309
+00:26:08,470 --> 00:26:14,130
+الجدول أحسن و أقمن بس الجدول في لحظة من اللحظات
+
+310
+00:26:14,130 --> 00:26:19,210
+ممكن يكلفك الصفحة كلها و ماتوصلهاش تمام فبالتالي
+
+311
+00:26:19,210 --> 00:26:23,730
+احنا أخدنا الجدول و بنينا على الجدول عشان نصلللشغل
+
+312
+00:26:23,730 --> 00:26:28,510
+بالشكل هذا طيب ناخد كمان عاصر او كمان مسائل ما هيك
+
+313
+00:26:28,510 --> 00:26:31,730
+انت لو طلعت مسائل الكتاب ايش بيقولك هتلاقي في
+
+314
+00:26:31,730 --> 00:26:35,070
+السؤال بيقولك باعتمادك على جدول الاحتمالات يعني
+
+315
+00:26:35,070 --> 00:26:38,270
+انا بطلب منك تستخدم جدول الاحتمالات و مرات تانية
+
+316
+00:26:38,270 --> 00:26:42,410
+بيقولك باستخدام الخطوات المنطقية او رياضيات
+
+317
+00:26:42,410 --> 00:26:48,950
+الخطوات المنطقية اثبت انه كذامن أول لحظة يجب أن
+
+318
+00:26:48,950 --> 00:26:53,690
+تحفظهم و ليش احنا حطناهم equivalent أو كيف اثبتنا
+
+319
+00:26:53,690 --> 00:26:58,470
+انهم equivalent؟ من يحفظهم؟ انت
+
+320
+00:27:05,720 --> 00:27:10,060
+وأنا بأنصحك يا شباب يعني ما تحاولش .. ما تحاولش في
+
+321
+00:27:10,060 --> 00:27:13,700
+المادة تأجل شغلها بعدين انت لسه في أول الفصل احنا
+
+322
+00:27:13,700 --> 00:27:16,920
+في الأسبوع التاني تمام؟ المسائل اللي بقولك في
+
+323
+00:27:16,920 --> 00:27:21,640
+الكتاب حلها حل منها جدش بتقدر ومعفن ما تحل .. ما
+
+324
+00:27:21,640 --> 00:27:28,890
+تحلش على ورق و ترميه شوف لك دفتر تمام؟ أبو الميةأو
+
+325
+00:27:28,890 --> 00:27:32,930
+مجموعة ورق وبتدبسوا مع بعض وانت حر بس في الآخر كل
+
+326
+00:27:32,930 --> 00:27:36,750
+ورقة .. كل حرف بتكتبه بحلو احتفظ فيه لإنه عند
+
+327
+00:27:36,750 --> 00:27:41,550
+المراجعة تمام؟ بتتثبت .. بتلاقي الأمور أفضل
+
+328
+00:27:41,550 --> 00:27:45,070
+بقولكاش إنه هذا الدفتر هتسلمني يا في الآخر وليه
+
+329
+00:27:45,070 --> 00:27:51,110
+علامات زي المدارس؟ لا يا أستاذي تمام؟ بالمناسبة
+
+330
+00:27:51,110 --> 00:27:55,770
+لابدوش نحل بلاش الأمر ماتركله تماما إيش بقوللي في
+
+331
+00:27:55,770 --> 00:28:05,630
+المسألة هذه؟بقول اثبت ان نفي الجوز هذا PR P AND Q
+
+332
+00:28:05,630 --> 00:28:15,830
+equivalent to NOT P AND NOT Q باعتمادك على series
+
+333
+00:28:15,830 --> 00:28:21,450
+of logical equivalence على سلسلة من ال logical
+
+334
+00:28:21,450 --> 00:28:23,870
+equivalence اللي بدك تتبعها يعني لو حلته بجدول
+
+335
+00:28:23,870 --> 00:28:25,690
+الاحتمالات غلط
+
+336
+00:28:28,170 --> 00:28:33,110
+تمام؟ اما الصعب هيك صح؟ على الآخر طيب الآن انا
+
+337
+00:28:33,110 --> 00:28:37,070
+بقولك اثبت ان الطرف هذا يساوي هذا قولتلك او نصحتك
+
+338
+00:28:37,070 --> 00:28:40,330
+انا دائما خد نظرة على الطرف التاني على الطرف
+
+339
+00:28:40,330 --> 00:28:44,990
+الأسهل اللي انت بدك تروح له هل هذا ممكن يكتب على
+
+340
+00:28:44,990 --> 00:28:49,710
+صورة تانية؟ لأ استعجل أزميلك و قال لأ بس انا بقول
+
+341
+00:28:49,710 --> 00:28:55,470
+لأ ممكن يكتب باري كيو بناء على دي مورجان لو ممكن
+
+342
+00:28:55,470 --> 00:28:59,270
+تكون الصورة هيليش أنا قاعد بقولك شوف الصورة هل
+
+343
+00:28:59,270 --> 00:29:03,110
+ممكن يكتب على صورة تانية ولا لأ؟ لأن أثناء البحث
+
+344
+00:29:03,110 --> 00:29:07,030
+.. أثناء .. أثناء ما أنت مركز في الخطوات ممكن تصل
+
+345
+00:29:07,030 --> 00:29:12,470
+للصورة المكافئة وانت فعليا .. لأن خلاص هذه اللي في
+
+346
+00:29:12,470 --> 00:29:19,670
+دماغك مش شايف إنك انت خلصت طيب تعالي نحل المسألة
+
+347
+00:29:19,670 --> 00:29:27,500
+اللي عندي هيو بقولي not P Rنقطة ال B و ال Q وهي
+
+348
+00:29:27,500 --> 00:29:34,700
+الأقواس لاحظ .. لاحظ أن النفي لو بقى خارج يمكن أن
+
+349
+00:29:34,700 --> 00:29:38,520
+يخدمني أو لا .. فممكن أن اعتبدها منهجي و اتركها
+
+350
+00:29:38,520 --> 00:29:42,940
+عنده .. او عفوا اعتبدها خطوة و اتركها و أصير أشغل
+
+351
+00:29:42,940 --> 00:29:50,140
+وين؟ على الجو والجوس وهذه كافة .. بدي ا .. بالضبط
+
+352
+00:29:50,140 --> 00:29:51,280
+.. بدي اوزع الآن
+
+353
+00:29:54,220 --> 00:29:59,720
+على العنصر اللي عندي تمام ما هي تهيئنا فيه هتصير
+
+354
+00:29:59,720 --> 00:30:10,680
+ال P عندي P or نقطة P and مرة تانية P or Q ممتاز
+
+355
+00:30:10,680 --> 00:30:19,440
+الأولى حرام عليك يا شيخ true لأن بينهم or لإن
+
+356
+00:30:19,440 --> 00:30:24,540
+اسمته false واحد قال الأولى falsetrue true and x
+
+357
+00:30:24,540 --> 00:30:33,160
+true ميزة equivalent to نفي ال B or ال Q خلصنا بدك
+
+358
+00:30:33,160 --> 00:30:39,020
+تجيب الخطوة التالتة الآن اللي هي نط ال B and نط ال
+
+359
+00:30:39,020 --> 00:30:44,860
+Q وبتكون انت وصلت للحل المطلوب يا السلام هي هيك
+
+360
+00:30:44,860 --> 00:30:49,380
+الآن كمان مرة بينفعش في لحظة من اللحظات وبيقوللي
+
+361
+00:30:49,380 --> 00:30:53,410
+ما تستخدمش جدول الاحتمالاتواطرحاش تستخدم جد و لا
+
+362
+00:30:53,410 --> 00:31:00,350
+احتمالات طبعا حاولت افصلك في الخطوات الا اكتر طبعا
+
+363
+00:31:00,350 --> 00:31:06,530
+شوف انا ايش سويت في الاول يعني
+
+364
+00:31:06,530 --> 00:31:12,490
+احنا اخدنا حل و قولنا خل النفي برا فبالحل التاني
+
+365
+00:31:12,490 --> 00:31:18,600
+اللي ممكن انا اشعر ان ابقى فيه ادخلت النفي لجوانفي
+
+366
+00:31:18,600 --> 00:31:23,840
+معناته not to be and نفي الجوز هذا خطوة التالية
+
+367
+00:31:23,840 --> 00:31:31,320
+صارت نفي تنفي تدخل الجوز نفي كمان مرة كمان
+
+368
+00:31:31,320 --> 00:31:38,280
+مرة في الآخر هتصل لنفس الحل هتصل لنفس الحل لكنه مع
+
+369
+00:31:38,280 --> 00:31:45,000
+خطوات .. شوف طالما خطواتك منطقية تمام غالبا هتصل
+
+370
+00:31:45,000 --> 00:31:50,490
+لحلوالحل هيكون تبعك صحيح، طالما أنك بتقلفش، يعني
+
+371
+00:31:50,490 --> 00:31:54,190
+أنك في الـ Pseuocyte، طالما أنك بتقلفش، يعني أنك
+
+372
+00:31:54,190 --> 00:32:00,450
+في السليم، تعالى نشوف المسألة هذه، بقول اثبت ان
+
+373
+00:32:00,450 --> 00:32:05,210
+هذه توتولوجيا، شو يعني توتولوجيا؟ ان قيمتها true
+
+374
+00:32:05,210 --> 00:32:08,210
+and cruel جدول الاحتمالات، بس اللي انا مديش جدول
+
+375
+00:32:08,210 --> 00:32:12,860
+الاحتمالاتمعناته انا بدي اختصر بنفس الكيفية و اذا
+
+376
+00:32:12,860 --> 00:32:18,580
+وصلت ل true ان هذه هيك تكافئ true خلصنا ما فهي
+
+377
+00:32:18,580 --> 00:32:22,560
+تتولوجي بدون جدول احتمالات تمام تعالى نشوف كيف ما
+
+378
+00:32:22,560 --> 00:32:26,960
+ممكن نشتغل فيها كمان مرة طب هنقول لأ ميت مرة
+
+379
+00:32:26,960 --> 00:32:32,820
+الأولوية دائما لمين للأقواس تمام معناته هقول له
+
+380
+00:32:32,820 --> 00:32:38,080
+هذا equivalent to بي اور بدي ادخل النفس الأول نقطة
+
+381
+00:32:38,080 --> 00:32:45,310
+بيR نقطة Q بناهي عادي موجله بصبوط الخطوة التانية
+
+382
+00:32:45,310 --> 00:32:53,030
+بدي أخد ال B و أدخله على الجثث و هذه تكافئ بي ار
+
+383
+00:32:53,030 --> 00:33:00,550
+نقطة بي ار ليش بدون أقواص؟ خلاص أنا بدت معاهم فمش
+
+384
+00:33:00,550 --> 00:33:12,410
+مشكلة بي ار نقطة Qالأولى هذه جداش قيمتها true
+
+385
+00:33:12,410 --> 00:33:18,250
+التانية true حران عليك P and Q هدول ايوة فالان
+
+386
+00:33:18,250 --> 00:33:21,950
+اصبحت انا على قانون السيطرة تبعد ل true مع ال R
+
+387
+00:33:21,950 --> 00:33:31,170
+true or P or not Q يكافئ true معناته انا بتكلم ان
+
+388
+00:33:31,170 --> 00:33:34,110
+ال compound proposition اللي قلت معايا هذا عبارة
+
+389
+00:33:34,110 --> 00:33:39,130
+عن tetralogy كيف اجت مش احنا في عندنا Pأو الـ true
+
+390
+00:33:39,130 --> 00:33:50,310
+true صح هي ال true وهي ال بي مع بعض وبينهم or و
+
+391
+00:33:50,310 --> 00:33:52,890
+بينهم or و أنا ضمنت واحدة من ال true في ال output
+
+392
+00:33:52,890 --> 00:33:56,150
+هو محصلة true على القانون
+
+393
+00:34:15,600 --> 00:34:23,080
+لأ لأ شويه اشفل حقا okay طيب هان هذه الأسئلة خلاص
+
+394
+00:34:23,080 --> 00:34:25,680
+طبعا احنا ال section هذه الأسئلة أخدتها عشوائية من
+
+395
+00:34:25,680 --> 00:34:34,780
+الكتاب و تعمدنا أرقام هماشي أرقام زوجية طبعا بدنا
+
+396
+00:34:34,780 --> 00:34:37,700
+الحل أو بدنا المحاضرة بحل هذا دي Morgan law
+
+397
+00:34:37,700 --> 00:34:42,380
+أثبتناها عمال يقول استخدم ال truth tableفي المسألة
+
+398
+00:34:42,380 --> 00:34:46,560
+التانية يا شباب المسألة التانية طلعش تقولي عمّاله
+
+399
+00:34:46,560 --> 00:34:49,780
+determine
+
+400
+00:34:49,780 --> 00:34:55,920
+whether يعني حدد إذا كانت هذه المسألة Totology ولا
+
+401
+00:34:55,920 --> 00:35:04,280
+لأ تخيل في لحظة من اللحظات كانت مكتوبة هنا دي show
+
+402
+00:35:04,280 --> 00:35:11,360
+that is a Totology إيش بك تساوي؟ هبدأ تشتغل؟
+
+403
+00:35:14,490 --> 00:35:18,810
+المسألة مختلفة تماما بالمناسبة determined حد ما
+
+404
+00:35:18,810 --> 00:35:24,340
+إذا كانت تتولوجي أو لأغير انها اثبت انها totality
+
+405
+00:35:24,340 --> 00:35:29,000
+طبعا ليش انا قاعد بقول كلام هذا؟ عشان انأكد على
+
+406
+00:35:29,000 --> 00:35:34,060
+مبدأ ان فهم السؤال مهم جدا .. فهم السؤال مهم جدا
+
+407
+00:35:34,060 --> 00:35:37,900
+خلينا نتكلم بنظرة ان والله انا فهمت السؤال
+
+408
+00:35:37,900 --> 00:35:42,320
+اثبتليها، لو اما هتروح معايا المسألة هتصل لمرحلة
+
+409
+00:35:42,320 --> 00:35:47,820
+.. هتصل لمرحلة و المسألة عايشةتجفل معاك على الرغم
+
+410
+00:35:47,820 --> 00:35:51,960
+ان كل خطواتك اللي كتبتها صح تعالى تجرب بس او ارجيك
+
+411
+00:35:51,960 --> 00:35:55,780
+انها بتجف و لا بتجفش لان في الآخر في الآخر لازم لو
+
+412
+00:35:55,780 --> 00:36:02,440
+كانت خطواتك منطقية متسلسلة خلاص طيب الآن حسب
+
+413
+00:36:02,440 --> 00:36:06,100
+المعادلة اللي عندي تعالى اكتبها يعني بشكل كويس في
+
+414
+00:36:06,100 --> 00:36:14,720
+عندي نط ال B and افتح جوز P implies Q الكل
+
+415
+00:36:16,500 --> 00:36:21,640
+implies not the Q الوزع
+
+416
+00:36:21,640 --> 00:36:27,080
+طيب اللي بدك هي بمشي الحل و ليش ماتفكر ان انا اخلص
+
+417
+00:36:27,080 --> 00:36:30,260
+من ال implies لان هو قاعد بقولي tautology معناته
+
+418
+00:36:30,260 --> 00:36:33,860
+انا في الآخر بده اوصل true and او false لان مش
+
+419
+00:36:33,860 --> 00:36:39,880
+هقدر اتكلم على القيام هذه صح؟ طيب الآن ال B
+
+420
+00:36:39,880 --> 00:36:46,070
+implies Q تكافئ not the Qنط .. عفوا .. نط ال B or
+
+421
+00:36:46,070 --> 00:36:51,850
+Q بصبوط؟ بدي أستبدل كل ال implies نفس المنطقة هذه
+
+422
+00:36:51,850 --> 00:37:01,410
+.. هذه تكافئ نط ال B and .. نط ال B or Q بصبوط؟
+
+423
+00:37:01,410 --> 00:37:05,590
+هذا ال implication .. الجثة الأول هذا implies ..
+
+424
+00:37:05,590 --> 00:37:08,930
+لحظة شوية .. نط ال Q عشان مانخربطش الشباب بصبوط؟
+
+425
+00:37:08,930 --> 00:37:12,770
+الآن هذا الجثة أو بدي أخلص من ال implies كمان مرة
+
+426
+00:37:14,640 --> 00:37:21,900
+بدي أنف الجوس الأول نط ال بي and نط بي or كيو الكل
+
+427
+00:37:21,900 --> 00:37:29,100
+or نط كيو حسب مفتنون نفسه هذا أصبت؟ الآن دخل ال or
+
+428
+00:37:29,100 --> 00:37:35,320
+أو ال نفي عارفان على الأقواص اللي عندك بتصير عندي
+
+429
+00:37:35,320 --> 00:37:43,160
+هان نفي نفي ال بي or الآن ده بتصير or بدك تنفي
+
+430
+00:37:43,160 --> 00:37:43,620
+الجوس
+
+431
+00:37:46,970 --> 00:37:55,830
+لسة ما بتدخلها جوا بتنفيها R not the Q يعني أنا
+
+432
+00:37:55,830 --> 00:37:58,870
+بجرد بس و ادخلت النفي على القوسين الان بدي أحل هذه
+
+433
+00:37:58,870 --> 00:38:03,090
+بي
+
+434
+00:38:03,090 --> 00:38:11,690
+ار الان بي كمان مرة and not the Q للقوس اللي عندي
+
+435
+00:38:11,690 --> 00:38:20,700
+R not the Qالان المسألة واضحة ان ولا عمرها حصير
+
+436
+00:38:20,700 --> 00:38:29,780
+Totology ليش؟ الان لاحظ تعالى ارتبها بي ار نط كيو
+
+437
+00:38:29,780 --> 00:38:32,740
+لو كانت نط كيو عبارة عن نط بي كان ضمنت انها
+
+438
+00:38:32,740 --> 00:38:41,180
+Totology مصبوط؟ ار بي ار نط كيو الاول فى لحظة من
+
+439
+00:38:41,180 --> 00:38:46,660
+اللحظات اذا انت كنت فاهم السؤالعلى show that it's
+
+440
+00:38:46,660 --> 00:38:52,960
+a tautology معناته انت هتبقى واقف هنا او هتبقى
+
+441
+00:38:52,960 --> 00:38:57,660
+تزيد في الخطوات المنطقية تبعتك على الرغم ان خطواتك
+
+442
+00:38:57,660 --> 00:39:01,920
+صحيحة 100% بس في الآخر مش هتصل لها tautology بينما
+
+443
+00:39:01,920 --> 00:39:06,060
+هو السؤال اللي بيقول ايه حدد ما اذا كانت tautology
+
+444
+00:39:06,060 --> 00:39:10,060
+او لأ طب عشان احدد ما كانت tautology او لأ معناته
+
+445
+00:39:10,060 --> 00:39:15,290
+مافيش قدام لغاية حل واحدجدول الاحتبالات جدول
+
+446
+00:39:15,290 --> 00:39:19,570
+الاحتبالات لماذا؟ لأنه غير بيبين هو تيتولوجيا ولا
+
+447
+00:39:19,570 --> 00:39:24,330
+لا أنا عمال بأثبت أن تيتولوجيا مش جادة بأثبت بظبط
+
+448
+00:39:24,330 --> 00:39:27,690
+وبالتالي هذه الخطوات الشباب منطقية لكنها لم تؤدي
+
+449
+00:39:27,690 --> 00:39:32,290
+تودي لك نتيجة مش هتقدر تحسم تقدر حد يقدر يحسم هنا
+
+450
+00:39:32,290 --> 00:39:36,810
+شباب؟ إذا أنت في لحظة من اللحظات لجيت والله أن في
+
+451
+00:39:36,810 --> 00:39:40,970
+عندك true و or ماعرف أقدر أقول تيتولوجيا false و
+
+452
+00:39:40,970 --> 00:39:46,300
+andبتقول عنها إيش؟ Contradiction يعني مستحيل تكون
+
+453
+00:39:46,300 --> 00:39:50,780
+Totology هل ممكن نصلّي هيك شغلها؟ طب ما هي ال B و
+
+454
+00:39:50,780 --> 00:39:53,700
+ال B لو أنا بدي أجمعهم مع بعض أو بدي أدخلهم بشكل
+
+455
+00:39:53,700 --> 00:39:57,980
+أو باخر مع بعض مش حصل للقيم المطلوبة عشان أقوله
+
+456
+00:39:57,980 --> 00:40:02,240
+ولا لأ فالحل بيجي أنك عندك وين؟ جدول الإحتمالات
+
+457
+00:40:02,240 --> 00:40:06,420
+عشان تحل هذه المشكلة طيب في جدول الإحتمالات كام
+
+458
+00:40:06,420 --> 00:40:12,700
+متغير عندي؟ اتنين He is not Totology بالمناسبة
+
+459
+00:40:15,720 --> 00:40:20,500
+is not tautology بيبينها بس بتقدرش تثبت بتقدرش
+
+460
+00:40:20,500 --> 00:40:25,280
+تثبت إلا غير تقولي هي عند القيمة x و y و z true و
+
+461
+00:40:25,280 --> 00:40:30,020
+true للقيم اللي عندك تدوني false طبعا يعني لو
+
+462
+00:40:30,020 --> 00:40:34,600
+اخترت مثلا على السريع متى هذه المعادلة ممكن تصير
+
+463
+00:40:34,600 --> 00:40:39,260
+false في حالة واحدة لو كانت true implies false
+
+464
+00:40:39,260 --> 00:40:46,250
+وعشان هذه تكون false معناته Q equal trueصح؟ طيب
+
+465
+00:40:46,250 --> 00:40:50,290
+عشان تكون المعادلة هذه true لازم الطرفين هدول
+
+466
+00:40:50,290 --> 00:40:55,270
+يكونوا true بصبوط هذه true and true معناته ال B
+
+467
+00:40:55,270 --> 00:41:04,610
+لازم تكون false صح؟ هاي القيامة اللي عندي انا
+
+468
+00:41:04,610 --> 00:41:09,970
+ماجول نقش المسألة عشان تكون المسألة عشان تكون true
+
+469
+00:41:09,970 --> 00:41:16,690
+تمام؟ بالشكل هذا وبالتاليهيصير عندي فالس او لفل
+
+470
+00:41:16,690 --> 00:41:28,110
+فالس لفل فالس true and true و false implies true
+
+471
+00:41:28,110 --> 00:41:32,690
+true true and true true implies true true لكن هذه
+
+472
+00:41:32,690 --> 00:41:36,290
+حالة من الحالات اللي موجودة عندي وبالتالي انا بدي
+
+473
+00:41:36,290 --> 00:41:39,710
+اقبل جد و الاحتمالات كلها عشان اقدر اشوف وين هذه
+
+474
+00:41:39,710 --> 00:41:47,430
+المسألة بيحصلفالس، متى المسألة هذه بتصير فالس؟ لو
+
+475
+00:41:47,430 --> 00:41:54,850
+كانت هذه فالس وهذه true، فح؟ متى ممكن تكون فالس؟
+
+476
+00:41:54,850 --> 00:42:01,910
+أيه، معناته الـQ بديها تساوي true عشان تكون هذه
+
+477
+00:42:01,910 --> 00:42:09,150
+false والـB هذي بديها تكون true و الـB equal true
+
+478
+00:42:11,210 --> 00:42:18,010
+بتصير لا فيها false بتكون
+
+479
+00:42:18,010 --> 00:42:25,730
+false وهذه بدها تكون true هذه عشان تكون true فالس
+
+480
+00:42:25,730 --> 00:42:30,810
+فالس ما تهزر في عندي حالة ان المسألة تقول فيها
+
+481
+00:42:30,810 --> 00:42:38,500
+لمين لل false بي equal true و Q equalfalse بطبقها
+
+482
+00:42:38,500 --> 00:42:41,720
+في المسألة هذه حتلاقيها تقول الى false وبتالي
+
+483
+00:42:41,720 --> 00:42:45,500
+المسألة هذه not tautology الأسهل أني أرسم جدوا
+
+484
+00:42:45,500 --> 00:42:48,640
+الاحتمال على السريع خصوصا أنه أربع جل أربع صفوف
+
+485
+00:42:48,640 --> 00:42:53,120
+وبقدر أحدد من القيم اللي ممكن إيش تأثر في المسألة
+
+486
+00:42:53,120 --> 00:43:01,000
+اللي موجودة عندي طيب البعديها عماله جات بقوللي
+
+487
+00:43:01,000 --> 00:43:09,580
+show that يعني اثبتB and Q implies R and B implies
+
+488
+00:43:09,580 --> 00:43:16,660
+R and Q implies R are not الشباب
+
+489
+00:43:16,660 --> 00:43:21,110
+يعني مافي اثبتوا انهم غير متساوياتعشان تثبت انهم
+
+490
+00:43:21,110 --> 00:43:25,630
+غير متساويات إياك تستخدم القوانين القوانين هتوصلك
+
+491
+00:43:25,630 --> 00:43:31,870
+لطريق مسدودة الحل جدول الاحتمالات او تحاول ترسم
+
+492
+00:43:31,870 --> 00:43:36,250
+جدول الاحتمالات على جانب وتشوف ايش الصف اللي بيخل
+
+493
+00:43:36,250 --> 00:43:43,450
+الجمالتين هدول مش متكافئات اكيد لو عند أول صف في
+
+494
+00:43:43,450 --> 00:43:47,730
+بتمسكو بحق خلاص معناته هدول الاتنين صار فيه انه
+
+495
+00:43:47,730 --> 00:43:53,580
+مختلفبالتالي عندنا كم قيمة يا شباب؟ عندنا تلت
+
+496
+00:43:53,580 --> 00:44:02,740
+متغيرات BQR true true true true false false false
+
+497
+00:44:02,740 --> 00:44:11,460
+true true false false true true false false true
+
+498
+00:44:11,460 --> 00:44:18,380
+false true false true false true false أصبت؟ طيب
+
+499
+00:44:18,670 --> 00:44:26,350
+الان دعنا على السريع الصف الأول true and true true
+
+500
+00:44:26,350 --> 00:44:31,290
+implies true true true true true true true true
+
+501
+00:44:31,290 --> 00:44:31,930
+true true true true true true true true true true
+
+502
+00:44:31,930 --> 00:44:31,930
+true true true true true true true true true true
+
+503
+00:44:31,930 --> 00:44:33,190
+true true true true true true true true true true
+
+504
+00:44:33,190 --> 00:44:33,190
+true true true true true true true true true true
+
+505
+00:44:33,190 --> 00:44:41,290
+true true true
+
+506
+00:44:41,290 --> 00:44:44,090
+true true true true true true true true true true
+
+507
+00:44:44,090 --> 00:44:44,330
+true true true true true true true true true true
+
+508
+00:44:44,330 --> 00:44:44,330
+true true true true true true true true true true
+
+509
+00:44:44,330 --> 00:44:44,330
+true true true true true true true true true true
+
+510
+00:44:44,330 --> 00:44:44,330
+true true true true true true true true true true
+
+511
+00:44:44,330 --> 00:44:44,330
+true true true true true true true true true true
+
+512
+00:44:44,330 --> 00:44:44,330
+true true true true true true true true true true
+
+513
+00:44:44,330 --> 00:44:44,330
+true true true true true true true true true true
+
+514
+00:44:44,330 --> 00:44:44,330
+true true true true true true true true true true
+
+515
+00:44:44,330 --> 00:44:44,330
+true true true true true true true true true true
+
+516
+00:44:44,330 --> 00:44:44,330
+true true true true true true true true true true
+
+517
+00:44:44,330 --> 00:44:44,330
+true true true true true true true true true true
+
+518
+00:44:44,330 --> 00:44:44,330
+true true true true true true true true true true
+
+519
+00:44:44,330 --> 00:44:44,330
+true true true true true true true true true true
+
+520
+00:44:44,330 --> 00:44:44,330
+true true true true true true true true true true
+
+521
+00:44:44,330 --> 00:44:47,260
+true true true true truetrue false implies false
+
+522
+00:44:47,260 --> 00:44:51,880
+true true and true true برضه الصف الأخير لأ اللى
+
+523
+00:44:51,880 --> 00:45:00,200
+بعده true true false true و true و false false
+
+524
+00:45:00,200 --> 00:45:05,320
+implies true او اعفر true implies false false يعني
+
+525
+00:45:05,320 --> 00:45:11,160
+true implies false true implies false و بينهم and
+
+526
+00:45:11,160 --> 00:45:15,430
+false معناته false و false برضه التانىبارا نشوف
+
+527
+00:45:15,430 --> 00:45:19,510
+التالت لاحظ
+
+528
+00:45:19,510 --> 00:45:23,490
+ان انت بتحسب على المعادلة نفسها ووحدها بس عشان
+
+529
+00:45:23,490 --> 00:45:29,610
+تتأكد انك انت خدت الصفوف واحد واحد الان true false
+
+530
+00:45:29,610 --> 00:45:34,670
+true false
+
+531
+00:45:34,670 --> 00:45:36,630
+implies true true
+
+532
+00:45:40,700 --> 00:45:45,980
+true implies true true false implies true true and
+
+533
+00:45:45,980 --> 00:45:54,020
+true true برضه متكافئات الصف الأخير true false
+
+534
+00:45:54,020 --> 00:46:02,740
+false true false false false implies true false
+
+535
+00:46:02,740 --> 00:46:04,420
+implies false true
+
+536
+00:46:11,830 --> 00:46:19,710
+الأن هذه true وهذه false وهذه false وهذه false
+
+537
+00:46:19,710 --> 00:46:25,270
+true implies false and false implies false true
+
+538
+00:46:25,270 --> 00:46:32,770
+true and falseالقيمتين هي هم اختلفوا وبالتالي هدول
+
+539
+00:46:32,770 --> 00:46:36,010
+القيمتين is not logically equivalent و بالذنب
+
+540
+00:46:36,010 --> 00:46:44,590
+اقوله عند القيمة B equal true, Q equal false وR
+
+541
+00:46:44,590 --> 00:46:49,090
+equal false هدول اللي بيقدوا ان القيم اللي عندي is
+
+542
+00:46:49,090 --> 00:46:53,200
+not equivalentواضح الأمور يا شباب؟ قبل ما أطلع
+
+543
+00:46:53,200 --> 00:46:56,260
+خلينا نشوف بس الأسئلة الكتاب انا هدقول الأسئلة دي
+
+544
+00:46:56,260 --> 00:46:58,780
+أجيبتهم من الكتاب طبعا وزي ما قلت لك اختارتهم بشكل
+
+545
+00:46:58,780 --> 00:47:01,400
+عشوائي لأ لسه ما خلصنا الشابتر واحد خلصنا section
+
+546
+00:47:01,400 --> 00:47:06,140
+واحد تلاتة دال فيه تقريبا اتنين
+
+547
+00:47:11,350 --> 00:47:16,490
+الان اخر شغله قبل ما نطلع لازم تاخد نظرة على أسئلة
+
+548
+00:47:16,490 --> 00:47:21,470
+الكتاب و انا حددتلك في ال slides السؤال من 1 ل 33
+
+549
+00:47:21,470 --> 00:47:25,250
+حاول تحلهم الأسئلة الفردية موجود حلولها في نهاية
+
+550
+00:47:25,250 --> 00:47:27,910
+الكتاب زي ما قلتلك المرة الماضية و انا جيبتلك
+
+551
+00:47:27,910 --> 00:47:31,030
+مجموعة من الأسئلة الزوجية تعالى عما لا بقولك use
+
+552
+00:47:31,030 --> 00:47:36,470
+the truth table عشان تتأكد من ال equivalence الان
+
+553
+00:47:36,470 --> 00:47:41,610
+هذه المعادلة ال truth table تبعها من كام صفحرام
+
+554
+00:47:41,610 --> 00:47:45,830
+عليكوا اتنين لان في عندك one variable اتنين اص
+
+555
+00:47:45,830 --> 00:47:51,330
+واحد اتنين طيب في المسألة في لقم تلاتة لما بيجي
+
+556
+00:47:51,330 --> 00:47:54,850
+بيقولك اثبت الشغلات هدا واربعة فاربعة جدول
+
+557
+00:47:54,850 --> 00:47:58,350
+الاحتمالات لاحظ يا شباب لما بيقولك استخدم جدول
+
+558
+00:47:58,350 --> 00:48:02,670
+الاحتمالات بيقولك استخدم ال truth table شوف مسألة
+
+559
+00:48:02,670 --> 00:48:06,890
+اتناشه سؤال اتناشه ايش بيقولك show that each
+
+560
+00:48:06,890 --> 00:48:11,610
+conditional statement in exercise عشر اللي فوقis a
+
+561
+00:48:11,610 --> 00:48:18,070
+tautology without using truth table.معناته انت
+
+562
+00:48:18,070 --> 00:48:22,790
+الآن شبك تساوي بتكاشي تستخدم جدول الاحتمالات،
+
+563
+00:48:22,790 --> 00:48:28,270
+بتكاشي تستخدم القوانين، صعبة؟ بهيكة نتيجة
+
+564
+00:48:28,270 --> 00:48:30,830
+المحاضرة، الله يعطيكم العافية
+
diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/FFRz-p6sRfY.srt b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/FFRz-p6sRfY.srt
new file mode 100644
index 0000000000000000000000000000000000000000..a3fbad53ec18da098412c6bc26ee856731ccde73
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/FFRz-p6sRfY.srt
@@ -0,0 +1,1975 @@
+
+1
+00:00:20,970 --> 00:00:22,970
+بسم الله والحمد لله والصلاة والسلام على رسول الله
+
+2
+00:00:22,970 --> 00:00:24,270
+الرحمن الرحيم، اليوم إن شاء الله يا شباب، هنبدأ بـ
+
+3
+00:00:24,270 --> 00:00:28,610
+Chapter جديد، اللي هو Chapter الاثبات الرياضي أو
+
+4
+00:00:28,610 --> 00:00:31,950
+proof techniques، تقنيات الاثبات الرياضي، and
+
+5
+00:00:31,950 --> 00:00:34,930
+mathematical induction، استنباط أو الاستقراء
+
+6
+00:00:34,930 --> 00:00:39,290
+الرياضي. لا أخفيكم أن كثيراً من الأحيان كنا نعاني
+
+7
+00:00:39,290 --> 00:00:43,010
+مشكلة في موضوع الاثبات، وبمجرد ما بيقول لك اثبت كذا
+
+8
+00:00:43,010 --> 00:00:47,470
+أو اثبت النظرية أو اعمل كذا، بنبدأ نعيش… بنبدأ
+
+9
+00:00:47,470 --> 00:00:53,060
+نتَرْجَع ونسيب الموضوع، لأسباب كثيرة أهمها أنه
+
+10
+00:00:53,060 --> 00:00:58,140
+ما كناش… يعني ما أحد علمنا من البداية أساسيات
+
+11
+00:00:58,140 --> 00:01:01,360
+الاثبات، يعني المعرفة اللي لازمة للِإثبات كلها
+
+12
+00:01:01,360 --> 00:01:06,380
+موجودة، والمسألة دائماً اللي فيها إثبات فيها مقدمات
+
+13
+00:01:06,380 --> 00:01:10,750
+كافية. تمام؟ إنك تمشي حسب العلم اللي درسته
+
+14
+00:01:10,750 --> 00:01:14,310
+والمعلومات اللي بتعرفها، وتوصل للنتيجة. لكن أحياناً
+
+15
+00:01:14,310 --> 00:01:18,350
+كيف أنا بدي أبدأ؟ من وين؟ وليه هيك؟ وبناءً أنا على
+
+16
+00:01:18,350 --> 00:01:22,330
+إيش هيك كان الإحساس؟ هذا اللي إيش؟ تكون الأمور أحياناً
+
+17
+00:01:22,330 --> 00:01:26,930
+بتمشي في الإثبات خطوة بخطوة، وبتحس أنه جفل. طب هل فيه
+
+18
+00:01:26,930 --> 00:01:29,350
+طريق ثاني ممكن أنا أسلكه، وتكون فيه نتيجة معينة؟
+
+19
+00:01:29,350 --> 00:01:33,420
+أه فيه، Section 1-7 اللي إحنا فاتحناها في Chapter
+
+20
+00:01:33,420 --> 00:01:37,920
+واحد، قلت لكم لاحقاً إن يا شباب هنرجع له، بتكلم على تلات
+
+21
+00:01:37,920 --> 00:01:42,900
+تقنيات مهمة في الإثبات لمعظم
+
+22
+00:01:42,900 --> 00:01:46,880
+الإثباتات اللي إحنا ممكن نتعرض لها، وبتيجي الـ
+
+23
+00:01:46,880 --> 00:01:49,740
+mathematical induction لاحقاً، أو الاستقراء الرياضي.
+
+24
+00:01:49,740 --> 00:01:53,580
+لما بيجي نتكلم على موضوع الـ sequences، شوفتوا مثلاً
+
+25
+00:01:53,580 --> 00:01:59,220
+معادلات الجمع تبع الـ sequences، كيف تم إثباتها؟
+
+26
+00:01:59,220 --> 00:02:03,820
+هذه نظرية مش عادية، بالاستقراء الرياضي لإيش؟ لأن الـ
+
+27
+00:02:03,820 --> 00:02:08,880
+sequence اللي عندك أعدادها غير منتهية، فبالتالي
+
+28
+00:02:08,880 --> 00:02:13,160
+فبالتالي كان هو بيفرض أنها صحيحة لحد مستوى معين، و
+
+29
+00:02:13,160 --> 00:02:16,040
+بيشوف هل… بيشوف بعد المستوى هذا، بيصل لنتيجة ثانية.
+
+30
+00:02:16,040 --> 00:02:20,440
+لو اتغيرت قيمة الـ N زائد واحد مثلاً، وهكذا. هنبدأ
+
+31
+00:02:20,440 --> 00:02:24,460
+اليوم إن شاء الله في مفاهيم الاستقراء، لكن ضروري
+
+32
+00:02:24,460 --> 00:02:27,140
+دائماً أستحضر مفاهيم الرياضيات البسيطة اللي إحنا
+
+33
+00:02:27,140 --> 00:02:31,160
+بنعرفها. من مفاهيم الرياضيات البسيطة إن مثلاً عملية
+
+34
+00:02:31,160 --> 00:02:35,860
+الجمع، عملية الضرب، عمليات إبدالية، بصحيح. بينما
+
+35
+00:02:35,860 --> 00:02:39,200
+عملية القسمة، وحتى عملية… عملية غير إبدالية. عملية الضرب
+
+36
+00:02:39,200 --> 00:02:42,660
+توزيعية على الجمع، وحتى… والعكس غير صحيح، بصحيح.
+
+37
+00:02:42,660 --> 00:02:46,530
+ولا لأ؟ وبالتالي… بالتالي هذه المفاهيم يجب أن
+
+38
+00:02:46,530 --> 00:02:49,710
+تكون حاضرة عندي… لما بجي بتكلم من أكبر: أن ولا
+
+39
+00:02:49,710 --> 00:02:56,990
+جذر الـ N؟ إن… من أكبر N ولا N تربيع؟ حتماً
+
+40
+00:02:56,990 --> 00:02:59,630
+الـ N تربيع. يعني لو بنقول… عشان نكون منصفين
+
+41
+00:02:59,630 --> 00:03:02,150
+نقول أكبر أو تساوي… الـ N تربيع…  مظبوط أو لا؟
+
+42
+00:03:02,150 --> 00:03:05,810
+وبالتالي ما أحد فينا… هذه المفاهيم بتوفيها… بس
+
+43
+00:03:05,810 --> 00:03:08,810
+دائماً نقطة البداية هي اللي بتشكل… اللي…
+
+44
+00:03:08,810 --> 00:03:13,990
+اللي ممكن إحنا نشوفه. لو فكرنا نتذكر أو حبينا نتذكر
+
+45
+00:03:13,990 --> 00:03:18,510
+بعض المفاهيم. الـ product of non-zero real numbers
+
+46
+00:03:18,510 --> 00:03:25,290
+is non-zero. لو أخدت أي عددين حقيقيين غير صفر
+
+47
+00:03:25,290 --> 00:03:30,850
+وضربتهم في بعض، الناتج هيكون لا يساوي صفر. ولا لأ؟
+
+48
+00:03:30,850 --> 00:03:34,270
+وهدم المسلمات، عشان… نقول لك إحنا مجموعة نلحقها ده
+
+49
+00:03:34,270 --> 00:03:38,730
+إحنا بنتذكرها. لو أخدت أي عدد لا يساوي الصفر وربعته،
+
+50
+00:03:39,730 --> 00:03:43,130
+فهيكون النتيجة تبعه positive. فهيكون النتيجة تبعه
+
+51
+00:03:43,130 --> 00:03:46,450
+positive، لأنه السالب والموجب عند التربيع بيديني
+
+52
+00:03:46,450 --> 00:03:51,690
+positive، موجب. الـ even integer، العدد الزوجي، بيكتب
+
+53
+00:03:51,690 --> 00:03:57,510
+على صورة اتنين في K. بقى لو اتكلم على even
+
+54
+00:03:57,510 --> 00:04:02,390
+integer، يعني Z، ما أتكلمش على real number، أتكلم على Z
+
+55
+00:04:02,390 --> 00:04:06,590
+بالدرجة الأولى. كل عدد زوجي يكتب على صورة 2K. هات
+
+56
+00:04:06,590 --> 00:04:11,620
+أي عدد زوجي بيديه لك، هتلاقي أربعة: 2 في 2، ستة:
+
+57
+00:04:11,620 --> 00:04:16,700
+و 30: 2 في 15، 2 في 18، وهكذا.
+
+58
+00:04:16,700 --> 00:04:24,340
+أما العدد الفردي يكتب على صورة 2K زائد واحد.
+
+59
+00:04:24,340 --> 00:04:29,020
+لأنه هو أكبر من العدد الزوجي بواحد أو ناقص واحد.
+
+60
+00:04:29,020 --> 00:04:36,060
+أرجيك فيها أو ناقص واحد. ليه؟ لأن الأعداد الصحيحة
+
+61
+00:04:36,060 --> 00:04:40,060
+إما عدد فردي أو عدد زوجي. بيبدأ الصفر زوجي، ورا واحد
+
+62
+00:04:40,060 --> 00:04:45,260
+فردي، اتنين زوجي، التلاتة صارت… العدد الثاني… العدد
+
+63
+00:04:45,260 --> 00:04:50,780
+الزوجي محصور بين عددين فرديين، والعكس صحيح، وهكذا.
+
+64
+00:04:50,780 --> 00:04:54,700
+بتبقى الـ sequence موجودة معايا، عشان هيك العدد
+
+65
+00:04:54,700 --> 00:04:59,230
+الفردي إما بياخد صورة 2K زائد واحد، أو 2
+
+66
+00:04:59,230 --> 00:05:03,030
+K ناقص واحد، وبأي صورة أنا أعتمد في الإثبات عندي؟
+
+67
+00:05:03,030 --> 00:05:07,930
+الصورة اللي ممكن تخدمك أكثر، الصورة اللي ممكن تخدمك
+
+68
+00:05:07,930 --> 00:05:12,750
+أكثر. ممكن الاثنين يكونوا في بعض المسائل، مش فارقة. أه،
+
+69
+00:05:12,750 --> 00:05:19,170
+ممكن. تمام. اللي بعده، لو أخدت أي عددين فرديين،
+
+70
+00:05:19,170 --> 00:05:25,020
+لو ضربتهم في بعض، الناتج تبعهم هيكون فردي. فردي، لو
+
+71
+00:05:25,020 --> 00:05:27,900
+أخذت أي عددين فرديين، خد لك أي عددين من الأصغر اللي
+
+72
+00:05:27,900 --> 00:05:32,640
+بتعرفهم الآن، وضربهم في دماغك، فردي. طبعاً في موضوع
+
+73
+00:05:32,640 --> 00:05:36,080
+الإثبات يا شباب، ما ينفعش تقول: الله أه صحيح، هي رقم
+
+74
+00:05:36,080 --> 00:05:39,480
+مثلاً: تلاتة في سبعة، 21. طب ما لربما في بقى
+
+75
+00:05:39,480 --> 00:05:42,760
+… في عدد فردي، خصوصاً إن الأعداد مجموعات غير
+
+76
+00:05:42,760 --> 00:05:47,710
+منتهية، لربما في عدد فردي بعيد أنت مش قادر تجيب
+
+77
+00:05:47,710 --> 00:05:53,510
+نتيجته بظبط، فما تقدرش تثبت بناءً على مثال. الإثبات بده
+
+78
+00:05:53,510 --> 00:05:59,310
+دائماً خطوات منطقية في تسلسل الأحداث. طيب الـ real
+
+79
+00:05:59,310 --> 00:06:02,710
+number، بقول عنه rational، العدد الحقيقي بقول عنه
+
+80
+00:06:02,710 --> 00:06:06,830
+عدد نسبي لو كان بكتبه على common fraction، إيش يعني
+
+81
+00:06:06,830 --> 00:06:11,970
+common fraction؟ بسط ومقام، والمقام لا يساوي صفر. الـ
+
+82
+00:06:11,970 --> 00:06:12,310
+prime
+
+83
+00:06:15,010 --> 00:06:17,390
+الـ prime هو عبارة عن positive integer أكبر من
+
+84
+00:06:17,390 --> 00:06:21,550
+واحد. اتنين، تلاتة، خمسة، سبعة، أحد عشر، مظبوط؟ لا
+
+85
+00:06:21,550 --> 00:06:25,470
+يُقبل القسمة إلا على نفسه وعلى واحد. بقول لك الـ divisor تبعه:
+
+86
+00:06:25,470 --> 00:06:31,010
+واحد، سالب واحد، بي وسالب بي، صحيح. بس لما اتكلمنا عن
+
+87
+00:06:31,010 --> 00:06:33,210
+الـ divisor المرة الماضية، الـ divisor لازم يكون
+
+88
+00:06:33,210 --> 00:06:38,810
+positive. الـ divisor لازم يكون… لما كتبنا إن الـ M
+
+89
+00:06:38,810 --> 00:06:50,490
+تساوي… أو الـ A قلنا تساوي D، Quantity، Quotient، دي
+
+90
+00:06:50,490 --> 00:06:56,190
+زائد Quotient
+
+91
+00:06:56,190 --> 00:07:02,750
+Quotient
+
+92
+00:07:02,750 --> 00:07:06,450
+Quotient Quotient Quotient Quotient Quotient
+
+93
+00:07:06,450 --> 00:07:07,630
+Quotient Quotient Quotient Quotient Quotient
+
+94
+00:07:07,630 --> 00:07:07,710
+Quotient Quotient Quotient Quotient Quotient
+
+95
+00:07:07,710 --> 00:07:10,570
+Quotient Quotient Quotient Quotient Quotient
+
+96
+00:07:10,570 --> 00:07:12,150
+Quotient Quotient Quotient Quotient Quotient
+
+97
+00:07:12,150 --> 00:07:16,220
+Quotient Quotient Quotient Quot… في الـ section اللي
+
+98
+00:07:16,220 --> 00:07:18,800
+كان في Chapter واحد، ليه كان محبوب في Chapter واحد؟
+
+99
+00:07:18,800 --> 00:07:22,460
+لأن فعلياً إحنا اتعلمنا شغل مهم جداً، لما اتكلمنا عن
+
+100
+00:07:22,460 --> 00:07:31,380
+الـ compound proposition، اللي هي P implies Q، أكثر
+
+101
+00:07:31,380 --> 00:07:38,260
+من 80% من النظريات بتعتمد على مبدأ if then، لو تحقق
+
+102
+00:07:38,260 --> 00:07:44,660
+المعطى هذا بتكون النتيجة عندك كذا. P implies Q، عشان
+
+103
+00:07:44,660 --> 00:07:49,320
+هيك حطينا introduction to proof، Section 1-7، لكن
+
+104
+00:07:49,320 --> 00:07:52,980
+قلت أنا بدي أجيلها تماماً، تمام، لحد ما نتكلم عن
+
+105
+00:07:52,980 --> 00:07:57,760
+الإثبات الرياضي كله في مرة واحدة. الآن عشان أثبت
+
+106
+00:07:57,760 --> 00:08:03,060
+النظرية، في عندي شغل اسمه direct proof، مباشر.
+
+107
+00:08:03,060 --> 00:08:08,220
+direct، يعني المسألة بتكون على صورة P و Q، وأنا بدي
+
+108
+00:08:08,220 --> 00:08:14,940
+أروح أمسك الـ P، تمام؟ ومن خلالها أبدأ أوصل لـ Q. إذا
+
+109
+00:08:14,940 --> 00:08:21,620
+تحققت الـ P، true، فالـ Q حتماً هتتحقق. إذا تحققت الـ
+
+110
+00:08:21,620 --> 00:08:26,560
+P، فالـ Q هتتحقق، عشان النظرية دي بتكون صحيحة. فأنت
+
+111
+00:08:26,560 --> 00:08:34,080
+الخطوات اللي هتبدأها، هتروح تقول: assume الـ P بـ
+
+112
+00:08:34,080 --> 00:08:35,840
+تفترض إن الـ P صحيحة، is true.
+
+113
+00:08:40,360 --> 00:08:44,820
+خلصنا، عشان تبدأ من هنا وتصل لنتيجة دائماً. طيب لو
+
+114
+00:08:44,820 --> 00:08:51,380
+أنا يا جماعة قلت لك اثبت لو كان if n و m أعداد فردية،
+
+115
+00:08:51,380 --> 00:09:03,340
+معناته حاصل جمعهم هيكون عدد زوجي. بقول: if الـ m and
+
+116
+00:09:03,340 --> 00:09:08,340
+الـ n are odd, then
+
+117
+00:09:09,360 --> 00:09:16,160
+الـ M زائد الـ N is even. لأن
+
+118
+00:09:16,160 --> 00:09:20,880
+بالمثال هذا، إيش الـ P؟ إيش الـ P عندي في المسألة؟
+
+119
+00:09:20,880 --> 00:09:28,100
+طبعاً if then، يعني implication، أصبت؟ M and، الـ M هي
+
+120
+00:09:28,100 --> 00:09:38,940
+الـ P، كل هذا. M is odd، N is odd، والـ Q: m زائد الـ n is
+
+121
+00:09:38,940 --> 00:09:44,020
+even. في أي حال، كيف بدي أمشي مع المسألة أنا؟ بدي
+
+122
+00:09:44,020 --> 00:09:52,400
+أفرض. خطوة رقم واحد في الحل، دائماً هتقول: assume الـ
+
+123
+00:09:52,400 --> 00:10:01,360
+P، إيش الـ P؟ is it true؟ إيش يعني؟ m is odd and الـ
+
+124
+00:10:01,360 --> 00:10:03,540
+n is odd.
+
+125
+00:10:08,290 --> 00:10:15,870
+خطوة 1، 2. بما أن M is odd، و N is odd، أنا عندي
+
+126
+00:10:15,870 --> 00:10:22,810
+صورة للعدد الفردي، ولا لأ؟ معناته الـ M هذه الـ
+
+127
+00:10:22,810 --> 00:10:28,570
+M تساوي 2K زائد واحد، for some K، لأي K برضه
+
+128
+00:10:28,570 --> 00:10:32,830
+النظر، إيش كان… لو أخدت الـ K سبعة، أخدت أربعة، أخدت
+
+129
+00:10:32,830 --> 00:10:37,810
+خمسين، أخدت مليون وسبعمية وخمسين ألف ومية وتلاتة
+
+130
+00:10:37,810 --> 00:10:42,270
+وتسعين، مش فارقة، أيش ما تكون، مظبوط؟ في الآخر أنت
+
+131
+00:10:42,270 --> 00:10:45,810
+بتضربها في اتنين، صارت عدد زوجي، أضفت لها واحد، أنت
+
+132
+00:10:45,810 --> 00:10:53,010
+ضامن إن العدد هذا عدد فردي. and الـ M is odd، بدها
+
+133
+00:10:53,010 --> 00:10:59,350
+تساوي…  أخذ نفس الـ K… لأ هي حالة خاصة، بتصير خد أي عدد
+
+134
+00:10:59,350 --> 00:11:11,430
+فردي آخر: 2H زائد واحد، where، بحيث
+
+135
+00:11:11,430 --> 00:11:18,890
+إن N، عفواً K و H تم… تم إلى… مين لازمت أعداد صحيحة.
+
+136
+00:11:18,890 --> 00:11:26,930
+كمان. إيش الخطوة بعد هيك؟ بيسأل عن مين؟ هو خلص…
+
+137
+00:11:26,930 --> 00:11:30,490
+الـ P فقط. أنا الآن في الخطوة 1 و 2، أو إنشاء
+
+138
+00:11:30,490 --> 00:11:33,890
+حتى كل هذه الخطوة رقم واحد، أنا بس حققت المطلوب
+
+139
+00:11:33,890 --> 00:11:39,410
+يعني فككت المعضلة اللي عندي، ووصلت لإن الـ P و
+
+140
+00:11:39,410 --> 00:11:44,010
+الـ N is odd، الـ M والـ N is odd، هي صورتهم هما
+
+141
+00:11:44,010 --> 00:11:49,390
+بيكونوا يشبههم، يعني تجمعهم هيكون عدد فردي. إيش الـ
+
+142
+00:11:49,390 --> 00:11:54,310
+direct؟ الخطوة الـ direct، مباشر، روحي M زائد N
+
+143
+00:11:57,200 --> 00:11:59,560
+ضربها الترقيم هذا مش أساسي، يعني عندنا في الحل
+
+144
+00:11:59,560 --> 00:12:03,380
+معناته كل واحدة بتقدر تقول: they assume كده، then
+
+145
+00:12:03,380 --> 00:12:07,080
+then، أو ترسم then على أنه implies، ما فيش… مش
+
+146
+00:12:07,080 --> 00:12:10,280
+خضرية كتير بس تكتب كل… كل جملة كتبها في صدر
+
+147
+00:12:10,280 --> 00:12:15,180
+عشان تبقى… ليه الترتيب… تبقى أك… أو البرهان ثابت. M
+
+148
+00:12:15,180 --> 00:12:25,720
+زائد N يساوي 2K زائد واحد زائد 2H زائد
+
+149
+00:12:25,720 --> 00:12:31,400
+واحد، عارفين قيمة الـ M وقيمة الـ N، أجمع الـ N، 2
+
+150
+00:12:31,400 --> 00:12:40,540
+K زائد 2H زائد 2، مظبوط؟ واحد زائد واحد
+
+151
+00:12:40,540 --> 00:12:46,380
+يعني بنجمع، بنرفع الأقواس، وبندمج، إذا بدك،
+
+152
+00:12:46,380 --> 00:12:49,960
+ممكن تزيدها كمان خطوة، ما فيش مشكلة في الموضوع. 2
+
+153
+00:12:49,960 --> 00:12:56,830
+K زائد 2H زائد 2. بس طبعاً الخبرة
+
+154
+00:12:56,830 --> 00:13:00,310
+هذه trivial، والأصل ما فيش عندك فيها مشكلة. 2K
+
+155
+00:13:00,310 --> 00:13:11,590
+و 2H، 2… خذ الاثنين على المشترك: 2(K زائد H)
+
+156
+00:13:11,590 --> 00:13:18,670
+زائد 2، هذه صورة يا شباب، صورة العدد الزوجي.
+
+157
+00:13:18,670 --> 00:13:23,290
+وأنا بأضمن إن K زائد H زائد واحد عبارة عن integers.
+
+158
+00:13:24,130 --> 00:13:29,090
+ليه؟ لأن الـ H والـ K عبارة عن integers، فحاصل جمعهم
+
+159
+00:13:29,090 --> 00:13:33,250
+هيكون integer، وأضفت لهم كمان واحد، فـ integer، فمنها
+
+160
+00:13:33,250 --> 00:13:39,830
+تثبت… is even. خلصنا.
+
+161
+00:13:39,830 --> 00:13:46,170
+تم إثبات إن لو كانت الـ M والـ N عبارة عن odd، هذا
+
+162
+00:13:46,170 --> 00:13:50,910
+وصلني إن الـ M زائد N is even، وكان الإثبات هذا
+
+163
+00:13:50,910 --> 00:13:55,450
+مباشر، يعني direct. أنا افترضت الـ M، أو افترضت الـ
+
+164
+00:13:55,450 --> 00:14:02,430
+P is true، ومشيت خطوات مباشرة باتجاه الـ Q، وأثبت
+
+165
+00:14:02,430 --> 00:14:07,890
+إنها true. مثال
+
+166
+00:14:07,890 --> 00:14:15,640
+ثاني. بقول: اثبت لو كانت الـ n is odd، if الـ n is odd،
+
+167
+00:14:15,640 --> 00:14:24,880
+then الـ n تربيع is odd. لو كانت if الـ n is odd، then
+
+168
+
+223
+00:19:22,720 --> 00:19:25,500
+تكتب البرنامج لاحقًا عشان تقدر تعمل ال loop، تعرف ال
+
+224
+00:19:25,500 --> 00:19:28,420
+loop متى بده يتوقف، وإيش اللي أنت بدك... بدكم في ال
+
+225
+00:19:28,420 --> 00:19:32,100
+next step بده يصير، فإذا ما كان الlogic عندك حاضر
+
+226
+00:19:32,100 --> 00:19:35,900
+بشكل سليم، وتقدر تأخذ المطلوب، وتحقق من خلاله، و
+
+227
+00:19:35,900 --> 00:19:38,960
+توصل للمقطع، أو عفواً، تأخذ المقطع، وتوصل للمطلوب
+
+228
+00:19:39,760 --> 00:19:42,260
+هيكون عندك مشكلة في البرمجة، يعني الموضوع المفروض
+
+229
+00:19:42,260 --> 00:19:46,360
+هذا بس بنمي التفكير المنطقي عندك، والتتابع. لاحظ
+
+230
+00:19:46,360 --> 00:19:51,540
+كنت قاعد أتكلم على خطوات متتالية منطقية، مظبوط؟ ولا
+
+231
+00:19:51,540 --> 00:19:55,080
+لأ، زي إيش؟ زي ما فكرت في الalgorithm، الalgorithm
+
+232
+00:19:55,080 --> 00:19:57,920
+هو عبارة عن مجموعة، أو sequence من الخطوات
+
+233
+00:19:57,920 --> 00:20:03,140
+المتتالية، معرفة بشكل صريح وواضح. التعريف كله بنعرف
+
+234
+00:20:03,140 --> 00:20:07,800
+القطعَات هاي، بس فعليًا صيغتها وترتيبها هي اللي مش
+
+235
+00:20:07,800 --> 00:20:12,800
+متعودين على كتابته. تعالَ نشوف مثال. هذا المثال
+
+236
+00:20:12,800 --> 00:20:19,040
+السابق اللي حليناه مع بعض. بقول أثبت the product of
+
+237
+00:20:19,040 --> 00:20:23,520
+two rational numbers is rational. يعني لو أخدت أي
+
+238
+00:20:23,520 --> 00:20:28,760
+عددين نسبيين، ضربتهم في بعض، الناتج نسبي.
+
+239
+00:20:28,760 --> 00:20:34,860
+لاحظ، ما جابليش P وQ، يعني أنا ما لقيتش الـ if و الـ then
+
+240
+00:20:34,860 --> 00:20:39,020
+موجودات، بس هما فعليًا موجودات في صياغتها، من صياغة الـ
+
+241
+00:20:39,020 --> 00:20:44,500
+if اللي كانت إيش؟ نكتبها سابقًا: The product of two
+
+242
+00:20:44,500 --> 00:20:48,620
+rational numbers. حاصل ضرب العدد، أو حاصل ضرب عددين
+
+243
+00:20:48,620 --> 00:20:53,140
+نسبيين بيعطيني عدد نسبي. The product of two rational
+
+244
+00:20:53,140 --> 00:21:01,950
+numbers هي الـ if، بيؤدي إلى هذا، صح؟ المعطى اللي عندك أنت
+
+245
+00:21:01,950 --> 00:21:06,370
+الـ if، الـ if two rational numbers، بس يعني هو كأنه
+
+246
+00:21:06,370 --> 00:21:13,170
+بيقول لك هيك: if الـ M and N، أو M and N are rational
+
+247
+00:21:13,170 --> 00:21:19,430
+then
+
+248
+00:21:19,430 --> 00:21:22,990
+the product of M and N is rational
+
+249
+00:21:22,990 --> 00:21:25,970
+بالـ N is rational
+
+250
+00:21:30,450 --> 00:21:34,930
+بس يأخذ المسألة اللي كنت أنا بحاجة أعوّضها، أو أعرف
+
+251
+00:21:34,930 --> 00:21:37,690
+إيش المعطى اللي موجود عندي؟ عشان أنا... هو ما أعطانيش
+
+252
+00:21:37,690 --> 00:21:41,730
+... ما جابليش إن الضرب هو معطى، هو مجرد قال لي لو كان
+
+253
+00:21:41,730 --> 00:21:46,130
+في عندك عددين، if الـ M and N are rational، لو كان الـ
+
+254
+00:21:46,130 --> 00:21:51,310
+M و الـ N عددين نسبيين، ينتميان إلى Q، معناته حاصل ضربهم
+
+255
+00:21:51,310 --> 00:21:58,230
+ينتمي إلى Q، تمام؟ معناته إحنا عرفنا الآن من الـ if
+
+256
+00:21:58,230 --> 00:22:07,350
+اللي عنده، هي الـ if two rational numbers، لأنه
+
+257
+00:22:07,350 --> 00:22:12,290
+مش قال لي the product، مضروبهما. لو قال لي the sum، أو
+
+258
+00:22:12,290 --> 00:22:16,810
+حاصل جمع، مجموعهم، وبالتالي كل المعطى اللي
+
+259
+00:22:16,810 --> 00:22:20,290
+موجود، أو اللي أنا محتاجه، دائمًا موجود أين؟ في السؤال
+
+260
+00:22:20,290 --> 00:22:24,470
+بس بدّي شوية أفكر في المسألة، زي ما أقول، بنفسية
+
+261
+00:22:24,470 --> 00:22:28,930
+هادئة. إذا أنت فكرت في المسألة وأنت خائف، المسألة
+
+262
+00:22:28,930 --> 00:22:31,630
+صعبة، مش هقدر أحلها. أما أقول خلاص، من البداية أنا
+
+263
+00:22:31,630 --> 00:22:35,410
+ما أنصح أخلّي المسألة، وأروح لمسألة ثانية. إذا أنت
+
+264
+00:22:35,410 --> 00:22:38,790
+رايح على المعركة بنفسية المهزوم، ما عبركة بتنتصر.
+
+265
+00:22:38,790 --> 00:22:44,250
+نقطة وسط على جديد الآن. فبالتالي أنا، هاي الـ if اللي
+
+266
+00:22:44,250 --> 00:22:49,770
+عندي، هروح أقول assume الـ
+
+267
+00:22:49,770 --> 00:22:56,710
+if، إيش الـ if تبعتي؟ يعني شباب، أي اسمين، أي كره
+
+268
+00:22:56,710 --> 00:23:00,110
+أي رمزين، أي حرفين، أي two variables، انتبهوا فيهم
+
+269
+00:23:00,110 --> 00:23:06,510
+تنتمي إلى Q، a rational number، هي مش هي نفس المعنى عشان أخفف
+
+270
+00:23:06,510 --> 00:23:09,270
+كتابة. تنتمي إلى Q، مش الـ Q هي عبارة عن rational
+
+271
+00:23:09,270 --> 00:23:15,650
+number. طيب ممتاز، شو يعني؟ إيش يعني؟ شو يعني m is
+
+272
+00:23:15,650 --> 00:23:21,750
+rational؟ أيوة، يعني الـ m تكتب على صورة بسط ومقام،
+
+273
+00:23:21,750 --> 00:23:23,070
+والمقام لا يساوي صفر.
+
+274
+00:23:26,260 --> 00:23:32,100
+مظبوط؟ معناته الـ M بدها تساوي A على B، والـ B لا
+
+275
+00:23:32,100 --> 00:23:41,340
+تساوي صفر، and الـ N بدها تساوي C على D، والـ D لا
+
+276
+00:23:41,340 --> 00:23:47,080
+تساوي صفر، ومش بس هيك، A وB وC وD عبارة عن integers
+
+277
+00:23:47,080 --> 00:23:49,820
+تمام؟
+
+278
+00:23:51,300 --> 00:23:58,340
+A و B تنتميان إلى Z، C و D تنتميان إلى Z، وهذا تعريف الـ
+
+279
+00:23:58,340 --> 00:24:01,660
+integer، أو الرقم الصحيح، الـ number. خلينا نكتبهم وراء بعض
+
+280
+00:24:01,660 --> 00:24:07,360
+بالشكل هذا: where الـ
+
+281
+00:24:07,360 --> 00:24:14,680
+A و الـ B تنتميان إلى Z، and الـ B لا تساوي صفر. الثاني،
+
+282
+00:24:14,680 --> 00:24:21,310
+الـ N تساوي، بنقول C على D، where لاحظوا أنا بأتكلم
+
+283
+00:24:21,310 --> 00:24:25,490
+على تعريف العدد النسبي، أنا ما بدأت في الحل، مجرد
+
+284
+00:24:25,490 --> 00:24:33,310
+بحلل الموضوع اللي عندي: where C وD تنتميان إلى Z، and
+
+285
+00:24:33,310 --> 00:24:41,790
+D لا تساوي صفر. مئة بالمئة، إيش الخطوة اللي بعد هيك؟
+
+286
+00:24:41,790 --> 00:24:45,950
+هو جاب الـ Q تبعتها خلاص، من الـ direct step،
+
+287
+00:24:45,950 --> 00:24:49,650
+الخطوة المباشرة اللي بده يروح فيها، اللي هي ضرب
+
+288
+00:24:50,530 --> 00:25:00,170
+أضربهم في بعض: M ضرب الـ N، يساوي A على B ضرب C على D.
+
+289
+00:25:00,170 --> 00:25:05,990
+نعرف نضربهم؟ نعرف نضربهم؟ البسط مع البسط، والمقام
+
+290
+00:25:05,990 --> 00:25:15,030
+مع المقام، يساوي AC على B في D، وهذه أنا أضمن منها
+
+291
+00:25:15,030 --> 00:25:29,030
+تنتمي إلى Q، ليش؟ لأن AC و BD تنتميان إلى Z، ومش بس هيك
+
+292
+00:25:29,030 --> 00:25:34,870
+و BD لا تساوي صفر. هذا الكلام أنا من أين جبته؟ حاصل
+
+293
+00:25:34,870 --> 00:25:41,570
+ضرب عددين صحيحين بيعطيني عدد صحيح، وحاصل ضرب أي
+
+294
+00:25:41,570 --> 00:25:45,810
+عددين غير الصفر بيكون عدد صحيح غير، لا يساوي صفر.
+
+295
+00:25:49,280 --> 00:25:54,240
+تنتمي إلى Q، معناته النظرية هذه صحيحة. معناته الـ
+
+296
+00:25:54,240 --> 00:25:59,620
+product of two rational numbers is rational، خلاص.
+
+297
+00:25:59,620 --> 00:26:03,240
+السؤال انتهى الأمر. بمجرد أن وصلنا للمطلوب، هو
+
+298
+00:26:03,240 --> 00:26:07,660
+جاي بيقول لك أثبت أن حاصل ضربهما هي ينتمي إلى Q.
+
+299
+00:26:07,660 --> 00:26:16,020
+وصلنا لها، نعم. شمعنى؟
+
+300
+00:26:18,010 --> 00:26:23,990
+أنت فرضت بس شكل الرمز، بس التعريف لأ، لأن إحنا قلنا
+
+301
+00:26:23,990 --> 00:26:27,870
+من البداية rational number، عدد نسبي، إيش هو؟ هو كل
+
+302
+00:26:27,870 --> 00:26:31,770
+عدد يكتب على صورة بسط ومقام، والمقام فيه لا يساوي
+
+303
+00:26:31,770 --> 00:26:37,070
+صفر. فهذا هو، أنا مجرد إني فرضت أن M و N عددين نسبيين،
+
+304
+00:26:37,070 --> 00:26:40,150
+عددين نسبيين، يعني لازم يكتب على صورة بسط ومقام،
+
+305
+00:26:40,150 --> 00:26:45,510
+والمقام لا يساوي صفر. كتبت التعريف، لأن هذا التعريف
+
+306
+00:26:45,510 --> 00:26:51,920
+إحنا كلنا بنعرفه. فأنا بدي أستغل معرفتي اللي
+
+307
+00:26:51,920 --> 00:26:56,580
+اتعلمناها، ومن إحنا بنفيدها بإيه؟ تمام؟ إني أنشئ مع
+
+308
+00:26:56,580 --> 00:27:07,360
+الإثبات بالشكل البسيط اللي موجود عندها، بتعلمني
+
+309
+00:27:07,360 --> 00:27:13,540
+لما اتكلمنا على الـ logic، قال في عندي P implies Q
+
+310
+00:27:13,540 --> 00:27:20,110
+هاتيته كافة. نقطة Q تعني نقطة B، وسميناها
+
+311
+00:27:20,110 --> 00:27:27,150
+Contrapositive، مظبوط؟
+
+312
+00:27:27,150 --> 00:27:36,010
+تمام. الآن، Contrapositive، في بعض المسائل يا شباب، مش
+
+313
+00:27:36,010 --> 00:27:42,370
+هتقدر، مش هتقدر تمشي فيها بالاتجاه الـ direct، يعني
+
+314
+00:27:42,370 --> 00:27:47,100
+ما تقدرش تأخذ الـ P وتوصل لـ Q منها. لو إجيت أقول لك
+
+315
+00:27:47,100 --> 00:27:54,820
+if الـ N تربيع is odd، then
+
+316
+00:27:54,820 --> 00:28:02,160
+الـ N is odd. لو أنا هان... هاي بيعطيني إياها صراحةً P
+
+317
+00:28:02,160 --> 00:28:08,700
+implies Q، هي الـ P وهي الـ Q، مظبوط؟ لو أنا بدي أفكر
+
+318
+00:28:08,700 --> 00:28:16,070
+بالـ P، معناته الـ N تربيع بدها تساوي 2K زائد واحد،
+
+319
+00:28:16,070 --> 00:28:22,970
+صح؟ الآن إيش الـ next step؟ بدي N، يعني أنا هاخذ
+
+320
+00:28:22,970 --> 00:28:28,090
+الجذر. الـ N بدها تساوي جذر الـ N، وليه بدها تساوي
+
+321
+00:28:28,090 --> 00:28:36,230
+الجذر لـ 2K زائد واحد. إيش بتقدر تساوي بعد هيك؟ إيش
+
+322
+00:28:36,230 --> 00:28:39,610
+الخطوة اللي بتقدر تمشيها بعد هيك؟ هل بتقدر تثبت أن
+
+323
+00:28:39,610 --> 00:28:44,550
+هو عدد فردي؟ لأ، لأن الناتج اللي عندك مش مكتوب على
+
+324
+00:28:44,550 --> 00:28:50,410
+صورة اثنين في عدد صحيح زائد أو ناقص واحد. خلاص، سكّرت
+
+325
+00:28:50,410 --> 00:28:54,570
+أساسًا ما بعرف اللي بيطلع تحت الجذر، حيطلع عدد
+
+326
+00:28:54,570 --> 00:29:00,650
+حقيقي ولا حيطلع عدد صحيح، وبالتالي المسألة سكّرت.
+
+327
+00:29:00,650 --> 00:29:04,910
+وغالبا، غالبًا كنا إحنا لما نشتغل هيك، بتجف معانا
+
+328
+00:29:04,910 --> 00:29:07,950
+المسألة، عاد، وندبرها. لأ، الطريقة الثانية موجودة، بس مش
+
+329
+00:29:07,950 --> 00:29:12,050
+ممكن تساويها. مش فاكرة الجذور اللي أنا وبدّي
+
+330
+00:29:12,050 --> 00:29:15,190
+التربيع، وبدّي منه الآن، كيف بدي أوصل لهذه؟
+
+331
+00:29:15,190 --> 00:29:23,270
+يعني؟ إيش بقى اتفك؟ هيها، إيش اتفك؟
+
+332
+00:29:23,270 --> 00:29:29,110
+ماشي الحال. كيف بقى اتفك؟ ماشي الحال. ام في ام
+
+333
+00:29:29,110 --> 00:29:31,450
+بيصير تساوي 2K زائد واحد.
+
+334
+00:29:37,000 --> 00:29:40,100
+أيه، بقت واحد تجسّم على الآن تقطع القرآن ناحية ثانية.
+
+335
+00:29:40,100 --> 00:29:48,780
+ما هي الآن تربيع هيها. لأ، غلط يا صاحبي! هو بيقول لك
+
+336
+00:29:48,780 --> 00:29:55,300
+الآن تربيع، القدر الآن تربيع هي القدر، عشان هي كان
+
+337
+00:29:55,300 --> 00:29:59,960
+الحل الآن، فلنروح نخلص من التربيع بالجذر، بدي أخلص
+
+338
+00:29:59,960 --> 00:30:04,390
+التربيع تبعتي الآن. هي صورتها، فأخذت الجذر على الطرفين،
+
+339
+00:30:04,390 --> 00:30:08,310
+عشان تبقى المعادلة صحيحة. سكّرت المسألة. فش خطوات، فش
+
+340
+00:30:08,310 --> 00:30:13,790
+حل بعد هيك. هل هذا يعني المسألة غلط؟ لأ، المسألة
+
+341
+00:30:13,790 --> 00:30:22,090
+صحيحة. هان تحت الجذر لأ لأ لأ، هان التربيع اللي هي
+
+342
+00:30:22,090 --> 00:30:27,550
+ده مش على الفاضي، هيك بتصير المسألة غلط. الآن لا تساوي
+
+343
+00:30:27,550 --> 00:30:31,370
+الجذر الآن. الآن تساوي الجذر التربيعي للـ الآن تربيع،
+
+344
+00:30:32,890 --> 00:30:41,970
+واللي بتساوي هاي؟ بإيش؟
+
+345
+00:30:41,970 --> 00:30:50,690
+ممتاز. X؟ X موجود عدد فردي ولا زوجي؟ سيبقوا هو
+
+346
+00:30:50,690 --> 00:30:56,250
+لحاله. الـ X اللي أنت اخترته عدد زوجي ولا عدد فردي؟
+
+347
+00:30:56,250 --> 00:31:02,210
+ولا حتعرف، لأنه خلاص كيف تطلع الـ 2K برا الجذر؟
+
+348
+00:31:08,660 --> 00:31:13,740
+الآن يا يحيى، إن تحت الجذر بيطلعش بهذه السهولة، يا
+
+349
+00:31:13,740 --> 00:31:18,620
+صاحبي! أنت بيطلع من الجذر لما بيكون القُصّ تربيعي، هو
+
+350
+00:31:18,620 --> 00:31:23,960
+بوافق قُصّ الجذر، طبعًا؟ يعني لو فرضًا إجيت قلت لك أنا
+
+351
+00:31:23,960 --> 00:31:27,620
+في عندي هان أربعة ك تربيع.
+
+352
+00:31:30,080 --> 00:31:35,600
+هذه قيمتها تساوي 2 ك تربيع تحت الجذر، والتي
+
+353
+00:31:35,600 --> 00:31:39,540
+تساوي 2 ك، هكذا يقول الحل 100%. أو لو إجيت
+
+354
+00:31:39,540 --> 00:31:45,840
+وقلت لك في عندي أربعة ك، أربعة ك تحت الجذر، هذه
+
+355
+00:31:45,840 --> 00:31:51,560
+تساوي 2 تربيع ك، تحت الجذر هذه تساوي 2 في
+
+356
+00:31:51,560 --> 00:31:53,520
+جذر الك، ك، هكذا صح.
+
+357
+00:31:56,290 --> 00:32:01,090
+لغْمَة فُزّور يا صاح، مش طالعة! الآن، وبالتالي ضروري
+
+358
+00:32:01,090 --> 00:32:05,530
+جدًا دائمًا لما تشتغل مع المسألة، اشتغل ضمن ما هو
+
+359
+00:32:05,530 --> 00:32:10,350
+معطى لك، ما تحاولش تفرض فرضيات مالهاش دخل في
+
+360
+00:32:10,350 --> 00:32:15,350
+الموضوع. الآن، قاعد بيقول لك عندك N تربيع، وبده منك
+
+361
+00:32:15,350 --> 00:32:19,550
+N. بيقول لك N تربيع is odd، بدك تحط له هي N تربيع صورة
+
+362
+00:32:19,550 --> 00:32:23,670
+هي odd، هي هي. بدك توصل للـ N. جيب الـ N بقى، تاخد الجذر.
+
+363
+00:32:23,670 --> 00:32:27,750
+فيش حل غير هيك. أخذنا الجذر بس ما وصلناش لـ odd. لا
+
+364
+00:32:27,750 --> 00:32:30,630
+لأ، جذر أقول odd ولا جذر أقول even، ولا جذر أتكلم
+
+365
+00:32:30,630 --> 00:32:34,270
+أساسًا. مش فاهم، ما بعرف اللي عندي. وبالتالي الحل
+
+366
+00:32:34,270 --> 00:32:39,630
+معناته اتجاهي أنا مش صحيح، اتجاهي أنا في الحل مش
+
+367
+00:32:39,630 --> 00:32:45,130
+صحيح. الآن، نلجأ لمين يا شباب؟ الـ Contrapositive هذه،
+
+368
+00:32:45,130 --> 00:32:51,910
+إيش الـ Contrapositive تبعت هذه؟ هذه الجملة معناته
+
+369
+00:32:51,910 --> 00:33:05,310
+if الـ N is not odd، then الـ N تربيع is not odd. سيبني
+
+370
+00:33:05,310 --> 00:33:08,630
+من الـ positive و الـ negative. إحنا بنتكلم على odd و
+
+371
+00:33:08,630 --> 00:33:15,530
+even، بنتكلمش على positive. مش هادي تكافئ هادي، ممكن
+
+372
+00:33:15,530 --> 00:33:21,330
+هادي تخدمّني. إيش يعني is not odd؟ يعني even، لأن
+
+373
+00:33:21,330 --> 00:33:29,410
+العدد الصحيح هو إما عدد فردي أو عدد زوجي. is even.
+
+374
+00:33:33,890 --> 00:33:39,890
+هكذا أسهل المسألة. ماذا سأقول أنا؟ assume، لاحظ هذه
+
+375
+00:33:39,890 --> 00:33:44,330
+الجملة، أنت مش مطلوب إنك تكتبها. هذه الجملة مش مطلوب
+
+376
+00:33:44,330 --> 00:33:48,070
+إنك تكتبها. المطلوب إنك تتحلّ، أو تبدأ تفكر بالاتجاه
+
+377
+00:33:48,070 --> 00:33:54,730
+هذا، عشان تقول assume not Q مباشرةً، لأن هي المسألة
+
+378
+00:33:54,730 --> 00:34:01,110
+اللي عندك هي فوق، و الـ if، أو N is not odd، اللي هي لا
+
+379
+00:34:01,110 --> 00:34:09,250
+في الـ Q، مظبوط؟ الـ if، سُمّيها Q. إيش يعني not Q؟ إن N is
+
+380
+00:34:09,250 --> 00:34:17,090
+even. not odd، not
+
+381
+00:34:17,090 --> 00:34:26,730
+odd، بين قوسين even. إيش يعني؟ يعني الـ N بتساوي اثنين
+
+382
+00:34:26,730 --> 00:34:31,590
+في K، وبس بدون زائد واحد. العدد زوجي، والـ K
+
+383
+00:34:31,590 --> 00:34:32,150
+تنتمي
+
+384
+00:34:37,950 --> 00:34:42,550
+ممتاز. الخطوة اللي بعدها هي إيش؟ بده منه هو N تربيع.
+
+385
+00:34:42,550 --> 00:34:49,650
+الـ N تربيع بدها تساوي 2K تربيع، ربعها، الجواب
+
+
+445
+00:40:22,340 --> 00:40:26,100
+هتكون odd يعني عمراً ما هتلاقيها أنها تكون عدد فردي
+
+446
+00:40:26,100 --> 00:40:31,020
+يبتلجأ الشباب دائماً لو أنت جئت بالنظرية هذه، غلط لو
+
+447
+00:40:31,020 --> 00:40:37,260
+أنا، على سبيل المثال، قلت لك حاصل جمع أي عددين فرديين
+
+448
+00:40:37,260 --> 00:40:38,440
+عدد فردي
+
+449
+00:40:42,810 --> 00:40:46,090
+غلط، خطأ، مثال بيقول: اتفضل، هذا مثال بيقول أن الكلام
+
+450
+00:40:46,090 --> 00:40:50,710
+هذا غلط، المثال واحد هذا كفيل بأن ينفي الكلام الذي
+
+451
+00:40:50,710 --> 00:40:55,730
+نقوله، لماذا؟ المثال ليس إثباتاً، نسميه نحن
+
+452
+00:40:55,730 --> 00:41:00,230
+counterexample، مثالاً مُناقضاً، يُنفي النظرية التي نحن
+
+453
+00:41:00,230 --> 00:41:04,150
+نقولها، أنا أَدَّعي أن الجمع أو حاصل جمع أي
+
+454
+00:41:04,150 --> 00:41:10,110
+عددين فرديين يعطيني عدد فردي، لأ، مباشرة قل غلط
+
+455
+00:41:10,110 --> 00:41:14,010
+واحد و ثلاثة أعداد فردية، مجموعها يساوي أربعة، عدد
+
+456
+00:41:14,010 --> 00:41:17,830
+زوجي، و انتهى الأمر، لست بحاجة أن تكتب الخطوات هذه
+
+457
+00:41:17,830 --> 00:41:23,290
+الإثبات، الخطوات هذه نتبعها إما إذا أردنا أن نثبت وإذا
+
+458
+00:41:23,290 --> 00:41:26,270
+كانت النظرية أو السؤال مكتوباً لك approve or
+
+459
+00:41:26,270 --> 00:41:31,110
+disapprove، إما أثبت أو أنفِ المعادلة التي عندك، هذا
+
+460
+00:41:31,110 --> 00:41:33,970
+الـ term، هذا يعني ضروري أن تفكر أو تحاول أن تستحضر لأنه
+
+461
+00:41:33,970 --> 00:41:37,930
+ممكن أن يكون الحل في سؤال أو في رقم، أن الرقم هذا غير
+
+462
+00:41:37,930 --> 00:41:40,610
+صحيح، وبالتالي كفى الله المؤمنين القتال
+
+463
+00:41:40,610 --> 00:41:44,210
+وبالتالي، إذا حاولت أن تثبت وأنت أصلاً تحاول أن تكون
+
+464
+00:41:44,210 --> 00:41:44,990
+غلط
+
+465
+00:42:15,250 --> 00:42:19,070
+أقول: أثبت لو
+
+466
+00:42:19,070 --> 00:42:25,010
+كانت الـ M زائد الـ N أكبر من خمسين، معناته
+
+467
+00:42:25,010 --> 00:42:30,370
+عندك إما الـ M أكبر من خمسة وعشرين أو الـ N أكبر من
+
+468
+00:42:30,370 --> 00:42:33,770
+خمسة وعشرين، فلو كانت اثنتين، تبقى المعادلة صحيحة لأن
+
+469
+00:42:33,770 --> 00:42:38,870
+بينهما علاقة R تبقى المعادلة صحيحة لأن بينهما علاقة R، أيش
+
+470
+00:42:38,870 --> 00:42:40,350
+أول عدد أكبر من خمسين؟
+
+471
+00:42:42,870 --> 00:42:50,650
+51، أُصبت؟ لو بتجسم الـ 51 لجزئين، يعني حللها لرقمين
+
+472
+00:42:50,650 --> 00:42:57,550
+مجموعهما معاً، حلل الـ 51، ستة وعشرين وخمسة وعشرين،
+
+473
+00:42:57,550 --> 00:43:03,910
+واحد منهما سيكون أكبر من خمسة وعشرين، سيبني
+
+474
+00:43:03,910 --> 00:43:07,190
+من الثاني، واحد سيكون أكبر، طيب لو قلت لك ستون أكبر
+
+475
+00:43:07,190 --> 00:43:11,510
+من خمسين أم لا؟ الحل هو 30، 30، هذان الرقمان صارا
+
+476
+00:43:11,510 --> 00:43:16,550
+أكبر من 25، وتبقى المسألة صحيحة 100%، لكن الأمثلة، كما
+
+477
+00:43:16,550 --> 00:43:21,330
+قلنا، لا تُثبت، الأمثلة نستخدمها عند النفي
+
+478
+00:43:21,330 --> 00:43:27,750
+نستخدمها عند النفي، بدك
+
+479
+00:43:27,750 --> 00:43:34,130
+تثبت الكلام هذا، هي معناته هي عندك الـ B هذه، هي الـ B
+
+480
+00:43:34,130 --> 00:43:42,450
+وهذه الـ Q، compound، الـ M، لو أنا بدأت أقول له assume
+
+481
+00:43:42,450 --> 00:43:52,990
+الـ B، إذا بدك تفترض الـ B، أيش يعني؟ يعني M زائد الـ N
+
+482
+00:43:52,990 --> 00:43:57,870
+أكبر من خمسين، تمام، next step، بدك أنت الـ M لحالها أو
+
+483
+00:43:57,870 --> 00:44:02,450
+الـ N لحالها، افترضت، معناته أن الـ M ستكون أكبر من
+
+484
+00:44:02,450 --> 00:44:07,060
+خمسين ناقص الـ N،  لنُقلّ على الطرف الثاني أو بين جملة
+
+485
+00:44:07,060 --> 00:44:11,760
+أضف سالب N للطرفين، عشان تبقى المعادلة صحيحة، بس
+
+486
+00:44:11,760 --> 00:44:16,280
+ما وصلت للصورة التي أريدها فعلاً، وكذلك الآن
+
+487
+00:44:16,280 --> 00:44:23,780
+الـ N ستكون أكبر من خمسين ناقص الـ N، بعد هذا، والخمسة
+
+488
+00:44:23,780 --> 00:44:26,600
+عشر التي أبحث عنها، ليس لها وجود، معناته الطريق الذي
+
+489
+00:44:26,600 --> 00:44:31,600
+أنا سائر فيه غلط، مباشرة، افكر بنقطة Q
+
+490
+00:44:34,890 --> 00:44:41,070
+assume النقطة Q، أيش النقطة Q؟ هذه الـ Q، صحيح، M
+
+491
+00:44:41,070 --> 00:44:50,150
+أكبر من 25 أو N أكبر من 25، نفيها: M أقل أو
+
+492
+00:44:50,150 --> 00:45:00,350
+تساوي 25، والـ or نفيها and، الـ N أقل أو تساوي
+
+493
+00:45:00,350 --> 00:45:01,730
+25
+
+494
+00:45:04,490 --> 00:45:09,430
+الخطوة التالية.. ماذا تقول يا مصطفى؟ آه، بدك تنفي الـ
+
+495
+00:45:09,430 --> 00:45:15,990
+.. بدك تنفي الـ Q كلها، بدك تنفي.. هذه الـ Q.. هذه
+
+496
+00:45:15,990 --> 00:45:22,490
+الـ Q، أقول لك: Q، M أكبر من خمسة وعشرين، and.. and..
+
+497
+00:45:22,490 --> 00:45:28,050
+عفواً، الـ R، and، أكبر من خمسة وعشرين، هذه كلها Q، دخل
+
+498
+00:45:28,050 --> 00:45:35,720
+عليها هنا، فيه De Morgan's Law، M أقل من 25، نفي الأولى
+
+499
+00:45:35,720 --> 00:45:39,860
+الآن تصبح or، أو الـ or تصبح and، والـ N أقل أو
+
+500
+00:45:39,860 --> 00:45:47,560
+تساوي 25، غلط
+
+501
+00:45:47,560 --> 00:45:52,020
+يا صاحبي، غلط، شوف، أنت لا يمكنك أن تقتطع النفي على كيفك
+
+502
+00:45:52,020 --> 00:45:58,330
+أنت الآن لا يمكنك أن تقتطع النفي على كيفك، لأن مع الـ OR
+
+503
+00:45:58,330 --> 00:46:02,250
+واحدة من الاثنتين تكفي لأن تكون true، إذا أنت نفيت
+
+504
+00:46:02,250 --> 00:46:07,150
+واحدة، طيب، هي تبقى true، تحافظ على المسألة true، عشان
+
+505
+00:46:07,150 --> 00:46:10,330
+هيك، لازم عندما تريد أن تنفي، تنفي الجملة بالكامل، تنفي الـ Q
+
+506
+00:46:10,330 --> 00:46:13,130
+بالكامل، قيمة الـ Q، تساوي الجملة هذه، compound
+
+507
+00:46:13,130 --> 00:46:22,850
+proposition، فتنفيها كلها، تمام، الخطوة التي بعدها هيك
+
+508
+00:46:22,850 --> 00:46:26,190
+بدك
+
+509
+00:46:26,190 --> 00:46:35,350
+تجمع: الـ M أقل أو تساوي خمسة وعشرين
+
+510
+00:46:35,350 --> 00:46:41,810
+زائد الـ N، عشان من هذا، تمام؟ بعد ما هي الـ N أقل
+
+511
+00:46:41,810 --> 00:46:49,930
+أو تساوي خمسة وعشرين، زائد أقل أو تساوي خمسة و
+
+512
+00:46:49,930 --> 00:46:54,710
+عشرين، تصحّح؟ هكذا، تدريج طبيعي للمسألة، من حيثياتك تعيد
+
+513
+00:46:54,710 --> 00:46:55,490
+بسهولة
+
+514
+00:46:57,740 --> 00:47:04,340
+كيف أتت؟ حاضر، نحن الآن عندنا الـ M أقل أو تساوي 25
+
+515
+00:47:04,340 --> 00:47:09,140
+صح؟ وأيش أنا أريد؟ أريد M زائد N، عشان تبقى المسألة
+
+516
+00:47:09,140 --> 00:47:14,840
+صحيحة، لازم أضع الـ M أين؟ للطرفين، M زائد N معاً
+
+517
+00:47:14,840 --> 00:47:21,510
+أقل من 25 زائد N، مضبوط؟ فـ M أقل من خمسة و
+
+518
+00:47:21,510 --> 00:47:27,190
+عشرين، تمام؟ وبالتالي، صارت الخمسة والعشرون زائد الـ N
+
+519
+00:47:27,190 --> 00:47:31,810
+أقل أو تساوي من خمسة وعشرين زائد خمسة وعشرين
+
+520
+00:47:31,810 --> 00:47:36,990
+مضبوط؟
+
+521
+00:47:36,990 --> 00:47:43,010
+واضحت؟ مئة بالمئة، معناته هذا يؤدي إلى أن الـ M زائد الـ N
+
+522
+00:47:43,010 --> 00:47:46,330
+أقل أو تساوي خمسين
+
+523
+00:47:48,110 --> 00:47:56,650
+في الـ B، أيش
+
+524
+00:47:56,650 --> 00:48:00,730
+مفهوم الـ contrapositive الذي وصلت إليه، أن لو كانت
+
+525
+00:48:00,730 --> 00:48:05,270
+الـ M زائد الـ N أكبر من خمسين، معناته واحدة من
+
+526
+00:48:05,270 --> 00:48:10,150
+الاثنتين على الأقل ستكون أكبر من خمسة وعشرين، يعني
+
+527
+00:48:10,150 --> 00:48:13,690
+أُجيب الـ Contrapositive عشان يُثبت.. أنا أُثبت
+
+528
+00:48:13,690 --> 00:48:16,670
+الـ Contrapositive، عشان أقول أن النظرية التي فوق
+
+529
+00:48:16,670 --> 00:48:23,650
+هي الأساس.. هي الصحيحة، واضحة الأمور؟
+
+530
+00:48:23,650 --> 00:48:31,430
+كمان
+
+531
+00:48:31,430 --> 00:48:31,910
+مثال؟
+
+532
+00:48:42,560 --> 00:48:50,320
+يقول لي: لو كانت الـ N تساوي A في B، واضح عندما يكتب لي
+
+533
+00:48:50,320 --> 00:48:56,440
+F، و then هو يُريحني من الـ B، والـ Q أصبحت هذه الـ B
+
+534
+00:48:56,440 --> 00:48:59,820
+then
+
+535
+00:48:59,820 --> 00:49:02,880
+هذه
+
+536
+00:49:02,880 --> 00:49:07,560
+الـ Q، يقول لي
+
+537
+00:49:07,560 --> 00:49:11,140
+بشرط أن الـ A والـ B are positive integers
+
+538
+00:49:13,220 --> 00:49:17,460
+تمام؟ A و B positive integers، مُعَبَّر مُعَبَّر مُعَبَّر
+
+539
+00:49:17,460 --> 00:49:18,960
+مُعَبَّر مُعَبَّر مُعَبَّر مُعَبَّر مُعَبَّر مُعَبَّر مُعَبَّر
+
+540
+00:49:18,960 --> 00:49:19,280
+مُعَبَّر مُعَبَّر مُعَبَّر مُعَبَّر مُعَبَّر مُعَبَّر مُعَبَّر
+
+541
+00:49:19,280 --> 00:49:19,440
+مُعَبَّر مُعَبَّر مُعَبَّر مُعَبَّر مُعَبَّر مُعَبَّر مُعَبَّر
+
+542
+00:49:19,440 --> 00:49:20,160
+مُعَبَّر مُعَبَّر مُعَبَّر مُعَبَّر مُعَبَّر مُعَبَّر مُعَبَّر
+
+543
+00:49:20,160 --> 00:49:39,820
+مُعَبَّر مُعَبَّر مُعَبَّر مُعَبَّر مُعَبَّر
+
+544
+00:49:43,110 --> 00:49:49,850
+A، B، انظر، لا تُرهقني بالتفاصيل، انتهى، الآن الـ A بدأت
+
+545
+00:49:49,850 --> 00:49:55,790
+تكون أقل من كذا، معناته أريد أن أحلل الـ N لأُحصل على
+
+546
+00:49:55,790 --> 00:49:58,570
+الجذر، أريد أن أحصل على جذر الـ N، في المسألة الـ A موجودة والـ
+
+547
+00:49:58,570 --> 00:50:05,070
+B موجودة، صح أم لا؟ الـ N، معناته جذر الـ N في ضرب
+
+548
+00:50:05,070 --> 00:50:10,830
+جذر الـ N تساوي ماذا.. لماذا أصغر، تساوي حتى هذه اللحظة
+
+549
+00:50:11,650 --> 00:50:19,750
+حتى اللحظة تساوي، مضبوط؟ طيب، من الكلام هذا ما
+
+550
+00:50:19,750 --> 00:50:28,590
+يُتوقع أن تُساوي ماذا؟ هو لاحظ عندما جاءني شباب
+
+551
+00:50:28,590 --> 00:50:35,370
+جاءني positive integers، الواحد positive أم لا؟
+
+552
+00:50:35,370 --> 00:50:40,050
+الواحد positive، لا، دعني أتحدث فقط عن الواحد، واحد
+
+553
+00:50:40,050 --> 00:50:44,590
+positive، لأنه لا يوجد ما يمنع أن تكون الـ A تساوي N والـ
+
+554
+00:50:44,590 --> 00:50:49,550
+B تساوي واحد، أو العكس، لم يُشر
+
+555
+00:50:49,550 --> 00:50:54,230
+في السؤال، سببه هي A مفتوحة، معناته ممكن في واحد من
+
+556
+00:50:54,230 --> 00:50:58,130
+الاحتمالات، يعني أنت ممكن أن تأتي وتقول لي الآن، أنا أستطيع
+
+557
+00:50:58,130 --> 00:51:04,950
+أقول، لو أنا أريد أن أحلّ أو أُجَزِّئ الـ N أو أُجَزِّئ
+
+558
+00:51:04,950 --> 00:51:11,430
+على B، أيش ستقول؟  جذر الـ N في جذر الـ N على
+
+559
+00:51:11,430 --> 00:51:18,270
+B، ستساوي الـ A، لاحظوا أني فعلياً لست قادراً على أخذ
+
+560
+00:51:18,270 --> 00:51:22,190
+decision، على الرغم من أنه ممكن، إذا أنا ضمنت هذين
+
+561
+00:51:22,190 --> 00:51:26,530
+أكبر من واحد، أستطيع أن آخذ decision، فيهم سيكون فيهم واحد
+
+562
+00:51:26,530 --> 00:51:31,490
+أقل من الجذر تبع الـ N، والثاني طبعاً سيكون أكبر أم
+
+563
+00:51:31,490 --> 00:51:37,240
+لا؟ يعني الآن، لو الآن الواحد، أنا مُستثنى عنده، كان
+
+564
+00:51:37,240 --> 00:51:42,840
+أستطيع أن آتي وأقول ببساطة، يعني هذا يُؤدي إلى أن الـ A أقل
+
+565
+00:51:42,840 --> 00:51:44,160
+أو تساوي جذر الـ N
+
+566
+00:51:47,650 --> 00:51:51,310
+الـ B أقل أو تساوي جذر الـ N، طيب لو الاثنتان تحققتا
+
+567
+00:51:51,310 --> 00:51:54,710
+معناته تحصل على الـ N، كلام مضبوط، طيب لو لم تتحقق
+
+568
+00:51:54,710 --> 00:51:59,490
+واحدة منهما، معناته هذه، لو كانت هذه False، معناته الـ
+
+569
+00:51:59,490 --> 00:52:04,210
+N، الـ A أكبر، مضبوط، وهذه ستكون أقل أو تساوي جذر الـ
+
+570
+00:52:04,210 --> 00:52:07,930
+N، جذر الـ N أكبر من جذر الـ N في جذر الـ N، ستطلع
+
+571
+00:52:07,930 --> 00:52:12,270
+أكبر من الـ N، فظلّ عندي مشكلة، لست قادراً على أخذ فيها
+
+572
+00:52:12,270 --> 00:52:16,670
+decision 100%، أنا أشعر أن الطريق سهل وواضح، لكن
+
+573
+00:52:17,400 --> 00:52:19,960
+فيه شغل ليس تماماً، طيب تعالَ شُفْ الـ contrapositive
+
+574
+00:52:19,960 --> 00:52:27,480
+تبعها، كيف وضعها؟ أيش ستفترض نقطة Q؟  أيضاً، أيش نقطة Q
+
+575
+00:52:27,480 --> 00:52:36,180
+ستقول أن الـ A أكبر من جذر الـ N، and الـ B أكبر من
+
+576
+00:52:36,180 --> 00:52:41,660
+جذر الـ N، 100%، هو أيش يقول؟ عملياً الـ N ستساوي
+
+577
+00:52:41,660 --> 00:52:44,840
+الـ A في B
+
+578
+00:52:47,840 --> 00:52:52,140
+أيضاً، ضرب الـ B ستساوي؟
+
+579
+00:52:52,140 --> 00:52:57,440
+أو بلاش، دعني أفعلها هكذا، كما في المثال السابق، A أكبر
+
+580
+00:52:57,440 --> 00:53:01,480
+من جذر الـ N، لو ضربت في B، أريد أن أضرب الطرف الثاني في
+
+581
+00:53:01,480 --> 00:53:07,980
+B، صح؟ طيب، والـ B هذا ماذا؟ أكبر من جذر الـ N؟ عفواً
+
+582
+00:53:07,980 --> 00:53:15,780
+ستكون أكبر من جذر الـ N في جذر الـ N، وهذا وصل إلى أن الـ
+
+583
+00:53:15,780 --> 00:53:25,690
+A أكبر من.. من الـ N، نقطة
+
+584
+00:53:25,690 --> 00:53:33,250
+الـ B، أم لا؟  أيٌّ منها؟  N تساوي A في B، أيش نفيها؟ أكبر
+
+585
+00:53:33,250 --> 00:53:40,190
+أو أصغر، أكبر أو أصغر، انتهى، ليس فيه or، أنا تحققت
+
+586
+00:53:40,190 --> 00:53:45,290
+واحدة منهما، انتهى، شوفت كيف يا مصطفى؟ كمان مرة، شباب
+
+587
+00:53:45,290 --> 00:53:54,170
+الآن، نفْي يساوي: الـ A، أو الـ N تساوي الـ A في B، نفيها أن
+
+588
+00:53:54,170 --> 00:53:57,630
+الـ A لا تساوي الـ A في B، الـ N لا تساوي الـ A في B، أيش
+
+589
+00:53:57,630 --> 00:54:02,290
+يعني؟ إما ستكون أكبر منها أو ستكون أصغر منها، أنا
+
+590
+00:54:02,290 --> 00:54:06,330
+قدرت أتحقق أنها أكبر منها، ما يعني أنه انتهى، حصلت
+
+591
+00:54:06,330 --> 00:54:10,410
+الـ Contrapositive، ليس داعي أن أفكر في الثانية
+
+592
+00:54:10,410 --> 00:54:13,630
+ليس داعي أن أفكر في شرط الـ Contrapositive
+
+593
+00:54:19,560 --> 00:54:23,060
+وبالتالي أنا انتهى البرهان تبعي، بقيت أقدر أقول في
+
+594
+00:54:23,060 --> 00:54:26,620
+حالة أن الـ N ستساوي الـ A في B، والـ A في B عبارة عن
+
+595
+00:54:26,620 --> 00:54:30,080
+positive integer، معناته الـ A أقل أو تساوي الـ N أو
+
+596
+00:54:30,080 --> 00:54:34,880
+الـ B أقل أو تساوي الـ N، الكلام صعب، يا شباب،
+
+597
+00:54:34,880 --> 00:54:40,260
+الفكرة، هذا الكلام مقنع أكثر من الكلام السابق من الـ
+
+598
+00:54:40,260 --> 00:54:44,560
+direct proof، وإن كان يبدو الـ Direct Proof أني
+
+599
+00:54:44,560 --> 00:54:48,880
+ماشي صح وماشي الأمور، عايش sequence، بس فيه شك عندما
+
+600
+00:54:48,880 --> 00:54:51,920
+كانت متساوية واحدة وما تبقى لن تُساوي، إذا فيه طريقة
+
+601
+00:54:51,920 --> 00:54:56,260
+أخرى أمشي معك بشكل جيد، أشتغل فيه بدون أي مشاكل
+
+602
+00:54:56,260 --> 00:54:59,420
+ستجد في بعض الأحيان أنه في مسائل ممكن أن تُصحّح بالـ
+
+603
+00:54:59,420 --> 00:55:05,320
+Direct و Contrapositive، اعتمد على أي واحد منهما، على
+
+604
+00:55:05,320 --> 00:55:10,840
+الذي أنت مركز عليه، صحيح 100%، على الذي تريد، إذا الاثنان
+
+605
+00:55:10,840 --> 00:55:13,320
+أنت مركز عليهما، إنه هذا وهذا، إيه أحد الدنيا
+
+606
+00:55:13,320 --> 00:55:18,600
+وانتهى الأمر؟  بس أنا والله عندي شكوك أن الـ direct 70% أو
+
+607
+00:55:18,600 --> 00:55:23,040
+80%، بينما الـ indirect أو
\ No newline at end of file
diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/FFRz-p6sRfY_postprocess.srt b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/FFRz-p6sRfY_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..b5ea0db84f27810c57f2b13a8b4d2b0e0355c2e0
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/FFRz-p6sRfY_postprocess.srt
@@ -0,0 +1,2572 @@
+1
+00:00:20,970 --> 00:00:22,970
+بسم الله والحمد لله والصلاة والسلام على رسول الله
+
+2
+00:00:22,970 --> 00:00:24,270
+الرحمن الرحيم اليوم ان شاء الله شباب هنبدأ ب
+
+3
+00:00:24,270 --> 00:00:28,610
+chapter جديد اللي هو chapter الاثبات الرياضي او
+
+4
+00:00:28,610 --> 00:00:31,950
+proof techniques تقنيات الاثبات الرياضي and
+
+5
+00:00:31,950 --> 00:00:34,930
+mathematical induction استنباط او الاستقراء
+
+6
+00:00:34,930 --> 00:00:39,290
+الرياضي لا اخفيكم ان كتير من الأحيان كنا بنعاني
+
+7
+00:00:39,290 --> 00:00:43,010
+مشكلة في الموضوع الاثبات وبمجرمة بيقولك اثبت كذا
+
+8
+00:00:43,010 --> 00:00:47,470
+او اثبت النظرية او اعمل كذا بنبدأ يعيش .. بنبدأ
+
+9
+00:00:47,470 --> 00:00:53,060
+نرج و بنسيب الموضوع مطلقالأسباب كثيرة أهمها أنه
+
+10
+00:00:53,060 --> 00:00:58,140
+ماكناش .. يعني ماحدش علمنا من البداية أساسيات
+
+11
+00:00:58,140 --> 00:01:01,360
+الإثبات يعني ال knowledge اللي لازمة للإثبات كلها
+
+12
+00:01:01,360 --> 00:01:06,380
+موجودة والمسألة دائمة اللي فيها إثبات فيها مواطيات
+
+13
+00:01:06,380 --> 00:01:10,750
+كافيةتمام؟ انك تمشي حسب العلم اللى دراسته
+
+14
+00:01:10,750 --> 00:01:14,310
+والمعلومات اللى بتعرفها و توصل للنتيجة لكن احيانا
+
+15
+00:01:14,310 --> 00:01:18,350
+كيف انا بدي ابدأ؟ من وين؟ وليش هيك؟ وبناء انا على
+
+16
+00:01:18,350 --> 00:01:22,330
+ايش هيك كان القلب هاد اللي ايش؟ تكون امور احيانا
+
+17
+00:01:22,330 --> 00:01:26,930
+بتمشي في الثبات خطوة تنتين و بتحس انه جفل طب هل في
+
+18
+00:01:26,930 --> 00:01:29,350
+طريق تانى ممكن انا اسلكها و تكون فيه معين نتيجة؟
+
+19
+00:01:29,350 --> 00:01:33,420
+اه فيهسيقشن واحد سبعة اللي احنا فشجناها في شابتر
+
+20
+00:01:33,420 --> 00:01:37,920
+واحد قلتلكوا لاحقا ان شباب هنرجعله بتكلم على تلات
+
+21
+00:01:37,920 --> 00:01:42,900
+تقنيات مهمة في الإثبات لمعظم
+
+22
+00:01:42,900 --> 00:01:46,880
+الإثباتات اللي احنا ممكن نتعرض لها وبتيجي ال
+
+23
+00:01:46,880 --> 00:01:49,740
+mathematical induction لاحقا أو الاستقراء الرياضي
+
+24
+00:01:49,740 --> 00:01:53,580
+لما بيجي نتكلم على موضوع ال sequences شوفتوا مثلا
+
+25
+00:01:53,580 --> 00:01:59,220
+معادلات الجامع تبعت ال sequencesكيف تم إثباتها؟
+
+26
+00:01:59,220 --> 00:02:03,820
+هذه نظرية مش عادية بالاستقراء الرياضي لإيش؟ لأن ال
+
+27
+00:02:03,820 --> 00:02:08,880
+sequence اللي عندك أعدادها غير منتهية فبالتالي
+
+28
+00:02:08,880 --> 00:02:13,160
+فبالتالي كان هو بيفرض أنها صحيحة لحد مستوى معين و
+
+29
+00:02:13,160 --> 00:02:16,040
+بشوف هل بقى شوف بعد المستوى هذا بصل لنتيجة تانية
+
+30
+00:02:16,040 --> 00:02:20,440
+لو اتغيرت كيمة ال N زائد واحد مثلا و هكذاهنبدأ
+
+31
+00:02:20,440 --> 00:02:24,460
+اليوم إن شاء الله في مفاهيم الاستقرار لكن ضروري
+
+32
+00:02:24,460 --> 00:02:27,140
+دائما أستحضر مفاهيم الرياضيات البسيطة اللي احنا
+
+33
+00:02:27,140 --> 00:02:31,160
+بنعرفها من مفاهيم الرياضيات البسيطة ان مثلا عملية
+
+34
+00:02:31,160 --> 00:02:35,860
+الجامع عملية الدرب عمليات إبدالية بصبوط بينما
+
+35
+00:02:35,860 --> 00:02:39,200
+عملية القسمة وقت رح عملية غير إبدالية عملية الدرب
+
+36
+00:02:39,200 --> 00:02:42,660
+توزيعية على الجامع وقت رح والعكس غير صحيح بصبوط
+
+37
+00:02:42,660 --> 00:02:46,530
+ولا لأ؟وبالتالي .. بالتالي هذه المفاهيم يجب أن
+
+38
+00:02:46,530 --> 00:02:49,710
+تكون حاضرة عندى .. لما بجي بتكلم من أكبر أن ولا
+
+39
+00:02:49,710 --> 00:02:56,990
+جذر الان؟ ان .. من أكبر أن ولا الان تربيع؟ حتما
+
+40
+00:02:56,990 --> 00:02:59,630
+الان تربيع .. يعني لو بنقول .. عشان نكون منصفين
+
+41
+00:02:59,630 --> 00:03:02,150
+نقول أكبر أو تساوي .. الان تربيع .. مصدود أو لا؟
+
+42
+00:03:02,150 --> 00:03:05,810
+وبالتالي ماحدش فينا هذه المفاهيم بتوفيها .. بس
+
+43
+00:03:05,810 --> 00:03:08,810
+دائما نقطة البداية هي اللى بتشكل أن .. اللى ..
+
+44
+00:03:08,810 --> 00:03:13,990
+اللى ممكن احنا نشوفهلو فكرنا نتذكر أو حبينا نتذكر
+
+45
+00:03:13,990 --> 00:03:18,510
+بعض المفاهيم الـ product of non-zero real number
+
+46
+00:03:18,510 --> 00:03:25,290
+is non-zero لو أخدت أي عددين حقيقيين غير صفر
+
+47
+00:03:25,290 --> 00:03:30,850
+وضربتهم في بعض النتج هيكون لا يساوي صفر ولا لأ
+
+48
+00:03:30,850 --> 00:03:34,270
+وهدم المسلمات عشانك نقول لك احنا مجموعة نلحقها ده
+
+49
+00:03:34,270 --> 00:03:38,730
+احنا بنتذكرها لو أخدت أي عدد لا يساوي الصفر وربعته
+
+50
+00:03:39,730 --> 00:03:43,130
+فهيكون النتيجة تبعه positive فهيكون النتيجة تبعه
+
+51
+00:03:43,130 --> 00:03:46,450
+positive لأنه السالب والموجب عند التربية بالديني
+
+52
+00:03:46,450 --> 00:03:51,690
+positive موجب ال even integer العدب الزوجي بيكتب
+
+53
+00:03:51,690 --> 00:03:57,510
+على صورة اتنين في كيه بقى لو اتكلم على even
+
+54
+00:03:57,510 --> 00:04:02,390
+integer يعني Z ماتكلمش على real number اتكلم على Z
+
+55
+00:04:02,390 --> 00:04:06,590
+بالدرجة الأولى كل عدد زوجي يكتب على اتنين كيه هات
+
+56
+00:04:06,590 --> 00:04:11,620
+أي عدد زوجي بيدكياههتلاقي اربعة اتنين في اتنين ستة
+
+57
+00:04:11,620 --> 00:04:16,700
+و تلاتين اتنين في تمنتاش اتنين في تمنتاش و هكذا
+
+58
+00:04:16,700 --> 00:04:24,340
+الان العدد الفردي يكتب على صورة اتنين ك زائد واحد
+
+59
+00:04:24,340 --> 00:04:29,020
+لان هو أكبر من العدد الزوجي بواحد او ناقص واحد
+
+60
+00:04:29,020 --> 00:04:36,060
+ارجيك فيها او ناقص واحدليش؟ لأن الأعداد الصحيحة
+
+61
+00:04:36,060 --> 00:04:40,060
+اما عدد فردي او عدد زوجي بيبدأ الصفر زوجي ورا واحد
+
+62
+00:04:40,060 --> 00:04:45,260
+فردي اتنين زوجي التلاتة صارت العدد التنيني العدد
+
+63
+00:04:45,260 --> 00:04:50,780
+الزوجي محصور بين عددين فرديا و العكس صحيح و هكذا
+
+64
+00:04:50,780 --> 00:04:54,700
+بتبقى ال sequence موجودة معايا عشان هيك العدد
+
+65
+00:04:54,700 --> 00:04:59,230
+الفردي اما بياخد صورة اتنين K زائد واحدأو اتنين
+
+66
+00:04:59,230 --> 00:05:03,030
+كمك بس واحد وبأي صورة انا اعتمد في الاثبات عندى
+
+67
+00:05:03,030 --> 00:05:07,930
+الصورة اللى ممكن تخدمك اكتر الصورة اللى ممكن تخدمك
+
+68
+00:05:07,930 --> 00:05:12,750
+اكتر ممكن تنتين يكونوا في بعض المسائل مش فارجة اه
+
+69
+00:05:12,750 --> 00:05:19,170
+ممكن تمام اللى بعده لو أخدت اي عددين فرديا فرديا
+
+70
+00:05:19,170 --> 00:05:25,020
+لو ضربتهم في بعض النتج تبعهم هيكون فرديفردي، لو
+
+71
+00:05:25,020 --> 00:05:27,900
+خدت أي عددين فرديين، خدلك أي عددين من الأصغار اللي
+
+72
+00:05:27,900 --> 00:05:32,640
+بتعرفهم الآن و ضربهم في دماغك فردي، طبعا في موضوع
+
+73
+00:05:32,640 --> 00:05:36,080
+الاثبات الشباب، مالفعش تقول الله أه صحيح، هي رقم
+
+74
+00:05:36,080 --> 00:05:39,480
+لإي تلاتة في سبعة واحد وعشرين، طب ما لربما في بقى
+
+75
+00:05:39,480 --> 00:05:42,760
+.. في عدد فردي خصوصا إن الإعداد مجموعات غير
+
+76
+00:05:42,760 --> 00:05:47,710
+منتهية، لربما في عدد فردي بعيدانت مش قادر تجيب
+
+77
+00:05:47,710 --> 00:05:53,510
+نتيجته بظبط فمتقدرش تثبت بناء على مثال اثبات بده
+
+78
+00:05:53,510 --> 00:05:59,310
+دائما خطوات منطقية في تسلسل الأحداث طيب ال real
+
+79
+00:05:59,310 --> 00:06:02,710
+number بقول عنه rational العدد الحقيقي بقول عنه
+
+80
+00:06:02,710 --> 00:06:06,830
+عدد نسبي لو كان بكتبه على common fraction ايش يعني
+
+81
+00:06:06,830 --> 00:06:11,970
+common fraction بسطه مقام والمقام لا يساوي صفر ال
+
+82
+00:06:11,970 --> 00:06:12,310
+prime
+
+83
+00:06:15,010 --> 00:06:17,390
+الـ prime هو عبارة عن positive integer أكبر من
+
+84
+00:06:17,390 --> 00:06:21,550
+واحد، اتنين، تلاتة، خمسة، سبعة، أحداشر، مظبوط؟ لا
+
+85
+00:06:21,550 --> 00:06:25,470
+يقبل قسم إلا على نفسه أنا بقولك ال divisor تباوته
+
+86
+00:06:25,470 --> 00:06:31,010
+واحد سالي واحد بي وسالب بي صحيح، بس لما اتكلمنا عن
+
+87
+00:06:31,010 --> 00:06:33,210
+ال divisor المرة الماضية ال divisor لازم يكون
+
+88
+00:06:33,210 --> 00:06:38,810
+positive ال divisor لازم يكون لما كتبنا أن ال M
+
+89
+00:06:38,810 --> 00:06:50,490
+تساوي أو ال A قلنا تساويD Quantity Quotient دي
+
+90
+00:06:50,490 --> 00:06:56,190
+زائد Quotient
+
+91
+00:06:56,190 --> 00:07:02,750
+Quotient
+
+92
+00:07:02,750 --> 00:07:06,450
+Quotient Quotient Quotient Quotient Quotient
+
+93
+00:07:06,450 --> 00:07:07,630
+Quotient Quotient Quotient Quotient Quotient
+
+94
+00:07:07,630 --> 00:07:07,710
+Quotient Quotient Quotient Quotient Quotient
+
+95
+00:07:07,710 --> 00:07:10,570
+Quotient Quotient Quotient Quotient Quotient
+
+96
+00:07:10,570 --> 00:07:12,150
+Quotient Quotient Quotient Quotient Quotient
+
+97
+00:07:12,150 --> 00:07:16,220
+Quotient Quotient Quotient Quotفى ال section اللى
+
+98
+00:07:16,220 --> 00:07:18,800
+كان فى chapter واحد ليش كان محبوب فى chapter واحد
+
+99
+00:07:18,800 --> 00:07:22,460
+لأن فعليا احنا اتعلمنا شغل مهم جدا لما اتكلمنا عن
+
+100
+00:07:22,460 --> 00:07:31,380
+ال compound proposition اللى هى D implies Q اكثر
+
+101
+00:07:31,380 --> 00:07:38,260
+من 80% من النظريات تعتمد على مبدأ if then لو تحقق
+
+102
+00:07:38,260 --> 00:07:44,660
+المعطى هذا بتكون النتيجة عندك كذاB implies Q عشان
+
+103
+00:07:44,660 --> 00:07:49,320
+هيك حطلنا introduction to proof فكشن واحد سبعة لكن
+
+104
+00:07:49,320 --> 00:07:52,980
+قلت انا بدي اجيلها تماما تمام لحد ما نتكلم عن
+
+105
+00:07:52,980 --> 00:07:57,760
+اثبات الرياضي كلها في مرة واحدة الان عشان اثبت
+
+106
+00:07:57,760 --> 00:08:03,060
+النظرية في عندي شغل اسمها direct proof مباشر
+
+107
+00:08:03,060 --> 00:08:08,220
+direct يعني المسألة بيتكون على صورة Bو Q و انا بدي
+
+108
+00:08:08,220 --> 00:08:14,940
+اروح امسك ال B تمام؟ و من خلالها تبدي أصل لـ Q إذا
+
+109
+00:08:14,940 --> 00:08:21,620
+تحققت ال B true فال Q حق مانعش هتتحقق إذا تحققت ال
+
+110
+00:08:21,620 --> 00:08:26,560
+B فال Q هتتحقق عشان النظرية دي بتكون صحيحة فإنت
+
+111
+00:08:26,560 --> 00:08:34,080
+الخطوات اللي هتبدأها هتروح تقولي assume ال B بك
+
+112
+00:08:34,080 --> 00:08:35,840
+تفترض إن ال B صحيحة is true
+
+113
+00:08:40,360 --> 00:08:44,820
+خلصنا عشان تبدأ من هنا و تصل لنتيجة دائما طيب لو
+
+114
+00:08:44,820 --> 00:08:51,380
+انا يا جيد قلتلك اثبت لو كان if n و m أعداد فردية
+
+115
+00:08:51,380 --> 00:09:03,340
+معناته حصل جامعهم هيكون عدد زوجي بقول if ال m and
+
+116
+00:09:03,340 --> 00:09:08,340
+ال n are odd then
+
+117
+00:09:09,360 --> 00:09:16,160
+الـ M زائد الـ N is even لأن
+
+118
+00:09:16,160 --> 00:09:20,880
+بالمثال هذا ميه ال B؟ ميه ال B عندي في المسألة؟
+
+119
+00:09:20,880 --> 00:09:28,100
+طبعا if then يعني implication أصبت؟ M and ال M هي
+
+120
+00:09:28,100 --> 00:09:38,940
+ال B كل هذا M is odd N is odd و ال Qm زائد ال b is
+
+121
+00:09:38,940 --> 00:09:44,020
+even في أي حال كيف بدي أمشي مع المسألة أنا؟ بدي
+
+122
+00:09:44,020 --> 00:09:52,400
+أفرض خطوة رقم واحد في الحل دائما هتقول assume ال
+
+123
+00:09:52,400 --> 00:10:01,360
+b إيش ال b؟ is it true؟ إيش يعني؟ m is odd and ال
+
+124
+00:10:01,360 --> 00:10:03,540
+m is odd
+
+125
+00:10:08,290 --> 00:10:15,870
+دقم واحد اتنين بما ان M is odd و M is odd انا فاني
+
+126
+00:10:15,870 --> 00:10:22,810
+عندي صورة للعدد الفردي و لا لأ معناته ال M هذه ال
+
+127
+00:10:22,810 --> 00:10:28,570
+M تساوي اتنين K زائد واحد for some K لأي K برضه
+
+128
+00:10:28,570 --> 00:10:32,830
+النظر ايش كانلو أخدت الـ K سبعة أخدت أربعة أخدت
+
+129
+00:10:32,830 --> 00:10:37,810
+خمسين أخدت مليون وسبعمية و خمسين ألف ومية و تلاتة
+
+130
+00:10:37,810 --> 00:10:42,270
+وتسعين مش فارقة، أيش ما تكون، مظبوط؟ في الآخر انت
+
+131
+00:10:42,270 --> 00:10:45,810
+بتضيوبها في اتنين صارت عدد زوجي، أضفتلها واحد انت
+
+132
+00:10:45,810 --> 00:10:53,010
+ضايما ان العدد هذا عدد فردي and ال M is odd بدها
+
+133
+00:10:53,010 --> 00:10:59,350
+تساوي أخد نفس ال Kلأ هي حالة خاصة بتصير خد أي عدد
+
+134
+00:10:59,350 --> 00:11:11,430
+فردي آخر اتنين في H زائد واحد where بحيث
+
+135
+00:11:11,430 --> 00:11:18,890
+انه N عفوا K وH تم تم إلى مين لازمت أعداد صحيحة
+
+136
+00:11:18,890 --> 00:11:26,930
+كمان ايش الخطوة بعد هيك بيسأل عن مين هو جايدخلصت
+
+137
+00:11:26,930 --> 00:11:30,490
+ال B فقط انا الان في الخطوة واحد و اتنين او انشأت
+
+138
+00:11:30,490 --> 00:11:33,890
+حتى كل هذه الخطوة رقم واحد انا بس حققت المطلوب
+
+139
+00:11:33,890 --> 00:11:39,410
+يعني فكفقت المعضلة اللي عندي و وصلت على ان ال B و
+
+140
+00:11:39,410 --> 00:11:44,010
+ال N is odd ال M و ال N is odd هى صورتهم هم
+
+141
+00:11:44,010 --> 00:11:49,390
+بيكونوا يشبههم يعني هتجمعهم هيكون عداد فردي ايش ال
+
+142
+00:11:49,390 --> 00:11:54,310
+direct الخطوة ال direct مباشر روحي M زائد N
+
+143
+00:11:57,200 --> 00:11:59,560
+درباك الترقيم هذا مش أساسي يعني عندنا في الحل
+
+144
+00:11:59,560 --> 00:12:03,380
+معناه كل واحدة بتقدر تقول they assume كده them
+
+145
+00:12:03,380 --> 00:12:07,080
+them او ترسم them على انه implies مافيش .. مش
+
+146
+00:12:07,080 --> 00:12:10,280
+خضرية كتير بس تكتب كل .. كل جملة كتبها في الصدر
+
+147
+00:12:10,280 --> 00:12:15,180
+عشان تبقى ليش الترتيب تبقى اك .. او البرهان ثابت M
+
+148
+00:12:15,180 --> 00:12:25,720
+زائد N يساوي اتنين K زائد واحد زائد اتنين Hزائد
+
+149
+00:12:25,720 --> 00:12:31,400
+واحد عوارف عن قيمة ال M وقيمة ال N اجمع ال N اتنين
+
+150
+00:12:31,400 --> 00:12:40,540
+K زائد اتنين H زائد اتنين مصبوط؟ واحد زائد واحد
+
+151
+00:12:40,540 --> 00:12:46,380
+يعني بلينجو سينما رفعت الأقواص وبدلت اذا بدكاش
+
+152
+00:12:46,380 --> 00:12:49,960
+ممكن تزيدها كمار خطوة مافيش مشكلة في الموضوع اتنين
+
+153
+00:12:49,960 --> 00:12:56,830
+K زائد واحد زائد اتنين H زائد واحدبس طبعا الخبرة
+
+154
+00:12:56,830 --> 00:13:00,310
+هذه trivial والاصل مافيش عندك فيها مشكلة اتنين K
+
+155
+00:13:00,310 --> 00:13:11,590
+اتنين H اتنين خد التاني على المشترك اتنين K زائد H
+
+156
+00:13:11,590 --> 00:13:18,670
+زائد واحد هذه صورة من الشباب صورة العدد الزودي
+
+157
+00:13:18,670 --> 00:13:23,290
+وانا بأضمن ان K زائد H زائد واحد عبارة عن integers
+
+158
+00:13:24,130 --> 00:13:29,090
+ليش؟ لأن الـH و الـK عبارة عن integers فحص الجمعهم
+
+159
+00:13:29,090 --> 00:13:33,250
+هيكون integer و دوستيلهم كمان واحد ف integer فمنها
+
+160
+00:13:33,250 --> 00:13:39,830
+توهان is even خلصنا
+
+161
+00:13:39,830 --> 00:13:46,170
+تم إثباتإن لو كانت ال M و ال N عبارة عن odd هذا
+
+162
+00:13:46,170 --> 00:13:50,910
+وصلني إن ال M زائد واحد is even وكان الإثبات هدى
+
+163
+00:13:50,910 --> 00:13:55,450
+مباشر يعني بينجو سين أنا افترضت ال M أو افترضت ال
+
+164
+00:13:55,450 --> 00:14:02,430
+B is true ومشيت خطوات مباشرة باتجاه ال Q و أثبت
+
+165
+00:14:02,430 --> 00:14:07,890
+انها true مثال
+
+166
+00:14:07,890 --> 00:14:15,640
+تاني بقول إثبتلو كانت ال n is odd if ال n is odd
+
+167
+00:14:15,640 --> 00:14:24,880
+then ال n تربيع is odd لو كانت if ال n is odd then
+
+168
+00:14:24,880 --> 00:14:30,060
+ال n تربيع is odd بالمناسبة هتفرج معاك حاجة يا
+
+169
+00:14:30,060 --> 00:14:35,780
+شباب لو حطناها hand سالب؟ لأهتصير معاك هذا في
+
+170
+00:14:35,780 --> 00:14:39,620
+الجوز ناقص واحد في الآخر ده اللي هتصير ناقص و
+
+171
+00:14:39,620 --> 00:14:42,460
+اتنين ناقص واحد و ناقص واحد ناقص اتنين مصبوط
+
+172
+00:14:42,460 --> 00:14:48,180
+فهتصير k زائد h ناقص اتنين مضروع في اتنين نفس
+
+173
+00:14:48,180 --> 00:14:53,980
+الحاجة هو ليش هيختلف معاك نفس الكلام هان الان جاعة
+
+174
+00:14:53,980 --> 00:14:58,420
+بقول لو كانت ال M is odd ماتو enter بيه is odd خد
+
+175
+00:14:58,420 --> 00:15:00,040
+ورقة مواحد هقوله assume
+
+176
+00:15:03,720 --> 00:15:10,400
+الـ B is true صحيحة ايش يعني يعني ال N is odd
+
+177
+00:15:10,400 --> 00:15:17,160
+معناته ال N بدها تساوي 2K زائد واحد او منقص واحد
+
+178
+00:15:17,160 --> 00:15:25,500
+مش فاهم يدري بالك كمان مرة هال K تنتمي إلى Z خطوة
+
+179
+00:15:25,500 --> 00:15:31,190
+اللي بعد هيكربيع ال N لان انا بتتكلم عن مين مع
+
+180
+00:15:31,190 --> 00:15:35,550
+التربيع انت الفكرة كمان مرة ان ال B تقول ال Q من
+
+181
+00:15:35,550 --> 00:15:39,330
+ال B انا بدى اوصل ل Q كانت ال Q هن عبارة عن جمع
+
+182
+00:15:39,330 --> 00:15:44,030
+العددين جمعتهم هن في المسألة تربيع بده ربيعها
+
+183
+00:15:44,030 --> 00:15:53,590
+بصبوط مع توقع التربيع تساوي 2K زائد 1 لكل تربيع
+
+184
+00:15:55,310 --> 00:15:59,390
+تعرف تربيع؟ ماشي الحالة الخلاص عشان اذكرك ان كل
+
+185
+00:15:59,390 --> 00:16:04,070
+المعلومات احنا بنعرفها تمام بس فعليا عملية تتبوحها
+
+186
+00:16:04,070 --> 00:16:07,770
+او تصفيتها هي المشكلة دائما عندنا مربع العدد اللي
+
+187
+00:16:07,770 --> 00:16:14,230
+عندك هنا مربع العدد يساوي تربيع الأول 2K تربيع
+
+188
+00:16:14,230 --> 00:16:16,090
+زائد تربيع التاني
+
+189
+00:16:19,360 --> 00:16:24,100
+زائد الأول في التاني في اتنين الأول في التاني في
+
+190
+00:16:24,100 --> 00:16:27,840
+اتنين اللي هو الأُس هنا بحافظ ان اقولك الأُس تروح
+
+191
+00:16:27,840 --> 00:16:32,760
+تلاقي تلاتة تروح تتنبل عليها نفس الكلام مش صحيح
+
+192
+00:16:32,760 --> 00:16:37,800
+تمام؟ الأول في التاني في اتنين هذي اتنين في اتنين
+
+193
+00:16:37,800 --> 00:16:46,050
+K في واحد مظبوط؟ طيب اتنين في اتنين Kاربعة في واحد
+
+194
+00:16:46,050 --> 00:16:52,530
+اربعة K واحد تربيع واحد واربعة K تربيع اربعة اتنين
+
+195
+00:16:52,530 --> 00:17:00,470
+K تربيع اربعة K تربيع تساوي اربعة K تربيع زائد
+
+196
+00:17:00,470 --> 00:17:08,560
+اربعة K زائد واحدالان الواحد هذه انا بدي ايها فى
+
+197
+00:17:08,560 --> 00:17:11,720
+صورة العدد الفردي لان عماريش بيقول لي اثبت ان الان
+
+198
+00:17:11,720 --> 00:17:16,320
+ترديع is odd لما بتكون الان is odd انا بدي ايها
+
+199
+00:17:16,320 --> 00:17:20,240
+معاكتوا بدي اخد العام المشترك وين هنا صورة العدد
+
+200
+00:17:20,240 --> 00:17:22,900
+العام الفردي العدد الفردي اللى انا فرضتها هي اتنين
+
+201
+00:17:22,900 --> 00:17:29,200
+ك زائد واحد فاخد اتنين عام المشترك بيبقى اتنين ك
+
+202
+00:17:29,200 --> 00:17:35,200
+ترديع زائد اتنين ك الكل زائد واحد
+
+203
+00:17:39,340 --> 00:17:50,020
+is odd و لا لا خلص البرهان وبالتالي عملية الوصول
+
+204
+00:17:50,020 --> 00:17:53,880
+او عملية الاثبات عملية سهلة لما انا فعليا امشي
+
+205
+00:17:53,880 --> 00:17:57,820
+قاعد خطوة ورا التانية الان كمان مرة مرخص الكلام
+
+206
+00:17:57,820 --> 00:18:02,180
+اللي انا بقوله كلام بسيط جدا اولا مجرد اللي اشوف
+
+207
+00:18:02,180 --> 00:18:09,920
+if و then if و then ايش بدي اساوي direct proofبدي
+
+208
+00:18:09,920 --> 00:18:13,660
+افترض ان ال B اتحققت عندي ايش ال B بتقولي بدي
+
+209
+00:18:13,660 --> 00:18:18,300
+اكتبها جداني بصور معادلات رياضية ايش ال Q بدها نمي
+
+210
+00:18:18,300 --> 00:18:21,680
+بدها جامع بدها اجمع بدها ضرب بدها ضرب بدي امشي ايش
+
+211
+00:18:21,680 --> 00:18:26,740
+بده ال Q عشان هيك اسمها Direct الان هذه التقرية
+
+212
+00:18:26,740 --> 00:18:32,840
+معظم البراهيم تعتمد عليها افظم افظم افظم وبالتالي
+
+213
+00:18:32,840 --> 00:18:36,000
+انا مافيش عندى مشكلة ان اصلا لما اثبت امشي مع
+
+214
+00:18:36,000 --> 00:18:39,200
+الواقعات اللي موجودة عندى هن واضح الامور يا شباب؟
+
+215
+00:18:40,310 --> 00:18:47,910
+في اي سؤال فيها لحظة القالب المثالير هدول؟ بس
+
+216
+00:18:47,910 --> 00:18:52,230
+طبعا نصيحة اليك ده ابدأ من القالب في الشبتر هذا
+
+217
+00:18:52,230 --> 00:18:59,610
+ارجع للكتاب حل الأمثلة حل قدر ما بتقدر من الأسئلة
+
+218
+00:18:59,610 --> 00:19:04,450
+خلي ورقة و جلم بيدك في السمارة وابدأ حللأن الشغل
+
+219
+00:19:04,450 --> 00:19:08,430
+بالممارسة، أنا متأكد بعضكم مصدوم الآن، أنا طبعا مش
+
+220
+00:19:08,430 --> 00:19:12,610
+مدي في الموضوع هذا، أنه بالتالي لازم تعود نفسك،
+
+221
+00:19:12,610 --> 00:19:18,300
+ليش؟شباب انت الان رايح بيتيجيها برمجة تمام؟ مفهوم
+
+222
+00:19:18,300 --> 00:19:22,720
+البرمجة ان انت بدك تقدر تحلل المطلوب عشان تقدر
+
+223
+00:19:22,720 --> 00:19:25,500
+تكتب البرنامج لاحقا عشان تقدر تعمل ال loop تعرف ال
+
+224
+00:19:25,500 --> 00:19:28,420
+loop متى بده يتجف وإيش اللي انت بدك .. بدكون في ال
+
+225
+00:19:28,420 --> 00:19:32,100
+next step بده يصير فإذا ماكانش ال logic عندك حاضر
+
+226
+00:19:32,100 --> 00:19:35,900
+بشكل سليم و تقدر تاخد المطلوب و تحقق من خلاله و
+
+227
+00:19:35,900 --> 00:19:38,960
+توصل للمقطع أو عفوا تاخد المقطع و توصل للمطلوب
+
+228
+00:19:39,760 --> 00:19:42,260
+هيكون عندك مشكلة في البرمجة يعني الموضوع المفروض
+
+229
+00:19:42,260 --> 00:19:46,360
+هذا بس بنمي التفكير المنطقي عندك و التتابع لاحظ
+
+230
+00:19:46,360 --> 00:19:51,540
+كنت قاعد اتكلم على خطوات متتالية منطقية مظبوط ولا
+
+231
+00:19:51,540 --> 00:19:55,080
+لأ زي ايش؟ زي ما فكرت في ال algorithm ال algorithm
+
+232
+00:19:55,080 --> 00:19:57,920
+هو عبارة عن مجموعة او sequence من الخطوات
+
+233
+00:19:57,920 --> 00:20:03,140
+المتتالية معرفة بشكل صريح و واضحالتعريف كله بنعرف
+
+234
+00:20:03,140 --> 00:20:07,800
+القطوعات هاي بس فعليا صيغتها وترتيبها هي اللي مش
+
+235
+00:20:07,800 --> 00:20:12,800
+متعودين على كتابته تعالى نشوف مثال هذا المثال
+
+236
+00:20:12,800 --> 00:20:19,040
+السابق اللي حلناه مع بعض بقول اثبت the product of
+
+237
+00:20:19,040 --> 00:20:23,520
+two rational number is rational يعني لو أخدت أي
+
+238
+00:20:23,520 --> 00:20:28,760
+على دين نسبيين ضربتهم في بعض حدين الناتج نسبة
+
+239
+00:20:28,760 --> 00:20:34,860
+لاحظها مجليش P و Qيعني أنا مالاقيتش ال F و ال then
+
+240
+00:20:34,860 --> 00:20:39,020
+موجودات بس هما فعليا موجودات في صياغها من صياغ ال
+
+241
+00:20:39,020 --> 00:20:44,500
+F اللي كانت إيش نكتبها سابقا The product of two
+
+242
+00:20:44,500 --> 00:20:48,620
+rational number حاصل ضرب العدد أو حاصل ضرب عددين
+
+243
+00:20:48,620 --> 00:20:53,140
+نسبيين بيديني عدد نسبي The product of two rational
+
+244
+00:20:53,140 --> 00:21:01,950
+numbers هي ال B يؤدي هيك صح؟المعطل اللي عندك انت
+
+245
+00:21:01,950 --> 00:21:06,370
+ال B ال B two rational number بس يعني هو كأن هو
+
+246
+00:21:06,370 --> 00:21:13,170
+بيقولك هيك if ال M and Q او M and N are rational
+
+247
+00:21:13,170 --> 00:21:19,430
+then
+
+248
+00:21:19,430 --> 00:21:22,990
+number
+
+249
+00:21:22,990 --> 00:21:25,970
+بال N is rational
+
+250
+00:21:30,450 --> 00:21:34,930
+بس ياخد المسألة اللي كنت أنا بحاجة أعوّلها أو أعرف
+
+251
+00:21:34,930 --> 00:21:37,690
+إيش المعطى اللي موجود عندي عشان أنا .. هو ماتدنيش
+
+252
+00:21:37,690 --> 00:21:41,730
+.. ماجليش إن الضرب هو معطى هو مجرد قال لي لو كان
+
+253
+00:21:41,730 --> 00:21:46,130
+في عندك عددين if ال M and M are rational لو كان ال
+
+254
+00:21:46,130 --> 00:21:51,310
+M و ال N عددين نسبيين تنتمي ل Q معناته حاصر ضربهم
+
+255
+00:21:51,310 --> 00:21:58,230
+ينتمي إلى Q تمام؟ معناته احنا عرفنا الآن من ال B
+
+256
+00:21:58,230 --> 00:22:07,350
+اللي عنديهي ال B two rational number لانه
+
+257
+00:22:07,350 --> 00:22:12,290
+مش قال لي the product مضروه لو قال لي the sum او
+
+258
+00:22:12,290 --> 00:22:16,810
+حاصل جمع الجمع مجموحهم وبالتالي كل المعطل اللي
+
+259
+00:22:16,810 --> 00:22:20,290
+موجود او اللي انا محتاجه دائما موجود وين في السؤال
+
+260
+00:22:20,290 --> 00:22:24,470
+بس بدي شوية افكر في المسألة زي ما اقوله بنفسية
+
+261
+00:22:24,470 --> 00:22:28,930
+هادية اذا انت فكرت في المسألة وانت خايفالمسألة
+
+262
+00:22:28,930 --> 00:22:31,630
+صعبة مش هقدر احلها اما اقعده خلاص من البداية انا
+
+263
+00:22:31,630 --> 00:22:35,410
+مانصح اخسيب المسألة و اروح لمسألة تانية اذا انت
+
+264
+00:22:35,410 --> 00:22:38,790
+رايح على المعركة بنفسيتي المهزوم و لاعبركة بتنتصر
+
+265
+00:22:38,790 --> 00:22:44,250
+نقطة وسط على جديد الان فبالتالي انا هاي ال B اللي
+
+266
+00:22:44,250 --> 00:22:49,770
+عندي هروح اقوله assume ال
+
+267
+00:22:49,770 --> 00:22:56,710
+B ايش ال B تبعتي يعني شباب امand اي اسمين اي كره
+
+268
+00:22:56,710 --> 00:23:00,110
+اي رمزين اي حرفين اي two variables انتحار فيهم
+
+269
+00:23:00,110 --> 00:23:06,510
+تنتمي ل q ا rational هى مش هي نفس المعنى عشان اخفف
+
+270
+00:23:06,510 --> 00:23:09,270
+كتابة تنتمي ل q مش ال q هي عبارة عن rational
+
+271
+00:23:09,270 --> 00:23:15,650
+number طيب ممتاز شو يعني ايش يعني شو يعني m is
+
+272
+00:23:15,650 --> 00:23:21,750
+rational ايوة يعني ال m تكتب على صورة بصق مقام
+
+273
+00:23:21,750 --> 00:23:23,070
+والمقام لا يساوي صفر
+
+274
+00:23:26,260 --> 00:23:32,100
+مصبوط؟معناته ال M بدها تساوي A على B وال B لا
+
+275
+00:23:32,100 --> 00:23:41,340
+تساوي صفر and ال M بدها تساوي C على D وال D لا
+
+276
+00:23:41,340 --> 00:23:47,080
+تساوي صفر ومش بس هيك A وB وC وD عبارة عن integers
+
+277
+00:23:47,080 --> 00:23:49,820
+تمام؟
+
+278
+00:23:51,300 --> 00:23:58,340
+A و B تنتمي إلى Z C و D تنتمي إلى Z وهذا تعريف ال
+
+279
+00:23:58,340 --> 00:24:01,660
+integer أو الرشد ال number خلّينا نكتبهم ورا بعض
+
+280
+00:24:01,660 --> 00:24:07,360
+بالشكل هذا where ال
+
+281
+00:24:07,360 --> 00:24:14,680
+A و ال B تنتمي إلى Z and ال B لا تساوي صفر التاني
+
+282
+00:24:14,680 --> 00:24:21,310
+ال N تساوي بقولنا C على D whereلاحظوا أنا بأتكلم
+
+283
+00:24:21,310 --> 00:24:25,490
+على تعريف العدد النسبي أنا مابديتش في الحل مجرد
+
+284
+00:24:25,490 --> 00:24:33,310
+بحلل الموضوع اللي عندي where C وD تنتمي إلى Z and
+
+285
+00:24:33,310 --> 00:24:41,790
+D لا تساوي صفر مية فالمية ايش الخطوة اللي بعد هيك؟
+
+286
+00:24:41,790 --> 00:24:45,950
+هو جالبه الـQ تبعته خلاص من الـD الـdirect step
+
+287
+00:24:45,950 --> 00:24:49,650
+الخطوة المباشرة اللي بده روح فيها اللي هي ضرب
+
+288
+00:24:50,530 --> 00:25:00,170
+أضربهم في بعض M ضرب ال M يساوي A على B ضرب C على D
+
+289
+00:25:00,170 --> 00:25:05,990
+نعرف نضربهم؟ نعرف نضربهم؟ البسط مع البسط و المقهر
+
+290
+00:25:05,990 --> 00:25:15,030
+مع المقهر يساوي AC على B في D وهذه أنا أزعج منها
+
+291
+00:25:15,030 --> 00:25:29,030
+تنتمي ل Q ليش؟لأن A C و B D تنتمي للـ Z ومش بس هيك
+
+292
+00:25:29,030 --> 00:25:34,870
+و B D A تساوي صفر هذا الكلام انا من اين جيبته حاصل
+
+293
+00:25:34,870 --> 00:25:41,570
+اي ضرب عددين صحيحين بيديني عدد صحيح وحاصل ضرب اي
+
+294
+00:25:41,570 --> 00:25:45,810
+عددين غير الصفر بيكون عدد صحيح غير لا يساوي صفر
+
+295
+00:25:49,280 --> 00:25:54,240
+تنتمي الى Q معناته النظرية هذه صحيحة معناته ال
+
+296
+00:25:54,240 --> 00:25:59,620
+product of two rational number is rational خلاص
+
+297
+00:25:59,620 --> 00:26:03,240
+السؤالة انتهى الامر بمجرد انت وصلتنا للمطلوب هو
+
+298
+00:26:03,240 --> 00:26:07,660
+جاي بيقولك اثبت ان حاصل درعهم هيو ينتمي الى Q
+
+299
+00:26:07,660 --> 00:26:16,020
+وصلنا لها نعم شمعة
+
+300
+00:26:18,010 --> 00:26:23,990
+انت فرضت بس شكل الرمز بس التعريف لأ لان احنا قلنا
+
+301
+00:26:23,990 --> 00:26:27,870
+من البداية rational number عدد نسبي ايش هو هو كل
+
+302
+00:26:27,870 --> 00:26:31,770
+عدد يكتب على صورة بسط ومقام والمقام فيه لا يساوي
+
+303
+00:26:31,770 --> 00:26:37,070
+صفر فهذا هو انا جرد اني فرضت ان ام ام عدد نسبية
+
+304
+00:26:37,070 --> 00:26:40,150
+عدد نسبية يعني لازم يكتب على صورة بسط ومقام
+
+305
+00:26:40,150 --> 00:26:45,510
+والمقام لا يساوي صفر كتبت التعريف لان هذا التعريف
+
+306
+00:26:45,510 --> 00:26:51,920
+احنا كلنا بنعرفهفأنا بدي أسخر معرفتي اللي
+
+307
+00:26:51,920 --> 00:26:56,580
+اتعلمناها من و احنا بتفيدها ايه تمام؟ اني انشي مع
+
+308
+00:26:56,580 --> 00:27:07,360
+الاثبات بالشكل البسيط اللي موجود عندها تعلمني
+
+309
+00:27:07,360 --> 00:27:13,540
+لما اتكلمنا مع ال logic قال في ندي بي implies Q
+
+310
+00:27:13,540 --> 00:27:20,110
+هاتيته كافةنقطة Q تعني نقطة B وسميناها
+
+311
+00:27:20,110 --> 00:27:27,150
+Contrapositive بظبط؟
+
+312
+00:27:27,150 --> 00:27:36,010
+تمام الان Contrapositive في بعض المسائل يا شباب مش
+
+313
+00:27:36,010 --> 00:27:42,370
+هتقدر مش هتقدر تمشي فيها بالاتجاه ال direct يعني
+
+314
+00:27:42,370 --> 00:27:47,100
+ما تقدرش تاخد ال Bوتوصل ل Q منها لو إيجي أقول لك
+
+315
+00:27:47,100 --> 00:27:54,820
+if ال N تربيع is odd then
+
+316
+00:27:54,820 --> 00:28:02,160
+ال N is odd لو أنا هان .. هاي بديني اياه صراحة B
+
+317
+00:28:02,160 --> 00:28:08,700
+implies Q هي ال B وهي ال Q مصبوح؟ لو أنا بدي أفطر
+
+318
+00:28:08,700 --> 00:28:16,070
+بال B معناته ال N تربيع بدها تساوي 2في K زائد واحد
+
+319
+00:28:16,070 --> 00:28:22,970
+فح؟ الان ايش ال next step؟ بده M يعني انا هاخد
+
+320
+00:28:22,970 --> 00:28:28,090
+الجذر ال M بدها تساوي جذر ال M وليه بدها تساوي
+
+321
+00:28:28,090 --> 00:28:36,230
+الجذر ل 2K زائد واحد ايش بتقدر تساوي بعد هيك؟ ايش
+
+322
+00:28:36,230 --> 00:28:39,610
+الخبوة اللي بتقدر تمشيها بعد هيك؟ هل بتقدر تثبت ان
+
+323
+00:28:39,610 --> 00:28:44,550
+هو عدد فردي؟لأ لأن اللغة اللي لك مش مكتوبة على
+
+324
+00:28:44,550 --> 00:28:50,410
+صورة اتنين في امتجار زائد او نقص واحد خلاص سكّرت
+
+325
+00:28:50,410 --> 00:28:54,570
+أساسا ماعرفش اللي بتطلع تحت together حيطلع عدد
+
+326
+00:28:54,570 --> 00:29:00,650
+حقيقي ولا حيطلع عدد صحيح وبالتالي المسألة سكّرت
+
+327
+00:29:00,650 --> 00:29:04,910
+وغالبا غالبا كنا احنا لما نشتغل هيك اتجف المعانا
+
+328
+00:29:04,910 --> 00:29:07,950
+المسألة عاد ودبرها لأ الطريقة التانية موجودة بس مش
+
+329
+00:29:07,950 --> 00:29:12,050
+ممكن تساويمش فاكرت الجدران اللي انا و بدّيه
+
+330
+00:29:12,050 --> 00:29:15,190
+التربيه و بدّيه منه الان كيف بدي اوصل هذه لها
+
+331
+00:29:15,190 --> 00:29:23,270
+يعني؟ ايش بقى اتفُك؟ هيها ايش اتفُك؟
+
+332
+00:29:23,270 --> 00:29:29,110
+ماشي الحال كيف بقى اتفُك؟ ماشي الحال ام في ام
+
+333
+00:29:29,110 --> 00:29:31,450
+بيبقى اتساوة اتنين كزائد واحد
+
+334
+00:29:37,000 --> 00:29:40,100
+أيه بقت واحد تجسم على الان تقطع القرآن ناحية تانية
+
+335
+00:29:40,100 --> 00:29:48,780
+ما هي الان تربيع هيها لا غلط يا صاحب هو بيقولك
+
+336
+00:29:48,780 --> 00:29:55,300
+الان تربيع القدر الان تربيع هي القدر عشان هي كان
+
+337
+00:29:55,300 --> 00:29:59,960
+الحل الأن فلنروح أخلص من التربيع بالجذر بدي أخلص
+
+338
+00:29:59,960 --> 00:30:04,390
+التربيع تبعتي الآنهي صوتها فاخدت الجذر على الطرفين
+
+339
+00:30:04,390 --> 00:30:08,310
+عشان تبقى المعادلة صحيحة سكت المسألة فش خطوات فش
+
+340
+00:30:08,310 --> 00:30:13,790
+حل بعد هيك هل هذا يعني المسألة غلط؟ لأ المسألة
+
+341
+00:30:13,790 --> 00:30:22,090
+صحيحة اهان تحت الجذر لأ لأ لأ اهان التربية اللي هي
+
+342
+00:30:22,090 --> 00:30:27,550
+ده مش ع الفاضي هيك بتصيب المسألة غلط الان لا تساوي
+
+343
+00:30:27,550 --> 00:30:31,370
+الجذر الان الان تساوي الجذر التربية الان تربية
+
+344
+00:30:32,890 --> 00:30:41,970
+واللي بتساوي هاي؟ بإيش؟
+
+345
+00:30:41,970 --> 00:30:50,690
+ممتاز X؟ X موجود عدد فردي و لا مزوجي؟ سيبقوا هو
+
+346
+00:30:50,690 --> 00:30:56,250
+لحاله ال X اللي انت اختار عدد زوجي و لا عدد فردي؟
+
+347
+00:30:56,250 --> 00:31:02,210
+ولا حتعرف لأنه خلاص كيف تطلع ال 2K برا الجدر؟
+
+348
+00:31:08,660 --> 00:31:13,740
+الان يا يحيى ان تحت الجذر بيطلعش بهذه السهولة يا
+
+349
+00:31:13,740 --> 00:31:18,620
+صاحبي انت بيطلع من الجذر لما بيكون القص تبقى هو
+
+350
+00:31:18,620 --> 00:31:23,960
+بوافق قص الجذر، طبعا؟ يعني لو فرضا اجد قلتلك انا
+
+351
+00:31:23,960 --> 00:31:27,620
+في عندي هان اربعة كتربيع
+
+352
+00:31:30,080 --> 00:31:35,600
+هذه قيمتها تساوي اتنين ك تربيع تحت الجدر والتي
+
+353
+00:31:35,600 --> 00:31:39,540
+تساوي اتنين ك هكذا يقول الحلول 100% او لو اتيت
+
+354
+00:31:39,540 --> 00:31:45,840
+وقلت لك في عندي اربعة ك اربعة ك تحت الجدر هذه
+
+355
+00:31:45,840 --> 00:31:51,560
+تساوي اتنين تربيع ك تحت الجدر هذه تساوي اتنين في
+
+356
+00:31:51,560 --> 00:31:53,520
+جذر الك ك هكذا صح
+
+357
+00:31:56,290 --> 00:32:01,090
+لغمة فزور يا صاح، مش طالعة، الآن وبالتالي ضروري
+
+358
+00:32:01,090 --> 00:32:05,530
+جدا دائما لما تشتغل مع المسألة اشتغل ضمن ما هو
+
+359
+00:32:05,530 --> 00:32:10,350
+معطقلك، ما تحاولش تفرض فرضياتمالهاش تدخل في
+
+360
+00:32:10,350 --> 00:32:15,350
+الموضوع.الان قعدته بيقولك عندك ان تربيع و بده منك
+
+361
+00:32:15,350 --> 00:32:19,550
+ان.قولك ان تربيع is odd بدك تحطله هى ان تربيع صورة
+
+362
+00:32:19,550 --> 00:32:23,670
+هى odd هى هى.بدك تصل للان.جيب الان بقى تاخد الجدر
+
+363
+00:32:23,670 --> 00:32:27,750
+.فيش حل غير هيك.أخدنا الجدر بس ماوصلناش ل odd.لا
+
+364
+00:32:27,750 --> 00:32:30,630
+لأ جدر أقول odd ولا جدر أقول even ولا جدر أتكلم
+
+365
+00:32:30,630 --> 00:32:34,270
+أساسا.مش فاهمش عارفش اللي عندي.وبالتالي الحل
+
+366
+00:32:34,270 --> 00:32:39,630
+معناته اتجاهي انامش صحيح اتجاهي انا في الحل مش
+
+367
+00:32:39,630 --> 00:32:45,130
+صحيح الان تخدم لمين يا شباب ال contrapositive هذى
+
+368
+00:32:45,130 --> 00:32:51,910
+ايش ال contrapositive تبعت هذى هذى الجملة معناتها
+
+369
+00:32:51,910 --> 00:33:05,310
+if الان is not odd then الان تربيه is not oddسيبني
+
+370
+00:33:05,310 --> 00:33:08,630
+من ال positive و ال negative احنا بتكلم على odd و
+
+371
+00:33:08,630 --> 00:33:15,530
+even بتكلمش على positive مش هادي تكافئ هادي ممكن
+
+372
+00:33:15,530 --> 00:33:21,330
+هادي تخدمني ايش يعني is not odd يعني even لإن
+
+373
+00:33:21,330 --> 00:33:29,410
+العدد الصحي هو اما عدد فردي او عدد زوجي is even
+
+374
+00:33:33,890 --> 00:33:39,890
+هكذا أسهل المسألة ماذا سأقول أنا assume لاحظ هذه
+
+375
+00:33:39,890 --> 00:33:44,330
+الجملة انت مش مطموض انك تكتبها هذه الجملة مش مطموض
+
+376
+00:33:44,330 --> 00:33:48,070
+انك تكتبها المطموض انك تتحلت او تبدأ تفكر بالاتجاه
+
+377
+00:33:48,070 --> 00:33:54,730
+هذا عشان تقول assume not q مباشرة لان هي المسألة
+
+378
+00:33:54,730 --> 00:34:01,110
+اللي عندك هي فوق و ال a او n is not odd اللي هي لا
+
+379
+00:34:01,110 --> 00:34:09,250
+في ال qمصبوط ال سيو نط كيو ايش يعني نط كيو ان is
+
+380
+00:34:09,250 --> 00:34:17,090
+even not odd not
+
+381
+00:34:17,090 --> 00:34:26,730
+odd بين جثين even ايش يعني يعني الان بتساوي اتنين
+
+382
+00:34:26,730 --> 00:34:31,590
+في كيه و بس بدون زائد واحد العدالة زوجي و الكيه
+
+383
+00:34:31,590 --> 00:34:32,150
+تنتمي
+
+384
+00:34:37,950 --> 00:34:42,550
+متاز الخبرة اللي بعد هي ايش بده منه هو ان تربيع
+
+385
+00:34:42,550 --> 00:34:49,650
+الان ان تربيع بدها تساوي اتنين ك تربيع ربع الجوز
+
+386
+00:34:49,650 --> 00:34:57,610
+لاربعة ك تربيعأنا بدي صورة اتنين مضروبة في كده بدي
+
+387
+00:34:57,610 --> 00:35:01,850
+اتنين انت لو هاد قلتلي even انا بصدقك بس اكتب انت
+
+388
+00:35:01,850 --> 00:35:07,490
+دايما وما تتركش لما يالواحد يسرح يساوي اتنين مضروب
+
+389
+00:35:07,490 --> 00:35:16,350
+في جوس اتنين كتر بيه is even هايو
+
+390
+00:35:16,350 --> 00:35:20,770
+مظهور ولا لأ صورة العدد الزوجي و هيك بس بتختم بكل
+
+391
+00:35:20,770 --> 00:35:22,330
+مهام تكتب ايش
+
+392
+00:35:25,170 --> 00:35:30,150
+contrapositive ليه هذي؟ بين جثين نط ال B وصلنا لنط
+
+393
+00:35:30,150 --> 00:35:33,310
+ال B وصلنا لcontrapositive ايش هو يعني؟ يعني لو
+
+394
+00:35:33,310 --> 00:35:40,670
+كان في ال أن تربيع is odd يعني أن تربيع تسعة جديش
+
+395
+00:35:40,670 --> 00:35:46,790
+قيمة الان؟ تلاتة أن تربيع تسعة و أربعين odd سبعة
+
+396
+00:35:46,790 --> 00:35:52,310
+أن تساول واحد و تمانينهكذا كانت السيارة في الاعداد
+
+397
+00:35:52,310 --> 00:35:57,490
+الموجودة وبالتالي انا اثبتها بشيء اسمها الـ Contra
+
+398
+00:35:57,490 --> 00:36:00,850
+Positive يعني الـ Direct Growth لاحظت ال Contra
+
+399
+00:36:00,850 --> 00:36:03,130
+Positive هي عبارة عن Direct بس مع فرضية
+
+400
+00:36:05,820 --> 00:36:10,120
+ليش انا اخترت نقطة Q كمان مرة؟ لأنه .. مش أسهل لأن
+
+401
+00:36:10,120 --> 00:36:16,340
+B implies Q ماوصلتنيش لحل فما هذه تكافئ نقطة Q
+
+402
+00:36:16,340 --> 00:36:22,720
+implies نقطة B فأنا أخدت هذه و اشتغلت عليها Direct
+
+403
+00:36:22,720 --> 00:36:27,600
+Proof فإذا كانت هذه تكافئ هذه يعني إذا اثنتت هذه
+
+404
+00:36:27,600 --> 00:36:31,820
+صحيحة فهذه صحيحة فروحت أخدت هذه و اشتغلت عليها
+
+405
+00:36:31,820 --> 00:36:33,900
+Direct Proof فوصلت للحل اللي موجود عندى
+
+406
+00:36:37,050 --> 00:36:41,210
+وين؟ لو كانت الان even معناته ان تربيه is evil
+
+407
+00:36:41,210 --> 00:36:45,790
+true و لو كانت الان تربيه is odd معناته الان is
+
+408
+00:36:45,790 --> 00:36:50,310
+odd true انا مابقدرش تقولي ان الان الان is evil لا
+
+409
+00:36:50,310 --> 00:36:55,910
+يا صاحبي لو كانت الان تربيه odd فهتكون odd مفروضة
+
+410
+00:36:55,910 --> 00:37:01,290
+منها اكيد انت كمان مرة مالجأت للحالة هادي الا غير
+
+411
+00:37:01,290 --> 00:37:04,490
+عشان تثبت انه هادي صحيحة الا غير عشان تثبت انه
+
+412
+00:37:04,490 --> 00:37:14,090
+هادي صحيحةتعالى نشوف كمان مثال بقول
+
+413
+00:37:14,090 --> 00:37:24,230
+اثبت ان لو كانت تلاتة N زائد اتنين is odd معناته
+
+414
+00:37:24,230 --> 00:37:27,630
+N is odd تقريبا لنفس المثال اللى احنا شوفناه قبل
+
+415
+00:37:27,630 --> 00:37:35,930
+شوية اثبت لو تلاتة N زائد اتنين is odd then ال N
+
+416
+00:37:39,080 --> 00:37:45,040
+هذه الـB وهذه الـQ وهذه الـQ في بينهم
+
+417
+00:37:45,040 --> 00:37:50,310
+الـimplicationمباشرة تفكر .. شوف يعني أنت عشان
+
+418
+00:37:50,310 --> 00:37:53,470
+نجيبلك إياها أنا مثال على الcontra positive انت
+
+419
+00:37:53,470 --> 00:37:57,170
+جاهز بتقول نجيبها مباشرة لكن انت في سؤال امتحان أو
+
+420
+00:37:57,170 --> 00:38:01,410
+سؤال quiz أو في أي مسألة انت فعليا إذا ما شوفتهاش
+
+421
+00:38:01,410 --> 00:38:04,770
+قبل هيك مش هتعرف بالدائرة ولا بالcontra positive
+
+422
+00:38:04,770 --> 00:38:09,330
+فمباشرة مش مختوح تساوي على الهانش هيك تاخد جلب
+
+423
+00:38:09,330 --> 00:38:13,820
+الرصاص تبعكتمام؟ و بتشتغل بال Direct شو يعني مفهوم
+
+424
+00:38:13,820 --> 00:38:17,460
+N تلاتة is odd؟ يعني تلاتة N زائد اتنين بيديها
+
+425
+00:38:17,460 --> 00:38:23,260
+تساوي اتنين في K زائد واحد اتنين
+
+426
+00:38:23,260 --> 00:38:30,380
+K زائد واحد okay تلاتة N تساوي اتنين K زائد واحد
+
+427
+00:38:30,380 --> 00:38:35,480
+مقص اتنين و تساوي اتنين K مقص واحد معناته ال N
+
+428
+00:38:35,480 --> 00:38:42,660
+بيديها تساوي اتنين K مقص واحد علىتلاتة هل هذي odd؟
+
+429
+00:38:42,660 --> 00:38:47,580
+هل هي odd؟ ماعرفش ماصلتش لصيغة ال odd اللي انا بقى
+
+430
+00:38:47,580 --> 00:38:52,660
+عارفها اللي هي 2k زائد واحد او 2k ماقص واحد
+
+431
+00:38:52,660 --> 00:38:56,860
+وبالتالي ماقدرش وبالتالي ال direct proof ماظبطش
+
+432
+00:38:56,860 --> 00:39:01,840
+معايا ايش الحل؟ مباشرة بتجرب ال contrapositive ايش
+
+433
+00:39:01,840 --> 00:39:08,020
+ال contrapositive؟ هتروح تقولي assume نطق
+
+434
+00:39:08,020 --> 00:39:16,120
+youاللي هي N is even نقطة
+
+435
+00:39:16,120 --> 00:39:19,740
+odd ممتاز
+
+436
+00:39:19,740 --> 00:39:30,440
+هذا بيقدر ان N تساوي 2K وK تنتمي لل Z طبعا خطوة
+
+437
+00:39:30,440 --> 00:39:34,960
+اللي بعد هيكش بده مني هو بده تلاتة N زائد 2 بدي
+
+438
+00:39:34,960 --> 00:39:42,110
+اعمل المعادلة هذهتلاتة ان زائد اتنين تساوي تلاتة
+
+439
+00:39:42,110 --> 00:39:47,130
+في اتنين K عوض عن الان اللي بتقيمتها اتنين K زائد
+
+440
+00:39:47,130 --> 00:39:54,310
+اتنين وتساوي ستة K زائد اتنين تلاتة في اتنين ستة
+
+441
+00:39:54,310 --> 00:40:00,210
+ستة K زائد اتنين خد التلاني العالم المشترك تلاتة K
+
+442
+00:40:00,210 --> 00:40:02,110
+زائد واحد
+
+443
+00:40:08,080 --> 00:40:15,980
+خلصنا احنا وصلنا نمشي Contra positive معناته
+
+444
+00:40:15,980 --> 00:40:22,340
+لما بتكون تلاتة N زائد اتنين is odd حتما اللي ال N
+
+445
+00:40:22,340 --> 00:40:26,100
+هتكون odd يعني عمراش هتلاقيها انها تكون عدد فردي
+
+446
+00:40:26,100 --> 00:40:31,020
+ابتلجأ الشباب دائما لو انت لجيت النظرية هذه غلط لو
+
+447
+00:40:31,020 --> 00:40:37,260
+انا ع سبيل المثالش قلتلكحاصل جامع اي عددين فرديين
+
+448
+00:40:37,260 --> 00:40:38,440
+عدد فردي
+
+449
+00:40:42,810 --> 00:40:46,090
+غلط خط لمثال بيقول اتفضل هاي مثال بيقول ان الكلام
+
+450
+00:40:46,090 --> 00:40:50,710
+هذا غلط، المثال واحد هذا كفيل انه ينفع الكلام اللي
+
+451
+00:40:50,710 --> 00:40:55,730
+بنقوله، ليش؟ المثال مش اثبات، بنسمي احنا
+
+452
+00:40:55,730 --> 00:41:00,230
+counterexample، مثال مبادر، بنصف النظرية اللي احنا
+
+453
+00:41:00,230 --> 00:41:04,150
+بنقولها، انا قاعد بتدعي ان الجمع او حاصل جمع اي
+
+454
+00:41:04,150 --> 00:41:10,110
+عددين فرديينبيعطيني عدد فردي لأ مباشرة قولي غلط
+
+455
+00:41:10,110 --> 00:41:14,010
+واحد و تلاتة أعداد فردية مجبوحهم يساوي أربع عدد
+
+456
+00:41:14,010 --> 00:41:17,830
+زوجي وخلصنا مش بحاجة أنك تروح تكتب الخطوات زي هذه
+
+457
+00:41:17,830 --> 00:41:23,290
+الإثبات الخطوات هذه بنتبعها إما بدنا نثبت وإذا
+
+458
+00:41:23,290 --> 00:41:26,270
+كانت النظرية أو السؤال مكتوب لك approve or
+
+459
+00:41:26,270 --> 00:41:31,110
+disapprove إما اثبت أو انفي المعادلة اللي عندك هذا
+
+460
+00:41:31,110 --> 00:41:33,970
+ال term معناته ضروري تفكر أو تحاول تستحضر لأنه
+
+461
+00:41:33,970 --> 00:41:37,930
+ممكن يكون الحلفي سؤال او في رقم ان الرقم هذا غير
+
+462
+00:41:37,930 --> 00:41:40,610
+صحيح وبالتالي خلاص كفى الله المؤمنين القتال
+
+463
+00:41:40,610 --> 00:41:44,210
+وبالتالي ان اختوح جارة تثنت انت أصلا بتحاول تكون
+
+464
+00:41:44,210 --> 00:41:44,990
+غلط
+
+465
+00:42:15,250 --> 00:42:19,070
+بقول اثبت لو
+
+466
+00:42:19,070 --> 00:42:25,010
+كانت ال M زائد ال N أكبر من خمسين معناته
+
+467
+00:42:25,010 --> 00:42:30,370
+عندك اما ال M أكبر من خمس وعشرين او ال N أكبر من
+
+468
+00:42:30,370 --> 00:42:33,770
+خمس وعشرين فلو كانت اتنين تبقى المعادلة صحيحة لانه
+
+469
+00:42:33,770 --> 00:42:38,870
+بينهم ايش R تبقى المعادلة صحيحة لانه بينهم R ايش
+
+470
+00:42:38,870 --> 00:42:40,350
+أول عدد أكبر من خمسين؟
+
+471
+00:42:42,870 --> 00:42:50,650
+51 اصبت؟ لو بتجسم ال 51 لجزئين يعني حللها لرقمين
+
+472
+00:42:50,650 --> 00:42:57,550
+جماعتهم مع بعض حلل ال 51 ستة و عشرين و خمسة و
+
+473
+00:42:57,550 --> 00:43:03,910
+عشرين واحد منهم هيكون اكبر من خمسة و عشرين سيبني
+
+474
+00:43:03,910 --> 00:43:07,190
+من التاني واحد هيكون اكبر طيب لو قلتلك ستين اكبر
+
+475
+00:43:07,190 --> 00:43:11,510
+من خمسين ولا لا؟الحلل هو 30 30 هذه الاثنين صاروا
+
+476
+00:43:11,510 --> 00:43:16,550
+أكبر من 25 وتبقى المسألة صحيحة 100% لكن الأمثلة زي
+
+477
+00:43:16,550 --> 00:43:21,330
+ما قلنا مابتثبتش الأمثلة بستخدمها عند النفي
+
+478
+00:43:21,330 --> 00:43:27,750
+بستخدمها عند النفي بدك
+
+479
+00:43:27,750 --> 00:43:34,130
+تثبت الكلام هذا هي معناته هي عندك ال B هذه هي ال B
+
+480
+00:43:34,130 --> 00:43:42,450
+وهذه ال QQ compound ال M لو انا بدأ أقول له assume
+
+481
+00:43:42,450 --> 00:43:52,990
+ال B اذا بدك تفترض ال B ايش يعني يعني M زائد ال N
+
+482
+00:43:52,990 --> 00:43:57,870
+أكبر من خمسين تمام next step بدك انت ال M لحاله او
+
+483
+00:43:57,870 --> 00:44:02,450
+ال N لحالها بصبرت معناته ان ال M هتكون أكبر من
+
+484
+00:44:02,450 --> 00:44:07,060
+خمسين ناقصالان نجلف على الطرف التاني او بين جثين
+
+485
+00:44:07,060 --> 00:44:11,760
+اضافت سالب ان للطرفين عشان تبقى المعاجلة صحيحة بس
+
+486
+00:44:11,760 --> 00:44:16,280
+ماوصلتش للصورة اللي انا بدي اياها فعلا و كذلك الان
+
+487
+00:44:16,280 --> 00:44:23,780
+الان هتكون اكبر من خمسين نقص الان بعد هيك و الخمسة
+
+488
+00:44:23,780 --> 00:44:26,600
+عشر اللي بدور عليها ملاش وجود معناته الطريق اللي
+
+489
+00:44:26,600 --> 00:44:31,600
+انا رايح فيها غلط مباشرة افكر نقطة Q
+
+490
+00:44:34,890 --> 00:44:41,070
+assume ال نقطة Q ايش النقطة Q؟ هاي ال Q مصبوط M
+
+491
+00:44:41,070 --> 00:44:50,150
+أكبر من 25 او N أكبر من 25 نفيها ماتوا ال M أقل أو
+
+492
+00:44:50,150 --> 00:45:00,350
+تساوي 25 و ال or هاد نفيها and ال N أقل أو تساوي
+
+493
+00:45:00,350 --> 00:45:01,730
+25
+
+494
+00:45:04,490 --> 00:45:09,430
+خطوة التالية .. ماذا تقول يا مصطفى؟ اه بدك تنفر ال
+
+495
+00:45:09,430 --> 00:45:15,990
+.. بدك تنفر ال Q كلها بدك تنفر .. هاي ال Q .. هاي
+
+496
+00:45:15,990 --> 00:45:22,490
+ال Q بقولك Q M أكبر من خمسة و عشرين and .. and ..
+
+497
+00:45:22,490 --> 00:45:28,050
+عفوا ال R and أكبر من خمسة و عشرين هذه كلها Q دخل
+
+498
+00:45:28,050 --> 00:45:35,720
+عليها هنا فيه دي Morgan lawأم أقل من 25 نفي الأولى
+
+499
+00:45:35,720 --> 00:45:39,860
+الان بتصير or او ال or بتصير and والان أقل او
+
+500
+00:45:39,860 --> 00:45:47,560
+تساوي 25 غلط
+
+501
+00:45:47,560 --> 00:45:52,020
+يا صاحبي غلط شوف انت بينفعش تقتطع النفي على كيفك
+
+502
+00:45:52,020 --> 00:45:58,330
+انت الان بينفعش تقتطع النفي على كيفكلأن مع الـ OR
+
+503
+00:45:58,330 --> 00:46:02,250
+واحدة من التانتين تكفي أن تكون true إذا انت نفيت
+
+504
+00:46:02,250 --> 00:46:07,150
+واحدة طب هي تبقى true تحافظ على المسألة true عشان
+
+505
+00:46:07,150 --> 00:46:10,330
+هيك لازم لما بدك تنفي تنفي الجث بالكامل تنفي ال Q
+
+506
+00:46:10,330 --> 00:46:13,130
+بالكامل قيمة الـ Q تساوي الجث هذا compound
+
+507
+00:46:13,130 --> 00:46:22,850
+proportion فتنفيها بكلها تمام الخطوة اللي بقال هيك
+
+508
+00:46:22,850 --> 00:46:26,190
+بدك
+
+509
+00:46:26,190 --> 00:46:35,350
+تجمعالـ M زائد الـ M أقل أو تساوي خمسة و عشرين
+
+510
+00:46:35,350 --> 00:46:41,810
+زائد الـ M عشان من هذا، تمام؟ بعد ما هي الـ N أقل
+
+511
+00:46:41,810 --> 00:46:49,930
+أو تساوي خمسة و عشرين زائد أقل أو تساوي خمسة و
+
+512
+00:46:49,930 --> 00:46:54,710
+عشرين، تظبط؟ هيك تدرج طبيعي للمسألة من خصيتك تعدي
+
+513
+00:46:54,710 --> 00:46:55,490
+بصلاة
+
+514
+00:46:57,740 --> 00:47:04,340
+كيف أجت؟ حاضر احنا الآن عندنا ال M أقل او تساوي 25
+
+515
+00:47:04,340 --> 00:47:09,140
+صح؟ و إيش أنا بدي؟ بدي M زائد M عشان تبقى المثلة
+
+516
+00:47:09,140 --> 00:47:14,840
+صحيحة لازم أحط ال M لمن؟ للطرفين M زائد M مع تقرار
+
+517
+00:47:14,840 --> 00:47:21,510
+أقل من 25 زائد M، مظبوط؟فما هي ال M أقل من خمسة و
+
+518
+00:47:21,510 --> 00:47:27,190
+عشرين تمام؟ وبالتالي صارت الخمسة و عشرين زائد ال M
+
+519
+00:47:27,190 --> 00:47:31,810
+أقل أو تساوي من خمسة و عشرين زائد خمسة و عشرين
+
+520
+00:47:31,810 --> 00:47:36,990
+مصبوط؟
+
+521
+00:47:36,990 --> 00:47:43,010
+واضحيت؟ مية لمية معناته هذا يؤدي أن ال M زائد ال M
+
+522
+00:47:43,010 --> 00:47:46,330
+أقل أو تساوي خمسين
+
+523
+00:47:48,110 --> 00:47:56,650
+مافي ال B ايش
+
+524
+00:47:56,650 --> 00:48:00,730
+مفهوم ال contrapositive اللي انا وصلتله ان لو كانت
+
+525
+00:48:00,730 --> 00:48:05,270
+ال N زائد ال N أكبر من خمسين معناته حلاجة واحدة من
+
+526
+00:48:05,270 --> 00:48:10,150
+التنتين على الأقل هتكون أكبر من خمسة وعشرينيعني
+
+527
+00:48:10,150 --> 00:48:13,690
+ابيجي الـ Contra Positive عشان يثبت .. انا بثبت
+
+528
+00:48:13,690 --> 00:48:16,670
+الـ Contra Positive عشان اقول ان النظرية اللي فوق
+
+529
+00:48:16,670 --> 00:48:23,650
+هي الأساس .. هي الصحيحة واضح الامور الشخصية؟
+
+530
+00:48:23,650 --> 00:48:31,430
+كمان
+
+531
+00:48:31,430 --> 00:48:31,910
+مثال؟
+
+532
+00:48:42,560 --> 00:48:50,320
+بقولي لو كانت ال N بدها تساوي AB واضح لما بكتب لي
+
+533
+00:48:50,320 --> 00:48:56,440
+F و then هو بريحني من ال B و ال Q بقت هاي ال B
+
+534
+00:48:56,440 --> 00:48:59,820
+then
+
+535
+00:48:59,820 --> 00:49:02,880
+هاي
+
+536
+00:49:02,880 --> 00:49:07,560
+ال Q بقولي
+
+537
+00:49:07,560 --> 00:49:11,140
+بشرط ان ال A و ال B are positive integers
+
+538
+00:49:13,220 --> 00:49:17,460
+تمام؟ a و b positive integers مُعبَر مُعبَر مُعبَر
+
+539
+00:49:17,460 --> 00:49:18,960
+مُعبَر مُعبَر مُعبَر مُعبَر مُعبَر مُعبَر مُعبَر
+
+540
+00:49:18,960 --> 00:49:19,280
+مُعبَر مُعبَر مُعبَر مُعبَر مُعبَر مُعبَر مُعبَر
+
+541
+00:49:19,280 --> 00:49:19,440
+مُعبَر مُعبَر مُعبَر مُعبَر مُعبَر مُعبَر مُعبَر
+
+542
+00:49:19,440 --> 00:49:20,160
+مُعبَر مُعبَر مُعبَر مُعبَر مُعبَر مُعبَر مُعبَر
+
+543
+00:49:20,160 --> 00:49:39,820
+مُعبَر مُعبَر مُعبَر مُعبَر مُعبَ
+
+544
+00:49:43,110 --> 00:49:49,850
+A B بصت مش تسيبني من التفاصيل خلصنا الآن ال A شبهة
+
+545
+00:49:49,850 --> 00:49:55,790
+بدت تكون أقل من كذا معناته بدي أحلل ال N عشان أجيب
+
+546
+00:49:55,790 --> 00:49:58,570
+الجذر بدي أجيب جذر ال N في المسألة ال A موجودة و
+
+547
+00:49:58,570 --> 00:50:05,070
+ال B موجودة صح ولا لأ ال N معناته جذر ال N في ضرب
+
+548
+00:50:05,070 --> 00:50:10,830
+جذر ال N تساوي ايه .. ليش أصغر تساوي لحد اللحظة
+
+549
+00:50:11,650 --> 00:50:19,750
+لحتى اللحظة تساوي، بصبوط؟ طيب، من الكلام هذا ما
+
+550
+00:50:19,750 --> 00:50:28,590
+يتوقع ان ممكن تساوي ايه؟ هو لاحظ لماشي جالي شباب
+
+551
+00:50:28,590 --> 00:50:35,370
+جالي positive integers، واحد positive ولا لا؟
+
+552
+00:50:35,370 --> 00:50:40,050
+الواحد positiveلأ خلّيني أتكلم بس على الواحد واحد
+
+553
+00:50:40,050 --> 00:50:44,590
+positive لأن مابيش اللي يمنع تكون ال A بتتسوى N و
+
+554
+00:50:44,590 --> 00:50:49,550
+ال B بتتسوى واحد أو العكس ماحكاش
+
+555
+00:50:49,550 --> 00:50:54,230
+في السؤال سببها هي A مفتوحة معناته ممكن في واحد من
+
+556
+00:50:54,230 --> 00:50:58,130
+الاحتمال يعني انت ممكن تيجي تقوللي الان انا بقدر
+
+557
+00:50:58,130 --> 00:51:04,950
+اقول لو انا بدي اخصل او بدي اجسم على Nأو بيتجسم
+
+558
+00:51:04,950 --> 00:51:11,430
+على B ايش هتروح تقول ايه جذر ال N في جذر ال N على
+
+559
+00:51:11,430 --> 00:51:18,270
+B بدها تساوي ال A لاحظوا ان انا فعليا مش قادر اخد
+
+560
+00:51:18,270 --> 00:51:22,190
+decision على الرغم انه ممكن هيا اذا انا ضمنت هدول
+
+561
+00:51:22,190 --> 00:51:26,530
+اكبر من واحد اقدر اخد decision فيهم هكون فيهم واحد
+
+562
+00:51:26,530 --> 00:51:31,490
+اقل من الجذر تبع ال N والتاني طبعا هيكون اكبر ولا
+
+563
+00:51:31,490 --> 00:51:37,240
+لايعني الان لو الان الواحد انا مستثنى عندى كان
+
+564
+00:51:37,240 --> 00:51:42,840
+بقدر اجي اقول كل بساطة يعني هذا بيقدى ان ال a اقل
+
+565
+00:51:42,840 --> 00:51:44,160
+او تساوي جذر ال n
+
+566
+00:51:47,650 --> 00:51:51,310
+الـ B أقل أو تساوي جذر الـ N طب لو التنتين اتحققوا
+
+567
+00:51:51,310 --> 00:51:54,710
+مياته بحصوله على الـ N كلام مصبوط طب لو ما اتحققتش
+
+568
+00:51:54,710 --> 00:51:59,490
+واحدة منهم مياته هذه لو كانت هذه False معناته الـ
+
+569
+00:51:59,490 --> 00:52:04,210
+N الـ A أكبر مصبوط وهذه هتكون أقل أو تساوي جذر الـ
+
+570
+00:52:04,210 --> 00:52:07,930
+N جذر الـ N أكبر من جذر الـ N في جذر الـ N هتطلع
+
+571
+00:52:07,930 --> 00:52:12,270
+أكبر من الـ N فظل في عندي مشكلة مش قادر أخد فيها
+
+572
+00:52:12,270 --> 00:52:16,670
+decision 100% انا حاسس ان الطريق سهل وواسطة لكن
+
+573
+00:52:17,400 --> 00:52:19,960
+فيها شغل مش تمام طب تعالى شوف ال contrapositive
+
+574
+00:52:19,960 --> 00:52:27,480
+تبعتها كيف وضعها ايش هفترض نقطة Q ابقى ايش نقطة Q
+
+575
+00:52:27,480 --> 00:52:36,180
+بقى تقول ان ال A أكبر من جذر ال M and ال B أكبر من
+
+576
+00:52:36,180 --> 00:52:41,660
+جذر ال M 100% هو ايش بيقول عماله ال M بدها تساوي
+
+577
+00:52:41,660 --> 00:52:44,840
+ال A في B
+
+578
+00:52:47,840 --> 00:52:52,140
+أي ضرب الـ B بدها تساوي؟
+
+579
+00:52:52,140 --> 00:52:57,440
+أو بلاش خلّيني أعملها هيك زي المثال السابق A أكبر
+
+580
+00:52:57,440 --> 00:53:01,480
+من جذر ال N لو ضربت في B بدي أضرب الطرف التاني في
+
+581
+00:53:01,480 --> 00:53:07,980
+B صح؟ طب و ال B هادم أيه أكبر من جذر ال N؟ عفوا
+
+582
+00:53:07,980 --> 00:53:15,780
+هتكون أكبر من جذر ال N في جذر ال N وهذا وصل أن ال
+
+583
+00:53:15,780 --> 00:53:25,690
+A بيأكبر من .. من الـ N نقطة
+
+584
+00:53:25,690 --> 00:53:33,250
+الـ B و لا لا ايه مدهة .. N تسوى AB ايش نفيها أكبر
+
+585
+00:53:33,250 --> 00:53:40,190
+أو أصغر أكبر أو أصغر خلاص مافيه or انا اتحققت
+
+586
+00:53:40,190 --> 00:53:45,290
+واحدة منهم خلصنا شوفت كيف يا مصطفى كمان مرة شباب
+
+587
+00:53:45,290 --> 00:53:54,170
+الان نفل يساويالـ A أو الـ N تساوي الـ AB نفيها أن
+
+588
+00:53:54,170 --> 00:53:57,630
+الـ A لا تساوي الـ AB الـ N لا تساوي الـ AB إيش
+
+589
+00:53:57,630 --> 00:54:02,290
+يعني؟ اما هتكون أكبر منها أو هتكون أصغر منها أنا
+
+590
+00:54:02,290 --> 00:54:06,330
+قدرت أتحقق أنها أكبر منها ما يعني أنه خلاص حصلت
+
+591
+00:54:06,330 --> 00:54:10,410
+الـ Contrapositive مافيش داعي أفكر بطنرة في التاني
+
+592
+00:54:10,410 --> 00:54:13,630
+مافيش داعي أن أفكر بقى ال condition Contrapositive
+
+593
+00:54:19,560 --> 00:54:23,060
+وبالتالي أنا انتهى البرهان تبعي بقيته بقدر اقول في
+
+594
+00:54:23,060 --> 00:54:26,620
+حالة ان ال N بدي هتساوي ال A بي و ال A بي عبارة عن
+
+595
+00:54:26,620 --> 00:54:30,080
+positive integer معناته ال A اقل او تساوي ال N او
+
+596
+00:54:30,080 --> 00:54:34,880
+ال B اقل او تساوي ال N الكلام مص صعب يا شباب
+
+597
+00:54:34,880 --> 00:54:40,260
+الفكرة هذا الكلام مقنع اكثر من الكلام السادق من ال
+
+598
+00:54:40,260 --> 00:54:44,560
+direct proofوإن كان ظاهر الـ Direct Proof إن أنا
+
+599
+00:54:44,560 --> 00:54:48,880
+ماشي صح وماشي الأمور عايش Sequence بس في شك لما
+
+600
+00:54:48,880 --> 00:54:51,920
+كانت متساوي واحدة وما تبقى مش هساوي إذا في طريقة
+
+601
+00:54:51,920 --> 00:54:56,260
+تانية بمشي معاك بشكل كويس اشتغل فيه بدون أي مشاكل
+
+602
+00:54:56,260 --> 00:54:59,420
+هتلاقي بعض الأحيان أنه في مسائل ممكن تصبط بال
+
+603
+00:54:59,420 --> 00:55:05,320
+Direct و Contrapositive اعتمد على أي واحد فيهم على
+
+604
+00:55:05,320 --> 00:55:10,840
+اللي انت مركز عليه صح 100%على بدك إيه؟ إذا الاتنين
+
+605
+00:55:10,840 --> 00:55:13,320
+أنت مركز عليهم إنه هذا وهذا، إيه أحد الدنيا
+
+606
+00:55:13,320 --> 00:55:18,600
+وخلصنا؟ بس أنا والله عندي شكوك إن ال direct 70% أو
+
+607
+00:55:18,600 --> 00:55:23,040
+80% بينما ال indirect أو ال contrapositive 100% لا
+
+608
+00:55:23,040 --> 00:55:25,900
+والله بعتمد ال 100% و بديش ال 30% بديش أجاذف في
+
+609
+00:55:25,900 --> 00:55:29,200
+الموضوع شوفتوا الفكرة؟ في الامتحان أيش المطموض
+
+610
+00:55:29,200 --> 00:55:33,280
+منيه؟ غالبا مش هقولك direct ولا indirect صاحبي
+
+611
+00:55:33,280 --> 00:55:37,820
+غالبا مش هقولك direct ولا indirect هقولك أثبت
+
+612
+00:55:37,820 --> 00:55:44,110
+وخلصناانت شبك تساوي اكتب اللي بدك هيه فالان تقولي
+
+613
+00:55:44,110 --> 00:55:46,910
+والله كان جذب مافيش كلام في ال .. في عندك اسيوم
+
+614
+00:55:46,910 --> 00:55:50,890
+ومنها انا بفهم انت ايش بدك تعمل فانت بتقرر عشان هي
+
+615
+00:55:50,890 --> 00:55:55,950
+نصيحة إلك مواد الرياضيات مواد البرمجة اكتب برصاص
+
+616
+00:55:55,950 --> 00:55:59,930
+سيبك من قلم الجاف وخل المحايا معاك لأنه ممكن تكتب
+
+617
+00:55:59,930 --> 00:56:03,450
+و تمسح أكتر من مرة فتبقى في عندك متساق تكتب بشكل
+
+618
+00:56:03,450 --> 00:56:11,510
+ألطفففيه موضوع مرتبط بالإثبات
+
+619
+00:56:11,510 --> 00:56:15,510
+الرياضي قبل أن نذهب لـmathematical induction اللي
+
+620
+00:56:15,510 --> 00:56:19,070
+هو بالcontradiction لكن عشان نبقى مساوية الشعبة
+
+621
+00:56:19,070 --> 00:56:23,190
+التانية سنقف لحد الهان تمام و المحاضرة تجاه ال
+
+622
+00:56:23,190 --> 00:56:29,250
+proof by contradiction إثبات بالتناقض إثبات
+
+623
+00:56:29,250 --> 00:56:32,170
+بالتناقض و بعدين نتكلم عن الmathematical induction
+
+624
+00:56:33,650 --> 00:56:40,370
+أخر خطوة بالمثال هذا تمام احنا ايش بنقول قاعدين
+
+625
+00:56:40,370 --> 00:56:43,830
+هنا جذر ال N بتاعي يعني من وين هذي الجذر التماية؟
+
+626
+00:56:43,830 --> 00:56:48,550
+احنا مش افترضنا انه A أكبر من جذر ال N and ال B
+
+627
+00:56:48,550 --> 00:56:54,630
+أكبر من جذر ال N مصبور؟ بناء على نفي ال Q صح؟ 100%
+
+628
+00:56:54,630 --> 00:56:58,570
+الان هو بده مني في المسألة بقول لو كانت ال N بدها
+
+629
+00:56:58,570 --> 00:57:03,580
+تساوي A في B معناته انا لازم اضربA في B و اشوف
+
+630
+00:57:03,580 --> 00:57:09,120
+علاقتهم مع N فروحت ضربت انا بقى اندي هي ال A أكبر
+
+631
+00:57:09,120 --> 00:57:13,060
+من جذر ال N ضربت ال A في B لازم أضرب الطرف التاني
+
+632
+00:57:13,060 --> 00:57:17,880
+في مين؟ في B عشان تبقى المعادلة صحيحة ممتاز انصلت
+
+633
+00:57:17,880 --> 00:57:22,860
+طرف هذا الآن جذر ال N مضروبة في B طب ما هي أساسا
+
+634
+00:57:22,860 --> 00:57:27,820
+ال B هذه أكبر من جذر ال N و في مضروبة معاها جذر ال
+
+635
+00:57:27,820 --> 00:57:34,360
+N؟معناته هتصير ان جذر ال N في B أكبر من جذر ال N
+
+636
+00:57:34,360 --> 00:57:43,180
+في جذر ال N و ال N بخصيتي التعدى بتصير AB أكبر من
+
+637
+00:57:43,180 --> 00:57:47,790
+جذر ال N في جذر ال Nوصلت الفكرة عن عمال ايش بس مش
+
+638
+00:57:47,790 --> 00:57:51,250
+قل هذا هي أخدت أول واحدة أضافت بيه لأقل عفين ضربت
+
+639
+00:57:51,250 --> 00:57:55,650
+بيه لأقل عفين طب ما هي هذي أساسا هي ال بيه أكبر من
+
+640
+00:57:55,650 --> 00:57:58,770
+جذر الأن طب مضربها دي في جذر الأن مضرب في جذر الأن
+
+641
+00:57:58,770 --> 00:58:02,770
+و بتصيب أحصل عندي معادلة من ترى أطراف خاصية التعدي
+
+642
+00:58:02,770 --> 00:58:06,710
+موجودة بينهم فبطبقها و بحصل على المطلوب اللي عندي
+
+643
+00:58:06,710 --> 00:58:10,650
+في أي سؤال تاني شباب الله يدخل عافيا
+
diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/G1lxhtUqbxw_postprocess.srt b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/G1lxhtUqbxw_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..ab0d2347fe65a1561994894f9de5a0c8a6a0aadc
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/G1lxhtUqbxw_postprocess.srt
@@ -0,0 +1,2332 @@
+1
+00:00:21,110 --> 00:00:23,070
+بسم الله والحمد لله والصلاة والسلام علي رسول الله
+
+2
+00:00:23,070 --> 00:00:25,530
+اليوم ان شاء الله شباب هنبدأ نتكلم عن ال
+
+3
+00:00:25,530 --> 00:00:29,210
+mathematical induction لكن بدي اعمل مراجعة سريعة
+
+4
+00:00:29,210 --> 00:00:32,710
+اللي احنا شوفناها سابقا في التقنيات الإثبات
+
+5
+00:00:32,710 --> 00:00:38,930
+الرياضي قولنا هتلاقي في الجزئية السابقة اما هتلاقي
+
+6
+00:00:38,930 --> 00:00:45,450
+مسألة مكتوبة بالشكل التالي if 3n زائد 2 is even
+
+7
+00:00:45,450 --> 00:00:56,490
+then n iseven هذه المسألة من نوع جاهزة وقلنا هذه
+
+8
+00:00:56,490 --> 00:01:04,210
+المسائل بيلزمني دائما احدد B وQ الآن هذه B وهذه Q
+
+9
+00:01:04,210 --> 00:01:18,150
+في المسائل التانية راح يقول لي the sum of two even
+
+10
+00:01:18,150 --> 00:01:19,130
+integers
+
+11
+00:01:21,520 --> 00:01:29,140
+is even integer the sum of two even integers لو
+
+12
+00:01:29,140 --> 00:01:33,960
+أنا سألتك مجموع أي عددين زوجيين هو عبارة عن عدد
+
+13
+00:01:33,960 --> 00:01:40,120
+زوجي إيش الموقع عندك عددين زوجيين معناته if هتكتب
+
+14
+00:01:40,120 --> 00:01:46,360
+هيك x and y are even integers
+
+15
+00:01:49,230 --> 00:01:55,150
+ممتاز هاي المواضيع if then X
+
+16
+00:01:55,150 --> 00:02:02,490
+زائد Y is even integer وهيك
+
+17
+00:02:02,490 --> 00:02:08,030
+بتكون انت حولت ل B و Q طيب طرق الإثبات اللي احنا
+
+18
+00:02:08,030 --> 00:02:14,310
+شوفناها كانت واحدة من ثلاثة واحد ال direct وكنت
+
+19
+00:02:14,310 --> 00:02:18,970
+بقول Assume ال B is true
+
+20
+00:02:21,650 --> 00:02:25,710
+كنت انتظر فرضت مين؟ فرضت الـ B يعني افترضت ان هذه
+
+21
+00:02:25,710 --> 00:02:30,790
+الـ true و من خلالها بدك تصل لمين؟ الـ Q في
+
+22
+00:02:30,790 --> 00:02:35,110
+المسألة هذه بتفترض ان X و Y هم ايضا انتجارين و من
+
+23
+00:02:35,110 --> 00:02:39,330
+خلالهم بدك تصل لمجموعة من O's is even integer هل
+
+24
+00:02:39,330 --> 00:02:44,810
+كانت صميم الحياة direct؟ اتنين يكون Contrapositive
+
+25
+00:02:44,810 --> 00:02:49,630
+كنت
+
+26
+00:02:49,630 --> 00:02:57,080
+بقول له assumeنقطة Q و بدك تسأل لمن؟ هل هذا صحيح؟
+
+27
+00:02:57,080 --> 00:03:04,900
+و بدك تسأل إن نقطة B صحيح؟ إيش نقطة Q هنا؟ M is
+
+28
+00:03:04,900 --> 00:03:13,230
+not even يعني M is oddX زائد Y is not even يعني is
+
+29
+00:03:13,230 --> 00:03:16,930
+odd وهذه الفرضية وبدأت أسفل ألاقيها في الأولى أن
+
+30
+00:03:16,930 --> 00:03:22,250
+تلاتة N زائد اتنين is odd وهذا نفس الكلام X under
+
+31
+00:03:22,250 --> 00:03:29,070
+or Y لإن ما فيها X or Y is odd بصبوط؟ طيب في
+
+32
+00:03:29,070 --> 00:03:37,250
+التالتة في ال contradiction كنت
+
+33
+00:03:37,250 --> 00:03:49,890
+بفرضحلت شغلتين Assume نقطة B and نقطة Q انا اسف B
+
+34
+00:03:49,890 --> 00:03:56,950
+and نقطة Q are true B
+
+35
+00:03:56,950 --> 00:04:00,670
+تتذكر عشان ما تنساش انا مين اللي بفرضها و العكس
+
+36
+00:04:00,670 --> 00:04:04,830
+بتفرض B و نقطة Q تمام تتذكر ان ال B implies Q
+
+37
+00:04:04,830 --> 00:04:10,800
+equivalent to B or نقطة Qهما نفسهم هدول. لأن أنا
+
+38
+00:04:10,800 --> 00:04:15,460
+ما خربت هدول التنتين. بقيتش الخطوة التالية، بدك
+
+39
+00:04:15,460 --> 00:04:19,160
+تشتغل مع أي واحدة منهم و تصل نين لل contradiction،
+
+40
+00:04:19,160 --> 00:04:23,000
+تصل التناقض مع التانية. بدك تمسك أي واحدة فيهم و
+
+41
+00:04:23,000 --> 00:04:27,760
+تصل التناقض مع التانية. هذه المثال كلها كنت بشتغل
+
+42
+00:04:27,760 --> 00:04:30,640
+فيها اما مظبطش معايا direct، بروح ل
+
+43
+00:04:30,640 --> 00:04:33,380
+contrapositive، بروح ل contradiction حسب المثال.
+
+44
+00:04:33,660 --> 00:04:37,250
+المثال الأول واضح، ممشيش معايا direct.لازم
+
+45
+00:04:37,250 --> 00:04:41,010
+Contrapositive او Contradiction المثال التاني لأ
+
+46
+00:04:41,010 --> 00:04:44,670
+بيمشي Direct بيمشي Direct و لو فكرت فيه
+
+47
+00:04:44,670 --> 00:04:50,370
+Contradiction برضه ممكن اصل لنفس النتيجة طيب لكن
+
+48
+00:04:50,370 --> 00:04:56,050
+في نوع من المسائل يا شباب لا في F ولا then ولا
+
+49
+00:04:56,050 --> 00:05:02,730
+بتقدر تصيب ال F و ال then مثل لو اجهجلني مجموع أول
+
+50
+00:05:02,730 --> 00:05:08,730
+ان من الأعدادمجموع أول N من الأعداد الصحيحة
+
+51
+00:05:08,730 --> 00:05:18,710
+الموجبة يساوي N في N زائد 1 على 2 The
+
+52
+00:05:18,710 --> 00:05:34,310
+sum of the first N positive integers is equal to
+
+53
+00:05:34,930 --> 00:05:42,610
+N في N زائد واحد على اتنين لو
+
+54
+00:05:42,610 --> 00:05:46,450
+تفكرنا في المسألة هذه و اتطلعنا فيها و حاولنا نعصر
+
+55
+00:05:46,450 --> 00:05:52,190
+دماغنا يانين اشمال بحيث اننا نديه ب F و then مش
+
+56
+00:05:52,190 --> 00:05:57,230
+هتقدر تصيغ F و then صحيحة ليش؟ لأنه أول ما بقعد
+
+57
+00:05:57,230 --> 00:06:01,060
+بتكلم على seriesمن الأرقام ماتتكلمش على واحد او
+
+58
+00:06:01,060 --> 00:06:05,020
+اتنين او تلاتة انك تفرض صوتهم بكل بساطة يعني احنا
+
+59
+00:06:05,020 --> 00:06:08,280
+في الأمثل السادقة كلها اللي مرت علينا كان كتير
+
+60
+00:06:08,280 --> 00:06:12,120
+نبقى بتتكلم على متغيرين ولا لأ اما بيقولي هاجأ قد
+
+61
+00:06:12,120 --> 00:06:15,580
+واحد قد واحد even او اتنين قد او اتنين even وفي
+
+62
+00:06:15,580 --> 00:06:18,760
+صورة معينة أنا ماكنت بثبتها بس الانجهة بتتكلم على
+
+63
+00:06:18,760 --> 00:06:24,230
+N من الأعدادسيقونس طويلة، ممكن تكون مليون رقم،
+
+64
+00:06:24,230 --> 00:06:27,990
+وممكن تكون خمسة، وبتعرف مع أي أنا اللي بدي أشتغل،
+
+65
+00:06:27,990 --> 00:06:30,410
+مع أي أنا اللي بدي أشتغل، وإيش الصغير اللي بدي
+
+66
+00:06:30,410 --> 00:06:35,050
+أتعامل معاها، مين بي .. مين بي .. مين كيو؟ مش حد
+
+67
+00:06:35,050 --> 00:06:40,110
+ولا جيهاعشان هيك في عندنا تقنية اسمها الـ
+
+68
+00:06:40,110 --> 00:06:43,070
+Mathematical induction أو الاستقراء الرياضي البعض
+
+69
+00:06:43,070 --> 00:06:46,470
+بيسميها الاستنباط الرياضي مش قضية كتير في الترجمة
+
+70
+00:06:46,470 --> 00:06:51,610
+استنباط استقرار الفكرة أنه أنا دايما بدي أنظر إلى
+
+71
+00:06:51,610 --> 00:06:57,050
+ما بعد المجموع هذا الآن لو أنا جيت فألتك و قلتلك
+
+72
+00:06:57,050 --> 00:07:03,990
+مجموع أول تلت أعداد صحيحة موجبة يساوي تلاتة في
+
+73
+00:07:03,990 --> 00:07:05,290
+أربعة على اتنين
+
+74
+00:07:09,030 --> 00:07:12,290
+أجمع الأرقام اللي أنا بقولك عليها مجموع أول تلات
+
+75
+00:07:12,290 --> 00:07:18,570
+أعداد موجبة تمام؟ يساوي تلاتة في أربعة على اتنين
+
+76
+00:07:18,570 --> 00:07:26,270
+ستة واحد زائد اتنين هي تلاتة زائد تلاتة ستة مجموع
+
+77
+00:07:26,270 --> 00:07:32,030
+أول عشر أعداد موجبة يساوي عشرة في احداشر على اتنين
+
+78
+00:07:32,030 --> 00:07:42,900
+سهلة لاحظت؟مجموع أول ميت عدد 100 في 101 على كليل
+
+79
+00:07:42,900 --> 00:07:46,520
+.. هيك صارت المسألة .. طيب المسألة هذه لحظة كل ما
+
+80
+00:07:46,520 --> 00:07:49,980
+بتكلم عن عددطب ما هي العداد أساسا غير منتهية
+
+81
+00:07:49,980 --> 00:07:53,740
+العداد الصحيح الموجب اللي أنا بتكلم عليها يعني غير
+
+82
+00:07:53,740 --> 00:07:57,280
+منتهية طب كيف بدي أثبتها؟ كيف بدي أحط صورة؟ كيف
+
+83
+00:07:57,280 --> 00:07:59,920
+بدي أحط limit؟ هذا اللي هيتكلموا .. هيتعلموا في ال
+
+84
+00:07:59,920 --> 00:08:03,020
+mathematical induction فكرة ال mathematical
+
+85
+00:08:03,020 --> 00:08:10,110
+induction يا شباب زي واحد بيطلع درج غير منتهيبيطلع
+
+86
+00:08:10,110 --> 00:08:14,870
+كل درج غير ممتهي كل ما بيطمأنى على الجدام بيحس ان
+
+87
+00:08:14,870 --> 00:08:18,570
+الدرج ايش بيشوف نهاية لكنه نهاية دي وهمية لما بيصل
+
+88
+00:08:18,570 --> 00:08:26,030
+لعندها بلاقس الدرج ايش ممتن زى ايش زى الصحراء
+
+89
+00:08:26,030 --> 00:08:29,010
+والميه لما بتكون تلفان او بتكون خايف بتشوف اللي هو
+
+90
+00:08:29,010 --> 00:08:33,410
+مش نهاية بس طالما في عندك كدف وبتشتغل عليه او عارف
+
+91
+00:08:33,410 --> 00:08:36,790
+انت هو اللي بتبقي اتجاهك تتحرك مش هيتهمك جداش
+
+92
+00:08:36,790 --> 00:08:41,250
+المسافة طويلة ولاش رايكوأنا ماتخافش، لأنك انت عارف
+
+93
+00:08:41,250 --> 00:08:46,190
+وين هدفك، لكن إذا أنت في الصحراء أو في البحر مرعوب
+
+94
+00:08:46,190 --> 00:08:50,530
+تمام؟ إنك أنا هموت من غرج أو هموت من عطش في
+
+95
+00:08:50,530 --> 00:08:54,770
+الصحراء، هتموت من الخوف، مش هتموت من العرج ولا من
+
+96
+00:08:54,770 --> 00:08:59,090
+الشيوخ، من العطش ولا من الغرج، في الأخر، إيش
+
+97
+00:08:59,090 --> 00:09:03,370
+الحقيقة الواقعة، الحقيقة اللي عندك؟ الحقيقة في
+
+98
+00:09:03,370 --> 00:09:08,070
+الدرج في السلل هذاانت واقف على درجة حقيقية و بدك
+
+99
+00:09:08,070 --> 00:09:12,230
+تتحرك .. ليش؟ للدرجة التالية .. مظلوك ولا لا؟ و كل
+
+100
+00:09:12,230 --> 00:09:15,630
+ما تصل درجة فيه كمان وراها .. كمان درجة .. هذا هو
+
+101
+00:09:15,630 --> 00:09:18,130
+ال mathematical induction .. دايما في .. بشوف اللي
+
+102
+00:09:18,130 --> 00:09:21,510
+في عيني دي .. كل ما بصر مرحلة .. بشوف على الأقل
+
+103
+00:09:21,510 --> 00:09:26,510
+next step طلعتها .. تمام؟ و إذا أنا قدرت أعمل
+
+104
+00:09:26,510 --> 00:09:33,370
+برهان .. أعمل برهان .. إذا الأن كانت صحيحة ..
+
+105
+00:09:33,370 --> 00:09:37,590
+تمام؟وقدرت أشوف إن الـ N زائد واحد اللي وراها
+
+106
+00:09:37,590 --> 00:09:41,930
+صحيحة بيكون الأمور تمام 100% بمعنى آخر هانا قاعد
+
+107
+00:09:41,930 --> 00:09:45,250
+بقولك في المثال مجموع أول N من الأعداد الموجبة
+
+108
+00:09:45,250 --> 00:09:48,930
+طبعا عشان أثبتها .. بديش أتكلم عن الـ N .. الـ N
+
+109
+00:09:48,930 --> 00:09:52,310
+غير منتهية الـ sequence هي غير منتهية إذا أثبتت إن
+
+110
+00:09:52,310 --> 00:09:58,170
+النظرية دي بتبقى صحيحة للـ N زائد واحد فخلصنا لأن
+
+111
+00:09:58,170 --> 00:10:02,810
+كل منصة اللي limit في رقم على الأقل في رقم واحد
+
+112
+00:10:02,810 --> 00:10:06,450
+أكبر منه لو زائد plus oneهنشوف إيش بدنا نسوي
+
+113
+00:10:06,450 --> 00:10:17,510
+الإثبات الرياضي بيعتمد
+
+114
+00:10:17,510 --> 00:10:22,510
+على predicate و غالبا ما اتكلم على natural numbers
+
+115
+00:10:22,510 --> 00:10:28,670
+إيش ال predicate؟ P of .. ال predicate function P
+
+116
+00:10:28,670 --> 00:10:34,110
+of X كل ال P of X هذهأنا بقدرش أتكلم عليها أو
+
+117
+00:10:34,110 --> 00:10:39,090
+بديهاش value إلا لو حددت قيمة الـ X تمام، وهيك
+
+118
+00:10:39,090 --> 00:10:43,590
+صارت predicate function أو عمّمت على كل ال
+
+119
+00:10:43,590 --> 00:10:48,850
+integrals وهيك صارت quantifier بصبت؟ وبهيك بصير
+
+120
+00:10:48,850 --> 00:10:56,690
+بقدر أديه أياش value باجي بقول والله B of X أكبر
+
+121
+00:10:56,690 --> 00:11:05,120
+أو تساوي صفر for all X كان تميل الـ Z Plustrue
+
+122
+00:11:05,120 --> 00:11:10,980
+true و لا لأ true او سيدي ها برضه بتبقى true مافيش
+
+123
+00:11:10,980 --> 00:11:18,120
+مشكلة في الموضوع الآن او اجي اقول بيقوه تلاتة
+
+124
+00:11:18,120 --> 00:11:21,080
+بتحقق المعادلة دي ولا بتحققهاش بتحققها بقدر اقول
+
+125
+00:11:21,080 --> 00:11:25,730
+عليها true او false لكن بيقوه صفرلأ تحققها
+
+126
+00:11:25,730 --> 00:11:28,830
+وبالتالي false وبالتالي لما بتكلم على mathematical
+
+127
+00:11:28,830 --> 00:11:33,110
+induction بتكلم على predicate function وانا بدي
+
+128
+00:11:33,110 --> 00:11:38,190
+استفيد منها الشغل اللي هيكون شغل بسيط جدا معناته
+
+129
+00:11:38,190 --> 00:11:41,990
+هو عماله بتديك propositional function P of N
+
+130
+00:11:41,990 --> 00:11:46,910
+وبيقولك اثبتها ان ال propositional function هذه
+
+131
+00:11:46,910 --> 00:11:51,400
+صحيحة او حقيقة لكل الاعدادالمماتلة حسب الـ
+
+132
+00:11:51,400 --> 00:11:54,280
+definition أو الـ domain اللي عندك عشان تثبت
+
+133
+00:11:54,280 --> 00:11:58,460
+الكلام هذا صح بيلزم الخطوة أقم واحد اللي بنسميها
+
+134
+00:11:58,460 --> 00:12:04,020
+ال basic step تثبت P of Zero is it true؟ تثبت P of
+
+135
+00:12:04,020 --> 00:12:08,680
+Zero is it true؟ والـ Zero هي يا شباب بتمثل الـ
+
+136
+00:12:08,680 --> 00:12:14,460
+first element in the sequence
+
+137
+00:12:18,110 --> 00:12:22,170
+أول element في الـ sequence اللي عندك مين أول
+
+138
+00:12:22,170 --> 00:12:24,430
+element؟ تعالى نرزقى على المثال اللي كتبته قبل
+
+139
+00:12:24,430 --> 00:12:30,890
+شوية مجموع أول n من الأعداد الصحيحة الموجبة أو من
+
+140
+00:12:30,890 --> 00:12:37,170
+الأعداد الطبيعية يساوي n في n زائد 1 على 2 مين ال
+
+141
+00:12:37,170 --> 00:12:42,750
+zero؟ ال واحد لأن أول element في ال sequence عندك
+
+142
+00:12:42,750 --> 00:12:46,070
+واحد باشي بقول P of واحد
+
+143
+00:12:48,650 --> 00:12:54,850
+P of 1 is true P of 1 بتقول أن مجموع الواحد يساوي
+
+144
+00:12:54,850 --> 00:13:01,630
+واحد في واحد زائد واحد على اتنين N في N زائد واحد
+
+145
+00:13:01,630 --> 00:13:05,270
+ولمّا بقول مجموع أول element واحد فيك يقول طب هو
+
+146
+00:13:05,270 --> 00:13:07,470
+بينفع أقول أنا مجموع أول element؟ أه بينفع لأنه
+
+147
+00:13:07,470 --> 00:13:13,370
+بنجمعله صفركمحايل جامعي وبالتالي هذه تساوي واحد
+
+148
+00:13:13,370 --> 00:13:16,970
+هذه بتسميها احنا ال base step الدرجة الأولى اللى
+
+149
+00:13:16,970 --> 00:13:21,250
+في السلن هذا حطيت ايجلك واتأكدت ان الدرجة متينة
+
+150
+00:13:21,250 --> 00:13:26,830
+ماقدرش اطلع لل next step من وراها فلازم تثبتها و
+
+151
+00:13:26,830 --> 00:13:33,310
+ال B of N هذه ال B of Zero هذههتتغير قيمة الـ Zero
+
+152
+00:13:33,310 --> 00:13:37,890
+حسب المسألة المفروض لكن لو انت كتبت بي أوف زيرو
+
+153
+00:13:37,890 --> 00:13:43,570
+كتبتلي بي أوف زيرو هيك is it true؟ وبعدين تقولي
+
+154
+00:13:43,570 --> 00:13:46,490
+ليش؟ بيدك تثبتلي تكتبلي الجملة هذه في المثال
+
+155
+00:13:46,490 --> 00:13:49,590
+السادق احنا هنعيد المثال بيقولي اكتبه بالتفصيل
+
+156
+00:13:49,590 --> 00:13:53,430
+بمعنى انك بيدك تثبت ال base تقولي انه فعليا هذا
+
+157
+00:13:53,430 --> 00:14:01,500
+كلام صحيح لأول element الخطوة التاليةبداك تفترض أن
+
+158
+00:14:01,500 --> 00:14:06,300
+الـ BN is true اللي هو ما أعطاك إياه تفترض أن
+
+159
+00:14:06,300 --> 00:14:11,980
+النظرية اللي أعطاك إياها صحيحة و تشوف هل النظرية
+
+160
+00:14:11,980 --> 00:14:16,680
+هذه صحيحة لل N زائد 1 يعني لو أضفت كمان element
+
+161
+00:14:16,680 --> 00:14:20,100
+على ال sequence element من نفس فصيلة ال sequence
+
+162
+00:14:20,100 --> 00:14:22,980
+مش element من هن دي لو أضفت كمان element من ال
+
+163
+00:14:22,980 --> 00:14:26,080
+sequence هذه على المجموع يبقى صحيح ولا لا يبقى
+
+164
+00:14:26,080 --> 00:14:31,390
+صحيح؟إذا وصلت من الـ B of N وصلت إن الـ BN is true
+
+165
+00:14:31,390 --> 00:14:34,530
+بي أن زاد واحد is true معناته النظرية هذه بتكون
+
+166
+00:14:34,530 --> 00:14:38,290
+هاش صحيحة و بقرادي بيسميها ال inductive step أو
+
+167
+00:14:38,290 --> 00:14:41,750
+الخطوة الاستقرائية و من ثم بدأوا حكتوا ب
+
+168
+00:14:41,750 --> 00:14:45,450
+conclusion إن النظرية المعبرة فوق معبرة فوق نظرية
+
+169
+00:14:45,450 --> 00:14:49,920
+صحيحةتمام؟ او الخاتمة و طبعا هذه ديباجة دائما
+
+170
+00:14:49,920 --> 00:14:53,600
+هتكون موجودة معناته ان مجموع أول n من الأعداد
+
+171
+00:14:53,600 --> 00:14:58,680
+الصحيحة الموجبة يساوي n في n زائد واحد على اتنين
+
+172
+00:14:58,680 --> 00:15:03,860
+is true for any positive n for any positive n
+
+173
+00:15:03,860 --> 00:15:12,020
+وخلينا نبدأ بالمثال مش مشكلة نرجع المرة تانية نبدأ
+
+174
+00:15:12,020 --> 00:15:13,220
+بالمثال اللي حكينا عليه
+
+175
+00:15:17,490 --> 00:15:21,530
+خلّينا نبدأ بالمثال اللي حكينا عليه الأولش المثال
+
+176
+00:15:21,530 --> 00:15:29,390
+كان بيقول مجموع أول n من الأعداد الطبيعية يساوي n
+
+177
+00:15:29,390 --> 00:15:35,170
+في n زائد 1 على 2 خطوة رقم 1 جلنا شباب اللي
+
+178
+00:15:35,170 --> 00:15:36,610
+سميناها ال basic step
+
+179
+00:15:42,620 --> 00:15:45,620
+ماذا تريد أن تثبت؟ تريد أن تثبت أن B of 0 هو
+
+180
+00:15:45,620 --> 00:15:50,220
+الحقيقة تريد أن تثبت أن أول خطوة في الـsequence
+
+181
+00:15:50,220 --> 00:15:57,720
+صحيحة B of 0 هو الحقيقة طبعا هنا الـ0 دلالة على
+
+182
+00:15:57,720 --> 00:16:01,120
+أنك تتكلم على أول قيمة أنا the animal أنك تكتبلي
+
+183
+00:16:01,120 --> 00:16:06,040
+ال value تبعتها تمام؟ عشان أنت ماتوهش من وين جبت
+
+184
+00:16:06,040 --> 00:16:11,830
+الواحد هيا؟ من ال sequence اللي عنديلأن هذي و كأنه
+
+185
+00:16:11,830 --> 00:16:19,350
+هيك بيقول مجموع ال I equal واحد ل N N
+
+186
+00:16:19,350 --> 00:16:26,510
+في N زائد واحد على اتنين ايش اول element؟ ال I اول
+
+187
+00:16:26,510 --> 00:16:33,830
+element ال واحد تمام is it true؟ ليش is it true؟
+
+188
+00:16:33,830 --> 00:16:39,650
+هتكون واحد يساوي ال واحد هذه المفروض انها تساوي
+
+189
+00:16:43,710 --> 00:16:48,910
+زائد واحد على اتنين وتساوي واحد في اتنين على اتنين
+
+190
+00:16:48,910 --> 00:16:53,870
+وتساوي واحد معناته P of واحد is true P of واحد is
+
+191
+00:16:53,870 --> 00:16:58,150
+true الخطوة
+
+192
+00:16:58,150 --> 00:17:07,350
+التانية اللي سمناها ال inductive step و
+
+193
+00:17:07,350 --> 00:17:10,030
+في ال inductive step ايش تساوي انك تفرض
+
+194
+00:17:12,500 --> 00:17:18,720
+B of N is true ايش يعني الـ B of N is true؟ هاي
+
+195
+00:17:18,720 --> 00:17:23,560
+الـ B of N تبعتك هذه
+
+196
+00:17:23,560 --> 00:17:27,800
+الـ B of N تمام؟
+
+197
+00:17:27,800 --> 00:17:31,260
+بيحتفرض ان الـ B of N is true وش بك تثبت؟ ايش بك
+
+198
+00:17:31,260 --> 00:17:36,020
+تثبت؟ بدك تشوف B of N زائد واحد is true or not
+
+199
+00:17:36,020 --> 00:17:40,980
+يعني الآن الأصل من هذه فهم؟ أنا بس بدك تقولك شغلة
+
+200
+00:17:40,980 --> 00:17:54,400
+بسيطةthen we have to show that b of n زائد واحد is
+
+201
+00:17:54,400 --> 00:17:59,120
+true too يعني
+
+202
+00:17:59,120 --> 00:18:04,300
+هذه الجزئية اللي احنا بندنشتغل عليها الآنالمفروض
+
+203
+00:18:04,300 --> 00:18:08,980
+انا بخرج هذه و بدي اشوف هل النظرية هذه بتتحقق لو
+
+204
+00:18:08,980 --> 00:18:11,920
+انا اضافت كمان element على ال sequence مش اي
+
+205
+00:18:11,920 --> 00:18:14,600
+element ال next element لو اضافته على ال sequence
+
+206
+00:18:14,600 --> 00:18:17,880
+تبقى صحيحة ولا لأ؟ شو يعني اضافة كمان element على
+
+207
+00:18:17,880 --> 00:18:23,440
+ال sequence هذا يا شباب؟ يعني مجموع أول n زائد
+
+208
+00:18:23,440 --> 00:18:30,340
+واحد من الإعداد يساوين زائد واحد مضروبة فيه ان
+
+209
+00:18:30,340 --> 00:18:35,360
+زائد واحد زائد واحد يعني بتعمل replacement لكل ان
+
+210
+00:18:35,360 --> 00:18:39,660
+بان زائد واحد يعني بين جثين ال target تبعنا هذا
+
+211
+00:18:39,660 --> 00:18:42,160
+بتكتب على الهانش هذا كل مرة الكلام مش لازم تكتبه
+
+212
+00:18:42,160 --> 00:18:46,460
+انت بتكتب على الهانش مهنت الصورة اللي انا بدي
+
+213
+00:18:46,460 --> 00:18:52,180
+اياها واحد زائد اتنين زائد تلاتةزائد N زائد واحد
+
+214
+00:18:52,180 --> 00:18:59,860
+يساوي N زائد واحد في N زائد واحد زائد واحد على
+
+215
+00:18:59,860 --> 00:19:05,820
+اتنين وهذا يصبح N زائد اتنين بصبوط هذا ليس الاثبات
+
+216
+00:19:05,820 --> 00:19:09,620
+هذا ليس الاثبات هذا الخطوة هذا الشكل اللي انت
+
+217
+00:19:09,620 --> 00:19:14,020
+بتاكيها و هقولك مثال بسيط كله بنعرفه و توحك هنا
+
+218
+00:19:14,020 --> 00:19:18,100
+كمان مرة لما تكون في الصحراء انت او في البحر و مش
+
+219
+00:19:18,100 --> 00:19:23,140
+عارف هدفكممكن تضيع، ولا لا، تروح يمين أو تروح
+
+220
+00:19:23,140 --> 00:19:27,780
+شمال، في حد بيسبح فيكوا شباب؟ تمام، المفروض علموك
+
+221
+00:19:27,780 --> 00:19:30,700
+في السباحة .. المفروض علموك في السباحة كل فترة و
+
+222
+00:19:30,700 --> 00:19:34,320
+تانية ترفع رأسك و تتطلعك .. ورايح .. ورايح،
+
+223
+00:19:34,320 --> 00:19:38,420
+باتجاهك، على هدفك، عشان تعدل المصير اللي روحك، لو
+
+224
+00:19:38,420 --> 00:19:41,380
+أنت من الناس اللي زينا أيام بتحط رأسها في الماء أو
+
+225
+00:19:41,380 --> 00:19:44,760
+بتبلت جدف، هتلاقي حالك إيش روحت شمال أو روحت يمين
+
+226
+00:19:45,470 --> 00:19:48,990
+تمام؟ وبالتالي يجب أن يكون عندك رؤية أين أريد أن
+
+227
+00:19:48,990 --> 00:19:51,930
+أذهب هذا هو الرؤية التي نتحدث عنها هذا هو الهدف
+
+228
+00:19:51,930 --> 00:19:56,430
+الذي أريد أن أحصل عليه الذي أريد أن أشاهده تمام؟
+
+229
+00:19:56,430 --> 00:20:00,390
+نعود مرة أخرى إذا كان هذا الشكل الذي أريده إذا كان
+
+230
+00:20:00,390 --> 00:20:05,230
+هذا الشكل الذي أريده إذا كان هذا الشكل اللي أريده
+
+231
+00:20:05,230 --> 00:20:07,750
+إذا كان هذا الشكل اللي أريده إذا كان هذا الشكل
+
+232
+00:20:07,750 --> 00:20:07,890
+اللي أريده إذا كان هذا الشكل اللي أريده إذا كان
+
+233
+00:20:07,890 --> 00:20:13,090
+هذا الشكل اللي أريده إذا كان هذا الشكل
+
+234
+00:20:15,920 --> 00:20:23,220
+ن في ن زائد واحد على اتنين مصبوط؟ هذا الفرضية لما
+
+235
+00:20:23,220 --> 00:20:24,860
+انا بقول بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+236
+00:20:24,860 --> 00:20:25,080
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+237
+00:20:25,080 --> 00:20:26,060
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+238
+00:20:26,060 --> 00:20:26,680
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+239
+00:20:26,680 --> 00:20:27,940
+بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه بيه
+
+240
+00:20:27,940 --> 00:20:28,540
+بيه بيه بيه بيه بيه بيه بيه
+
+241
+00:20:43,200 --> 00:20:46,940
+أنا اخترق الـ Next Element في الـ Sequence العدد
+
+242
+00:20:46,940 --> 00:20:50,840
+اللي بيجي ورا الـ N مباشرة في الـ Sequence تمام؟
+
+243
+00:20:50,840 --> 00:20:55,780
+ورا الـ N ايش بيجي؟ N زاد واحد و بما أني اضفته
+
+244
+00:20:55,780 --> 00:21:02,520
+يعني معناته لازم اضيفه على الطرف التاني عشان تبقى
+
+245
+00:21:02,520 --> 00:21:08,160
+المعادلة صحيحة و لا او بين جثين عشان احنا ماتتوهش
+
+246
+00:21:08,160 --> 00:21:10,860
+نكتب شغلة بسيطة Add
+
+247
+00:21:12,780 --> 00:21:21,660
+ن زائد واحد وهذا يؤدي واحد زائد اتنين زائد تلاتة
+
+248
+00:21:21,660 --> 00:21:31,100
+زائد ان زائد ان زائد واحد يساوي ان فان زائد واحد
+
+249
+00:21:31,100 --> 00:21:38,460
+على اتنين زائد ان زائد واحدالمسألة المفروض تكون
+
+250
+00:21:38,460 --> 00:21:42,140
+خلصة بسبب مسألة حساب بسيطة بكل معينة الكلمة ايش
+
+251
+00:21:42,140 --> 00:21:46,980
+اللي عندنا هنا؟ انا رقمين بدي اجمعهم وفي مقام هي
+
+252
+00:21:46,980 --> 00:21:53,160
+تبدأ واحدة المقامات ولا لأ؟ وهذه تساوي خد التنين
+
+253
+00:21:53,160 --> 00:21:58,600
+عين المشترك في المقام تصير في عندي N ثم N زائد
+
+254
+00:21:58,600 --> 00:22:07,270
+واحد زائد اتنين ثم N زائد واحد مظبوط شباب؟صح؟ ولا
+
+255
+00:22:07,270 --> 00:22:09,770
+بيقول كيف احنا جيبناها بيقول احنا كيف جيبناها مش
+
+256
+00:22:09,770 --> 00:22:16,410
+مشكلة الآن لما بتوحد المقالات تمام بتدور على
+
+257
+00:22:16,410 --> 00:22:20,470
+الهامل المشترك بين التنين او المضاعف المشترك
+
+258
+00:22:20,470 --> 00:22:25,890
+الأكبر الأصغر بين التنين المضاعف المشترك الأصغر ما
+
+259
+00:22:25,890 --> 00:22:30,310
+بين التنين تنين و واحد المضاعف الأصغر المشترك تنين
+
+260
+00:22:30,310 --> 00:22:34,690
+الآن بتجسم اتنين على اتنين واحد تضربها في البسط و
+
+261
+00:22:34,690 --> 00:22:41,180
+بتضيفهم هنا1 زائد 1 زائد 2 على 1 عشان ماحدش يخربط
+
+262
+00:22:41,180 --> 00:22:46,080
+من هذا المقام تبعها 1 2 على 1 2 تضربها في البصمة و
+
+263
+00:22:46,080 --> 00:22:49,620
+تجمعها للمسألة اللي عندك هنا حسب الإشارة اللي عندك
+
+264
+00:22:50,830 --> 00:22:55,290
+تساوى المسألة هي بس بدي شوية ترتيب هيك ادخل ال N
+
+265
+00:22:55,290 --> 00:22:59,850
+على الجوص تصبح عندك N في N N تربيع N في N N في
+
+266
+00:22:59,850 --> 00:23:03,930
+واحد N اتنين في N زائد اتنين و تساوى صار في عندي N
+
+267
+00:23:03,930 --> 00:23:09,350
+تربيع زائد N زائد اتنين N زائد اتنين الكل على
+
+268
+00:23:09,350 --> 00:23:18,170
+اتنين وهذه تساوى على اتنين N تربيع زائد
+
+269
+00:23:21,200 --> 00:23:26,720
+زائد اتنين؟ زائد اتنين؟ زائد اتنين؟ زائد اتنين؟
+
+270
+00:23:26,720 --> 00:23:26,900
+زائد اتنين؟ زائد اتنين؟ زائد اتنين؟ زائد اتنين؟
+
+271
+00:23:26,900 --> 00:23:31,180
+زائد اتنين؟ زائد اتنين؟ زائد اتنين؟ زائد اتنين؟
+
+272
+00:23:31,180 --> 00:23:32,340
+زائد اتنين؟ زائد اتنين؟ زائد اتنين؟ زائد اتنين؟
+
+273
+00:23:32,340 --> 00:23:36,300
+زائد اتنين؟ زائد اتنين؟ زائد اتنين؟ زائد اتنين؟
+
+274
+00:23:36,300 --> 00:23:45,120
+زائد اتنين؟ زائد اتنين؟ زائد اتنين؟ زائد اتنين؟ثم
+
+275
+00:23:45,120 --> 00:23:50,460
+و هنديها المعاملة التالت اتنين اللي هي واحد في
+
+276
+00:23:50,460 --> 00:23:56,500
+اتنين تبقى لنا ناخد الإشارات ليش زايد زايد؟ لأنه
+
+277
+00:23:56,500 --> 00:24:04,040
+الآن هذا قيمة تلاتة و هذه موجة، معناته موجة و
+
+278
+00:24:04,040 --> 00:24:12,000
+موجة، معناته هذا تساوي N زائد واحد في N زائد اتنين
+
+279
+00:24:13,260 --> 00:24:20,480
+على 2 وهي ستكون P of N زائد واحد خلص البرهان يا
+
+280
+00:24:20,480 --> 00:24:26,680
+صاحبي هذه الخطوة التانية لاحظ كل الحل في الخطوة
+
+281
+00:24:26,680 --> 00:24:30,840
+التانية يا شباب الخطوة التالفة كلامها بسيط الخطوة
+
+282
+00:24:30,840 --> 00:24:37,420
+الرقم ثلاثة هي ال conclusion معناته
+
+283
+00:24:37,420 --> 00:24:43,880
+the sum او تكتب القرن القرن هذابتكتب المعادلة عادي
+
+284
+00:24:43,880 --> 00:24:51,320
+زي ما هي 1 زائد 2 زائد n equal n في n زائد 1 على 2
+
+285
+00:24:51,320 --> 00:24:58,360
+is it true for any positive integer n حسب المعادلة
+
+286
+00:24:58,360 --> 00:25:02,320
+وحسب المعادلة المكتوبة عندك عشان ايه بقولتلك اللي
+
+287
+00:25:02,320 --> 00:25:06,080
+تحت هذه دي budget ثابت مش هتصور فيها ولا إشي وال
+
+288
+00:25:06,080 --> 00:25:10,470
+first stepلأن مافيش فيها .. مافيش فيها شغل كتير،
+
+289
+00:25:10,470 --> 00:25:13,950
+شغلك فعليا وين؟ في الخطوة التانية، في الـ
+
+290
+00:25:13,950 --> 00:25:14,550
+inductive step
+
+291
+00:25:34,680 --> 00:25:37,180
+تعالى الأمور واضحة يا شباب تمام؟ في المثال هذا
+
+292
+00:25:37,180 --> 00:25:41,720
+تعالى نشوف .. طبعا ال conclusion حاولت اتفرج بين
+
+293
+00:25:41,720 --> 00:25:45,260
+المعادلات بقى مشكلة طيب تعالى نشوف المثال اللي
+
+294
+00:25:45,260 --> 00:25:50,220
+احنا فشجناه هذا ايش المثال هذا بيقول ايه؟ بيقول
+
+295
+00:25:50,220 --> 00:25:59,860
+اثبت ان مجموع اول K من ال odd integers is equal to
+
+296
+00:25:59,860 --> 00:26:01,040
+the square of
+
+297
+00:26:04,970 --> 00:26:16,230
+زائد تلاتة زائد خمسة زائد بكيف odd integer equal
+
+298
+00:26:16,230 --> 00:26:22,750
+to كتر بيه؟ ليش أنا كتبت هيك الشباب؟ سبتلك إيادي
+
+299
+00:26:22,750 --> 00:26:27,910
+فاضية؟ لأنه احنا بنتكلم عن أعداد فردية، صح؟ والعدد
+
+300
+00:26:27,910 --> 00:26:34,920
+الفردي له ثورتين إما اتنين K زائد واحدأو اتنين K
+
+301
+00:26:34,920 --> 00:26:40,040
+ناقص واحد، مظبوط؟ طيب، الآن، هلأ، بدك تقوى أي صورة
+
+302
+00:26:40,040 --> 00:26:44,380
+من العدد الفردي؟ لو كان بتتكلم على عدد زودي،
+
+303
+00:26:44,380 --> 00:26:50,920
+ماعنديش مشكلة، تمام؟ بس الآن، بتتكلم على عدد فردي،
+
+304
+00:26:50,920 --> 00:26:53,720
+أيوة، إما بالزاد أو باللاجس، أي صورة اللي هتبقى
+
+305
+00:26:53,720 --> 00:26:59,080
+اعتمدها، بدك حسبة بسيطة على سبيل المثال، نقول تالت
+
+306
+00:26:59,080 --> 00:27:07,810
+عدد فرديثالث أدد فردي ايش هو؟ خمسة شو علاقة الخمسة
+
+307
+00:27:07,810 --> 00:27:15,850
+مع التلاتة؟ اتنين في تلاتة ستة نقص واحد وبالتالي
+
+308
+00:27:15,850 --> 00:27:19,810
+انا المعادلة تبعتي هتكون مع النقص مش مع الزائد لأن
+
+309
+00:27:19,810 --> 00:27:23,550
+لو مع الزائد هديني مين؟ هديني السبعة اتنين في
+
+310
+00:27:23,550 --> 00:27:27,850
+تلاتة ستة زائد واحد سبعة وانا بتكلم هي التالت اللي
+
+311
+00:27:27,850 --> 00:27:38,120
+عندي معناته الصورة اللي هعتمدها2k-1 تمام يا شباب؟
+
+312
+00:27:38,120 --> 00:27:42,540
+اعيدها تاني ايش هو جاعت بيقوللي هان؟ مجموع اول
+
+313
+00:27:42,540 --> 00:27:48,580
+كامل اعداد فردية، مجموع اول خمس اعداد فردية يسوى
+
+314
+00:27:48,580 --> 00:27:49,080
+25
+
+315
+00:27:51,920 --> 00:27:56,540
+مربع الخمسة ايش العدل الفرد الخامس اللي عندك؟ واحد
+
+316
+00:27:56,540 --> 00:28:03,400
+ثلاثة خمسة سبعة تسعة الخامس تسعة اللي هي اتنين في
+
+317
+00:28:03,400 --> 00:28:07,580
+خمسة عشرة اذا انا بدأ اقوله زائد واحد ماكنت بتتكلم
+
+318
+00:28:07,580 --> 00:28:12,680
+عن العدل السالس احداشر بدا اعتمد على الصور اتنين
+
+319
+00:28:12,680 --> 00:28:17,460
+كيه معاقس واحد ممتازبعد هذا الكلام أنا مش هكون
+
+320
+00:28:17,460 --> 00:28:21,840
+موجود لو جبتلك مثلة على غراها عشان انت .. لأ،
+
+321
+00:28:21,840 --> 00:28:26,160
+الاصل اللي انت تفكر فيها بالمنطق هذا تمام ال basic
+
+322
+00:28:26,160 --> 00:28:33,120
+step طبعا
+
+323
+00:28:33,120 --> 00:28:37,460
+هذا هو بيمثل العدد اللي في المنزلة K أو الترتيب K
+
+324
+00:28:37,460 --> 00:28:44,440
+K odd integer ال
+
+325
+00:28:44,440 --> 00:28:45,140
+basic step
+
+326
+00:28:49,740 --> 00:28:57,220
+الخطوة الأساسية P of ايش يا شباب؟ P of ايش يا
+
+327
+00:28:57,220 --> 00:29:02,280
+شباب؟ قلت P of أول element في ال sequence من أول
+
+328
+00:29:02,280 --> 00:29:05,800
+element في ال sequence عندك؟ واحد من أول element
+
+329
+00:29:05,800 --> 00:29:13,640
+في ال sequence؟ واحد معناته P of واحد is true
+
+330
+00:29:14,590 --> 00:29:23,930
+مجموع أول عدد فردي يساوي واحد تربيع مجموع أول عدد
+
+331
+00:29:23,930 --> 00:29:28,410
+فردي يساوي واحد تربيع انا عمال بحاول أسقط او أعيد
+
+332
+00:29:28,410 --> 00:29:35,810
+سياقة الجملة هذه على اول element ان الواحد تساوي
+
+333
+00:29:35,810 --> 00:29:43,110
+.. ليش صح؟ ده اي معادلة واحد تربيع الخطوة رقم
+
+334
+00:29:43,110 --> 00:29:47,620
+اتنيناللي اسمناها الـ Inductive step وهي فيها كل
+
+335
+00:29:47,620 --> 00:29:52,460
+الشغل Inductive
+
+336
+00:29:52,460 --> 00:29:58,600
+step طيب مهم جدا في ال Inductive step تكون انت
+
+337
+00:29:58,600 --> 00:30:04,900
+عارف اين بدك تروح ايش الشكل اللي بدك تحصل عليه ايش
+
+338
+00:30:04,900 --> 00:30:11,280
+الشكل المفروض تحصل عليهمجموع أول K زائد واحد من
+
+339
+00:30:11,280 --> 00:30:17,620
+الأعداد الفردية يساوي K زائد واحد تربيع هكذا سيحصل
+
+340
+00:30:17,620 --> 00:30:21,560
+صياغته كمان مرة ال step inductive اللي أنا بدور
+
+341
+00:30:21,560 --> 00:30:27,960
+عليها D of N زائد واحد صيغتها مجموع أول K زائد
+
+342
+00:30:27,960 --> 00:30:35,480
+واحد من الأعداد يساوي K زائد واحد تربيع
+
+343
+00:30:37,280 --> 00:30:42,720
+يعني إذا قلت مجموعة أول خمس أعداد هي K كم هي K
+
+344
+00:30:42,720 --> 00:30:47,700
+زائد واحد؟ ستة مجموعة أول ست أعداد فردية هتكون
+
+345
+00:30:47,700 --> 00:30:53,280
+خمسة زائد واحد تربيع نفس الكلام يعني بين جثين اللي
+
+346
+00:30:53,280 --> 00:30:57,000
+في ال induction step أنا هوصل على إنه K زائد واحد
+
+347
+00:30:57,000 --> 00:31:05,320
+تربيع بدأ تساوي أيوة هذه الصورة اللي أنا بتكونهذا
+
+348
+00:31:05,320 --> 00:31:08,900
+بعد ما تكون عندها تعالي نكتبها خلّيني نبدأ خطوة
+
+349
+00:31:08,900 --> 00:31:18,120
+خطوة بعد أن هذا سأقول Assume B of N is true افترض
+
+350
+00:31:18,120 --> 00:31:22,820
+ان المعادلة هذه صحيحة بس ايوة هلقيت احنا ديك أصبر
+
+351
+00:31:22,820 --> 00:31:26,720
+شوية ممتاز الآن خلّيني مع الخطوة الأولى أنا فرضي
+
+352
+00:31:26,720 --> 00:31:34,330
+تهيأها 101 زائد 3 زائد 5 زائدزائد اتنين K ماقص
+
+353
+00:31:34,330 --> 00:31:41,790
+واحد يساوي K تربيع الخطوة التالية من ال next
+
+354
+00:31:41,790 --> 00:31:47,690
+element في ال sequence؟ اتنين
+
+355
+00:31:47,690 --> 00:31:48,970
+K عبارة عن عدد زوجي
+
+356
+00:31:54,150 --> 00:31:57,750
+أنا بدي ال next element في ال sequence في المثال
+
+357
+00:31:57,750 --> 00:32:02,630
+السابق كان بيقول للمجموعة أول n من الأعداد الموجبة
+
+358
+00:32:02,630 --> 00:32:05,610
+ما جليش أعداد زوجي ولا أعداد فردي فكان ال next
+
+359
+00:32:05,610 --> 00:32:10,190
+element زائد واحد، مظهر؟ لكن ال next element في
+
+360
+00:32:10,190 --> 00:32:16,860
+الأعداد الفردية بيضيف اتنين، بيضيف اتنين عليههتصير
+
+361
+00:32:16,860 --> 00:32:21,560
+اتنين K زائد واحد يعني اول خمس أعداد فردية هتصير
+
+362
+00:32:21,560 --> 00:32:27,000
+تسعة لما اتكلمنا عن العدد الفردي السادس كنا بنزيد
+
+363
+00:32:27,000 --> 00:32:30,480
+اتنين اللي هو احداش مصيد ولا لأ وبالتالي هو هذا
+
+364
+00:32:30,480 --> 00:32:33,260
+السؤال اللي سألت عنه السؤال كمصبوح؟ وبالتالي هصير
+
+365
+00:32:33,260 --> 00:32:39,380
+عندي واحد زائد تلاتة زائد خمسة زائد اتنين K ماقص
+
+366
+00:32:39,380 --> 00:32:43,140
+واحد زائد
+
+367
+00:32:43,960 --> 00:32:52,000
+أتنين K زائد واحد يساوي الكتر
+
+368
+00:32:52,000 --> 00:32:58,580
+بيه زائد اتنين
+
+369
+00:32:58,580 --> 00:33:02,680
+K زائد واحد
+
+370
+00:33:02,680 --> 00:33:06,580
+ليش
+
+371
+00:33:06,580 --> 00:33:11,980
+حطت الجواز؟ لإن عشان أقول لك أنها درجة واحد ما هو
+
+372
+00:33:11,980 --> 00:33:16,580
+هذي اللي أبقى في طريقة مضبوطة فيهاتمام يا شباب؟
+
+373
+00:33:16,580 --> 00:33:19,940
+الآن .. واضحة كتير .. ليش .. ليش أبقى أخطر قيمة
+
+374
+00:33:19,940 --> 00:33:25,440
+هذه يا شباب؟ لأن هذا هو عبارة عن الـ K زائد واحد
+
+375
+00:33:25,440 --> 00:33:33,080
+من الأعداد الفردية إذا كان هذا هو الـ K إذا
+
+376
+00:33:33,080 --> 00:33:37,320
+كان هذا هو الـ K معناته هذا هيكون K زائد واحد يعني
+
+377
+00:33:37,320 --> 00:33:40,540
+العدد الفردي التالي واحنا بنعرف الفرق بين كل عدد
+
+378
+00:33:40,540 --> 00:33:41,960
+فردي واللي .. واللي وراه
+
+379
+00:33:50,460 --> 00:33:56,920
+الان ايش العدد الفردي التالي للخمسة؟ العدد الفردي
+
+380
+00:33:56,920 --> 00:34:03,060
+التالي للخمسة؟ سبعة. جدش الفرق بين هدا و هدا؟
+
+381
+00:34:03,060 --> 00:34:08,400
+اتنين. العدد الفردي التالي للسبعة؟ تسعة. بتبقى
+
+382
+00:34:08,400 --> 00:34:15,990
+اتنين. العدد .. لو كان الآن عند اتنين Kنقص واحد،
+
+383
+00:34:15,990 --> 00:34:20,250
+عدد فردي، إيش العدد الفردي التالي إليه؟ بأضيف
+
+384
+00:34:20,250 --> 00:34:29,890
+اتنين، أظبط؟ تصير اتنين K نقص واحد وزاد اتنين؟ بس،
+
+385
+00:34:29,890 --> 00:34:32,550
+الفكرة ده كمان مرة اللي أنا بدي أضيف على ال
+
+386
+00:34:32,550 --> 00:34:36,710
+sequence ال next element من ال sequence نفسها، مش
+
+387
+00:34:36,710 --> 00:34:39,250
+من دماغي، ال next element في ال sequence
+
+388
+00:34:50,250 --> 00:34:57,370
+زي اتنين لمين؟ ممتاز
+
+389
+00:34:57,370 --> 00:35:00,910
+احنا في الآخر طيّرنا سالب واحد صار في عندك two
+
+390
+00:35:00,910 --> 00:35:06,790
+constant سالب واحد وموجب اتنين موجب واحد صح انت
+
+391
+00:35:06,790 --> 00:35:11,930
+اللي بتقوله صح بس هيك هتقولي اتنين ك معكس واحد زي
+
+392
+00:35:11,930 --> 00:35:12,450
+اتنين
+
+393
+00:35:21,880 --> 00:35:28,160
+مش هتبقى له هيك طيب لإن أنا في الآخر بدي ال gods
+
+394
+00:35:28,160 --> 00:35:30,420
+hand بدي ناحية .. ناحية .. ناحية .. ناحية .. ناحية
+
+395
+00:35:30,420 --> 00:35:31,480
+.. ناحية .. ناحية .. ناحية .. ناحية .. ناحية ..
+
+396
+00:35:31,480 --> 00:35:31,720
+ناحية .. ناحية .. ناحية .. ناحية .. ناحية .. ناحية
+
+397
+00:35:31,720 --> 00:35:32,840
+.. ناحية .. ناحية .. ناحية .. ناحية .. ناحية ..
+
+398
+00:35:32,840 --> 00:35:33,740
+ناحية .. ناحية .. ناحية .. ناحية .. ناحية .. ناحية
+
+399
+00:35:33,740 --> 00:35:36,840
+.. ناحية .. ناحية .. ناحية .. ناحية .. ناحية ..
+
+400
+00:35:36,840 --> 00:35:37,520
+ناحية .. ناحية .. ناحية .. ناحية .. ناحية .. ناحية
+
+401
+00:35:37,520 --> 00:35:39,420
+.. ناحية .. ناحية .. ناحية .. ناحية .. ناحية ..
+
+402
+00:35:39,420 --> 00:35:47,680
+ناحية .. ناحية .. ناحية .. ناحية .. ناحية ..
+
+403
+00:35:47,680 --> 00:35:59,300
+ناحية ..تربيع K زائد واحد تربيع اللي هي هذه P
+
+404
+00:35:59,300 --> 00:36:07,620
+of N زائد واحد انتهى البرهان طبيعي
+
+405
+00:36:07,620 --> 00:36:14,600
+لازم أقول K K تمام؟ الآن خلص البرهان ده الخطوة
+
+406
+00:36:14,600 --> 00:36:29,310
+تالتة conclusion تلاتة تكتب من هناthe sum of
+
+407
+00:36:29,310 --> 00:36:41,250
+the first k odd integers equal to k تربيع is true
+
+408
+00:36:41,250 --> 00:36:49,210
+for any positive k
+
+409
+00:36:50,590 --> 00:36:56,830
+لأي عدد K نصبوت؟ بلص هدا هي في السؤال مثلا زي هذه
+
+410
+00:36:56,830 --> 00:37:00,790
+في علامتين مضمونات في جيب تك ال basic step و ال
+
+411
+00:37:00,790 --> 00:37:05,590
+conclusion بتاخد العلامة اللي فوق، بتاخدش العلامة
+
+412
+00:37:05,590 --> 00:37:09,670
+اللي تحت لإن هو هيك لإن هو .. مش حق .. والله
+
+413
+00:37:09,670 --> 00:37:12,870
+هينضعفش .. مش عشانك طويل انت بدك تمشي الدرجة خطوة
+
+414
+00:37:12,870 --> 00:37:18,290
+بعد خطوة لأ يا عم نحترفش بيبقيك أمرا فتاخد العلامة
+
+415
+00:37:18,290 --> 00:37:25,360
+الأولى، بس إزاي أنت كتبتهاصح طيب بسيطة
+
+416
+00:37:25,360 --> 00:37:33,880
+100% لمين
+
+417
+00:37:33,880 --> 00:37:38,460
+ده هتضيفه لأني
+
+418
+00:37:38,460 --> 00:37:42,840
+فاهم عليه هوش هو عشق وقعد بقول انا اضيف هن زائد
+
+419
+00:37:42,840 --> 00:37:48,760
+اتنين مش صح الكلامالتانية مش ال next element في ال
+
+420
+00:37:48,760 --> 00:37:58,140
+sequence اللي أنا بضيفه هان ال next element in the
+
+421
+00:37:58,140 --> 00:38:01,380
+sequence مين ال element اللي بعد هذا في ال
+
+422
+00:38:01,380 --> 00:38:05,730
+sequence؟هك اللي انا بقوله قاعد هذا ال position لل
+
+423
+00:38:05,730 --> 00:38:11,950
+next element في ال sequence ال next المثال يعني
+
+424
+00:38:11,950 --> 00:38:15,830
+ربنا قدر ان هذا المثال بتكلم جميعنا عن الأعداد
+
+425
+00:38:15,830 --> 00:38:20,110
+فردية الفرق بين كل أعداد فرد يقولني ورا اتنين هذا
+
+426
+00:38:20,110 --> 00:38:23,330
+لا يعني ان انا بضرح اضيف الفرق لأ انا بضرح اضيف ال
+
+427
+00:38:23,330 --> 00:38:26,890
+next element اللي هو يساوي ال element هذا ساعد
+
+428
+00:38:26,890 --> 00:38:27,270
+اتنين
+
+429
+00:38:30,300 --> 00:38:55,640
+انت بتضيف صورة لعدد الفرد التالي اثبت
+
+430
+00:38:55,640 --> 00:39:03,530
+ان الان اقل من اتنين انfor any or for all positive
+
+431
+00:39:03,530 --> 00:39:12,090
+integers n لأي عدد صحيح موجب ال n هتكون أقل من
+
+432
+00:39:12,090 --> 00:39:18,330
+اتنين ن اه صحيح راشد هتثبت انا ولا باخدش رأيك
+
+433
+00:39:18,330 --> 00:39:24,150
+عشانك حضرت عرسق زمان رياضي انت الآن بدك تثبت هذا
+
+434
+00:39:24,150 --> 00:39:24,550
+الكلام
+
+435
+00:39:35,810 --> 00:39:43,550
+B of جداش شباب All positive
+
+436
+00:39:43,550 --> 00:39:49,370
+integers الصفر موجب ولا سالب؟ اتهلأمر معاكم
+
+437
+00:39:49,370 --> 00:39:53,850
+المسألة محددالك من وين تبدأ مش على كيفك ماج تبدأ
+
+438
+00:39:53,850 --> 00:39:58,230
+تمام؟ ثم عند الصفر كمان في مشكلة تانية ال B of صفر
+
+439
+00:39:58,230 --> 00:40:03,790
+لا تتحقق الصفر الصفر مش أقل من الصفر
+
+440
+00:40:06,370 --> 00:40:11,150
+بس الواحد أقل من التنين، مظبوط؟ وبالتالي المسألة
+
+441
+00:40:11,150 --> 00:40:18,370
+مضطها حالها من أين بيكتب ده بي of واحد is true
+
+442
+00:40:18,370 --> 00:40:28,190
+since لأنه الواحد أقل من التنين في واحد، صح؟
+
+443
+00:40:28,190 --> 00:40:30,230
+هيك صح، تمام
+
+444
+00:40:36,290 --> 00:40:40,630
+inductive step assume
+
+445
+00:40:40,630 --> 00:40:44,630
+b
+
+446
+00:40:44,630 --> 00:40:58,350
+of n is true ايش يعني b of n يا شباب ان ال n اصغر
+
+447
+00:40:58,350 --> 00:41:06,060
+من 2n ممتاز الان ايش الهدف تبعناما هو الـ Next؟
+
+448
+00:41:06,060 --> 00:41:10,040
+الـ B of N زائد واحد كيف صورتها؟ الـ B of N زائد
+
+449
+00:41:10,040 --> 00:41:13,960
+واحد كيف صورتها يا شباب؟ ان N زائد واحد أقل من
+
+450
+00:41:13,960 --> 00:41:19,760
+اتنين مضغوطة في N زائد واحد الـ B of N زائد واحد
+
+451
+00:41:19,760 --> 00:41:26,320
+تستبدل كل N ب N زائد واحد كل N ب N زائد واحد يعني
+
+452
+00:41:26,320 --> 00:41:32,500
+الـ B of N زائد واحد تساوي
+
+453
+00:41:34,580 --> 00:41:39,160
+ان زائد واحد هتكون اقل من اتنين في ان زائد واحد
+
+454
+00:41:39,160 --> 00:41:45,740
+اللي هي بين جثين اتنين في ان زائد اتنين مظبوط دخلت
+
+455
+00:41:45,740 --> 00:41:49,180
+اتنين بس عشان اي واحدة تيجي معاك اجرب اللي تيجي
+
+456
+00:41:49,180 --> 00:41:56,960
+معاك بشكل أسرع تمسك فيها تمام عشان
+
+457
+00:41:56,960 --> 00:42:06,750
+ال next element كباعة الان ايش هو؟ن زائد واحد عشان
+
+458
+00:42:06,750 --> 00:42:12,870
+امسك الان زائد واحد في المعادلة هذه ان
+
+459
+00:42:12,870 --> 00:42:19,910
+زائد واحد اقل من اتنين ان زائد واحد مصبوط الكلام
+
+460
+00:42:19,910 --> 00:42:22,770
+عشان تبقى المعادلة هذه صحيحة اضيف الواحد على اتنين
+
+461
+00:42:23,630 --> 00:42:26,650
+ليش مااخترتش اتنين N او اتنين K زائد واحد او ما
+
+462
+00:42:26,650 --> 00:42:33,390
+شابه؟ لأن هذا المثل هو جد بقول positive integer و
+
+463
+00:42:33,390 --> 00:42:38,430
+ال next لل N هو عبارة عن N زائد واحد، مصبوط؟ و
+
+464
+00:42:38,430 --> 00:42:42,720
+لاحظ أنا بجمعشلا بجمع ولا إيرو أنا واقف عند ال N
+
+465
+00:42:42,720 --> 00:42:46,200
+إيش اللي بالي ورا ال N ال element التالي N زائد
+
+466
+00:42:46,200 --> 00:42:51,060
+واحد ف ال N زائد واحد هذه عشان تطلع في عادة العدرة
+
+467
+00:42:51,060 --> 00:42:56,760
+صح أضفنا ال واحد على اقنع فين، مصبوط؟ هل الصورة
+
+468
+00:42:56,760 --> 00:43:04,100
+هذه هي هذه؟ لأ طب الحل، الحل بسيط جدا ال واحد أقل
+
+469
+00:43:04,100 --> 00:43:09,400
+من اتنين، مصبوط؟ هذه كمان أقل من اتنين N، هيها؟
+
+470
+00:43:10,310 --> 00:43:18,410
+زائد 2 و لا شو رايكوا؟ الان 2L زائد 1 أقل من 2L
+
+471
+00:43:18,410 --> 00:43:23,270
+زائد 2 و لا في غلط في المسألة؟ ال integer اللي
+
+472
+00:43:23,270 --> 00:43:26,230
+وراها يعني ماليش ناخد بال integer اللي وراها حتى
+
+473
+00:43:26,230 --> 00:43:29,990
+لو كان بديفركس 70 أنا معنى 2 هي الصورة اللي بديها
+
+474
+00:43:29,990 --> 00:43:36,730
+و أنا هذه اللي وصلت لها، فعلا؟ الان هذه و هذهالفرق
+
+475
+00:43:36,730 --> 00:43:40,970
+انه بدي استبدل الاتنين بواحد طبما هي الاتنين اكبر
+
+476
+00:43:40,970 --> 00:43:48,170
+من الواحد فانا اشتغلت على المثال هذه ان شئت ان شئت
+
+477
+00:43:48,170 --> 00:43:52,610
+يا سيد يقول ماشي الحال زائد واحد زائد كمان واحد
+
+478
+00:43:52,610 --> 00:44:00,210
+لان العدد هذا اصغر من اللي بعده لان فانا هاجيبها
+
+479
+00:44:00,210 --> 00:44:04,690
+مباشرة لان المنطق شوفيعني مستحيل تقولي هذا غلط
+
+480
+00:44:04,690 --> 00:44:09,190
+الكلام لأن هذه هي هذا و الواحد أقل من اتنين
+
+481
+00:44:09,190 --> 00:44:14,690
+فبالتالي طيب و بخاصيتي التعدي هذا يؤدي ان ال n
+
+482
+00:44:14,690 --> 00:44:20,930
+زائد واحد أقل من اتنين و بدي اخد عياب المشترك كمان
+
+483
+00:44:20,930 --> 00:44:26,670
+بدي اخد اتنين عياب المشترك اه
+
+484
+00:44:26,670 --> 00:44:30,530
+اكيد اكيد صح لو سبت زي ما هي مافي مشكلة سوى اللي
+
+485
+00:44:30,530 --> 00:44:30,870
+بدها هي
+
+486
+00:44:33,790 --> 00:44:40,570
+وها دي bn زائد واحد خلص البرهان ال conclusion
+
+487
+00:44:40,570 --> 00:44:47,870
+معناته أحلى
+
+488
+00:44:47,870 --> 00:44:51,110
+أشي في السؤال ال conclusion هو إذا أنت ماعرفتش
+
+489
+00:44:51,110 --> 00:44:55,150
+تعمل ال inductive step مابتقدرش تتكلم على
+
+490
+00:44:55,150 --> 00:44:59,350
+conclusion تمام ال conclusion هم اتبعونا السؤال
+
+491
+00:44:59,350 --> 00:45:01,010
+كانوا مأكيد ان الجواب هكون صح
+
+492
+00:45:05,650 --> 00:45:10,330
+هنعيد مرة تانية، الآن نعم أنا هعطيك علامة على ال
+
+493
+00:45:10,330 --> 00:45:13,470
+conclusion صحيح؟ بس إذا أنت مش كاتب ال inductive
+
+494
+00:45:13,470 --> 00:45:16,490
+step مش هتاخد العلامة لأنك ماوصلتش ل ال conclusion
+
+495
+00:45:16,490 --> 00:45:19,990
+انت اللي بيصل ل ال conclusion اللي بيثبت صح هو
+
+496
+00:45:19,990 --> 00:45:23,570
+اللي أجبره يثبت، إذا أنت ماقدرتش تثبت كيف اعطله
+
+497
+00:45:23,570 --> 00:45:29,380
+صح؟ مايمكن الكلام هذا غلطيا سيد يماشي الحلقة بدي
+
+498
+00:45:29,380 --> 00:45:35,460
+أجيبك proof or disproof حسب
+
+499
+00:45:35,460 --> 00:45:38,320
+كل مسألة لو كنت بقعدك في مسألة ممكن تبدأ فيها من
+
+500
+00:45:38,320 --> 00:45:44,900
+سفر طيب خلّيني أشوف المسألة الأخيرة خلّيني أشوف
+
+501
+00:45:44,900 --> 00:45:55,190
+المسألة الأخيرة أكتبها فوق بقول ايه a زائد arزائد
+
+502
+00:45:55,190 --> 00:46:05,390
+AR تربيع زائد AR أُس N يساوي A مضروبة في R أُس N
+
+503
+00:46:05,390 --> 00:46:16,490
+زائد واحد ناقص A على R ناقص واحد وال
+
+504
+00:46:16,490 --> 00:46:23,930
+R لا تساوي الواحد عشان بس أقدر أخربش يعني مش أكتر
+
+505
+00:46:34,070 --> 00:46:46,070
+الان ال basic step بيقف
+
+506
+00:46:46,070 --> 00:46:51,890
+جداش بيقف
+
+507
+00:46:51,890 --> 00:46:56,470
+جداش هي ال sequence عندكالـ Sequence هذه Geometric
+
+508
+00:46:56,470 --> 00:47:01,270
+Sequence
+
+509
+00:47:01,270 --> 00:47:06,890
+أول element وين يا شباب؟ أول element قداش قيمته؟
+
+510
+00:47:06,890 --> 00:47:12,010
+أول element في الـ Sequence قداش قيمته؟ يا ابن
+
+511
+00:47:12,010 --> 00:47:15,090
+الناس، هاي الـ Sequence أول element في الـ
+
+512
+00:47:15,090 --> 00:47:20,530
+Sequence قداش قيمته؟ A الآن ال index أو الان ال
+
+513
+00:47:20,530 --> 00:47:25,940
+counter اللي مع الألم الـ A قداش قيمته؟صفر لأن هذا
+
+514
+00:47:25,940 --> 00:47:29,740
+المفروض AR
+
+515
+00:47:29,740 --> 00:47:33,460
+أص صفر وهذا AR أص واحد هيك ال sequence مظبوط ولا
+
+516
+00:47:33,460 --> 00:47:38,540
+لأ؟معناته اذا كنا بيقول بي اوف زيرو تقدرش تقول بي
+
+517
+00:47:38,540 --> 00:47:43,700
+اوف ايه؟أول element في ال sequence ال index تبعه
+
+518
+00:47:43,700 --> 00:47:50,580
+قداشر؟صفر كمان؟أول element في ال sequence صفر لأن
+
+519
+00:47:50,580 --> 00:47:54,220
+كل الشغل وين يا شباب؟مع ال N مش مع ال A ولا مع ال
+
+520
+00:47:54,220 --> 00:47:58,700
+R لما كانت أول element في ال sequence اللي هي ال
+
+521
+00:47:58,700 --> 00:48:01,740
+sequence صفر واحد اتنين تلاتة أربعة ال A و ال R
+
+522
+00:48:01,740 --> 00:48:08,160
+تابتت بس اللي بتغير معايا ال N P of Zero is true
+
+523
+00:48:08,160 --> 00:48:12,520
+ليش؟
+
+524
+00:48:13,370 --> 00:48:21,130
+لأنه بحتوظ عن الانب زيرو A في R أس Zero زائد واحد
+
+525
+00:48:21,130 --> 00:48:27,930
+واحد ناقص A على R ناقص واحد خد ال A على المشترك
+
+526
+00:48:27,930 --> 00:48:37,870
+أول
+
+527
+00:48:37,870 --> 00:48:39,710
+element قيمته A
+
+528
+00:48:42,230 --> 00:48:45,750
+خلصنا ما هي ال B of او ال basic step متحدث عندى
+
+529
+00:48:45,750 --> 00:48:53,430
+خطوة تانية inductive
+
+530
+00:48:53,430 --> 00:48:58,650
+step هتروح
+
+531
+00:48:58,650 --> 00:49:04,730
+تقوله assume B
+
+532
+00:49:04,730 --> 00:49:09,070
+of N is
+
+533
+00:49:09,070 --> 00:49:14,120
+true ايش يعني B of N is true؟المعادلة هذه متحققة
+
+534
+00:49:14,120 --> 00:49:25,660
+يعني هذا يؤدي إلى a زائد ar زائد ar تربيع زائد ar
+
+535
+00:49:25,660 --> 00:49:37,160
+أس n يساوي a في r أس n زائد واحد ناقص ال a على r
+
+536
+00:49:37,160 --> 00:49:42,670
+ناقص واحد هذا ال P of nهذه اللي كتبته عبارة عن P
+
+537
+00:49:42,670 --> 00:49:48,530
+of N الان بدك تضيف على ال sequence اللي بتتكلم عن
+
+538
+00:49:48,530 --> 00:49:55,570
+مجموع اول N من ال geometric sequence يساوي كذا طب
+
+539
+00:49:55,570 --> 00:49:58,510
+مين ال next element في ال geometric sequence اللي
+
+540
+00:49:58,510 --> 00:50:02,470
+بيك تضيفه؟ اللي انا بك اضيفه هو element اللي انا
+
+541
+00:50:02,470 --> 00:50:08,630
+بدي اضيفه هو element A زائد AR زائد AR تربيع زائد
+
+542
+00:50:09,440 --> 00:50:16,420
+زائد AR أُس M زائد بداك تضيف element الآن ال next
+
+543
+00:50:16,420 --> 00:50:21,880
+element في ال sequence المتدادة الهندسية كل الفرق
+
+544
+00:50:21,880 --> 00:50:25,700
+بين ال element وال element اللي يليه R مظلوم اللي
+
+545
+00:50:25,700 --> 00:50:28,980
+سمّالها ال ratio R وبالتالي ال next element هو
+
+546
+00:50:28,980 --> 00:50:35,840
+عبارة عن ايه؟ فR زائد 1 وطبعا هذا بنضيفه أكبر في
+
+547
+00:50:35,840 --> 00:50:36,240
+التاني
+
+548
+00:50:51,250 --> 00:50:55,390
+بأكد كمان مرة أنا بضيف الـ Next Element على الـ
+
+549
+00:50:55,390 --> 00:50:58,230
+Sequence بشوف مين الـ Next Element في الـ Sequence
+
+550
+00:50:58,230 --> 00:51:04,950
+في حسب المسألة اللي عندى بتختلف تمام؟ الآن مقعد
+
+551
+00:51:04,950 --> 00:51:08,970
+الشغل يانهار حيصير صح؟ هذا خلصنا توحد المقابات
+
+552
+00:51:08,970 --> 00:51:16,270
+وتجمع ساوي R
+
+553
+00:51:16,270 --> 00:51:27,250
+ناقص واحدAR أُس N زائد واحد ناقص ال A زائد R ناقص
+
+554
+00:51:27,250 --> 00:51:39,470
+واحد مضروبة في AR أُس N زائد واحد تساوي AR أُس N
+
+555
+00:51:39,470 --> 00:51:44,470
+زائد واحد ناقص ال A زائد
+
+556
+00:51:45,420 --> 00:51:52,340
+الان R مضروبة في AR أس N زائد واحد هتصير عندى AR
+
+557
+00:51:52,340 --> 00:51:58,260
+أس N زائد اتنين جابل جابل ال B of N زائد واحد كيف
+
+558
+00:51:58,260 --> 00:52:07,080
+شكلها كيف شكل B of N زائد واحد شباب استبدل كل M ب
+
+559
+00:52:07,080 --> 00:52:13,900
+N زائد واحد هتصير عندى AR أس N زائد اتنين هي هي
+
+560
+00:52:14,680 --> 00:52:23,060
+الآن في عندي AR أُس N زائد واحد مضروبة في R عند
+
+561
+00:52:23,060 --> 00:52:27,540
+الضغط تجمع الأساس إذا اقتحت الأساسات R و R N زائد
+
+562
+00:52:27,540 --> 00:52:37,860
+واحد زائد واحد AR أُس N زائد اتنين ناقص AR أُس N
+
+563
+00:52:37,860 --> 00:52:42,420
+زائد واحد أنا مضروبة في سالب واحد الآن
+
+564
+00:52:44,770 --> 00:52:49,830
+الـ A R أُس N هذا بالناقص وهذا بالموجب هذه واحدة
+
+565
+00:52:49,830 --> 00:52:53,950
+السالبة و واحدة الموجبة على R ناقص واحد صفة
+
+566
+00:52:53,950 --> 00:52:59,110
+المسألة تساوي A
+
+567
+00:52:59,110 --> 00:53:08,310
+R أُس N زائد اتنين ناقص A على R ناقص واحد وهذا
+
+568
+00:53:08,310 --> 00:53:15,920
+أيضا تساوي B of N زائد واحدخلصت الـ inductive step
+
+569
+00:53:15,920 --> 00:53:24,740
+وبتكتب ال conclusion انت تمام؟ كمان
+
+570
+00:53:24,740 --> 00:53:29,480
+مرة شباب مفتاح حل المسألة دائما في اختيارك او في
+
+571
+00:53:29,480 --> 00:53:34,260
+معرفتك ل ال next element ويكون عندك بُعد نظر تشوف
+
+572
+00:53:34,260 --> 00:53:39,680
+P of M زائد 1 اذا هدول الشغلتين اتمكنت منهم صح انت
+
+573
+00:53:39,680 --> 00:53:45,280
+المسألة سهلة ولا في أسهل من هيكأه خلاص .. خلاص
+
+574
+00:53:45,280 --> 00:53:47,340
+الشبكة كلها .. مابديش أكتر من هي كمان .. اللي
+
+575
+00:53:47,340 --> 00:53:50,480
+الأول بشوف .. الأمر مش صعب .. بس شوف المسألة ايش
+
+576
+00:53:50,480 --> 00:53:55,280
+قاعد بقولك .. ال N greater than 4 .. يعني ال basic
+
+577
+00:53:55,280 --> 00:54:00,220
+step تبقى جديش .. P of جديش .. P of خمسة .. لأنه
+
+578
+00:54:00,220 --> 00:54:06,720
+اتنين قصة أربعة .. ستة عشر .. و أربعة تردية ستة
+
+579
+00:54:06,720 --> 00:54:10,580
+عشر .. و الستة عشر مش أكبر من ستة عشر ..عشان يثبت
+
+580
+00:54:10,580 --> 00:54:13,340
+.. هو .. هو .. أساسا هو يدّيك إيه هي .. جالك أكبر
+
+581
+00:54:13,340 --> 00:54:17,280
+من أربع، يعني خمسة، الآن اتنين وعشان خمسة، اتنين
+
+582
+00:54:17,280 --> 00:54:22,380
+وثلاثين، أكبر من خمسة تربية من خمسة عشرين، true،
+
+583
+00:54:22,380 --> 00:54:23,160
+لاعطيكوا العافية يا شباب
+
diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/G1lxhtUqbxw_raw.json b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/G1lxhtUqbxw_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..fc5decb67e649619e186da132e0e24e1ac96648e
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/G1lxhtUqbxw_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4969, "start": 21.11, "end": 49.69, "text": "بسم الله والحمد لله والصلاة والسلام علي رسول الله اليوم ان شاء الله شباب هنبدأ نتكلم عن ال mathematical induction لكن بدي اعمل مراجعة سريعة اللي احنا شوفناها سابقا في التقنيات الإثبات الرياضي قولنا هتلاقي في الجزئية السابقة اما هتلاقي مسألة مكتوبة بالشكل التالي if 3n زائد 2 is even then n is", "tokens": [3555, 38251, 21984, 16070, 35571, 3215, 24976, 3224, 16070, 9381, 15040, 3660, 16070, 3794, 37440, 25894, 12602, 3794, 12610, 21984, 45595, 20498, 16472, 13412, 16606, 21984, 13412, 3555, 16758, 8032, 1863, 44510, 10721, 8717, 2655, 4117, 19528, 18871, 2423, 18894, 33371, 44381, 4724, 16254, 1975, 25957, 1211, 3714, 2288, 26108, 27884, 8608, 16572, 27884, 13672, 1829, 1975, 5016, 8315, 13412, 38688, 8315, 11296, 8608, 16758, 4587, 995, 8978, 16712, 4587, 22653, 9307, 33688, 12984, 3555, 9307, 2423, 16572, 46958, 1829, 12174, 12610, 8315, 8032, 2655, 15040, 38436, 8978, 25724, 11622, 19986, 10632, 21136, 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إيش الموقع عندك عددين زوجيين معناته if هتكتب هيك x and y are even integers", "tokens": [271, 754, 24922, 264, 2408, 295, 732, 754, 41674, 45164, 41850, 8608, 10721, 1211, 2655, 4117, 3714, 7435, 2304, 45367, 36632, 6225, 3215, 3215, 9957, 30767, 29245, 1829, 9957, 31439, 6225, 3555, 9640, 3660, 18871, 6225, 3215, 3215, 30767, 29245, 1829, 11933, 1829, 8592, 9673, 30543, 3615, 43242, 4117, 6225, 3215, 3215, 9957, 30767, 29245, 1829, 9957, 20449, 8315, 47395, 498, 8032, 2655, 4117, 2655, 3555, 39896, 4117, 2031, 293, 288, 366, 754, 41674], "avg_logprob": -0.20864583532015482, "compression_ratio": 1.5575757575757576, "no_speech_prob": 0.0, "words": [{"start": 81.52, "end": 81.8, "word": "is", "probability": 0.2900390625}, {"start": 81.8, "end": 82.24, "word": " even", "probability": 0.724609375}, {"start": 82.24, "end": 84.58, "word": " integer", "probability": 0.8017578125}, {"start": 84.58, "end": 86.5, "word": " the", "probability": 0.34521484375}, {"start": 86.5, "end": 86.86, "word": 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172.34, "end": 172.98, "word": "نقطة", "probability": 0.5921223958333334}, {"start": 172.98, "end": 173.32, "word": " Q", "probability": 0.424560546875}, {"start": 173.32, "end": 173.8, "word": " و", "probability": 0.301513671875}, {"start": 173.8, "end": 174.06, "word": " بدك", "probability": 0.51702880859375}, {"start": 174.06, "end": 174.42, "word": " تسأل", "probability": 0.9530029296875}, {"start": 174.42, "end": 174.96, "word": " لمن؟", "probability": 0.4319661458333333}, {"start": 174.96, "end": 175.88, "word": " هل", "probability": 0.481597900390625}, {"start": 175.88, "end": 176.02, "word": " هذا", "probability": 0.278564453125}, {"start": 176.02, "end": 177.08, "word": " صحيح؟", "probability": 0.79912109375}, {"start": 177.08, "end": 177.12, "word": " و", "probability": 0.40869140625}, {"start": 177.12, "end": 177.42, "word": " بدك", "probability": 0.818603515625}, {"start": 177.42, "end": 178.16, "word": " تسأل", "probability": 0.9822998046875}, {"start": 178.16, "end": 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contrapositive، بروح ل contradiction حسب المثال. المثال الأول واضح، ممشيش معايا direct.", "tokens": [3224, 15042, 8717, 36178, 16095, 8032, 3215, 12610, 13, 5296, 33456, 41850, 19446, 16490, 2288, 3555, 2655, 8032, 3215, 12610, 16712, 29399, 9957, 13, 4724, 4587, 36081, 8592, 33962, 9566, 2407, 3660, 16712, 6027, 10632, 12399, 47525, 4117, 6055, 8592, 2655, 17082, 1211, 20449, 36632, 36764, 24401, 3660, 9154, 16095, 4032, 6055, 36520, 8717, 9957, 24976, 34937, 12399, 6055, 36520, 16712, 8315, 4587, 11242, 20449, 16712, 7649, 10632, 13, 47525, 4117, 46811, 3794, 4117, 36632, 36764, 24401, 3660, 8978, 16095, 4032, 6055, 36520, 16712, 8315, 4587, 11242, 20449, 16712, 7649, 10632, 13, 29538, 9673, 12984, 6027, 28242, 11296, 9122, 29399, 4724, 8592, 2655, 17082, 1211, 8978, 11296, 1975, 15042, 3714, 19913, 3555, 9566, 8592, 20449, 995, 25528, 2047, 12399, 4724, 32887, 5016, 5296, 660, 4007, 329, 2187, 12399, 4724, 32887, 5016, 5296, 34937, 11331, 35457, 9673, 12984, 6027, 13, 9673, 12984, 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"probability": 0.772802734375}, {"start": 830.67, "end": 831.19, "word": " انك", "probability": 0.8798828125}, {"start": 831.19, "end": 831.43, "word": " بيدك", "probability": 0.8089192708333334}, {"start": 831.43, "end": 831.71, "word": " تثبت", "probability": 0.98779296875}, {"start": 831.71, "end": 831.81, "word": " ال", "probability": 0.98095703125}, {"start": 831.81, "end": 832.25, "word": " base", "probability": 0.60888671875}, {"start": 832.25, "end": 832.75, "word": " تقولي", "probability": 0.73828125}, {"start": 832.75, "end": 832.89, "word": " انه", "probability": 0.650390625}, {"start": 832.89, "end": 833.23, "word": " فعليا", "probability": 0.836181640625}, {"start": 833.23, "end": 833.43, "word": " هذا", "probability": 0.76171875}, {"start": 833.43, "end": 833.77, "word": " كلام", "probability": 0.826904296875}, {"start": 833.77, "end": 834.17, "word": " صحيح", "probability": 0.9959716796875}, {"start": 834.17, "end": 834.47, "word": " لأول", "probability": 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"probability": 0.82110595703125}, {"start": 859.54, "end": 859.66, "word": " ال", "probability": 0.94873046875}, {"start": 859.66, "end": 860.1, "word": " sequence", "probability": 0.9638671875}, {"start": 860.1, "end": 860.4, "word": " مش", "probability": 0.5087890625}, {"start": 860.4, "end": 860.64, "word": " element", "probability": 0.96044921875}, {"start": 860.64, "end": 860.82, "word": " من", "probability": 0.9736328125}, {"start": 860.82, "end": 861.02, "word": " هن", "probability": 0.4571533203125}, {"start": 861.02, "end": 861.24, "word": " دي", "probability": 0.654296875}, {"start": 861.24, "end": 861.72, "word": " لو", "probability": 0.85400390625}, {"start": 861.72, "end": 862.1, "word": " أضفت", "probability": 0.97998046875}, {"start": 862.1, "end": 862.34, "word": " كمان", "probability": 0.9855143229166666}, {"start": 862.34, "end": 862.66, "word": " element", "probability": 0.97314453125}, {"start": 862.66, "end": 862.86, "word": " من", "probability": 0.98193359375}, 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وصلت إن الـ BN is true بي أن زاد واحد is true معناته النظرية هذه بتكون هاش صحيحة و بقرادي بيسميها ال inductive step أو الخطوة الاستقرائية و من ثم بدأوا حكتوا ب conclusion إن النظرية المعبرة فوق معبرة فوق نظرية صحيحة", "tokens": [28814, 15730, 4032, 36520, 2655, 9154, 2423, 39184, 363, 295, 426, 4032, 36520, 2655, 36145, 2423, 39184, 363, 45, 307, 2074, 4724, 1829, 14739, 30767, 18513, 36764, 24401, 307, 2074, 20449, 8315, 47395, 28239, 19913, 2288, 10632, 29538, 39894, 30544, 8032, 33599, 20328, 5016, 1829, 5016, 3660, 4032, 4724, 4587, 23557, 16254, 4724, 1829, 38251, 1829, 11296, 2423, 31612, 488, 1823, 34051, 33962, 9566, 2407, 3660, 42963, 14851, 4587, 2288, 16373, 10632, 4032, 9154, 38637, 2304, 47525, 10721, 14407, 11331, 4117, 2655, 14407, 4724, 10063, 36145, 28239, 19913, 2288, 10632, 9673, 3615, 3555, 25720, 6156, 30543, 20449, 3555, 25720, 6156, 30543, 8717, 19913, 2288, 10632, 20328, 5016, 1829, 5016, 3660], "avg_logprob": -0.2846283875070177, "compression_ratio": 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"probability": 0.834716796875}], "temperature": 1.0}, {"id": 70, "seek": 189156, "start": 1864.92, "end": 1891.56, "text": "هذا بعد ما تكون عندها تعالي نكتبها خلّيني نبدأ خطوة خطوة بعد أن هذا سأقول Assume B of N is true افترض ان المعادلة هذه صحيحة بس ايوة هلقيت احنا ديك أصبر شوية ممتاز الآن خلّيني مع الخطوة الأولى أنا فرضي تهيأها 101 زائد 3 زائد 5 زائد", "tokens": [3224, 15730, 39182, 19446, 6055, 30544, 43242, 11296, 6055, 3615, 6027, 1829, 8717, 4117, 2655, 3555, 11296, 16490, 1211, 11703, 9957, 1829, 8717, 44510, 10721, 16490, 9566, 2407, 3660, 16490, 9566, 2407, 3660, 39182, 14739, 23758, 8608, 10721, 39648, 6281, 2540, 363, 295, 426, 307, 2074, 1975, 5172, 2655, 43042, 16472, 9673, 3615, 18513, 37977, 29538, 20328, 5016, 1829, 5016, 3660, 4724, 3794, 1975, 1829, 2407, 3660, 8032, 1211, 4587, 36081, 1975, 5016, 8315, 11778, 1829, 4117, 5551, 9381, 26890, 13412, 2407, 10632, 3714, 2304, 2655, 31377, 6024, 48506, 16490, 1211, 11703, 9957, 1829, 20449, 33962, 9566, 2407, 3660, 16247, 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"probability": 0.654296875}, {"start": 1877.74, "end": 1878.12, "word": " افترض", "probability": 0.8992919921875}, {"start": 1878.12, "end": 1878.28, "word": " ان", "probability": 0.60302734375}, {"start": 1878.28, "end": 1878.74, "word": " المعادلة", "probability": 0.9703369140625}, {"start": 1878.74, "end": 1878.94, "word": " هذه", "probability": 0.430419921875}, {"start": 1878.94, "end": 1879.5, "word": " صحيحة", "probability": 0.98564453125}, {"start": 1879.5, "end": 1881.76, "word": " بس", "probability": 0.6888427734375}, {"start": 1881.76, "end": 1882.14, "word": " ايوة", "probability": 0.6552734375}, {"start": 1882.14, "end": 1882.34, "word": " هلقيت", "probability": 0.45880126953125}, {"start": 1882.34, "end": 1882.46, "word": " احنا", "probability": 0.7311197916666666}, {"start": 1882.46, "end": 1882.68, "word": " ديك", "probability": 0.571044921875}, {"start": 1882.68, "end": 1882.82, "word": " أصبر", "probability": 0.7835286458333334}, {"start": 1882.82, "end": 1883.16, "word": " شوية", "probability": 0.9303385416666666}, {"start": 1883.16, "end": 1883.58, "word": " ممتاز", "probability": 0.8919677734375}, {"start": 1883.58, "end": 1884.6, "word": " الآن", "probability": 0.662353515625}, {"start": 1884.6, "end": 1885.26, "word": " خلّيني", "probability": 0.92080078125}, {"start": 1885.26, "end": 1885.42, "word": " مع", "probability": 0.19775390625}, {"start": 1885.42, "end": 1885.72, "word": " الخطوة", "probability": 0.9483642578125}, {"start": 1885.72, "end": 1886.12, "word": " الأولى", "probability": 0.978515625}, {"start": 1886.12, "end": 1886.38, "word": " أنا", "probability": 0.4013671875}, {"start": 1886.38, "end": 1886.72, "word": " فرضي", "probability": 0.86083984375}, {"start": 1886.72, "end": 1887.52, "word": " تهيأها", "probability": 0.78095703125}, {"start": 1887.52, "end": 1887.8, "word": " 101", "probability": 0.56494140625}, {"start": 1887.8, "end": 1888.82, "word": " زائد", "probability": 0.6338297526041666}, {"start": 1888.82, "end": 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"end": 1893.13, "word": "زائد", "probability": 0.7019856770833334}, {"start": 1893.13, "end": 1893.59, "word": " اتنين", "probability": 0.82073974609375}, {"start": 1893.59, "end": 1893.87, "word": " K", "probability": 0.37353515625}, {"start": 1893.87, "end": 1894.33, "word": " ماقص", "probability": 0.7167154947916666}, {"start": 1894.33, "end": 1894.85, "word": " واحد", "probability": 0.9853515625}, {"start": 1894.85, "end": 1895.91, "word": " يساوي", "probability": 0.931640625}, {"start": 1895.91, "end": 1897.03, "word": " K", "probability": 0.8056640625}, {"start": 1897.03, "end": 1897.83, "word": " تربيع", "probability": 0.71929931640625}, {"start": 1897.83, "end": 1899.43, "word": " الخطوة", "probability": 0.963623046875}, {"start": 1899.43, "end": 1900.67, "word": " التالية", "probability": 0.9925130208333334}, {"start": 1900.67, "end": 1901.39, "word": " من", "probability": 0.449462890625}, {"start": 1901.39, "end": 1901.57, "word": " ال", "probability": 0.81982421875}, {"start": 1901.57, "end": 1901.79, "word": " next", "probability": 0.625}, {"start": 1901.79, "end": 1902.15, "word": " element", "probability": 0.953125}, {"start": 1902.15, "end": 1902.33, "word": " في", "probability": 0.912109375}, {"start": 1902.33, "end": 1902.43, "word": " ال", "probability": 0.88427734375}, {"start": 1902.43, "end": 1903.57, "word": " sequence؟", "probability": 0.53955078125}, {"start": 1903.57, "end": 1907.69, "word": " اتنين", "probability": 0.815673828125}, {"start": 1907.69, "end": 1907.79, "word": " K", "probability": 0.951171875}, {"start": 1907.79, "end": 1907.95, "word": " عبارة", "probability": 0.9114990234375}, {"start": 1907.95, "end": 1907.95, "word": " عن", "probability": 0.99560546875}, {"start": 1907.95, "end": 1908.55, "word": " عدد", "probability": 0.96484375}, {"start": 1908.55, "end": 1908.97, "word": " زوجي", "probability": 0.93701171875}], "temperature": 1.0}, {"id": 72, "seek": 193543, "start": 1914.15, "end": 1935.43, "text": "أنا بدي ال next element في ال sequence في المثال السابق كان بيقول للمجموعة أول n من الأعداد الموجبة ما جليش أعداد زوجي ولا أعداد فردي فكان ال next element زائد واحد، مظهر؟ لكن ال next element في الأعداد الفردية بيضيف اتنين، بيضيف اتنين عليه", "tokens": [10721, 8315, 4724, 16254, 2423, 958, 4478, 8978, 2423, 8310, 8978, 9673, 12984, 6027, 21136, 16758, 4587, 25961, 4724, 1829, 39648, 5296, 19528, 7435, 2304, 2407, 27884, 5551, 12610, 297, 9154, 16247, 22488, 18513, 9673, 29245, 49401, 19446, 10874, 20292, 8592, 5551, 22488, 18513, 30767, 29245, 1829, 49429, 5551, 22488, 18513, 6156, 2288, 16254, 6156, 41361, 2423, 958, 4478, 30767, 16373, 3215, 36764, 24401, 12399, 3714, 19913, 3224, 2288, 22807, 44381, 2423, 958, 4478, 8978, 16247, 22488, 18513, 27188, 2288, 3215, 10632, 4724, 1829, 11242, 33911, 1975, 2655, 1863, 9957, 12399, 4724, 1829, 11242, 33911, 1975, 2655, 1863, 9957, 47356], "avg_logprob": -0.20173267267718173, "compression_ratio": 1.9504950495049505, "no_speech_prob": 0.0, "words": 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since لأنه الواحد أقل من التنين في واحد، صح؟ هيك صح، تمام", "tokens": [3555, 3794, 2423, 14407, 24401, 5551, 4587, 1211, 9154, 16712, 1863, 9957, 12399, 3714, 19913, 3555, 2407, 9566, 22807, 46599, 6027, 2655, 6027, 1829, 9673, 3794, 10721, 37977, 3714, 11242, 9566, 11296, 11331, 6027, 11296, 9154, 5551, 9957, 4724, 1829, 4117, 2655, 3555, 11778, 3224, 4724, 1829, 295, 36764, 24401, 307, 2074, 1670, 5296, 33456, 3224, 2423, 14407, 24401, 5551, 4587, 1211, 9154, 16712, 1863, 9957, 8978, 36764, 24401, 12399, 20328, 5016, 22807, 39896, 4117, 20328, 5016, 12399, 46811, 10943], "avg_logprob": -0.27276233390525534, "compression_ratio": 1.6645569620253164, "no_speech_prob": 0.0, "words": [{"start": 2406.37, "end": 2406.85, "word": "بس", "probability": 0.77880859375}, {"start": 2406.85, "end": 2407.65, "word": " الواحد", "probability": 0.8937174479166666}, {"start": 2407.65, "end": 2408.33, "word": " أقل", "probability": 0.8829752604166666}, {"start": 2408.33, "end": 2408.51, "word": " من", 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0.948486328125}, {"start": 3229.58, "end": 3229.82, "word": " شوف", "probability": 0.986328125}, {"start": 3229.82, "end": 3230.28, "word": " المسألة", "probability": 0.660888671875}, {"start": 3230.28, "end": 3230.48, "word": " ايش", "probability": 0.638916015625}, {"start": 3230.48, "end": 3230.64, "word": " قاعد", "probability": 0.7763671875}, {"start": 3230.64, "end": 3231.2, "word": " بقولك", "probability": 0.94580078125}, {"start": 3231.2, "end": 3232.24, "word": " ..", "probability": 0.309326171875}, {"start": 3232.24, "end": 3232.34, "word": " ال", "probability": 0.67529296875}, {"start": 3232.34, "end": 3232.52, "word": " N", "probability": 0.1451416015625}, {"start": 3232.52, "end": 3232.92, "word": " greater", "probability": 0.51708984375}, {"start": 3232.92, "end": 3233.44, "word": " than", "probability": 0.9501953125}, {"start": 3233.44, "end": 3234.08, "word": " 4", "probability": 0.572265625}, {"start": 3234.08, "end": 3234.34, "word": " ..", "probability": 0.62353515625}, {"start": 3234.34, "end": 3234.94, "word": " يعني", "probability": 0.76708984375}, {"start": 3234.94, "end": 3235.06, "word": " ال", "probability": 0.935546875}, {"start": 3235.06, "end": 3235.28, "word": " basic", "probability": 0.7548828125}, {"start": 3235.28, "end": 3235.56, "word": " step", "probability": 0.6962890625}, {"start": 3235.56, "end": 3235.82, "word": " تبقى", "probability": 0.7869873046875}, {"start": 3235.82, "end": 3236.46, "word": " جديش", "probability": 0.5772298177083334}, {"start": 3236.46, "end": 3237.2, "word": " ..", "probability": 0.83251953125}, {"start": 3237.2, "end": 3237.38, "word": " P", "probability": 0.6123046875}, {"start": 3237.38, "end": 3237.52, "word": " of", "probability": 0.89404296875}, {"start": 3237.52, "end": 3238.02, "word": " جديش", "probability": 0.9747721354166666}, {"start": 3238.02, "end": 3238.16, "word": " ..", "probability": 0.409912109375}, {"start": 3238.16, "end": 3238.26, "word": " P", "probability": 0.876953125}, {"start": 3238.26, "end": 3238.42, "word": " of", "probability": 0.94580078125}, {"start": 3238.42, "end": 3239.0, "word": " خمسة", "probability": 0.94482421875}, {"start": 3239.0, "end": 3239.88, "word": " ..", "probability": 0.83740234375}, {"start": 3239.88, "end": 3240.22, "word": " لأنه", "probability": 0.75341796875}, {"start": 3240.22, "end": 3241.42, "word": " اتنين", "probability": 0.8531494140625}, {"start": 3241.42, "end": 3241.72, "word": " قصة", "probability": 0.5574544270833334}, {"start": 3241.72, "end": 3242.16, "word": " أربعة", "probability": 0.89794921875}, {"start": 3242.16, "end": 3242.38, "word": " ..", "probability": 0.689453125}, {"start": 3242.38, "end": 3243.04, "word": " ستة", "probability": 0.74560546875}, {"start": 3243.04, "end": 3243.36, "word": " عشر", "probability": 0.73876953125}, {"start": 3243.36, "end": 3244.72, "word": " ..", "probability": 0.92333984375}, {"start": 3244.72, "end": 3244.84, "word": " و", "probability": 0.546875}, {"start": 3244.84, "end": 3245.48, "word": " أربعة", "probability": 0.88232421875}, {"start": 3245.48, "end": 3246.3, "word": " تردية", "probability": 0.806640625}, {"start": 3246.3, "end": 3246.72, "word": " ستة", "probability": 0.7884928385416666}, {"start": 3246.72, "end": 3246.98, "word": " عشر", "probability": 0.982177734375}, {"start": 3246.98, "end": 3247.04, "word": " ..", "probability": 0.9482421875}, {"start": 3247.04, "end": 3247.16, "word": " و", "probability": 0.806640625}, {"start": 3247.16, "end": 3247.46, "word": " الستة", "probability": 0.849609375}, {"start": 3247.46, "end": 3247.62, "word": " عشر", "probability": 0.9921875}, {"start": 3247.62, "end": 3247.82, "word": " مش", "probability": 0.97607421875}, {"start": 3247.82, "end": 3248.2, "word": " أكبر", "probability": 0.9412434895833334}, {"start": 3248.2, "end": 3248.34, "word": " من", "probability": 0.9873046875}, {"start": 3248.34, "end": 3248.64, "word": " ستة", "probability": 0.9318033854166666}, {"start": 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46309, 9957, 12399, 2074, 12399, 20193, 3615, 9566, 1829, 4117, 14407, 18863, 31845, 10632, 35186, 13412, 3555, 16758], "avg_logprob": -0.2941261574074074, "compression_ratio": 1.8372093023255813, "no_speech_prob": 3.5762786865234375e-07, "words": [{"start": 3249.9, "end": 3250.3, "word": "عشان", "probability": 0.84765625}, {"start": 3250.3, "end": 3250.58, "word": " يثبت", "probability": 0.81072998046875}, {"start": 3250.58, "end": 3250.64, "word": " ..", "probability": 0.274169921875}, {"start": 3250.64, "end": 3250.86, "word": " هو", "probability": 0.90185546875}, {"start": 3250.86, "end": 3250.88, "word": " ..", "probability": 0.52099609375}, {"start": 3250.88, "end": 3251.02, "word": " هو", "probability": 0.9462890625}, {"start": 3251.02, "end": 3251.12, "word": " ..", "probability": 0.51611328125}, {"start": 3251.12, "end": 3251.42, "word": " أساسا", "probability": 0.69830322265625}, {"start": 3251.42, "end": 3251.52, "word": " هو", "probability": 0.87646484375}, {"start": 3251.52, "end": 3251.82, "word": " يدّيك", "probability": 0.83515625}, {"start": 3251.82, "end": 3251.96, "word": " إيه", "probability": 0.5814412434895834}, {"start": 3251.96, "end": 3252.16, "word": " هي", "probability": 0.5712890625}, {"start": 3252.16, "end": 3252.44, "word": " ..", "probability": 0.63525390625}, {"start": 3252.44, "end": 3252.84, "word": " جالك", "probability": 0.7035725911458334}, {"start": 3252.84, "end": 3253.34, "word": " أكبر", "probability": 0.9817708333333334}, {"start": 3253.34, "end": 3253.5, "word": " من", "probability": 0.9873046875}, {"start": 3253.5, "end": 3253.86, "word": " أربع،", "probability": 0.70184326171875}, {"start": 3253.86, "end": 3253.98, "word": " يعني", "probability": 0.924072265625}, {"start": 3253.98, "end": 3254.92, "word": " خمسة،", "probability": 0.89169921875}, {"start": 3254.92, "end": 3255.38, "word": " الآن", "probability": 0.815673828125}, {"start": 3255.38, "end": 3255.88, "word": " اتنين", "probability": 0.871337890625}, {"start": 3255.88, "end": 3256.0, "word": " وعشان", "probability": 0.486358642578125}, {"start": 3256.0, "end": 3256.9, "word": " خمسة،", "probability": 0.91201171875}, {"start": 3256.9, "end": 3257.28, "word": " اتنين", "probability": 0.9456787109375}, {"start": 3257.28, "end": 3258.7, "word": " وثلاثين،", "probability": 0.9126674107142857}, {"start": 3258.7, "end": 3259.14, "word": " أكبر", "probability": 0.9798177083333334}, {"start": 3259.14, "end": 3259.28, "word": " من", "probability": 0.994140625}, {"start": 3259.28, "end": 3259.66, "word": " خمسة", "probability": 0.9781494140625}, {"start": 3259.66, "end": 3259.98, "word": " تربية", "probability": 0.64129638671875}, {"start": 3259.98, "end": 3260.06, "word": " من", "probability": 0.97607421875}, {"start": 3260.06, "end": 3260.34, "word": " خمسة", "probability": 0.9388427734375}, {"start": 3260.34, "end": 3260.7, "word": " عشرين،", "probability": 0.81640625}, {"start": 3260.7, "end": 3262.38, "word": " true،", "probability": 0.666748046875}, {"start": 3262.38, "end": 3262.72, "word": " لاعطيكوا", "probability": 0.56439208984375}, {"start": 3262.72, "end": 3262.92, "word": " العافية", "probability": 0.7228190104166666}, {"start": 3262.92, "end": 3263.06, "word": " يا", "probability": 0.5986328125}, {"start": 3263.06, "end": 3263.16, "word": " شباب", "probability": 0.9518229166666666}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3263.495, "duration_after_vad": 3044.88062499999}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/JYdKdPOF5Ho.srt b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/JYdKdPOF5Ho.srt
new file mode 100644
index 0000000000000000000000000000000000000000..eeca4c1e0fa9cf43b8fe30ef285f35e6acc5d9e9
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/JYdKdPOF5Ho.srt
@@ -0,0 +1,2065 @@
+1
+00:00:20,700 --> 00:00:22,700
+بسم الله والحمد لله والصلاة والسلام على رسول الله
+
+2
+00:00:22,700 --> 00:00:25,860
+اليوم إن شاء الله تعالى هنكمل في جهة الـ chapter
+
+3
+00:00:25,860 --> 00:00:29,460
+structures لكن الـ section تبعتنا من section مختلف
+
+4
+00:00:29,460 --> 00:00:32,420
+تمامًا، الكتاب مفرد الـ relations في chapter مستقل
+
+5
+00:00:32,420 --> 00:00:35,680
+اللي هو chapter تسعة، بس الـ chapter اللي احنا كنا
+
+6
+00:00:35,680 --> 00:00:40,460
+فيه، اتنين كنا بنتكلم على الـ basic structure set و
+
+7
+00:00:40,460 --> 00:00:44,240
+function مظبوط، و sequence و matrix و الـ relation
+
+8
+00:00:44,240 --> 00:00:46,860
+هذه، زي ما هنشوف كمان شوية، هي عبارة عن مجموعات
+
+9
+00:00:46,860 --> 00:00:47,820
+relations
+
+10
+00:00:54,300 --> 00:00:59,160
+الآن، لما بجيء بتكلم على الـ relation، الـ relation هي
+
+11
+00:00:59,160 --> 00:01:06,540
+عبارة عن علاقات ما بين المجموعات، حضرتك كطالب في
+
+12
+00:01:06,540 --> 00:01:13,100
+التخصص في الكلية في المساق، الآن تخيل، تخيل مجموعة
+
+13
+00:01:13,100 --> 00:01:19,720
+الكليات وطلاب، relation ولا لا؟ الطالب تخصص كذا، أو
+
+14
+00:01:19,720 --> 00:01:23,640
+الطالب مسجل في كلية كذا، في المساقات، الطالب درس
+
+15
+00:01:23,640 --> 00:01:25,980
+المساق، أو يدرس المساق الفلاني، أو نجح في المساق
+
+16
+00:01:25,980 --> 00:01:31,420
+عبارة عن الـ relation، الناس والألوان اللي بتحبها، و
+
+17
+00:01:31,420 --> 00:01:34,260
+الفواكه اللي بتحب تاكلها، الأخرى هي عبارة عن groups
+
+18
+00:01:34,260 --> 00:01:38,540
+أو sets، مجموعات، وفي بينهم relation، واحنا شفنا
+
+19
+00:01:38,540 --> 00:01:41,140
+نوع من الـ relation يا شباب، لما اتكلمنا على الـ
+
+20
+00:01:41,140 --> 00:01:45,600
+Cartesian product بين مجموعتين ولا لأ؟ قلنا بينتج
+
+21
+00:01:45,600 --> 00:01:52,690
+عنها مجموعة بتشكل أزواج مرتبة، A تنتمي لـ A وB
+
+22
+00:01:52,690 --> 00:01:56,170
+تنتمي لـ B، ولا لها؟ مش هذا تعريف الـ cross
+
+23
+00:01:56,170 --> 00:02:00,570
+product كان؟ وكل هذا الزوج المرتب هو الـ tuple
+
+24
+00:02:00,570 --> 00:02:04,770
+الـ
+
+25
+00:02:04,770 --> 00:02:09,210
+tuple، هذا زوج مرتب، لا يساوي AB، لا تساوي BA، و
+
+26
+00:02:09,210 --> 00:02:11,730
+اتكلمنا عليها،  ساحينها، هنشوف إنه فعليًا هذا موجود
+
+27
+00:02:13,900 --> 00:02:17,160
+وبالتالي أنا الـ relationship between six elements
+
+28
+00:02:17,160 --> 00:02:21,180
+أو الـ element اللي في المجموعات بتمثل structure
+
+29
+00:02:21,180 --> 00:02:24,660
+وعشان هي أنا روحت جيبتها وين؟ في الـ chapter الـ
+
+30
+00:02:24,660 --> 00:02:28,780
+structure، وبالتالي هي عبارة عن subset من الـ
+
+31
+00:02:28,780 --> 00:02:32,660
+Cartesian product، يعني أنا مابعتش عن الكلام اللي
+
+32
+00:02:32,660 --> 00:02:37,580
+أنا أخدته سابقًا، طيب وين بيلزمني هذا الكلام؟ ليش
+
+33
+00:02:37,580 --> 00:02:40,690
+أنا بمحتاج أفهم الـ relation من البداية، صح؟ الـ
+
+34
+00:02:40,690 --> 00:02:42,490
+relations، الـ implementation تبعتها، والـ
+
+35
+00:02:42,490 --> 00:02:45,850
+application تبعتها للناس اللي بتشتغل في الكمبيوتر
+
+36
+00:02:45,850 --> 00:02:50,210
+كبيرة جدًا، لما تدرس مساق الـ database واحد، هنتكلم
+
+37
+00:02:50,210 --> 00:02:56,510
+على relation ما بين الـ entities فيه، عندك الطالب و
+
+38
+00:02:56,510 --> 00:03:00,170
+المساق، different sets، مجموعة الطلاب ومجموعة
+
+39
+00:03:00,170 --> 00:03:03,810
+المساقات، في بينهم relation اللي هو المساق، تسجيل
+
+40
+00:03:03,810 --> 00:03:07,470
+المساق خلال الفصل الواحد، وبالتالي هتصرف فيه
+
+41
+00:03:07,470 --> 00:03:12,930
+relation، بنجيب، نتكلم الناس، أو بلاش المطارات في
+
+42
+00:03:12,930 --> 00:03:17,510
+العالم، كل مطار والـ connected airport التاني اللي
+
+43
+00:03:17,510 --> 00:03:21,410
+ممكن يتواصل معاه عشان يوصل خط الطيارة، تمام؟ فدي
+
+44
+00:03:21,410 --> 00:03:25,610
+عبارة عن relation ما بين المطارات، الـ google map أو
+
+45
+00:03:25,610 --> 00:03:29,350
+الـ map اللي على الجوال هي عبارة عن relation بين الـ
+
+46
+00:03:29,350 --> 00:03:31,950
+two points والـ road اللي بينهم، أو الـ route اللي
+
+47
+00:03:31,950 --> 00:03:34,630
+بينهم، هو عبارة عن البث للـ relation أنه فيه
+
+48
+00:03:34,630 --> 00:03:37,670
+connection، أو فيه طريق ما بين الـ city A والـ city
+
+49
+00:03:37,670 --> 00:03:41,530
+B، وبالتالي الـ implementation والتطبيقات تبعت الـ
+
+50
+00:03:41,530 --> 00:03:45,170
+relation كبيرة وكبيرة جدًا، حتى لما بتكلم على مستوى
+
+51
+00:03:45,170 --> 00:03:50,050
+الشبكات، كمان بتكلم على المجموعات، groups و sets، و
+
+52
+00:03:50,050 --> 00:03:54,730
+بتكلم على الـ permissions، الصلاحيات اللي ممنوحة للـ
+
+53
+00:03:54,730 --> 00:03:57,750
+users اللي موجودين عندي، وبرضه بتكلم على relation
+
+54
+00:03:57,750 --> 00:04:04,710
+لأن في الـ relation هنا يا شباب، في عندي مصطلح unary
+
+55
+00:04:04,710 --> 00:04:12,870
+إيش unary؟ أحادي، أو binary، ثنائي
+
+56
+00:04:12,870 --> 00:04:16,390
+..ثنائي
+
+57
+00:04:16,390 --> 00:04:21,030
+..ثنائي..ثنائي..ثنائي
+
+58
+00:04:21,030 --> 00:04:22,910
+..ثنائي..ثنائي..ثنائي..ثنائي..ثنائي..
+
+59
+00:04:24,480 --> 00:04:32,480
+طبعًا، آخر إن نلاحظ إن الإناري دي هيك، إيش ما اختلفت
+
+60
+00:04:32,480 --> 00:04:37,800
+الـn  بتمثل عدد المجموعات اللي بيمتلكها الـ
+
+61
+00:04:37,800 --> 00:04:42,020
+relation، لعدد المجموعات المشاركة في الـ relation
+
+62
+00:04:42,020 --> 00:04:46,400
+يعني لو قلنا على سبيل المثال، بدنا نشكل فريق برمجة
+
+63
+00:04:46,400 --> 00:04:52,410
+فريق برمجة من قسم يعني، كل فريق لازم يكون فيه عضو من
+
+64
+00:04:52,410 --> 00:04:57,490
+قسم مختلف، وحققوا الحد الأقصى للفريق أربعة، إيش
+
+65
+00:04:57,490 --> 00:05:00,370
+هنسوي؟ هنقول والله مثلًا واحد من الـ multimedia،
+
+66
+00:05:00,370 --> 00:05:02,210
+واحد من الـ mobile computing، واحد software
+
+67
+00:05:02,210 --> 00:05:05,170
+development، واحد computer science، فريق التاني،
+
+68
+00:05:05,170 --> 00:05:08,730
+لاحظ أنا بتكلم على أربعة، أربع مجموعات مختلفة
+
+69
+00:05:08,730 --> 00:05:14,080
+شاركت في تشكيل الفريق، طيب لو كل رجل في الفريق
+
+70
+00:05:14,080 --> 00:05:17,920
+يريد أن يأخذ منزلة الرئيس ونائب الرئيس وأمين
+
+71
+00:05:17,920 --> 00:05:21,940
+الفريق مثلًا، وExecutor، سامي زي ما بدك، أو Documenter
+
+72
+00:05:21,940 --> 00:05:28,200
+وبالتالي صار كل position له ترتيب مهم بالنسبة لنا
+
+73
+00:05:28,200 --> 00:05:33,260
+وهنا أنا ما بديش تفهم إنه لما أنا بتكلم على
+
+74
+00:05:33,260 --> 00:05:36,980
+relation، معناته أنا بتكلم على table زي ما قلنا، و
+
+75
+00:05:36,980 --> 00:05:40,780
+الـ table هذا بيحدد الرقم، لما أنا بتكلم
+
+76
+00:05:44,810 --> 00:05:49,730
+3 tuple، معناته إن أنا بتكلم عن علاقة
+
+77
+00:05:49,730 --> 00:05:54,730
+ثلاثية بين 3 components موجودة عندي، لما بتكلم على
+
+78
+00:05:54,730 --> 00:06:01,530
+الـ 2 tuple، الحد اللي احنا بنعرف اسمها ordered pair
+
+79
+00:06:01,530 --> 00:06:07,810
+زوج مرتب a وb، الزوج المرتب، معناته الأقواس، بنسميها
+
+80
+00:06:07,810 --> 00:06:12,500
+tuple، والـ elements اللي موجودات فيه بنسميها الـ
+
+81
+00:06:12,500 --> 00:06:15,860
+Elemental Fattable، مش خضرياتنا، كتير المعلومات كلها
+
+82
+00:06:15,860 --> 00:06:21,360
+هنيجي تباعًا إن شاء الله تعالى، طيب الآن أنا بتكلم
+
+83
+00:06:21,360 --> 00:06:24,820
+أو في تركيزنا في الـ chapter هذا على الـ binary
+
+84
+00:06:24,820 --> 00:06:31,180
+relation، تركيزنا الآن على الـ binary relation، الـ
+
+85
+00:06:31,180 --> 00:06:34,700
+binary relation معناته إن في عندي two sets، A وB
+
+86
+00:06:34,700 --> 00:06:39,800
+وبالتالي الـ binary relation ما بين A وB هي عبارة
+
+87
+00:06:39,800 --> 00:06:48,560
+عن subset من الكارتيزي البرودكت، R تساوي الأزواج
+
+88
+00:06:48,560 --> 00:06:55,540
+المرتبة، two double أو binary أو ordered pair، بحيث
+
+89
+00:06:55,540 --> 00:07:02,420
+إن A تنتمي إلى A، وB تنتمي إلى B، بنعرف البرودكت كله
+
+90
+00:07:02,420 --> 00:07:07,040
+ممكن تضيف أي condition لاحقًا عشان تحدد هيئة بشكل
+
+91
+00:07:07,040 --> 00:07:08,000
+أدق
+
+92
+00:07:11,120 --> 00:07:18,360
+ممكن أن أعرفها بشكل مختلف عن التعريف السابق، بحيث
+
+93
+00:07:18,360 --> 00:07:21,800
+أن أقول إن الـ relation تتعرف بالأزواج المرتبة A وB
+
+94
+00:07:21,800 --> 00:07:30,560
+بتنتمي إلى R، وهذا معناته A related to B، إذا
+
+95
+00:07:30,560 --> 00:07:33,160
+أنا جيت كلامي على الطالب والمساق اللي بيدرسه
+
+96
+00:07:33,160 --> 00:07:40,740
+هقول أحمد study discrete mathematics، هاني بيلعب
+
+97
+00:07:40,740 --> 00:07:45,920
+football على أنه الـ favorite sport، لو اجينا نتكلم عن
+
+98
+00:07:45,920 --> 00:07:50,960
+الفاكهة اللي بتحبها، إيش اسمك؟ محمد، محمد likes
+
+99
+00:07:50,960 --> 00:07:55,600
+strawberry، فراولة، جزء خاص من الـ relation، جزء خاص
+
+100
+00:07:55,600 --> 00:07:58,760
+من الـ relation، أو من الـ Cartesian product، لو عناصر
+
+101
+00:07:58,760 --> 00:08:05,260
+الـ A في نفسها، يعني A cross الـ A، يعني ممكن أنا أحقق
+
+102
+00:08:05,260 --> 00:08:11,090
+relation من خلال A cross الـ A، كارتيزيان الـ product
+
+103
+00:08:11,090 --> 00:08:14,310
+بين الـ A ونفسها، هالكلام صحيح بيصير؟ آه بيصير
+
+104
+00:08:14,310 --> 00:08:18,170
+تخيل لو أنا جيت وقلت لك هي الـ A equal واحد، و
+
+105
+00:08:18,170 --> 00:08:25,210
+اتنين، وتلاتة، والـ relation تبعتنا بدها تساوي A و
+
+106
+00:08:25,210 --> 00:08:28,870
+B، حيث الـ B أكبر من الـ A
+
+107
+00:08:34,960 --> 00:08:41,800
+مفهوم الـ Head relation، كل الأزواج المرتبة اللي
+
+108
+00:08:41,800 --> 00:08:46,080
+في الـ Cartesian product في الـ A و A، بحيث أن الـ B
+
+109
+00:08:46,080 --> 00:08:58,240
+تكون أكبر من الـ A، 1 و2، 1 و3، 2 و3، Head
+
+110
+00:08:58,240 --> 00:09:03,320
+relation، Cartesian
+
+111
+00:09:03,320 --> 00:09:07,750
+product هو السقف تبعك، عندك مجموعتين، عدد العناصر في
+
+112
+00:09:07,750 --> 00:09:12,430
+الأولى أربعة، وفي الثانية خمسة، أكبر relation ممكن
+
+113
+00:09:12,430 --> 00:09:16,950
+تتشكل، قد إيش؟ أربعة في خمسة، عشرين element
+
+114
+00:09:16,950 --> 00:09:20,890
+أربعة في خمسة، ليش؟ عشرين element، الآن أنا عندي
+
+115
+00:09:20,890 --> 00:09:25,250
+هنا بقول لك A في A، تمام؟ والـ relation هي subset من
+
+116
+00:09:25,250 --> 00:09:30,490
+من الـ A، subset، احنا متفقين، وبالتالي كحد أقصى هنا
+
+117
+00:09:30,490 --> 00:09:35,490
+ممكن تكون تسع عناصر، لكن لما أنا بروح بقيدها من خلال
+
+118
+00:09:35,490 --> 00:09:38,930
+الـ definition، معناته أنا صرت أنا بحدد عدد عناصر
+
+119
+00:09:38,930 --> 00:09:42,590
+مختلف، لاحظوا يا شباب إنه مازلت في الـ relation
+
+120
+00:09:42,590 --> 00:09:46,250
+بتكلم على المجموعات ولا لا؟ ما بعدتش لحتى اللحظة عن
+
+121
+00:09:46,250 --> 00:09:50,870
+المجموعات مطلقًا، هذا
+
+122
+00:09:50,870 --> 00:09:54,250
+المثال اللي قلناه، مجموعة الطلاب، الـ A بتمثل مجموعة
+
+123
+00:09:54,250 --> 00:10:00,270
+الطلاب، والـ B بتمثل مجموعة الـ courses، معناته احنا
+
+124
+00:10:00,270 --> 00:10:05,810
+بنتكلم، نقدر نتكلم، نقول زوج المرتب A وB هي العلاقة
+
+125
+00:10:05,810 --> 00:10:10,870
+ما بين A تمثل طالب، وB تمثل مساق، وبالتالي student
+
+126
+00:10:10,870 --> 00:10:18,850
+A taking course أو studying course B، طبعًا
+
+127
+00:10:18,850 --> 00:10:22,550
+الـ definition ممكن تكتب بصورة ثانية، محمد والفراولة
+
+128
+00:10:22,550 --> 00:10:30,110
+هيهم، X likes Y، الآن A set of people، والـ R
+
+129
+00:10:30,110 --> 00:10:35,860
+describes who likes fruit، يعني الـ Y بتمثل مين؟
+
+130
+00:10:35,860 --> 00:10:40,440
+الفروت، وبالتالي X like Y هي الـ relation اللي
+
+131
+00:10:40,440 --> 00:10:43,520
+موجودة عندنا هنا، الآن ممكن الـ relation برضه تنكتب
+
+132
+00:10:43,520 --> 00:10:48,080
+أو تتعرف بشكل مختلف تمامًا، لما أنا أجي أقول لك إن الـ
+
+133
+00:10:48,080 --> 00:10:54,540
+A تساوي الـ natural number، وجيت قلت الـ relation
+
+134
+00:10:54,540 --> 00:11:00,400
+تبعتي، قلنا نقراها X related Y، X related Y، لاحظ هو
+
+135
+00:11:00,400 --> 00:11:04,270
+تكلم فقط على مجموعة واحدة، زي ما في المثال هذا
+
+136
+00:11:04,270 --> 00:11:09,290
+مباشرة بيأتي لذهنك cross product between A في A
+
+137
+00:11:09,290 --> 00:11:12,830
+cross product between A في A، وهاد الـ relation
+
+138
+00:11:12,830 --> 00:11:16,010
+هتكون subset منها، الـ subset منها، كيف أعرف الـ
+
+139
+00:11:16,010 --> 00:11:22,630
+definition؟ X أقل أو تساوي الـ Y، زي المثال تقريبًا
+
+140
+00:11:22,630 --> 00:11:29,850
+هذا اللي أنا كتبته الآن
+
+141
+00:11:29,850 --> 00:11:33,360
+بما أن الـ relation، بما أن الـ relation هي عبارة عن
+
+142
+00:11:33,360 --> 00:11:37,920
+مجموعة، بما يعني بقدر أطبق عليها كل العمليات
+
+143
+00:11:37,920 --> 00:11:47,080
+الخاصة بالمجموعات، اللي هما التقاطع،
+
+144
+00:11:47,080 --> 00:11:53,160
+الاتحاد، الـ difference، والـ..الـ.. خلصناها؟ ما
+
+145
+00:11:53,160 --> 00:11:55,720
+خلصناهاش، ده في واحدة.. أيوة، المتممة يا أحمد، إيش
+
+146
+00:11:55,720 --> 00:12:02,770
+اسمها يا دي؟ المتممة.. المتممة، أيوة، الآن معناته
+
+147
+00:12:02,770 --> 00:12:06,230
+أنا فعليًا بتكلم، لأنه كمان مرة ما تنساش أنا بتكلم
+
+148
+00:12:06,230 --> 00:12:10,030
+مازال قاعدين من الـ definition، set builder notation
+
+149
+00:12:10,030 --> 00:12:13,950
+أنا بتكلم على مجموعة، وبالتالي بطبق العمليات بتاعة
+
+150
+00:12:13,950 --> 00:12:18,250
+المجموعات على كل العناصر اللي في الـ relation اللي
+
+151
+00:12:18,250 --> 00:12:25,170
+موجودة عندي، اتحاد، تقاطع، difference، والمتممة، بدي
+
+152
+00:12:25,170 --> 00:12:31,490
+أسأل سؤال في المثال السابق، على هذا، احنا قلنا الآن
+
+153
+00:12:31,490 --> 00:12:40,290
+R بدها تساوي أزواج المرتبة X وY، حيث X أصغر أو
+
+154
+00:12:40,290 --> 00:12:48,090
+تساوي الـ Y، طبعًا، and X وY تنتمي لـ natural number
+
+155
+00:12:48,090 --> 00:12:53,370
+مش قضية كتير هذا بالنسبة لنا، طيب الآن هات المتممة
+
+156
+00:12:53,370 --> 00:12:58,170
+تبعتها، إيش المتممة؟ الـ complement
+
+157
+00:13:04,420 --> 00:13:11,480
+دي المتممة R، شرطها X
+
+158
+00:13:11,480 --> 00:13:21,980
+وY، X أكبر من Y، بدون ما يتساوي، لأنه أنا بدي العناصر اللي
+
+159
+00:13:21,980 --> 00:13:25,760
+في المتممة، من المتممة، من الـ universe اللي هي N
+
+160
+00:13:25,760 --> 00:13:29,700
+في N، الـ universe تبعتنا لـ N، في N، أنا هدول منهم
+
+161
+00:13:29,700 --> 00:13:35,160
+subset، فبدي الباقي، جيبهم لي، والله إنكم تدرسوا يا شباب
+
+162
+00:13:35,160 --> 00:13:41,320
+عشان الحل، هنتكلم الآن في خصائص الـ relation، هنتكلم
+
+163
+00:13:41,320 --> 00:13:48,980
+في خصائص الـ relation، أول خاصية reflexive، طيب قبل
+
+164
+00:13:48,980 --> 00:13:53,160
+ما نتكلم عن الـ reflexive، لما أنا يا شباب بتكلم A
+
+165
+00:13:53,160 --> 00:13:58,860
+في A، يعني لو كانت عدد عناصر الـ A اتنين، لما بتكلم
+
+166
+00:13:58,860 --> 00:14:02,570
+اتنين في اتنين، لو كانت تلاتة، تلاتة في تلاتة، هو عدد
+
+167
+00:14:02,570 --> 00:14:07,230
+العناصر، ف بصورة .. وكأني بتكلم على square matrix
+
+168
+00:14:07,230 --> 00:14:12,730
+لو أنت تيجي تصفّهم أو ترتبهم، واحد واثنين، واحد و
+
+169
+00:14:12,730 --> 00:14:17,990
+تلاتة، أو عفواً، واحد وواحد، واحد واثنين، واحد و
+
+170
+00:14:17,990 --> 00:14:24,850
+تلاتة، بعد هيك اثنين وواحد، اثنين واثنين، اثنين و
+
+171
+00:14:24,850 --> 00:14:31,280
+تلاتة، بعدها تلاتة وواحد، تلاتة واثنين، تلاتة و
+
+172
+00:14:31,280 --> 00:14:35,900
+تلاتة، وكأني بتكلم على square matrix، تلاتة في
+
+173
+00:14:35,900 --> 00:14:38,560
+تلاتة، صح؟ اسمها مربعة
+
+174
+00:14:43,560 --> 00:14:47,580
+المصفوفة طبعًا، وكأني قاعد بقول لك هذه تمثل I
+
+223
+00:18:45,810 --> 00:18:50,110
+متقابقة
+
+224
+00:18:50,110 --> 00:18:58,810
+أو متماثلة متناظرة،  محلّكم أنتم بالترجمة العربية صح
+
+225
+00:18:58,810 --> 00:19:04,390
+تمام؟ الآن مفهوم التقابق أو التناظر أن هذا الـ
+
+226
+00:19:04,390 --> 00:19:06,950
+element هو هذا، هذا جدش الـ element .. هذا واحد
+
+227
+00:19:06,950 --> 00:19:12,590
+اتنين تلاتة، هنا واحد اتنين تلاتة، مصبوط؟ هذا جدش
+
+228
+00:19:12,590 --> 00:19:18,800
+رقم الـ element هذا، عفوا، هذا a12 الصف الأول العمودي
+
+229
+00:19:18,800 --> 00:19:29,020
+الثاني يساوي a21، هذا a13 يساوي a31 وهكذا، وهكذا منها
+
+230
+00:19:29,020 --> 00:19:33,560
+حيش متماثلة symmetric، سميناها المصفوفة symmetric
+
+231
+00:19:33,560 --> 00:19:38,240
+matrix، الآن هذا الكلام بدي أسقطه على الـ relation
+
+232
+00:19:39,340 --> 00:19:42,540
+لاحظوا العلاقة جدش؟ علاقة بالـ relation، علاقة
+
+233
+00:19:42,540 --> 00:19:45,320
+بالمصفوفات، فأنا روحت جيبته من .. عشان ايه؟ روحت
+
+234
+00:19:45,320 --> 00:19:48,940
+جيبته من chapter 9؟ وحققته وين؟ في الـ chapter ..
+
+235
+00:19:48,940 --> 00:19:52,980
+قبل ما تنسى، لأن أنا عارف إنه اللي بندرسه عشان ننساه
+
+236
+00:19:52,980 --> 00:19:56,220
+احنا الآن، تعالى الـ relation، في الـ relation بنقول
+
+237
+00:19:56,220 --> 00:20:04,040
+إذا لكل زوج مرتب for all a و b تنتمي للـ relation
+
+238
+00:20:04,040 --> 00:20:13,970
+for all a و b تنتمي للـ relation، هذا يؤدي أن b و a
+
+239
+00:20:13,970 --> 00:20:17,590
+تنتمي للـ relation، بقول عن الـ relation عندي هالـ
+
+240
+00:20:17,590 --> 00:20:22,110
+Symmetric، بقول عن الـ relation عندي هالـ Symmetric
+
+241
+00:20:22,110 --> 00:20:27,470
+الـ relation هذه، هل هي Symmetric؟ هل الـ relation
+
+242
+00:20:27,470 --> 00:20:32,270
+هذه Symmetric؟ طيب الآن، هل هي Symmetric؟ لأ، تعالى
+
+243
+00:20:32,270 --> 00:20:37,610
+نشوف واحد من الأمثلة، أقول لك واحد و واحد، a أكبر أو
+
+244
+00:20:37,610 --> 00:20:45,470
+تساوي a، بصبوط صورتها واحد و واحد، صح، لكن الآن
+
+245
+00:20:45,470 --> 00:20:50,750
+اتنين و واحد تحقق الـ relation، اتنين و واحد تنتمي
+
+246
+00:20:50,750 --> 00:20:56,310
+إلى الـ R، لكن but
+
+247
+00:20:56,310 --> 00:21:01,180
+الواحد والثاني اللي هي صورتها، أو انعكاسها
+
+248
+00:21:01,180 --> 00:21:05,160
+تماثلها لا تنتمي للـ relation، معناته الـ R is not
+
+249
+00:21:05,160 --> 00:21:15,780
+symmetric، R is not symmetric، تمام؟
+
+250
+00:21:15,780 --> 00:21:19,740
+الـ definition بسيط وسهل، بدأنا نرى على الـ relation
+
+251
+00:21:19,740 --> 00:21:24,800
+على كل العناصر اللي فيها، كل عنصر فيه صورته أو
+
+252
+00:21:24,800 --> 00:21:29,850
+انعكاسه موجود، تمام؟ a و b بلاجئله b و a؟ معناته
+
+253
+00:21:29,850 --> 00:21:33,690
+الـ relation اللي عندي هنا Symmetric، تعالى نشوف
+
+254
+00:21:33,690 --> 00:21:40,950
+المثال هذا، افترض على نفس الـ A، هذه R تساوي واحد و
+
+255
+00:21:40,950 --> 00:21:49,150
+اتنين، اتنين و واحد، بس
+
+256
+00:21:49,150 --> 00:21:52,090
+هي relation،  هي subset من الـ Cartesian product
+
+257
+00:21:52,090 --> 00:21:59,350
+صح، relation، Binary relation، هل هي
+
+258
+00:21:59,350 --> 00:22:06,090
+Symmetric؟ هل هي Symmetric؟ يا راجل، تجلى، هل هي
+
+259
+00:22:06,090 --> 00:22:10,650
+Symmetric؟ خد كل element، هي الـ element الأول واحد
+
+260
+00:22:10,650 --> 00:22:15,550
+و اتنين، بينتمي للـ relation، ايش انعكاسه؟ اتنين و
+
+261
+00:22:15,550 --> 00:22:19,350
+واحد، تنتمي للـ relation؟ تنتمي للـ relation، العنصر
+
+262
+00:22:19,350 --> 00:22:23,430
+الثاني، اتنين و واحد، بينتمي للـ relation، انعكاسه؟
+
+263
+00:22:24,080 --> 00:22:27,640
+واحد واثنين، تنتمي للـ relation، معناته الـ relation
+
+264
+00:22:27,640 --> 00:22:34,480
+هذه symmetric، ما تفتش، ما تفتش
+
+265
+00:22:34,480 --> 00:22:39,600
+أنا قلت كلمة سهلة وبسيطة، الـ properties هذه انفكت
+
+266
+00:22:39,600 --> 00:22:44,680
+عن بعض، not related together، أنا
+
+267
+00:22:44,680 --> 00:22:50,480
+بسألك symmetric، تقولي reflexive، اليوم
+
+268
+00:22:50,480 --> 00:22:55,300
+اليوم، من برا، حاجات مجلوبة، مش صح الجواب يا
+
+269
+00:22:55,300 --> 00:23:02,120
+صاحبي، مش logic بالمرة، هو أنا
+
+270
+00:23:02,120 --> 00:23:05,380
+باسألك في الـ symmetric، الـ condition مختلف تماما،
+
+271
+00:23:05,380 --> 00:23:09,860
+الآن، not symmetric، symmetric، symmetric،
+
+272
+00:23:09,860 --> 00:23:15,200
+reflexive، reflexive، not reflexive، لو أنا سألتك
+
+273
+00:23:15,200 --> 00:23:19,160
+reflexive، not reflexive، ايه وايه، مش لأن تمي،
+
+274
+00:23:19,160 --> 00:23:21,900
+واحد و واحد مش موجود، خلصنا، ما تدوريش، ما تكملش
+
+275
+00:23:28,850 --> 00:23:36,370
+الآن في عندي تعريف جديد، اسمه Anti-symmetric، ومن
+
+276
+00:23:36,370 --> 00:23:44,050
+الآن انتبه معايا، Anti-symmetric، لا
+
+277
+00:23:44,050 --> 00:23:51,130
+تساوي كل
+
+278
+00:23:51,130 --> 00:23:54,290
+هدول، different definitions، different properties
+
+279
+00:23:57,110 --> 00:24:02,810
+لكن بنقدر نقول لو كانت symmetric، مش هتكون Anti-
+
+280
+00:24:02,810 --> 00:24:06,030
+symmetric، ولو كانت Anti-symmetric، مش هتكون
+
+281
+00:24:06,030 --> 00:24:09,410
+symmetric، بس ممكن تكون الـ relation لا symmetric
+
+282
+00:24:09,410 --> 00:24:17,990
+ولا Anti-symmetric، تمام؟ ولا reflexive كمان، الآن
+
+283
+00:24:17,990 --> 00:24:25,070
+إيش اللي بنقوله بكل بساطة؟ بنقول، كتالة، لو جينا أو
+
+284
+00:24:25,070 --> 00:24:29,630
+أخذنا كل الأزواج المرتبة اللي في الـ relation، كل
+
+285
+00:24:29,630 --> 00:24:34,310
+الأزواج المرتبة اللي في الـ relation، تمام؟ مش
+
+286
+00:24:34,310 --> 00:24:38,210
+هنجيب، وانعكاس إلا الزوج المرتب اللي فيه الـ a
+
+287
+00:24:38,210 --> 00:24:43,890
+تساوي b، ليش؟ لأن انعكاسه هو نفسه، يعني بكتب
+
+288
+00:24:43,890 --> 00:24:47,550
+بنفسهم، نفس العناصر المتماثلة في الأزواج
+
+289
+00:24:47,550 --> 00:24:51,730
+المرتبة، حاول أسقطها من فحصك الـ symmetric والـ
+
+290
+00:24:51,730 --> 00:24:57,250
+antisymmetric، الآن لو أنا أجيب وقلت لك الـ R هذه
+
+291
+00:24:57,250 --> 00:25:07,550
+واحد و واحد، اتنين و واحد، وواحد و اتنين، مرتبط؟
+
+292
+00:25:07,550 --> 00:25:15,730
+مرتبط، ليش؟ لأ، مرتبط، هذا ايش انعكاسه؟ نفسه، وهذا
+
+293
+00:25:15,730 --> 00:25:20,950
+انعكاس نفسه، بقدّرها، هذا وهذا، بدّلنا، مظبوط؟ و
+
+294
+00:25:20,950 --> 00:25:25,080
+بالتالي، مرتبط، الآن هل هي Anti-Symmetric؟ لأ، نقطة
+
+295
+00:25:25,080 --> 00:25:28,760
+Anti-Symmetric، خلصنا، لأن فيها أزواج مرتبة غير
+
+296
+00:25:28,760 --> 00:25:33,740
+الواحد وواحد، فيها ايش انعكاس، لكن تعالى شوف هذه
+
+297
+00:25:33,740 --> 00:25:44,100
+Symmetric
+
+298
+00:25:44,100 --> 00:25:50,410
+لأ، Anti-Symmetric، true، Anti-Symmetric، Anti-
+
+299
+00:25:50,410 --> 00:25:53,790
+symmetric، التعريف تبقى الـ Anti-Symmetric فيقول
+
+300
+00:25:53,790 --> 00:25:59,090
+كالتالي، كل الأزواج المرتبة لعناصرها مختلفة ليس لها
+
+301
+00:25:59,090 --> 00:26:05,670
+صور، كل العناصر، أو كل الأزواج المرتبة لعناصرها
+
+302
+00:26:05,670 --> 00:26:10,930
+مختلفة ليس لها صور، خلصنا، هذا خلينا اللي هي أنا
+
+303
+00:26:10,930 --> 00:26:17,510
+صورته نفسه، هذا فيه صورة؟ لأ، معناته Anti-Symmetric
+
+304
+00:26:21,170 --> 00:26:25,550
+شوف الـ relation هذه،  احباز السنة شوية، هذه R تساوي
+
+305
+00:26:25,550 --> 00:26:34,130
+واحد و واحد، واحد و اتنين، اتنين و واحد
+
+306
+00:26:34,130 --> 00:26:40,850
+و واحد، واحد و تلاتة، symmetric؟
+
+307
+00:26:40,850 --> 00:26:49,570
+symmetric؟ لأ، لحظة شوية، not symmetric، ليش؟
+
+308
+00:26:50,300 --> 00:26:57,260
+ليش؟ لأن واحد و تلاتة تنتمي للـ relation، but تلاتة
+
+309
+00:26:57,260 --> 00:27:01,600
+و واحد لا تنتمي للـ relation، بالمناسبة، لما بدك تنفي
+
+310
+00:27:01,600 --> 00:27:05,420
+بدك تقولي ليش .. لما بدك تنفي، هبقى هتقولي ليش
+
+311
+00:27:05,420 --> 00:27:12,500
+..طيب .. antisymmetric؟ لأ، not antisymmetric
+
+312
+00:27:17,400 --> 00:27:22,160
+ليش not antisymmetric؟ لأن الواحد واتنين تنتمي للـ
+
+313
+00:27:22,160 --> 00:27:28,860
+relation، and
+
+314
+00:27:28,860 --> 00:27:32,600
+الواحد لا تساوي الاتنين
+
+315
+00:27:34,540 --> 00:27:39,420
+والواحد لا تساوي التلاتة، الجزئية الأخيرة هذه، لو
+
+316
+00:27:39,420 --> 00:27:43,460
+أنت قررت لي إياها وما كتبتهاش، okay، ليش؟ عشان احنا
+
+317
+00:27:43,460 --> 00:27:46,340
+قلنا من البداية، الأزواج المرتبة اللي فيها العنصر
+
+318
+00:27:46,340 --> 00:27:50,700
+متشابه، بدي أسقطها من عملية الفحص، يعني هي بين جسدين
+
+319
+00:27:50,700 --> 00:27:54,480
+لها تأثير معاك في الـ symmetric ولا تأثير معاك في
+
+320
+00:27:54,480 --> 00:27:55,260
+الـ antisymmetric
+
+321
+00:28:02,930 --> 00:28:05,770
+هذه مجموعة من الأمثلة زي اللي شوفناها قبل شوية
+
+322
+00:28:05,770 --> 00:28:13,290
+symmetric و Anti-symmetric،  ولا هذه ولا هذه، طيب في
+
+323
+00:28:13,290 --> 00:28:21,430
+عندك خاصية الرابعة، Transitive، خاصية التعدي، مفهومها
+
+324
+00:28:21,430 --> 00:28:31,490
+for any، for all a و b، and b و c تنتمي للـ relation
+
+325
+00:28:32,690 --> 00:28:36,830
+ماذا يعني؟ انتبه معايا، ماذا يعني؟ لازم يكون عندك
+
+326
+00:28:36,830 --> 00:28:42,630
+زوجين مرتبين، زوجين مرتبات مختلفين، نهاية الأول
+
+327
+00:28:42,630 --> 00:28:49,090
+تساوي بداية الثاني، إذا وجد أي زوجين مرتبين بالشكل
+
+328
+00:28:49,090 --> 00:28:54,870
+هذا، و لاجئت أن a و c، اللي هي بداية الأول ونهاية
+
+329
+00:28:54,870 --> 00:28:57,650
+الثانية، بتنتمي للـ relation، معناته اللي بقول عنها
+
+330
+00:28:57,650 --> 00:29:01,550
+متعدية، يعني بين بصين الأربعة
+
+331
+00:29:03,270 --> 00:29:08,910
+بتقبل القسمة على اتنين، صح؟ الثمانية بتقبل القسمة على
+
+332
+00:29:08,910 --> 00:29:15,010
+أربعة، فالـ ثمانية بتقبل القسمة على اتنين، فعملية القسمة
+
+333
+00:29:15,010 --> 00:29:17,550
+اللي أنا ممكن اسميها transitive،  ضمن الـ
+
+334
+00:29:17,550 --> 00:29:22,890
+condition اللي موجود عندي، وين
+
+335
+00:29:22,890 --> 00:29:27,630
+ما بتشوف يساوي، أقل من، أو أكبر من، أو subset، يعني
+
+336
+00:29:27,630 --> 00:29:30,270
+إننا بنتكلم على transitive، بتكون الـ relation اللي
+
+337
+00:29:30,270 --> 00:29:34,720
+عندنا transitive، الـ relation هذه transitive أو
+
+338
+00:29:34,720 --> 00:29:41,040
+transitive، تعالى شوف بشكل عام، transitive أو
+
+339
+00:29:41,040 --> 00:29:45,740
+transitive أو transitive أو transitive أو
+
+340
+00:29:45,740 --> 00:29:51,020
+transitive أو transitive
+
+341
+00:29:51,020 --> 00:29:52,120
+أو transitive أو transitive أو transitive أو
+
+342
+00:29:52,120 --> 00:29:52,160
+transitive أو transitive أو transitive أو
+
+343
+00:29:52,160 --> 00:29:52,360
+transitive أو transitive أو transitive أو
+
+344
+00:29:52,360 --> 00:29:52,380
+transitive أو transitive أو transitive أو
+
+345
+00:29:52,380 --> 00:29:52,980
+transitive أو transitive أو transitive أو
+
+346
+00:29:52,980 --> 00:29:54,520
+transitive أو transitive أو transitive أو
+
+347
+00:29:54,520 --> 00:29:56,260
+transitive أو transitive أو transitive أو
+
+348
+00:29:56,260 --> 00:30:04,810
+transitive أو transitive، الـ c و الـ c أكبر أو
+
+349
+00:30:04,810 --> 00:30:08,790
+تساوي الـ b، الرتب، الموضوع المثل هذا يعني أن الـ c
+
+350
+00:30:08,790 --> 00:30:15,350
+أكبر أو تساوي الـ b، أكبر أو تساوي الـ a، وبالتالي
+
+351
+00:30:15,350 --> 00:30:20,450
+الـ c أكبر أو تساوي الـ a، وبالتالي أصبح الـ a والـ
+
+352
+00:30:20,450 --> 00:30:24,890
+الـ c ينتمي للـ relation، فأصبحت الـ relation هذه
+
+353
+00:30:24,890 --> 00:30:28,810
+transitive، أصبحت الـ relation transitive، واضح يا
+
+354
+00:30:28,810 --> 00:30:29,150
+شباب؟
+
+355
+00:30:31,900 --> 00:30:36,620
+طيب .. ما زال أوضح .. تعالوا نشوف .. أنتم لا جدش
+
+356
+00:30:36,620 --> 00:30:40,960
+فاهمين من الكلام اللي بنقوله .. انطبق الأربع خصائص
+
+357
+00:30:40,960 --> 00:30:48,940
+.. أتذكر كمان مرة .. كمان مرة .. Reflexive .. a و
+
+358
+00:30:48,940 --> 00:30:52,260
+a تنتمي للـ relation .. لكل عناصر a .. لكل عناصر
+
+359
+00:30:52,260 --> 00:30:56,300
+مجموعة a .. Symmetric .. كل زوج مرتب a و b في الـ
+
+360
+00:30:56,300 --> 00:30:59,340
+relation .. b و a لازم يكون موجود في الـ relation
+
+361
+00:30:59,340 --> 00:31:05,100
+عشان تكون Symmetric .. Antisymmetric، كل زوج مرتب a
+
+362
+00:31:05,100 --> 00:31:10,000
+و b في الـ relation، b و a لا ينتمي للـ relation، لـ
+
+363
+00:31:10,000 --> 00:31:15,420
+Transitive، لكل زوجين a و b و b و c، a و c لازم يكون
+
+364
+00:31:15,420 --> 00:31:19,840
+ينتمي في الـ relation، بيقول عنها Transitive، بقول لك
+
+365
+00:31:19,840 --> 00:31:25,560
+هي الـ a الآن
+
+366
+00:31:25,560 --> 00:31:30,600
+بقول R1، نتكلم على R1
+
+367
+00:31:34,700 --> 00:31:38,060
+R1، مش عارف ألاقيه محله على اللوحة، عشان نبقى ضمن الـ
+
+368
+00:31:38,060 --> 00:31:42,160
+slides، وما نبعدش كتير، وما نجلمش أبو حسن معانا، الآن
+
+369
+00:31:42,160 --> 00:31:50,760
+R1 reflexive، كيف بتحكم عليها reflexive؟ بدك تروح
+
+370
+00:31:50,760 --> 00:31:55,780
+على عناصر الـ A، كم عنصر في الـ A؟ 1,2,3,4، بدك تدور
+
+371
+00:31:55,780 --> 00:32:04,510
+على 4 أزواج مرتبة، 1 و 1، 2 و 2، 3 و 3، الآن 1 و 1
+
+372
+00:32:04,510 --> 00:32:08,390
+موجود، اتنين و اتنين موجود، تلاتة و تلاتة مش موجود
+
+373
+00:32:08,390 --> 00:32:14,690
+بقول is not reflexive، لأن تلاتة و تلاتة لا تنتمي لـ
+
+374
+00:32:14,690 --> 00:32:24,990
+R1، طيب symmetric؟ طيب تعالى نشوف symmetric
+
+375
+00:32:24,990 --> 00:32:29,310
+هل هي symmetric؟ بدك تبدأ تفحص، سيبك من الأزواج
+
+376
+00:32:29,310 --> 00:32:34,990
+المرتبة اللي قُلنا متشابهات، واحد و اتنين صورتها ..
+
+377
+00:32:34,990 --> 00:32:38,390
+اتنين و واحد، هي موجودة .. اتنين و واحد صورتها هي
+
+378
+00:32:38,390 --> 00:32:41,870
+.. خلاصنا .. تلاتة و أربعة .. الأصل يكون أربعة و
+
+379
+00:32:41,870 --> 00:32:46,110
+تلاتة .. معناته not symmetric .. not symmetric ..
+
+380
+00:32:46,110 --> 00:32:52,410
+وليش؟ لأن تقول تلاتة و أربعة تنتمي للـ relation ..
+
+381
+00:32:52,410 --> 00:32:58,290
+but، أربعة و تلاتة لا تنتمي للـ relation ..
+
+382
+00:33:04,640 --> 00:33:09,440
+Antisymmetric برضه لأ، لإيش؟ لأن عندي واحد و اتنين
+
+383
+00:33:09,440 --> 00:33:15,580
+تنتمي للـ relation، and، اتنين و واحد تنتمي للـ
+
+384
+00:33:15,580 --> 00:33:20,520
+relation،  واحد معناته هي not reflexive, not
+
+385
+00:33:20,520 --> 00:33:26,250
+symmetric, not antisymmetric, transitive، لاتش اسمها
+
+386
+00:33:26,250 --> 00:33:29,750
+دي، أيوة هي بالظبط، طيب في الـ transitive، تعالى تشوف
+
+387
+00:33:29,750 --> 00:33:34,890
+شوية، اشتغل معاها صح، عشان ما تفوتش ولا عنصر، لأن لو
+
+388
+00:33:34,890 --> 00:33:40,090
+فوتت element واحد منهم، ممكن تغلط، ايش تساوي؟ امشي
+
+389
+00:33:40,090 --> 00:33:45,030
+معاهم، انسالي .. انسالي كل الأزواج المرتبة، تمام؟
+
+390
+00:33:45,030 --> 00:33:49,770
+اللي بتبدأ بـ .. اللي فيها عناصر متشابهات، تمام؟
+
+391
+00:33:49,770 --> 00:33:54,380
+لأن هذا already هيؤدي للعناصر التانية، الآن ايش تساوي؟
+
+392
+00:33:54,380 --> 00:33:58,720
+تبدأ تحصر عناصر، واحد و واحد، انسانية واحد .. أنا
+
+393
+00:33:58,720 --> 00:34:03,020
+بدي أفحص يا شباب .. واحد و اتنين .. هذه .. بتجيب لي
+
+394
+00:34:03,020 --> 00:34:06,680
+كل الأزواج المرتبة اللي بتبدأ باتنين .. هذه في
+
+395
+00:34:06,680 --> 00:34:11,860
+عندي هذا .. اتنين و واحد .. و اتنين و اتنين .. في
+
+396
+00:34:11,860 --> 00:34:15,
+
+445
+00:38:32,070 --> 00:38:35,710
+بديش إياها لأنها already فهذه بتعطيني واحد و واحد
+
+446
+00:38:35,710 --> 00:38:42,750
+بيمتلك الـ relation الآن واحد و أربعة، أربعة و واحد
+
+447
+00:38:42,750 --> 00:38:46,190
+بدي يعطيني واحد و واحد كمان مرة تنتمي للـ relation
+
+448
+00:38:46,190 --> 00:38:55,190
+بعد هيك في عندي أربعة و واحد، مع واحد و اثنين، و
+
+449
+00:38:55,190 --> 00:39:00,670
+واحد و أربعة، هذا الأصل، مش يعطيني أربعة و اثنين
+
+450
+00:39:00,670 --> 00:39:06,170
+أربعة و اثنين موجود، لا ينتمي للـ relation، ما أكملش
+
+451
+00:39:06,170 --> 00:39:07,530
+فحص not transitive
+
+452
+00:39:10,430 --> 00:39:15,150
+كيف؟ غيب عنك لأنك أنت حولت تشتغل بشكل Random، والـ
+
+453
+00:39:15,150 --> 00:39:18,750
+Random اللي أطبقه، هو أنا عم بشتغل بطريقة
+
+454
+00:39:18,750 --> 00:39:22,110
+Systematic، منتظمة، إذا أنت اتعودت عليها، هتمشي
+
+455
+00:39:22,110 --> 00:39:27,230
+معك بسرعة يا شباب، الأمور، نعم، فأول المحاضرة، لو
+
+456
+00:39:27,230 --> 00:39:29,150
+أنك كنت حاضر، كان جواك عرفت إيش نستفيد منه في
+
+457
+00:39:29,150 --> 00:39:32,430
+حياتنا، إيش نستفيد من الـ relations؟
+
+458
+00:39:39,680 --> 00:39:43,840
+أه، شوية يا شباب، زميلنا بيقول ليش قلنا أن
+
+459
+00:39:43,840 --> 00:39:47,960
+Symmetric لتعني Anti-Symmetric، تعالى شوف الـ
+
+460
+00:39:47,960 --> 00:39:52,360
+relation هاي، بالتفصيل، شرحها معك، الـ definition بدي
+
+461
+00:39:52,360 --> 00:39:56,120
+أروح معك مباشرةً لمثال بسيط جداً، فترض أن الـ R تساوي
+
+462
+00:39:56,120 --> 00:40:04,280
+واحد و اثنين، اثنين و واحد، واحد و ثلاثة، في تعريف الـ
+
+463
+00:40:04,280 --> 00:40:10,420
+Symmetric، لكل زوج مرتب، انعكاسه موجود، 1 و 2 انعكاسه
+
+464
+00:40:10,420 --> 00:40:16,500
+.. 2 و 1 .. 2 و 1 انعكاسه .. 1 و 2 .. 1 و 3 ليس
+
+465
+00:40:16,500 --> 00:40:23,320
+لديها انعكس، .. هذا يعني أنها ليست Symmetric، لا
+
+466
+00:40:23,320 --> 00:40:27,160
+أقدر أن أقول عليها Anti-Symmetric، لماذا؟ لأن في
+
+467
+00:40:27,160 --> 00:40:30,960
+الـ Anti-Symmetric، بقول قاعدته، كل العناصر اللي في
+
+468
+00:40:30,960 --> 00:40:34,740
+العلاقة ليس لديها انعكس إلا لو كانت الـ A تساوي
+
+469
+00:40:34,740 --> 00:40:42,470
+الـ B، الآن هذه، هذه كون واحد و اثنين انعكاسها ينتمي
+
+470
+00:40:42,470 --> 00:40:49,510
+للـ relation، فهي  تُسمّى Anti-symmetric، لأ
+
+471
+00:40:49,510 --> 00:40:52,910
+نسيبنا من اللي خلصناه، نجاوب بس على جانب السؤال، نقف
+
+472
+00:40:52,910 --> 00:40:56,490
+Anti-symmetric، الآن لو كانت Symmetric، معناته هذا
+
+473
+00:40:56,490 --> 00:41:01,910
+غايب، مضبوط، Symmetric، نقف Anti-symmetric، لو هذا
+
+474
+00:41:01,910 --> 00:41:09,480
+غايب، صارت Anti-symmetric، لكن ليس Symmetric، مضبوط، لكن
+
+475
+00:41:09,480 --> 00:41:13,660
+في حالة من الحالات، جاية في الوسط، لا هي Symmetric
+
+476
+00:41:13,660 --> 00:41:16,500
+ولا هي Anti-symmetric، مثل الحالة اللي موجودة هنا
+
+477
+00:41:16,500 --> 00:41:21,160
+عشان هيك ما أقدرش أقول كلها not Symmetric، Anti-
+
+478
+00:41:21,160 --> 00:41:27,800
+Symmetric، طيب الباقيات بتكملها لحالك، لأن أعتقد أنه
+
+479
+00:41:27,800 --> 00:41:34,770
+بعد هي كان خلاص، طيب الآن، أقفز معك من
+
+480
+00:41:34,770 --> 00:41:39,550
+تسعة واحد، لتسعة أربعة، أو تسعة خمسة، مش فاكر الـ
+
+481
+00:41:39,550 --> 00:41:43,510
+section، الآن في الـ section هذا، بنتكلم على
+
+482
+00:41:43,510 --> 00:41:47,110
+equivalence relation، لو الـ relation حققت مجموعة من
+
+483
+00:41:47,110 --> 00:41:52,150
+الخصائص، اللي هم reflexive، و symmetric، و transitive
+
+484
+00:41:52,150 --> 00:41:56,390
+بقول عنها equivalence relation، بقول عنها
+
+485
+00:41:56,390 --> 00:41:58,170
+equivalence relation
+
+486
+00:42:01,110 --> 00:42:05,730
+وبنرمز للـ equivalence إما بالرمز هذا، أو بثلاث
+
+487
+00:42:05,730 --> 00:42:10,190
+شرطات، تعالى الـ relation اللي موجودة عندي على
+
+488
+00:42:10,190 --> 00:42:17,630
+السريع، الأصل هذا إيش؟ واحد و واحد، و اثنين و اثنين،
+
+489
+00:42:17,630 --> 00:42:22,070
+ثلاثة و ثلاثة، reflexive، واحد و اثنين، و اثنين و
+
+490
+00:42:22,070 --> 00:42:25,310
+واحد، واحد و ثلاثة، ثلاثة و واحد، اثنين و واحد، هي
+
+491
+00:42:25,310 --> 00:42:27,430
+symmetric
+
+492
+00:42:29,190 --> 00:42:34,350
+transitive، و transitive كمان، ما تقرأ، تسألش، أنا بسألك
+
+493
+00:42:34,350 --> 00:42:37,910
+هل هي equivalence relation؟ ما في داعي تروح تفحص
+
+494
+00:42:37,910 --> 00:42:41,870
+الأربع properties، بدي ثلاثة منهم، reflexive، and
+
+495
+00:42:41,870 --> 00:42:47,770
+symmetric، و transitive، من ناحية الـ transitive، هي واحد
+
+496
+00:42:47,770 --> 00:42:53,750
+و اثنين، هادي مع هادي، بتعطيني واحد و واحد، موجودة، واحد
+
+497
+00:42:53,750 --> 00:43:00,200
+في غيرها، واحد و اثنين، واحد و ثلاثة، هي موجودة، خلصنا
+
+498
+00:43:00,200 --> 00:43:06,120
+اللي بعده، واحد و ثلاثة، ثلاثة و واحد، بتعطيني واحد و
+
+499
+00:43:06,120 --> 00:43:10,260
+واحد، ثلاثة و اثنين، بتعطيني واحد و اثنين، already
+
+500
+00:43:10,260 --> 00:43:15,040
+موجودة، اللي بعده، اثنين و واحد، اثنين و واحد، واحد و
+
+501
+00:43:15,040 --> 00:43:20,060
+اثنين، اثنين و اثنين، هيها، واحد اثنين و ثلاثة، هيها
+
+502
+00:43:21,140 --> 00:43:25,480
+اثنين و ثلاثة، already موجودة، اللي بعده، ثلاثة و واحد،
+
+503
+00:43:25,480 --> 00:43:32,620
+واحد و .. ثلاثة و اثنين، ثلاثة و اثنين، هيها، بعد هيك
+
+504
+00:43:32,620 --> 00:43:38,300
+ثلاثة و ثلاثة، هيها، خلصنا، اثنين و ثلاثة، ثلاثة و
+
+505
+00:43:38,300 --> 00:43:47,100
+واحد، بعده اثنين و واحد، هيها، و ثلاثة و ثلاثة، بناخد
+
+506
+00:43:47,100 --> 00:43:49,040
+.. احنا بنقول اللي هو already موجودة، وبالتالي
+
+507
+00:43:49,040 --> 00:43:52,020
+transitive، وبالتالي الـ relation transitive، نعم
+
+508
+00:43:52,020 --> 00:43:59,160
+يعني كل relation reflexive هي symmetric؟ نعم، كل
+
+509
+00:43:59,160 --> 00:44:04,060
+relation reflexive؟ لا، لا، لا، لا، لا، لا، ممكن مثال؟
+
+510
+00:44:04,060 --> 00:44:04,960
+أه، ممكن مثال
+
+511
+00:44:16,440 --> 00:44:21,360
+Symmetric، not reflexive، هاي الـ relation Symmetric
+
+512
+00:44:21,360 --> 00:44:28,300
+not reflexive، أنتَ
+
+513
+00:44:28,300 --> 00:44:36,640
+هيك حكيت؟ هيك مقصودك، كل reflexive Symmetric؟ أه، وين
+
+514
+00:44:36,640 --> 00:44:40,900
+انعكاسه؟ نفسه، احنا حكينا عن الكلام ده، مش منه، عشان
+
+515
+00:44:40,900 --> 00:44:45,280
+هيك قلنا، حاول تجاهلها من الفحص، انعكاسه هو نفسه
+
+516
+00:44:47,660 --> 00:44:50,600
+طيب، الآن، بالتالي، لما تكون الـ relation اللي عندي
+
+517
+00:44:50,600 --> 00:44:56,210
+كمان مرة reflexive، Symmetric، و Transitive، معناته أن
+
+518
+00:44:56,210 --> 00:44:59,530
+أنا بتكلم على equivalence relation، equivalence
+
+519
+00:44:59,530 --> 00:45:03,070
+relation، ليش بتهمني الـ equivalence relation؟ لأن
+
+520
+00:45:03,070 --> 00:45:06,630
+فعلياً، علاقة العناصر مع بعضهم، هتشكل عندي مجموعات
+
+521
+00:45:06,630 --> 00:45:11,510
+هسميهم equivalent classes، والـ equivalent classes
+
+522
+00:45:11,510 --> 00:45:15,610
+هذه عبارة عن مجموعات، التقاطع بينها  ∅، أو
+
+523
+00:45:15,610 --> 00:45:21,490
+المجموعتين متساويتين تماماً، ليش؟ لأن لما باجي بقول
+
+524
+00:45:22,930 --> 00:45:27,870
+reflexive، يعني كل عنصر مع نفسه، مضبوط، و symmetric، كل
+
+525
+00:45:27,870 --> 00:45:31,730
+عنصرين مختلفين، لهم صورهم موجودة، يعني لما بدي
+
+526
+00:45:31,730 --> 00:45:36,210
+بقول الواحد related مع الواحد، حتماً، والواحد و الاثنين
+
+527
+00:45:36,210 --> 00:45:39,950
+موجودة، في معناته الواحد related للثنين، والاثنين
+
+528
+00:45:39,950 --> 00:45:44,570
+related للواحد، الـ equivalent class هو عبارة عن
+
+529
+00:45:44,570 --> 00:45:47,610
+المجموعة، ورمزها هو عبارة عن المجموعة اللي بتحتوي
+
+530
+00:45:47,610 --> 00:45:52,330
+على مين؟ على الـ B، العنصر الثاني، العنصر الثاني من
+
+531
+00:45:52,330 --> 00:45:58,110
+الزوج المرتب، والـ B تنتمي، أو الـ A related to B، الـ A
+
+532
+00:45:58,110 --> 00:46:04,410
+related to B، أو ببلغة أبسط، A و B تنتمي للـ relation
+
+533
+00:46:04,410 --> 00:46:10,050
+أنا بيهمني مين؟ مجموعة الـ B، هذه في المثال السابق، هذا
+
+534
+00:46:11,680 --> 00:46:14,760
+الـ M، كانت كم equivalent class عندي؟ عدد الـ
+
+535
+00:46:14,760 --> 00:46:18,740
+classes، بِعدد عناصر الـ A، عدد الـ classes equivalent
+
+536
+00:46:18,740 --> 00:46:25,280
+classes، بِعدد عناصر الـ A، يعني عندي واحد، وعندي اثنين،
+
+537
+00:46:25,280 --> 00:46:31,820
+وعندي ثلاثة، هي عبارة عن المجموعة اللي بتحتوي على
+
+538
+00:46:31,820 --> 00:46:37,000
+العناصر اللي related مع الواحد، هي الواحد، واحد،
+
+539
+00:46:37,000 --> 00:46:41,420
+اثنين، ثلاثة
+
+540
+00:46:43,260 --> 00:46:51,340
+{1، 2، 3}، مجموعة الآن من العناصر الـ related مع الاثنين،
+
+541
+00:46:51,340 --> 00:46:52,880
+هي الاثنين
+
+542
+00:47:02,630 --> 00:47:06,050
+الآن لاحظوا أن الثلاث عناصر، أو الثلاث مجموعات،
+
+543
+00:47:06,050 --> 00:47:10,210
+متساويات، وهذا من خصائص الـ equivalent class، أول
+
+544
+00:47:10,210 --> 00:47:15,390
+حاجة، equivalent class، نائمتي، إيش يعني نائمتي؟ يعني
+
+545
+00:47:15,390 --> 00:47:18,710
+مستحيل، تكون فيه، على الأقل، هيكون عندك العنصر
+
+546
+00:47:18,710 --> 00:47:24,670
+related لنفسه، عشان يحقق الـ reflexive، اثنين، أن لو
+
+547
+00:47:24,670 --> 00:47:30,540
+أخذت أي two classes، لو أخذت أي two classes، التقاطع
+
+548
+00:47:30,540 --> 00:47:34,920
+بينهم ∅، ولو كان لا يساوي الـ ∅، معناته الاثنتين
+
+549
+00:47:34,920 --> 00:47:39,600
+متساويات، لو كان التقاطع بينهم لا يساوي الـ ∅،
+
+550
+00:47:39,600 --> 00:47:43,620
+فالـ تقاطع بينهم، أو المجموعتين متساويات، وهذا اللي
+
+551
+00:47:43,620 --> 00:47:48,820
+صار معناته في المثال السابق، اتحادهم كلهم بيعطيني
+
+552
+00:47:48,820 --> 00:47:55,400
+مين؟ بيعطيني الـ A، في المثال السابق، هنا قلنا واحد،
+
+553
+00:47:55,400 --> 00:47:59,100
+واثنين، وثلاثة، كلهم كانوا يساوي إيش؟ الـ A، فتّقاطعهم
+
+554
+00:47:59,100 --> 00:48:02,800
+في، لكن كلهم كان إيش يساوي؟ الـ class تبع الـ A، يساوي
+
+555
+00:48:02,800 --> 00:48:05,860
+الـ 1، يساوي الـ class تبع الـ 2، يساوي الـ class تبع
+
+556
+00:48:05,860 --> 00:48:10,920
+الثلاثة، واتحادهم كلهم، هاي .. هاي مجموعة جديدة
+
+557
+00:48:10,920 --> 00:48:17,740
+equivalence relation، شوفوا يا شباب، لو أنا سألتك .. لو
+
+558
+00:48:17,740 --> 00:48:21,990
+أنا سألتك، هاتلي الـ equivalent classes من الـ
+
+559
+00:48:21,990 --> 00:48:26,950
+equivalence relation، ما تتعبش راسك، و تروح تفحص هل
+
+560
+00:48:26,950 --> 00:48:30,490
+هي equivalence relation ولا لأ، إلا لو أنا سألتك،
+
+561
+00:48:30,490 --> 00:48:37,230
+قلت لك، هل هذه equivalence relation؟ if yes, give me
+
+562
+00:48:38,010 --> 00:48:42,650
+equivalent classes، أو اكتب لي equivalent Classes، تمام؟
+
+563
+00:48:42,650 --> 00:48:46,190
+لكن لو أنا قلت لك، هاتلي الـ equivalent Classes مباشرةً،
+
+564
+00:48:46,190 --> 00:48:49,990
+فأنا بفترض أن هذه equivalent relation، يعني Reflexive،
+
+565
+00:48:49,990 --> 00:48:53,930
+و Symmetric، و Transitive، وأنت بدك إيش تجيب؟ القيم
+
+566
+00:48:53,930 --> 00:49:03,450
+الموجودة، الآن، الواحد واحد،
+
+567
+00:49:03,450 --> 00:49:10,470
+و اثنين، و ثلاثة، والاثنين، وأنت مغمض، واحد و اثنين، و
+
+568
+00:49:10,470 --> 00:49:15,030
+ثلاثة، بدون هذا الكلام، أنا بجيب talk، الاثنين related
+
+569
+00:49:15,030 --> 00:49:19,350
+مع نفسها، لأنها reflexive، مضبوط، والاثنين مع الواحد،
+
+570
+00:49:19,350 --> 00:49:23,710
+لأنها symmetric، هيها already، و transitive، لأنها
+
+571
+00:49:23,710 --> 00:49:27,330
+متعدية، مضبوط، مع الثلاثة، وبالتالي الـ equivalent
+
+572
+00:49:27,330 --> 00:49:32,450
+class تبع الثلاثة، هتساويهم، واحد و اثنين و ثلاثة، الـ
+
+573
+00:49:32,450 --> 00:49:33,690
+equivalent class تبع الأربعة
+
+574
+00:49:36,580 --> 00:49:44,660
+الأربعة related مع نفسها، أربعة و خمسة، أربعة و خمسة،
+
+575
+00:49:44,660 --> 00:49:50,440
+و مباشرةً هتكون عندك الخمسة، يا رب تكون بتفهم، بس
+
+576
+00:49:50,440 --> 00:49:55,160
+عشانك تفهم، الآن،
+
+577
+00:49:55,160 --> 00:50:03,210
+التقاطعات بينهم، إما ∅، أو كل الـ elements، أو بيكونوا
+
+578
+00:50:03,210 --> 00:50:07,950
+متساويتين، تمام؟ لو أخذت واحد و اثنين، التقاطع، كل
+
+579
+00:50:07,950 --> 00:50:11,530
+المجموعة، اثنين و ثلاثة، واحد و ثلاثة، كل المجموعة،
+
+580
+00:50:11,530 --> 00:50:16,090
+لكن ثلاثة و أربعة، ∅، فإما بروح this joint،
+
+581
+00:50:16,090 --> 00:50:21,350
+إما ∅، أو بيكونوا متساويتين، لو عملت اتحاد
+
+582
+00:50:21,350 --> 00:50:26,510
+للمجموعات هذه، هأحصل على مين؟ على كل الـ A، تعالوا
+
+583
+00:50:26,510 --> 00:50:27,230
+كمان مثال
+
+584
+00:50:34,710 --> 00:50:41,870
+كم class عندي هنا؟ كم class عندي هنا؟ ستة، واحد،
+
+585
+00:50:41,870 --> 00:50:48,570
+واحد، و ثلاثة، و خمسة، هيهم، و مباشرةً عليها الـ class،
+
+586
+00:50:48,570 --> 00:50:51,870
+تبع الثلاثة هذه، تساوي الـ class تبع الثلاثة، وتساوي
+
+587
+00:50:51,870 --> 00:50:59,550
+الـ class تبع الخمسة، طيب، اثنين، اثنين و ستة، والـ class
+
+588
+00:50:59,550 --> 00:51:03,570
+تبع الاثنين، تساوي الـ class تبع الستة، ضلت عند مين؟
+
+589
+00:51:04,950 --> 00:51:12,030
+أربعة، واحنا بنقولها زي واحد، أربعة لحالها،
+
+590
+00:51:12,030 --> 00:51:18,990
+والخمسة مع الثلاثة، والثانية مع الستة، هاي الست
+
+591
+00:51:18,990 --> 00:51:24,980
+classes، خذ أي اثنين، تقاطع بين هذا وهذا، ∅، تقاطع
+
+592
+00:51:24,980 --> 00:51:28,900
+بين هذا وهذا، ∅، ولو قلنا 6 و 2، تقاطع بينهم، ∅، 6 و 1،
+
+593
+00:51:28,900 --> 00:51:34,900
+تقاطع بينهم، ∅، 6 و 2، تقاطع بينهم، متساويتين، وبالتالي
+
+594
+00:51:34,900 --> 00:51:39,140
+هيديني ميزة الـ classes اللي موجودة عندك، بقدر
+
+595
+00:51:39,140 --> 00:51:45,740
+أصنف عناصر الـ relation لـ classes، إذا تحققت فيها
+
+596
+00:51:45,740 --> 00:51:52,000
+الخصائص السابقة، طيب الآن، partition، الـ Partition
+
+597
+00:51:52,000 --> 00:51:57,380
+إيش يعني؟ تقسيم، Partitions، أقسام، البنزين
+
+598
+00:51:57,380 --> 00:52:01,320
+يقولوا، والله تقطيع، والله فلان، فلان جعان،
+
+599
+00:52:01,320 --> 00:52:05,020
+اليوم، وجاب الكيكة، وقطعها أربع قطع، عملها
+
+600
+00:52:05,020 --> 00:52:08,960
+partition، هل في تقاطع بين القطع اللي اتقطعت؟
+
+601
+00:52:08,960 --> 00:52:13,440
+يعني هل في مناطق مشتركة بين القطعتين؟ مستحيل،
+
+602
+00:52:13,440 --> 00:52:16,360
+ما حدش هيِرضى، بعض الناس، بدأت، إيش اسمه؟ تحرك
+
+603
+00:52:16,360 --> 00:52:20,580
+لساناتها، وتصحصح كويس، لسه مش مفطرين، عشان هيك
+
+604
+00:52:20,580 --> 00:52:23,900
+يا رامد تراها، الآن، غير هيك، في الـ partition اللي
+
+605
+00:52:23,900 --> 00:52:27,960
+أنت بتعرفه، الـ disk، القرص الصلب اللي عندك، بيقول لك
+
+606
+00:52:27,960 --> 00:52:31,640
+اعمله partition، يعني عمله لتلات أقسام،
+
+607
+00:52:31,640 --> 00:52:36,670
+partitions، اعمله C و D و E، جسمه، هل ضروري الـ
+
+608
+00:52:36,670 --> 00:52:39,510
+partitions يكون متساويات؟ لا، ما حدش بيقول أنه يكون
+
+609
+00:52:39,510 --> 00:52:45,390
+متساويات، بس التقاطع بينهم ∅، التقاطع بينهم ∅،
+
+610
+00:52:45,390 --> 00:52:50,250
+واتحادهم كلهم بيديني مين؟ بيديني الـ partition اللي
+
+611
+00:52:50,250 --> 00:52:58,530
+موجودة عندها، ففعلياً، أي مجموعة A، تمام؟ هي عبارة عن
+
+612
+00:52:58,530 --> 00:53:03,070
+collection من الـ disjoint non-empty، عشان تستخدم
+
+613
+00:53:03,
\ No newline at end of file
diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/JYdKdPOF5Ho_postprocess.srt b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/JYdKdPOF5Ho_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..f9860e460bb8b28bf69f4eaeddf041079dc66d60
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/JYdKdPOF5Ho_postprocess.srt
@@ -0,0 +1,2636 @@
+1
+00:00:20,700 --> 00:00:22,700
+بسم الله والحمد لله والصلاة والسلام على رسول الله
+
+2
+00:00:22,700 --> 00:00:25,860
+اليوم ان شاء الله تعالى هنكمل في جهة chapter ال
+
+3
+00:00:25,860 --> 00:00:29,460
+structures لكن ال section تبعتنا من section مختلف
+
+4
+00:00:29,460 --> 00:00:32,420
+تماما الكتاب مفرد ال relations في chapter مستقل
+
+5
+00:00:32,420 --> 00:00:35,680
+اللي هو chapter تسعة بس ال chapter اللي احنا كنا
+
+6
+00:00:35,680 --> 00:00:40,460
+فيه اتنين كنا بنتكلم على ال basic structure set و
+
+7
+00:00:40,460 --> 00:00:44,240
+function مظبوط و sequence و matrix و ال relation
+
+8
+00:00:44,240 --> 00:00:46,860
+هذه زي ما هنشوف كمان شوية هي عبارة عن مجموعات
+
+9
+00:00:46,860 --> 00:00:47,820
+relations
+
+10
+00:00:54,300 --> 00:00:59,160
+الان لما بجي بتكلم على ال relation ال relation هي
+
+11
+00:00:59,160 --> 00:01:06,540
+عبارة عن علاقات ما بين المجموعات حضرتك كطالب في
+
+12
+00:01:06,540 --> 00:01:13,100
+التخصص في الكلية في المساق الان تخيل تخيل مجموعة
+
+13
+00:01:13,100 --> 00:01:19,720
+الكليات و طلاب relation ولا لا الطالب تخصص كذاأو
+
+14
+00:01:19,720 --> 00:01:23,640
+الطالب مسجل في كلية كذا في المساقات الطالب درس
+
+15
+00:01:23,640 --> 00:01:25,980
+المساق أو يدرس المساق الفلاني أو نجح في المساق
+
+16
+00:01:25,980 --> 00:01:31,420
+عبارة عن ال relation الناس و الألوان اللي بتحبها و
+
+17
+00:01:31,420 --> 00:01:34,260
+الفواكه اللي بتحب تاكلها الاخرى هي عبارة عن groups
+
+18
+00:01:34,260 --> 00:01:38,540
+او sets مجموعات و في بينهم relation و احنا شفنا
+
+19
+00:01:38,540 --> 00:01:41,140
+نوع من ال relation يا شباب لما اتكلمنا على ال
+
+20
+00:01:41,140 --> 00:01:45,600
+Cartesian product بين مجموعتين ولا لأ؟ قلنا بينتج
+
+21
+00:01:45,600 --> 00:01:52,690
+عنها مجموعة بتشكل أزوادمرتبة A تنتمي لـ A و B
+
+22
+00:01:52,690 --> 00:01:56,170
+تنتمي لـ B و لا لها؟ مش هذا تعريف الـ cross
+
+23
+00:01:56,170 --> 00:02:00,570
+product كان؟ و كل هذا الزوج المرتب هو الـ tuple
+
+24
+00:02:00,570 --> 00:02:04,770
+الـ
+
+25
+00:02:04,770 --> 00:02:09,210
+tuple هذا زوج مرتب لا يساوي AB لا تساوي BA و
+
+26
+00:02:09,210 --> 00:02:11,730
+اتكلمنا عليها ساحينها هنشوف إنه فعليا هذا موجود
+
+27
+00:02:13,900 --> 00:02:17,160
+وبالتالي أنا ال relationship between six elements
+
+28
+00:02:17,160 --> 00:02:21,180
+أو ال element اللي في المجموعات بتمثل structure
+
+29
+00:02:21,180 --> 00:02:24,660
+وعشان هي أنا روحت جيبتها وين؟ في ال chapter ال
+
+30
+00:02:24,660 --> 00:02:28,780
+structure وبالتالي هي عبارة عن subset من ال
+
+31
+00:02:28,780 --> 00:02:32,660
+Cartesian product يعني أنا مابعتش عن الكلام اللي
+
+32
+00:02:32,660 --> 00:02:37,580
+أنا أخدته سابقا طيب وين بيلزمني هذا الكلام؟ ليش
+
+33
+00:02:37,580 --> 00:02:40,690
+أنا بمهم أفهم ال relation من البداية صح؟الـ
+
+34
+00:02:40,690 --> 00:02:42,490
+Relations الـ implementation تبعتها و ال
+
+35
+00:02:42,490 --> 00:02:45,850
+application تبعتها للناس اللي بتشتغل في الكمبيوتر
+
+36
+00:02:45,850 --> 00:02:50,210
+كبيرة جدا لما تدرس مساق ال database واحد هنتكلم
+
+37
+00:02:50,210 --> 00:02:56,510
+على relation ما بين ال entities فيه عندك الطالب و
+
+38
+00:02:56,510 --> 00:03:00,170
+المساق different setsمجموعة القلاب ومجموعة
+
+39
+00:03:00,170 --> 00:03:03,810
+المساقات في بينهم relation اللي هو المساق تسجيل
+
+40
+00:03:03,810 --> 00:03:07,470
+المساق خلال الفصل الواحد وبالتالي هتصرف فيه
+
+41
+00:03:07,470 --> 00:03:12,930
+relation بنجيب نتكلم الناس أو بلاش المطارات في
+
+42
+00:03:12,930 --> 00:03:17,510
+العالم كل مطار و ال connected airport التاني اللي
+
+43
+00:03:17,510 --> 00:03:21,410
+ممكن يتواصل معاه عشان يوصل خط الطيارة تمام فدي
+
+44
+00:03:21,410 --> 00:03:25,610
+عبارة عن relation ما بين المطارات ال google map او
+
+45
+00:03:25,610 --> 00:03:29,350
+ال map اللي على الجوالهي عبارة عن relation بين الـ
+
+46
+00:03:29,350 --> 00:03:31,950
+two points والـ road اللي بينهم أو الـ route اللي
+
+47
+00:03:31,950 --> 00:03:34,630
+بينهم هو عبارة عن البث لل relation أنه فيه
+
+48
+00:03:34,630 --> 00:03:37,670
+connection أو فيه طريق ما بين ال city A و ال city
+
+49
+00:03:37,670 --> 00:03:41,530
+B وبالتالي ال implementation و التطبيقات تبعت ال
+
+50
+00:03:41,530 --> 00:03:45,170
+relation كبيرة و كبيرة جدا حتى لما بتكلم على مستوى
+
+51
+00:03:45,170 --> 00:03:50,050
+الشبكات كمان بتكلم على المجموعات groups و sets و
+
+52
+00:03:50,050 --> 00:03:54,730
+بتكلم على ال permissions الصلاحيات اللي ممنوحةلل
+
+53
+00:03:54,730 --> 00:03:57,750
+users اللي موجودين عندى و برضه بتكلم على relation
+
+54
+00:03:57,750 --> 00:04:04,710
+لان فى ال relation هنا شباب فى عندى مصطلح unary
+
+55
+00:04:04,710 --> 00:04:12,870
+ايش unary؟ احادي او binary ثنائي
+
+56
+00:04:12,870 --> 00:04:16,390
+.. ثنائي
+
+57
+00:04:16,390 --> 00:04:21,030
+.. ثنائي .. ثنائي .. ثنائي
+
+58
+00:04:21,030 --> 00:04:22,910
+.. ثنائي .. ثنائي .. ثنائي .. ثنائي .. ثنائي ..
+
+59
+00:04:24,480 --> 00:04:32,480
+طبعا اخر ان نلاحظ ان الانها دي هيك ايش ما اختلفت
+
+60
+00:04:32,480 --> 00:04:37,800
+الانهاش بتمثل عدد المجموعات اللي بيمتموه لل
+
+61
+00:04:37,800 --> 00:04:42,020
+relation لعدد المجموعات المشاركة في ال relation
+
+62
+00:04:42,020 --> 00:04:46,400
+يعني لو قلنا على سبيل المثال بدنا نشكل فريق برمجة
+
+63
+00:04:46,400 --> 00:04:52,410
+فريق برمجة من قلب يعني كل فريق لازم يكون في عضومن
+
+64
+00:04:52,410 --> 00:04:57,490
+قسم مختلف و حققوا الحد الأقصى للفريق أربعة، إيش
+
+65
+00:04:57,490 --> 00:05:00,370
+هنساوي؟ هنقول والله مثلا واحد من ال multimedia،
+
+66
+00:05:00,370 --> 00:05:02,210
+واحد من ال mobile computing، واحد software
+
+67
+00:05:02,210 --> 00:05:05,170
+development، واحد computer science، فريق التاني،
+
+68
+00:05:05,170 --> 00:05:08,730
+لاحظ أنا بتكلم على أربعة، أربع مجموعات مختلفة
+
+69
+00:05:08,730 --> 00:05:14,080
+شاركت في تشكيلالفريق طيب لو جل كل رجل في الفريق
+
+70
+00:05:14,080 --> 00:05:17,920
+يريد أن يأخذ منزلة الرئيس وناقب الرئيس وامين
+
+71
+00:05:17,920 --> 00:05:21,940
+الفريق مثلا وExecutor سامي زي ما بدك او Documenter
+
+72
+00:05:21,940 --> 00:05:28,200
+وبالتالي صار كل position له ترتيب مهم بالنسبة لنا
+
+73
+00:05:28,200 --> 00:05:33,260
+وهنا انا مابديش تفهم انه لما انا بتكلم على
+
+74
+00:05:33,260 --> 00:05:36,980
+relation معناته انا بتكلم على table زي ما قلنا و
+
+75
+00:05:36,980 --> 00:05:40,780
+ال table هذا بيسبق الرقم لما انا بتكلم
+
+76
+00:05:44,810 --> 00:05:49,730
+3 tuple معناته ان انا بتتكلم عن علاقة
+
+77
+00:05:49,730 --> 00:05:54,730
+ثلاثية بين 3 components موجودة عندى لما بتكلم على
+
+78
+00:05:54,730 --> 00:06:01,530
+ال 2 tuple حد اللى احنا بنعرف اسمها ordered pair
+
+79
+00:06:01,530 --> 00:06:07,810
+زوج مرتب a و b الزوج المرتب معناته الأقواص بتسميها
+
+80
+00:06:07,810 --> 00:06:12,500
+tuple و ال elements اللى موجودات فيه يسمواالـ
+
+81
+00:06:12,500 --> 00:06:15,860
+Elemental Fattable مش خضرياتنا كتير المعلومات كلها
+
+82
+00:06:15,860 --> 00:06:21,360
+هنتيجي تباعا ان شاء الله تعالى طيب الآن انا بتكلم
+
+83
+00:06:21,360 --> 00:06:24,820
+او في تركيزنا في ال chapter هذا على ال binary
+
+84
+00:06:24,820 --> 00:06:31,180
+relation تركيزنا الآن على ال binary relation ال
+
+85
+00:06:31,180 --> 00:06:34,700
+binary relation معناته ان في عندي two sets A و B
+
+86
+00:06:34,700 --> 00:06:39,800
+وبالتالي ال binary relation ما بين A و B هي عبارة
+
+87
+00:06:39,800 --> 00:06:48,560
+عن subset من الكارتيزياالبرودكت R تساوي الأزواج
+
+88
+00:06:48,560 --> 00:06:55,540
+المرتبة two double او binary او ordered pair بحيث
+
+89
+00:06:55,540 --> 00:07:02,420
+ان A تنتمي الى A وB تنتمي الى B تعرف البرودكت كله
+
+90
+00:07:02,420 --> 00:07:07,040
+ممكن تضيف اي condition لاحقا عشان تحدد هيش بشكل
+
+91
+00:07:07,040 --> 00:07:08,000
+اقل
+
+92
+00:07:11,120 --> 00:07:18,360
+ممكن ان اعرفها بشكل مختلف عن التعريف السابق بحيث
+
+93
+00:07:18,360 --> 00:07:21,800
+ان اقول ان ال relation تتعرف بالأزواج المرتبة A وB
+
+94
+00:07:21,800 --> 00:07:30,560
+بتنتمي الى R وهذا معناته A related to B اذا
+
+95
+00:07:30,560 --> 00:07:33,160
+انا اجيت كلامتي على الطالب و المثالق اللي بدرسه
+
+96
+00:07:33,160 --> 00:07:40,740
+هقول احمد study discrete mathematicsهاني بلايز
+
+97
+00:07:40,740 --> 00:07:45,920
+فوتبول على انه ال favorite sport لو اجينا نتكلم عن
+
+98
+00:07:45,920 --> 00:07:50,960
+الفاكهة اللي بتحبها ايش اسمك؟ محمد محمد likes
+
+99
+00:07:50,960 --> 00:07:55,600
+strawberry فراولة جزء خاص من ال relation جزء خاص
+
+100
+00:07:55,600 --> 00:07:58,760
+من ال relation او من ال Cartesian product لو عناصر
+
+101
+00:07:58,760 --> 00:08:05,260
+ال a في نفسها يعني a cross ال a يعني ممكن انا احقق
+
+102
+00:08:05,260 --> 00:08:11,090
+relation من خلالA cross الـ A كارتيزان ال product
+
+103
+00:08:11,090 --> 00:08:14,310
+بين الـ A و نفسها هالكلام صحيح بيصير؟ أه بيصير
+
+104
+00:08:14,310 --> 00:08:18,170
+تخيل لو أنا جيتها و قلتلك هي ال A equal واحد و
+
+105
+00:08:18,170 --> 00:08:25,210
+اتنين و تلاتة و ال relation تبعتنا بدها تساوي A و
+
+106
+00:08:25,210 --> 00:08:28,870
+B حيث ال B أكبر من ال A
+
+107
+00:08:34,960 --> 00:08:41,800
+مفهوم الـ Head relation كل الأزواج المرتبة اللي
+
+108
+00:08:41,800 --> 00:08:46,080
+في الـ Cartesian product في الـA وA بحيث أن الـB
+
+109
+00:08:46,080 --> 00:08:58,240
+تكون أكبر من الـA 1 و 2 1 و 3 2 و 3 Head
+
+110
+00:08:58,240 --> 00:09:03,320
+relation Cartesian
+
+111
+00:09:03,320 --> 00:09:07,750
+product هو السقف تبعكعندك مجموعتين عدد العناصر في
+
+112
+00:09:07,750 --> 00:09:12,430
+الأولى أربعة وفي الثانية خمسة أكبر relation ممكن
+
+113
+00:09:12,430 --> 00:09:16,950
+تتشكل جدش حد يومها أربعة في خمسة عشرين element
+
+114
+00:09:16,950 --> 00:09:20,890
+أربعة في خمسة ليش نجس عشرين element الآن أنا عندي
+
+115
+00:09:20,890 --> 00:09:25,250
+هان بقولك A في A تمام؟ وال relation هي subset من
+
+116
+00:09:25,250 --> 00:09:30,490
+من ال A subset احنا متفقين وبالتالي كحد أقصى هان
+
+117
+00:09:30,490 --> 00:09:35,490
+ممكن تكون تسع عناصر لكن لما أنا بروح بقيدهامن خلال
+
+118
+00:09:35,490 --> 00:09:38,930
+الـ definition معناته انا صرت انا بحدد عدد عناصر
+
+119
+00:09:38,930 --> 00:09:42,590
+مختلف لاحظوا يا شباب انه مازلت في ال relation
+
+120
+00:09:42,590 --> 00:09:46,250
+بتتكلم على المجموعات ولا لا مابعدتش لحتى اللحظة عن
+
+121
+00:09:46,250 --> 00:09:50,870
+المجموعات مطلقا هذا
+
+122
+00:09:50,870 --> 00:09:54,250
+المثال اللي قلناه مجموعة الطلاب ال a بتمثل مجموعة
+
+123
+00:09:54,250 --> 00:10:00,270
+الطلاب و ال b بتمثل مجموعة ال courses معناته احنا
+
+124
+00:10:00,270 --> 00:10:05,810
+بنتكلم نقدر نتكلم نقول زوج المرتب a و bهي العلاقة
+
+125
+00:10:05,810 --> 00:10:10,870
+ما بين A تمثل طالب و B تمثل مساق و بالتالي student
+
+126
+00:10:10,870 --> 00:10:18,850
+A taking course او studying course B طبعا
+
+127
+00:10:18,850 --> 00:10:22,550
+ال definition ممكن تكتب صورة تانية محمد و الفراولة
+
+128
+00:10:22,550 --> 00:10:30,110
+هيهم X likes Y الان A set of people و ال R
+
+129
+00:10:30,110 --> 00:10:35,860
+describes who likes fruitيعني ال Y بتمثل مين؟
+
+130
+00:10:35,860 --> 00:10:40,440
+الفروت و بالتالي X like Y هي ال relation اللي
+
+131
+00:10:40,440 --> 00:10:43,520
+موجودة عندنا هنا الان ممكن ال relation برضه تنكتب
+
+132
+00:10:43,520 --> 00:10:48,080
+او تتعرف بشكل مختلف تماما لما انا عاش اقولك لت ال
+
+133
+00:10:48,080 --> 00:10:54,540
+A تساوي ال natural number و جيت قلت ال relation
+
+134
+00:10:54,540 --> 00:11:00,400
+تبعتي قلنا نقراها X related Y X related Y لاحظ هو
+
+135
+00:11:00,400 --> 00:11:04,270
+تكلم فقطعلى مجموعة واحدة زي ما في المثال هذا
+
+136
+00:11:04,270 --> 00:11:09,290
+مباشرة بادر لذهنك cross product between a في a
+
+137
+00:11:09,290 --> 00:11:12,830
+cross product between a في a و هاد ال relation
+
+138
+00:11:12,830 --> 00:11:16,010
+هتكون subset منها ال subset منها كيف أعرف ال
+
+139
+00:11:16,010 --> 00:11:22,630
+definition x أقل أو تساوي ال y زي المثال تقريبا
+
+140
+00:11:22,630 --> 00:11:29,850
+هذا اللي أنا كتبنا الان
+
+141
+00:11:29,850 --> 00:11:33,360
+بما أن ال relationبما أن ال relation هي عبارة عن
+
+142
+00:11:33,360 --> 00:11:37,920
+مجموعة، بما يعني بقدر أطبق عليها كل العمليات
+
+143
+00:11:37,920 --> 00:11:47,080
+الخاصة بالمجموعات اللي هما التقابق،
+
+144
+00:11:47,080 --> 00:11:53,160
+الاتحاد، ال difference و ال .. ال .. خلصولها؟ ما
+
+145
+00:11:53,160 --> 00:11:55,720
+تخلصوش، ده في واحدة .. ايوة الشرط يا أحمد، إيش
+
+146
+00:11:55,720 --> 00:12:02,770
+اسمها يا دي؟ المتممة .. المتممةأيوة الآن معناته
+
+147
+00:12:02,770 --> 00:12:06,230
+أنا فعليا بتكلم لأنه كمان مرة ما تنساش أنا بتكلم
+
+148
+00:12:06,230 --> 00:12:10,030
+مازال كايم من ال definition set builder notation
+
+149
+00:12:10,030 --> 00:12:13,950
+أنا بتكلم على مجموعة وبالتالي بطبق العمليات بتاعة
+
+150
+00:12:13,950 --> 00:12:18,250
+المجموعات على كل العناصر اللي في ال relation اللي
+
+151
+00:12:18,250 --> 00:12:25,170
+موجودة عندي اتحاد تقاقع difference والمتممة بدي
+
+152
+00:12:25,170 --> 00:12:31,490
+أسأل سؤال في المثال السابقعلى هذا احنا قولنا الان
+
+153
+00:12:31,490 --> 00:12:40,290
+R بدها تساوي ازواد المرتبة X و Y حيث X اصغر او
+
+154
+00:12:40,290 --> 00:12:48,090
+تساوي ال Y طبعا and X و Y تنتمي ل natural number
+
+155
+00:12:48,090 --> 00:12:53,370
+مش قضية كتير هذا بالنسبة لنا طيب الآن هات للمتمن
+
+156
+00:12:53,370 --> 00:12:58,170
+ما تبعتها ايش المتمن من ال compliment
+
+157
+00:13:04,420 --> 00:13:11,480
+دى المتممة R شرط H ساوى X
+
+158
+00:13:11,480 --> 00:13:21,980
+وY X أكبر بدون ما يتساوي لأنه أنا بدى العناصر اللى
+
+159
+00:13:21,980 --> 00:13:25,760
+فى المتممة من المتممة من ال university اللى هى N
+
+160
+00:13:25,760 --> 00:13:29,700
+في N ال university تبعتنا ل N في N أنا هدولة منهم
+
+161
+00:13:29,700 --> 00:13:35,160
+سبست فبدى الباقى جهيهملأ والله انكم تدرسوا يا شباب
+
+162
+00:13:35,160 --> 00:13:41,320
+عشان الحل هنتكلم الآن في خصائص ال relation هنتكلم
+
+163
+00:13:41,320 --> 00:13:48,980
+في خصائص ال relation اول خاصية reflexive طيب قبل
+
+164
+00:13:48,980 --> 00:13:53,160
+ما نتكلم عن ال reflexive لما انا يا شباب بتكلم a
+
+165
+00:13:53,160 --> 00:13:58,860
+في a يعني لو كانت عدد عناصر ال a اتنين لما بتكلم
+
+166
+00:13:58,860 --> 00:14:02,570
+اتنين في اتنين لو كانت تلاتةتلاتة في تلاتة هو عدد
+
+167
+00:14:02,570 --> 00:14:07,230
+العراسة فصوته ل .. و كإني بتكلم على square matrix
+
+168
+00:14:07,230 --> 00:14:12,730
+لو أنت تيجي تصفقهم أو ترتبهم واحد و اتنين واحد و
+
+169
+00:14:12,730 --> 00:14:17,990
+تلاتة او عفوا واحد و واحد و واحد و اتنين واحد و
+
+170
+00:14:17,990 --> 00:14:24,850
+تلاتة بعد هيك اتنين و واحد اتنين و اتنين اتنين و
+
+171
+00:14:24,850 --> 00:14:31,280
+تلاتة بعدها تلاتة و واحد تلاتة و اتنينتلاتة و
+
+172
+00:14:31,280 --> 00:14:35,900
+تلاتة و كأنني بتكلم على square matrix تلاتة في
+
+173
+00:14:35,900 --> 00:14:38,560
+تلاتة صح اسمها مربعة
+
+174
+00:14:43,560 --> 00:14:47,580
+المصفوفة طبعا وكأنني قاعد بقولك هذه تمثل I و
+
+175
+00:14:47,580 --> 00:14:53,340
+التاني تمثل ال J الصف و العمود الان لما بتكلم على
+
+176
+00:14:53,340 --> 00:14:57,260
+ال relation هذه reflexive بدي اتكلم العلاصر اللي
+
+177
+00:14:57,260 --> 00:15:03,720
+في النص هذه لازم تكون موجودة اللي هي تمثل AII AII
+
+178
+00:15:03,720 --> 00:15:07,740
+او AIJ و I تساوي الجي بين جثين لما انا بدي اقول ان
+
+179
+00:15:07,740 --> 00:15:13,790
+ال relation هذه reflexive لكل علاصر ال Aكل عنصر في
+
+180
+00:15:13,790 --> 00:15:17,870
+الـA، كم عنصر في الـA؟ تلاتة تدور على تلات أزواج
+
+181
+00:15:17,870 --> 00:15:23,030
+مرتبة اللي هم واحد و واحد صورتهم ايه و ايه واحد و
+
+182
+00:15:23,030 --> 00:15:27,470
+واحد اتنين و اتنين تلاتة و تلاتة لو كانت الأزواج
+
+183
+00:15:27,470 --> 00:15:30,710
+المرتبة هذه موجودة في ال relation بنقول عن ال
+
+184
+00:15:30,710 --> 00:15:36,190
+relation reflexive يعني خط للعكاس هذا موجود exist
+
+185
+00:15:36,190 --> 00:15:39,490
+دي البيانات اللي موجودة فيه أو العناصر اللي فيه
+
+186
+00:15:39,490 --> 00:15:44,870
+صحيحةالان بدي اسألك ال relation هذي اللي انا
+
+187
+00:15:44,870 --> 00:15:53,970
+كاتبها هنا R هل R reflexive؟ هى ال R الان مش ممكن
+
+188
+00:15:53,970 --> 00:15:59,550
+تساوي بدك تروح على عناصر ال A كمان مرةبداك تدور
+
+189
+00:15:59,550 --> 00:16:03,090
+على تلت أزواج مرتبة بالتحديد لو كانت ال a فيها
+
+190
+00:16:03,090 --> 00:16:06,530
+أربع عناصر معناه أنك تدور عليها أربعة فيها n بدك
+
+191
+00:16:06,530 --> 00:16:09,970
+تدور علي ال n لو واحد من ال n اللي بدنا ندور عليه
+
+192
+00:16:09,970 --> 00:16:14,450
+هو مش موجود معناته not reflexive بتنتهي الصفة الآن
+
+193
+00:16:14,450 --> 00:16:19,850
+واحد واحد هل واحد واحد موجود؟ لأ معناته R is not
+
+194
+00:16:19,850 --> 00:16:21,310
+reflexive
+
+195
+00:16:25,280 --> 00:16:28,680
+أو غير رفليكسيف. لماذا؟ لأن واحد و واحد ليس موجود،
+
+196
+00:16:28,680 --> 00:16:33,420
+فالباقي ماتدورش، خلاص انسى الموضوع، وإما أول واحد
+
+197
+00:16:33,420 --> 00:16:39,660
+مابتلاقيهوش، تكملش بحث. طيب، تخيل في الشرق هذا أو
+
+198
+00:16:39,660 --> 00:16:44,320
+في هذا الـfunction، روحت سميتلك function تانية أو
+
+199
+00:16:44,320 --> 00:16:47,420
+.. okay مش قضية .. function تانية و روحت بحيث أني
+
+200
+00:16:47,420 --> 00:16:50,140
+قلتلك أن الـR أكبر أو تساوي
+
+201
+00:16:53,780 --> 00:17:00,280
+قلت لك R أكبر او تساوي هتسيب
+
+202
+00:17:00,280 --> 00:17:05,200
+.. الآن إيش لك تساوي؟ بدك تروح تدور واحد و واحد
+
+203
+00:17:05,200 --> 00:17:09,100
+وحق الشرط .. معناه تبين Terminal relation اتنين و
+
+204
+00:17:09,100 --> 00:17:12,180
+اتنين شوف كمان مرة انا أعمالي بجرب معاك بدون ما
+
+205
+00:17:12,180 --> 00:17:16,180
+اكتب العلاصر جدامي اتنين و اتنين .. اتنين أكبر أو
+
+206
+00:17:16,180 --> 00:17:20,220
+تساوي اتنين؟true تلاتة أكبر أو تساوي تلاتة true
+
+207
+00:17:20,220 --> 00:17:23,840
+معناته واحد و واحد و اتنين و اتنين و تلاتة و تلاتة
+
+208
+00:17:23,840 --> 00:17:34,000
+بينتبهوا لل relation معناته R is reflexive تمام؟
+
+209
+00:17:34,000 --> 00:17:37,040
+و
+
+210
+00:17:37,040 --> 00:17:44,580
+اما تلاقي فيه تساوي تمام؟ و اما تلاقي فيه تساوي
+
+211
+00:17:44,580 --> 00:17:49,650
+معناته في عندك reflexiveطبعا في حالة الأقل أو
+
+212
+00:17:49,650 --> 00:17:54,370
+الأكبر زي ما جربت ده انسى الموضوع مش هتحققش خاصية
+
+213
+00:17:54,370 --> 00:17:58,490
+تانية symmetric طب مهمش انا بدي ارجع مرة تانية
+
+214
+00:17:58,490 --> 00:18:02,130
+شباب لل definition او خليها ده مش قضية كتير
+
+215
+00:18:02,130 --> 00:18:05,950
+symmetric
+
+216
+00:18:05,950 --> 00:18:10,010
+الصفات اللي انا بقولها منفصلة عن بعضها symmetric
+
+217
+00:18:10,010 --> 00:18:17,870
+يعني متماثلة اقولها في المصفوفة المتماثلةAij
+
+218
+00:18:17,870 --> 00:18:23,650
+بيتساوي AJI وإذا بتتذكر لما اتكلمنا يا رامي يا
+
+219
+00:18:23,650 --> 00:18:30,130
+بعاصي على مصفوفة تلاتة في تلاتة الآن قلنا عن أسر
+
+220
+00:18:30,130 --> 00:18:33,810
+القطر الرئيسي هيها مالاش داخل فيها ولا لأ لإن
+
+221
+00:18:33,810 --> 00:18:41,010
+already A11 A22 A33 هي نفسها لو بدّلنا ال I و ال J
+
+222
+00:18:41,010 --> 00:18:45,810
+مظلوك ولا لأ طيب الآن بتكلم على هذاوبتكلم على هذا
+
+223
+00:18:45,810 --> 00:18:50,110
+متقابقة
+
+224
+00:18:50,110 --> 00:18:58,810
+أو متماثلة متناظرة محلاكم أنتم بالترجمة العربى صح
+
+225
+00:18:58,810 --> 00:19:04,390
+تمام؟ الآن مفهوم التقابق أو التناظر أن هذا ال
+
+226
+00:19:04,390 --> 00:19:06,950
+element هو هذا هذا جدش ال element .. هذا واحد
+
+227
+00:19:06,950 --> 00:19:12,590
+اتنين تلاتة هنا واحد اتنين تلاتة مصبوط؟ هذا جدش
+
+228
+00:19:12,590 --> 00:19:18,800
+رقم ال element هذا عفواهذا a12 الصف الأول العمودي
+
+229
+00:19:18,800 --> 00:19:29,020
+التاني يساوي a21 هذا a13 يساوي a31 وهكذا هكذا منها
+
+230
+00:19:29,020 --> 00:19:33,560
+حيش متماثلة symmetric سميناها المصفوفة symmetric
+
+231
+00:19:33,560 --> 00:19:38,240
+matrix الآن هذا الكلام بدي أسقطه على ال relation
+
+232
+00:19:39,340 --> 00:19:42,540
+لاحظوا العلاقة جديش؟ علاقة بال relation علاقة
+
+233
+00:19:42,540 --> 00:19:45,320
+بالمصفوفات فانا روحت جيبته من .. عشان ايه؟ روحت
+
+234
+00:19:45,320 --> 00:19:48,940
+جيبته من chapter 9؟ و حققته وين؟ في ال chapter ..
+
+235
+00:19:48,940 --> 00:19:52,980
+قبل ما تنسى لإن انا عارف انه اللي بندرس عشان ننساه
+
+236
+00:19:52,980 --> 00:19:56,220
+احنا الان تعالى ال relation في ال relation بنقول
+
+237
+00:19:56,220 --> 00:20:04,040
+إذا لكل زوج مرتب for all a و b تنتمي لل relation
+
+238
+00:20:04,040 --> 00:20:13,970
+for all aوB تنتمي للـ relation هذا بيؤدي ان بي و A
+
+239
+00:20:13,970 --> 00:20:17,590
+تنتمي لل relation بقول عن ال relation عندي هال
+
+240
+00:20:17,590 --> 00:20:22,110
+Symmetric بقول عن ال relation عندي هال Symmetric
+
+241
+00:20:22,110 --> 00:20:27,470
+ال relation هادي هل هي Symmetric؟ هل ال relation
+
+242
+00:20:27,470 --> 00:20:32,270
+هادي Symmetric؟ طيب الآن هل هي Symmetric؟ لأ تعالى
+
+243
+00:20:32,270 --> 00:20:37,610
+نشوف واحد من الأمثلةأقول لك واحد و واحد ا أكبر أو
+
+244
+00:20:37,610 --> 00:20:45,470
+تساوي ايه بصبوط صورتها واحد و واحد صح لكن الآن
+
+245
+00:20:45,470 --> 00:20:50,750
+اتنين و واحد تحقق ال relation اتنين و واحد تنتمي
+
+246
+00:20:50,750 --> 00:20:56,310
+إلى ال R لكن but
+
+247
+00:20:56,310 --> 00:21:01,180
+الواحد والتاني اللي هي صورتهاأو انعكاس التي
+
+248
+00:21:01,180 --> 00:21:05,160
+تماثلها لا تنتمي للـ relation معناته الـR is not
+
+249
+00:21:05,160 --> 00:21:15,780
+symmetric R is not symmetric تمام؟
+
+250
+00:21:15,780 --> 00:21:19,740
+الـ definition بسيط وسهل بدأت نرى على ال relation
+
+251
+00:21:19,740 --> 00:21:24,800
+على كل العناصر اللي فيها كل عنصر فيه صورته أو
+
+252
+00:21:24,800 --> 00:21:29,850
+انعكاسه موجودتمام؟ A و B بلاجئله بي و ايه؟ معناته
+
+253
+00:21:29,850 --> 00:21:33,690
+ال relation اللي عندي هان Symmetric تعالى نشوف
+
+254
+00:21:33,690 --> 00:21:40,950
+المثال هذا افترض على نفس ال A ها دي R تساوي واحد و
+
+255
+00:21:40,950 --> 00:21:49,150
+اتنين اتنين و واحد بس
+
+256
+00:21:49,150 --> 00:21:52,090
+هي relation مش هي subset من ال Cartesian product
+
+257
+00:21:52,090 --> 00:21:59,350
+صح relation relationBinary relation هل هي
+
+258
+00:21:59,350 --> 00:22:06,090
+Symmetric؟ هل هي Symmetric؟ يا راجل تجلى هل هي
+
+259
+00:22:06,090 --> 00:22:10,650
+Symmetric؟ خد كل element هي ال element الأول واحد
+
+260
+00:22:10,650 --> 00:22:15,550
+و اتنين بينتمي لل relation ايش انعكاسه؟ اتنين و
+
+261
+00:22:15,550 --> 00:22:19,350
+واحد تنتمي لل relation؟ تنتمي لل relation العنصر
+
+262
+00:22:19,350 --> 00:22:23,430
+التاني اتنين و واحد بينتمي لل relation انعكاسه؟
+
+263
+00:22:24,080 --> 00:22:27,640
+واحد واثنين تنتمي للـ relation معناته ال relation
+
+264
+00:22:27,640 --> 00:22:34,480
+هذي symmetric ماتفتش ماتفتش
+
+265
+00:22:34,480 --> 00:22:39,600
+انا قولت كلمة سهلة وبسيطة ال properties هذي انفككت
+
+266
+00:22:39,600 --> 00:22:44,680
+عن بعض not related together انا
+
+267
+00:22:44,680 --> 00:22:50,480
+بسألك symmetric تقولي reflexive اليوم
+
+268
+00:22:50,480 --> 00:22:55,300
+اليوش اليوممن برا حاجات مجلوبة، مش صح الجواب يا
+
+269
+00:22:55,300 --> 00:23:02,120
+صاحبي، مش logic بالمرة هو أنا
+
+270
+00:23:02,120 --> 00:23:05,380
+باسألك في الـsymmetric ال condition مختلف تماما،
+
+271
+00:23:05,380 --> 00:23:09,860
+الان not symmetric، symmetric، symmetric،
+
+272
+00:23:09,860 --> 00:23:15,200
+reflexive، reflexive، not reflexive، لو أنا سألتك
+
+273
+00:23:15,200 --> 00:23:19,160
+reflexive، not reflexive، ايه و ايه مش لإن تمي،
+
+274
+00:23:19,160 --> 00:23:21,900
+واحد و واحد مش موجود خلصنا، ماتدوري، ماتكملش
+
+275
+00:23:28,850 --> 00:23:36,370
+الان في عندي تعريف جديد اسمه Anti-symmetric و من
+
+276
+00:23:36,370 --> 00:23:44,050
+الان انتبه معايا Anti-symmetric لا
+
+277
+00:23:44,050 --> 00:23:51,130
+تساوي كل
+
+278
+00:23:51,130 --> 00:23:54,290
+هدول different definitions different properties
+
+279
+00:23:57,110 --> 00:24:02,810
+لكن بنقدر نقول لو كانت symmetric مش هتكون Anti
+
+280
+00:24:02,810 --> 00:24:06,030
+-symmetric و لو كانت Anti-symmetric مش هتكون
+
+281
+00:24:06,030 --> 00:24:09,410
+symmetric بس ممكن تكون ال relation لا symmetric
+
+282
+00:24:09,410 --> 00:24:17,990
+ولا Anti-symmetric تمام؟ و ولا reflexive كمان الآن
+
+283
+00:24:17,990 --> 00:24:25,070
+إيش اللي بنقوله بكل بساطة؟ بنقول كتالةلو نجينا أو
+
+284
+00:24:25,070 --> 00:24:29,630
+أخدنا كل الأزواج المرتبة اللي في ال relation كل
+
+285
+00:24:29,630 --> 00:24:34,310
+الأزواج المرتبة اللي في ال relation تمام؟ مش
+
+286
+00:24:34,310 --> 00:24:38,210
+هالنجيل و انعكاس إلا الزوج المرتب اللي فيه الـA
+
+287
+00:24:38,210 --> 00:24:43,890
+تساوي بيه ليش؟ لأن انعكس هو نفسه يعني بكتب
+
+288
+00:24:43,890 --> 00:24:47,550
+بينجوسين، بينجوسين العناصر المتماثلة في الأزواج
+
+289
+00:24:47,550 --> 00:24:51,730
+المرتبة حاول اسقطها من فحصك الـsymmetric و
+
+290
+00:24:51,730 --> 00:24:57,250
+الـantisymmetricالان لو انا اجيب و قلتلك ال R هذي
+
+291
+00:24:57,250 --> 00:25:07,550
+واحد و واحد اتنين و واحد و واحد و اتنين مرتبط؟
+
+292
+00:25:07,550 --> 00:25:15,730
+مرتبط ليش لأ؟ مرتبط هذا ايش انعكاسه؟ نفسه و هذا
+
+293
+00:25:15,730 --> 00:25:20,950
+انعكاس نفسه بقد لها هذا و هذا بدلها مظبوط؟ و
+
+294
+00:25:20,950 --> 00:25:25,080
+بالتالي مرتبطالان هل هي Anti-Symmetric لأ نقطة
+
+295
+00:25:25,080 --> 00:25:28,760
+Anti-Symmetric خلصنا لأن فيها أزواج مرتبة غير
+
+296
+00:25:28,760 --> 00:25:33,740
+الواحد وواحد فيها إيش انعكاس لكن تعالى شوف هذه
+
+297
+00:25:33,740 --> 00:25:44,100
+Symmetric
+
+298
+00:25:44,100 --> 00:25:50,410
+لأ Anti-Symmetric true Anti-SymmetricAnti
+
+299
+00:25:50,410 --> 00:25:53,790
+-Symmetric التعريف تبقى الـ Anti-Symmetric فيقول
+
+300
+00:25:53,790 --> 00:25:59,090
+كالتالي كل الأزواج المرتبة لعناصرها مختلفة ليس لها
+
+301
+00:25:59,090 --> 00:26:05,670
+صور كل العناصر أو كل الأزواج المرتبة لعناصرها
+
+302
+00:26:05,670 --> 00:26:10,930
+مختلفة ليس لها صور خلصنا هذا خبّيني اللي هي أنا
+
+303
+00:26:10,930 --> 00:26:17,510
+صورته نفسي هذا فيه صورة؟ لأ معناته Anti-Symmetric
+
+304
+00:26:21,170 --> 00:26:25,550
+شوف ال relation هاي احباز السنة شوية هاي R تساوي
+
+305
+00:26:25,550 --> 00:26:34,130
+واحد و واحد واحد و اتنين اتنين
+
+306
+00:26:34,130 --> 00:26:40,850
+و واحد واحد و تلاتة symmetric؟
+
+307
+00:26:40,850 --> 00:26:49,570
+symmetric؟ لأ لحظة شوية not symmetric ليش؟
+
+308
+00:26:50,300 --> 00:26:57,260
+ليش؟ لأن واحد و تلاتة تنتمي لل relation but تلاتة
+
+309
+00:26:57,260 --> 00:27:01,600
+و واحد لا تنتمي لل relation بالمناسبة لما بدك تنفي
+
+310
+00:27:01,600 --> 00:27:05,420
+بدك تقوللي ليش .. لما بدك تنفي هبقى هتقوللي ليش
+
+311
+00:27:05,420 --> 00:27:12,500
+..طيب .. antisymmetric؟ لأ not antisymmetric
+
+312
+00:27:17,400 --> 00:27:22,160
+ليش not antisymmetric؟ لأن الواحد واتنين تنتمي لل
+
+313
+00:27:22,160 --> 00:27:28,860
+relation and
+
+314
+00:27:28,860 --> 00:27:32,600
+الواحد لا تساوي الاتنين
+
+315
+00:27:34,540 --> 00:27:39,420
+والواحد لا تساوي التيرين الجزئية الأخيرة هذه لو
+
+316
+00:27:39,420 --> 00:27:43,460
+أنت قررتلي إياها وما كتبتاش okay ليش؟ عشان احنا
+
+317
+00:27:43,460 --> 00:27:46,340
+قولنا من البداية الأزواج المرتبة اللي فيها العنصر
+
+318
+00:27:46,340 --> 00:27:50,700
+متشابه بدي أسقطها من عملية الفحص يعني هي بين جسدين
+
+319
+00:27:50,700 --> 00:27:54,480
+لهي مأثرة معاك في الـsymmetric ولا مأثرة معاك في
+
+320
+00:27:54,480 --> 00:27:55,260
+الـantisymmetric
+
+321
+00:28:02,930 --> 00:28:05,770
+هذه مجموعة من الأمثلة زى اللى شوفناها قبل شوية
+
+322
+00:28:05,770 --> 00:28:13,290
+symmetric و Anti-symmetric و لاهاي و لاهاي طيب فى
+
+323
+00:28:13,290 --> 00:28:21,430
+عندك خاصية الرابعة Transitive خاصية التعدى مفهومها
+
+324
+00:28:21,430 --> 00:28:31,490
+for any for all a و b and b و c تنتمي لل relation
+
+325
+00:28:32,690 --> 00:28:36,830
+ماذا يعني انتبه معايا؟ ماذا يعني؟ لازم يكون عندك
+
+326
+00:28:36,830 --> 00:28:42,630
+زوجين مرتبين زوجين مرتبات مختلفين نهاية الأول
+
+327
+00:28:42,630 --> 00:28:49,090
+تساوي بداية الثاني إذا وجد أي زوجين مرتبين بالشكل
+
+328
+00:28:49,090 --> 00:28:54,870
+هذا و لاجئت أن a و c اللي هي بداية الأول و نهاية
+
+329
+00:28:54,870 --> 00:28:57,650
+التانية بتنتمي لل relation معناته اللي بقول عنها
+
+330
+00:28:57,650 --> 00:29:01,550
+متعددة يعني بين بصين الأربعة
+
+331
+00:29:03,270 --> 00:29:08,910
+بتقبل الجسم على اتنين صح؟ التمانية بتقبل الجسم على
+
+332
+00:29:08,910 --> 00:29:15,010
+اربعة فالتمانية بتقبل الجسم على اتنين فعملية القسم
+
+333
+00:29:15,010 --> 00:29:17,550
+اللي انا ممكن اسميها transitive و لا لا ضمن ال
+
+334
+00:29:17,550 --> 00:29:22,890
+condition اللي موجود عندي وين
+
+335
+00:29:22,890 --> 00:29:27,630
+ما بتشوف يساوي اقل من او اكبر من او subset يعني
+
+336
+00:29:27,630 --> 00:29:30,270
+اننا بنتكلم على transitive بتكون ال relation اللي
+
+337
+00:29:30,270 --> 00:29:34,720
+عندنا transitive ال relation هذهtransitive او
+
+338
+00:29:34,720 --> 00:29:41,040
+transitive تعالى شوف بشكل عام transitive او
+
+339
+00:29:41,040 --> 00:29:45,740
+transitive او transitive او transitive او
+
+340
+00:29:45,740 --> 00:29:51,020
+transitive او transitive
+
+341
+00:29:51,020 --> 00:29:52,120
+او transitive او transitive او transitive او
+
+342
+00:29:52,120 --> 00:29:52,160
+transitive او transitive او transitive او
+
+343
+00:29:52,160 --> 00:29:52,360
+transitive او transitive او transitive او
+
+344
+00:29:52,360 --> 00:29:52,380
+transitive او transitive او transitive او
+
+345
+00:29:52,380 --> 00:29:52,980
+transitive او transitive او transitive او
+
+346
+00:29:52,980 --> 00:29:54,520
+transitive او transitive او transitive او
+
+347
+00:29:54,520 --> 00:29:56,260
+transitive او transitive او transitive او
+
+348
+00:29:56,260 --> 00:30:04,810
+transitive او transitiveالـ C and الـ C أكبر أو
+
+349
+00:30:04,810 --> 00:30:08,790
+تساوي الـ B الرتب الموضوع المثل هذا يعني أن الـ C
+
+350
+00:30:08,790 --> 00:30:15,350
+أكبر أو تساوي الـ B أكبر أو تساوي الـ A وبالتالي
+
+351
+00:30:15,350 --> 00:30:20,450
+الـ C أكبر أو تساوي الـ A وبالتالي أصبح الـ A و
+
+352
+00:30:20,450 --> 00:30:24,890
+الـ C ينتمي لل relation فأصبحت ال relation هذه
+
+353
+00:30:24,890 --> 00:30:28,810
+transitive أصبحت ال relation transitive واضح يا
+
+354
+00:30:28,810 --> 00:30:29,150
+شباب؟
+
+355
+00:30:31,900 --> 00:30:36,620
+طيب .. ما زال هوضح .. تعالوا نشوف .. انتوا لا جداش
+
+356
+00:30:36,620 --> 00:30:40,960
+فاهمين من الكلام اللي بنقوله .. انطبق الأربع خصائص
+
+357
+00:30:40,960 --> 00:30:48,940
+.. اتذكر كمان مرة .. كمان مرة .. Reflexive .. A و
+
+358
+00:30:48,940 --> 00:30:52,260
+A تنتمي لل relation .. لكل عناصر A .. لكل عناصر
+
+359
+00:30:52,260 --> 00:30:56,300
+مجموعة A .. Symmetric .. كل زوج مرتب A و B في ال
+
+360
+00:30:56,300 --> 00:30:59,340
+relation .. B و A لازم يكون موجود في ال relation
+
+361
+00:30:59,340 --> 00:31:05,100
+عشان تكون Symmetric ..Antisymmetric كل زوج مرتب A
+
+362
+00:31:05,100 --> 00:31:10,000
+و B في ال relation B و A لا ينتمي لل relation لـ
+
+363
+00:31:10,000 --> 00:31:15,420
+Transitive لكل زوجين A و B و B و C A و C لازم يكون
+
+364
+00:31:15,420 --> 00:31:19,840
+ينتمي في ال relation بيقول عنها Transitive بقولك
+
+365
+00:31:19,840 --> 00:31:25,560
+هي ال A الان
+
+366
+00:31:25,560 --> 00:31:30,600
+بقول R1 نتكلم على R1
+
+367
+00:31:34,700 --> 00:31:38,060
+R1 مش عارف اتلاقى محلة على اللوحة عشان نبقى ضمن ال
+
+368
+00:31:38,060 --> 00:31:42,160
+slides ومانبعدش كتير ومانجلمش أبو حسن معانا الان
+
+369
+00:31:42,160 --> 00:31:50,760
+R1 reflexive كيف بتحكم عليها reflexive؟ بدك تروح
+
+370
+00:31:50,760 --> 00:31:55,780
+على عناصر ال A كم عنصر في ال A؟ 1,2,3,4 بدك تدور
+
+371
+00:31:55,780 --> 00:32:04,510
+على 4 أزواج مرتبة 1 و 1 2 و 2 3 و 3الان 1 و 1
+
+372
+00:32:04,510 --> 00:32:08,390
+موجود اتنين و اتنين موجود تلاتة و تلاتة مش موجود
+
+373
+00:32:08,390 --> 00:32:14,690
+بقول is not reflexive لان تلاتة و تلاتة لا تنتمي ل
+
+374
+00:32:14,690 --> 00:32:24,990
+R1 طيب symmetric؟ طيب تعالى نشوف symmetric
+
+375
+00:32:24,990 --> 00:32:29,310
+هل هي symmetric؟ بدك تبدأ تفحص سيبك من الأزواج
+
+376
+00:32:29,310 --> 00:32:34,990
+المرتبة اللي قلهم متشادهاتواحد و اتنين صورتها ..
+
+377
+00:32:34,990 --> 00:32:38,390
+اتنين و واحد هي موجودة .. اتنين و واحد صورتها هي
+
+378
+00:32:38,390 --> 00:32:41,870
+.. خلاصنا .. تلاتة و أربعة .. الأصل يكون أربعة و
+
+379
+00:32:41,870 --> 00:32:46,110
+تلاتة .. معناته not symmetric .. not symmetric ..
+
+380
+00:32:46,110 --> 00:32:52,410
+و ليش؟ لأن تقول تلاتة و أربعة تنتمي لل relation ..
+
+381
+00:32:52,410 --> 00:32:58,290
+but أربعة و تلاتة لا تنتمي لل relation ..
+
+382
+00:33:04,640 --> 00:33:09,440
+Antisymmetric برضه لأ لإيش لأن عندي واحد و اتنين
+
+383
+00:33:09,440 --> 00:33:15,580
+تنتمي لل relation and اتنين و واحد تنتمي لل
+
+384
+00:33:15,580 --> 00:33:20,520
+relation ر واحد معناته هي not reflexive, not
+
+385
+00:33:20,520 --> 00:33:26,250
+symmetric, not antisymmetric, transitiveلاتش اسمها
+
+386
+00:33:26,250 --> 00:33:29,750
+دي، أيوة هي بالظبط.طيب في الـtransitive تعالى تشوف
+
+387
+00:33:29,750 --> 00:33:34,890
+شوية اشتغل معاها صح عشان ما تفوتش ولا عوصل لإن لو
+
+388
+00:33:34,890 --> 00:33:40,090
+فوتت element واحد منهم ممكن تغلط.إيش تساوي؟ امشي
+
+389
+00:33:40,090 --> 00:33:45,030
+معاهم انسالي .. انسالي كل الأزواج المرتبة تمام؟
+
+390
+00:33:45,030 --> 00:33:49,770
+اللي بتبدأ يش .. اللي فيها عناصر متشابهات تمام؟
+
+391
+00:33:49,770 --> 00:33:54,380
+لإن هذا already هيؤدل العوصل التانيالان ايش تساوي؟
+
+392
+00:33:54,380 --> 00:33:58,720
+تبدأ تحصر عناصر واحد و واحد انسانية واحد .. انا
+
+393
+00:33:58,720 --> 00:34:03,020
+بدي افحص يا شباب .. واحد و اتنين .. هاي .. بتجيبلي
+
+394
+00:34:03,020 --> 00:34:06,680
+كل الأزواج المرتبة اللي بتبدأ باتنين .. هاي في
+
+395
+00:34:06,680 --> 00:34:11,860
+عندي هذا .. اتنين و واحد .. و اتنين و اتنين .. في
+
+396
+00:34:11,860 --> 00:34:15,720
+غيره؟ خلصنا .. هذا ايش بيقدّي؟ هذا الأصل واحد و
+
+397
+00:34:15,720 --> 00:34:21,260
+واحد .. بينكمل الـA .. مصبوط؟وهذا سيبقى 1 و 2
+
+398
+00:34:21,260 --> 00:34:26,780
+ينتمي ل R1 اتنين
+
+399
+00:34:26,780 --> 00:34:31,520
+و واحد كل الأزواد المرتبة اللي تبقى بواحد في عندي
+
+400
+00:34:31,520 --> 00:34:38,700
+واحد و واحد و واحد و اتنين اتنين و واحد ينتمي ل R1
+
+401
+00:34:38,700 --> 00:34:43,300
+و اتنين و اتنين ينتمي ل R1
+
+402
+00:34:49,830 --> 00:34:52,330
+باخد الـ A و الـ C من الزوج و بصحى بحصل زوج المرتب
+
+403
+00:34:52,330 --> 00:34:56,290
+الناتج هل بينتمي ال relation ولا لأ؟ الان كمل
+
+404
+00:34:56,290 --> 00:35:01,870
+مخلصتش اربعة و تلاتة تلاتة او اربعة احنا نكمل هنا
+
+405
+00:35:01,870 --> 00:35:06,030
+هي تلاتة و اربعة كل الأزواج المرتبة اللي بتبدأ
+
+406
+00:35:06,030 --> 00:35:11,390
+باربعة في عندي اربعة و واحد و عندي اربعة و اربعة
+
+407
+00:35:11,390 --> 00:35:17,590
+الاصل هذا الشيطاني تلاتة و واحد موجود
+
+408
+00:35:17,590 --> 00:35:23,330
+تلاتة و واحدلا ينتمي ل R1 ماتوا متكمل الشغل not
+
+409
+00:35:23,330 --> 00:35:28,810
+transitive متكمل الشغل اه بك تمشي كل الخطوات هذه
+
+410
+00:35:28,810 --> 00:35:34,610
+اذا قدرت تلقطه من اول مرة انت زي انت كمان مرة اذا
+
+411
+00:35:34,610 --> 00:35:37,470
+انت جادر تجيبه من مجرد النظر تقولي اه هاي هم اتفضل
+
+412
+00:35:37,470 --> 00:35:40,510
+انا ماعندي مشكلة في الآخر انا بدي تقولي not
+
+413
+00:35:40,510 --> 00:35:45,050
+transitive ليش؟ لكن انا بقولك اذا انت ماعودتش نفسك
+
+414
+00:35:45,050 --> 00:35:50,190
+تمشي بالخطوات هذه هتغلط فيها حتماهنا في شغلة تانية
+
+415
+00:35:50,190 --> 00:35:53,750
+ممكن احنا نختزلها يا شباب الأزواج المرتبة لهيك
+
+416
+00:35:53,750 --> 00:36:02,510
+الزوج المرتب المتساوي تمام؟ يعني تخيل A و A مع A و
+
+417
+00:36:02,510 --> 00:36:09,430
+C ايه الشخص اللي بيعطيني؟ A و C بصبت؟ كذلك لما
+
+418
+00:36:09,430 --> 00:36:13,430
+باجي انا بقول A و C مع C و C ايه الشخص اللي
+
+419
+00:36:13,430 --> 00:36:17,830
+بيعطيني؟ A و C وبالتالي ممكن انت في شكل مباشر
+
+420
+00:36:19,150 --> 00:36:22,330
+تستثنيهم هدول وين ما يكون في عندي في المقارنة هذه
+
+421
+00:36:22,330 --> 00:36:29,510
+زوج مرتب متساوي ما تكتبهوش عشان تمشي خطوة للأمام
+
+422
+00:36:29,510 --> 00:36:31,970
+بس طبعا أنا جاعة بقولك ما تكتبهوش من أنا على إيه
+
+423
+00:36:31,970 --> 00:36:36,010
+اللي هو أنا مشغل دناقي صح وفاهم إنه في الآخر الزوج
+
+424
+00:36:36,010 --> 00:36:39,410
+المرتب في الـtransitive هتديني نفس ال element
+
+425
+00:36:39,410 --> 00:36:42,390
+وبالتالي already هو موجود وبالتالي أنا بقدر أعمل
+
+426
+00:36:42,390 --> 00:36:46,270
+skip لهيك element و أجلل على حالي بعد وقت الفحص
+
+427
+00:36:47,380 --> 00:36:53,020
+طيب، معناته R1 is not reflexive، not symmetric،
+
+428
+00:36:53,020 --> 00:37:01,460
+not antisymmetric، not transitive، not كلشي،
+
+429
+00:37:01,460 --> 00:37:06,580
+all not طيب،
+
+430
+00:37:06,580 --> 00:37:10,840
+فهنشوف كمان مثال ب relation تانية و ناخد على سبيل
+
+431
+00:37:10,840 --> 00:37:16,440
+المثال R3 خلينا ناخد على سبيل المثال R3
+
+432
+00:37:19,750 --> 00:37:26,410
+R تلاتة واحد و واحد واحد و اتنين واحد و اربعة
+
+433
+00:37:26,410 --> 00:37:31,910
+reflexive
+
+434
+00:37:31,910 --> 00:37:35,890
+ليش
+
+435
+00:37:35,890 --> 00:37:40,290
+reflexive؟ واحد و واحد اتنين اتنين تلاتة تلاتة
+
+436
+00:37:40,290 --> 00:37:42,210
+اربعة اربعة symmetric
+
+437
+00:37:48,590 --> 00:37:52,530
+واحد و اتنين اتنين و واحد واحد و اربعة اربعة و
+
+438
+00:37:52,530 --> 00:37:58,150
+واحد والباقي متشابهات فهي symmetric مباشرة Anti
+
+439
+00:37:58,150 --> 00:38:02,810
+-symmetric لأ
+
+440
+00:38:02,810 --> 00:38:07,370
+not Anti-symmetric عشان أيه قلتلك قبل شوية لما
+
+441
+00:38:07,370 --> 00:38:11,010
+تكون symmetric مستحيل تكون Anti-symmetric و لو
+
+442
+00:38:11,010 --> 00:38:13,750
+كانت Anti-symmetric مستحيل تكون symmetric
+
+443
+00:38:13,750 --> 00:38:17,970
+Transitive هلأ بدك شوية ايه اش
+
+444
+00:38:27,610 --> 00:38:32,070
+الأزوادي اللي بتبدأ اتنين و واحد اتنين و اتنين
+
+445
+00:38:32,070 --> 00:38:35,710
+بديش اياها لانها already فهذه بتديني واحد و واحد
+
+446
+00:38:35,710 --> 00:38:42,750
+بيمتمل ال relation الان واحد و أربعةأربعة و واحد
+
+447
+00:38:42,750 --> 00:38:46,190
+بدي يعطيني واحد و واحد كمان مرة تنتمي لل relation
+
+448
+00:38:46,190 --> 00:38:55,190
+بعد هيك في عندي أربعة و واحد مع واحد و اتنين و
+
+449
+00:38:55,190 --> 00:39:00,670
+واحد و أربعة هذا الأصل مش يعطيني أربعة و اتنين
+
+450
+00:39:00,670 --> 00:39:06,170
+أربعة و اتنين موجود لا ينتمي لل relation ماكملش
+
+451
+00:39:06,170 --> 00:39:07,530
+فحص not transitive
+
+452
+00:39:10,430 --> 00:39:15,150
+كيف؟ غيب عنك لأنك انت حولت تشتغل شكل Random والـ
+
+453
+00:39:15,150 --> 00:39:18,750
+Random اللي أطب فيه، هو أنا عم بشتغل بطريقة
+
+454
+00:39:18,750 --> 00:39:22,110
+Systematic، منتظرة، إذا أنت اتعودت عليها، هتمشي
+
+455
+00:39:22,110 --> 00:39:27,230
+معاك بسرعة يا شباب الأمور، نعم، فأول المحاضرة، لو
+
+456
+00:39:27,230 --> 00:39:29,150
+أنك كنت حاضر، كان جواك عرفت إيش بنستفيد منه في
+
+457
+00:39:29,150 --> 00:39:32,430
+حياتنا، إيش بنستفيد من ال relations؟
+
+458
+00:39:39,680 --> 00:39:43,840
+أه شوية يا شباب زميلنا بيقول ليش قلنا النط
+
+459
+00:39:43,840 --> 00:39:47,960
+Symmetric لتعني Anti-Symmetric تعالى شوف ال
+
+460
+00:39:47,960 --> 00:39:52,360
+relation هاي بالشد شرح دي معاك ال definition بدي
+
+461
+00:39:52,360 --> 00:39:56,120
+أروح معاك مباشرة لمثال بسيط جدا فترض ان ال R تساوي
+
+462
+00:39:56,120 --> 00:40:04,280
+واحد و اتنين اتنين و واحد واحد و تلاتة في تعريف ال
+
+463
+00:40:04,280 --> 00:40:10,420
+Symmetric لكل زوج مرتب انعكاسه موجود1 و 2 انعكسه
+
+464
+00:40:10,420 --> 00:40:16,500
+.. 2 و 1 .. 2 و 1 انعكسه .. 1 و 2 .. 1 و 3 ليس
+
+465
+00:40:16,500 --> 00:40:23,320
+لديها انعكس .. هذا يعني انها ليست سيماترك .. لا
+
+466
+00:40:23,320 --> 00:40:27,160
+أقدر أن أقول عليها انت سيماترك .. لماذا؟ لأن في
+
+467
+00:40:27,160 --> 00:40:30,960
+الانت سيماترك .. بقول كتالة .. كل العناصر اللي في
+
+468
+00:40:30,960 --> 00:40:34,740
+العلاقة ليست لديها انعكس إلا لو كانت الـA تسوى
+
+469
+00:40:34,740 --> 00:40:42,470
+الـBالان هذه هذه كون واحد و اتنين انعكاسها ينتمي
+
+470
+00:40:42,470 --> 00:40:49,510
+لل relation فهي نقف Anti-symmetric لأ
+
+471
+00:40:49,510 --> 00:40:52,910
+سيبنا من اللي خلصنا بنانجوب بس على جانب السؤال نقف
+
+472
+00:40:52,910 --> 00:40:56,490
+Anti-symmetric الان لو كانت Symmetric معناته هذا
+
+473
+00:40:56,490 --> 00:41:01,910
+غايب مصبوط Symmetric نقف Anti-symmetric لو هذا
+
+474
+00:41:01,910 --> 00:41:09,480
+غايب صارتانتي سيماتريك لكن ليس سيماتريك بصبت لكن
+
+475
+00:41:09,480 --> 00:41:13,660
+في حالة من الحالات جاية في الوسط لا هي سيماتريك
+
+476
+00:41:13,660 --> 00:41:16,500
+ولا هي انتي سيماتريك مثل الحالة اللي موجودة هنا
+
+477
+00:41:16,500 --> 00:41:21,160
+عشان هيك ماقدرش اقول كل not symmetric انتي
+
+478
+00:41:21,160 --> 00:41:27,800
+سيماتريك طيب البجيات بتكملهم لحالك لان اعتقد انه
+
+479
+00:41:27,800 --> 00:41:34,770
+بعد هي كان خلاص طيب الآنهك مباشرة أنا قفزت معاك من
+
+480
+00:41:34,770 --> 00:41:39,550
+تسعة واحد لتسعة أربعة أو تسعة خمسة مش فاكر ال
+
+481
+00:41:39,550 --> 00:41:43,510
+section الآن في ال section هدا بنتكلم على
+
+482
+00:41:43,510 --> 00:41:47,110
+equivalence relation لو ال relation حققت مجموعة من
+
+483
+00:41:47,110 --> 00:41:52,150
+الخصائص اللي هم reflexive و symmetric و transitive
+
+484
+00:41:52,150 --> 00:41:56,390
+بقول عنها equivalence relation بقول عنها
+
+485
+00:41:56,390 --> 00:41:58,170
+equivalence relation
+
+486
+00:42:01,110 --> 00:42:05,730
+وبنرمز لل equivalence اما بالمادة هاي او بالتلت
+
+487
+00:42:05,730 --> 00:42:10,190
+شرطات تعالى ال relation اللى موجودة عندى على
+
+488
+00:42:10,190 --> 00:42:17,630
+السريع الاصل هذا ايش؟ واحد و واحد و اتنين و اتنين
+
+489
+00:42:17,630 --> 00:42:22,070
+تلاتة و تلاتة reflexive واحد و اتنين و اتنين و
+
+490
+00:42:22,070 --> 00:42:25,310
+واحد واحد و تلاتة تلاتة و واحد اتنين و واحد هي
+
+491
+00:42:25,310 --> 00:42:27,430
+symmetric
+
+492
+00:42:29,190 --> 00:42:34,350
+transitive وtransitive كمان مقرأ تسألش أنا بسألك
+
+493
+00:42:34,350 --> 00:42:37,910
+هل هي equivalence relation مافيش داية تروح تفحص
+
+494
+00:42:37,910 --> 00:42:41,870
+الأربع properties بدي تلاتة منهم reflexive and
+
+495
+00:42:41,870 --> 00:42:47,770
+symmetric وtransitive من ناحية التهدي هي واحد
+
+496
+00:42:47,770 --> 00:42:53,750
+واثنين هادي مع هادي تديني واحد وواحد موجودة واحد
+
+497
+00:42:53,750 --> 00:43:00,200
+في غيرها واحد بالتنينواحد و تلاتة هي موجودة خلصنا
+
+498
+00:43:00,200 --> 00:43:06,120
+اللي بعده واحد و تلاتة تلاتة و واحد تديني واحد و
+
+499
+00:43:06,120 --> 00:43:10,260
+واحد تلاتة و اتنين تديني واحد و اتنين already
+
+500
+00:43:10,260 --> 00:43:15,040
+موجودة اللي بعده اتنين و واحد اتنين و واحد واحد و
+
+501
+00:43:15,040 --> 00:43:20,060
+اتنين اتنين و اتنين هيها واحد اتنين و تلاتة هيها
+
+502
+00:43:21,140 --> 00:43:25,480
+أتنين و تلاتة already موجودة لبعده تلاتة و واحد
+
+503
+00:43:25,480 --> 00:43:32,620
+واحد و .. تلاتة و اتنين تلاتة و اتنين هيها بعد هيك
+
+504
+00:43:32,620 --> 00:43:38,300
+تلاتة و تلاتة هيها خلصنا اتنين و تلاتة تلاتة و
+
+505
+00:43:38,300 --> 00:43:47,100
+واحد بعده اتنين و واحد هيها و تلاتة و تلاتةبناخد
+
+506
+00:43:47,100 --> 00:43:49,040
+.. احنا بيقول اللي هو already موجودة وبالتالي
+
+507
+00:43:49,040 --> 00:43:52,020
+transitive وبالتالي ال relation transitive نعم
+
+508
+00:43:52,020 --> 00:43:59,160
+يعني كل relation reflexive هي symmetric؟ نعم كل
+
+509
+00:43:59,160 --> 00:44:04,060
+relation reflexive؟ لأ لأ لأ لأ لأ لأ ممكن مثال؟
+
+510
+00:44:04,060 --> 00:44:04,960
+اه ممكن مثال
+
+511
+00:44:16,440 --> 00:44:21,360
+symmetric not reflexive هاي ال relation symmetric
+
+512
+00:44:21,360 --> 00:44:28,300
+not reflexive انت
+
+513
+00:44:28,300 --> 00:44:36,640
+هيك حكيت؟ هيك مقصودك كل reflexive symmetric اه وين
+
+514
+00:44:36,640 --> 00:44:40,900
+انعكاسه؟ نفسه احنا حكينا عن الكلام ده مش منه عشان
+
+515
+00:44:40,900 --> 00:44:45,280
+هيك قولنا حاول تجاهلها من الفحص انعكاسه هو نفسه
+
+516
+00:44:47,660 --> 00:44:50,600
+طيب، الآن بالتالي لما تكون ال relation اللي عندي
+
+517
+00:44:50,600 --> 00:44:56,210
+كمان مرة reflexiveSymmetric و Transitive معناته ان
+
+518
+00:44:56,210 --> 00:44:59,530
+انا بتكلم على equivalence relation equivalence
+
+519
+00:44:59,530 --> 00:45:03,070
+relation ليش بتهمني ال equivalence relation لأن
+
+520
+00:45:03,070 --> 00:45:06,630
+فعليا علاقة العناصر مع بعضهم هتشكل عندى مجموعات
+
+521
+00:45:06,630 --> 00:45:11,510
+هسميهم equivalent classes وال equivalent classes
+
+522
+00:45:11,510 --> 00:45:15,610
+هذه عبارة عن مجموعات التقاطع بينها Phi او
+
+523
+00:45:15,610 --> 00:45:21,490
+المجموعتين متساويتين تماما ليش لان لما باجي بقول
+
+524
+00:45:22,930 --> 00:45:27,870
+reflexive يعني كل عنصر مع نفسه مظبوط وsymmetric كل
+
+525
+00:45:27,870 --> 00:45:31,730
+عنصرين المختلفين لهم صوتهم موجودة يعني لما بدي
+
+526
+00:45:31,730 --> 00:45:36,210
+بقول الواحد related مع الواحد حتما والواحد والتنين
+
+527
+00:45:36,210 --> 00:45:39,950
+موجودة في معناته الواحد related للتنين والتنين
+
+528
+00:45:39,950 --> 00:45:44,570
+relatedللواحد ال equivalent class هو عبارة عن
+
+529
+00:45:44,570 --> 00:45:47,610
+المجموعة وهي رمزه هو عبارة عن المجموعة اللي بتحتوي
+
+530
+00:45:47,610 --> 00:45:52,330
+على مين؟ على ال B العنصر التاني العنصر التاني من
+
+531
+00:45:52,330 --> 00:45:58,110
+الزوج المرتم وال B تنتمي او ال A related to B ال A
+
+532
+00:45:58,110 --> 00:46:04,410
+related to B او بلين جوسين A وB تنتمي لل relation
+
+533
+00:46:04,410 --> 00:46:10,050
+انا بهمن مين؟ مجموعة ال B هذه في المثال السابق هذا
+
+534
+00:46:11,680 --> 00:46:14,760
+الـ M كانت كام equivalent class عندي عدد ال
+
+535
+00:46:14,760 --> 00:46:18,740
+classes بعدد عناصر ال A عدد ال classes equivalent
+
+536
+00:46:18,740 --> 00:46:25,280
+classes بعدد عناصر ال A يعني عندي واحد وعندي تنين
+
+537
+00:46:25,280 --> 00:46:31,820
+وعندي تلاتة هي عبارة عن المجموعة اللي بتحتوي على
+
+538
+00:46:31,820 --> 00:46:37,000
+العناصر اللي related مع الواحد هي الواحد واحد
+
+539
+00:46:37,000 --> 00:46:41,420
+اتنين تلاتة
+
+540
+00:46:43,260 --> 00:46:51,340
+1 2 3 مجموعة الان من العناصر ال related مع التنين
+
+541
+00:46:51,340 --> 00:46:52,880
+هي التنين
+
+542
+00:47:02,630 --> 00:47:06,050
+الان لاحظوا ان التلت عناصر أو التلت مجموعات
+
+543
+00:47:06,050 --> 00:47:10,210
+متساويات وهذا من خصائص ال equivalent class اول
+
+544
+00:47:10,210 --> 00:47:15,390
+حاجة equivalent class نائمتي ايش يعني نائمتي؟ يعني
+
+545
+00:47:15,390 --> 00:47:18,710
+مستحيل تكون فيه على الأقل هيكون عندك العنصر
+
+546
+00:47:18,710 --> 00:47:24,670
+related لنفسه عشان يحقق ال reflexive اتنين ان لو
+
+547
+00:47:24,670 --> 00:47:30,540
+أخدت اي two classesلو اخدت اي two classes التقاطع
+
+548
+00:47:30,540 --> 00:47:34,920
+بينهم فاي ولو كان لا يساوي الفاي معناته التنتين
+
+549
+00:47:34,920 --> 00:47:39,600
+متساويات لو كان التقاطع بينهم لا يساوي الفاي
+
+550
+00:47:39,600 --> 00:47:43,620
+فالتقاطع بينهم او المجموعتين متساويات وهذا اللي
+
+551
+00:47:43,620 --> 00:47:48,820
+صار معناه في المثال السابق اتحادهم كلهم بيعطيين
+
+552
+00:47:48,820 --> 00:47:55,400
+مين؟ بيعطيين ال a في المثال السابق هان قولنا واحد
+
+553
+00:47:55,400 --> 00:47:59,100
+واثنين وتلاتة كلهم كانوا يساوي ايش؟الـ A فتقطعهم
+
+554
+00:47:59,100 --> 00:48:02,800
+في لكن كلهم كان ايه تساوي؟ ال class تبع ال A تساوي
+
+555
+00:48:02,800 --> 00:48:05,860
+ال 1 تساوي ال class تبع ال 2 تساوي ال class تبع
+
+556
+00:48:05,860 --> 00:48:10,920
+التلاتة واتحادهم كلهم هاي .. هاي مجموعة جديدة
+
+557
+00:48:10,920 --> 00:48:17,740
+equivalence relation شوف الشباب لو انا سألتك .. لو
+
+558
+00:48:17,740 --> 00:48:21,990
+انا سألتكهاتلي ال equivalent classes من ال
+
+559
+00:48:21,990 --> 00:48:26,950
+equivalence relation ما تتعبش راسك و تروح تفحص هل
+
+560
+00:48:26,950 --> 00:48:30,490
+هي equivalence relation ولا لأ إلا لو أنا سألتك
+
+561
+00:48:30,490 --> 00:48:37,230
+قلتلك هل هذه equivalence relation if yes give me
+
+562
+00:48:38,010 --> 00:48:42,650
+covalent classes او اكتب لـ Covalent Classes تمام؟
+
+563
+00:48:42,650 --> 00:48:46,190
+لكن لو انا قلت لك هكلي ل Covalent Classes مباشرة
+
+564
+00:48:46,190 --> 00:48:49,990
+فانا بفترض ان هذه Covalent relation يعني Reflexive
+
+565
+00:48:49,990 --> 00:48:53,930
+و Symmetric و Transitive وانت بدك ايش تجيب القيم
+
+566
+00:48:53,930 --> 00:49:03,450
+الموجودة الان الواحد واحد
+
+567
+00:49:03,450 --> 00:49:10,470
+و اتنين و تلاتةوالتنين وانت مغمض واحد و اتنين و
+
+568
+00:49:10,470 --> 00:49:15,030
+تلاتة بلون هذا الكلام أنا جيب talk التنين related
+
+569
+00:49:15,030 --> 00:49:19,350
+مع نفسها لانها reflexive مظبوط والتنين مع الواحد
+
+570
+00:49:19,350 --> 00:49:23,710
+لانها symmetric هيها already وtransitive لانها
+
+571
+00:49:23,710 --> 00:49:27,330
+متعدية مظبوط مع التلاتة وبالتالي ال equivalent
+
+572
+00:49:27,330 --> 00:49:32,450
+class تبع التلاتة هتسويهم واحد و اتنين و تلاتة ال
+
+573
+00:49:32,450 --> 00:49:33,690
+equivalent class تبع الأربعة
+
+574
+00:49:36,580 --> 00:49:44,660
+الاربعة related مع نفسها اربعة و خمسة اربعة و خمسة
+
+575
+00:49:44,660 --> 00:49:50,440
+و مباشرة هتكون عندك الخمسة يا رب تكون بتضحك بس
+
+576
+00:49:50,440 --> 00:49:55,160
+عشانك فاهم الان
+
+577
+00:49:55,160 --> 00:50:03,210
+التقاقعات بينهم اما فيأو كل ال elements أو بيكونوا
+
+578
+00:50:03,210 --> 00:50:07,950
+متساويتين تمام؟ لو أخدت واحد و اتنين التقاطع كل
+
+579
+00:50:07,950 --> 00:50:11,530
+المجموعة اتنين و تلاتة واحد و تلاتة كل المجموعة
+
+580
+00:50:11,530 --> 00:50:16,090
+لكن تلاتة و أربعة فاي فشي يا إما بروح this joint
+
+581
+00:50:16,090 --> 00:50:21,350
+يا إما في أو بتون يكونوا متساويتين لو عملت اتحاد
+
+582
+00:50:21,350 --> 00:50:26,510
+للمجموعات هذه هحصل على مين؟ على كل ال ايه تعالي
+
+583
+00:50:26,510 --> 00:50:27,230
+كمان مثال
+
+584
+00:50:34,710 --> 00:50:41,870
+كم class عندي هان؟ كم class عندي هان؟ ستة واحد
+
+585
+00:50:41,870 --> 00:50:48,570
+واحد و تلاتة و خمسة هيهم و مباشرة عليها ال class
+
+586
+00:50:48,570 --> 00:50:51,870
+تبع التلاتة هذه تساوي ال class تبع التلاتة و تساوي
+
+587
+00:50:51,870 --> 00:50:59,550
+ال class تبع الخمسة طيب تنين تنين و ستة و ال class
+
+588
+00:50:59,550 --> 00:51:03,570
+تبع التنين تساوي ال class تبع الستة ضلت عند مين؟
+
+589
+00:51:04,950 --> 00:51:12,030
+تلاتة و احنا نقولها زي واحد، أربعة لحالها،
+
+590
+00:51:12,030 --> 00:51:18,990
+و الخمسة مع التلاتة، و التانية مع الستة، هاي الست
+
+591
+00:51:18,990 --> 00:51:24,980
+classes، خد أي اتنين، تقاطع بين هذا و هذا5 تقاطع
+
+592
+00:51:24,980 --> 00:51:28,900
+بين هذا و هذا 5 و لو قلنا 6 و 2 تقاطع بينهم 6 و 1
+
+593
+00:51:28,900 --> 00:51:34,900
+تقاطع بينهم 5 6 و 2 تقاطع بينهم متساويين وبالتالي
+
+594
+00:51:34,900 --> 00:51:39,140
+هيدفع رأي ميزة ال classes اللي موجودة عندك بقدر
+
+595
+00:51:39,140 --> 00:51:45,740
+أصنف العناصر ال relation ل classes إذا تحققت فيها
+
+596
+00:51:45,740 --> 00:51:52,000
+الخصائص السابقة طيب الآن partitionالـ Partition
+
+597
+00:51:52,000 --> 00:51:57,380
+ايش يعني؟ تقسيم .. Partitions أقسام .. البنيزين
+
+598
+00:51:57,380 --> 00:52:01,320
+يقولوا و الله تقطيع .. و الله فلان .. فلان جعان
+
+599
+00:52:01,320 --> 00:52:05,020
+اليوم و جاب الكيكة و قطعها أربع جطع .. عملها
+
+600
+00:52:05,020 --> 00:52:08,960
+partition .. هل في تقاطع بين الجطع اللي اتقطعت؟
+
+601
+00:52:08,960 --> 00:52:13,440
+يعني هل في مناطق مشتركة بين الجطعتين؟ مستحيل،
+
+602
+00:52:13,440 --> 00:52:16,360
+ماحدش حيرضى .. بعض الناس بدأت .. إيش اسمه؟ اتحرك
+
+603
+00:52:16,360 --> 00:52:20,580
+لساناتها و تصح صحي كويس ..لسه مش مفطرين، عشان هيك
+
+604
+00:52:20,580 --> 00:52:23,900
+يا رامد تراهين، الآن غير هيك في ال partition اللي
+
+605
+00:52:23,900 --> 00:52:27,960
+أنت بتعرفه، ال disk، القرص الصلب اللي عندك، بيقولك
+
+606
+00:52:27,960 --> 00:52:31,640
+اعمله partition، انجلي عمله لتالت أقسام،
+
+607
+00:52:31,640 --> 00:52:36,670
+partitions، اعملوا C وD وEجسمه هل ضروري ال
+
+608
+00:52:36,670 --> 00:52:39,510
+partitions يكون متساويات؟ لأ ماحدش بيقول أنه يكون
+
+609
+00:52:39,510 --> 00:52:45,390
+متساويات بس التقابل بينهم فاي التقابل بينهم فاي
+
+610
+00:52:45,390 --> 00:52:50,250
+واتحادهم كلهم بيدين مين؟ بيدين ال partition اللي
+
+611
+00:52:50,250 --> 00:52:58,530
+موجود عندها ففعليا أي مجموعة A تمام؟ هي عبارة عن
+
+612
+00:52:58,530 --> 00:53:03,070
+collection من الـdisjoint non-empty عشان تستخدم
+
+613
+00:53:03,070 --> 00:53:08,230
+الفايمن المجموعات واتحادهم كلهم بتديني ال a
+
+614
+00:53:08,230 --> 00:53:13,410
+بالمثال السابق لما انا قلت a بدها تساوي واحد
+
+615
+00:53:13,410 --> 00:53:18,690
+واثنين وتلاتة واربعة وقلتلك اعملي اياهم على three
+
+616
+00:53:18,690 --> 00:53:25,730
+partitions اعملي اياهم على three partitions هتقولي
+
+617
+00:53:25,730 --> 00:53:30,590
+ايه واحد بدها تساوي واحد واثنين واحد تاني يقولي
+
+618
+00:53:30,590 --> 00:53:35,110
+واحد واثنين وتلاتة وحرهيحطها كلها بس مش هيقدر
+
+619
+00:53:35,110 --> 00:53:38,930
+يعملهم three partitions و لو حطيتوا الانصر الرادع
+
+620
+00:53:38,930 --> 00:53:44,270
+تالتها هتتقيد و مش هتعمل three partitions لأن
+
+621
+00:53:44,270 --> 00:53:48,930
+الأصل التقاطع يراني سيبك مالحكي الأصل في التقاطع
+
+622
+00:53:48,930 --> 00:53:56,310
+يكون five وبالتالي هيك أفضل شغلة اتنين بدها تساوي
+
+623
+00:53:56,310 --> 00:54:04,830
+تلاتة و اتلاتةبتساوي أربعة هدول الأربع مجموعات
+
+624
+00:54:04,830 --> 00:54:11,470
+this joint اتحادهم بيعطيني كل ال a بيعطيني كل ال a
+
+625
+00:54:11,470 --> 00:54:17,970
+في توزيع تاني ممكن تصير؟ أه ممكن بدل التنين مكان
+
+626
+00:54:17,970 --> 00:54:21,310
+التلاتة أول واحد بتصير الحكاية التبديل و التواثيق
+
+627
+00:54:21,310 --> 00:54:25,450
+اللي هنجيها لاحقا لما نتكلم على الأعداد لما نتكلم
+
+628
+00:54:25,450 --> 00:54:29,810
+على أنظمة العد بنصير نتكلم على التبديل و التواثيق
+
+629
+00:54:29,810 --> 00:54:33,500
+في حينها ان شاء اللهطيب وبالتالي أنا فهمت مبدأ ال
+
+630
+00:54:33,500 --> 00:54:38,680
+partition اللي عندي هنا في عندي definition بسيط
+
+631
+00:54:38,680 --> 00:54:44,940
+بدنا نحفظه بكل بساطة زي محفظة الأربع خصائص
+
+632
+00:54:44,940 --> 00:54:48,300
+بتتذكرهم؟ وقولنا لما تكون reflexive وsymmetric
+
+633
+00:54:48,300 --> 00:54:51,900
+وtransitive اسة منها equivalence relation
+
+634
+00:54:51,900 --> 00:54:54,960
+equivalence relation في عندي partial order
+
+635
+00:54:54,960 --> 00:55:00,100
+relation أو both set relation أو both setRelation
+
+636
+00:55:00,100 --> 00:55:06,820
+لما تكون Reflexive و Antisymmetric و Transitive ..
+
+637
+00:55:06,820 --> 00:55:11,420
+Reflexive و Antisymmetric و Transitive بنقول
+
+638
+00:55:11,420 --> 00:55:17,320
+partial order أو بوسط .. ليش؟ هتحس إنه فعليًا
+
+639
+00:55:17,320 --> 00:55:22,760
+هيصيرها جايين في اتجاه اللي هو مش .. مافيش انعكاس
+
+640
+00:55:22,760 --> 00:55:25,960
+في اتجاه التاني، يعني محصورة في واحد من الأقطار أو
+
+641
+00:55:25,960 --> 00:55:29,630
+تحت واحد من الأقطار اللي موجودة عندك هناالـ
+
+642
+00:55:29,630 --> 00:55:33,430
+division القسمة
+
+643
+00:55:33,430 --> 00:55:42,010
+هل هي symmetric؟ ال division هل هي symmetric؟
+
+644
+00:55:42,010 --> 00:55:45,550
+انا بسألك ال division هل هي symmetric؟ عملية
+
+645
+00:55:45,550 --> 00:55:49,910
+القسمة هل هي symmetric؟ لو a بتجبل .. لو b بتجبل
+
+646
+00:55:49,910 --> 00:55:55,370
+الجسمة على ال a بظبط لأ لأن العملية مش إبدالية
+
+647
+00:55:55,370 --> 00:56:01,910
+عملية القسمة مش إبداليةوبالتالي هي مستحيلة تكون
+
+648
+00:56:01,910 --> 00:56:05,710
+symmetrical هذه مثالة على antisymmetric لكنها
+
+649
+00:56:05,710 --> 00:56:10,690
+transitive ولا عرعير Transitive مصبوب؟ لأن اللي
+
+650
+00:56:10,690 --> 00:56:16,450
+بيقبل الجسم على التلاتةكمان؟ اللي بيجبن الجسم على
+
+651
+00:56:16,450 --> 00:56:20,450
+التاسعة بيجبن الجسم على التلاتة و اللي بيجبن الجسم
+
+652
+00:56:20,450 --> 00:56:24,330
+على الستة بيجبن الجسم على التنين مصطلح لأ؟ و هكذا
+
+653
+00:56:24,330 --> 00:56:28,230
+وبالتالي هي Transitive و Reflexive لأن كل عنصر
+
+654
+00:56:28,230 --> 00:56:33,510
+بيجبن الجسم على نفسه فهذا احنا بنسميها Bosset
+
+655
+00:56:33,510 --> 00:56:38,590
+relation أو partial order relation بس في عندكوا
+
+656
+00:56:38,590 --> 00:56:39,770
+خطأ واحد في ال slides
+
+657
+00:56:42,390 --> 00:56:49,630
+تسعة واحد مش تمانية واحد موجود على الموديل تمام
+
+658
+00:56:49,630 --> 00:56:55,070
+تمام ال slides و الكتاب موجودين طيب في اي سؤال
+
+659
+00:56:55,070 --> 00:56:57,910
+شباب الله يعطيكم العافية احنا اليوم هناك
+
diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/JYdKdPOF5Ho_raw.json b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/JYdKdPOF5Ho_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..938243db81c91f73535849392cd1d1ed5c53140e
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/JYdKdPOF5Ho_raw.json
@@ -0,0 +1 @@
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اللي أنا أخدته سابقا طيب وين بيلزمني هذا الكلام؟ ليش أنا بمهم أفهم ال relation من البداية صح؟", "tokens": [37746, 6027, 2655, 6027, 1829, 41850, 2423, 2480, 1296, 2309, 4959, 34051, 2423, 4478, 13672, 1829, 8978, 9673, 7435, 2304, 45367, 9307, 39894, 2304, 12984, 1211, 3877, 4032, 3615, 8592, 7649, 39896, 41850, 12602, 2407, 33753, 10874, 1829, 3555, 2655, 11296, 4032, 9957, 22807, 8978, 2423, 7187, 2423, 3877, 46599, 6027, 2655, 6027, 1829, 39896, 6225, 3555, 9640, 3660, 18871, 25993, 9154, 2423, 22478, 42434, 1674, 37495, 22653, 41850, 3714, 16758, 34268, 8592, 18871, 2423, 28820, 10943, 13672, 1829, 41850, 5551, 9778, 3215, 47395, 8608, 16758, 4587, 995, 23032, 1829, 3555, 4032, 9957, 4724, 26895, 11622, 2304, 22653, 23758, 2423, 28820, 10943, 22807, 32239, 8592, 41850, 4724, 2304, 16095, 5551, 5172, 16095, 2423, 9721, 9154, 29739, 28259, 10632, 20328, 5016, 22807], "avg_logprob": -0.21080942671807085, "compression_ratio": 1.8093525179856116, "no_speech_prob": 0.0, "words": 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relation اللي عندي هان Symmetric تعالى نشوف المثال هذا افترض على نفس ال A ها دي R تساوي واحد و اتنين اتنين و واحد بس هي relation مش هي subset من ال Cartesian product صح relation relation", "tokens": [39237, 10943, 22807, 316, 4032, 363, 4724, 15040, 7435, 19986, 43761, 4724, 1829, 4032, 1975, 1829, 3224, 22807, 20449, 8315, 47395, 2423, 9721, 13672, 1829, 18871, 16254, 8032, 7649, 3902, 2174, 17475, 37279, 6027, 7578, 8717, 8592, 38688, 9673, 12984, 6027, 23758, 1975, 5172, 2655, 43042, 15844, 8717, 36178, 2423, 316, 8032, 995, 11778, 1829, 497, 6055, 3794, 995, 45865, 36764, 24401, 4032, 1975, 2655, 1863, 9957, 1975, 2655, 1863, 9957, 4032, 36764, 24401, 4724, 3794, 39896, 9721, 37893, 39896, 25993, 9154, 2423, 22478, 42434, 1674, 20328, 5016, 9721, 9721], "avg_logprob": -0.3202266352517264, "compression_ratio": 1.591549295774648, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1286.83, "end": 1287.55, "word": "تمام؟", "probability": 0.5609130859375}, {"start": 1287.55, 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"end": 1296.61, "word": " دي", "probability": 0.632080078125}, {"start": 1296.61, "end": 1297.61, "word": " R", "probability": 0.71728515625}, {"start": 1297.61, "end": 1298.17, "word": " تساوي", "probability": 0.80859375}, {"start": 1298.17, "end": 1300.83, "word": " واحد", "probability": 0.796630859375}, {"start": 1300.83, "end": 1300.95, "word": " و", "probability": 0.953125}, {"start": 1300.95, "end": 1301.35, "word": " اتنين", "probability": 0.936279296875}, {"start": 1301.35, "end": 1302.85, "word": " اتنين", "probability": 0.8814697265625}, {"start": 1302.85, "end": 1302.95, "word": " و", "probability": 0.8974609375}, {"start": 1302.95, "end": 1303.37, "word": " واحد", "probability": 0.96630859375}, {"start": 1303.37, "end": 1309.15, "word": " بس", "probability": 0.966064453125}, {"start": 1309.15, "end": 1309.43, "word": " هي", "probability": 0.447998046875}, {"start": 1309.43, "end": 1309.85, "word": " relation", "probability": 0.72998046875}, {"start": 1309.85, "end": 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element الأول واحد و اتنين بينتمي لل relation ايش انعكاسه؟ اتنين و واحد تنتمي لل relation؟ تنتمي لل relation العنصر التاني اتنين و واحد بينتمي لل relation انعكاسه؟", "tokens": [33, 4066, 9721, 8032, 1211, 39896, 3902, 2174, 17475, 22807, 8032, 1211, 39896, 3902, 2174, 17475, 22807, 35186, 12602, 26108, 1211, 6055, 7435, 23942, 8032, 1211, 39896, 3902, 2174, 17475, 22807, 16490, 3215, 28242, 4478, 39896, 2423, 4478, 16247, 12610, 36764, 24401, 4032, 1975, 2655, 1863, 9957, 4724, 9957, 39237, 1829, 24976, 9721, 1975, 1829, 8592, 16472, 3615, 4117, 32277, 3224, 22807, 1975, 2655, 1863, 9957, 4032, 36764, 24401, 6055, 29399, 2304, 1829, 24976, 9721, 22807, 6055, 29399, 2304, 1829, 24976, 9721, 18863, 1863, 9381, 2288, 16712, 7649, 1829, 1975, 2655, 1863, 9957, 4032, 36764, 24401, 4724, 9957, 39237, 1829, 24976, 9721, 16472, 3615, 4117, 32277, 3224, 22807], "avg_logprob": -0.20298164481416756, "compression_ratio": 2.207865168539326, "no_speech_prob": 2.6226043701171875e-06, "words": 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{"id": 49, "seek": 137148, "start": 1344.08, "end": 1371.48, "text": "واحد واثنين تنتمي للـ relation معناته ال relation هذي symmetric ماتفتش ماتفتش انا قولت كلمة سهلة وبسيطة ال properties هذي انفككت عن بعض not related together انا بسألك symmetric تقولي reflexive اليوم اليوش اليوم", "tokens": [14407, 24401, 4032, 5718, 104, 1863, 9957, 6055, 29399, 2304, 1829, 24976, 39184, 9721, 20449, 8315, 47395, 2423, 9721, 8032, 8848, 1829, 32330, 3714, 9307, 5172, 2655, 8592, 3714, 9307, 5172, 2655, 8592, 1975, 8315, 12174, 12610, 2655, 9122, 19528, 3660, 8608, 3224, 37977, 4032, 3555, 3794, 1829, 9566, 3660, 2423, 7221, 8032, 8848, 1829, 16472, 5172, 4117, 4117, 2655, 18871, 45030, 11242, 406, 4077, 1214, 1975, 8315, 4724, 3794, 10721, 23275, 32330, 6055, 39648, 1829, 23802, 488, 45595, 20498, 45595, 2407, 8592, 45595, 20498], "avg_logprob": -0.3577398162248523, "compression_ratio": 1.5566502463054188, "no_speech_prob": 0.0, "words": [{"start": 1344.08, "end": 1344.62, "word": "واحد", 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Reflexive .. A و A تنتمي لل relation .. لكل عناصر A .. لكل عناصر مجموعة A .. Symmetric .. كل زوج مرتب A و B في ال relation .. 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"word": " ماعودتش", "probability": 0.90478515625}, {"start": 2144.71, "end": 2145.05, "word": " نفسك", "probability": 0.99755859375}, {"start": 2145.05, "end": 2145.37, "word": " تمشي", "probability": 0.9684244791666666}, {"start": 2145.37, "end": 2145.87, "word": " بالخطوات", "probability": 0.90888671875}, {"start": 2145.87, "end": 2146.23, "word": " هذه", "probability": 0.916015625}, {"start": 2146.23, "end": 2147.27, "word": " هتغلط", "probability": 0.91025390625}, {"start": 2147.27, "end": 2147.49, "word": " فيها", "probability": 0.9931640625}, {"start": 2147.49, "end": 2147.93, "word": " حتما", "probability": 0.7189127604166666}], "temperature": 1.0}, {"id": 77, "seek": 217783, "start": 2149.27, "end": 2177.83, "text": "هنا في شغلة تانية ممكن احنا نختزلها يا شباب الأزواج المرتبة لهيك الزوج المرتب المتساوي تمام؟ يعني تخيل A و A مع A و C ايه الشخص اللي بيعطيني؟ A و C بصبت؟ كذلك لما باجي انا بقول A و C مع C و C ايه الشخص اللي بيعطيني؟ A و C وبالتالي ممكن انت في شكل مباشر", "tokens": 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"probability": 0.8671875}, {"start": 2217.14, "end": 2221.46, "word": " كلشي،", "probability": 0.8013916015625}, {"start": 2221.46, "end": 2221.74, "word": " all", "probability": 0.1494140625}, {"start": 2221.74, "end": 2223.2, "word": " not", "probability": 0.87939453125}, {"start": 2223.2, "end": 2226.58, "word": " طيب،", "probability": 0.8118896484375}, {"start": 2226.58, "end": 2227.06, "word": " فهنشوف", "probability": 0.8306640625}, {"start": 2227.06, "end": 2227.32, "word": " كمان", "probability": 0.7840169270833334}, {"start": 2227.32, "end": 2227.76, "word": " مثال", "probability": 0.9775390625}, {"start": 2227.76, "end": 2228.22, "word": " ب", "probability": 0.873046875}, {"start": 2228.22, "end": 2228.54, "word": " relation", "probability": 0.88818359375}, {"start": 2228.54, "end": 2229.02, "word": " تانية", "probability": 0.9881184895833334}, {"start": 2229.02, "end": 2230.18, "word": " و", "probability": 0.50439453125}, {"start": 2230.18, "end": 2230.48, "word": " ناخد", "probability": 0.7801920572916666}, {"start": 2230.48, "end": 2230.6, "word": " على", "probability": 0.82763671875}, {"start": 2230.6, "end": 2230.84, "word": " سبيل", "probability": 0.9930013020833334}, {"start": 2230.84, "end": 2231.34, "word": " المثال", "probability": 0.9943033854166666}, {"start": 2231.34, "end": 2232.8, "word": " R3", "probability": 0.9453125}, {"start": 2232.8, "end": 2233.82, "word": " خلينا", "probability": 0.7681477864583334}, {"start": 2233.82, "end": 2234.06, "word": " ناخد", "probability": 0.9962565104166666}, {"start": 2234.06, "end": 2234.18, "word": " على", "probability": 0.94873046875}, {"start": 2234.18, "end": 2234.54, "word": " سبيل", "probability": 0.9915364583333334}, {"start": 2234.54, "end": 2235.04, "word": " المثال", "probability": 0.99462890625}, {"start": 2235.04, "end": 2236.44, "word": " R3", "probability": 0.9755859375}], "temperature": 1.0}, {"id": 80, "seek": 226221, "start": 2239.75, "end": 2262.21, "text": "R تلاتة واحد و واحد واحد و اتنين واحد و اربعة reflexive ليش reflexive؟ واحد و واحد اتنين اتنين تلاتة تلاتة اربعة اربعة symmetric", "tokens": [49, 6055, 1211, 9307, 3660, 36764, 24401, 4032, 36764, 24401, 36764, 24401, 4032, 1975, 2655, 1863, 9957, 36764, 24401, 4032, 1975, 25513, 27884, 23802, 488, 32239, 8592, 23802, 488, 22807, 36764, 24401, 4032, 36764, 24401, 1975, 2655, 1863, 9957, 1975, 2655, 1863, 9957, 6055, 1211, 9307, 3660, 6055, 1211, 9307, 3660, 1975, 25513, 27884, 1975, 25513, 27884, 32330], "avg_logprob": -0.22086864810878948, "compression_ratio": 2.11340206185567, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2239.75, "end": 2240.05, "word": "R", "probability": 0.587890625}, {"start": 2240.05, "end": 2240.65, "word": " تلاتة", "probability": 0.7571563720703125}, {"start": 2240.65, "end": 2241.83, "word": " واحد", "probability": 0.7462158203125}, {"start": 2241.83, "end": 2241.95, "word": " و", "probability": 0.8955078125}, {"start": 2241.95, "end": 2242.47, "word": " واحد", 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"text": "بناخد .. احنا بيقول اللي هو already موجودة وبالتالي transitive وبالتالي ال relation transitive نعم يعني كل relation reflexive هي symmetric؟ نعم كل relation reflexive؟ لأ لأ لأ لأ لأ لأ ممكن مثال؟ اه ممكن مثال", "tokens": [3555, 1863, 47283, 3215, 4386, 1975, 5016, 8315, 4724, 1829, 39648, 13672, 1829, 31439, 1217, 3714, 29245, 23328, 3660, 46599, 6027, 2655, 6027, 1829, 1145, 2187, 46599, 6027, 2655, 6027, 1829, 2423, 9721, 1145, 2187, 8717, 25957, 37495, 22653, 28242, 9721, 23802, 488, 39896, 32330, 22807, 8717, 25957, 28242, 9721, 23802, 488, 22807, 5296, 10721, 5296, 10721, 5296, 10721, 5296, 10721, 5296, 10721, 5296, 10721, 3714, 43020, 50113, 6027, 22807, 1975, 3224, 3714, 43020, 50113, 6027], "avg_logprob": -0.25933442642162374, "compression_ratio": 1.8242424242424242, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2626.68, "end": 2627.1, "word": "بناخد", "probability": 0.6420745849609375}, {"start": 2627.1, "end": 2627.2, "word": " ..", "probability": 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symmetric not reflexive انت هيك حكيت؟ هيك مقصودك كل reflexive symmetric اه وين انعكاسه؟ نفسه احنا حكينا عن الكلام ده مش منه عشان هيك قولنا حاول تجاهلها من الفحص انعكاسه هو نفسه", "tokens": [3187, 2174, 17475, 406, 23802, 488, 8032, 47302, 2423, 9721, 32330, 406, 23802, 488, 16472, 2655, 39896, 4117, 11331, 4117, 36081, 22807, 39896, 4117, 3714, 4587, 9381, 23328, 4117, 28242, 23802, 488, 32330, 1975, 3224, 4032, 9957, 16472, 3615, 4117, 32277, 3224, 22807, 8717, 36178, 3224, 1975, 5016, 8315, 11331, 4117, 1829, 8315, 18871, 2423, 28820, 10943, 11778, 3224, 37893, 9154, 3224, 6225, 8592, 7649, 39896, 4117, 12174, 12610, 8315, 11331, 995, 12610, 6055, 7435, 40294, 1211, 11296, 9154, 27188, 5016, 9381, 16472, 3615, 4117, 32277, 3224, 31439, 8717, 36178, 3224], "avg_logprob": -0.2870244523105414, "compression_ratio": 1.7486631016042782, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2656.44, "end": 2656.98, "word": "symmetric", "probability": 0.6332194010416666}, {"start": 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3406.23, "end": 3409.63, "word": " تمام", "probability": 0.5394287109375}, {"start": 3409.63, "end": 3411.37, "word": " تمام", "probability": 0.6689453125}, {"start": 3411.37, "end": 3411.75, "word": " ال", "probability": 0.73974609375}, {"start": 3411.75, "end": 3412.23, "word": " slides", "probability": 0.94091796875}, {"start": 3412.23, "end": 3412.71, "word": " و", "probability": 0.6396484375}, {"start": 3412.71, "end": 3413.05, "word": " الكتاب", "probability": 0.94970703125}, {"start": 3413.05, "end": 3413.61, "word": " موجودين", "probability": 0.9835205078125}, {"start": 3413.61, "end": 3414.55, "word": " طيب", "probability": 0.95263671875}, {"start": 3414.55, "end": 3414.81, "word": " في", "probability": 0.83154296875}, {"start": 3414.81, "end": 3414.89, "word": " اي", "probability": 0.751953125}, {"start": 3414.89, "end": 3415.07, "word": " سؤال", "probability": 0.9484049479166666}, {"start": 3415.07, "end": 3415.49, "word": " شباب", "probability": 0.8585611979166666}, {"start": 3415.49, "end": 3416.75, "word": " الله", "probability": 0.84423828125}, {"start": 3416.75, "end": 3417.01, "word": " يعطيكم", "probability": 0.631256103515625}, {"start": 3417.01, "end": 3417.35, "word": " العافية", "probability": 0.8435872395833334}, {"start": 3417.35, "end": 3417.57, "word": " احنا", "probability": 0.9490559895833334}, {"start": 3417.57, "end": 3417.73, "word": " اليوم", "probability": 0.971923828125}, {"start": 3417.73, "end": 3417.91, "word": " هناك", "probability": 0.752685546875}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3418.1863125, "duration_after_vad": 3230.281249999981}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/JYdKdPOF5Ho_raw.srt b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/JYdKdPOF5Ho_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..17efbdc998f1fd0038946a3902594006e9d7faa6
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/JYdKdPOF5Ho_raw.srt
@@ -0,0 +1,2640 @@
+1
+00:00:20,700 --> 00:00:22,700
+بسم الله والحمد لله والصلاة والسلام على رسول الله
+
+2
+00:00:22,700 --> 00:00:25,860
+اليوم ان شاء الله تعالى هنكمل في جهة chapter ال
+
+3
+00:00:25,860 --> 00:00:29,460
+structures لكن ال section تبعتنا من section مختلف
+
+4
+00:00:29,460 --> 00:00:32,420
+تماما الكتاب مفرد ال relations في chapter مستقل
+
+5
+00:00:32,420 --> 00:00:35,680
+اللي هو chapter تسعة بس ال chapter اللي احنا كنا
+
+6
+00:00:35,680 --> 00:00:40,460
+فيه اتنين كنا بنتكلم على ال basic structure set و
+
+7
+00:00:40,460 --> 00:00:44,240
+function مظبوط و sequence و matrix و ال relation
+
+8
+00:00:44,240 --> 00:00:46,860
+هذه زي ما هنشوف كمان شوية هي عبارة عن مجموعات
+
+9
+00:00:46,860 --> 00:00:47,820
+relations
+
+10
+00:00:54,300 --> 00:00:59,160
+الان لما بجي بتكلم على ال relation ال relation هي
+
+11
+00:00:59,160 --> 00:01:06,540
+عبارة عن علاقات ما بين المجموعات حضرتك كطالب في
+
+12
+00:01:06,540 --> 00:01:13,100
+التخصص في الكلية في المساق الان تخيل تخيل مجموعة
+
+13
+00:01:13,100 --> 00:01:19,720
+الكليات و طلاب relation ولا لا الطالب تخصص كذاأو
+
+14
+00:01:19,720 --> 00:01:23,640
+الطالب مسجل في كلية كذا في المساقات الطالب درس
+
+15
+00:01:23,640 --> 00:01:25,980
+المساق أو يدرس المساق الفلاني أو نجح في المساق
+
+16
+00:01:25,980 --> 00:01:31,420
+عبارة عن ال relation الناس و الألوان اللي بتحبها و
+
+17
+00:01:31,420 --> 00:01:34,260
+الفواكه اللي بتحب تاكلها الاخرى هي عبارة عن groups
+
+18
+00:01:34,260 --> 00:01:38,540
+او sets مجموعات و في بينهم relation و احنا شفنا
+
+19
+00:01:38,540 --> 00:01:41,140
+نوع من ال relation يا شباب لما اتكلمنا على ال
+
+20
+00:01:41,140 --> 00:01:45,600
+Cartesian product بين مجموعتين ولا لأ؟ قلنا بينتج
+
+21
+00:01:45,600 --> 00:01:52,690
+عنها مجموعة بتشكل أزوادمرتبة A تنتمي لـ A و B
+
+22
+00:01:52,690 --> 00:01:56,170
+تنتمي لـ B و لا لها؟ مش هذا تعريف الـ cross
+
+23
+00:01:56,170 --> 00:02:00,570
+product كان؟ و كل هذا الزوج المرتب هو الـ tuple
+
+24
+00:02:00,570 --> 00:02:04,770
+الـ
+
+25
+00:02:04,770 --> 00:02:09,210
+tuple هذا زوج مرتب لا يساوي AB لا تساوي BA و
+
+26
+00:02:09,210 --> 00:02:11,730
+اتكلمنا عليها ساحينها هنشوف إنه فعليا هذا موجود
+
+27
+00:02:13,900 --> 00:02:17,160
+وبالتالي أنا ال relationship between six elements
+
+28
+00:02:17,160 --> 00:02:21,180
+أو ال element اللي في المجموعات بتمثل structure
+
+29
+00:02:21,180 --> 00:02:24,660
+وعشان هي أنا روحت جيبتها وين؟ في ال chapter ال
+
+30
+00:02:24,660 --> 00:02:28,780
+structure وبالتالي هي عبارة عن subset من ال
+
+31
+00:02:28,780 --> 00:02:32,660
+Cartesian product يعني أنا مابعتش عن الكلام اللي
+
+32
+00:02:32,660 --> 00:02:37,580
+أنا أخدته سابقا طيب وين بيلزمني هذا الكلام؟ ليش
+
+33
+00:02:37,580 --> 00:02:40,690
+أنا بمهم أفهم ال relation من البداية صح؟الـ
+
+34
+00:02:40,690 --> 00:02:42,490
+Relations الـ implementation تبعتها و ال
+
+35
+00:02:42,490 --> 00:02:45,850
+application تبعتها للناس اللي بتشتغل في الكمبيوتر
+
+36
+00:02:45,850 --> 00:02:50,210
+كبيرة جدا لما تدرس مساق ال database واحد هنتكلم
+
+37
+00:02:50,210 --> 00:02:56,510
+على relation ما بين ال entities فيه عندك الطالب و
+
+38
+00:02:56,510 --> 00:03:00,170
+المساق different setsمجموعة القلاب ومجموعة
+
+39
+00:03:00,170 --> 00:03:03,810
+المساقات في بينهم relation اللي هو المساق تسجيل
+
+40
+00:03:03,810 --> 00:03:07,470
+المساق خلال الفصل الواحد وبالتالي هتصرف فيه
+
+41
+00:03:07,470 --> 00:03:12,930
+relation بنجيب نتكلم الناس أو بلاش المطارات في
+
+42
+00:03:12,930 --> 00:03:17,510
+العالم كل مطار و ال connected airport التاني اللي
+
+43
+00:03:17,510 --> 00:03:21,410
+ممكن يتواصل معاه عشان يوصل خط الطيارة تمام فدي
+
+44
+00:03:21,410 --> 00:03:25,610
+عبارة عن relation ما بين المطارات ال google map او
+
+45
+00:03:25,610 --> 00:03:29,350
+ال map اللي على الجوالهي عبارة عن relation بين الـ
+
+46
+00:03:29,350 --> 00:03:31,950
+two points والـ road اللي بينهم أو الـ route اللي
+
+47
+00:03:31,950 --> 00:03:34,630
+بينهم هو عبارة عن البث لل relation أنه فيه
+
+48
+00:03:34,630 --> 00:03:37,670
+connection أو فيه طريق ما بين ال city A و ال city
+
+49
+00:03:37,670 --> 00:03:41,530
+B وبالتالي ال implementation و التطبيقات تبعت ال
+
+50
+00:03:41,530 --> 00:03:45,170
+relation كبيرة و كبيرة جدا حتى لما بتكلم على مستوى
+
+51
+00:03:45,170 --> 00:03:50,050
+الشبكات كمان بتكلم على المجموعات groups و sets و
+
+52
+00:03:50,050 --> 00:03:54,730
+بتكلم على ال permissions الصلاحيات اللي ممنوحةلل
+
+53
+00:03:54,730 --> 00:03:57,750
+users اللي موجودين عندى و برضه بتكلم على relation
+
+54
+00:03:57,750 --> 00:04:04,710
+لان فى ال relation هنا شباب فى عندى مصطلح unary
+
+55
+00:04:04,710 --> 00:04:12,870
+ايش unary؟ احادي او binary ثنائي
+
+56
+00:04:12,870 --> 00:04:16,390
+.. ثنائي
+
+57
+00:04:16,390 --> 00:04:21,030
+.. ثنائي .. ثنائي .. ثنائي
+
+58
+00:04:21,030 --> 00:04:22,910
+.. ثنائي .. ثنائي .. ثنائي .. ثنائي .. ثنائي ..
+
+59
+00:04:24,480 --> 00:04:32,480
+طبعا اخر ان نلاحظ ان الانها دي هيك ايش ما اختلفت
+
+60
+00:04:32,480 --> 00:04:37,800
+الانهاش بتمثل عدد المجموعات اللي بيمتموه لل
+
+61
+00:04:37,800 --> 00:04:42,020
+relation لعدد المجموعات المشاركة في ال relation
+
+62
+00:04:42,020 --> 00:04:46,400
+يعني لو قلنا على سبيل المثال بدنا نشكل فريق برمجة
+
+63
+00:04:46,400 --> 00:04:52,410
+فريق برمجة من قلب يعني كل فريق لازم يكون في عضومن
+
+64
+00:04:52,410 --> 00:04:57,490
+قسم مختلف و حققوا الحد الأقصى للفريق أربعة، إيش
+
+65
+00:04:57,490 --> 00:05:00,370
+هنساوي؟ هنقول والله مثلا واحد من ال multimedia،
+
+66
+00:05:00,370 --> 00:05:02,210
+واحد من ال mobile computing، واحد software
+
+67
+00:05:02,210 --> 00:05:05,170
+development، واحد computer science، فريق التاني،
+
+68
+00:05:05,170 --> 00:05:08,730
+لاحظ أنا بتكلم على أربعة، أربع مجموعات مختلفة
+
+69
+00:05:08,730 --> 00:05:14,080
+شاركت في تشكيلالفريق طيب لو جل كل رجل في الفريق
+
+70
+00:05:14,080 --> 00:05:17,920
+يريد أن يأخذ منزلة الرئيس وناقب الرئيس وامين
+
+71
+00:05:17,920 --> 00:05:21,940
+الفريق مثلا وExecutor سامي زي ما بدك او Documenter
+
+72
+00:05:21,940 --> 00:05:28,200
+وبالتالي صار كل position له ترتيب مهم بالنسبة لنا
+
+73
+00:05:28,200 --> 00:05:33,260
+وهنا انا مابديش تفهم انه لما انا بتكلم على
+
+74
+00:05:33,260 --> 00:05:36,980
+relation معناته انا بتكلم على table زي ما قلنا و
+
+75
+00:05:36,980 --> 00:05:40,780
+ال table هذا بيسبق الرقم لما انا بتكلم
+
+76
+00:05:44,810 --> 00:05:49,730
+3 tuple معناته ان انا بتتكلم عن علاقة
+
+77
+00:05:49,730 --> 00:05:54,730
+ثلاثية بين 3 components موجودة عندى لما بتكلم على
+
+78
+00:05:54,730 --> 00:06:01,530
+ال 2 tuple حد اللى احنا بنعرف اسمها ordered pair
+
+79
+00:06:01,530 --> 00:06:07,810
+زوج مرتب a و b الزوج المرتب معناته الأقواص بتسميها
+
+80
+00:06:07,810 --> 00:06:12,500
+tuple و ال elements اللى موجودات فيه يسمواالـ
+
+81
+00:06:12,500 --> 00:06:15,860
+Elemental Fattable مش خضرياتنا كتير المعلومات كلها
+
+82
+00:06:15,860 --> 00:06:21,360
+هنتيجي تباعا ان شاء الله تعالى طيب الآن انا بتكلم
+
+83
+00:06:21,360 --> 00:06:24,820
+او في تركيزنا في ال chapter هذا على ال binary
+
+84
+00:06:24,820 --> 00:06:31,180
+relation تركيزنا الآن على ال binary relation ال
+
+85
+00:06:31,180 --> 00:06:34,700
+binary relation معناته ان في عندي two sets A و B
+
+86
+00:06:34,700 --> 00:06:39,800
+وبالتالي ال binary relation ما بين A و B هي عبارة
+
+87
+00:06:39,800 --> 00:06:48,560
+عن subset من الكارتيزياالبرودكت R تساوي الأزواج
+
+88
+00:06:48,560 --> 00:06:55,540
+المرتبة two double او binary او ordered pair بحيث
+
+89
+00:06:55,540 --> 00:07:02,420
+ان A تنتمي الى A وB تنتمي الى B تعرف البرودكت كله
+
+90
+00:07:02,420 --> 00:07:07,040
+ممكن تضيف اي condition لاحقا عشان تحدد هيش بشكل
+
+91
+00:07:07,040 --> 00:07:08,000
+اقل
+
+92
+00:07:11,120 --> 00:07:18,360
+ممكن ان اعرفها بشكل مختلف عن التعريف السابق بحيث
+
+93
+00:07:18,360 --> 00:07:21,800
+ان اقول ان ال relation تتعرف بالأزواج المرتبة A وB
+
+94
+00:07:21,800 --> 00:07:30,560
+بتنتمي الى R وهذا معناته A related to B اذا
+
+95
+00:07:30,560 --> 00:07:33,160
+انا اجيت كلامتي على الطالب و المثالق اللي بدرسه
+
+96
+00:07:33,160 --> 00:07:40,740
+هقول احمد study discrete mathematicsهاني بلايز
+
+97
+00:07:40,740 --> 00:07:45,920
+فوتبول على انه ال favorite sport لو اجينا نتكلم عن
+
+98
+00:07:45,920 --> 00:07:50,960
+الفاكهة اللي بتحبها ايش اسمك؟ محمد محمد likes
+
+99
+00:07:50,960 --> 00:07:55,600
+strawberry فراولة جزء خاص من ال relation جزء خاص
+
+100
+00:07:55,600 --> 00:07:58,760
+من ال relation او من ال Cartesian product لو عناصر
+
+101
+00:07:58,760 --> 00:08:05,260
+ال a في نفسها يعني a cross ال a يعني ممكن انا احقق
+
+102
+00:08:05,260 --> 00:08:11,090
+relation من خلالA cross الـ A كارتيزان ال product
+
+103
+00:08:11,090 --> 00:08:14,310
+بين الـ A و نفسها هالكلام صحيح بيصير؟ أه بيصير
+
+104
+00:08:14,310 --> 00:08:18,170
+تخيل لو أنا جيتها و قلتلك هي ال A equal واحد و
+
+105
+00:08:18,170 --> 00:08:25,210
+اتنين و تلاتة و ال relation تبعتنا بدها تساوي A و
+
+106
+00:08:25,210 --> 00:08:28,870
+B حيث ال B أكبر من ال A
+
+107
+00:08:34,960 --> 00:08:41,800
+مفهوم الـ Head relation كل الأزواج المرتبة اللي
+
+108
+00:08:41,800 --> 00:08:46,080
+في الـ Cartesian product في الـA وA بحيث أن الـB
+
+109
+00:08:46,080 --> 00:08:58,240
+تكون أكبر من الـA 1 و 2 1 و 3 2 و 3 Head
+
+110
+00:08:58,240 --> 00:09:03,320
+relation Cartesian
+
+111
+00:09:03,320 --> 00:09:07,750
+product هو السقف تبعكعندك مجموعتين عدد العناصر في
+
+112
+00:09:07,750 --> 00:09:12,430
+الأولى أربعة وفي الثانية خمسة أكبر relation ممكن
+
+113
+00:09:12,430 --> 00:09:16,950
+تتشكل جدش حد يومها أربعة في خمسة عشرين element
+
+114
+00:09:16,950 --> 00:09:20,890
+أربعة في خمسة ليش نجس عشرين element الآن أنا عندي
+
+115
+00:09:20,890 --> 00:09:25,250
+هان بقولك A في A تمام؟ وال relation هي subset من
+
+116
+00:09:25,250 --> 00:09:30,490
+من ال A subset احنا متفقين وبالتالي كحد أقصى هان
+
+117
+00:09:30,490 --> 00:09:35,490
+ممكن تكون تسع عناصر لكن لما أنا بروح بقيدهامن خلال
+
+118
+00:09:35,490 --> 00:09:38,930
+الـ definition معناته انا صرت انا بحدد عدد عناصر
+
+119
+00:09:38,930 --> 00:09:42,590
+مختلف لاحظوا يا شباب انه مازلت في ال relation
+
+120
+00:09:42,590 --> 00:09:46,250
+بتتكلم على المجموعات ولا لا مابعدتش لحتى اللحظة عن
+
+121
+00:09:46,250 --> 00:09:50,870
+المجموعات مطلقا هذا
+
+122
+00:09:50,870 --> 00:09:54,250
+المثال اللي قلناه مجموعة الطلاب ال a بتمثل مجموعة
+
+123
+00:09:54,250 --> 00:10:00,270
+الطلاب و ال b بتمثل مجموعة ال courses معناته احنا
+
+124
+00:10:00,270 --> 00:10:05,810
+بنتكلم نقدر نتكلم نقول زوج المرتب a و bهي العلاقة
+
+125
+00:10:05,810 --> 00:10:10,870
+ما بين A تمثل طالب و B تمثل مساق و بالتالي student
+
+126
+00:10:10,870 --> 00:10:18,850
+A taking course او studying course B طبعا
+
+127
+00:10:18,850 --> 00:10:22,550
+ال definition ممكن تكتب صورة تانية محمد و الفراولة
+
+128
+00:10:22,550 --> 00:10:30,110
+هيهم X likes Y الان A set of people و ال R
+
+129
+00:10:30,110 --> 00:10:35,860
+describes who likes fruitيعني ال Y بتمثل مين؟
+
+130
+00:10:35,860 --> 00:10:40,440
+الفروت و بالتالي X like Y هي ال relation اللي
+
+131
+00:10:40,440 --> 00:10:43,520
+موجودة عندنا هنا الان ممكن ال relation برضه تنكتب
+
+132
+00:10:43,520 --> 00:10:48,080
+او تتعرف بشكل مختلف تماما لما انا عاش اقولك لت ال
+
+133
+00:10:48,080 --> 00:10:54,540
+A تساوي ال natural number و جيت قلت ال relation
+
+134
+00:10:54,540 --> 00:11:00,400
+تبعتي قلنا نقراها X related Y X related Y لاحظ هو
+
+135
+00:11:00,400 --> 00:11:04,270
+تكلم فقطعلى مجموعة واحدة زي ما في المثال هذا
+
+136
+00:11:04,270 --> 00:11:09,290
+مباشرة بادر لذهنك cross product between a في a
+
+137
+00:11:09,290 --> 00:11:12,830
+cross product between a في a و هاد ال relation
+
+138
+00:11:12,830 --> 00:11:16,010
+هتكون subset منها ال subset منها كيف أعرف ال
+
+139
+00:11:16,010 --> 00:11:22,630
+definition x أقل أو تساوي ال y زي المثال تقريبا
+
+140
+00:11:22,630 --> 00:11:29,850
+هذا اللي أنا كتبنا الان
+
+141
+00:11:29,850 --> 00:11:33,360
+بما أن ال relationبما أن ال relation هي عبارة عن
+
+142
+00:11:33,360 --> 00:11:37,920
+مجموعة، بما يعني بقدر أطبق عليها كل العمليات
+
+143
+00:11:37,920 --> 00:11:47,080
+الخاصة بالمجموعات اللي هما التقابق،
+
+144
+00:11:47,080 --> 00:11:53,160
+الاتحاد، ال difference و ال .. ال .. خلصولها؟ ما
+
+145
+00:11:53,160 --> 00:11:55,720
+تخلصوش، ده في واحدة .. ايوة الشرط يا أحمد، إيش
+
+146
+00:11:55,720 --> 00:12:02,770
+اسمها يا دي؟ المتممة .. المتممةأيوة الآن معناته
+
+147
+00:12:02,770 --> 00:12:06,230
+أنا فعليا بتكلم لأنه كمان مرة ما تنساش أنا بتكلم
+
+148
+00:12:06,230 --> 00:12:10,030
+مازال كايم من ال definition set builder notation
+
+149
+00:12:10,030 --> 00:12:13,950
+أنا بتكلم على مجموعة وبالتالي بطبق العمليات بتاعة
+
+150
+00:12:13,950 --> 00:12:18,250
+المجموعات على كل العناصر اللي في ال relation اللي
+
+151
+00:12:18,250 --> 00:12:25,170
+موجودة عندي اتحاد تقاقع difference والمتممة بدي
+
+152
+00:12:25,170 --> 00:12:31,490
+أسأل سؤال في المثال السابقعلى هذا احنا قولنا الان
+
+153
+00:12:31,490 --> 00:12:40,290
+R بدها تساوي ازواد المرتبة X و Y حيث X اصغر او
+
+154
+00:12:40,290 --> 00:12:48,090
+تساوي ال Y طبعا and X و Y تنتمي ل natural number
+
+155
+00:12:48,090 --> 00:12:53,370
+مش قضية كتير هذا بالنسبة لنا طيب الآن هات للمتمن
+
+156
+00:12:53,370 --> 00:12:58,170
+ما تبعتها ايش المتمن من ال compliment
+
+157
+00:13:04,420 --> 00:13:11,480
+دى المتممة R شرط H ساوى X
+
+158
+00:13:11,480 --> 00:13:21,980
+وY X أكبر بدون ما يتساوي لأنه أنا بدى العناصر اللى
+
+159
+00:13:21,980 --> 00:13:25,760
+فى المتممة من المتممة من ال university اللى هى N
+
+160
+00:13:25,760 --> 00:13:29,700
+في N ال university تبعتنا ل N في N أنا هدولة منهم
+
+161
+00:13:29,700 --> 00:13:35,160
+سبست فبدى الباقى جهيهملأ والله انكم تدرسوا يا شباب
+
+162
+00:13:35,160 --> 00:13:41,320
+عشان الحل هنتكلم الآن في خصائص ال relation هنتكلم
+
+163
+00:13:41,320 --> 00:13:48,980
+في خصائص ال relation اول خاصية reflexive طيب قبل
+
+164
+00:13:48,980 --> 00:13:53,160
+ما نتكلم عن ال reflexive لما انا يا شباب بتكلم a
+
+165
+00:13:53,160 --> 00:13:58,860
+في a يعني لو كانت عدد عناصر ال a اتنين لما بتكلم
+
+166
+00:13:58,860 --> 00:14:02,570
+اتنين في اتنين لو كانت تلاتةتلاتة في تلاتة هو عدد
+
+167
+00:14:02,570 --> 00:14:07,230
+العراسة فصوته ل .. و كإني بتكلم على square matrix
+
+168
+00:14:07,230 --> 00:14:12,730
+لو أنت تيجي تصفقهم أو ترتبهم واحد و اتنين واحد و
+
+169
+00:14:12,730 --> 00:14:17,990
+تلاتة او عفوا واحد و واحد و واحد و اتنين واحد و
+
+170
+00:14:17,990 --> 00:14:24,850
+تلاتة بعد هيك اتنين و واحد اتنين و اتنين اتنين و
+
+171
+00:14:24,850 --> 00:14:31,280
+تلاتة بعدها تلاتة و واحد تلاتة و اتنينتلاتة و
+
+172
+00:14:31,280 --> 00:14:35,900
+تلاتة و كأنني بتكلم على square matrix تلاتة في
+
+173
+00:14:35,900 --> 00:14:38,560
+تلاتة صح اسمها مربعة
+
+174
+00:14:43,560 --> 00:14:47,580
+المصفوفة طبعا وكأنني قاعد بقولك هذه تمثل I و
+
+175
+00:14:47,580 --> 00:14:53,340
+التاني تمثل ال J الصف و العمود الان لما بتكلم على
+
+176
+00:14:53,340 --> 00:14:57,260
+ال relation هذه reflexive بدي اتكلم العلاصر اللي
+
+177
+00:14:57,260 --> 00:15:03,720
+في النص هذه لازم تكون موجودة اللي هي تمثل AII AII
+
+178
+00:15:03,720 --> 00:15:07,740
+او AIJ و I تساوي الجي بين جثين لما انا بدي اقول ان
+
+179
+00:15:07,740 --> 00:15:13,790
+ال relation هذه reflexive لكل علاصر ال Aكل عنصر في
+
+180
+00:15:13,790 --> 00:15:17,870
+الـA، كم عنصر في الـA؟ تلاتة تدور على تلات أزواج
+
+181
+00:15:17,870 --> 00:15:23,030
+مرتبة اللي هم واحد و واحد صورتهم ايه و ايه واحد و
+
+182
+00:15:23,030 --> 00:15:27,470
+واحد اتنين و اتنين تلاتة و تلاتة لو كانت الأزواج
+
+183
+00:15:27,470 --> 00:15:30,710
+المرتبة هذه موجودة في ال relation بنقول عن ال
+
+184
+00:15:30,710 --> 00:15:36,190
+relation reflexive يعني خط للعكاس هذا موجود exist
+
+185
+00:15:36,190 --> 00:15:39,490
+دي البيانات اللي موجودة فيه أو العناصر اللي فيه
+
+186
+00:15:39,490 --> 00:15:44,870
+صحيحةالان بدي اسألك ال relation هذي اللي انا
+
+187
+00:15:44,870 --> 00:15:53,970
+كاتبها هنا R هل R reflexive؟ هى ال R الان مش ممكن
+
+188
+00:15:53,970 --> 00:15:59,550
+تساوي بدك تروح على عناصر ال A كمان مرةبداك تدور
+
+189
+00:15:59,550 --> 00:16:03,090
+على تلت أزواج مرتبة بالتحديد لو كانت ال a فيها
+
+190
+00:16:03,090 --> 00:16:06,530
+أربع عناصر معناه أنك تدور عليها أربعة فيها n بدك
+
+191
+00:16:06,530 --> 00:16:09,970
+تدور علي ال n لو واحد من ال n اللي بدنا ندور عليه
+
+192
+00:16:09,970 --> 00:16:14,450
+هو مش موجود معناته not reflexive بتنتهي الصفة الآن
+
+193
+00:16:14,450 --> 00:16:19,850
+واحد واحد هل واحد واحد موجود؟ لأ معناته R is not
+
+194
+00:16:19,850 --> 00:16:21,310
+reflexive
+
+195
+00:16:25,280 --> 00:16:28,680
+أو غير رفليكسيف. لماذا؟ لأن واحد و واحد ليس موجود،
+
+196
+00:16:28,680 --> 00:16:33,420
+فالباقي ماتدورش، خلاص انسى الموضوع، وإما أول واحد
+
+197
+00:16:33,420 --> 00:16:39,660
+مابتلاقيهوش، تكملش بحث. طيب، تخيل في الشرق هذا أو
+
+198
+00:16:39,660 --> 00:16:44,320
+في هذا الـfunction، روحت سميتلك function تانية أو
+
+199
+00:16:44,320 --> 00:16:47,420
+.. okay مش قضية .. function تانية و روحت بحيث أني
+
+200
+00:16:47,420 --> 00:16:50,140
+قلتلك أن الـR أكبر أو تساوي
+
+201
+00:16:53,780 --> 00:17:00,280
+قلت لك R أكبر او تساوي هتسيب
+
+202
+00:17:00,280 --> 00:17:05,200
+.. الآن إيش لك تساوي؟ بدك تروح تدور واحد و واحد
+
+203
+00:17:05,200 --> 00:17:09,100
+وحق الشرط .. معناه تبين Terminal relation اتنين و
+
+204
+00:17:09,100 --> 00:17:12,180
+اتنين شوف كمان مرة انا أعمالي بجرب معاك بدون ما
+
+205
+00:17:12,180 --> 00:17:16,180
+اكتب العلاصر جدامي اتنين و اتنين .. اتنين أكبر أو
+
+206
+00:17:16,180 --> 00:17:20,220
+تساوي اتنين؟true تلاتة أكبر أو تساوي تلاتة true
+
+207
+00:17:20,220 --> 00:17:23,840
+معناته واحد و واحد و اتنين و اتنين و تلاتة و تلاتة
+
+208
+00:17:23,840 --> 00:17:34,000
+بينتبهوا لل relation معناته R is reflexive تمام؟
+
+209
+00:17:34,000 --> 00:17:37,040
+و
+
+210
+00:17:37,040 --> 00:17:44,580
+اما تلاقي فيه تساوي تمام؟ و اما تلاقي فيه تساوي
+
+211
+00:17:44,580 --> 00:17:49,650
+معناته في عندك reflexiveطبعا في حالة الأقل أو
+
+212
+00:17:49,650 --> 00:17:54,370
+الأكبر زي ما جربت ده انسى الموضوع مش هتحققش خاصية
+
+213
+00:17:54,370 --> 00:17:58,490
+تانية symmetric طب مهمش انا بدي ارجع مرة تانية
+
+214
+00:17:58,490 --> 00:18:02,130
+شباب لل definition او خليها ده مش قضية كتير
+
+215
+00:18:02,130 --> 00:18:05,950
+symmetric
+
+216
+00:18:05,950 --> 00:18:10,010
+الصفات اللي انا بقولها منفصلة عن بعضها symmetric
+
+217
+00:18:10,010 --> 00:18:17,870
+يعني متماثلة اقولها في المصفوفة المتماثلةAij
+
+218
+00:18:17,870 --> 00:18:23,650
+بيتساوي AJI وإذا بتتذكر لما اتكلمنا يا رامي يا
+
+219
+00:18:23,650 --> 00:18:30,130
+بعاصي على مصفوفة تلاتة في تلاتة الآن قلنا عن أسر
+
+220
+00:18:30,130 --> 00:18:33,810
+القطر الرئيسي هيها مالاش داخل فيها ولا لأ لإن
+
+221
+00:18:33,810 --> 00:18:41,010
+already A11 A22 A33 هي نفسها لو بدّلنا ال I و ال J
+
+222
+00:18:41,010 --> 00:18:45,810
+مظلوك ولا لأ طيب الآن بتكلم على هذاوبتكلم على هذا
+
+223
+00:18:45,810 --> 00:18:50,110
+متقابقة
+
+224
+00:18:50,110 --> 00:18:58,810
+أو متماثلة متناظرة محلاكم أنتم بالترجمة العربى صح
+
+225
+00:18:58,810 --> 00:19:04,390
+تمام؟ الآن مفهوم التقابق أو التناظر أن هذا ال
+
+226
+00:19:04,390 --> 00:19:06,950
+element هو هذا هذا جدش ال element .. هذا واحد
+
+227
+00:19:06,950 --> 00:19:12,590
+اتنين تلاتة هنا واحد اتنين تلاتة مصبوط؟ هذا جدش
+
+228
+00:19:12,590 --> 00:19:18,800
+رقم ال element هذا عفواهذا a12 الصف الأول العمودي
+
+229
+00:19:18,800 --> 00:19:29,020
+التاني يساوي a21 هذا a13 يساوي a31 وهكذا هكذا منها
+
+230
+00:19:29,020 --> 00:19:33,560
+حيش متماثلة symmetric سميناها المصفوفة symmetric
+
+231
+00:19:33,560 --> 00:19:38,240
+matrix الآن هذا الكلام بدي أسقطه على ال relation
+
+232
+00:19:39,340 --> 00:19:42,540
+لاحظوا العلاقة جديش؟ علاقة بال relation علاقة
+
+233
+00:19:42,540 --> 00:19:45,320
+بالمصفوفات فانا روحت جيبته من .. عشان ايه؟ روحت
+
+234
+00:19:45,320 --> 00:19:48,940
+جيبته من chapter 9؟ و حققته وين؟ في ال chapter ..
+
+235
+00:19:48,940 --> 00:19:52,980
+قبل ما تنسى لإن انا عارف انه اللي بندرس عشان ننساه
+
+236
+00:19:52,980 --> 00:19:56,220
+احنا الان تعالى ال relation في ال relation بنقول
+
+237
+00:19:56,220 --> 00:20:04,040
+إذا لكل زوج مرتب for all a و b تنتمي لل relation
+
+238
+00:20:04,040 --> 00:20:13,970
+for all aوB تنتمي للـ relation هذا بيؤدي ان بي و A
+
+239
+00:20:13,970 --> 00:20:17,590
+تنتمي لل relation بقول عن ال relation عندي هال
+
+240
+00:20:17,590 --> 00:20:22,110
+Symmetric بقول عن ال relation عندي هال Symmetric
+
+241
+00:20:22,110 --> 00:20:27,470
+ال relation هادي هل هي Symmetric؟ هل ال relation
+
+242
+00:20:27,470 --> 00:20:32,270
+هادي Symmetric؟ طيب الآن هل هي Symmetric؟ لأ تعالى
+
+243
+00:20:32,270 --> 00:20:37,610
+نشوف واحد من الأمثلةأقول لك واحد و واحد ا أكبر أو
+
+244
+00:20:37,610 --> 00:20:45,470
+تساوي ايه بصبوط صورتها واحد و واحد صح لكن الآن
+
+245
+00:20:45,470 --> 00:20:50,750
+اتنين و واحد تحقق ال relation اتنين و واحد تنتمي
+
+246
+00:20:50,750 --> 00:20:56,310
+إلى ال R لكن but
+
+247
+00:20:56,310 --> 00:21:01,180
+الواحد والتاني اللي هي صورتهاأو انعكاس التي
+
+248
+00:21:01,180 --> 00:21:05,160
+تماثلها لا تنتمي للـ relation معناته الـR is not
+
+249
+00:21:05,160 --> 00:21:15,780
+symmetric R is not symmetric تمام؟
+
+250
+00:21:15,780 --> 00:21:19,740
+الـ definition بسيط وسهل بدأت نرى على ال relation
+
+251
+00:21:19,740 --> 00:21:24,800
+على كل العناصر اللي فيها كل عنصر فيه صورته أو
+
+252
+00:21:24,800 --> 00:21:29,850
+انعكاسه موجودتمام؟ A و B بلاجئله بي و ايه؟ معناته
+
+253
+00:21:29,850 --> 00:21:33,690
+ال relation اللي عندي هان Symmetric تعالى نشوف
+
+254
+00:21:33,690 --> 00:21:40,950
+المثال هذا افترض على نفس ال A ها دي R تساوي واحد و
+
+255
+00:21:40,950 --> 00:21:49,150
+اتنين اتنين و واحد بس
+
+256
+00:21:49,150 --> 00:21:52,090
+هي relation مش هي subset من ال Cartesian product
+
+257
+00:21:52,090 --> 00:21:59,350
+صح relation relationBinary relation هل هي
+
+258
+00:21:59,350 --> 00:22:06,090
+Symmetric؟ هل هي Symmetric؟ يا راجل تجلى هل هي
+
+259
+00:22:06,090 --> 00:22:10,650
+Symmetric؟ خد كل element هي ال element الأول واحد
+
+260
+00:22:10,650 --> 00:22:15,550
+و اتنين بينتمي لل relation ايش انعكاسه؟ اتنين و
+
+261
+00:22:15,550 --> 00:22:19,350
+واحد تنتمي لل relation؟ تنتمي لل relation العنصر
+
+262
+00:22:19,350 --> 00:22:23,430
+التاني اتنين و واحد بينتمي لل relation انعكاسه؟
+
+263
+00:22:24,080 --> 00:22:27,640
+واحد واثنين تنتمي للـ relation معناته ال relation
+
+264
+00:22:27,640 --> 00:22:34,480
+هذي symmetric ماتفتش ماتفتش
+
+265
+00:22:34,480 --> 00:22:39,600
+انا قولت كلمة سهلة وبسيطة ال properties هذي انفككت
+
+266
+00:22:39,600 --> 00:22:44,680
+عن بعض not related together انا
+
+267
+00:22:44,680 --> 00:22:50,480
+بسألك symmetric تقولي reflexive اليوم
+
+268
+00:22:50,480 --> 00:22:55,300
+اليوش اليوممن برا حاجات مجلوبة، مش صح الجواب يا
+
+269
+00:22:55,300 --> 00:23:02,120
+صاحبي، مش logic بالمرة هو أنا
+
+270
+00:23:02,120 --> 00:23:05,380
+باسألك في الـsymmetric ال condition مختلف تماما،
+
+271
+00:23:05,380 --> 00:23:09,860
+الان not symmetric، symmetric، symmetric،
+
+272
+00:23:09,860 --> 00:23:15,200
+reflexive، reflexive، not reflexive، لو أنا سألتك
+
+273
+00:23:15,200 --> 00:23:19,160
+reflexive، not reflexive، ايه و ايه مش لإن تمي،
+
+274
+00:23:19,160 --> 00:23:21,900
+واحد و واحد مش موجود خلصنا، ماتدوري، ماتكملش
+
+275
+00:23:28,850 --> 00:23:36,370
+الان في عندي تعريف جديد اسمه Anti-symmetric و من
+
+276
+00:23:36,370 --> 00:23:44,050
+الان انتبه معايا Anti-symmetric لا
+
+277
+00:23:44,050 --> 00:23:51,130
+تساوي كل
+
+278
+00:23:51,130 --> 00:23:54,290
+هدول different definitions different properties
+
+279
+00:23:57,110 --> 00:24:02,810
+لكن بنقدر نقول لو كانت symmetric مش هتكون Anti
+
+280
+00:24:02,810 --> 00:24:06,030
+-symmetric و لو كانت Anti-symmetric مش هتكون
+
+281
+00:24:06,030 --> 00:24:09,410
+symmetric بس ممكن تكون ال relation لا symmetric
+
+282
+00:24:09,410 --> 00:24:17,990
+ولا Anti-symmetric تمام؟ و ولا reflexive كمان الآن
+
+283
+00:24:17,990 --> 00:24:25,070
+إيش اللي بنقوله بكل بساطة؟ بنقول كتالةلو نجينا أو
+
+284
+00:24:25,070 --> 00:24:29,630
+أخدنا كل الأزواج المرتبة اللي في ال relation كل
+
+285
+00:24:29,630 --> 00:24:34,310
+الأزواج المرتبة اللي في ال relation تمام؟ مش
+
+286
+00:24:34,310 --> 00:24:38,210
+هالنجيل و انعكاس إلا الزوج المرتب اللي فيه الـA
+
+287
+00:24:38,210 --> 00:24:43,890
+تساوي بيه ليش؟ لأن انعكس هو نفسه يعني بكتب
+
+288
+00:24:43,890 --> 00:24:47,550
+بينجوسين، بينجوسين العناصر المتماثلة في الأزواج
+
+289
+00:24:47,550 --> 00:24:51,730
+المرتبة حاول اسقطها من فحصك الـsymmetric و
+
+290
+00:24:51,730 --> 00:24:57,250
+الـantisymmetricالان لو انا اجيب و قلتلك ال R هذي
+
+291
+00:24:57,250 --> 00:25:07,550
+واحد و واحد اتنين و واحد و واحد و اتنين مرتبط؟
+
+292
+00:25:07,550 --> 00:25:15,730
+مرتبط ليش لأ؟ مرتبط هذا ايش انعكاسه؟ نفسه و هذا
+
+293
+00:25:15,730 --> 00:25:20,950
+انعكاس نفسه بقد لها هذا و هذا بدلها مظبوط؟ و
+
+294
+00:25:20,950 --> 00:25:25,080
+بالتالي مرتبطالان هل هي Anti-Symmetric لأ نقطة
+
+295
+00:25:25,080 --> 00:25:28,760
+Anti-Symmetric خلصنا لأن فيها أزواج مرتبة غير
+
+296
+00:25:28,760 --> 00:25:33,740
+الواحد وواحد فيها إيش انعكاس لكن تعالى شوف هذه
+
+297
+00:25:33,740 --> 00:25:44,100
+Symmetric
+
+298
+00:25:44,100 --> 00:25:50,410
+لأ Anti-Symmetric true Anti-SymmetricAnti
+
+299
+00:25:50,410 --> 00:25:53,790
+-Symmetric التعريف تبقى الـ Anti-Symmetric فيقول
+
+300
+00:25:53,790 --> 00:25:59,090
+كالتالي كل الأزواج المرتبة لعناصرها مختلفة ليس لها
+
+301
+00:25:59,090 --> 00:26:05,670
+صور كل العناصر أو كل الأزواج المرتبة لعناصرها
+
+302
+00:26:05,670 --> 00:26:10,930
+مختلفة ليس لها صور خلصنا هذا خبّيني اللي هي أنا
+
+303
+00:26:10,930 --> 00:26:17,510
+صورته نفسي هذا فيه صورة؟ لأ معناته Anti-Symmetric
+
+304
+00:26:21,170 --> 00:26:25,550
+شوف ال relation هاي احباز السنة شوية هاي R تساوي
+
+305
+00:26:25,550 --> 00:26:34,130
+واحد و واحد واحد و اتنين اتنين
+
+306
+00:26:34,130 --> 00:26:40,850
+و واحد واحد و تلاتة symmetric؟
+
+307
+00:26:40,850 --> 00:26:49,570
+symmetric؟ لأ لحظة شوية not symmetric ليش؟
+
+308
+00:26:50,300 --> 00:26:57,260
+ليش؟ لأن واحد و تلاتة تنتمي لل relation but تلاتة
+
+309
+00:26:57,260 --> 00:27:01,600
+و واحد لا تنتمي لل relation بالمناسبة لما بدك تنفي
+
+310
+00:27:01,600 --> 00:27:05,420
+بدك تقوللي ليش .. لما بدك تنفي هبقى هتقوللي ليش
+
+311
+00:27:05,420 --> 00:27:12,500
+..طيب .. antisymmetric؟ لأ not antisymmetric
+
+312
+00:27:17,400 --> 00:27:22,160
+ليش not antisymmetric؟ لأن الواحد واتنين تنتمي لل
+
+313
+00:27:22,160 --> 00:27:28,860
+relation and
+
+314
+00:27:28,860 --> 00:27:32,600
+الواحد لا تساوي الاتنين
+
+315
+00:27:34,540 --> 00:27:39,420
+والواحد لا تساوي التيرين الجزئية الأخيرة هذه لو
+
+316
+00:27:39,420 --> 00:27:43,460
+أنت قررتلي إياها وما كتبتاش okay ليش؟ عشان احنا
+
+317
+00:27:43,460 --> 00:27:46,340
+قولنا من البداية الأزواج المرتبة اللي فيها العنصر
+
+318
+00:27:46,340 --> 00:27:50,700
+متشابه بدي أسقطها من عملية الفحص يعني هي بين جسدين
+
+319
+00:27:50,700 --> 00:27:54,480
+لهي مأثرة معاك في الـsymmetric ولا مأثرة معاك في
+
+320
+00:27:54,480 --> 00:27:55,260
+الـantisymmetric
+
+321
+00:28:02,930 --> 00:28:05,770
+هذه مجموعة من الأمثلة زى اللى شوفناها قبل شوية
+
+322
+00:28:05,770 --> 00:28:13,290
+symmetric و Anti-symmetric و لاهاي و لاهاي طيب فى
+
+323
+00:28:13,290 --> 00:28:21,430
+عندك خاصية الرابعة Transitive خاصية التعدى مفهومها
+
+324
+00:28:21,430 --> 00:28:31,490
+for any for all a و b and b و c تنتمي لل relation
+
+325
+00:28:32,690 --> 00:28:36,830
+ماذا يعني انتبه معايا؟ ماذا يعني؟ لازم يكون عندك
+
+326
+00:28:36,830 --> 00:28:42,630
+زوجين مرتبين زوجين مرتبات مختلفين نهاية الأول
+
+327
+00:28:42,630 --> 00:28:49,090
+تساوي بداية الثاني إذا وجد أي زوجين مرتبين بالشكل
+
+328
+00:28:49,090 --> 00:28:54,870
+هذا و لاجئت أن a و c اللي هي بداية الأول و نهاية
+
+329
+00:28:54,870 --> 00:28:57,650
+التانية بتنتمي لل relation معناته اللي بقول عنها
+
+330
+00:28:57,650 --> 00:29:01,550
+متعددة يعني بين بصين الأربعة
+
+331
+00:29:03,270 --> 00:29:08,910
+بتقبل الجسم على اتنين صح؟ التمانية بتقبل الجسم على
+
+332
+00:29:08,910 --> 00:29:15,010
+اربعة فالتمانية بتقبل الجسم على اتنين فعملية القسم
+
+333
+00:29:15,010 --> 00:29:17,550
+اللي انا ممكن اسميها transitive و لا لا ضمن ال
+
+334
+00:29:17,550 --> 00:29:22,890
+condition اللي موجود عندي وين
+
+335
+00:29:22,890 --> 00:29:27,630
+ما بتشوف يساوي اقل من او اكبر من او subset يعني
+
+336
+00:29:27,630 --> 00:29:30,270
+اننا بنتكلم على transitive بتكون ال relation اللي
+
+337
+00:29:30,270 --> 00:29:34,720
+عندنا transitive ال relation هذهtransitive او
+
+338
+00:29:34,720 --> 00:29:41,040
+transitive تعالى شوف بشكل عام transitive او
+
+339
+00:29:41,040 --> 00:29:45,740
+transitive او transitive او transitive او
+
+340
+00:29:45,740 --> 00:29:51,020
+transitive او transitive
+
+341
+00:29:51,020 --> 00:29:52,120
+او transitive او transitive او transitive او
+
+342
+00:29:52,120 --> 00:29:52,160
+transitive او transitive او transitive او
+
+343
+00:29:52,160 --> 00:29:52,160
+transitive او transitive او transitive او
+
+344
+00:29:52,160 --> 00:29:52,360
+transitive او transitive او transitive او
+
+345
+00:29:52,360 --> 00:29:52,380
+transitive او transitive او transitive او
+
+346
+00:29:52,380 --> 00:29:52,980
+transitive او transitive او transitive او
+
+347
+00:29:52,980 --> 00:29:54,520
+transitive او transitive او transitive او
+
+348
+00:29:54,520 --> 00:29:56,260
+transitive او transitive او transitive او
+
+349
+00:29:56,260 --> 00:30:04,810
+transitive او transitiveالـ C and الـ C أكبر أو
+
+350
+00:30:04,810 --> 00:30:08,790
+تساوي الـ B الرتب الموضوع المثل هذا يعني أن الـ C
+
+351
+00:30:08,790 --> 00:30:15,350
+أكبر أو تساوي الـ B أكبر أو تساوي الـ A وبالتالي
+
+352
+00:30:15,350 --> 00:30:20,450
+الـ C أكبر أو تساوي الـ A وبالتالي أصبح الـ A و
+
+353
+00:30:20,450 --> 00:30:24,890
+الـ C ينتمي لل relation فأصبحت ال relation هذه
+
+354
+00:30:24,890 --> 00:30:28,810
+transitive أصبحت ال relation transitive واضح يا
+
+355
+00:30:28,810 --> 00:30:29,150
+شباب؟
+
+356
+00:30:31,900 --> 00:30:36,620
+طيب .. ما زال هوضح .. تعالوا نشوف .. انتوا لا جداش
+
+357
+00:30:36,620 --> 00:30:40,960
+فاهمين من الكلام اللي بنقوله .. انطبق الأربع خصائص
+
+358
+00:30:40,960 --> 00:30:48,940
+.. اتذكر كمان مرة .. كمان مرة .. Reflexive .. A و
+
+359
+00:30:48,940 --> 00:30:52,260
+A تنتمي لل relation .. لكل عناصر A .. لكل عناصر
+
+360
+00:30:52,260 --> 00:30:56,300
+مجموعة A .. Symmetric .. كل زوج مرتب A و B في ال
+
+361
+00:30:56,300 --> 00:30:59,340
+relation .. B و A لازم يكون موجود في ال relation
+
+362
+00:30:59,340 --> 00:31:05,100
+عشان تكون Symmetric ..Antisymmetric كل زوج مرتب A
+
+363
+00:31:05,100 --> 00:31:10,000
+و B في ال relation B و A لا ينتمي لل relation لـ
+
+364
+00:31:10,000 --> 00:31:15,420
+Transitive لكل زوجين A و B و B و C A و C لازم يكون
+
+365
+00:31:15,420 --> 00:31:19,840
+ينتمي في ال relation بيقول عنها Transitive بقولك
+
+366
+00:31:19,840 --> 00:31:25,560
+هي ال A الان
+
+367
+00:31:25,560 --> 00:31:30,600
+بقول R1 نتكلم على R1
+
+368
+00:31:34,700 --> 00:31:38,060
+R1 مش عارف اتلاقى محلة على اللوحة عشان نبقى ضمن ال
+
+369
+00:31:38,060 --> 00:31:42,160
+slides ومانبعدش كتير ومانجلمش أبو حسن معانا الان
+
+370
+00:31:42,160 --> 00:31:50,760
+R1 reflexive كيف بتحكم عليها reflexive؟ بدك تروح
+
+371
+00:31:50,760 --> 00:31:55,780
+على عناصر ال A كم عنصر في ال A؟ 1,2,3,4 بدك تدور
+
+372
+00:31:55,780 --> 00:32:04,510
+على 4 أزواج مرتبة 1 و 1 2 و 2 3 و 3الان 1 و 1
+
+373
+00:32:04,510 --> 00:32:08,390
+موجود اتنين و اتنين موجود تلاتة و تلاتة مش موجود
+
+374
+00:32:08,390 --> 00:32:14,690
+بقول is not reflexive لان تلاتة و تلاتة لا تنتمي ل
+
+375
+00:32:14,690 --> 00:32:24,990
+R1 طيب symmetric؟ طيب تعالى نشوف symmetric
+
+376
+00:32:24,990 --> 00:32:29,310
+هل هي symmetric؟ بدك تبدأ تفحص سيبك من الأزواج
+
+377
+00:32:29,310 --> 00:32:34,990
+المرتبة اللي قلهم متشادهاتواحد و اتنين صورتها ..
+
+378
+00:32:34,990 --> 00:32:38,390
+اتنين و واحد هي موجودة .. اتنين و واحد صورتها هي
+
+379
+00:32:38,390 --> 00:32:41,870
+.. خلاصنا .. تلاتة و أربعة .. الأصل يكون أربعة و
+
+380
+00:32:41,870 --> 00:32:46,110
+تلاتة .. معناته not symmetric .. not symmetric ..
+
+381
+00:32:46,110 --> 00:32:52,410
+و ليش؟ لأن تقول تلاتة و أربعة تنتمي لل relation ..
+
+382
+00:32:52,410 --> 00:32:58,290
+but أربعة و تلاتة لا تنتمي لل relation ..
+
+383
+00:33:04,640 --> 00:33:09,440
+Antisymmetric برضه لأ لإيش لأن عندي واحد و اتنين
+
+384
+00:33:09,440 --> 00:33:15,580
+تنتمي لل relation and اتنين و واحد تنتمي لل
+
+385
+00:33:15,580 --> 00:33:20,520
+relation ر واحد معناته هي not reflexive, not
+
+386
+00:33:20,520 --> 00:33:26,250
+symmetric, not antisymmetric, transitiveلاتش اسمها
+
+387
+00:33:26,250 --> 00:33:29,750
+دي، أيوة هي بالظبط.طيب في الـtransitive تعالى تشوف
+
+388
+00:33:29,750 --> 00:33:34,890
+شوية اشتغل معاها صح عشان ما تفوتش ولا عوصل لإن لو
+
+389
+00:33:34,890 --> 00:33:40,090
+فوتت element واحد منهم ممكن تغلط.إيش تساوي؟ امشي
+
+390
+00:33:40,090 --> 00:33:45,030
+معاهم انسالي .. انسالي كل الأزواج المرتبة تمام؟
+
+391
+00:33:45,030 --> 00:33:49,770
+اللي بتبدأ يش .. اللي فيها عناصر متشابهات تمام؟
+
+392
+00:33:49,770 --> 00:33:54,380
+لإن هذا already هيؤدل العوصل التانيالان ايش تساوي؟
+
+393
+00:33:54,380 --> 00:33:58,720
+تبدأ تحصر عناصر واحد و واحد انسانية واحد .. انا
+
+394
+00:33:58,720 --> 00:34:03,020
+بدي افحص يا شباب .. واحد و اتنين .. هاي .. بتجيبلي
+
+395
+00:34:03,020 --> 00:34:06,680
+كل الأزواج المرتبة اللي بتبدأ باتنين .. هاي في
+
+396
+00:34:06,680 --> 00:34:11,860
+عندي هذا .. اتنين و واحد .. و اتنين و اتنين .. في
+
+397
+00:34:11,860 --> 00:34:15,720
+غيره؟ خلصنا .. هذا ايش بيقدّي؟ هذا الأصل واحد و
+
+398
+00:34:15,720 --> 00:34:21,260
+واحد .. بينكمل الـA .. مصبوط؟وهذا سيبقى 1 و 2
+
+399
+00:34:21,260 --> 00:34:26,780
+ينتمي ل R1 اتنين
+
+400
+00:34:26,780 --> 00:34:31,520
+و واحد كل الأزواد المرتبة اللي تبقى بواحد في عندي
+
+401
+00:34:31,520 --> 00:34:38,700
+واحد و واحد و واحد و اتنين اتنين و واحد ينتمي ل R1
+
+402
+00:34:38,700 --> 00:34:43,300
+و اتنين و اتنين ينتمي ل R1
+
+403
+00:34:49,830 --> 00:34:52,330
+باخد الـ A و الـ C من الزوج و بصحى بحصل زوج المرتب
+
+404
+00:34:52,330 --> 00:34:56,290
+الناتج هل بينتمي ال relation ولا لأ؟ الان كمل
+
+405
+00:34:56,290 --> 00:35:01,870
+مخلصتش اربعة و تلاتة تلاتة او اربعة احنا نكمل هنا
+
+406
+00:35:01,870 --> 00:35:06,030
+هي تلاتة و اربعة كل الأزواج المرتبة اللي بتبدأ
+
+407
+00:35:06,030 --> 00:35:11,390
+باربعة في عندي اربعة و واحد و عندي اربعة و اربعة
+
+408
+00:35:11,390 --> 00:35:17,590
+الاصل هذا الشيطاني تلاتة و واحد موجود
+
+409
+00:35:17,590 --> 00:35:23,330
+تلاتة و واحدلا ينتمي ل R1 ماتوا متكمل الشغل not
+
+410
+00:35:23,330 --> 00:35:28,810
+transitive متكمل الشغل اه بك تمشي كل الخطوات هذه
+
+411
+00:35:28,810 --> 00:35:34,610
+اذا قدرت تلقطه من اول مرة انت زي انت كمان مرة اذا
+
+412
+00:35:34,610 --> 00:35:37,470
+انت جادر تجيبه من مجرد النظر تقولي اه هاي هم اتفضل
+
+413
+00:35:37,470 --> 00:35:40,510
+انا ماعندي مشكلة في الآخر انا بدي تقولي not
+
+414
+00:35:40,510 --> 00:35:45,050
+transitive ليش؟ لكن انا بقولك اذا انت ماعودتش نفسك
+
+415
+00:35:45,050 --> 00:35:50,190
+تمشي بالخطوات هذه هتغلط فيها حتماهنا في شغلة تانية
+
+416
+00:35:50,190 --> 00:35:53,750
+ممكن احنا نختزلها يا شباب الأزواج المرتبة لهيك
+
+417
+00:35:53,750 --> 00:36:02,510
+الزوج المرتب المتساوي تمام؟ يعني تخيل A و A مع A و
+
+418
+00:36:02,510 --> 00:36:09,430
+C ايه الشخص اللي بيعطيني؟ A و C بصبت؟ كذلك لما
+
+419
+00:36:09,430 --> 00:36:13,430
+باجي انا بقول A و C مع C و C ايه الشخص اللي
+
+420
+00:36:13,430 --> 00:36:17,830
+بيعطيني؟ A و C وبالتالي ممكن انت في شكل مباشر
+
+421
+00:36:19,150 --> 00:36:22,330
+تستثنيهم هدول وين ما يكون في عندي في المقارنة هذه
+
+422
+00:36:22,330 --> 00:36:29,510
+زوج مرتب متساوي ما تكتبهوش عشان تمشي خطوة للأمام
+
+423
+00:36:29,510 --> 00:36:31,970
+بس طبعا أنا جاعة بقولك ما تكتبهوش من أنا على إيه
+
+424
+00:36:31,970 --> 00:36:36,010
+اللي هو أنا مشغل دناقي صح وفاهم إنه في الآخر الزوج
+
+425
+00:36:36,010 --> 00:36:39,410
+المرتب في الـtransitive هتديني نفس ال element
+
+426
+00:36:39,410 --> 00:36:42,390
+وبالتالي already هو موجود وبالتالي أنا بقدر أعمل
+
+427
+00:36:42,390 --> 00:36:46,270
+skip لهيك element و أجلل على حالي بعد وقت الفحص
+
+428
+00:36:47,380 --> 00:36:53,020
+طيب، معناته R1 is not reflexive، not symmetric،
+
+429
+00:36:53,020 --> 00:37:01,460
+not antisymmetric، not transitive، not كلشي،
+
+430
+00:37:01,460 --> 00:37:06,580
+all not طيب،
+
+431
+00:37:06,580 --> 00:37:10,840
+فهنشوف كمان مثال ب relation تانية و ناخد على سبيل
+
+432
+00:37:10,840 --> 00:37:16,440
+المثال R3 خلينا ناخد على سبيل المثال R3
+
+433
+00:37:19,750 --> 00:37:26,410
+R تلاتة واحد و واحد واحد و اتنين واحد و اربعة
+
+434
+00:37:26,410 --> 00:37:31,910
+reflexive
+
+435
+00:37:31,910 --> 00:37:35,890
+ليش
+
+436
+00:37:35,890 --> 00:37:40,290
+reflexive؟ واحد و واحد اتنين اتنين تلاتة تلاتة
+
+437
+00:37:40,290 --> 00:37:42,210
+اربعة اربعة symmetric
+
+438
+00:37:48,590 --> 00:37:52,530
+واحد و اتنين اتنين و واحد واحد و اربعة اربعة و
+
+439
+00:37:52,530 --> 00:37:58,150
+واحد والباقي متشابهات فهي symmetric مباشرة Anti
+
+440
+00:37:58,150 --> 00:38:02,810
+-symmetric لأ
+
+441
+00:38:02,810 --> 00:38:07,370
+not Anti-symmetric عشان أيه قلتلك قبل شوية لما
+
+442
+00:38:07,370 --> 00:38:11,010
+تكون symmetric مستحيل تكون Anti-symmetric و لو
+
+443
+00:38:11,010 --> 00:38:13,750
+كانت Anti-symmetric مستحيل تكون symmetric
+
+444
+00:38:13,750 --> 00:38:17,970
+Transitive هلأ بدك شوية ايه اش
+
+445
+00:38:27,610 --> 00:38:32,070
+الأزوادي اللي بتبدأ اتنين و واحد اتنين و اتنين
+
+446
+00:38:32,070 --> 00:38:35,710
+بديش اياها لانها already فهذه بتديني واحد و واحد
+
+447
+00:38:35,710 --> 00:38:42,750
+بيمتمل ال relation الان واحد و أربعةأربعة و واحد
+
+448
+00:38:42,750 --> 00:38:46,190
+بدي يعطيني واحد و واحد كمان مرة تنتمي لل relation
+
+449
+00:38:46,190 --> 00:38:55,190
+بعد هيك في عندي أربعة و واحد مع واحد و اتنين و
+
+450
+00:38:55,190 --> 00:39:00,670
+واحد و أربعة هذا الأصل مش يعطيني أربعة و اتنين
+
+451
+00:39:00,670 --> 00:39:06,170
+أربعة و اتنين موجود لا ينتمي لل relation ماكملش
+
+452
+00:39:06,170 --> 00:39:07,530
+فحص not transitive
+
+453
+00:39:10,430 --> 00:39:15,150
+كيف؟ غيب عنك لأنك انت حولت تشتغل شكل Random والـ
+
+454
+00:39:15,150 --> 00:39:18,750
+Random اللي أطب فيه، هو أنا عم بشتغل بطريقة
+
+455
+00:39:18,750 --> 00:39:22,110
+Systematic، منتظرة، إذا أنت اتعودت عليها، هتمشي
+
+456
+00:39:22,110 --> 00:39:27,230
+معاك بسرعة يا شباب الأمور، نعم، فأول المحاضرة، لو
+
+457
+00:39:27,230 --> 00:39:29,150
+أنك كنت حاضر، كان جواك عرفت إيش بنستفيد منه في
+
+458
+00:39:29,150 --> 00:39:32,430
+حياتنا، إيش بنستفيد من ال relations؟
+
+459
+00:39:39,680 --> 00:39:43,840
+أه شوية يا شباب زميلنا بيقول ليش قلنا النط
+
+460
+00:39:43,840 --> 00:39:47,960
+Symmetric لتعني Anti-Symmetric تعالى شوف ال
+
+461
+00:39:47,960 --> 00:39:52,360
+relation هاي بالشد شرح دي معاك ال definition بدي
+
+462
+00:39:52,360 --> 00:39:56,120
+أروح معاك مباشرة لمثال بسيط جدا فترض ان ال R تساوي
+
+463
+00:39:56,120 --> 00:40:04,280
+واحد و اتنين اتنين و واحد واحد و تلاتة في تعريف ال
+
+464
+00:40:04,280 --> 00:40:10,420
+Symmetric لكل زوج مرتب انعكاسه موجود1 و 2 انعكسه
+
+465
+00:40:10,420 --> 00:40:16,500
+.. 2 و 1 .. 2 و 1 انعكسه .. 1 و 2 .. 1 و 3 ليس
+
+466
+00:40:16,500 --> 00:40:23,320
+لديها انعكس .. هذا يعني انها ليست سيماترك .. لا
+
+467
+00:40:23,320 --> 00:40:27,160
+أقدر أن أقول عليها انت سيماترك .. لماذا؟ لأن في
+
+468
+00:40:27,160 --> 00:40:30,960
+الانت سيماترك .. بقول كتالة .. كل العناصر اللي في
+
+469
+00:40:30,960 --> 00:40:34,740
+العلاقة ليست لديها انعكس إلا لو كانت الـA تسوى
+
+470
+00:40:34,740 --> 00:40:42,470
+الـBالان هذه هذه كون واحد و اتنين انعكاسها ينتمي
+
+471
+00:40:42,470 --> 00:40:49,510
+لل relation فهي نقف Anti-symmetric لأ
+
+472
+00:40:49,510 --> 00:40:52,910
+سيبنا من اللي خلصنا بنانجوب بس على جانب السؤال نقف
+
+473
+00:40:52,910 --> 00:40:56,490
+Anti-symmetric الان لو كانت Symmetric معناته هذا
+
+474
+00:40:56,490 --> 00:41:01,910
+غايب مصبوط Symmetric نقف Anti-symmetric لو هذا
+
+475
+00:41:01,910 --> 00:41:09,480
+غايب صارتانتي سيماتريك لكن ليس سيماتريك بصبت لكن
+
+476
+00:41:09,480 --> 00:41:13,660
+في حالة من الحالات جاية في الوسط لا هي سيماتريك
+
+477
+00:41:13,660 --> 00:41:16,500
+ولا هي انتي سيماتريك مثل الحالة اللي موجودة هنا
+
+478
+00:41:16,500 --> 00:41:21,160
+عشان هيك ماقدرش اقول كل not symmetric انتي
+
+479
+00:41:21,160 --> 00:41:27,800
+سيماتريك طيب البجيات بتكملهم لحالك لان اعتقد انه
+
+480
+00:41:27,800 --> 00:41:34,770
+بعد هي كان خلاص طيب الآنهك مباشرة أنا قفزت معاك من
+
+481
+00:41:34,770 --> 00:41:39,550
+تسعة واحد لتسعة أربعة أو تسعة خمسة مش فاكر ال
+
+482
+00:41:39,550 --> 00:41:43,510
+section الآن في ال section هدا بنتكلم على
+
+483
+00:41:43,510 --> 00:41:47,110
+equivalence relation لو ال relation حققت مجموعة من
+
+484
+00:41:47,110 --> 00:41:52,150
+الخصائص اللي هم reflexive و symmetric و transitive
+
+485
+00:41:52,150 --> 00:41:56,390
+بقول عنها equivalence relation بقول عنها
+
+486
+00:41:56,390 --> 00:41:58,170
+equivalence relation
+
+487
+00:42:01,110 --> 00:42:05,730
+وبنرمز لل equivalence اما بالمادة هاي او بالتلت
+
+488
+00:42:05,730 --> 00:42:10,190
+شرطات تعالى ال relation اللى موجودة عندى على
+
+489
+00:42:10,190 --> 00:42:17,630
+السريع الاصل هذا ايش؟ واحد و واحد و اتنين و اتنين
+
+490
+00:42:17,630 --> 00:42:22,070
+تلاتة و تلاتة reflexive واحد و اتنين و اتنين و
+
+491
+00:42:22,070 --> 00:42:25,310
+واحد واحد و تلاتة تلاتة و واحد اتنين و واحد هي
+
+492
+00:42:25,310 --> 00:42:27,430
+symmetric
+
+493
+00:42:29,190 --> 00:42:34,350
+transitive وtransitive كمان مقرأ تسألش أنا بسألك
+
+494
+00:42:34,350 --> 00:42:37,910
+هل هي equivalence relation مافيش داية تروح تفحص
+
+495
+00:42:37,910 --> 00:42:41,870
+الأربع properties بدي تلاتة منهم reflexive and
+
+496
+00:42:41,870 --> 00:42:47,770
+symmetric وtransitive من ناحية التهدي هي واحد
+
+497
+00:42:47,770 --> 00:42:53,750
+واثنين هادي مع هادي تديني واحد وواحد موجودة واحد
+
+498
+00:42:53,750 --> 00:43:00,200
+في غيرها واحد بالتنينواحد و تلاتة هي موجودة خلصنا
+
+499
+00:43:00,200 --> 00:43:06,120
+اللي بعده واحد و تلاتة تلاتة و واحد تديني واحد و
+
+500
+00:43:06,120 --> 00:43:10,260
+واحد تلاتة و اتنين تديني واحد و اتنين already
+
+501
+00:43:10,260 --> 00:43:15,040
+موجودة اللي بعده اتنين و واحد اتنين و واحد واحد و
+
+502
+00:43:15,040 --> 00:43:20,060
+اتنين اتنين و اتنين هيها واحد اتنين و تلاتة هيها
+
+503
+00:43:21,140 --> 00:43:25,480
+أتنين و تلاتة already موجودة لبعده تلاتة و واحد
+
+504
+00:43:25,480 --> 00:43:32,620
+واحد و .. تلاتة و اتنين تلاتة و اتنين هيها بعد هيك
+
+505
+00:43:32,620 --> 00:43:38,300
+تلاتة و تلاتة هيها خلصنا اتنين و تلاتة تلاتة و
+
+506
+00:43:38,300 --> 00:43:47,100
+واحد بعده اتنين و واحد هيها و تلاتة و تلاتةبناخد
+
+507
+00:43:47,100 --> 00:43:49,040
+.. احنا بيقول اللي هو already موجودة وبالتالي
+
+508
+00:43:49,040 --> 00:43:52,020
+transitive وبالتالي ال relation transitive نعم
+
+509
+00:43:52,020 --> 00:43:59,160
+يعني كل relation reflexive هي symmetric؟ نعم كل
+
+510
+00:43:59,160 --> 00:44:04,060
+relation reflexive؟ لأ لأ لأ لأ لأ لأ ممكن مثال؟
+
+511
+00:44:04,060 --> 00:44:04,960
+اه ممكن مثال
+
+512
+00:44:16,440 --> 00:44:21,360
+symmetric not reflexive هاي ال relation symmetric
+
+513
+00:44:21,360 --> 00:44:28,300
+not reflexive انت
+
+514
+00:44:28,300 --> 00:44:36,640
+هيك حكيت؟ هيك مقصودك كل reflexive symmetric اه وين
+
+515
+00:44:36,640 --> 00:44:40,900
+انعكاسه؟ نفسه احنا حكينا عن الكلام ده مش منه عشان
+
+516
+00:44:40,900 --> 00:44:45,280
+هيك قولنا حاول تجاهلها من الفحص انعكاسه هو نفسه
+
+517
+00:44:47,660 --> 00:44:50,600
+طيب، الآن بالتالي لما تكون ال relation اللي عندي
+
+518
+00:44:50,600 --> 00:44:56,210
+كمان مرة reflexiveSymmetric و Transitive معناته ان
+
+519
+00:44:56,210 --> 00:44:59,530
+انا بتكلم على equivalence relation equivalence
+
+520
+00:44:59,530 --> 00:45:03,070
+relation ليش بتهمني ال equivalence relation لأن
+
+521
+00:45:03,070 --> 00:45:06,630
+فعليا علاقة العناصر مع بعضهم هتشكل عندى مجموعات
+
+522
+00:45:06,630 --> 00:45:11,510
+هسميهم equivalent classes وال equivalent classes
+
+523
+00:45:11,510 --> 00:45:15,610
+هذه عبارة عن مجموعات التقاطع بينها Phi او
+
+524
+00:45:15,610 --> 00:45:21,490
+المجموعتين متساويتين تماما ليش لان لما باجي بقول
+
+525
+00:45:22,930 --> 00:45:27,870
+reflexive يعني كل عنصر مع نفسه مظبوط وsymmetric كل
+
+526
+00:45:27,870 --> 00:45:31,730
+عنصرين المختلفين لهم صوتهم موجودة يعني لما بدي
+
+527
+00:45:31,730 --> 00:45:36,210
+بقول الواحد related مع الواحد حتما والواحد والتنين
+
+528
+00:45:36,210 --> 00:45:39,950
+موجودة في معناته الواحد related للتنين والتنين
+
+529
+00:45:39,950 --> 00:45:44,570
+relatedللواحد ال equivalent class هو عبارة عن
+
+530
+00:45:44,570 --> 00:45:47,610
+المجموعة وهي رمزه هو عبارة عن المجموعة اللي بتحتوي
+
+531
+00:45:47,610 --> 00:45:52,330
+على مين؟ على ال B العنصر التاني العنصر التاني من
+
+532
+00:45:52,330 --> 00:45:58,110
+الزوج المرتم وال B تنتمي او ال A related to B ال A
+
+533
+00:45:58,110 --> 00:46:04,410
+related to B او بلين جوسين A وB تنتمي لل relation
+
+534
+00:46:04,410 --> 00:46:10,050
+انا بهمن مين؟ مجموعة ال B هذه في المثال السابق هذا
+
+535
+00:46:11,680 --> 00:46:14,760
+الـ M كانت كام equivalent class عندي عدد ال
+
+536
+00:46:14,760 --> 00:46:18,740
+classes بعدد عناصر ال A عدد ال classes equivalent
+
+537
+00:46:18,740 --> 00:46:25,280
+classes بعدد عناصر ال A يعني عندي واحد وعندي تنين
+
+538
+00:46:25,280 --> 00:46:31,820
+وعندي تلاتة هي عبارة عن المجموعة اللي بتحتوي على
+
+539
+00:46:31,820 --> 00:46:37,000
+العناصر اللي related مع الواحد هي الواحد واحد
+
+540
+00:46:37,000 --> 00:46:41,420
+اتنين تلاتة
+
+541
+00:46:43,260 --> 00:46:51,340
+1 2 3 مجموعة الان من العناصر ال related مع التنين
+
+542
+00:46:51,340 --> 00:46:52,880
+هي التنين
+
+543
+00:47:02,630 --> 00:47:06,050
+الان لاحظوا ان التلت عناصر أو التلت مجموعات
+
+544
+00:47:06,050 --> 00:47:10,210
+متساويات وهذا من خصائص ال equivalent class اول
+
+545
+00:47:10,210 --> 00:47:15,390
+حاجة equivalent class نائمتي ايش يعني نائمتي؟ يعني
+
+546
+00:47:15,390 --> 00:47:18,710
+مستحيل تكون فيه على الأقل هيكون عندك العنصر
+
+547
+00:47:18,710 --> 00:47:24,670
+related لنفسه عشان يحقق ال reflexive اتنين ان لو
+
+548
+00:47:24,670 --> 00:47:30,540
+أخدت اي two classesلو اخدت اي two classes التقاطع
+
+549
+00:47:30,540 --> 00:47:34,920
+بينهم فاي ولو كان لا يساوي الفاي معناته التنتين
+
+550
+00:47:34,920 --> 00:47:39,600
+متساويات لو كان التقاطع بينهم لا يساوي الفاي
+
+551
+00:47:39,600 --> 00:47:43,620
+فالتقاطع بينهم او المجموعتين متساويات وهذا اللي
+
+552
+00:47:43,620 --> 00:47:48,820
+صار معناه في المثال السابق اتحادهم كلهم بيعطيين
+
+553
+00:47:48,820 --> 00:47:55,400
+مين؟ بيعطيين ال a في المثال السابق هان قولنا واحد
+
+554
+00:47:55,400 --> 00:47:59,100
+واثنين وتلاتة كلهم كانوا يساوي ايش؟الـ A فتقطعهم
+
+555
+00:47:59,100 --> 00:48:02,800
+في لكن كلهم كان ايه تساوي؟ ال class تبع ال A تساوي
+
+556
+00:48:02,800 --> 00:48:05,860
+ال 1 تساوي ال class تبع ال 2 تساوي ال class تبع
+
+557
+00:48:05,860 --> 00:48:10,920
+التلاتة واتحادهم كلهم هاي .. هاي مجموعة جديدة
+
+558
+00:48:10,920 --> 00:48:17,740
+equivalence relation شوف الشباب لو انا سألتك .. لو
+
+559
+00:48:17,740 --> 00:48:21,990
+انا سألتكهاتلي ال equivalent classes من ال
+
+560
+00:48:21,990 --> 00:48:26,950
+equivalence relation ما تتعبش راسك و تروح تفحص هل
+
+561
+00:48:26,950 --> 00:48:30,490
+هي equivalence relation ولا لأ إلا لو أنا سألتك
+
+562
+00:48:30,490 --> 00:48:37,230
+قلتلك هل هذه equivalence relation if yes give me
+
+563
+00:48:38,010 --> 00:48:42,650
+covalent classes او اكتب لـ Covalent Classes تمام؟
+
+564
+00:48:42,650 --> 00:48:46,190
+لكن لو انا قلت لك هكلي ل Covalent Classes مباشرة
+
+565
+00:48:46,190 --> 00:48:49,990
+فانا بفترض ان هذه Covalent relation يعني Reflexive
+
+566
+00:48:49,990 --> 00:48:53,930
+و Symmetric و Transitive وانت بدك ايش تجيب القيم
+
+567
+00:48:53,930 --> 00:49:03,450
+الموجودة الان الواحد واحد
+
+568
+00:49:03,450 --> 00:49:10,470
+و اتنين و تلاتةوالتنين وانت مغمض واحد و اتنين و
+
+569
+00:49:10,470 --> 00:49:15,030
+تلاتة بلون هذا الكلام أنا جيب talk التنين related
+
+570
+00:49:15,030 --> 00:49:19,350
+مع نفسها لانها reflexive مظبوط والتنين مع الواحد
+
+571
+00:49:19,350 --> 00:49:23,710
+لانها symmetric هيها already وtransitive لانها
+
+572
+00:49:23,710 --> 00:49:27,330
+متعدية مظبوط مع التلاتة وبالتالي ال equivalent
+
+573
+00:49:27,330 --> 00:49:32,450
+class تبع التلاتة هتسويهم واحد و اتنين و تلاتة ال
+
+574
+00:49:32,450 --> 00:49:33,690
+equivalent class تبع الأربعة
+
+575
+00:49:36,580 --> 00:49:44,660
+الاربعة related مع نفسها اربعة و خمسة اربعة و خمسة
+
+576
+00:49:44,660 --> 00:49:50,440
+و مباشرة هتكون عندك الخمسة يا رب تكون بتضحك بس
+
+577
+00:49:50,440 --> 00:49:55,160
+عشانك فاهم الان
+
+578
+00:49:55,160 --> 00:50:03,210
+التقاقعات بينهم اما فيأو كل ال elements أو بيكونوا
+
+579
+00:50:03,210 --> 00:50:07,950
+متساويتين تمام؟ لو أخدت واحد و اتنين التقاطع كل
+
+580
+00:50:07,950 --> 00:50:11,530
+المجموعة اتنين و تلاتة واحد و تلاتة كل المجموعة
+
+581
+00:50:11,530 --> 00:50:16,090
+لكن تلاتة و أربعة فاي فشي يا إما بروح this joint
+
+582
+00:50:16,090 --> 00:50:21,350
+يا إما في أو بتون يكونوا متساويتين لو عملت اتحاد
+
+583
+00:50:21,350 --> 00:50:26,510
+للمجموعات هذه هحصل على مين؟ على كل ال ايه تعالي
+
+584
+00:50:26,510 --> 00:50:27,230
+كمان مثال
+
+585
+00:50:34,710 --> 00:50:41,870
+كم class عندي هان؟ كم class عندي هان؟ ستة واحد
+
+586
+00:50:41,870 --> 00:50:48,570
+واحد و تلاتة و خمسة هيهم و مباشرة عليها ال class
+
+587
+00:50:48,570 --> 00:50:51,870
+تبع التلاتة هذه تساوي ال class تبع التلاتة و تساوي
+
+588
+00:50:51,870 --> 00:50:59,550
+ال class تبع الخمسة طيب تنين تنين و ستة و ال class
+
+589
+00:50:59,550 --> 00:51:03,570
+تبع التنين تساوي ال class تبع الستة ضلت عند مين؟
+
+590
+00:51:04,950 --> 00:51:12,030
+تلاتة و احنا نقولها زي واحد، أربعة لحالها،
+
+591
+00:51:12,030 --> 00:51:18,990
+و الخمسة مع التلاتة، و التانية مع الستة، هاي الست
+
+592
+00:51:18,990 --> 00:51:24,980
+classes، خد أي اتنين، تقاطع بين هذا و هذا5 تقاطع
+
+593
+00:51:24,980 --> 00:51:28,900
+بين هذا و هذا 5 و لو قلنا 6 و 2 تقاطع بينهم 6 و 1
+
+594
+00:51:28,900 --> 00:51:34,900
+تقاطع بينهم 5 6 و 2 تقاطع بينهم متساويين وبالتالي
+
+595
+00:51:34,900 --> 00:51:39,140
+هيدفع رأي ميزة ال classes اللي موجودة عندك بقدر
+
+596
+00:51:39,140 --> 00:51:45,740
+أصنف العناصر ال relation ل classes إذا تحققت فيها
+
+597
+00:51:45,740 --> 00:51:52,000
+الخصائص السابقة طيب الآن partitionالـ Partition
+
+598
+00:51:52,000 --> 00:51:57,380
+ايش يعني؟ تقسيم .. Partitions أقسام .. البنيزين
+
+599
+00:51:57,380 --> 00:52:01,320
+يقولوا و الله تقطيع .. و الله فلان .. فلان جعان
+
+600
+00:52:01,320 --> 00:52:05,020
+اليوم و جاب الكيكة و قطعها أربع جطع .. عملها
+
+601
+00:52:05,020 --> 00:52:08,960
+partition .. هل في تقاطع بين الجطع اللي اتقطعت؟
+
+602
+00:52:08,960 --> 00:52:13,440
+يعني هل في مناطق مشتركة بين الجطعتين؟ مستحيل،
+
+603
+00:52:13,440 --> 00:52:16,360
+ماحدش حيرضى .. بعض الناس بدأت .. إيش اسمه؟ اتحرك
+
+604
+00:52:16,360 --> 00:52:20,580
+لساناتها و تصح صحي كويس ..لسه مش مفطرين، عشان هيك
+
+605
+00:52:20,580 --> 00:52:23,900
+يا رامد تراهين، الآن غير هيك في ال partition اللي
+
+606
+00:52:23,900 --> 00:52:27,960
+أنت بتعرفه، ال disk، القرص الصلب اللي عندك، بيقولك
+
+607
+00:52:27,960 --> 00:52:31,640
+اعمله partition، انجلي عمله لتالت أقسام،
+
+608
+00:52:31,640 --> 00:52:36,670
+partitions، اعملوا C وD وEجسمه هل ضروري ال
+
+609
+00:52:36,670 --> 00:52:39,510
+partitions يكون متساويات؟ لأ ماحدش بيقول أنه يكون
+
+610
+00:52:39,510 --> 00:52:45,390
+متساويات بس التقابل بينهم فاي التقابل بينهم فاي
+
+611
+00:52:45,390 --> 00:52:50,250
+واتحادهم كلهم بيدين مين؟ بيدين ال partition اللي
+
+612
+00:52:50,250 --> 00:52:58,530
+موجود عندها ففعليا أي مجموعة A تمام؟ هي عبارة عن
+
+613
+00:52:58,530 --> 00:53:03,070
+collection من الـdisjoint non-empty عشان تستخدم
+
+614
+00:53:03,070 --> 00:53:08,230
+الفايمن المجموعات واتحادهم كلهم بتديني ال a
+
+615
+00:53:08,230 --> 00:53:13,410
+بالمثال السابق لما انا قلت a بدها تساوي واحد
+
+616
+00:53:13,410 --> 00:53:18,690
+واثنين وتلاتة واربعة وقلتلك اعملي اياهم على three
+
+617
+00:53:18,690 --> 00:53:25,730
+partitions اعملي اياهم على three partitions هتقولي
+
+618
+00:53:25,730 --> 00:53:30,590
+ايه واحد بدها تساوي واحد واثنين واحد تاني يقولي
+
+619
+00:53:30,590 --> 00:53:35,110
+واحد واثنين وتلاتة وحرهيحطها كلها بس مش هيقدر
+
+620
+00:53:35,110 --> 00:53:38,930
+يعملهم three partitions و لو حطيتوا الانصر الرادع
+
+621
+00:53:38,930 --> 00:53:44,270
+تالتها هتتقيد و مش هتعمل three partitions لأن
+
+622
+00:53:44,270 --> 00:53:48,930
+الأصل التقاطع يراني سيبك مالحكي الأصل في التقاطع
+
+623
+00:53:48,930 --> 00:53:56,310
+يكون five وبالتالي هيك أفضل شغلة اتنين بدها تساوي
+
+624
+00:53:56,310 --> 00:54:04,830
+تلاتة و اتلاتةبتساوي أربعة هدول الأربع مجموعات
+
+625
+00:54:04,830 --> 00:54:11,470
+this joint اتحادهم بيعطيني كل ال a بيعطيني كل ال a
+
+626
+00:54:11,470 --> 00:54:17,970
+في توزيع تاني ممكن تصير؟ أه ممكن بدل التنين مكان
+
+627
+00:54:17,970 --> 00:54:21,310
+التلاتة أول واحد بتصير الحكاية التبديل و التواثيق
+
+628
+00:54:21,310 --> 00:54:25,450
+اللي هنجيها لاحقا لما نتكلم على الأعداد لما نتكلم
+
+629
+00:54:25,450 --> 00:54:29,810
+على أنظمة العد بنصير نتكلم على التبديل و التواثيق
+
+630
+00:54:29,810 --> 00:54:33,500
+في حينها ان شاء اللهطيب وبالتالي أنا فهمت مبدأ ال
+
+631
+00:54:33,500 --> 00:54:38,680
+partition اللي عندي هنا في عندي definition بسيط
+
+632
+00:54:38,680 --> 00:54:44,940
+بدنا نحفظه بكل بساطة زي محفظة الأربع خصائص
+
+633
+00:54:44,940 --> 00:54:48,300
+بتتذكرهم؟ وقولنا لما تكون reflexive وsymmetric
+
+634
+00:54:48,300 --> 00:54:51,900
+وtransitive اسة منها equivalence relation
+
+635
+00:54:51,900 --> 00:54:54,960
+equivalence relation في عندي partial order
+
+636
+00:54:54,960 --> 00:55:00,100
+relation أو both set relation أو both setRelation
+
+637
+00:55:00,100 --> 00:55:06,820
+لما تكون Reflexive و Antisymmetric و Transitive ..
+
+638
+00:55:06,820 --> 00:55:11,420
+Reflexive و Antisymmetric و Transitive بنقول
+
+639
+00:55:11,420 --> 00:55:17,320
+partial order أو بوسط .. ليش؟ هتحس إنه فعليًا
+
+640
+00:55:17,320 --> 00:55:22,760
+هيصيرها جايين في اتجاه اللي هو مش .. مافيش انعكاس
+
+641
+00:55:22,760 --> 00:55:25,960
+في اتجاه التاني، يعني محصورة في واحد من الأقطار أو
+
+642
+00:55:25,960 --> 00:55:29,630
+تحت واحد من الأقطار اللي موجودة عندك هناالـ
+
+643
+00:55:29,630 --> 00:55:33,430
+division القسمة
+
+644
+00:55:33,430 --> 00:55:42,010
+هل هي symmetric؟ ال division هل هي symmetric؟
+
+645
+00:55:42,010 --> 00:55:45,550
+انا بسألك ال division هل هي symmetric؟ عملية
+
+646
+00:55:45,550 --> 00:55:49,910
+القسمة هل هي symmetric؟ لو a بتجبل .. لو b بتجبل
+
+647
+00:55:49,910 --> 00:55:55,370
+الجسمة على ال a بظبط لأ لأن العملية مش إبدالية
+
+648
+00:55:55,370 --> 00:56:01,910
+عملية القسمة مش إبداليةوبالتالي هي مستحيلة تكون
+
+649
+00:56:01,910 --> 00:56:05,710
+symmetrical هذه مثالة على antisymmetric لكنها
+
+650
+00:56:05,710 --> 00:56:10,690
+transitive ولا عرعير Transitive مصبوب؟ لأن اللي
+
+651
+00:56:10,690 --> 00:56:16,450
+بيقبل الجسم على التلاتةكمان؟ اللي بيجبن الجسم على
+
+652
+00:56:16,450 --> 00:56:20,450
+التاسعة بيجبن الجسم على التلاتة و اللي بيجبن الجسم
+
+653
+00:56:20,450 --> 00:56:24,330
+على الستة بيجبن الجسم على التنين مصطلح لأ؟ و هكذا
+
+654
+00:56:24,330 --> 00:56:28,230
+وبالتالي هي Transitive و Reflexive لأن كل عنصر
+
+655
+00:56:28,230 --> 00:56:33,510
+بيجبن الجسم على نفسه فهذا احنا بنسميها Bosset
+
+656
+00:56:33,510 --> 00:56:38,590
+relation أو partial order relation بس في عندكوا
+
+657
+00:56:38,590 --> 00:56:39,770
+خطأ واحد في ال slides
+
+658
+00:56:42,390 --> 00:56:49,630
+تسعة واحد مش تمانية واحد موجود على الموديل تمام
+
+659
+00:56:49,630 --> 00:56:55,070
+تمام ال slides و الكتاب موجودين طيب في اي سؤال
+
+660
+00:56:55,070 --> 00:56:57,910
+شباب الله يعطيكم العافية احنا اليوم هناك
+
diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/WNoF4_EDCFs.srt b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/WNoF4_EDCFs.srt
new file mode 100644
index 0000000000000000000000000000000000000000..6578344c1975e834288e8c1d7264ffee5280e1c7
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/WNoF4_EDCFs.srt
@@ -0,0 +1,2414 @@
+1
+00:00:20,810 --> 00:00:22,750
+بسم الله الحمد لله والصلاة والسلام على رسول الله
+
+2
+00:00:22,750 --> 00:00:27,890
+اليوم إن شاء الله يا شباب هنكمل أو هنعمل review بسيط
+
+3
+00:00:27,890 --> 00:00:30,930
+الأهم الشغلات اللي خدناها المحاضرة الماضية، وهنكمل
+
+4
+00:00:30,930 --> 00:00:33,750
+في الـ chapter اللي احنا ما زلنا فيه، اللي هو الـ
+
+5
+00:00:33,750 --> 00:00:38,370
+fundamental logic. طبعًا كنا المحاضرة الماضية
+
+6
+00:00:38,370 --> 00:00:41,990
+اتكلمنا على الـ connectors أو الـ logical operators
+
+7
+00:00:41,990 --> 00:00:45,530
+اللي ممكن أنا استخدمها مع الـ proposition وكل ما
+
+8
+00:00:45,530 --> 00:00:49,250
+عرفنا الـ proposition هو عبارة عن statement تاخد
+
+9
+00:00:49,250 --> 00:00:53,200
+إما true أو false، وقلنا الـ statement هي عبارة عن
+
+10
+00:00:53,200 --> 00:00:57,080
+sentence إما بتوصف شيء، جملة خبرية أو جملة وصفية.
+
+11
+00:00:57,080 --> 00:01:00,620
+وبعد هيك شفنا الـ connectors اللي موجود عندنا هنا.
+
+12
+00:01:00,620 --> 00:01:05,140
+وبعدين تكلمنا على الـ connectors، قلنا إن الـ by أو الـ
+
+13
+00:01:05,140 --> 00:01:09,780
+negation أو النفي هي عبارة عن unary operator. إيش
+
+14
+00:01:09,780 --> 00:01:12,920
+يعني unary؟ إنه بيشتغل... أحدها بيشتغل على operator
+
+15
+00:01:12,920 --> 00:01:18,250
+واحد، بينما باقي الـ operators كلها binary. الـ
+
+16
+00:01:18,250 --> 00:01:22,490
+conjunction، الـ and، الـ conjunction، الـ or، والـ
+
+17
+00:01:22,490 --> 00:01:25,990
+implication أو الـ conditional statement، الـ implies.
+
+18
+00:01:25,990 --> 00:01:30,690
+طبعًا في الـ implies يا شباب، لما عملنا جدول
+
+19
+00:01:30,690 --> 00:01:34,870
+الاحتمالات، قلنا كالتالي: true implies true، true.
+
+20
+00:01:34,870 --> 00:01:35,670
+true true true true true true true true true true
+
+21
+00:01:35,670 --> 00:01:35,930
+true true true true true true true true true true
+
+22
+00:01:35,930 --> 00:01:36,470
+true true true true true true true true true true
+
+23
+00:01:36,470 --> 00:01:39,340
+true true. هذه الحالة الوحيدة اللي غير منطقية
+
+24
+00:01:39,340 --> 00:01:43,080
+لأن إذا أنتَ اجتهدت ودرست، لازم تقول الأمر عملية
+
+25
+00:01:43,080 --> 00:01:46,540
+تؤدي إلى النجاح، وبالتالي هذه العملية أو الحالة الوحيدة
+
+26
+00:01:46,540 --> 00:01:52,130
+المرفوضة. وبالتالي ممكن ألخص هيك: في كل الحالات تبع الـ
+
+27
+00:01:52,130 --> 00:01:56,610
+implication، هتديني true، ما عدا true implies false
+
+28
+00:01:56,610 --> 00:01:59,550
+بتكون هذه الحالة اللي عندي false. وقلنا في عندي
+
+29
+00:01:59,550 --> 00:02:03,470
+مجموعة من الـ expressions بالإنجليزية، تستخدم عشان
+
+30
+00:02:03,470 --> 00:02:07,710
+تشتغل أو تحل مكان الـ if then أو الـ implication: if
+
+31
+00:02:07,710 --> 00:02:15,480
+b then q, not q when b, a necessary condition for b is q.
+
+32
+00:02:15,480 --> 00:02:19,300
+وهذه كل هذه المصطلحات فيها معاني، تجدها ضمن الـ
+
+33
+00:02:19,300 --> 00:02:23,300
+text عندما تقوم بترجمة للنص اللي موجود عندك. وبعد
+
+34
+00:02:23,300 --> 00:02:26,260
+ذلك، تكلمنا عن الـ binary conditional أو تكلمنا في
+
+35
+00:02:26,260 --> 00:02:28,580
+الـ implication نفسه. في عندي الـ converse، وفي عندي الـ
+
+36
+00:02:28,580 --> 00:02:32,080
+contrapositive، وفي عندي الـ inverse. الـ
+
+37
+00:02:32,080 --> 00:02:37,060
+biconditional: p biconditional q، هتكون تديني الـ
+
+38
+00:02:37,060 --> 00:02:41,920
+true في حالة واحدة فقط، إن العنصرين متساويات، يعني
+
+39
+00:02:41,920 --> 00:02:45,820
+true biconditional true، true. ليش؟ لأن هذه عبارة
+
+40
+00:02:45,820 --> 00:02:53,220
+عن الـ p biconditional q، equivalent to p implies q
+
+41
+00:02:53,220 --> 00:03:01,220
+and q implies p. وبالتالي السهمين موجودين بتضارب.
+
+42
+00:03:01,220 --> 00:03:05,510
+وبالتالي، هادي بتديني true لما يكون العنصرين true.
+
+43
+00:03:05,510 --> 00:03:09,250
+وطبعًا الكلمات الدالة عليها: p is necessary and
+
+44
+00:03:09,250 --> 00:03:14,570
+sufficient for q، p then q، and conversely p if and only if q.
+
+45
+00:03:14,570 --> 00:03:20,290
+واتكلمنا على الأولويات
+
+46
+00:03:20,290 --> 00:03:23,390
+للعمليات الحسابية أو للعمليات المنطقية،  لأنديها.
+
+47
+00:03:23,390 --> 00:03:27,110
+وقلنا الشيء الجديد اللي اتعلمناه زمان، هو الأساس
+
+48
+00:03:27,110 --> 00:03:32,320
+الأولوية الأولى للأقواس، الأولوية الأولى للأقواس.
+
+49
+00:03:32,320 --> 00:03:41,020
+بعدين النفي، والـ and، والـ implication اللي موجودة
+
+50
+00:03:41,020 --> 00:03:45,260
+عندها. وتكلمنا على جدول الاحتمالات، عشان أعبي لأي
+
+51
+00:03:45,260 --> 00:03:49,140
+compound propositional. وقلنا ضروري في جدول
+
+52
+00:03:49,140 --> 00:03:53,600
+الاحتمالات، إن أعد كم variable موجود عندي، كم
+
+53
+00:03:53,600 --> 00:03:57,300
+simple proposition موجود في المثال اللي عندي، كم؟
+
+54
+00:03:57,300 --> 00:04:05,480
+اتنين. قلنا اتنين. الـ base هذه اللي هي بتمثل true or
+
+55
+00:04:05,480 --> 00:04:16,340
+false، عدد الـ variables، عدد
+
+56
+00:04:16,340 --> 00:04:19,520
+الـ proposition اللي موجودة عندي، بدها تساوي عدد
+
+57
+00:04:19,520 --> 00:04:22,640
+الصفوف اللي موجودة في الجدول، عدد الصفوف اللي
+
+58
+00:04:22,640 --> 00:04:27,420
+موجودة في الجدول. وبالتالي، الصف الأول، قلنا بنقسم
+
+59
+00:04:27,420 --> 00:04:32,470
+الأربعة هذه على اتنين: 2 true و2 false. الصفر اللي
+
+60
+00:04:32,470 --> 00:04:36,690
+بعدين، باخد الناتج تبع العمود الأول، هم الـ 2، وبقسمه
+
+61
+00:04:36,690 --> 00:04:41,170
+على 2: 1 true و1 false. وبذكرك كمان مرة: لو كان في
+
+62
+00:04:41,170 --> 00:04:45,560
+ثلاثة متغيرات، بتكلم على اتنين أو ثلاثة يعني
+
+63
+00:04:45,560 --> 00:04:49,280
+ثمانية. العمود الأول حيكون: أربعة true وأربعة false.
+
+64
+00:04:49,280 --> 00:04:53,120
+الأربعة هتصير اتنين: اتنين true، اتنين false. اتنين
+
+65
+00:04:53,120 --> 00:04:56,820
+هتصير واحد: واحد true، واحد false. وابدأ بنفس الـ
+
+66
+00:04:56,820 --> 00:05:00,560
+sequence اللي حكينا عليها سابقًا، تمام؟ لحد الآن احنا
+
+67
+00:05:00,560 --> 00:05:03,740
+مازلنا بالراجع، قاعدين بنعمل شغل حكيناه المرة الماضية.
+
+68
+00:05:03,740 --> 00:05:07,880
+ماشي. الحل الآن في الأولويات. تعالَ نشتغل على
+
+69
+00:05:07,880 --> 00:05:10,580
+الأولويات في المثال اللي موجود عندنا، مع أننا
+
+70
+00:05:10,580 --> 00:05:12,420
+حليناه يعني على اللوح، واشتغلنا عليه المحاضرة
+
+71
+00:05:12,420 --> 00:05:16,740
+الماضية. p
+
+72
+00:05:16,740 --> 00:05:22,180
+implies q. جدول الاحتمالات، عبيته كـ binary operators.
+
+73
+00:05:22,180 --> 00:05:26,220
+في عنده two operands. وزعت الجدول. الأولوية الأولى
+
+74
+00:05:26,220 --> 00:05:32,640
+لمين؟ للأقواس. (p or q). هحلها في داخل الأقواس: (p or q). true or
+
+75
+00:05:32,640 --> 00:05:38,390
+true، true. true or false، true. false or true، true.
+
+76
+00:05:38,390 --> 00:05:43,110
+false or false، false. إذا كنت ناسي الـ or، لازم
+
+77
+00:05:43,110 --> 00:05:47,610
+تتذكرها. بعديه إيش بقى دلوقتي؟ القصة كلها بتيجي في
+
+78
+00:05:47,610 --> 00:05:51,970
+الأولويات. النفي، الـ negation، بدك تنفي اللي في داخل
+
+79
+00:05:51,970 --> 00:05:56,490
+القوس كله. وبالتالي، هادي هتصير: false، false، false،
+
+80
+00:05:56,490 --> 00:06:02,440
+true. الخطوة التالتة: إنك تعمل الـ implication بين
+
+81
+00:06:02,440 --> 00:06:07,080
+مين ومين؟ بين الـ p والعمود الأخير. true implies
+
+82
+00:06:07,080 --> 00:06:12,080
+false... false. هقول: هذه الحالة الوحيدة في الـ
+
+83
+00:06:12,080 --> 00:06:15,400
+implication المرفوضة، لما تكون عندي true implies
+
+84
+00:06:15,400 --> 00:06:22,760
+false. true implies false... false. true implies
+
+85
+00:06:22,760 --> 00:06:26,820
+false... false. نفس الحالة. الأفضل: الـ false implies
+
+86
+00:06:26,820 --> 00:06:36,330
+false... true. false implies true؟ true. ليش
+
+87
+00:06:36,330 --> 00:06:40,830
+الـ false يا صاحبي؟ ليش؟ زي اللي فوق؟ حرام عليك
+
+88
+00:06:40,830 --> 00:06:51,590
+يا شيخ، أنتَ
+
+89
+00:06:51,590 --> 00:06:54,970
+ما درستش... ما درستش للامتحان النهائي، وبلغة علامتك
+
+90
+00:06:54,970 --> 00:07:00,110
+60، ناجح. أنتَ اللي قلت: ما زال فوق بتجيب لها ولا
+
+91
+00:07:00,110 --> 00:07:04,830
+بتجيب لها إيش؟ بتجيب لها، لأنها منطقية. يعني هو مش
+
+92
+00:07:04,830 --> 00:07:11,370
+منطقية كتير، بس أنتَ راضٍ عنها. هي عارفة ممتاز، تمام؟
+
+93
+00:07:11,370 --> 00:07:14,570
+وبالتالي، قلنا كمان مرة: في الـ implication، حالة
+
+94
+00:07:14,570 --> 00:07:19,450
+واحدة فقط اللي بتديني false، اللي هي true implies
+
+95
+00:07:19,450 --> 00:07:23,840
+false. يعني أنتَ درست واجتهدت ونجحت، بتجيب الدنيا.
+
+96
+00:07:23,840 --> 00:07:26,360
+بتقدم، قلب، مراجعة، بتروح للمدرس، بتروح للـ... مظهر
+
+97
+00:07:26,360 --> 00:07:29,260
+عليها، وهذه الشيء... لأن الشغل غير منطقي، بتصير
+
+98
+00:07:29,260 --> 00:07:32,700
+بالنسبة لك، لحد ما يجيبوا لك الدليل القاطع. هم
+
+99
+00:07:32,700 --> 00:07:35,680
+هيواجهوا الامتحان تبعتك: مش هذا اسمك وهذا خطك، أه،
+
+100
+00:07:35,680 --> 00:07:38,320
+تصير تشوف الأسئلة اللي أنتَ حليتها، تقول أنا باجيب
+
+101
+00:07:38,320 --> 00:07:43,300
+الـ... بلاش، الهيروغليف كمان. أنا ممكن آخد عليه
+
+102
+00:07:43,300 --> 00:07:44,740
+علامة من الهيروغليف.
+
+103
+00:07:48,840 --> 00:07:52,280
+وبالتالي، لما اتكلمت على الـ properties أو الـ
+
+104
+00:07:52,280 --> 00:07:56,240
+precedence أو الأولويات للعملية الحسابية، مهم جدًا
+
+105
+00:07:56,240 --> 00:08:00,260
+تطبقها. نفس النظرة. هي الجدول الثاني. كم variable
+
+106
+00:08:00,260 --> 00:08:05,360
+موجود عندي؟ كم simple proposition موجود؟ اتنين: p
+
+107
+00:08:05,360 --> 00:08:08,260
+and q. اتنين. أقصى اتنين: أربعة. يعني عدد صفوف الجدول
+
+108
+00:08:08,260 --> 00:08:14,120
+الأربعة هي. عبيتها. الأولوية اللي جوا الأقواس هي اللي
+
+109
+00:08:14,120 --> 00:08:17,340
+جوا الأقواس، اللي جت فيها نفي. الأولوية للنفي نقطة
+
+110
+00:08:17,340 --> 00:08:22,600
+الـ p. فحسبت نقطة الـ p. بعد هيك، نقطة (p or q) كـ أقواس.
+
+111
+00:08:22,600 --> 00:08:30,060
+حسبناها. الآن، الأقواس الثانية: (p or q). طبعًا، الحلقة
+
+112
+00:08:30,060 --> 00:08:33,600
+المفروضة،  ديه بتقول إنك أنت عارف إيش الـ output تبع
+
+113
+00:08:33,600 --> 00:08:38,990
+كل operator موجود عندي. والـ biconditional... قلنا
+
+114
+00:08:38,990 --> 00:08:43,370
+مع الـ biconditional، الـ true في حالة إذا العنصرين
+
+115
+00:08:43,370 --> 00:08:49,070
+متشابهين... false biconditional true... false...
+
+116
+00:08:49,070 --> 00:08:52,050
+false biconditional true... false... true by
+
+117
+00:08:52,050 --> 00:08:54,970
+conditional true... true... false by conditional
+
+118
+00:08:54,970 --> 00:09:00,430
+true... false... هتكون الـ output true، تمام؟
+
+119
+00:09:02,600 --> 00:09:05,800
+الآن، هذا أول شغل جديد، أبعدها في محاضرة. يعني الكلام
+
+120
+00:09:05,800 --> 00:09:08,060
+كله اللي احنا أخذناه المحاضرة الماضية. هيك المفروض.
+
+121
+00:09:08,060 --> 00:09:15,120
+الآن، احنا مرّ عليك بالبرمجة الـ bitwise، مرّ عليك
+
+122
+00:09:15,120 --> 00:09:19,040
+الـ logical and، ومرّ عليك الـ bitwise and. المفروض
+
+123
+00:09:19,040 --> 00:09:22,700
+هيك. لو ما مرّش، لأن بنعرفك عليها الآن يا شباب. لو
+
+124
+00:09:22,700 --> 00:09:31,300
+أنا جيت قلت لك: في عندك p and q، p and q، وجيت قلت لك
+
+125
+00:09:31,300 --> 00:09:39,300
+إن قيمة الـ p هذه false، قيمة الـ p هذه false، بتقدر
+
+126
+00:09:39,300 --> 00:09:42,640
+تعمل estimation للـ... false... false... false...
+
+127
+00:09:42,640 --> 00:09:42,720
+False .. False .. False .. False .. False .. False
+
+128
+00:09:42,720 --> 00:09:43,960
+.. False .. False .. False .. False .. False ..
+
+129
+00:09:43,960 --> 00:09:45,080
+False .. False .. False .. False .. False .. False
+
+130
+00:09:45,080 --> 00:09:46,300
+.. False .. False .. False .. False .. False ..
+
+131
+00:09:46,300 --> 00:09:46,320
+.. False .. False .. False .. False .. False ..
+
+132
+00:09:46,320 --> 00:09:46,340
+False .. False .. False .. False .. False .. False
+
+133
+00:09:46,340 --> 00:09:46,800
+.. False .. False .. False .. False .. False ..
+
+134
+00:09:46,800 --> 00:09:58,300
+False .. False ..
+
+135
+00:09:58,930 --> 00:10:04,990
+وقلت لك: بكون قيمتها واحدة
+
+136
+00:10:04,990 --> 00:10:07,590
+true. معناته: البرمجة الواحدة الواحدة الواحدة
+
+137
+00:10:07,590 --> 00:10:09,050
+الواحدة الواحدة الواحدة الواحدة الواحدة الواحدة
+
+138
+00:10:09,050 --> 00:10:09,370
+الواحدة الواحدة الواحدة الواحدة الواحدة الواحدة
+
+139
+00:10:09,370 --> 00:10:11,850
+الواحدة الواحدة الواحدة الواحدة الواحدة الواحدة
+
+140
+00:10:11,850 --> 00:10:16,230
+الواحدة الواحدة الواحدة الواحدة الواحدة الواحدة
+
+141
+00:10:16,230 --> 00:10:25,110
+الواحدة الواحدة الواحدة الواحدة الوا
+
+142
+00:10:26,430 --> 00:10:30,210
+لازم الثاني يتحقق، لأن علشان بيعتمد بنفس المنطق
+
+143
+00:10:30,210 --> 00:10:34,990
+هذا لو جاء الـ condition الأول false، خلاص بيكملش
+
+144
+00:10:34,990 --> 00:10:37,830
+حساب الـ condition، بيعتبر إن الـ condition ده كله
+
+145
+00:10:37,830 --> 00:10:41,970
+عشان false. ولو في الآخر جاء الـ condition الأول
+
+146
+00:10:41,970 --> 00:10:46,330
+true، ما بدورش على قيمة الـ condition الثاني، بيكفي
+
+147
+00:10:46,330 --> 00:10:49,570
+واحد. وهذا هو الضامن للـ output اللي موجود عندي. هن
+
+148
+00:10:49,570 --> 00:10:53,190
+هذا اللي احنا بنسميه الـ logical operator، لكن في
+
+149
+00:10:53,190 --> 00:10:56,850
+البرمجة، في عندي operator آخر، اسمه bitwise. بالـ
+
+150
+00:10:56,850 --> 00:11:01,430
+bitwise، إيش بروح بساوي؟ بروح بكتب لقيمة الـ x as bit
+
+151
+00:11:01,430 --> 00:11:04,950
+و
+
+152
+00:11:04,950 --> 00:11:10,190
+أكبر من قيمة الخمسة مثلًا، أو جداش قيمتي. هاي يا شباب
+
+153
+00:11:10,190 --> 00:11:17,870
+بغض النظر. إيش بروح بساوي؟ من اسمها bitwise، إيش الـ
+
+154
+00:11:17,870 --> 00:11:22,690
+bit؟ هو عبارة عن symbol، إما بتكون قيمته صفر أو واحد.
+
+155
+00:11:22,690 --> 00:11:26,950
+هاي الـ bit، هذا bit مظبوط، وهذا bit. فمفهوم الـ
+
+156
+00:11:26,950 --> 00:11:31,210
+bitwise، اللي بيبدأ يعمل المقارنة أو يقدم المقارنة
+
+157
+00:11:31,210 --> 00:11:36,930
+bit by bit. يعني هيك: واحد أكبر أو تساوي، أكبر من
+
+158
+00:11:36,930 --> 00:11:42,270
+واحد، false. خلاص بوقف. لو جت true، إيش بروح بساوي؟
+
+159
+00:11:42,270 --> 00:11:46,310
+بنتقل لـ next character. خلينا نقول هيك: أكبر أو
+
+160
+00:11:46,310 --> 00:11:51,650
+تساوي، عشان نقول true. الصفر أكبر أو تساوي واحد، false.
+
+161
+00:11:51,650 --> 00:11:55,790
+هذا الـ bitwise، يعني بتشتغل على مستوى الـ bit، واحد
+
+162
+00:11:55,790 --> 00:11:58,650
+الـ bit، الـ bit. وبالتالي، الآلية اللي احنا بيجيب
+
+163
+00:11:58,650 --> 00:12:01,730
+نتكلم عنها على الكمبيوتر، احنا قاعدين بنمثل الـ data
+
+164
+00:12:01,730 --> 00:12:05,970
+بمجموعة من الـ bits، as binary. ولا لا؟ يعني بتتخزن as
+
+165
+00:12:05,970 --> 00:12:10,130
+binary، سواء كانت على الـ disk أو في الـ memory. والـ bit
+
+166
+00:12:10,130 --> 00:12:12,950
+هو عبارة عن symbol، زي ما قلنا، بياخد إما صفر أو
+
+167
+00:12:12,950 --> 00:12:18,560
+واحد. ولما أنا بتكلم على binary digit، معناته الرقم
+
+168
+00:12:18,560 --> 00:12:20,880
+اللي عندي أو الحرف اللي عندي، بيتمثل كاملاً بالـ
+
+169
+00:12:20,880 --> 00:12:29,300
+binary. والـ true value، قبلها في الـ bit واحد، والـ
+
+170
+00:12:29,300 --> 00:12:36,160
+false قبلها صفر. ولو أنا بدي قاعد أطبق الـ logical
+
+171
+00:12:36,160 --> 00:12:38,740
+operators اللي شفتهم قبل شوية، على مستوى الـ bits،
+
+172
+00:12:38,740 --> 00:12:42,580
+هقول: one and one، one.
+
+173
+00:12:44,990 --> 00:12:55,490
+one or one؟ one. one xor one؟ zero. ليش؟ لأنه
+
+174
+00:12:55,490 --> 00:12:58,250
+لازم يكون واحد على الأكثر منهم true، واحنا عملنا
+
+175
+0
+
+223
+00:17:13,160 --> 00:17:19,360
+تسلمنا إياهم يا عيلة خلينا نشوف مع بعض الكتاب
+
+224
+00:17:19,360 --> 00:17:23,640
+تشوف الأسئلة تعالى نشوف بس على السريع نعمل zoom
+
+225
+00:17:23,640 --> 00:17:31,080
+شوية لبعض الأسئلة هاي مثلا لأ
+
+226
+00:17:31,080 --> 00:17:35,780
+هو فعلا على الصفحة تلاتة وثلاثين هاي هو بدأ يعد
+
+227
+00:17:35,780 --> 00:17:40,180
+من بعد المقدمة اللي عندك ليكن بقولك الآن which of
+
+228
+00:17:40,180 --> 00:17:44,520
+these sentences are a proposition what are the
+
+229
+00:17:44,520 --> 00:17:49,500
+truth value of those that are propositions
+
+230
+00:17:49,500 --> 00:17:53,400
+يعني مين من هدول propositions وإيش ال truth value
+
+231
+00:17:53,400 --> 00:17:58,340
+تبعها لو أنا قلت لك بيان بيان بيان بيان بيان بيان
+
+232
+00:17:58,340 --> 00:17:58,580
+بيان بيان بيان بيان بيان بيان بيان بيان بيان بيان
+
+233
+00:17:58,580 --> 00:17:58,700
+بيان بيان بيان بيان بيان بيان بيان بيان بيان بيان
+
+234
+00:17:58,700 --> 00:17:58,820
+بيان بيان بيان بيان بيان بيان بيان بيان بيان بيان
+
+235
+00:17:58,820 --> 00:17:59,460
+بيان بيان بيان بيان بيان بيان بيان بيان بيان بيان
+
+236
+00:17:59,460 --> 00:18:00,640
+بيان بيان بيان بيان بيان بيان بيان بيان بيان بيان
+
+237
+00:18:00,640 --> 00:18:04,860
+بيان بيان بيان بيان بيان بيان بيان بيان
+
+238
+00:18:04,860 --> 00:18:11,840
+ب
+
+239
+00:18:15,150 --> 00:18:17,570
+بتروح تدرس الجغرافيا الأمريكية وبتجيبها براحتك أنا
+
+240
+00:18:17,570 --> 00:18:20,770
+مش عارف بس هنا أنا بقدر أجي أقول لك خمسة زائد سبعة
+
+241
+00:18:20,770 --> 00:18:25,070
+equal عشرة is a proposition وقيمته false تمام
+
+242
+00:18:25,070 --> 00:18:31,210
+answer this question is not a proposition ليش؟
+
+243
+00:18:31,210 --> 00:18:35,750
+لأنها عبارة عن order لأنها عبارة عن order تعالى
+
+244
+00:18:35,750 --> 00:18:42,630
+نشوف هي مثلا في السؤال ثمانية إحنا
+
+245
+00:18:42,630 --> 00:18:44,130
+شبدنا في ال .. okay
+
+246
+00:18:47,320 --> 00:18:49,700
+بقول لك في الـ8 لو كانت الـP والـQ عبارة عن الـ
+
+247
+00:18:49,700 --> 00:18:54,580
+propositions الـP I bought a lottery ticket this week
+
+248
+00:18:54,580 --> 00:19:01,660
+أنا اشتريت بطاقة نصيب هذا الأسبوع مين هذي؟ الـP الـQ
+
+249
+00:19:01,660 --> 00:19:06,380
+I won the million dollar jackpot هو ربح المليون من
+
+250
+00:19:06,380 --> 00:19:11,320
+اليانصيب ربح أكبر جائزة الكبرى اللي هي
+
+251
+00:19:11,320 --> 00:19:16,340
+المليون دولار يا عيني عليك يا شيخ طب حللي أي
+
+252
+00:19:16,340 --> 00:19:21,220
+proposition أيوة الآن بيروح بيقول إيه بيقول
+
+253
+00:19:21,220 --> 00:19:25,080
+express each of these propositions تعالى نشوف
+
+254
+00:19:25,080 --> 00:19:29,580
+الأولى نط في الـB هو إيش بيقول ليه في B I bought a
+
+255
+00:19:29,580 --> 00:19:34,820
+lottery ticket this week I didn't buy a lottery
+
+256
+00:19:34,820 --> 00:19:38,880
+ticket this week أنا ما شاركتش لأنه كمان مرة في
+
+257
+00:19:38,880 --> 00:19:43,340
+الأولى أقول لك أنا اشتريت وخلصت نفيها هتقول له أنا
+
+258
+00:19:43,340 --> 00:19:44,860
+ما شاركتش أنا ما شاركتش أنا ما شاركتش أنا ما شاركتش أنا
+
+259
+00:19:44,860 --> 00:19:44,940
+ما شاركتش أنا ما شاركتش أنا ما شاركتش أنا ما شاركتش أنا
+
+260
+00:19:44,940 --> 00:19:45,980
+ما شاركتش أنا ما شاركتش أنا ما شاركتش أنا ما شاركتش أنا
+
+261
+00:19:45,980 --> 00:19:46,240
+ما شاركتش أنا ما شاركتش أنا ما شاركتش أنا ما شاركتش أنا
+
+262
+00:19:46,240 --> 00:19:50,380
+ما شاركتش أنا ما شاركتش أنا ما شاركتش أنا ما شاركتش أنا
+
+263
+00:19:50,380 --> 00:19:55,660
+ما شاركتش أنا ما شاركتش أنا ما شاركتش أنا ما شاركتش أنا
+
+264
+00:19:55,660 --> 00:19:57,400
+ما شاركتش أ
+
+265
+00:20:06,750 --> 00:20:09,070
+ما شاء الله عليك أقول لكم مرة طب واحديك عشان أنا
+
+266
+00:20:09,070 --> 00:20:13,210
+عارف أجاوب صح ولا غلط نقيم ال proposition اللي أنت
+
+267
+00:20:13,210 --> 00:20:18,350
+بتقوله على فرض أنه proposition آه شباب if I
+
+268
+00:20:18,350 --> 00:20:25,410
+didn't buy a lottery ticket this week then I will
+
+269
+00:20:25,410 --> 00:20:31,550
+not I would not يعني إذا أنا ما شاركتش البطاقة مش
+
+270
+00:20:31,550 --> 00:20:35,750
+هربح جائزة المليون، بس، مضبوط؟ في الأقل بالكلام،
+
+271
+00:20:35,750 --> 00:20:39,670
+كلام بسيط، بتقدر تحل طبعا، آخر شغلة بدأ أقولها يا
+
+272
+00:20:39,670 --> 00:20:43,370
+شباب طيب، هاي، بيجي أقول الـdetermine على سبيل
+
+273
+00:20:43,370 --> 00:20:45,350
+المثال سؤال 16، determine whether these by
+
+274
+00:20:45,350 --> 00:20:50,330
+conditionals are true or false؟ وين الـ by
+
+275
+00:20:50,330 --> 00:20:52,890
+conditionals؟ كلهم، من إيه لدي هدول يبقوا by
+
+276
+00:20:52,890 --> 00:20:55,990
+conditionals؟ إيش مطلوب منك؟ تعمل evaluation
+
+277
+00:20:58,500 --> 00:21:05,720
+الـB والـevaluation للـQ الـproposition من
+
+278
+00:21:05,720 --> 00:21:09,780
+بعدهم اقترح اثنين زائد اثنين equal أربعة true واحد
+
+279
+00:21:09,780 --> 00:21:13,700
+زائد واحد equal اثنين true true in biconditional
+
+280
+00:21:13,700 --> 00:21:19,900
+true true true دعونا نشوف الأخيرة صفر أكبر من واحد
+
+281
+00:21:19,900 --> 00:21:26,180
+false و الاثنين أكبر من واحد true by conditional
+
+282
+00:21:26,180 --> 00:21:29,940
+false by conditional true false false by
+
+283
+00:21:29,940 --> 00:21:33,380
+conditional by conditional وبالتالي هذه الأسئلة
+
+284
+00:21:33,380 --> 00:21:38,120
+ليش أنا بقول لك حل؟ لأن عشان تقدر تمرس يدك على وفهم
+
+285
+00:21:38,120 --> 00:21:40,420
+الـpropositions لأن الأسئلة في الآخر الامتحانات و
+
+286
+00:21:40,420 --> 00:21:44,300
+الاختبارات هتيجي من هنا بتوسع مداركك أكثر كل ما قرأت
+
+287
+00:21:44,300 --> 00:21:49,640
+من الأسئلة فيك تحل من بعد 25 أو 35 عادي جرب ما فيش
+
+288
+00:21:49,640 --> 00:21:53,460
+مشكلة في الموضوع مش مستحيلة explain without using
+
+289
+00:21:53,460 --> 00:21:58,200
+the truth table دخل في الإثبات الرياضي وإحنا لسه
+
+290
+00:21:58,200 --> 00:22:03,400
+ما لاش ندخل في الموضوع هذا بي أو نت كيو and is it
+
+291
+00:22:03,400 --> 00:22:06,980
+true when بي أو نت كيو have the same truth value؟
+
+292
+00:22:06,980 --> 00:22:10,240
+إيش قاعد بقول لك في السؤال هذا؟ بقول لك لو كانت بي و
+
+293
+00:22:10,240 --> 00:22:15,980
+كيو و ار لهم نفس القيمة تمام؟ وهي false
+
+294
+00:22:20,360 --> 00:22:25,120
+تمام؟ بدون جدول الاحتمالات اثبت لي أو أعطيني القيمة
+
+295
+00:22:25,120 --> 00:22:28,780
+تبعها إيش ممكن تروح تساوي؟ بدك تعوض مكان كل P وQ
+
+296
+00:22:28,780 --> 00:22:35,180
+وR بالـvalue بالـtruth value تمام؟ بالـtruth value
+
+297
+00:22:35,180 --> 00:22:37,820
+وتشوف هل فعليا هتصل معك على true ولا لأ
+
+298
+00:22:37,820 --> 00:22:41,360
+بالمناسبة في آخر الكتاب هتلاقي الحلول للمسائل
+
+299
+00:22:41,360 --> 00:22:48,140
+الفردية عشان هيك هنعتمد اعتمادا رئيسيا  علشان .. على
+
+300
+00:22:48,140 --> 00:22:52,260
+الكتاب .. لأ لأ .. اسمها .. على الكتاب حل جدر ما
+
+301
+00:22:52,260 --> 00:22:55,340
+بتقدر من الأسئلة وغالبا يا أستاذ هتلاقي واحد و
+
+302
+00:22:55,340 --> 00:22:59,060
+اثنين في الأسئلة متشابهة ثلاثة أو أربعة متشابهة
+
+303
+00:22:59,060 --> 00:23:05,240
+الفرق بينهم مش كبير فأنت ما تغشش نفسك و تروح تحفظ
+
+304
+00:23:05,240 --> 00:23:10,040
+الأسئلة من هناك لأن الفاضي هتكون الأمر طيب هذا
+
+305
+00:23:10,040 --> 00:23:16,380
+الموضوع الكتاب وخلصنا منه من التطبيقات المهمة
+
+306
+00:23:19,560 --> 00:23:24,760
+لأ الـpropositional logic اسم الكتاب تبعنا
+
+307
+00:23:24,760 --> 00:23:28,140
+discrete mathematics and its applications
+
+308
+00:23:28,140 --> 00:23:32,000
+و التطبيقات تبعها أهم من الـapplications المهمة
+
+309
+00:23:32,000 --> 00:23:35,800
+للـlogical أو للـpropositional logic دائما يا شباب
+
+310
+00:23:35,800 --> 00:23:42,170
+كلام الناس بيحتمل التأويل كلام بين البشر ..
+
+311
+00:23:42,170 --> 00:23:46,470
+الكلام بين البشر عادة بيحتمل التأويل بمعنى آخر
+
+312
+00:23:46,470 --> 00:23:51,910
+فلان قال كلمتين ممكن تتحول لشتيمة، مصدق؟ يقول
+
+313
+00:23:51,910 --> 00:23:54,930
+غلط في حاجة، بينها واحد ثاني يقول لك لأ، هو كان جاسوس
+
+314
+00:23:54,930 --> 00:23:59,130
+يقول كذا، هنا إحنا بنقول أن في ambiguity، في دائما
+
+315
+00:23:59,130 --> 00:24:03,650
+في نوع من الغموض أو في احتمالية لأكثر من تفسير في
+
+316
+00:24:03,650 --> 00:24:08,410
+الكلام، يعني لو جاء فلان قال ما شاء الله فلان جمر
+
+317
+00:24:15,010 --> 00:24:18,490
+يا عيني عليك، شوف كيف اشتغل الـlogic، تمام؟ واحد
+
+318
+00:24:18,490 --> 00:24:22,650
+قال فهم الكلمة، فهم الكلمة على أن وجهه منور زي
+
+319
+00:24:22,650 --> 00:24:26,870
+الجمر، وواحد ثاني مخه جافل، جافل خالص، يعني دهن
+
+320
+00:24:26,870 --> 00:24:29,350
+وقيد لما زهجان، جالك يعني هو اللي بيكون فوق
+
+321
+00:24:29,350 --> 00:24:33,430
+الصحابة في رص الشهر الهجري، تمام؟ شوف اختلف
+
+322
+00:24:33,430 --> 00:24:39,130
+التأويل، ليش؟ لأن غالبا لغة الإنسان الكلمات فيها
+
+323
+00:24:39,130 --> 00:24:43,430
+معاني، ودائما الcontext، نص الكلام أو سياق الكلام
+
+324
+00:24:43,430 --> 00:24:48,370
+له معنى، لكن هذا للأسف في الرياضيات في الكمبيوتر في
+
+325
+00:24:48,370 --> 00:24:52,850
+الهندسة هذا الكلام ما لوش وزن اللي مطلوب فيه
+
+326
+00:24:52,850 --> 00:24:56,610
+اختصاصات يا بيضاء يا سوداء تروح و توصف ما فيش علاقة غير
+
+327
+00:24:56,610 --> 00:25:00,130
+هيك عشان هيك عشان نتعلم الـproposition واحد زائد
+
+328
+00:25:00,130 --> 00:25:03,570
+واحد بيساوي اثنين خلاص أما بيقول الله تروح و توصف
+
+329
+00:25:03,570 --> 00:25:07,330
+تبع للشغلات المنطقية أو الحقيقية اللي إحنا بنتعامل
+
+330
+00:25:07,330 --> 00:25:09,250
+معاها من أهم التطبيقات
+
+331
+00:25:11,860 --> 00:25:15,700
+تبع الـpropositional logic هاي الـsentence هاي
+
+332
+00:25:15,700 --> 00:25:19,940
+لما بتروح أنت تترجم الجملة .. تترجم الجملة عشان
+
+333
+00:25:19,940 --> 00:25:24,580
+تشيل عنها أي غموض يعني مثلا بيجي يقول لك you can
+
+334
+00:25:24,580 --> 00:25:28,600
+access the internet from campus أنت تحقق لك الوصول
+
+335
+00:25:28,600 --> 00:25:32,600
+للإنترنت في داخل حرم الجامعة لو كنت من تخصص علوم
+
+336
+00:25:32,600 --> 00:25:39,380
+الحاسوب بغض النظر الآن هذا الكلام .. هذا الكلام عشان
+
+337
+00:25:39,380 --> 00:25:42,800
+حد يجي واحد يراجعنا فيه ويقول طب لو كانت تخصص
+
+338
+00:25:42,800 --> 00:25:46,840
+multimedia لو كانت تخصص كذا إيش بنصير؟ بده يتحول ل
+
+339
+00:25:46,840 --> 00:25:51,340
+proposition لازم يتحول لـproposition الآن كم
+
+340
+00:25:51,340 --> 00:25:55,180
+statement موجود عندي أنا يا شباب تعالى نشوف you
+
+341
+00:25:55,180 --> 00:25:59,580
+can access the internet from campus معناته أنا هاي
+
+342
+00:25:59,580 --> 00:26:00,540
+في عندي أول جملة
+
+343
+00:26:04,340 --> 00:26:08,480
+خليني أسميها ADP أو أي رمز بدك إياه وكم في عندي
+
+344
+00:26:08,480 --> 00:26:14,880
+only if معناته أنا بتكلم ب high connector اللي
+
+345
+00:26:14,880 --> 00:26:19,860
+هي الـimplication you are a computer science major
+
+346
+00:26:19,860 --> 00:26:25,960
+لو كان أنت تخصصك high Q مفادها
+
+347
+00:26:25,960 --> 00:26:32,280
+لو أنت كنت computer science معناته
+
+348
+00:26:32,280 --> 00:26:32,780
+بتقدر
+
+349
+00:26:36,950 --> 00:26:41,650
+B لو أنت كنت في Computer Science معناته بتحقق لك
+
+350
+00:26:41,650 --> 00:26:45,590
+تتصل بالإنترنت من داخل حرم الجامعة لهذا الكلام
+
+351
+00:26:45,590 --> 00:26:48,790
+ما حدش هيجي يراجعك فيه ويقول لك جد إيه لأن الـ
+
+352
+00:26:48,790 --> 00:26:52,830
+proposition يا إما true يا false الآن بتحقق الأولى
+
+353
+00:26:52,830 --> 00:26:59,390
+Q كانت بـtrue وfalse مش مجال والثانية حسب layout
+
+354
+00:26:59,390 --> 00:27:04,170
+وبالتالي فعليا هذه واحدة من أهم التطبيقات موضوع الـ
+
+355
+00:27:04,170 --> 00:27:08,570
+translation وإحنا شفنا المرة الماضية بالمثال هذا
+
+356
+00:27:08,570 --> 00:27:13,250
+إيش قلنا بالمثال هذا؟ قلنا بكل بساطة ممنوع تركب
+
+357
+00:27:13,250 --> 00:27:21,210
+الـcyclone إلا لو كنت أكبر من 16 سنة أو طولك أكبر
+
+358
+00:27:21,210 --> 00:27:24,830
+من 4 أقدام ممنوع
+
+359
+00:27:26,480 --> 00:27:29,940
+آه لا يمكنك .. عفوا .. لا يمكنك ركوب الـcyclone
+
+360
+00:27:29,940 --> 00:27:32,900
+لو كنت أقل من أربعة أقدام يعني لو كنت أكبر من أربعة
+
+361
+00:27:32,900 --> 00:27:38,060
+أقدام .. مسموح لك .. لو كان عمرك فوق الستة عشر سنة
+
+362
+00:27:38,060 --> 00:27:41,740
+وأنت أقل من أربعة أقدام .. مسموح لك .. وبالتالي
+
+363
+00:27:41,740 --> 00:27:46,080
+الآن الجملة اللي موجودة عندها .. you can ride the
+
+364
+00:27:46,080 --> 00:27:51,420
+cyclone بي .. معناته نفي الـبي .. لأنها منفية ..
+
+365
+00:27:51,420 --> 00:27:55,040
+you cannot .. مضبوط؟ .. بدك تفرج .. دائما تفصل
+
+366
+00:27:55,040 --> 00:27:55,580
+النفي ..
+
+367
+00:28:07,250 --> 00:28:12,870
+تقريبا تقريبا تقريبا تقريبا
+
+368
+00:28:12,870 --> 00:28:16,850
+تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا
+
+369
+00:28:16,850 --> 00:28:17,370
+تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا
+
+370
+00:28:17,370 --> 00:28:17,450
+تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا
+
+371
+00:28:17,450 --> 00:28:17,590
+تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا
+
+372
+00:28:17,590 --> 00:28:24,570
+تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا
+
+373
+00:28:28,860 --> 00:28:33,320
+على الأقل لا الـlist على الأقل الـlist nothing إلا
+
+374
+00:28:33,320 --> 00:28:36,860
+لو كنت .. إلا لو كنت هي الـcondition الثانية هذا ما
+
+375
+00:28:36,860 --> 00:28:43,100
+بنقول لك وهينسميها الـR من المحصلة يا شباب من
+
+376
+00:28:43,100 --> 00:28:49,760
+المحصلة نفي B هيك
+
+377
+00:28:49,760 --> 00:28:55,140
+مضبوط أنت مش هتركب الـcyclone إيش اللي جاب له
+
+378
+00:28:55,140 --> 00:28:57,040
+الشروط
+
+379
+00:29:01,290 --> 00:29:10,310
+Q and or طب لو تحققت أي واحدة منهم آه ممتاز طب
+
+380
+00:29:10,310 --> 00:29:15,110
+تعالى نشوف هذه unless you are older than not الـR
+
+381
+00:29:15,110 --> 00:29:22,490
+إذا كان عمرك أو طولك أقل من أربعة أقدام وعمرك أقل
+
+382
+00:29:22,490 --> 00:29:25,970
+من أربعة عشر سنة أو أقل من ستة عشر سنة مش هتركب
+
+383
+00:29:25,970 --> 00:29:35,020
+الـسايكلون أنت شوف لو حطيت القرش كان بيصير؟ لو كان
+
+384
+00:29:35,020 --> 00:29:41,600
+.. لو كان طولك أقل من أربعة أقدام أو عمرك أقل من 14
+
+385
+00:29:41,600 --> 00:29:47,700
+سنة من 16 سنة مش هتركب لأ مش شايف الكلام اللي
+
+386
+00:29:47,700 --> 00:29:54,240
+بيجيك اللي بيجيك كانت تالي أنت هتركب
+
+387
+00:29:54,240 --> 00:29:59,220
+الـcyclone هذه في حالة واحدة فقط لو كان طولك أكبر
+
+388
+00:29:59,220 --> 00:30:06,080
+من أربعة أو عمرك أكبر من 16 نفيها .. نفيها مش
+
+389
+00:30:06,080 --> 00:30:10,220
+هترجع بالـcyclone المحصلة لو كان طولك أقل من أربعة
+
+390
+00:30:10,220 --> 00:30:16,620
+أقدام وعمرك أقل من 16 لأن الأكبر من 16 هتستثنى
+
+391
+00:30:16,620 --> 00:30:19,760
+لمين؟ للطول .. كانت بغطي الموضوع للطول فأنت
+
+392
+00:30:19,760 --> 00:30:24,280
+باكتفي بها فتتحول لـend الترجمة إيه مهمة جدا يا
+
+393
+00:30:24,280 --> 00:30:28,250
+شباب في فهم الكلام إيه اللي موجود عنها؟ أنا رجعت
+
+394
+00:30:28,250 --> 00:30:33,530
+الرجوع في الموضوع طيب دعنا نشوف التطبيق الثاني وين
+
+395
+00:30:33,530 --> 00:30:38,170
+مهمنا أهم التطبيقات المهمة في الـsystem
+
+396
+00:30:38,170 --> 00:30:41,050
+specification الناس اللي بتشتغل في هندسة البرمجيات
+
+397
+00:30:41,050 --> 00:30:44,710
+أو تصنيع البرامج أو حتى في تصنيع الـhardware مهم
+
+398
+00:30:44,710 --> 00:30:48,750
+جدا من البداية حدد متطلب
+
+445
+00:35:14,460 --> 00:35:19,060
+هادي P و هادي Q و هاي فيه بينهم or معناته الـ
+
+446
+00:35:19,060 --> 00:35:25,980
+proposition الأول P or Q صح الـ specification
+
+447
+00:35:25,980 --> 00:35:32,680
+التاني Diagnostic message is not فيها نفي stored in the
+
+448
+00:35:32,680 --> 00:35:39,300
+buffer. نفي الـ B معناته هي نط الـ B كمان مرة الـ
+
+449
+00:35:39,300 --> 00:35:44,680
+specification الأول والثاني. الثالث if if
+
+450
+00:35:44,680 --> 00:35:49,400
+معناته فيها communication مصبوط. الـ connector
+
+451
+00:35:49,400 --> 00:35:53,880
+diagnostic message is stored in the buffer بيه.
+
+452
+00:35:53,880 --> 00:35:56,240
+then
+
+453
+00:35:58,170 --> 00:36:01,630
+retransmitted. it is retransmitted. Q وبالتالي الـ
+
+454
+00:36:01,630 --> 00:36:08,150
+proposition الأخير بتقول إلى Q عشان افحص الـ
+
+455
+00:36:08,150 --> 00:36:11,110
+consistency تبعتهم، أو التناسق تبعتهم، الـ parameters
+
+456
+00:36:11,110 --> 00:36:14,370
+high، أو تبعت الـ specification high. بدي اعتمد على
+
+457
+00:36:14,370 --> 00:36:18,450
+مين يا شباب؟ بدي اعتمد على القيم المنطقية، القيم
+
+458
+00:36:18,450 --> 00:36:24,130
+المنطقية لمين؟ الـ B أو الـ Q. أول حاجة المفروض أن
+
+459
+00:36:24,130 --> 00:36:27,350
+تتفكر فيها، تتطلع في التلاتة الـ Proposition
+
+460
+00:36:27,350 --> 00:36:32,410
+الموجودة قدامك. مين أكثر variable بأثر في التلاتة
+
+461
+00:36:32,410 --> 00:36:37,850
+الموجودة؟ بي ولا كيو؟ بي. بيعني تحاول تركز شغلك
+
+462
+00:36:37,850 --> 00:36:42,070
+وين؟ مع الـ B. لأن واضح أن الـ B العامل أكثر تأثيرا
+
+463
+00:36:42,070 --> 00:36:48,610
+في التلات خصائص الموجودة. طيب بي، بي هذه إما هتاخد
+
+464
+00:36:48,610 --> 00:36:53,610
+true أو هتاخد الـ False. في غير هيك، وبالتالي الأمر
+
+465
+00:36:53,610 --> 00:36:58,570
+بسيط. تعالى نشوف لو قلنا أن الـ B equal true. لو
+
+466
+00:36:58,570 --> 00:37:05,410
+افترضت أن الـ B equal true، ايش هدا هيكون؟ true. لو
+
+467
+00:37:05,410 --> 00:37:12,990
+هدا false، والتالت الـ true implies Q. الله يعطيك
+
+468
+00:37:12,990 --> 00:37:17,210
+العافية. true implies شغل مجهولة، متقدرش تحددها الـ
+
+469
+00:37:17,210 --> 00:37:22,540
+truth value. معناته أنا في عندي مشكلتها، وفي عند
+
+470
+00:37:22,540 --> 00:37:27,100
+القيمتين هدول في بينهم تناقض، وبالتالي بقدرش اتكلم
+
+471
+00:37:27,100 --> 00:37:31,360
+على الـ consistency تبع النظام. بوضح .. هيك بناء على
+
+472
+00:37:31,360 --> 00:37:34,380
+الـ truth، على الـ true value بتاعة الـ P، بقدرش اخد
+
+473
+00:37:34,380 --> 00:37:41,440
+decision. طيب دعونا نشوف الحالة التانية، لو
+
+474
+00:37:41,440 --> 00:37:48,620
+قلت هذه false. معناته الـ output مش مجهولة. الـ Q الـ
+
+475
+00:37:48,620 --> 00:37:52,560
+output Q مش مجهولة، مظهور ولا لأ؟ هتعتمد اعتماد كله
+
+476
+00:37:52,560 --> 00:38:03,340
+على الـ Q. طيب true و false implies أي
+
+477
+00:38:03,340 --> 00:38:11,200
+حاجة. أذكرك true implies true، true. true implies
+
+478
+00:38:11,200 --> 00:38:15,560
+false، false. الحالة الوحيدة اللي موجودة false
+
+479
+00:38:15,560 --> 00:38:22,820
+implies true، true. false implies false، true. هذه
+
+480
+00:38:22,820 --> 00:38:26,020
+الحالة الوحيدة. هل هي هذه؟ احنا عمالا بنقول هنا
+
+481
+00:38:26,020 --> 00:38:30,500
+false، وبالتالي هذه true. تعالى اطلع في الـ values
+
+482
+00:38:30,500 --> 00:38:37,200
+اللي موجودة عندك. شو واضح؟ احسن من جدل. واضح أن في
+
+483
+00:38:37,200 --> 00:38:41,880
+اعتمادية كبيرة على قيمة الـ B، ومش بس هيك، كمان لما
+
+484
+00:38:41,880 --> 00:38:46,930
+بتكون قيمة الـ B false، برضه اللي فوق بقدر احصل على
+
+485
+00:38:46,930 --> 00:38:50,610
+قيمة. لاحظوا أن علامة المجهول في المثال السابق، لما
+
+486
+00:38:50,610 --> 00:38:54,710
+كانت false، اختفت. بين جسين، يعني صار النظام واضح. اما
+
+487
+00:38:54,710 --> 00:38:58,290
+true أو false، وبقدر اتكلم أن العناصر هدولا
+
+488
+00:38:58,290 --> 00:39:02,850
+consistent، أو متناسقات، تبعل الـ truth value، أو when
+
+489
+00:39:02,850 --> 00:39:04,790
+B is false.
+
+490
+00:39:12,640 --> 00:39:16,480
+طبعا الخطوات كمان مرة. أنا روحت وزعت الرموز تبعتي
+
+491
+00:39:16,480 --> 00:39:20,440
+الجمل اللي حددت. الجمل اللي موجودة. بعد هيك، سرت أدور
+
+492
+00:39:20,440 --> 00:39:24,620
+هاي الـ three proposition اللي موجودة عندي. P R Q. نط
+
+493
+00:39:24,620 --> 00:39:29,400
+الـ P، بي implies Q. هيهم. وواحدة قالت بدي اخزن أو بدي
+
+494
+00:39:29,400 --> 00:39:31,980
+أعطي قيمة بحيث أن الـ specification هاد تصير true.
+
+495
+00:39:31,980 --> 00:39:37,540
+متى ممكن يصيروا true كلهم؟ مش هصير فيه true إلا غير
+
+496
+00:39:37,540 --> 00:39:40,420
+لو أنا كانت الـ P أخدت
+
+497
+00:39:41,750 --> 00:39:44,830
+false. هنا لو كانت الـ B أخدت false، وبالتالي هي
+
+498
+00:39:44,830 --> 00:39:47,770
+true. true. يعني أصبح غالبيتهم أخدت قيمة true.
+
+499
+00:39:47,770 --> 00:39:50,750
+وبالتالي الجملة الأخيرة بقدر أقول على الـ system
+
+500
+00:39:50,750 --> 00:39:56,250
+اللي عندي أنا consistent، تبعل قيمة true. برضه من
+
+501
+00:39:56,250 --> 00:39:59,470
+التطبيقات اللي موجودة. يعني هذا التطبيق رغم أنه
+
+502
+00:39:59,470 --> 00:40:05,890
+مهم، الشباب، ترجمة، ترجمة system specification، تطبيق
+
+503
+00:40:05,890 --> 00:40:10,160
+التالت في الـ logical أو في الـ boolean search. كلكم
+
+504
+00:40:10,160 --> 00:40:13,360
+بتستخدموا الـ Google عشان تقوموا بالبحث. لو أنتَ
+
+505
+00:40:13,360 --> 00:40:22,600
+روحت كتابة discrete mathematics في محرك
+
+506
+00:40:22,600 --> 00:40:27,060
+البحث، ايش اللي هيطلع؟ ايش الناتج اللي هيطلع عندك؟
+
+507
+00:40:27,060 --> 00:40:31,500
+كبشة، ياريت تقضّ علي بمنطق، عشان الكبشة هذه في
+
+508
+00:40:31,500 --> 00:40:36,040
+السوق، مش هذه المتعلق
+
+509
+00:40:36,040 --> 00:40:40,320
+بالنص اللي دخلته، كيف تتعامل مع النص؟ أولاً النص
+
+510
+00:40:40,320 --> 00:40:47,520
+هذا تم تقسيمه بناء على الـ space، لـ two statements
+
+511
+00:40:47,520 --> 00:40:55,340
+كلمات، والرابط اللي بينهم or. لأن هدف محرك البحث ..
+
+512
+00:40:55,340 --> 00:41:01,740
+هدف محرك البحث، ازودك بأكبر نتيجة ممكنة، بأكبر عدد
+
+513
+00:41:01,740 --> 00:41:05,520
+من النتائج. ليش؟ عشان تقدر تلاقي القيامة اللي بدك
+
+514
+00:41:05,520 --> 00:41:09,390
+إياها، أو الشغلات اللي بتدور عليها. طيب هذا متى بيكون
+
+515
+00:41:09,390 --> 00:41:13,330
+النتيجة true؟ لو كان النص، أو الـ metadata بتحتوي
+
+516
+00:41:13,330 --> 00:41:18,750
+على discrete أو mathematics، أو الإثنتين مع بعض. عشان
+
+517
+00:41:18,750 --> 00:41:20,790
+هيك. لو فتشت في الـ Google search، في الـ pages اللي
+
+518
+00:41:20,790 --> 00:41:24,650
+قلت معاك، هتلاقي أنه بعد شوية سيحرضك الـ discrete
+
+519
+00:41:24,650 --> 00:41:29,070
+لَحَال، والـ mathematics لحال. بس مش هجيبلك ولا شغلة
+
+520
+00:41:29,070 --> 00:41:33,110
+اللي لها علاقة مثلاً بالـ biology. ليش؟ لأنها مش من
+
+521
+00:41:33,110 --> 00:41:37,320
+ضمن الـ terms اللي موجودة عندك. هنابدك إياهم، يفترضهم
+
+522
+00:41:37,320 --> 00:41:44,140
+كلمة واحدة. استخدم علامات التنصيص على كل الجملة.
+
+523
+00:41:44,140 --> 00:41:47,880
+بيصير هذا بتعامل معاه as one parameter، discrete
+
+524
+00:41:47,880 --> 00:41:53,240
+mathematics، as one word. بيصير يدور عليها. وإذا أنتَ
+
+525
+00:41:53,240 --> 00:41:57,760
+بدك تستخدم another condition، صار بإمكانك تستخدم الـ
+
+526
+00:41:57,760 --> 00:42:01,660
+and أو الـ or، وتحقق الـ second condition.
+
+527
+00:42:06,510 --> 00:42:11,810
+وطبعاً الـ output أو الـ result بتطلع تبعاً للـ and والـ
+
+528
+00:42:11,810 --> 00:42:15,970
+or، عشان يخلّي النتيجة اللي عندك أكثر فهماً، أو
+
+529
+00:42:15,970 --> 00:42:21,670
+أكثر منطقية. التقنية الرابعة في الـ gates، في
+
+530
+00:42:21,670 --> 00:42:27,930
+البوابات، البوابات الإلكترونية. Digital Design. تذكروا
+
+531
+00:42:27,930 --> 00:42:30,850
+المحاضرة الأول لما قلنا الـ Discrete Mathematics
+
+532
+00:42:30,850 --> 00:42:32,950
+مهمة للناس اللي بتشتغل في الـ Computer Science
+
+533
+00:42:32,950 --> 00:42:36,170
+Computer Engineering أو الـ Electrical Engineering.
+
+534
+00:42:36,170 --> 00:42:40,030
+ومن أول المساقات اللي بتدرسها، مادة أو مساق اسمه
+
+535
+00:42:40,030 --> 00:42:43,930
+تصميم منطقي، عشان نقدر نصمم اللوحات أو نصمم برامج
+
+536
+00:42:43,930 --> 00:42:47,730
+صح. التصميم المنطقي بيعتمد على البوابات اللي موجودة
+
+537
+00:42:47,730 --> 00:42:55,400
+قدامنا. النفي، اسمها inverter. الـ OR
+
+538
+00:42:55,400 --> 00:43:00,260
+والـ AND، طبعاً الـ XOR. طب ما هي الـ XOR أساساً مكوّنة
+
+539
+00:43:00,260 --> 00:43:10,380
+من الـ AND والـ OR. لكن فيها لها gate.
+
+540
+00:43:10,380 --> 00:43:16,400
+B و Q، والـ output B XOR Q. هذه صارت من الرسمات
+
+541
+00:43:16,400 --> 00:43:20,600
+المتداولة، على الرقم، اللي هي compound proposition
+
+542
+00:43:20,600 --> 00:43:24,350
+أو compound gate. برضه من الشغلات، أو التطبيق الخامس
+
+543
+00:43:24,350 --> 00:43:29,950
+مذكور في الكتاب، بس ما أحبش اجيبه. الـ
+
+544
+00:43:29,950 --> 00:43:36,310
+Basel Logic، الألغاز المنطقية. أنت الآن لو جالنا لك
+
+545
+00:43:36,310 --> 00:43:42,370
+في فلاح على ضفة نهر، تمام؟ يارا، جبتها اه؟ هل فطر
+
+546
+00:43:42,370 --> 00:43:45,810
+الفلاحين فيه، إحنا؟ بس لو أنت فكرت فيها بمنطق، بتحل
+
+547
+00:43:45,810 --> 00:43:51,660
+الآن الفلاح هذا، معاه كلبه، معاه وزة، ومعاه شوية
+
+548
+00:43:51,660 --> 00:43:57,040
+شعير أو شوية جُمْح، وبده ينتقل بالقارب على الناحية
+
+549
+00:43:57,040 --> 00:44:01,560
+التانية، وما بيقدرش إلا ياخد شغلة واحدة معاه.
+
+550
+00:44:01,560 --> 00:44:08,460
+الآن الـ rules اللي موجودة: إذا الكلب والوزة مع بعض
+
+551
+00:44:08,460 --> 00:44:16,640
+هيتاكلها. إذا الوزة والجُمْح مع بعض هيتاكل. الآن الحل الوحيد
+
+552
+00:44:16,640 --> 00:44:22,100
+إذا ترك الجُمْح لوحده ممكن ينسَرج، مظبوط. أي شروق،
+
+553
+00:44:22,100 --> 00:44:24,740
+طبعاً أنا ممكن أكون مش حافظها كويس، بس في الآخر،
+
+554
+00:44:24,740 --> 00:44:28,800
+بناء على ايش هيبدأ تتحل؟ بناء على الكلام اللي أنا
+
+555
+00:44:28,800 --> 00:44:34,460
+ذكرته، فيه تناقضات، propositions، مظبوط، بدك تحط
+
+556
+00:44:34,460 --> 00:44:38,080
+بحيث أن تبقى الـ statement دائماً true،
+
+557
+00:44:38,080 --> 00:44:42,140
+مظبوط ولا لا؟ وهي كانت عدد الكلام، وهيك بصيّ في
+
+558
+00:44:42,140 --> 00:44:44,380
+المنظر، يعني تخيل أنه روحت
+
+559
+00:44:48,140 --> 00:44:52,180
+يا عين عليك! أنا بقول يعني العقرية دائماً تتجلى، يعني
+
+560
+00:44:52,180 --> 00:44:59,220
+عنّا. طيب، اه نعم، لا.
+
+561
+00:44:59,220 --> 00:45:02,200
+إحنا خلاص عليه كده، وبس أنا بدّكر ..  بَاجي بذكرك
+
+562
+00:45:02,200 --> 00:45:04,680
+التطبيق اللي يستخدم، أنت المفروض أخذته بما فيه
+
+563
+00:45:04,680 --> 00:45:09,440
+الكفاية. طيب ننتقل
+
+564
+00:45:09,440 --> 00:45:11,920
+للـ section اللي بعده.
+
+565
+00:45:15,780 --> 00:45:19,700
+لا، فيش مراجعة يا حبيبي! كلنا نمشي. Propositional
+
+566
+00:45:19,700 --> 00:45:23,340
+Logic. Proposition Equivalence. الآن يا شباب بدّينا
+
+567
+00:45:23,340 --> 00:45:28,000
+نفتح دماغنا شوية، ونعمل مراجعة عشان خاطرك، للعناصر
+
+568
+00:45:28,000 --> 00:45:33,100
+بشكل سريع، للـ operators اللي أخذناهم. أخذنا الـ not، صح؟
+
+569
+00:45:33,100 --> 00:45:38,380
+وأخذنا الـ and. الـ and متى بتكون true يا شباب؟
+
+570
+00:45:38,380 --> 00:45:44,520
+لما تكون الـ two operands true. الـ or لما كان واحد
+
+571
+00:45:44,520 --> 00:45:51,540
+منهم على الأقل true. الـ XOR لما يكونوا الإثنين
+
+572
+00:45:51,540 --> 00:45:56,080
+مختلفين. لما يكونوا الإثنين مختلفين. الـ implication
+
+573
+00:45:56,080 --> 00:46:01,040
+بتديني false في حالة true implies to false. ليش هذا
+
+574
+00:46:01,040 --> 00:46:04,480
+الكلام اللي أنا بقوله؟ مهم جداً عشان نفهم الكلام اللي
+
+575
+00:46:04,480 --> 00:46:09,280
+بده يصير هنا. والـ bi-conditional بتديني true لما
+
+576
+00:46:09,280 --> 00:46:16,450
+تكون الإثنين متشابهتين. مظبوط. لما يكونوا متشابهتين. الآن
+
+577
+00:46:16,450 --> 00:46:23,350
+في عندنا بعض التعريفات المهمة. لو كان في عندي
+
+578
+00:46:23,350 --> 00:46:32,090
+compound proposition وقيمته دائماً true، مثل
+
+579
+00:46:32,090 --> 00:46:35,710
+P or not P.
+
+580
+00:46:39,480 --> 00:46:44,600
+أو not الـ P. لو بدك تعمل جدول الاحتمالات، كان متغير
+
+581
+00:46:44,600 --> 00:46:49,920
+كان احتمال عندي أربعة. أربعة منين؟ إثنين × إثنين. أقصى
+
+582
+00:46:49,920 --> 00:46:53,560
+إثنين × أربعة، بتاخد الصفر بجدارة إن شاء الله تعالى، على
+
+583
+00:46:53,560 --> 00:47:01,900
+السؤال. لأن عندك P هي الـ one operand. P true
+
+584
+00:47:01,900 --> 00:47:09,440
+أو false. وهي not الـ P: false، true. الآن العملية هذه
+
+585
+00:47:09,440 --> 00:47:14,680
+P or not الـ P: true or false، true. false or true، true.
+
+586
+00:47:14,680 --> 00:47:20,660
+true. لاحظ أنه دائماً دائماً الـ definite true دائماً
+
+587
+00:47:20,660 --> 00:47:25,100
+صحيحة. هذا الثاني إحنا بنسميه tautology. tautology
+
+588
+00:47:25,100 --> 00:47:30,920
+هو عبارة عن compound proposition، قيمته دائماً true.
+
+589
+00:47:30,920 --> 00:47:37,460
+قيمته دائماً true. الـ compound proposition الثانية كان
+
+590
+00:47:37,460 --> 00:47:44,560
+متغير فيها؟ إثنين. كم عدد الاحتمالات في الجدول؟ أربعة.
+
+591
+00:47:44,560 --> 00:47:48,400
+تعالى
+
+592
+00:47:48,400 --> 00:47:51,780
+نشوف هل دائماً بتديني true ولا لأ؟ بمعنى أن أنا
+
+593
+00:47:51,780 --> 00:47:55,260
+هأثبت بس هدول بالجدول الاحتمالات. بعد هيك أنتَ حر
+
+594
+00:47:55,260 --> 00:48:06,200
+تصدق ولا ما تصدقش. طيب not P and not Q. true، true، false.
+
+595
+00:48:06,200 --> 00:48:13,540
+false. هاي الأربع احتمالات. true، false، true، false.
+
+596
+00:48:13,540 --> 00:48:20,160
+حسب ما قلنا، الأولوية للأقواس. ايش هان دي جوا الأقواس؟
+
+597
+00:48:20,160 --> 00:48:31,320
+P and Q. P and Q. صح. الأولى
+
+598
+00:48:31,320 --> 00:48:33,940
+true، والباقي false. إن فيها
+
+599
+00:48:36,880 --> 00:48:39,380
+اه، ليش أكتب كمان عمود؟ إذا كان بيمكن أحلها بسرعة
+
+600
+00:48:39,380 --> 00:48:45,900
+أنا ولا لأ؟ بتصير الأولى false، والباقي true. مية مية.
+
+601
+00:48:45,900 --> 00:48:59,540
+طيب الآن بدي هدول: not P or not Q. false
+
+602
+00:48:59,540 --> 00:49:06,220
+or الـ false، false. true or true.
+
+603
+00:49:11,830 --> 00:49:23,510
+false or true، true. true or false، true. true or true، true.
+
+604
+00:49:23,510 --> 00:49:27,910
+by and or by conditional، ما عكستش
+
+605
+00:49:27,910 --> 00:49:33,410
+حاجة يا أستاذ، أنا مش صح في العمود
+
+606
+00:49:33,410 --> 00:49:39,210
+الأخير. أنا كنت بجيب القيامة هذه not .. not الـ B هذه
+
+607
+00:49:39,210 --> 00:49:43,210
+الـ B. true. notها أو لا فيها false. والـ Q for true.
+
+608
+00:49:43,210 --> 00:49:50,750
+لا، فيها false. false or الـ false. false. إجيتها عكسهم.
+
+609
+00:49:50,750 --> 00:49:58,290
+true or false، true. الآن آخر شغل الحمد لله، الأخير، لما
+
+610
+00:49:58,290 --> 00:50:00,590
+يكون متساويتين في الـ bi-conditional بتكون الـ
+
+611
+00:50:00,590 --> 00:50:06,580
+output true. وبالتالي هذه جدول الاحتمالات. طبعاً إذا
+
+612
+00:50:06,580 --> 00:50:09,420
+أنت كان عندك مشكلة لك، فيعمل الجدول بالشكل هذا، أو
+
+613
+00:50:09,420 --> 00:50:18,360
+ممكن تغلط. أنا بأنصحك تشتغل واحدة واحدة. بـ
+
+614
+00:50:18,360 --> 00:50:22,360
+Contradiction. Contradiction. ايش يعني
+
+615
+00:50:22,360 --> 
+
+667
+00:54:47,600 --> 00:54:56,820
+الـ و الـ أو الـ و بتديني false تمام لو أنا
+
+668
+00:54:56,820 --> 00:55:01,340
+كانت واحدة من الـ input false طب لو كانت واحدة true
+
+669
+00:55:01,340 --> 00:55:06,370
+والتانية مجهولة، إيش الـ output؟ B اللي هي المجهول
+
+670
+00:55:06,370 --> 00:55:13,450
+يعني بين قوسين، لو أنا قلت B and true، هذي تكافئ مين؟
+
+671
+00:55:13,450 --> 00:55:18,270
+تكافئ B لأن لو كانت true، true and true true، و لو
+
+672
+00:55:18,270 --> 00:55:24,550
+كانت false، هتكون false كذلك. P or الـ false برضه
+
+673
+00:55:24,550 --> 00:55:30,730
+equivalent to مين؟ to B، false or الـ false؟ false
+
+674
+00:55:30,730 --> 00:55:37,600
+true or الـ false؟ true. هدول بنسميهم قوانين الوحدة
+
+675
+00:55:37,600 --> 00:55:44,520
+وكأنه الـ true هي المحايد مع الـ and، و الـ false هي
+
+676
+00:55:44,520 --> 00:55:54,900
+المحايد مع الـ or، domination أو السيطرة، عكسه بي or
+
+677
+00:55:54,900 --> 00:56:03,880
+true، true بي and الـ false، false. يعني لما بكون في
+
+678
+00:56:03,880 --> 00:56:09,420
+عندي false بالـ end، فبتكلم على false، و لما بكون في
+
+679
+00:56:09,420 --> 00:56:14,020
+عندي true مع الـ or، بتكلم على true. وهذا المبدأ اللي
+
+680
+00:56:14,020 --> 00:56:16,340
+بيشتغل عليه الـ logical operator بالبرمجة كلها
+
+681
+00:56:16,340 --> 00:56:20,180
+بمجرد ألاقي الـ operand الأول قيمته معروفة true، و
+
+682
+00:56:20,180 --> 00:56:24,360
+الـ condition بيعتمد على الـ or، ببورش بحسبش، خلاص هي
+
+683
+00:56:24,360 --> 00:56:27,840
+واحدة على الأقل، وبالتالي هذا هم سميها domination
+
+684
+00:56:27,840 --> 00:56:28,440
+laws
+
+685
+00:56:31,410 --> 00:56:39,090
+قانون الاختزال: P and الـ P = P، لأن لو كانت الـ true
+
+686
+00:56:39,090 --> 00:56:43,030
+and true = true، لو كانت false، false and false = false
+
+687
+00:56:43,030 --> 00:56:49,750
+كذلك P or الـ P = برضه P، false or الـ false = false، true
+
+688
+00:56:49,750 --> 00:56:59,210
+or true = true. شوف القوانين هذه. الـ negation، الـ نفي: P
+
+689
+00:56:59,210 --> 00:57:04,430
+and نقطة P = false، لأن لو كانت true، هتصير false لأنه
+
+690
+00:57:04,430 --> 00:57:08,970
+معاكس بعض، وقلنا في الـ contradiction قبل شوية P، R
+
+691
+00:57:08,970 --> 00:57:15,170
+نقطة الـ B = true، و نفي النفي = نقطة نقطة الـ B، على
+
+692
+00:57:15,170 --> 00:57:21,550
+المبدأ، نفي النفي إثبات. commutative، تبديل، الإبدال
+
+693
+00:57:21,550 --> 00:57:27,810
+خاصية الإبدال: P and Q equivalent to Q and B، و P or
+
+694
+00:57:27,810 --> 00:57:37,680
+Q equivalent to Q، B، R. P and Q and R، توجيه التجميع: P
+
+695
+00:57:37,680 --> 00:57:42,780
+and Q and R، توجيه التجميع: P and Q and R، توجيه
+
+696
+00:57:42,780 --> 00:57:47,520
+التجميع: P and Q and R، توجيه التجميع: P and Q and R
+
+697
+00:57:47,520 --> 00:57:47,640
+توجيه التجميع: P and Q and R، توجيه التجميع: P and Q
+
+698
+00:57:47,640 --> 00:57:48,000
+التجميع: P and Q and R، توجيه التجميع: P and Q and R
+
+699
+00:57:48,000 --> 00:57:50,500
+توجيه التجميع: P and Q and R، توجيه التجميع: P and Q
+
+700
+00:57:50,500 --> 00:57:56,200
+and R، توجيه التجميع: P and Q and R، توجيه التجميع: P
+
+701
+00:57:56,200 --> 00:57:59,920
+and Q and
+
+702
+00:57:59,920 --> 00:58:03,630
+R، توجيه التجميع: P and تمام؟ و الـ and هي عبارة عن
+
+703
+00:58:03,630 --> 00:58:11,350
+binary operator، هذه تكافئ (P and Q) and الـ R، أو تكافئ P and (Q
+
+704
+00:58:11,350 --> 00:58:18,430
+and الـ R) تمام؟ خاصية التجميع
+
+705
+00:58:18,430 --> 00:58:23,550
+و الـ R تمام؟ خاصية التجميع
+
+706
+00:58:28,780 --> 00:58:34,480
+و كذلك مع الـ or،  و كذلك مع الـ or في خاصية التوزيع ..
+
+707
+00:58:34,480 --> 00:58:42,000
+خاصية التوزيع: P .. توزيع مين على مين يا شباب؟
+
+708
+00:58:42,000 --> 00:58:48,940
+توزيع الـ and على .. على قوس الـ or، أو توزيع الـ or
+
+709
+00:58:48,940 --> 00:58:52,740
+على قوس الـ and. طبعا لو كانوا التنتين نفس
+
+710
+00:58:52,740 --> 00:58:55,840
+الإشارة، نفس الـ operator، أصبحنا نتكلم عن عملية
+
+711
+00:58:55,840 --> 00:59:04,200
+تجميع. طيب تعالوا نشوف الأولى: P and Q or الـ R، تستخدم
+
+712
+00:59:04,200 --> 00:59:14,200
+كمان مرة: (P and Q) or (P and R)، كمان مرة: (P and Q) or الـ
+
+713
+00:59:14,200 --> 00:59:21,820
+R، تستخدم كمان مرة: (P and Q) or (P and R)، كمان مرة: P
+
+714
+00:59:21,820 --> 00:59:22,400
+and Q or P and R، كمان مرة: P and Q or P and R، كمان
+
+715
+00:59:22,400 --> 00:59:22,540
+مرة P and Q or P and R، كمان مرة P and Q
+
+716
+00:59:22,540 --> 00:59:22,580
+or P and R، كمان مرة P and Q or P and R، كمان مرة P
+
+717
+00:59:22,580 --> 00:59:30,160
+مرة P and Q or P and R، كمان مرة P and  عشان أخدت
+
+718
+00:59:30,160 --> 00:59:33,960
+الـ متغيرات المتساويات، إيش لازم أساوي؟ بدي أعمل جدوى
+
+719
+00:59:33,960 --> 00:59:37,000
+الاحتمالات، جدوى الاحتمالات لهذه المسألة من كام
+
+720
+00:59:37,000 --> 00:59:45,020
+صف؟ أربع صفوف غلط، تمان صفوف، لأن في عندي ثلاثة
+
+721
+00:59:45,020 --> 00:59:49,480
+متغيرات، اثنين أقصى ثلاثة، بتكلم على ثمانية، بتكلم
+
+722
+00:59:49,480 --> 00:59:53,420
+على ثمانية، وبالتالي المفروض إنت تعمل جدوى
+
+723
+00:59:53,420 --> 00:59:59,890
+الاحتمالات من ثمان صفوف، P Q R، و تبقى إيش؟ تشتغل عليهم
+
+724
+00:59:59,890 --> 01:00:05,170
+إذا تلاقيك نفس قيم الـ truth value في آخر عمودين،
+
+725
+01:00:05,170 --> 01:00:09,530
+معناته في عندي إيش؟ التكافؤ، في قانون جديد بالنسبة
+
+726
+01:00:09,530 --> 01:00:13,510
+إلي: دي مورغان لاو، دي مورغان لاو، بيقول كتير، لو احنا
+
+727
+01:00:13,510 --> 01:00:21,410
+نفينا compound proposition مربوط بـ and، يساوي نفي
+
+728
+01:00:21,410 --> 01:00:28,220
+كل واحد فيهم، مربوطين بـ or، يعني نفي P and Q = نفي الـ
+
+729
+01:00:28,220 --> 01:00:33,360
+P or نفي الـ Q، و العكس صحيح. دي مورغان بيقول بيقول
+
+730
+01:00:33,360 --> 01:00:42,240
+أنه فعليا النفي هذه بتغير الإشارة، يعني عشان تنجح في
+
+731
+01:00:42,240 --> 01:00:49,680
+المساق، لازم تنجح في النص و في النهائي، تمام؟ لازم
+
+732
+01:00:49,680 --> 01:00:56,270
+تنجح في النص و في النهائي، عكسها الرصوب في المساق
+
+733
+01:00:56,270 --> 01:01:01,570
+يعني إما بترسب في النهائي أو بترسب في النص، في، وطبعا
+
+734
+01:01:01,570 --> 01:01:06,010
+رسبت بالتنائي، من تناسب مظبوط ولا لأ؟ الله أبعد عنك
+
+735
+01:01:06,010 --> 01:01:09,150
+شر الصوت، طبعا تمام يا شباب؟ طيب لو بدنا نثبت هذا
+
+736
+01:01:09,150 --> 01:01:16,490
+الكلام، جدولا احتمالات، نثبت واحدة منهم:  نفي B و Q كام
+
+737
+01:01:16,490 --> 01:01:26,250
+variable عندي؟  True false false true false true
+
+738
+01:01:26,250 --> 01:01:34,570
+false. الآن نفي الـ B، وهي نفي الـ Q، هذه: false false
+
+739
+01:01:34,570 --> 01:01:44,910
+true true false true false true. الآن نفي الـ B and Q:
+
+740
+01:01:44,910 --> 01:01:51,880
+B and Q: true and true = true، نفيها: false. true and
+
+741
+01:01:51,880 --> 01:01:58,020
+false = true، and false = false، نفيها: true. true false
+
+742
+01:01:58,020 --> 01:02:02,340
+and true = false، نفيها: true. false and false = false،
+
+743
+01:02:02,340 --> 01:02:12,300
+نفيها: true. طيب الأخيرة: نفي الـ B or نفي الـ Q: false
+
+744
+01:02:12,300 --> 01:02:19,540
+or false = false، false or true = true، true or false
+
+745
+01:02:20,240 --> 01:02:25,840
+= true، true or true = true. معناته حصلت على نفس الـ truth
+
+746
+01:02:25,840 --> 01:02:29,720
+values في جدول الاحتمالات كله، و بالتالي حصلت على
+
+747
+01:02:29,720 --> 01:02:34,820
+نفس الـ value الموجودة. هذا الـ De Morgan’s Law، و أعطيكم
+
+748
+01:02:34,820 --> 01:02:36,660
+الله يعافيكم، نكمل المرة اللي جاية إن شاء الله.
+
diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/WNoF4_EDCFs_postprocess.srt b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/WNoF4_EDCFs_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..4f1608b8f1e1895854bd3991322237b6f4f81ada
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/WNoF4_EDCFs_postprocess.srt
@@ -0,0 +1,2992 @@
+1
+00:00:20,810 --> 00:00:22,750
+بسم الله الحمد لله والصلاة والسلام على رسول الله
+
+2
+00:00:22,750 --> 00:00:27,890
+اليوم ان شاء الله شباب هنكمل او هنعمل review بسيط
+
+3
+00:00:27,890 --> 00:00:30,930
+الأهم الشغلات اللي خدناها المحاضرة الماضية و هنكمل
+
+4
+00:00:30,930 --> 00:00:33,750
+في ال chapter اللي احنا ما زلنا فيه اللي هو ال
+
+5
+00:00:33,750 --> 00:00:38,370
+fundamental logic طبعا كنا المحاضرة الماضية
+
+6
+00:00:38,370 --> 00:00:41,990
+اتكلمنا على ال connectors او ال logical operators
+
+7
+00:00:41,990 --> 00:00:45,530
+اللي ممكن انا استخدمها مع ال proposition و كل ما
+
+8
+00:00:45,530 --> 00:00:49,250
+عرفنا ال proposition هو عبارة عن statement تاخد
+
+9
+00:00:49,250 --> 00:00:53,200
+اما trueأو false وقلنا ال statement هي عبارة عن
+
+10
+00:00:53,200 --> 00:00:57,080
+sentence إما بتوصف لشغل جملة خبرية أو جملة وصفية
+
+11
+00:00:57,080 --> 00:01:00,620
+وبعد هيك شفنا ال connectors اللي موجود عندنا هنا
+
+12
+00:01:00,620 --> 00:01:05,140
+وبعد تقللنا على ال connectors قلنا إن ال by أو ال
+
+13
+00:01:05,140 --> 00:01:09,780
+negation أو النفي هي عبارة عن unary operator إيش
+
+14
+00:01:09,780 --> 00:01:12,920
+يعني unary؟ إنه بيشتغل .. أحد بيشتغل على operator
+
+15
+00:01:12,920 --> 00:01:18,250
+واحد بينما باقي ال operatorsكلها binary ال
+
+16
+00:01:18,250 --> 00:01:22,490
+conjunction ال and ال conjunction ال or و ال
+
+17
+00:01:22,490 --> 00:01:25,990
+implication او ال conditional statement ال implies
+
+18
+00:01:25,990 --> 00:01:30,690
+طبعا في ال implies يا شباب لما عملنا جدول
+
+19
+00:01:30,690 --> 00:01:34,870
+الاحتمالات قلنا كالتالي true implies true true
+
+20
+00:01:34,870 --> 00:01:35,670
+true true true true true true true true true true
+
+21
+00:01:35,670 --> 00:01:35,930
+true true true true true true true true true true
+
+22
+00:01:35,930 --> 00:01:36,470
+true true true true true true true true true true
+
+23
+00:01:36,470 --> 00:01:39,340
+true trueفالس هذه الحالة الوحيدة اللي غير منطقية
+
+24
+00:01:39,340 --> 00:01:43,080
+لأن إذا انت شهادت ودرست لازم تقول الأمر العملية
+
+25
+00:01:43,080 --> 00:01:46,540
+إلى النجاح وبالتالي هذه العملية أو الحالة الوحيدة
+
+26
+00:01:46,540 --> 00:01:52,130
+المرفوضةوبالتالي ممكن ألخص هيك في كل الحلات تبع ال
+
+27
+00:01:52,130 --> 00:01:56,610
+implication هتديني true ما عادة true implies false
+
+28
+00:01:56,610 --> 00:01:59,550
+بتكون هذه الحالة اللي عندي false وقولنا في عندي
+
+29
+00:01:59,550 --> 00:02:03,470
+مجموعة من ال expressions بالانجليزية تستخدم عشان
+
+30
+00:02:03,470 --> 00:02:07,710
+تشتغل او تحل مكان ال if then او ال implication if
+
+31
+00:02:07,710 --> 00:02:15,480
+b then q not q when b a necessary conditionfor B
+
+32
+00:02:15,480 --> 00:02:19,300
+is Q وهذه كل هذه المصطلحات فيها معاني تجدها ضمن ال
+
+33
+00:02:19,300 --> 00:02:23,300
+text عندما تقوم بترجمة للنص اللي موجودة عندها وبعد
+
+34
+00:02:23,300 --> 00:02:26,260
+ذلك تكلمنا عن ال binary conditional او تكلمنا في
+
+35
+00:02:26,260 --> 00:02:28,580
+ال implication نفسه في عند ال converse و في عند ال
+
+36
+00:02:28,580 --> 00:02:32,080
+contrapositive و في عند ال inverse ال
+
+37
+00:02:32,080 --> 00:02:37,060
+biconditional بي biconditional Q هتكون تديني ال
+
+38
+00:02:37,060 --> 00:02:41,920
+true في حالة واحدة فقط ان التنتين متساوياتيعني
+
+39
+00:02:41,920 --> 00:02:45,820
+true by conditional true true ليش؟ لأن هذه عبارة
+
+40
+00:02:45,820 --> 00:02:53,220
+عن ال B by conditional Q equivalent to B implies Q
+
+41
+00:02:53,220 --> 00:03:01,220
+and Q implies B وبالتالي السهمين موجودين بتضابط
+
+42
+00:03:01,220 --> 00:03:05,510
+وبالتالي هايبتديني true لما كنتم تنتقلون لـ True
+
+43
+00:03:05,510 --> 00:03:09,250
+وطبعا الكلمات الدالة عليها بي is necessary and
+
+44
+00:03:09,250 --> 00:03:14,570
+sufficient for a Q بي then كيو and conversely بي
+
+45
+00:03:14,570 --> 00:03:20,290
+and if and الا if كيو واتكلمنا على الأولويات
+
+46
+00:03:20,290 --> 00:03:23,390
+للعمليات الحسابية أو للعمليات المنطقية لانديهان
+
+47
+00:03:23,390 --> 00:03:27,110
+وقلنا الشيء الجديد اللي اتعلمناه زمان هو الأساس
+
+48
+00:03:27,110 --> 00:03:32,320
+الأولويه الأولى للأقواسالأولوية الأولى للأقواص
+
+49
+00:03:32,320 --> 00:03:41,020
+بعدين النفي and R و ال implication اللي موجودة
+
+50
+00:03:41,020 --> 00:03:45,260
+عندها وتكلمنا على جدول الاحتمالات عشان اعبي لأي
+
+51
+00:03:45,260 --> 00:03:49,140
+compound propositional وقلنا ضروري في جدول
+
+52
+00:03:49,140 --> 00:03:53,600
+الاحتمالات ان اعد كام variable موجود عندى كام
+
+53
+00:03:53,600 --> 00:03:57,300
+simple proposition موجود في المثال اللي عندها كم؟
+
+54
+00:03:57,300 --> 00:04:05,480
+اتنين قلنا اتنينالـ base هذه اللي هي بتمثل true or
+
+55
+00:04:05,480 --> 00:04:16,340
+false عدد ال variables عدد
+
+56
+00:04:16,340 --> 00:04:19,520
+ال proposition اللي موجودة عندى بدأت ساوي عدد
+
+57
+00:04:19,520 --> 00:04:22,640
+الصفوف اللي موجودة في الجدول عدد الصفوف اللي
+
+58
+00:04:22,640 --> 00:04:27,420
+موجودة في الجدول وبالتالي الصف الأول جلنا بنجسم
+
+59
+00:04:27,420 --> 00:04:32,470
+الأربعة هذه لإتنين2 true و 2 false الصفر اللي
+
+60
+00:04:32,470 --> 00:04:36,690
+بعدين باخد الناتج تبع العمود الأول هم ال 2 و بجسمه
+
+61
+00:04:36,690 --> 00:04:41,170
+على 2 1 true و 1 false و بذكرك كمان مرة لو كان في
+
+62
+00:04:41,170 --> 00:04:45,560
+MDI تلت متغيراتبتكلم على اتنين او ثلاثة يعني
+
+63
+00:04:45,560 --> 00:04:49,280
+تمانية العمود الأول حاسمه أربعة true وأربعة false
+
+64
+00:04:49,280 --> 00:04:53,120
+الأربعة هتصير اتنين اتنين true اتنين false اتنين
+
+65
+00:04:53,120 --> 00:04:56,820
+هتصير واحد واحد true واحد false وابدأ بنفس ال
+
+66
+00:04:56,820 --> 00:05:00,560
+sequence اللي حكينا عليها سابقا تمام لحد الآن احنا
+
+67
+00:05:00,560 --> 00:05:03,740
+مازلنا بالراجع قاعدين شغل حكيناه المرة الماضية
+
+68
+00:05:03,740 --> 00:05:07,880
+ماشي الحل الآن في الأولوياتتعالى نشتغل على
+
+69
+00:05:07,880 --> 00:05:10,580
+الأولويات في المثال اللى موجود عندنا مع أننا
+
+70
+00:05:10,580 --> 00:05:12,420
+حلمناه يعني على اللوح و اشتغلنا على المحاضرة
+
+71
+00:05:12,420 --> 00:05:16,740
+الماضية بي
+
+72
+00:05:16,740 --> 00:05:22,180
+implies Q جدول الاحتمالات عبيته ك binary operators
+
+73
+00:05:22,180 --> 00:05:26,220
+في عنده two operands وزعت الجدول الأولوية الأولى
+
+74
+00:05:26,220 --> 00:05:32,640
+لمين؟ للأقواص PRQ هجلوا في داخل القواص PRQ true or
+
+75
+00:05:32,640 --> 00:05:38,390
+true true true or falsetrue false or true true
+
+76
+00:05:38,390 --> 00:05:43,110
+false or false false إذا كانت ناسي ال or لازم
+
+77
+00:05:43,110 --> 00:05:47,610
+تتذكرها لبعده إيش بقى دلوقتي القصة كلها بتتيجي في
+
+78
+00:05:47,610 --> 00:05:51,970
+الأولويات النفي ال negation بدك تنفي اللي في داخل
+
+79
+00:05:51,970 --> 00:05:56,490
+القصة كله وبالتالي هذي هتصير false false false
+
+80
+00:05:56,490 --> 00:06:02,440
+true الأخر خطوة التالتةإنك تعمل ال implication بين
+
+81
+00:06:02,440 --> 00:06:07,080
+مين و مين بين ال B و العمود الأخير true implies
+
+82
+00:06:07,080 --> 00:06:12,080
+false .. false هقول هذا الحالة الوحيدة في ال
+
+83
+00:06:12,080 --> 00:06:15,400
+implication المرفوضة لما تكون عندي true implies
+
+84
+00:06:15,400 --> 00:06:22,760
+false true implies false .. false true implies
+
+85
+00:06:22,760 --> 00:06:26,820
+false .. false نفس الحالة الأفضل ال false implies
+
+86
+00:06:26,820 --> 00:06:36,330
+false .. truefalse implies true؟ true ليش
+
+87
+00:06:36,330 --> 00:06:40,830
+اللي false يا صاحبي؟ ليش؟ زي اللي فوق؟ حرام عليك
+
+88
+00:06:40,830 --> 00:06:51,590
+يا شيخ انت
+
+89
+00:06:51,590 --> 00:06:54,970
+مادرستش .. مادرستش للامتحان النهائي و بلغة علامتك
+
+90
+00:06:54,970 --> 00:07:00,110
+60 ناجحأنت اللي قلت مازال فوق بتجبالها ولا
+
+91
+00:07:00,110 --> 00:07:04,830
+بتجبالهااش؟ بتجبالها لأنها منطقية يعني هو مش
+
+92
+00:07:04,830 --> 00:07:11,370
+منطقية كثير بس انت رضاك عنها هي عارف ممتاز تمام؟
+
+93
+00:07:11,370 --> 00:07:14,570
+وبالتالي قلنا كمان مرة في ال implication حالة
+
+94
+00:07:14,570 --> 00:07:19,450
+واحدة فقط اللي بتديني false اللي هي true implies
+
+95
+00:07:19,450 --> 00:07:23,840
+false يعني أنت درست واجتهدت وناسبتبتجلب الدنيا،
+
+96
+00:07:23,840 --> 00:07:26,360
+بتقدم قلب مراجعة، بتروح للمدرس، بتروح للعنيب، مظهر
+
+97
+00:07:26,360 --> 00:07:29,260
+عليها وهذه الشيء .. لأن الشغل غير منطقي بتصير
+
+98
+00:07:29,260 --> 00:07:32,700
+بالنسبة لك لحد ما يجيبوا لك الدليل القاطع، هم
+
+99
+00:07:32,700 --> 00:07:35,680
+هيواجه الامتحان تبعتك مش هدا اسمك و هدا خطك، أه،
+
+100
+00:07:35,680 --> 00:07:38,320
+تصير تشوف الأسئلة اللي انت حللها، تقول أنا باجبح
+
+101
+00:07:38,320 --> 00:07:43,300
+ال .. بلاش، الهيروغليفي كمان، أنا ممكن تاخد عليه
+
+102
+00:07:43,300 --> 00:07:44,740
+علامة من الهيروغليفي
+
+103
+00:07:48,840 --> 00:07:52,280
+وبالتالي لما اتكلمت على ال properties او ال
+
+104
+00:07:52,280 --> 00:07:56,240
+precedence او الاولويات للعملية الحسابية مهم جدا
+
+105
+00:07:56,240 --> 00:08:00,260
+اطبقها نفس النظارة هي الجدول التاني كام variable
+
+106
+00:08:00,260 --> 00:08:05,360
+موجود عندى كام simple proposition موجود اتنين P
+
+107
+00:08:05,360 --> 00:08:08,260
+and Q اتنين اقصى اتنين اربعة يعني عدد صفوف الجدول
+
+108
+00:08:08,260 --> 00:08:14,120
+الأربعة هي عبيتهمالأولوية اللى جوا الأقواص هي في
+
+109
+00:08:14,120 --> 00:08:17,340
+جوا الجواص اللى جت فيه نفي الأولية اللى نفي نقطة
+
+110
+00:08:17,340 --> 00:08:22,600
+ال B فحسبت نقطة ال B بعد هيك نقطة ال B or Q كجواص
+
+111
+00:08:22,600 --> 00:08:30,060
+حسبناها الآن الجواص التاني B or Q طبعا الحلقة
+
+112
+00:08:30,060 --> 00:08:33,600
+المفروضة ديش تقول انك انت عارف ايش ال output تبع
+
+113
+00:08:33,600 --> 00:08:38,990
+كل operator موجود عندىوال by conditional .. قلنا
+
+114
+00:08:38,990 --> 00:08:43,370
+مع ال by conditional ال true في حالة إذا أن عنصرين
+
+115
+00:08:43,370 --> 00:08:49,070
+متشابهين .. false by conditional true .. false ..
+
+116
+00:08:49,070 --> 00:08:52,050
+false by conditional true .. false .. true by
+
+117
+00:08:52,050 --> 00:08:54,970
+conditional true .. true .. false by conditional
+
+118
+00:08:54,970 --> 00:09:00,430
+true .. false .. هتكون ال output true تمام؟
+
+119
+00:09:02,600 --> 00:09:05,800
+الان هاد اول شغل جديد ابعدها في محاضرة يعني الكلام
+
+120
+00:09:05,800 --> 00:09:08,060
+كله اتوا احنا اخدناه المحاضرة الماضي هيك المفروض
+
+121
+00:09:08,060 --> 00:09:15,120
+الان احنا مرت عليك بالبرمجة ال bit twice مرت عليك
+
+122
+00:09:15,120 --> 00:09:19,040
+ال logical and و مرت عليك ال bit twice and المفروض
+
+123
+00:09:19,040 --> 00:09:22,700
+هيك لو ما مرتش لان بنعرفك عليها الان يا شباب لو
+
+124
+00:09:22,700 --> 00:09:31,300
+انا اجيب قلتلك في عندك P and QP and Q و جيت قلتلك
+
+125
+00:09:31,300 --> 00:09:39,300
+ان قيمة ال P هذي False قيمة ال P هذي False بتقدر
+
+126
+00:09:39,300 --> 00:09:42,640
+تعمل estimation لل .. False .. False .. False ..
+
+127
+00:09:42,640 --> 00:09:42,720
+False .. False .. False .. False .. False .. False
+
+128
+00:09:42,720 --> 00:09:43,960
+.. False .. False .. False .. False .. False ..
+
+129
+00:09:43,960 --> 00:09:45,080
+False .. False .. False .. False .. False .. False
+
+130
+00:09:45,080 --> 00:09:46,300
+.. False .. False .. False .. False .. False ..
+
+131
+00:09:46,300 --> 00:09:46,320
+.. False .. False .. False .. False .. False ..
+
+132
+00:09:46,320 --> 00:09:46,340
+False .. False .. False .. False .. False .. False
+
+133
+00:09:46,340 --> 00:09:46,800
+.. False .. False .. False .. False .. False ..
+
+134
+00:09:46,800 --> 00:09:58,300
+False .. False ..
+
+135
+00:09:58,930 --> 00:10:04,990
+و قلت لك بيكوينترو واحدة
+
+136
+00:10:04,990 --> 00:10:07,590
+true معناته البرمجة الواحدة الواحدة الواحدة
+
+137
+00:10:07,590 --> 00:10:09,050
+الواحدة الواحدة الواحدة الواحدة الواحدة الواحدة
+
+138
+00:10:09,050 --> 00:10:09,370
+الواحدة الواحدة الواحدة الواحدة الواحدة الواحدة
+
+139
+00:10:09,370 --> 00:10:11,850
+الواحدة الواحدة الواحدة الواحدة الواحدة الواحدة
+
+140
+00:10:11,850 --> 00:10:16,230
+الواحدة الواحدة الواحدة الواحدة الواحدة الواحدة
+
+141
+00:10:16,230 --> 00:10:25,110
+الواحدة الواحدة الواحدة الواحدة الوا
+
+142
+00:10:26,430 --> 00:10:30,210
+لازم التاني يتحققه لأن علشان بيعتمد بنفس المنطق
+
+143
+00:10:30,210 --> 00:10:34,990
+هذا لو لجأ ال condition الأول false خلاص بيكمش
+
+144
+00:10:34,990 --> 00:10:37,830
+حسبة ال condition بيعتبر ان ال condition ده كله
+
+145
+00:10:37,830 --> 00:10:41,970
+عشان false ولو في الأخر لجأ ال condition الأول
+
+146
+00:10:41,970 --> 00:10:46,330
+true مابدورش على قيمة ال condition التاني بيكفي
+
+147
+00:10:46,330 --> 00:10:49,570
+واحد وهذا هو الضامن لل output اللي موجود عندي هن
+
+148
+00:10:49,570 --> 00:10:53,190
+هل ده اللي احنا بنسميها ال logical operator لكن في
+
+149
+00:10:53,190 --> 00:10:56,850
+البرمجة في عندي operator آخر اسمه bitwiseبالـ
+
+150
+00:10:56,850 --> 00:11:01,430
+bitwise ايش بروح بساوي بروح بكتب لقيمة ال X as bit
+
+151
+00:11:01,430 --> 00:11:04,950
+و
+
+152
+00:11:04,950 --> 00:11:10,190
+أكبر من قيمة الخمسة مثلا او جداش قيمتي هاي شباب
+
+153
+00:11:10,190 --> 00:11:17,870
+بغابة النظر ايش بروح بساوي من اسمها bitwise ايش ال
+
+154
+00:11:17,870 --> 00:11:22,690
+bitهو عبارة عن symbol اما بتكون قيمته صفر او واحد
+
+155
+00:11:22,690 --> 00:11:26,950
+هاي ال bit هذا bit مظبوط وهذا bit فمفهوم ال
+
+156
+00:11:26,950 --> 00:11:31,210
+bitwise اللي بيبدأ يعمل المقارنة او يقد المقارنة
+
+157
+00:11:31,210 --> 00:11:36,930
+bit by bit يعني هيك واحد اكبر او تساوي اكبر من
+
+158
+00:11:36,930 --> 00:11:42,270
+واحد false خلاص بجف لو لجيها true ايش بروح بساوي
+
+159
+00:11:42,270 --> 00:11:46,310
+بنتقل ل next character خلينا نقول هيك اكبر او
+
+160
+00:11:46,310 --> 00:11:51,650
+تساوي عشان نقول trueالصفر أكبر او تساوي واحد فالس
+
+161
+00:11:51,650 --> 00:11:55,790
+هذا ال bit twice يعني بتشتغل على مستوى ال bit واحد
+
+162
+00:11:55,790 --> 00:11:58,650
+ال bit ال bit وبالتالي الآية اللي احنا بيجيب
+
+163
+00:11:58,650 --> 00:12:01,730
+نتكلمها على الكمبيوتر احنا جاعدين بنمثل ال data
+
+164
+00:12:01,730 --> 00:12:05,970
+بمجموعة من ال bits as binary ولا لا يعني بتتخزن as
+
+165
+00:12:05,970 --> 00:12:10,130
+binary سواء كانت على القص أو في ال memory وال bit
+
+166
+00:12:10,130 --> 00:12:12,950
+هو عبارة عن سيمبول زي ما قلنا بياخد منه ام صفر او
+
+167
+00:12:12,950 --> 00:12:18,560
+واحدولمّا أنا بتكلم على binary digit معناته الرقم
+
+168
+00:12:18,560 --> 00:12:20,880
+اللي عندي أو الحرف اللي عندي بيتمثل كاملا بال
+
+169
+00:12:20,880 --> 00:12:29,300
+binary و ال true value قبلها في ال bit واحد و ال
+
+170
+00:12:29,300 --> 00:12:36,160
+false قبلها صفر و لو أنا بدي قاعد يطبق ال logical
+
+171
+00:12:36,160 --> 00:12:38,740
+operators اللي شفتهم قبل شوية على مستوى ال bits
+
+172
+00:12:38,740 --> 00:12:42,580
+هقول one and one one
+
+173
+00:12:44,990 --> 00:12:55,490
+one or ال one؟ one one x or ال one؟ zero ليش؟ لأنه
+
+174
+00:12:55,490 --> 00:12:58,250
+لازم يكون واحد على الأكثر منهم true و احنا عملنا
+
+175
+00:12:58,250 --> 00:13:01,570
+.. قولنا عملنا replication لكل true بواحد و لكل
+
+176
+00:13:01,570 --> 00:13:07,190
+false بصفر طيب ال alpha موضوع ال bitwise كمان في
+
+177
+00:13:07,190 --> 00:13:11,190
+عندي .. لما نقول bit string ال bit string هو عبارة
+
+178
+00:13:11,190 --> 00:13:13,790
+عن أي sequence من ال bits اللي انت بتكتبهم
+
+179
+00:13:16,480 --> 00:13:22,300
+هذه سيكوانس جداش تقولها اربعة
+
+180
+00:13:22,300 --> 00:13:30,020
+كبشة احد عشر بت طولها
+
+181
+00:13:30,020 --> 00:13:37,720
+احد عشر بت كمان؟ بيت و رابع حلو برضه معاه تقول ال
+
+182
+00:13:37,720 --> 00:13:40,980
+bits اللي موجودة عندى لما بتطبق عليهم ال bit twice
+
+183
+00:13:40,980 --> 00:13:44,700
+or or ب twice and or
+
+184
+00:13:47,370 --> 00:13:52,670
+بتراتب الـ two operands تحت بعض بحيث ان ال most
+
+185
+00:13:52,670 --> 00:13:59,470
+significant digit يكون تحت بعضه بمعنى يعني لو قلت
+
+186
+00:13:59,470 --> 00:14:05,390
+انا هاي X يتساوي 11001101 و جيت قلت ال Y equal
+
+187
+00:14:05,390 --> 00:14:09,770
+10011 لما بدكتيجي ترتبهم
+
+188
+00:14:13,230 --> 00:14:17,310
+الـ Most Significant صحيك؟ أكثر من 100 أيوة الأولى
+
+189
+00:14:17,310 --> 00:14:19,650
+و أنا رتبتهم على الـ Most Significant خلّينا نقول
+
+190
+00:14:19,650 --> 00:14:23,750
+لو ألف و متين و سبعة و تلت مية و خمسة مين الـ Most
+
+191
+00:14:23,750 --> 00:14:28,930
+Significant؟ الـ Most Significant الأكبر منزلة ..
+
+192
+00:14:28,930 --> 00:14:33,930
+بينفع تقوم تحت بعض يا شباب؟ لأ بقيت و أنا بتتكلم
+
+193
+00:14:33,930 --> 00:14:37,370
+على ال least significant digit عشان .. فاكر ان هذه
+
+194
+00:14:37,370 --> 00:14:39,490
+منزلة ما جديش يا شباب هذه اتنين أُس
+
+195
+00:14:50,150 --> 00:14:55,490
+أقل منزلة اقل
+
+196
+00:14:55,490 --> 00:15:00,690
+منزلة اقل منزلة اقل منزلة اقل منزلة
+
+197
+00:15:03,960 --> 00:15:10,860
+أي صفر صفر صفر صفر صفر صفر صفر صفر صفر صفر صفر صفر
+
+198
+00:15:10,860 --> 00:15:16,680
+صفر صفر صفر صفر صفر صفر صفر صفر صفر صفر صفر صفر
+
+199
+00:15:16,680 --> 00:15:17,680
+صفر صفر صفر صفر صفر صفر صفر صفر صفر صفر صفر صفر
+
+200
+00:15:17,680 --> 00:15:19,580
+صفر صفر صفر صفر صفر صفر صفر صفر صفر صفر صفر صفر
+
+201
+00:15:19,580 --> 00:15:23,800
+صفر صفر صفر صفر صفر صفر صفر صفر صفر صفر صفر صفر
+
+202
+00:15:23,800 --> 00:15:29,880
+صفر صفر صفر
+
+203
+00:15:29,880 --> 00:15:33,780
+صفر صفر صفر صفر صفر صفر صفر صفر صفر صفر صفرهم
+
+204
+00:15:33,780 --> 00:15:38,260
+التقوا باسمها اول bit ال output تبع ال result اللي
+
+205
+00:15:38,260 --> 00:15:41,500
+موجودة تعالى نشوف هل في عندى تنين من نفس ال length
+
+206
+00:15:41,500 --> 00:15:46,580
+عندى two operands من نفس ال length الان رتبت most
+
+207
+00:15:46,580 --> 00:15:49,360
+significant digit او ال least بما انهم التنين من
+
+208
+00:15:49,360 --> 00:15:53,080
+نفس الطول ماعندكاش مشكلة في الموضوع لكن لو كان
+
+209
+00:15:53,080 --> 00:15:59,000
+اختلفت بدك تعتمد على ال least significant digitب
+
+210
+00:15:59,000 --> 00:16:04,760
+twice or صفر or الواحد واحد واحد or الصفر واحد
+
+211
+00:16:04,760 --> 00:16:09,220
+واحد or الواحد واحد واحد or الواحد واحد واحد or
+
+212
+00:16:09,220 --> 00:16:15,200
+الواحد صفر or الصفر صفر بالنسبة لل and نفس النظام
+
+213
+00:16:15,200 --> 00:16:19,280
+صفر and الواحد صفر و هكذا شو المعكوس؟
+
+214
+00:16:21,900 --> 00:16:25,480
+أيش السلامتك؟ كله زي ما هو، مافيش اشي تغير واحد
+
+215
+00:16:25,480 --> 00:16:28,220
+and واحد واحد true and true true مافيش اشي تغير
+
+216
+00:16:28,220 --> 00:16:31,860
+فيها مطلقا وال XOR لما بيكونوا التانية متساويات
+
+217
+00:16:31,860 --> 00:16:35,900
+بتديني false XOR بتديني false لما تكونوا التانية
+
+218
+00:16:35,900 --> 00:16:42,540
+متساويات الآن صفر واحد واحد واحد وصفر واحد واحد
+
+219
+00:16:42,540 --> 00:16:48,500
+واحد صفر واحد وكده هاي هاي مثلا صفر وصفر هتكون
+
+220
+00:16:48,500 --> 00:16:58,280
+تديني صفرطيب خيك section 11 في الكتاب خلص ايش
+
+221
+00:16:58,280 --> 00:17:05,720
+المطموب؟ المطموب منك ترجع للكتاب وتشوف الأسئلة على
+
+222
+00:17:05,720 --> 00:17:13,160
+الأقل تحل من 1 ل 35 بلك
+
+223
+00:17:13,160 --> 00:17:19,360
+تسلمنا إياهم يا عيلة خلينا نشوف مع بعض الكتابو
+
+224
+00:17:19,360 --> 00:17:23,640
+تشوف الأسئلة تعالى نشوف بس على السريع نعمل zoom
+
+225
+00:17:23,640 --> 00:17:31,080
+شوية لبعض الأسئلة هاي مثلا لأ
+
+226
+00:17:31,080 --> 00:17:35,780
+هو فعلا على الصفحه تلاته و تلاتين هاي هو بدأ يعد
+
+227
+00:17:35,780 --> 00:17:40,180
+من بعد المقدمة اللي عندك ليكن بقولك الآن which of
+
+228
+00:17:40,180 --> 00:17:44,520
+these sentences are a proposition what are the
+
+229
+00:17:44,520 --> 00:17:49,500
+truth value of theseof those that are proposition
+
+230
+00:17:49,500 --> 00:17:53,400
+يعني مين من هدول proposition و إيش ال truth value
+
+231
+00:17:53,400 --> 00:17:58,340
+تبعتها لو أنا قلتلك بيان بيان بيان بيان بيان بيان
+
+232
+00:17:58,340 --> 00:17:58,580
+بيان بيان بيان بيان بيان بيان بيان بيان بيان بيان
+
+233
+00:17:58,580 --> 00:17:58,700
+بيان بيان بيان بيان بيان بيان بيان بيان بيان بيان
+
+234
+00:17:58,700 --> 00:17:58,820
+بيان بيان بيان بيان بيان بيان بيان بيان بيان بيان
+
+235
+00:17:58,820 --> 00:17:59,460
+بيان بيان بيان بيان بيان بيان بيان بيان بيان بيان
+
+236
+00:17:59,460 --> 00:18:00,640
+بيان بيان بيان بيان بيان بيان بيان بيان بيان بيان
+
+237
+00:18:00,640 --> 00:18:04,860
+بيان بيان بيان بيان بيان بيان بيان بيان
+
+238
+00:18:04,860 --> 00:18:11,840
+ب
+
+239
+00:18:15,150 --> 00:18:17,570
+بتروح تدرس الجغراف الأمريكية و بتجيبها براحتك أنا
+
+240
+00:18:17,570 --> 00:18:20,770
+مش عارف بس هنا أنا بقدر أجي أقولك خمسة زائد سبعة
+
+241
+00:18:20,770 --> 00:18:25,070
+equal عشرة is a proposition و قيمته false تمام
+
+242
+00:18:25,070 --> 00:18:31,210
+answer this question is not a proposition ليش؟
+
+243
+00:18:31,210 --> 00:18:35,750
+لأنها عبارة عن order لأنها عبارة عن order تعالى
+
+244
+00:18:35,750 --> 00:18:42,630
+نشوف هي مثلا في السؤال تمانية احنا
+
+245
+00:18:42,630 --> 00:18:44,130
+شبدنا في ال .. okay
+
+246
+00:18:47,320 --> 00:18:49,700
+بقولك في الـ8 لو كانت الـP و الـQ عبارة عن الـ
+
+247
+00:18:49,700 --> 00:18:54,580
+proposition الـP I bought lottery ticket this week
+
+248
+00:18:54,580 --> 00:19:01,660
+أنا اشتريت بطاقة نصيب لسبوع هذا مين هذي؟ الـP الـQ
+
+249
+00:19:01,660 --> 00:19:06,380
+I won the million dollar jackpot هو ربح المليون من
+
+250
+00:19:06,380 --> 00:19:11,320
+التاعة اللي هي نصيب ربح أكبر جائزة الكبرى اللي هي
+
+251
+00:19:11,320 --> 00:19:16,340
+المليون دولاريا عيني عليك يا شيخ طب حللي اي
+
+252
+00:19:16,340 --> 00:19:21,220
+proposition ايوة الانش بيروح بيقول ايه بيقول
+
+253
+00:19:21,220 --> 00:19:25,080
+express each of these propositions تعالى نشوف
+
+254
+00:19:25,080 --> 00:19:29,580
+الأول نط في ال B هو إيش بيقول ليه في B I bought a
+
+255
+00:19:29,580 --> 00:19:34,820
+lottery ticket this week I didn'tbuy a lottery
+
+256
+00:19:34,820 --> 00:19:38,880
+ticket this week انا ماشاركش لانه كمان مرة في
+
+257
+00:19:38,880 --> 00:19:43,340
+الاول اقولك انا اشتريت وخلصت تنفيها هتقوله انا
+
+258
+00:19:43,340 --> 00:19:44,860
+ماشارتش انا ماشارتش انا ماشارتش انا ماشارتش انا
+
+259
+00:19:44,860 --> 00:19:44,940
+ماشارتش انا ماشارتش انا ماشارتش انا ماشارتش انا
+
+260
+00:19:44,940 --> 00:19:45,980
+ماشارتش انا ماشارتش انا ماشارتش انا ماشارتش انا
+
+261
+00:19:45,980 --> 00:19:46,240
+ماشارتش انا ماشارتش انا ماشارتش انا ماشارتش انا
+
+262
+00:19:46,240 --> 00:19:50,380
+ماشارتش انا ماشارتش انا ماشارتش انا ماشارتش انا
+
+263
+00:19:50,380 --> 00:19:55,660
+ماشارتش انا ماشارتش انا ماشارتش انا ماشارتش انا
+
+264
+00:19:55,660 --> 00:19:57,400
+ماشارتش ا
+
+265
+00:20:06,750 --> 00:20:09,070
+ماشاء الله عليك اقولكوا مرة طب واحديك عشان انا
+
+266
+00:20:09,070 --> 00:20:13,210
+عارف اجاوب صح ولا غلط نقيم ال proposition اللي انت
+
+267
+00:20:13,210 --> 00:20:18,350
+بتقوله على فرض ان هو proposition اه شباب if I
+
+268
+00:20:18,350 --> 00:20:25,410
+didn't buy a lottery ticket this week then I will
+
+269
+00:20:25,410 --> 00:20:31,550
+not I would notيعني إذا أنا ما شاركتش البطاقة مش
+
+270
+00:20:31,550 --> 00:20:35,750
+هربح جهازة المليون، بس، مصبوط؟ في الأقل بالكلام،
+
+271
+00:20:35,750 --> 00:20:39,670
+كلام بسيط، بتقدر تحل طبعا، أخر شغلة بدأ أقولها يا
+
+272
+00:20:39,670 --> 00:20:43,370
+شباب طيب، هاي، بيجي أقول الـdetermine على سبيل
+
+273
+00:20:43,370 --> 00:20:45,350
+المثال سؤال 16، determine whether these by
+
+274
+00:20:45,350 --> 00:20:50,330
+conditional are true or false؟ وين ال by
+
+275
+00:20:50,330 --> 00:20:52,890
+conditional؟ كلهم، من إيه لدي هدول يبقوا by
+
+276
+00:20:52,890 --> 00:20:55,990
+conditional؟ إيش مطلوب منك؟ تعمل evaluation
+
+277
+00:20:58,500 --> 00:21:05,720
+الـ B والـ Evaluation للـ Q الـ Proposition من
+
+278
+00:21:05,720 --> 00:21:09,780
+بعدهم اقترح اتنين زائد اتنين equal اربعة true واحد
+
+279
+00:21:09,780 --> 00:21:13,700
+زائد واحد equal اتنين true true in biconditional
+
+280
+00:21:13,700 --> 00:21:19,900
+true true true دعونا نشوف الأخيرة صفر أكبر من واحد
+
+281
+00:21:19,900 --> 00:21:26,180
+false والتنين أكبر من واحد trueby conditional
+
+282
+00:21:26,180 --> 00:21:29,940
+false by conditional true false false by
+
+283
+00:21:29,940 --> 00:21:33,380
+conditional by conditional وبالتالي هذه الأسئلة
+
+284
+00:21:33,380 --> 00:21:38,120
+ليش أنا بقولك حل؟ لأن عشان تقدر تمرس إيدك على وفهم
+
+285
+00:21:38,120 --> 00:21:40,420
+ال proposition لأن الأسئلة في الآخر الامتحانات و
+
+286
+00:21:40,420 --> 00:21:44,300
+الكوزات هتيجي من هنا بتوسع مداركك أكتر كل ما قرأت
+
+287
+00:21:44,300 --> 00:21:49,640
+من الأسئلة فيك تحل من بعد 25 أو 35 عادي جرب مافيش
+
+288
+00:21:49,640 --> 00:21:53,460
+مشكلة في الموضوع مش مستحيلة explain without using
+
+289
+00:21:53,460 --> 00:21:58,200
+the truth tableدخل في الإثبات الرياضي و احنا لسه
+
+290
+00:21:58,200 --> 00:22:03,400
+مالاش ندخل في الموضوع هذا بي او نت كيو and is it
+
+291
+00:22:03,400 --> 00:22:06,980
+true when بي او نت كيو have the same truth value؟
+
+292
+00:22:06,980 --> 00:22:10,240
+ايش قاعد بقولك في السؤال هذا؟ بقولك لو كانت بي و
+
+293
+00:22:10,240 --> 00:22:15,980
+كيو و ار لهم نفس القيمة تمام؟ وهي false
+
+294
+00:22:20,360 --> 00:22:25,120
+تمام؟ بدون جدول الاحتمالات اثبتلي او ادينا القيمة
+
+295
+00:22:25,120 --> 00:22:28,780
+تبعتها ايش ممكن تروح تساوي؟ بدك تعود مكان كل P وQ
+
+296
+00:22:28,780 --> 00:22:35,180
+وR بال value بال truth value تمام؟ بال truth value
+
+297
+00:22:35,180 --> 00:22:37,820
+و تشوف هل فعليا هتصل معاك على true ولا لأ
+
+298
+00:22:37,820 --> 00:22:41,360
+بالمناسبة في اخر الكتاب هتلاقي الحلول للمسائل
+
+299
+00:22:41,360 --> 00:22:48,140
+الفردية عشان هيك هنعتمد اعتماد رئيسي علشان ..على
+
+300
+00:22:48,140 --> 00:22:52,260
+الكتاب .. لأ لأ .. اسمها .. على الكتاب حل جدر ما
+
+301
+00:22:52,260 --> 00:22:55,340
+بتقدر من الأسئلة و غالبا يا أستاذ هتلاقي واحد و
+
+302
+00:22:55,340 --> 00:22:59,060
+اتنين في الأسئلة متشابهات تلاتة أو أربعة متشابهات
+
+303
+00:22:59,060 --> 00:23:05,240
+الفرق بينهم مش كبير فانت ماتغشش نفسك وتروح تحفظ
+
+304
+00:23:05,240 --> 00:23:10,040
+الأسئلة من هناك لأن الفاضي هتكون الأمر طيب هذا
+
+305
+00:23:10,040 --> 00:23:16,380
+الموضوع الكتاب و خلصنا منه من التطبيقات المهمة
+
+306
+00:23:19,560 --> 00:23:24,760
+لأ ال propositional logic اسم الكتاب تبعنا
+
+307
+00:23:24,760 --> 00:23:28,140
+discrete mathematics and its application
+
+308
+00:23:28,140 --> 00:23:32,000
+والتطبيقات تبعتها الأهم من ال application المهمة
+
+309
+00:23:32,000 --> 00:23:35,800
+لل logical أو لل propositional logic دايما يا شباب
+
+310
+00:23:35,800 --> 00:23:42,170
+كلام الناس بيحتمل التأويلالكلام بين البشر ..
+
+311
+00:23:42,170 --> 00:23:46,470
+الكلام بين البشر عادة بيحتمل التأويل بمعنى آخر
+
+312
+00:23:46,470 --> 00:23:51,910
+فلان جال كلمتين ممكن تتحدهمش اشتيما، مصدق؟ يقول
+
+313
+00:23:51,910 --> 00:23:54,930
+غلط في حاجة، بينها واحد تاني يقولك لأ، هو كان جاسس
+
+314
+00:23:54,930 --> 00:23:59,130
+يقول كذا، هنا احنا بنقول ان في ambiguity، في دائما
+
+315
+00:23:59,130 --> 00:24:03,650
+في نوع من الغموض او في احتمالية لأكثر من تفسير في
+
+316
+00:24:03,650 --> 00:24:08,410
+الكلام، يعني لو اجى فلان قال ما شاء الله فلان جمر
+
+317
+00:24:15,010 --> 00:24:18,490
+يا عيني عليك، شوف كيف اشتغل الـ Logic، تمام؟ واحد
+
+318
+00:24:18,490 --> 00:24:22,650
+قال فهم الكلمة، فهم الكلمة على أن وجهه منور زي
+
+319
+00:24:22,650 --> 00:24:26,870
+الجمر، وواحد تاني مخه جافل، جافل خالص، يعني دهن
+
+320
+00:24:26,870 --> 00:24:29,350
+وقيدا لما زهجان، جالك يعني هو اللي بيكون فوق
+
+321
+00:24:29,350 --> 00:24:33,430
+الصحابة في رص الشهر الهجري، تمام؟ شوف اختلف
+
+322
+00:24:33,430 --> 00:24:39,130
+التأويل، ليش؟ لأن غالبا لغة الإنسان الكلمات فيها
+
+323
+00:24:39,130 --> 00:24:43,430
+معاني، ودائما ال context نص الكلام أو سياق الكلام
+
+324
+00:24:43,430 --> 00:24:48,370
+له معنى،لكن هذا للأسف في الرياضيات في الكمبيوتر في
+
+325
+00:24:48,370 --> 00:24:52,850
+الهندسة هذا الكلام مالوش وزن اللي مطلوب فيه
+
+326
+00:24:52,850 --> 00:24:56,610
+اختخاصات يا بيض يا سودة تروح و فوص مافيش علاقة غير
+
+327
+00:24:56,610 --> 00:25:00,130
+هيكاد عشان هيكاد نتعلم ال proposition واحد زائد
+
+328
+00:25:00,130 --> 00:25:03,570
+واحد بيساوي اتنين خلاص اما بيقول الله تروح و فوص
+
+329
+00:25:03,570 --> 00:25:07,330
+تبع للشغلات المنطقية او الحقيقية اللي احنا بنتعامل
+
+330
+00:25:07,330 --> 00:25:09,250
+معاها من أهم التطبيقات
+
+331
+00:25:11,860 --> 00:25:15,700
+تبعت الـ propositional logic هاي ال sentence هاي
+
+332
+00:25:15,700 --> 00:25:19,940
+لما بتروح انت تترجم الجملة .. تترجم الجملة عشان
+
+333
+00:25:19,940 --> 00:25:24,580
+تشيل عنها اي غموض يعني مثلا بيجي يقولك you can
+
+334
+00:25:24,580 --> 00:25:28,600
+access the internet from campus انت يحققلك الوصول
+
+335
+00:25:28,600 --> 00:25:32,600
+للإنترنت في داخل حرم الجامعة لو كنت من تخصص علوم
+
+336
+00:25:32,600 --> 00:25:39,380
+الحسوببغض النظر الان هذا الكلام .. هذا الكلام عشان
+
+337
+00:25:39,380 --> 00:25:42,800
+حد يشيجي واحد يراجعنا فيه ويقول طب لو كانت تخصص
+
+338
+00:25:42,800 --> 00:25:46,840
+multimedia لو كانت تخصص كذا ايش بنصير؟ بده يتحول ل
+
+339
+00:25:46,840 --> 00:25:51,340
+proposition لازم يتحول ل proposition الان كام
+
+340
+00:25:51,340 --> 00:25:55,180
+statement موجود عندي انا يا شباب تعالى نشوف you
+
+341
+00:25:55,180 --> 00:25:59,580
+can access the internet from campus معناته انا هاي
+
+342
+00:25:59,580 --> 00:26:00,540
+في عندي اول جملة
+
+343
+00:26:04,340 --> 00:26:08,480
+خلّيني أسميها ADP أو أي رمز بدك إياه وكامه في عندي
+
+344
+00:26:08,480 --> 00:26:14,880
+only if معناته أنا بتكلم high connector اللي
+
+345
+00:26:14,880 --> 00:26:19,860
+هي ال implication you are a computer science major
+
+346
+00:26:19,860 --> 00:26:25,960
+لو كان انت تخصصك high Q مفادها
+
+347
+00:26:25,960 --> 00:26:32,280
+لو انت كنت computer science معناته
+
+348
+00:26:32,280 --> 00:26:32,780
+بتقدر
+
+349
+00:26:36,950 --> 00:26:41,650
+B لو انت كنت في Computer Science مانعته بتحققلك
+
+350
+00:26:41,650 --> 00:26:45,590
+تتصل بالإنترنت من داخل حرم الجامعة لهذا الكلام
+
+351
+00:26:45,590 --> 00:26:48,790
+ماحدش هيجي يراجعك فيه ويقولك جد ايه لأن ال
+
+352
+00:26:48,790 --> 00:26:52,830
+proposition يا إما true يا false الأن بتحقق الأولى
+
+353
+00:26:52,830 --> 00:26:59,390
+Q كان بـTrue و False مش مجال والتانيةحسب layout
+
+354
+00:26:59,390 --> 00:27:04,170
+وبالتالي فعليا هذه واحدة من أهم التطبيقات موضوع ال
+
+355
+00:27:04,170 --> 00:27:08,570
+translation واحنا شوفنا المرة الماضية بالمثال هذا
+
+356
+00:27:08,570 --> 00:27:13,250
+ايش قولنا بالمثال هذا؟ قولنا بكل بساطة ممنوع تركب
+
+357
+00:27:13,250 --> 00:27:21,210
+ال cyclone إلا لو كنت أكبر من 16 سنة أو طولك أكبر
+
+358
+00:27:21,210 --> 00:27:24,830
+من 4 أقدام ممنوع
+
+359
+00:27:26,480 --> 00:27:29,940
+أه لا يمكنك .. عفوا .. لا يمكنك ركوب الـ Cyclone
+
+360
+00:27:29,940 --> 00:27:32,900
+لو كنت أقل من أربع أقدام يعني لو كنت أكبر من أربع
+
+361
+00:27:32,900 --> 00:27:38,060
+أقدام .. مسموح لك .. لو كان عمرك فوق السطن عشر سنة
+
+362
+00:27:38,060 --> 00:27:41,740
+و أنت أقل من أربع أقدام .. مسموح لك .. وبالتالي
+
+363
+00:27:41,740 --> 00:27:46,080
+الآن الجملة اللي موجودة عندها .. you can ride the
+
+364
+00:27:46,080 --> 00:27:51,420
+cyclone بي .. معناته I نط ال بي .. لأنها منفية ..
+
+365
+00:27:51,420 --> 00:27:55,040
+you cannot .. مظبوط؟ .. بدك تفرج .. دائما تفصل
+
+366
+00:27:55,040 --> 00:27:55,580
+النفي ..
+
+367
+00:28:07,250 --> 00:28:12,870
+تقريبا تقريبا تقريبا تقريبا
+
+368
+00:28:12,870 --> 00:28:16,850
+تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا
+
+369
+00:28:16,850 --> 00:28:17,370
+تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا
+
+370
+00:28:17,370 --> 00:28:17,450
+تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا
+
+371
+00:28:17,450 --> 00:28:17,590
+تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا
+
+372
+00:28:17,590 --> 00:28:24,570
+تقريبا تقريبا تقريبا تقريبا تقريبا تقريب
+
+373
+00:28:28,860 --> 00:28:33,320
+على الأقل لا ال list على الأقل ال list nothing إلا
+
+374
+00:28:33,320 --> 00:28:36,860
+لو كنت .. إلا لو كنت هي ال condition التاني هذا ما
+
+375
+00:28:36,860 --> 00:28:43,100
+بنقولك و هينسميها ال R من المحصلة يا شباب من
+
+376
+00:28:43,100 --> 00:28:49,760
+المحصلة نفل B هيك
+
+377
+00:28:49,760 --> 00:28:55,140
+مظبوط انت مش هتركب ال cyclone ايش اللي جابله
+
+378
+00:28:55,140 --> 00:28:57,040
+الشروط
+
+379
+00:29:01,290 --> 00:29:10,310
+Q and or طب لو اتحققت اي واحدة منهم اه ممتاز طب
+
+380
+00:29:10,310 --> 00:29:15,110
+تعالى نشوف هذه unless you are older than not ال R
+
+381
+00:29:15,110 --> 00:29:22,490
+اذا كان عمرك او قولك اقل من اربع اقدام و عمرك اقل
+
+382
+00:29:22,490 --> 00:29:25,970
+من اربعة عشر سنة او اقل من ست عشر سنة مش هتركب
+
+383
+00:29:25,970 --> 00:29:35,020
+السايكلونانت شوف لو حطيت القرش كان بيصير؟ لو كان
+
+384
+00:29:35,020 --> 00:29:41,600
+.. لو كان طولك أقل من أربع أقدام أو عمرك أقل من 14
+
+385
+00:29:41,600 --> 00:29:47,700
+سنة من 16 سنة مش هتركب لأ مش شايف الكلام اللي
+
+386
+00:29:47,700 --> 00:29:54,240
+بينجالك اللي بينجالك كانت تالي انت هتركب
+
+387
+00:29:54,240 --> 00:29:59,220
+ال cyclone هذي في حالة واحدة فقط لو كان طولكأكبر
+
+388
+00:29:59,220 --> 00:30:06,080
+من أربعة أو عمرك أكبر من 16 نفيها .. نفيها مش
+
+389
+00:30:06,080 --> 00:30:10,220
+هترجع بال Cyclone المحاصلة لو كان طولك أقل من أربع
+
+390
+00:30:10,220 --> 00:30:16,620
+أقدام و عمرك أقل من 16 لأن الأكبر من 16 هتستثنى
+
+391
+00:30:16,620 --> 00:30:19,760
+لمين؟ للطول .. كانت بغطي الموضوع للطول فانت
+
+392
+00:30:19,760 --> 00:30:24,280
+باكتلفيها فتتحول ل end الترجمة أيه مهمة جدا يا
+
+393
+00:30:24,280 --> 00:30:28,250
+شباب في فهم الكلام إيه اللي موجود عنها؟أنا رجعت
+
+394
+00:30:28,250 --> 00:30:33,530
+الرجوع في الموضوع طيب دعنا نشوف التطبيق التاني وين
+
+395
+00:30:33,530 --> 00:30:38,170
+مهمنا الأهم التطبيقات المهمة في ال system
+
+396
+00:30:38,170 --> 00:30:41,050
+specification الناس اللي بتشتغل في هندسة البرمجيات
+
+397
+00:30:41,050 --> 00:30:44,710
+أو تصنيع البرامج أو حتى في تصنيع ال hardware مهم
+
+398
+00:30:44,710 --> 00:30:48,750
+جدا من البداية حدد متطلبات النظام أو خصائص النظام
+
+399
+00:30:48,750 --> 00:30:53,950
+خصائص النظام برضه هذه ممكن تحتوي تحتمل تأويل او
+
+400
+00:30:53,950 --> 00:31:00,840
+ممكن ينتبه نوع من الغموض مثلهاجي أقول إنه البرنامج
+
+401
+00:31:00,840 --> 00:31:07,180
+بيقبل رقم، شو طبيعة الرقم هذا؟ لأن الرقم إنتج
+
+402
+00:31:07,180 --> 00:31:11,200
+الرقم، و الـ Double رقم ولا لا؟ وبالتالي هذا
+
+403
+00:31:11,200 --> 00:31:14,880
+الكلام لا ينفعش، لازم يتوضح بشكل الكلام أكثر دقة
+
+404
+00:31:14,880 --> 00:31:18,180
+منه، لما بنجيب نمتقل لموضوع الكلام اللي بالشكل
+
+405
+00:31:18,180 --> 00:31:23,670
+هذا، لازم أحمل مواصفات البرنامجas propositional
+
+406
+00:31:23,670 --> 00:31:26,690
+logic لأن في ال logic كمان مرة شباب يا true يا
+
+407
+00:31:26,690 --> 00:31:29,290
+false واش مجال وبالتالي انا بقدر اتكلم على النظام
+
+408
+00:31:29,290 --> 00:31:32,810
+موافق المواصفات او يطابق المواصفات ولا لا يطابق
+
+409
+00:31:32,810 --> 00:31:40,510
+تعالى نشوف المثال اللى موجود عندى هان the
+
+410
+00:31:40,510 --> 00:31:47,150
+automated reply الرد القالي cannot send
+
+411
+00:31:49,570 --> 00:31:53,610
+The automated reply cannot send هذه الجملة الأولى
+
+412
+00:31:53,610 --> 00:31:59,790
+و لا شو رايك؟ Not ال بي يعني و كأن ال بي هي عبارة
+
+413
+00:31:59,790 --> 00:32:08,550
+The automated reply sent تم إرسال الرد الآلي When
+
+414
+00:32:08,550 --> 00:32:09,870
+ال connector
+
+415
+00:32:13,380 --> 00:32:18,340
+والـ F وإذا بترجع مهيأة Q and P وكانت واحدة من ال
+
+416
+00:32:18,340 --> 00:32:20,700
+alternatives اللي ممكن تكتب عليها ال implication
+
+417
+00:32:20,700 --> 00:32:29,820
+طيب ال file system is full Q يعني هو مش قاعد بيقول
+
+418
+00:32:29,820 --> 00:32:33,800
+إيه بيقول إن الرساء أو الرد الآلي مش هيتم لو كان
+
+419
+00:32:33,800 --> 00:32:39,720
+النظام أو ال file مليان تعالي أعملها proposition
+
+420
+00:32:41,130 --> 00:32:44,230
+عشان مايظلش فيها اي نوع من الغموض بدي اجي أقول ال
+
+421
+00:32:44,230 --> 00:32:49,430
+B هي ال automated reply و ال Q ال file system is
+
+422
+00:32:49,430 --> 00:32:55,070
+full نقطة ال B cannot be sent تمام؟ و في الآخر
+
+423
+00:32:55,070 --> 00:33:02,040
+هتصير هيكد if the file system is full thenThe
+
+424
+00:33:02,040 --> 00:33:08,600
+automated reply will not be sent. مظبوط او لا؟
+
+425
+00:33:08,600 --> 00:33:12,980
+وبالتالي انا فهمت من ال win انه قاعد اتكلم على ال
+
+426
+00:33:12,980 --> 00:33:15,300
+connector اللي هي ال implication من يقول إلى
+
+427
+00:33:15,300 --> 00:33:25,320
+التاني احنا كانت عندنا Q وين ال B؟ Q تتحقق
+
+428
+00:33:25,320 --> 00:33:30,020
+لما تتحقق ال B من ال B اللي عندي هنا يا شباب؟
+
+429
+00:33:35,080 --> 00:33:41,660
+وبالتالي أصبحت عندى Q implies نط ال B إذا النظام
+
+430
+00:33:41,660 --> 00:33:46,960
+full أو ال file system is full الرد القالي مش
+
+431
+00:33:46,960 --> 00:33:51,440
+هيشتغل أو الرد القالي مش هيرسل تقدرش تجلب الجملة
+
+432
+00:33:51,440 --> 00:33:55,940
+لأن الجملة فيها واحدة تقول إلى التانية تمام؟
+
+433
+00:34:02,310 --> 00:34:04,550
+بارض من المسائل اللي هي علاقة بالـ System
+
+434
+00:34:04,550 --> 00:34:07,850
+Specification أو خصائص النظام أو مواصفات النظام
+
+435
+00:34:07,850 --> 00:34:11,790
+لما بيجي بقولك افحصل هل المتطلبات هذه consistent
+
+436
+00:34:11,790 --> 00:34:15,750
+مع بعضها ولا لأ متوافقة مع بعضها ولا لأ لأن
+
+437
+00:34:15,750 --> 00:34:19,630
+المفروض ان اي نظام مايكونش فيه تناقض مصبوط ولا لأ
+
+438
+00:34:19,630 --> 00:34:23,410
+يعني يؤدي دايما ان ال system شغال بشكل كويس تعالى
+
+439
+00:34:23,410 --> 00:34:27,850
+نشوف بيجي بقوللي determine whether these system
+
+440
+00:34:27,850 --> 00:34:29,670
+specifications are consistent
+
+441
+00:34:53,560 --> 00:34:59,760
+الرسالة التشخيصية مستخدمة في الـ Bufferor it is
+
+442
+00:34:59,760 --> 00:35:05,840
+retransmitted برضه انا هاي فيه عندي in the buffer
+
+443
+00:35:05,840 --> 00:35:09,180
+هاي الرسالة الأولى او ال proposition الأول هاي
+
+444
+00:35:09,180 --> 00:35:14,460
+connector و هاي retransmitted لو انا بدأ اقول ان
+
+445
+00:35:14,460 --> 00:35:19,060
+هادي P و هادي Q و هاي فيه بينهم or معناته ال
+
+446
+00:35:19,060 --> 00:35:25,980
+proposition الأول P or Q صح ال specification
+
+447
+00:35:25,980 --> 00:35:32,680
+التانيDiagnostic message is not فيها نفي stored in
+
+448
+00:35:32,680 --> 00:35:39,300
+the buffer نفي الـB معناته هي نط الـB كمان مرة ال
+
+449
+00:35:39,300 --> 00:35:44,680
+specification الأول والثالث الثاني الثالث if if
+
+450
+00:35:44,680 --> 00:35:49,400
+معناته فيها communication مصبوط connector ال
+
+451
+00:35:49,400 --> 00:35:53,880
+diagnostic message is stored in the buffer بيه
+
+452
+00:35:53,880 --> 00:35:56,240
+then
+
+453
+00:35:58,170 --> 00:36:01,630
+retransmitted it is retransmitted Q وبالتالي ال
+
+454
+00:36:01,630 --> 00:36:08,150
+proposition الأخير بتقول إلى Q عشان افحص ال
+
+455
+00:36:08,150 --> 00:36:11,110
+consistency تبعتهم او التناسق تبعتهم ال parameters
+
+456
+00:36:11,110 --> 00:36:14,370
+high او تبعت ال specification high بدي اعتمد على
+
+457
+00:36:14,370 --> 00:36:18,450
+مين يا شباب؟ بدي اعتمد على القيم المنطقية القيم
+
+458
+00:36:18,450 --> 00:36:24,130
+المنطقية لمين؟الـ B أو الـ Q أول حاجة المفروض أن
+
+459
+00:36:24,130 --> 00:36:27,350
+تتفكر فيها تتطلع في التلاتة الـ Proposition
+
+460
+00:36:27,350 --> 00:36:32,410
+الموجودة قدامك مين أكثر variable بأثر في التلاتة
+
+461
+00:36:32,410 --> 00:36:37,850
+الموجودة بي و لا كيو؟ بي بيعني تحاول تركز شغلك
+
+462
+00:36:37,850 --> 00:36:42,070
+وين؟ مع الـ B لان واضح أن الـ B العامل أكثر تأثيرا
+
+463
+00:36:42,070 --> 00:36:48,610
+في التلات خصائص الموجودة طيب بي بي هذه إما هتاخد
+
+464
+00:36:48,610 --> 00:36:53,610
+trueأو حتى أخد الـ False في غير هيك وبالتالي الأمر
+
+465
+00:36:53,610 --> 00:36:58,570
+بسيط تعالى نشوف لو قلنا ان ال B equal true لو
+
+466
+00:36:58,570 --> 00:37:05,410
+افترضت ان ال B equal true ايش هدا هيكون؟ true لو
+
+467
+00:37:05,410 --> 00:37:12,990
+هدا false والتالت ال true implies Q الله يعطيك
+
+468
+00:37:12,990 --> 00:37:17,210
+العافية true implies شغل مجهولة متقدرش تحديها ال
+
+469
+00:37:17,210 --> 00:37:22,540
+truth valueمعناته انا في عندى مشكلتها وفي عند
+
+470
+00:37:22,540 --> 00:37:27,100
+القيمتين هدول في بينهم تناقض وبالتالي بقدرش اتكلم
+
+471
+00:37:27,100 --> 00:37:31,360
+على ال consistency تبع النظام بوضح .. هيك بناء على
+
+472
+00:37:31,360 --> 00:37:34,380
+ال truth على ال true value بتاعة ال P بقدرش اخد
+
+473
+00:37:34,380 --> 00:37:41,440
+decision طيب دعالى نشوف الحالة التانية لو
+
+474
+00:37:41,440 --> 00:37:48,620
+قولت هذه false معناته ال output مش مجهولة Qالـ
+
+475
+00:37:48,620 --> 00:37:52,560
+output Q مش مجهولة مظهور ولا لأ؟ هتعتبد اعتباد كله
+
+476
+00:37:52,560 --> 00:38:03,340
+على الـ Q طيب hand true و hand false implies أي
+
+477
+00:38:03,340 --> 00:38:11,200
+حاجة أذكرك true implies true true true implies
+
+478
+00:38:11,200 --> 00:38:15,560
+false false الحالة الوحيدة اللي موجودة false
+
+479
+00:38:15,560 --> 00:38:22,820
+implies truetrue false implies false true هذه
+
+480
+00:38:22,820 --> 00:38:26,020
+الحالة الوحيدة هل هي هذه احنا عمالا بنقول هنا
+
+481
+00:38:26,020 --> 00:38:30,500
+false وبالتالي هذه true تعالى اطلع في ال values
+
+482
+00:38:30,500 --> 00:38:37,200
+اللى موجود عندك شو واضحها احسن من جدل واضح ان في
+
+483
+00:38:37,200 --> 00:38:41,880
+اعتمادية كبيرة على قيمة ال B ومش بس هيك كمان لما
+
+484
+00:38:41,880 --> 00:38:46,930
+بتكون قيمة ال B falseبرضه اللى فوق بقدر احصل على
+
+485
+00:38:46,930 --> 00:38:50,610
+قيمة لاحظوا ان علامة المجهول في المثال السابق لما
+
+486
+00:38:50,610 --> 00:38:54,710
+كانت false اختفت بين جسين يعني صار النظام واضح اما
+
+487
+00:38:54,710 --> 00:38:58,290
+true او false و بقدر اتكلم ان العناصر هدولا
+
+488
+00:38:58,290 --> 00:39:02,850
+Consistence او متناسقات تبعل ل truth value او when
+
+489
+00:39:02,850 --> 00:39:04,790
+b is false
+
+490
+00:39:12,640 --> 00:39:16,480
+طبعا الخطوات كمان مرة انا روحت وزعت الرموز تبعتي
+
+491
+00:39:16,480 --> 00:39:20,440
+الجمل اللي حددت الجمل اللي موجودة بعد هيكسرت اتدور
+
+492
+00:39:20,440 --> 00:39:24,620
+هاي ال three proposition اللي موجودة عندى PRQ نط
+
+493
+00:39:24,620 --> 00:39:29,400
+ال P بي implies Q هيهم و احد قالت بدي اخزن او بدي
+
+494
+00:39:29,400 --> 00:39:31,980
+ادى قيمة بحيث ان ال specification هاد تصير true
+
+495
+00:39:31,980 --> 00:39:37,540
+متى ممكن يصيروا true كلهم مش هصير فيه true الا غير
+
+496
+00:39:37,540 --> 00:39:40,420
+لو انا كانت ال P اخدت
+
+497
+00:39:41,750 --> 00:39:44,830
+false هنا لو كانت الـ B أخدت false وبالتالي هي
+
+498
+00:39:44,830 --> 00:39:47,770
+true true يعني أصبح غالبيتهم أخدت قيمة true
+
+499
+00:39:47,770 --> 00:39:50,750
+وبالتالي الجملة الأخيرة بقدر أقول على ال system
+
+500
+00:39:50,750 --> 00:39:56,250
+اللي عندي أنا consistency تبعل قيمة true برضه من
+
+501
+00:39:56,250 --> 00:39:59,470
+التطبيقات اللي موجودة يعني هذا التطبيق رغم أنه
+
+502
+00:39:59,470 --> 00:40:05,890
+مقدس الشباب ترجمة ترجمة system specification تطبيق
+
+503
+00:40:05,890 --> 00:40:10,160
+التالت في ال logical أو في ال boolean searchكلكم
+
+504
+00:40:10,160 --> 00:40:13,360
+بتستخدموا الـ Google عشان تقوموا بالبحث لو أنت
+
+505
+00:40:13,360 --> 00:40:22,600
+روحت كتابة discrete mathematics في محرك
+
+506
+00:40:22,600 --> 00:40:27,060
+البحث، إيش اللي هيطلع؟ إيش الناتج اللي هيطلع عندك؟
+
+507
+00:40:27,060 --> 00:40:31,500
+كبشة، ياريت تقض علي بمنطق، عشان الكبشة هذه في
+
+508
+00:40:31,500 --> 00:40:36,040
+السوق، مش هذه المتعلق
+
+509
+00:40:36,040 --> 00:40:40,320
+بالنص اللي دخلته، كيف تمتعامل مع النص؟أولاً النص
+
+510
+00:40:40,320 --> 00:40:47,520
+هذا تم تقسيمه بناء على الـ space لـ two statements
+
+511
+00:40:47,520 --> 00:40:55,340
+كلمات والرابق اللي بينهم or لأنه هدف محرك البحث ..
+
+512
+00:40:55,340 --> 00:41:01,740
+هدف محرك البحث ازودك بأكبر نتيجة ممكنة بأكبر عدد
+
+513
+00:41:01,740 --> 00:41:05,520
+من النتائج ليش؟ عشان تقدر تلاقي القيامة اللي بدك
+
+514
+00:41:05,520 --> 00:41:09,390
+إياها أو الشغلات اللي بتدور عليهاطيب هذا متى بيكون
+
+515
+00:41:09,390 --> 00:41:13,330
+النتيجة true؟ لو كان النص أو الـ metadata بتحتوي
+
+516
+00:41:13,330 --> 00:41:18,750
+على discrete أو mathematics أو التنتين مع بعض عشان
+
+517
+00:41:18,750 --> 00:41:20,790
+هيك لو فتشت في ال google search في ال pages اللي
+
+518
+00:41:20,790 --> 00:41:24,650
+قلت معاك هتلاقي انه بعد شوية سيحرضك ال discrete
+
+519
+00:41:24,650 --> 00:41:29,070
+لحال و ال mathematics لحال بس مش هجيبلك ولا شغلة
+
+520
+00:41:29,070 --> 00:41:33,110
+اللي لها علاقة مثلا بال biology ليش؟ لأنها مش من
+
+521
+00:41:33,110 --> 00:41:37,320
+ضمن ال terms اللي موجودة عندك هنابدك إياهم يفترضهم
+
+522
+00:41:37,320 --> 00:41:44,140
+كلمة واحدة استخدم علامات التنصيص على كل الجملة
+
+523
+00:41:44,140 --> 00:41:47,880
+بيصير هذا بتعامل معاه as one parameter discrete
+
+524
+00:41:47,880 --> 00:41:53,240
+mathematics as one word بيصير يدور عليها وإذا أنت
+
+525
+00:41:53,240 --> 00:41:57,760
+بدك تستخدم another condition صار بإمكانك تستخدم ال
+
+526
+00:41:57,760 --> 00:42:01,660
+and أو ال or و تحقق ال second condition
+
+527
+00:42:06,510 --> 00:42:11,810
+وطبعا ال output او ال result بتطلع تبعا لل and و
+
+528
+00:42:11,810 --> 00:42:15,970
+ال or عشان يخلّي النتيجة اللي عندك اكثر فاهمة او
+
+529
+00:42:15,970 --> 00:42:21,670
+اكثر منطقية التقنية الرابعة في ال gates في
+
+530
+00:42:21,670 --> 00:42:27,930
+البوابات البوابات الإلكترونيةDigital Design تذكروا
+
+531
+00:42:27,930 --> 00:42:30,850
+المحلقاء الأول لما قلنا الـ Discrete Mathematics
+
+532
+00:42:30,850 --> 00:42:32,950
+مهمة للناس اللي بتشغل في ال Computer Science
+
+533
+00:42:32,950 --> 00:42:36,170
+Computer Engineering أو ال Electrical Engineering
+
+534
+00:42:36,170 --> 00:42:40,030
+ومن أول المساقات اللي بتدوسها مادة أو مساق اسمه
+
+535
+00:42:40,030 --> 00:42:43,930
+تصميم منطقي عشان نقدر يصمم اللوحات أو يصمم برامج
+
+536
+00:42:43,930 --> 00:42:47,730
+صح التصميم المنطقي بيعتمد على البوابات اللي موجودة
+
+537
+00:42:47,730 --> 00:42:55,400
+قدامنا النفي اسمها inverter تجلب التيارةالـ OR
+
+538
+00:42:55,400 --> 00:43:00,260
+والـ AND طبعا ال XOR طب ما هي ال XOR أساسا مكوّلة
+
+539
+00:43:00,260 --> 00:43:10,380
+ما بين الجميع لكن فيها لها gate B
+
+540
+00:43:10,380 --> 00:43:16,400
+و Q و ال output B XOR Q هذه صارت من الرسمات
+
+541
+00:43:16,400 --> 00:43:20,600
+المتداولة على الرقم اللي هي compound proposition
+
+542
+00:43:20,600 --> 00:43:24,350
+أو compound gateبرضه من الشغلات او التطبيق الخامس
+
+543
+00:43:24,350 --> 00:43:29,950
+مذكور في الكتاب بس ماحبش اجيبه الـ
+
+544
+00:43:29,950 --> 00:43:36,310
+Basel Logic الألغاز المنطقية انت الآن لو جالنا لك
+
+545
+00:43:36,310 --> 00:43:42,370
+في فلاح على ضفة نهر تمام؟ يارا تجيبتوا اه؟ هل فطر
+
+546
+00:43:42,370 --> 00:43:45,810
+الفلاحين فيه احنا؟ بس لو انت فكرت فيها بمنطق بتحل
+
+547
+00:43:45,810 --> 00:43:51,660
+الان الفلاح هذا معاه كلبو معاه وزة و معاه شوية
+
+548
+00:43:51,660 --> 00:43:57,040
+شعير أو شوية جمح و بده ينتقل بالقارب على الناحية
+
+549
+00:43:57,040 --> 00:44:01,560
+التانية و مابيقدرش اللي غير ياخد شغلة واحدة معاه
+
+550
+00:44:01,560 --> 00:44:08,460
+الآن ال rules اللي موجودة إذا الكلب و الوزة مع بعض
+
+551
+00:44:08,460 --> 00:44:16,640
+هيكلها إذا الوزة و الجمح هيتاكل الآن الحل الوحيد و
+
+552
+00:44:16,640 --> 00:44:22,100
+إذا طرك الجمح لوحدهممكن ينسرج، مظبوط، اي شروق،
+
+553
+00:44:22,100 --> 00:44:24,740
+طبعا انا ممكن اكون مش حافظها كويس، بس في الآخر،
+
+554
+00:44:24,740 --> 00:44:28,800
+بناء على ايش هيبدأ تتحلل؟ بناء على الكلام اللي انا
+
+555
+00:44:28,800 --> 00:44:34,460
+ذكرته، فيه تناقضات، preposition، مظبوط، بدك تحط
+
+556
+00:44:34,460 --> 00:44:38,080
+بحيث ان تبقى ال statement دائما معاكيش، true،
+
+557
+00:44:38,080 --> 00:44:42,140
+مظبوط ولا لا؟ وهي كانت عدد الكلام، وهيك بصيوا في
+
+558
+00:44:42,140 --> 00:44:44,380
+المنظر، يعني تخيل انه روحت
+
+559
+00:44:48,140 --> 00:44:52,180
+يا عين عليك انا بقول يعني العقرية دايما تتجلى يعنى
+
+560
+00:44:52,180 --> 00:44:59,220
+عننا طيب اه نعم لا
+
+561
+00:44:59,220 --> 00:45:02,200
+احنا خلاص عليه كده و بس انا بدكر .. جاعد باذكرك
+
+562
+00:45:02,200 --> 00:45:04,680
+التطبيق اللى يستخدن انت المفروض اخدته بما فيه
+
+563
+00:45:04,680 --> 00:45:09,440
+الكفاية طيب نمتقل
+
+564
+00:45:09,440 --> 00:45:11,920
+لل section اللى بعده
+
+565
+00:45:15,780 --> 00:45:19,700
+لا فيش مراجعة يا حبيبي كلينا نمشي Propositional
+
+566
+00:45:19,700 --> 00:45:23,340
+Logic Proposition Equivalence الان يا شباب بدينا
+
+567
+00:45:23,340 --> 00:45:28,000
+نفتح دهنك شوية و نعمل مراجعة عشان خاطرك للعناصر
+
+568
+00:45:28,000 --> 00:45:33,100
+بشكل سريع لل operators اللي أخدناهم أخدنا اننا فيه
+
+569
+00:45:33,100 --> 00:45:38,380
+صح؟ و أخدنا ال end ال end متى بتكون true يا شباب؟
+
+570
+00:45:38,380 --> 00:45:44,520
+لما تكون ال two operands true ال orلما كان واحد
+
+571
+00:45:44,520 --> 00:45:51,540
+منهم على الأقل true الـ XR لما كونوا التنين
+
+572
+00:45:51,540 --> 00:45:56,080
+مختلفين لما كونوا التنين مختلفين ال implication
+
+573
+00:45:56,080 --> 00:46:01,040
+بتديني false في حالة true implies to false ليش هذا
+
+574
+00:46:01,040 --> 00:46:04,480
+الكلام أنا بقوله؟ مهم جدا عشان نفهم الكلام اللي
+
+575
+00:46:04,480 --> 00:46:09,280
+بده يصير هنا وال by conditional بتديني true لما
+
+576
+00:46:09,280 --> 00:46:16,450
+تكون التنتين متشابهتينبصبوط لما كنت متشابهتين الان
+
+577
+00:46:16,450 --> 00:46:23,350
+في عند بعض التعريفات المهمة لو كان في عندي
+
+578
+00:46:23,350 --> 00:46:32,090
+compound proposition وقيمته دائما true مثل
+
+579
+00:46:32,090 --> 00:46:35,710
+P or نقطة P
+
+580
+00:46:39,480 --> 00:46:44,600
+أو نطّ الـ P لو بدك تعمل جدول الاحتمالات كان متغير
+
+581
+00:46:44,600 --> 00:46:49,920
+كان محتمال عندي اربعة اربع منين اتنين اتنين اقصى
+
+582
+00:46:49,920 --> 00:46:53,560
+اتنين اربع تاخد الصفر بجدارة ان شاء الله تعالى على
+
+583
+00:46:53,560 --> 00:47:01,900
+السؤال لأن عندك P هي ال بي مات one operand P true
+
+584
+00:47:01,900 --> 00:47:09,440
+او false وهي نطّ ال بيfalse true الان العملية هذه
+
+585
+00:47:09,440 --> 00:47:14,680
+P or نقطة ال P true or false true false or true
+
+586
+00:47:14,680 --> 00:47:20,660
+true لاحظ انه دائما دائما ال definite true دائما
+
+587
+00:47:20,660 --> 00:47:25,100
+صحيحة هذا التاني احنا بنسميه tautology tautology
+
+588
+00:47:25,100 --> 00:47:30,920
+هو عبارة عن compound proposition قيمته دائما true
+
+589
+00:47:30,920 --> 00:47:37,460
+قيمته دائما true ال compound proposition التانيكان
+
+590
+00:47:37,460 --> 00:47:44,560
+متغير مولود فيه؟ 2 كم عدد الاحتمالات في الجدول؟ 4
+
+591
+00:47:44,560 --> 00:47:48,400
+تعالى
+
+592
+00:47:48,400 --> 00:47:51,780
+نشوف هل دائما بتديني true ولا لأ؟ مابعنى ان انا
+
+593
+00:47:51,780 --> 00:47:55,260
+هثبت بس هدول بالجدول الاحتمالات بعد هيك انت حار
+
+594
+00:47:55,260 --> 00:48:06,200
+صدق ولا ماتصدقش طيب high P high Q true truefalse
+
+595
+00:48:06,200 --> 00:48:13,540
+false هاي الأربع احتمالات true false true false
+
+596
+00:48:13,540 --> 00:48:20,160
+حسب ما قلنا الأولوية للأقواص إيش هان دي جوا القواص
+
+597
+00:48:20,160 --> 00:48:31,320
+P and Q P and Q صح الأولى
+
+598
+00:48:31,320 --> 00:48:33,940
+true والباقي false إن فيها
+
+599
+00:48:36,880 --> 00:48:39,380
+أه ليش اكتب كمان عمود اذا كان بيمكن احلها بسرعة
+
+600
+00:48:39,380 --> 00:48:45,900
+انا ولا لأ بتصير الأولى false والباقي true مية مية
+
+601
+00:48:45,900 --> 00:48:59,540
+طيب الان بدي هدول نط ال P او نط ال Q false
+
+602
+00:48:59,540 --> 00:49:06,220
+or ال false false true or true
+
+603
+00:49:11,830 --> 00:49:23,510
+false or true true true or false true or true true
+
+604
+00:49:23,510 --> 00:49:27,910
+by and or by conditional ماعكستش
+
+605
+00:49:27,910 --> 00:49:33,410
+حاجة يا أستاذ أنا مش صح في العمود
+
+606
+00:49:33,410 --> 00:49:39,210
+الأخيرأنا كنت بجلب القيامة هذه نط .. نط الـ B هذه
+
+607
+00:49:39,210 --> 00:49:43,210
+الـ B true نطها او لا فيها false والـ Q for true
+
+608
+00:49:43,210 --> 00:49:50,750
+لا فيها false false or ال false false إجيتها عكسهم
+
+609
+00:49:50,750 --> 00:49:58,290
+true or false true الآن أخر شغل الحمود الأخير لما
+
+610
+00:49:58,290 --> 00:50:00,590
+يكون متساويتين في ال by conditional بتكون ال
+
+611
+00:50:00,590 --> 00:50:06,580
+output true وبالتاليهذه جدول الاحتمالات طبعا اذا
+
+612
+00:50:06,580 --> 00:50:09,420
+انت كان عندك مشكلة لك فيعمل الجدول بالشكل هذا او
+
+613
+00:50:09,420 --> 00:50:18,360
+ممكن تغلط انا بأنصحك اشتغل واحدة واحدة بـ
+
+614
+00:50:18,360 --> 00:50:22,360
+Contradiction Contradiction ايش يعني
+
+615
+00:50:22,360 --> 00:50:27,540
+Contradiction؟ تناقض الانصر و لقيده لو جمعت بينهم
+
+616
+00:50:27,540 --> 00:50:37,280
+and دايما كنت false and andالان لو كانت ال true
+
+617
+00:50:37,280 --> 00:50:45,580
+true false هتصير false و true بينهم and true and
+
+618
+00:50:45,580 --> 00:50:49,960
+false false and true false وبالتالي هذا بيسميه
+
+619
+00:50:49,960 --> 00:50:56,180
+Contradiction او فيه and تناقض طيب لاحظ هذه ال
+
+620
+00:50:56,180 --> 00:50:59,240
+compound proposition التاني هو عبارة عن ال
+
+621
+00:50:59,240 --> 00:51:02,680
+compound proposition هذا بس واحد ايه سويت فيه
+
+622
+00:51:02,680 --> 00:51:10,260
+نفيتهنفيته مصبوط فتلاقش ككل ال output اللي كانت
+
+623
+00:51:10,260 --> 00:51:14,940
+true إيه صارت؟ صارت كلها false وهذه أمثلة على
+
+624
+00:51:14,940 --> 00:51:17,880
+compound proposition بنسميه contradiction يعني
+
+625
+00:51:17,880 --> 00:51:21,160
+دايما ال output بتبعته false بغض النظر إيه كانت
+
+626
+00:51:21,160 --> 00:51:26,720
+القيامة المدخلة له بسيط
+
+627
+00:51:26,720 --> 00:51:28,800
+الكلام حتى اللحظة ولا لا؟
+
+628
+00:51:39,990 --> 00:51:43,130
+الان عشان اقول ان ال proposition اللي لو كان فيه
+
+629
+00:51:43,130 --> 00:51:45,390
+اندو تو compound proposition او فيه اندو تو
+
+630
+00:51:45,390 --> 00:51:49,170
+propositions و بدى اقول بينهم فيه تساوي او تكافؤ
+
+631
+00:51:49,170 --> 00:51:53,670
+هرمز لك تكافؤ اما بالتلات شحطات هذه اللي يساوي
+
+632
+00:51:53,670 --> 00:52:00,310
+equivalence او بالسهم هذا و طبعا بقول عنهم
+
+633
+00:52:00,310 --> 00:52:05,070
+متساويات ان لو كانت ال P و Q تدوني نفس ال logical
+
+634
+00:52:05,070 --> 00:52:10,740
+valueتمام؟ عند كل الاحتمالات اللي موجودة طيب تعالى
+
+635
+00:52:10,740 --> 00:52:23,440
+نشوف المثال هذا تحل القضية الأولوية
+
+636
+00:52:23,440 --> 00:52:27,460
+دائما للأقواص
+
+637
+00:52:27,460 --> 00:52:32,260
+تعالى نشوف يا شباب تقول لي هى في عندك two compound
+
+638
+00:52:32,260 --> 00:52:38,210
+proposition و اثبتلي انهم متساوياتأولا في أول شرط
+
+639
+00:52:38,210 --> 00:52:43,270
+في شروط التساوي انتبه هل لهم نفس ال variable نفس
+
+640
+00:52:43,270 --> 00:52:46,990
+عدد ال variables اه لو اختلفوا في عدد ال variables
+
+641
+00:52:46,990 --> 00:52:50,490
+معناه الجدول الاحتمالات هيختلف وبالتالي ليش مقارنة
+
+642
+00:52:50,490 --> 00:52:55,050
+ما بينهم بي و كيو موجودة في الطرفين معناه ان انا
+
+643
+00:52:55,050 --> 00:53:00,770
+بدأ ابني جدول احتمالات للتانين نقطة بي و نقطة كيو
+
+644
+00:53:00,770 --> 00:53:07,070
+عبينا الجدول نفت العملية بي or كيو و نفيتهاو روح
+
+645
+00:53:07,070 --> 00:53:10,850
+تجيب ال PN نقطة Q نفيتها الان عشان اقول ان ال two
+
+646
+00:53:10,850 --> 00:53:15,890
+compound proposition هدول متساويات لازم يكون لهم
+
+647
+00:53:15,890 --> 00:53:21,250
+نفس ال truth value عند كل الاحتمالات نفس ال truth
+
+648
+00:53:21,250 --> 00:53:24,970
+value عند كل الاحتمالات يعني في الصف الأول لازم
+
+649
+00:53:24,970 --> 00:53:27,750
+يكونوا متكافئان في الصف التالي لازم يكونوا
+
+650
+00:53:27,750 --> 00:53:30,790
+متكافئين في الصف التالت متكافئين في الصف الرابع
+
+651
+00:53:30,790 --> 00:53:34,490
+متكافئين لو واحد من الصفة في اختلفه not equivalent
+
+652
+00:53:34,490 --> 00:53:41,930
+مافيش بينهم تكافئماشي الحال اعيد تانى الأمر بسيط
+
+653
+00:53:41,930 --> 00:53:45,050
+جدا بنقول ان ال two compound propositions
+
+654
+00:53:45,050 --> 00:53:50,490
+equivalent او متكافئين لو ال truth value تبعتهم
+
+655
+00:53:50,490 --> 00:53:55,430
+متساوية في كل صفوف جدول الاحتمالات اللى تم انشاءه
+
+656
+00:53:55,430 --> 00:53:58,550
+للاتنين بنفعش اتوح جدول احتمالات لكل واحد بشكل
+
+657
+00:53:58,550 --> 00:54:04,270
+مستقل لازم يكون نفس الجدول عشان تقدر تقارن النتيجة
+
+658
+00:54:05,250 --> 00:54:09,370
+مع بعضها، واضح يا شباب؟ لو واحدة اختلفت، يعني لو
+
+659
+00:54:09,370 --> 00:54:12,690
+جدلاً قلنا إنه هادي، طلعت true، معناته هادي
+
+660
+00:54:12,690 --> 00:54:17,070
+لاتوكافق هادي، انسى الموضوع، ما تكملش، بتوقف و
+
+661
+00:54:17,070 --> 00:54:19,470
+بتقول الـ210 is not equivalent، مافيش فيه بينهم
+
+662
+00:54:19,470 --> 00:54:25,190
+تكافق، ماشي الحل يا شباب؟
+
+663
+00:54:25,190 --> 00:54:32,970
+طيب
+
+664
+00:54:35,400 --> 00:54:37,840
+في مجموعة القوانين اللي لها علاقة بالـ equivalence
+
+665
+00:54:37,840 --> 00:54:41,980
+في عندي مجموعة من القوانين المهمة القانون الأول
+
+666
+00:54:41,980 --> 00:54:47,600
+قانون ال identity قانون الوحدة لان شباب احنا قولنا
+
+667
+00:54:47,600 --> 00:54:56,820
+ال and و ال or ال and بتديني false تمام لو انا
+
+668
+00:54:56,820 --> 00:55:01,340
+كانت واحدة من ال input false طب لو كانت واحدة true
+
+669
+00:55:01,340 --> 00:55:06,370
+والتانية مجهولة ايش ال output؟B اللي هي المجهول
+
+670
+00:55:06,370 --> 00:55:13,450
+يعني بين جثين لو أنا قلت B and true هذي تكافئ مين؟
+
+671
+00:55:13,450 --> 00:55:18,270
+تكافئ B لأن لو كانت true true and true true و لو
+
+672
+00:55:18,270 --> 00:55:24,550
+كانت false هتكون false كذلك P or ال false برضه
+
+673
+00:55:24,550 --> 00:55:30,730
+equivalent to مين؟ to B false or ال false؟ false
+
+674
+00:55:30,730 --> 00:55:37,600
+true or ال false؟ trueهدول بنسميهم قوانين الوحدة
+
+675
+00:55:37,600 --> 00:55:44,520
+وكأنه ال true هي المحايد مع ال and و ال false هي
+
+676
+00:55:44,520 --> 00:55:54,900
+المحايد مع الأخر domination أو السيطرة عكسه بي or
+
+677
+00:55:54,900 --> 00:56:03,880
+true true بي and ال falsefalse يعني لما بكون في
+
+678
+00:56:03,880 --> 00:56:09,420
+عندي false بال end فبتكلم على false و لما بكون في
+
+679
+00:56:09,420 --> 00:56:14,020
+عندي true مع ال or بتكلم على true وهذا المبدأ اللي
+
+680
+00:56:14,020 --> 00:56:16,340
+بيشتغل عليه ال logical operator بالبرمجة كلها
+
+681
+00:56:16,340 --> 00:56:20,180
+بمجرد ألاقي ال operand الأول قيمته معروفة true و
+
+682
+00:56:20,180 --> 00:56:24,360
+ال condition بيعتمد على ال or ببورش بحسبش خلاص هي
+
+683
+00:56:24,360 --> 00:56:27,840
+واحدة على الأقل وبالتالي هذا هم سميها domination
+
+684
+00:56:27,840 --> 00:56:28,440
+laws
+
+685
+00:56:31,410 --> 00:56:39,090
+قانون الاختزال P and ال P P لأن لو كانت ال true
+
+686
+00:56:39,090 --> 00:56:43,030
+and true true لو كانت false false and false false
+
+687
+00:56:43,030 --> 00:56:49,750
+كذلك P or ال P برضه P false or ال false false true
+
+688
+00:56:49,750 --> 00:56:59,210
+or true true شوف القوانين هذه ال negation ال نفي P
+
+689
+00:56:59,210 --> 00:57:04,430
+and نقطة Pfalse لأن لو كانت true هتصير false لأنه
+
+690
+00:57:04,430 --> 00:57:08,970
+معاكس بعض وقلنا في ال contradiction قبل شوية PR
+
+691
+00:57:08,970 --> 00:57:15,170
+نقطة ال B true و نفي النفي نقطة نقطة ال B على
+
+692
+00:57:15,170 --> 00:57:21,550
+المبدأ نفي النفي إثبات commutative تبديل الإبدال
+
+693
+00:57:21,550 --> 00:57:27,810
+خاصية الإبدال P and Q equivalent to Q and B و P or
+
+694
+00:57:27,810 --> 00:57:37,680
+Q equivalent to Q,B,RP and Q and R توجيه التجميع P
+
+695
+00:57:37,680 --> 00:57:42,780
+and Q and R توجيه التجميع P and Q and R توجيه
+
+696
+00:57:42,780 --> 00:57:47,520
+التجميع P and Q and R توجيه التجميع P and Q and R
+
+697
+00:57:47,520 --> 00:57:47,640
+توجيه التجميع P and Q and R توجيه التجميع P and Q
+
+698
+00:57:47,640 --> 00:57:48,000
+التجميع P and Q and R توجيه التجميع P and Q and R
+
+699
+00:57:48,000 --> 00:57:50,500
+توجيه التجميع P and Q and R توجيه التجميع P and Q
+
+700
+00:57:50,500 --> 00:57:56,200
+and R توجيه التجميع P and Q and R توجيه التجميع P
+
+701
+00:57:56,200 --> 00:57:59,920
+and Q and
+
+702
+00:57:59,920 --> 00:58:03,630
+R توجيه التجميع P andتمام؟ و ال and هي عبارة عن
+
+703
+00:58:03,630 --> 00:58:11,350
+binary operator هذه تكافئ P and Q في قوس كل and ال
+
+704
+00:58:11,350 --> 00:58:18,430
+R أو تكافئ P and Q
+
+705
+00:58:18,430 --> 00:58:23,550
+and ال R تمام؟ خاصية التجميل
+
+706
+00:58:28,780 --> 00:58:34,480
+و كذلك مع الار و كذلك مع الار في خاصية التوزيع ..
+
+707
+00:58:34,480 --> 00:58:42,000
+خاصية التوزيع P .. توزيع مين على مين يا شباب؟
+
+708
+00:58:42,000 --> 00:58:48,940
+توزيع ال and على .. على الجوس الار أو توزيع الار
+
+709
+00:58:48,940 --> 00:58:52,740
+على الجوس بال and طبعا لو كانوا التنتين نفس
+
+710
+00:58:52,740 --> 00:58:55,840
+الإشارة نفس ال operator أصبحنا نتكلم عن عملية
+
+711
+00:58:55,840 --> 00:59:04,200
+تجميل طيبتعالى نشوف الأولى P and Q or ال R تستخدم
+
+712
+00:59:04,200 --> 00:59:14,200
+كمان مرة P and Q او P and R كمان مرة P and Q or ال
+
+713
+00:59:14,200 --> 00:59:21,820
+R تستخدم كمان مرة P and Q او P and R كمان مرة P
+
+714
+00:59:21,820 --> 00:59:22,400
+and Q او P and R كمان مرة P and Q او P and R كمان
+
+715
+00:59:22,400 --> 00:59:22,540
+and R كمان مرة P and Q او P and R كمان مرة P and Q
+
+716
+00:59:22,540 --> 00:59:22,580
+او P and R كمان مرة P and Q او P and R كمان مرة P
+
+717
+00:59:22,580 --> 00:59:30,160
+مرة P and Q او P and R كمان مرة P andعشان أخدت
+
+718
+00:59:30,160 --> 00:59:33,960
+النقادات المتساويات ايش لازم أساوي؟ بدي أعمل جدوى
+
+719
+00:59:33,960 --> 00:59:37,000
+الاحتمالات جدوى الاحتمالات لهذه المسألة من كام
+
+720
+00:59:37,000 --> 00:59:45,020
+صفر؟ اربع صفوف غلط تمان صفوف لأن في عندي تلت
+
+721
+00:59:45,020 --> 00:59:49,480
+متغيرات اتنين اقصى ثلاثة بتكلم على تمانية بتكلم
+
+722
+00:59:49,480 --> 00:59:53,420
+على تمانية وبالتالي المفروض انت تعمل جدوى
+
+723
+00:59:53,420 --> 00:59:59,890
+الاحتمالات من تمان صفوف PQR و تبقى ايش؟تشتغل عليهم
+
+724
+00:59:59,890 --> 01:00:05,170
+إذا تدعيك نفس قيم ال truth value في آخر عمودين،
+
+725
+01:00:05,170 --> 01:00:09,530
+ماتوا في عندي إيش؟ التكافأة في قانون جديد بالنسبة
+
+726
+01:00:09,530 --> 01:00:13,510
+إلي دي مورجان لاو دي مورجان لاو بقول كتاري لو احنا
+
+727
+01:00:13,510 --> 01:00:21,410
+نفينا compound proposition مربوط ب and يساوي نفي
+
+728
+01:00:21,410 --> 01:00:28,220
+كل واحد فيهم مربوطين بRيعني نط P and Q equal نط ال
+
+729
+01:00:28,220 --> 01:00:33,360
+P over نط ال Q و العكس صحيح دي مورجلنش بيقول بيقول
+
+730
+01:00:33,360 --> 01:00:42,240
+أنه فعليا النط هذه بتجلب الإشارة يعني عشان تنجح في
+
+731
+01:00:42,240 --> 01:00:49,680
+المساق لازم تنجح في النص و في النهائي تمام؟ لازم
+
+732
+01:00:49,680 --> 01:00:56,270
+تنجح في النص و في النهائيأكسها الرصوب في المساق
+
+733
+01:00:56,270 --> 01:01:01,570
+يعني إما بترصب في النهائي أو بترصب في النصفي وطبعا
+
+734
+01:01:01,570 --> 01:01:06,010
+رصبت بالتنائم من تناسب مظبوط ولا لأ؟ الله أبعد عنك
+
+735
+01:01:06,010 --> 01:01:09,150
+شرر الصوت طبعا تمام يا شباب؟ طيب لو بدنا نثبت هذا
+
+736
+01:01:09,150 --> 01:01:16,490
+الكلام جد و لا احتمالات نثبت واحدة منهم B و Q كام
+
+737
+01:01:16,490 --> 01:01:26,250
+variable عندي؟ نم Truefalse false true false true
+
+738
+01:01:26,250 --> 01:01:34,570
+false الان نط ال b وهي نط ال q هذه false false
+
+739
+01:01:34,570 --> 01:01:44,910
+true true false true false true الان نط ال b and q
+
+740
+01:01:44,910 --> 01:01:51,880
+b and q true and true true نفيها falsetrue and
+
+741
+01:01:51,880 --> 01:01:58,020
+false true and false false نفيها true true false
+
+742
+01:01:58,020 --> 01:02:02,340
+and true false نفيها true false and false false
+
+743
+01:02:02,340 --> 01:02:12,300
+نفيها true طيب الأخيرة نط ال B or نط ال Q false
+
+744
+01:02:12,300 --> 01:02:19,540
+or false false false or true true true or false
+
+745
+01:02:20,240 --> 01:02:25,840
+true true true true معناته حصلت على نفس ال truth
+
+746
+01:02:25,840 --> 01:02:29,720
+values في جدول الاحتمالات كله و بالتالي حصلت على
+
+747
+01:02:29,720 --> 01:02:34,820
+نفس ال value الموجودة هذا ال demo جان له و أعطيكم
+
+748
+01:02:34,820 --> 01:02:36,660
+الله عافية نكمل المرة اللي جاي ان شاء الله
+
diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/WNoF4_EDCFs_raw.json b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/WNoF4_EDCFs_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..7f7ab0453d38be50aa2f23b089ed51ff24157cf9
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/WNoF4_EDCFs_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4975, "start": 20.81, "end": 49.75, "text": "بسم الله الحمد لله والصلاة والسلام على رسول الله اليوم ان شاء الله شباب هنكمل او هنعمل review بسيط الأهم الشغلات اللي خدناها المحاضرة الماضية و هنكمل في ال chapter اللي احنا ما زلنا فيه اللي هو ال fundamental logic طبعا كنا المحاضرة الماضية اتكلمنا على ال connectors او ال logical operators اللي ممكن انا استخدمها مع ال proposition و كل ما عرفنا ال proposition هو عبارة عن statement تاخد اما true", "tokens": [3555, 38251, 21984, 21542, 2304, 3215, 24976, 3224, 16070, 9381, 15040, 3660, 16070, 3794, 37440, 15844, 12602, 3794, 12610, 21984, 45595, 20498, 16472, 13412, 16606, 21984, 13412, 3555, 16758, 8032, 1863, 24793, 1211, 1975, 2407, 8032, 1863, 25957, 1211, 3131, 4724, 3794, 1829, 9566, 16247, 16095, 25124, 17082, 1211, 9307, 13672, 1829, 16490, 3215, 8315, 11296, 9673, 5016, 46958, 25720, 9673, 46958, 10632, 4032, 8032, 1863, 24793, 1211, 8978, 2423, 7187, 13672, 1829, 1975, 5016, 8315, 19446, 30767, 1211, 8315, 8978, 3224, 13672, 1829, 31439, 2423, 8088, 9952, 23032, 3555, 3615, 995, 9122, 8315, 9673, 5016, 46958, 25720, 9673, 46958, 10632, 1975, 2655, 4117, 19528, 8315, 15844, 2423, 31865, 1975, 2407, 2423, 14978, 19077, 13672, 1829, 3714, 43020, 1975, 8315, 44713, 9778, 40448, 11296, 20449, 2423, 24830, 4032, 28242, 19446, 6225, 28480, 8315, 2423, 24830, 31439, 6225, 3555, 9640, 3660, 18871, 5629, 6055, 47283, 3215, 1975, 15042, 2074], "avg_logprob": -0.15257970278695127, "compression_ratio": 2.003174603174603, "no_speech_prob": 3.5762786865234375e-07, "words": [{"start": 20.81, "end": 21.09, "word": "بسم", "probability": 0.85400390625}, {"start": 21.09, "end": 21.21, "word": " الله", "probability": 0.96142578125}, {"start": 21.21, "end": 21.49, "word": " الحمد", "probability": 0.8385416666666666}, {"start": 21.49, "end": 21.63, "word": " لله", "probability": 0.93408203125}, {"start": 21.63, "end": 21.89, "word": " والصلاة", "probability": 0.8858642578125}, {"start": 21.89, "end": 22.19, "word": " والسلام", "probability": 0.94140625}, {"start": 22.19, "end": 22.33, "word": " على", "probability": 0.3955078125}, {"start": 22.33, "end": 22.57, "word": " رسول", "probability": 0.9288736979166666}, {"start": 22.57, "end": 22.75, "word": " الله", "probability": 0.92529296875}, {"start": 22.75, "end": 23.43, "word": " اليوم", "probability": 0.923828125}, {"start": 23.43, "end": 23.57, "word": " ان", "probability": 0.425537109375}, {"start": 23.57, "end": 23.67, "word": " شاء", "probability": 0.969970703125}, {"start": 23.67, "end": 23.69, "word": " الله", "probability": 0.916015625}, {"start": 23.69, "end": 24.03, "word": " شباب", "probability": 0.8313802083333334}, {"start": 24.03, "end": 25.85, "word": " هنكمل", "probability": 0.8919677734375}, {"start": 25.85, "end": 26.95, "word": " او", "probability": 0.739013671875}, {"start": 26.95, "end": 27.31, "word": " هنعمل", "probability": 0.9677734375}, {"start": 27.31, "end": 27.55, "word": " review", "probability": 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proposition ليش؟ لأنها عبارة عن order لأنها عبارة عن order تعالى نشوف هي مثلا في السؤال تمانية احنا شبدنا في ال .. okay", "tokens": [3555, 2655, 32887, 5016, 6055, 3215, 2288, 3794, 25724, 17082, 23557, 5172, 16247, 2304, 16572, 4117, 10632, 4032, 39894, 7435, 1829, 3555, 11296, 4724, 23557, 33753, 4117, 41850, 37893, 6225, 9640, 5172, 4724, 3794, 34105, 41850, 4724, 28543, 2288, 5551, 7435, 1829, 5551, 39648, 4117, 16490, 2304, 3794, 3660, 30767, 16373, 3215, 8608, 3555, 27884, 2681, 6225, 8592, 25720, 307, 257, 24830, 4032, 12174, 32640, 47395, 7908, 46811, 10943, 1867, 341, 1168, 307, 406, 257, 24830, 32239, 8592, 22807, 5296, 33456, 11296, 6225, 3555, 9640, 3660, 18871, 1668, 5296, 33456, 11296, 6225, 3555, 9640, 3660, 18871, 1668, 37279, 6027, 7578, 8717, 8592, 38688, 39896, 50113, 15040, 8978, 21136, 33604, 6027, 46811, 7649, 10632, 1975, 5016, 8315, 13412, 3555, 3215, 8315, 8978, 2423, 4386, 1392], "avg_logprob": -0.19824999570846558, "compression_ratio": 1.6813186813186813, 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I bought lottery ticket this week أنا اشتريت بطاقة نصيب لسبوع هذا مين هذي؟ الـP الـQ I won the million dollar jackpot هو ربح المليون من التاعة اللي هي نصيب ربح أكبر جائزة الكبرى اللي هي المليون دولار", "tokens": [3555, 39648, 4117, 8978, 2423, 39184, 23, 45164, 25961, 2655, 2423, 39184, 47, 4032, 2423, 39184, 48, 6225, 3555, 9640, 3660, 18871, 2423, 39184, 24830, 2423, 39184, 47, 286, 4243, 27391, 10550, 341, 1243, 41850, 1975, 8592, 2655, 16572, 2655, 4724, 9566, 995, 28671, 8717, 9381, 1829, 3555, 5296, 35457, 45367, 23758, 3714, 9957, 8032, 8848, 1829, 22807, 2423, 39184, 47, 2423, 39184, 48, 286, 1582, 264, 2459, 7241, 7109, 17698, 31439, 12602, 49628, 9673, 20292, 11536, 9154, 16712, 995, 27884, 13672, 1829, 39896, 8717, 9381, 1829, 3555, 12602, 49628, 5551, 4117, 26890, 10874, 16373, 11622, 3660, 33251, 26890, 7578, 13672, 1829, 39896, 9673, 20292, 11536, 11778, 12610, 9640], "avg_logprob": -0.3323863617398522, "compression_ratio": 1.5905511811023623, "no_speech_prob": 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بتدوسها مادة أو مساق اسمه تصميم منطقي عشان نقدر يصمم اللوحات أو يصمم برامج صح التصميم المنطقي بيعتمد على البوابات اللي موجودة قدامنا النفي اسمها inverter تجلب التيارة", "tokens": [35, 328, 1686, 12748, 6055, 8848, 37983, 14407, 9673, 5016, 1211, 4587, 16606, 16247, 12610, 5296, 15042, 12174, 1211, 8315, 2423, 39184, 19839, 7600, 15776, 37541, 3714, 16095, 3660, 24976, 8315, 3794, 13672, 1829, 39894, 8592, 17082, 1211, 8978, 2423, 22289, 8976, 22289, 16215, 34051, 2423, 12575, 15888, 16215, 4032, 27842, 5551, 12610, 9673, 3794, 995, 4587, 9307, 13672, 1829, 39894, 3215, 41779, 11296, 3714, 18513, 3660, 34051, 47524, 995, 4587, 24525, 2304, 3224, 6055, 9381, 2304, 32640, 9154, 9566, 38436, 6225, 8592, 7649, 8717, 28543, 2288, 7251, 9381, 2304, 2304, 13672, 2407, 5016, 9307, 34051, 7251, 9381, 2304, 2304, 4724, 2288, 10943, 7435, 20328, 5016, 16712, 9381, 2304, 32640, 9673, 1863, 9566, 38436, 4724, 1829, 34268, 2304, 3215, 15844, 29739, 14407, 3555, 9307, 13672, 1829, 3714, 29245, 23328, 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"تمام؟ عند كل الاحتمالات اللي موجودة طيب تعالى نشوف المثال هذا تحل القضية الأولوية دائما للأقواص تعالى نشوف يا شباب تقول لي هى في عندك two compound proposition و اثبتلي انهم متساويات", "tokens": [39237, 10943, 22807, 43242, 28242, 42963, 33753, 2304, 6027, 9307, 13672, 1829, 3714, 29245, 23328, 3660, 23032, 1829, 3555, 37279, 6027, 7578, 8717, 8592, 38688, 9673, 12984, 6027, 23758, 6055, 5016, 1211, 25062, 11242, 10632, 16247, 12610, 2407, 10632, 11778, 16373, 15042, 24976, 10721, 4587, 2407, 33546, 37279, 6027, 7578, 8717, 8592, 38688, 35186, 13412, 3555, 16758, 6055, 39648, 32239, 8032, 7578, 8978, 43242, 4117, 732, 14154, 24830, 4032, 1975, 12984, 3555, 2655, 20292, 16472, 16095, 44650, 3794, 995, 45865, 9307], "avg_logprob": -0.28563261177481675, "compression_ratio": 1.5846153846153845, "no_speech_prob": 0.0, "words": [{"start": 3126.5, "end": 3127.32, "word": "تمام؟", "probability": 0.5857950846354166}, {"start": 3127.32, "end": 3127.56, "word": " عند", "probability": 0.625}, 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123, "seek": 342007, "start": 3391.41, "end": 3420.07, "text": "قانون الاختزال P and ال P P لأن لو كانت ال true and true true لو كانت false false and false false كذلك P or ال P برضه P false or ال false false true or true true شوف القوانين هذه ال negation ال نفي P and نقطة P", "tokens": [4587, 7649, 11536, 2423, 47283, 2655, 11622, 6027, 430, 293, 2423, 430, 430, 5296, 33456, 45164, 25961, 2655, 2423, 2074, 293, 2074, 2074, 45164, 25961, 2655, 7908, 7908, 293, 7908, 7908, 9122, 8848, 23275, 430, 420, 2423, 430, 4724, 43042, 3224, 430, 7908, 420, 2423, 7908, 7908, 2074, 420, 2074, 2074, 13412, 38688, 25062, 2407, 7649, 9957, 29538, 2423, 2485, 399, 2423, 8717, 41185, 430, 293, 8717, 47432, 3660, 430], "avg_logprob": -0.36707746310972833, "compression_ratio": 1.74375, "no_speech_prob": 0.0, "words": [{"start": 3391.4100000000003, "end": 3392.13, "word": "قانون", "probability": 0.6417032877604166}, {"start": 3392.13, "end": 3392.85, "word": " الاختزال", "probability": 0.812744140625}, 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23032, 1829, 3555, 16247, 9778, 48923, 8717, 9566, 2423, 363, 420, 8717, 9566, 2423, 1249, 7908, 420, 7908, 7908, 7908, 420, 2074, 2074, 2074, 420, 7908], "avg_logprob": -0.24148995189794473, "compression_ratio": 2.2718446601941746, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 3711.4, "end": 3711.72, "word": "true", "probability": 0.66650390625}, {"start": 3711.72, "end": 3711.88, "word": " and", "probability": 0.890625}, {"start": 3711.88, "end": 3712.38, "word": " false", "probability": 0.89453125}, {"start": 3712.38, "end": 3712.74, "word": " true", "probability": 0.147216796875}, {"start": 3712.74, "end": 3713.78, "word": " and", "probability": 0.85400390625}, {"start": 3713.78, "end": 3714.34, "word": " false", "probability": 0.90966796875}, {"start": 3714.34, "end": 3715.28, "word": " false", "probability": 0.6591796875}, {"start": 3715.28, "end": 3715.88, "word": " نفيها", "probability": 0.9514973958333334}, {"start": 3715.88, "end": 3716.56, "word": " true", "probability": 0.9482421875}, {"start": 3716.56, "end": 3717.2, "word": " true", "probability": 0.232421875}, {"start": 3717.2, "end": 3718.02, "word": " false", "probability": 0.67822265625}, {"start": 3718.02, "end": 3718.24, "word": " and", "probability": 0.9658203125}, {"start": 3718.24, "end": 3718.58, "word": " true", "probability": 0.96826171875}, {"start": 3718.58, "end": 3719.22, "word": " false", "probability": 0.8408203125}, {"start": 3719.22, "end": 3719.74, "word": " نفيها", "probability": 0.93994140625}, {"start": 3719.74, "end": 3720.04, "word": " true", "probability": 0.990234375}, {"start": 3720.04, "end": 3720.86, "word": " false", "probability": 0.66259765625}, {"start": 3720.86, "end": 3721.12, "word": " and", "probability": 0.9560546875}, {"start": 3721.12, "end": 3721.58, "word": " false", "probability": 0.900390625}, {"start": 3721.58, "end": 3722.34, "word": " false", "probability": 0.87744140625}, {"start": 3722.34, "end": 3722.78, "word": " نفيها", "probability": 0.9527994791666666}, {"start": 3722.78, "end": 3723.06, "word": " true", "probability": 0.99365234375}, {"start": 3723.06, "end": 3724.06, "word": " طيب", "probability": 0.7821451822916666}, {"start": 3724.06, "end": 3724.84, "word": " الأخيرة", "probability": 0.93798828125}, {"start": 3724.84, "end": 3725.66, "word": " نط", "probability": 0.837890625}, {"start": 3725.66, "end": 3725.84, "word": " ال", "probability": 0.7587890625}, {"start": 3725.84, "end": 3726.12, "word": " B", "probability": 0.468505859375}, {"start": 3726.12, "end": 3726.98, "word": " or", "probability": 0.399169921875}, {"start": 3726.98, "end": 3727.94, "word": " نط", "probability": 0.964111328125}, {"start": 3727.94, "end": 3728.04, "word": " ال", "probability": 0.7783203125}, {"start": 3728.04, "end": 3728.34, "word": " Q", "probability": 0.95068359375}, {"start": 3728.34, "end": 3732.3, "word": " false", "probability": 0.62109375}, {"start": 3732.3, "end": 3732.52, "word": " or", "probability": 0.95703125}, {"start": 3732.52, "end": 3733.04, "word": " false", "probability": 0.89697265625}, {"start": 3733.04, "end": 3735.18, "word": " false", "probability": 0.84375}, {"start": 3735.18, "end": 3736.54, "word": " false", "probability": 0.775390625}, {"start": 3736.54, "end": 3736.72, "word": " or", "probability": 0.8984375}, {"start": 3736.72, "end": 3737.12, "word": " true", "probability": 0.98291015625}, {"start": 3737.12, "end": 3738.32, "word": " true", "probability": 0.9560546875}, {"start": 3738.32, "end": 3738.88, "word": " true", "probability": 0.94873046875}, {"start": 3738.88, "end": 3739.1, "word": " or", "probability": 0.94970703125}, {"start": 3739.1, "end": 3739.54, "word": " false", "probability": 0.91259765625}], "temperature": 1.0}, {"id": 135, "seek": 375666, "start": 3740.24, "end": 3756.66, "text": "true true true true معناته حصلت على نفس ال truth values في جدول الاحتمالات كله و بالتالي حصلت على نفس ال value الموجودة هذا ال demo جان له و أعطيكم الله عافية نكمل المرة اللي جاي ان شاء الله", "tokens": [6903, 622, 2074, 2074, 2074, 20449, 8315, 47395, 11331, 36520, 2655, 15844, 8717, 36178, 2423, 3494, 4190, 8978, 10874, 3215, 12610, 42963, 33753, 2304, 6027, 9307, 28242, 3224, 4032, 20666, 2655, 6027, 1829, 11331, 36520, 2655, 15844, 8717, 36178, 2423, 2158, 9673, 29245, 23328, 3660, 23758, 2423, 10723, 10874, 7649, 46740, 4032, 5551, 3615, 9566, 1829, 24793, 21984, 6225, 31845, 10632, 8717, 24793, 1211, 9673, 25720, 13672, 1829, 10874, 47302, 16472, 13412, 16606, 21984], "avg_logprob": -0.25874998728434245, "compression_ratio": 1.728813559322034, "no_speech_prob": 9.119510650634766e-06, "words": [{"start": 3740.24, "end": 3740.64, "word": "true", "probability": 0.510986328125}, {"start": 3740.64, "end": 3741.0, "word": " true", "probability": 0.43798828125}, {"start": 3741.0, "end": 3741.38, "word": " true", "probability": 0.6748046875}, {"start": 3741.38, "end": 3742.26, "word": " true", "probability": 0.8623046875}, {"start": 3742.26, "end": 3743.06, "word": " معناته", "probability": 0.7369384765625}, {"start": 3743.06, "end": 3744.2, "word": " حصلت", "probability": 0.9288736979166666}, {"start": 3744.2, "end": 3744.34, "word": " على", "probability": 0.95556640625}, {"start": 3744.34, "end": 3744.78, "word": " نفس", "probability": 0.993408203125}, {"start": 3744.78, "end": 3745.56, "word": " ال", "probability": 0.4794921875}, {"start": 3745.56, "end": 3745.84, "word": " truth", "probability": 0.9140625}, {"start": 3745.84, "end": 3746.4, "word": " values", "probability": 0.85498046875}, {"start": 3746.4, "end": 3746.66, "word": " في", "probability": 0.81494140625}, {"start": 3746.66, "end": 3746.96, "word": " جدول", "probability": 0.9103190104166666}, {"start": 3746.96, "end": 3747.52, "word": " الاحتمالات", "probability": 0.96416015625}, {"start": 3747.52, "end": 3747.8, "word": " كله", "probability": 0.691650390625}, {"start": 3747.8, "end": 3748.2, "word": " و", "probability": 0.59033203125}, {"start": 3748.2, "end": 3748.94, "word": " بالتالي", "probability": 0.80267333984375}, {"start": 3748.94, "end": 3749.42, "word": " حصلت", "probability": 0.9820963541666666}, {"start": 3749.42, "end": 3749.72, "word": " على", "probability": 0.94482421875}, {"start": 3749.72, "end": 3750.48, "word": " نفس", "probability": 0.99072265625}, {"start": 3750.48, "end": 3750.62, "word": " ال", "probability": 0.9599609375}, {"start": 3750.62, "end": 3750.98, "word": " value", "probability": 0.98095703125}, {"start": 3750.98, "end": 3751.72, "word": " الموجودة", "probability": 0.966552734375}, {"start": 3751.72, "end": 3752.02, "word": " هذا", "probability": 0.77978515625}, {"start": 3752.02, "end": 3752.12, "word": " ال", "probability": 0.8994140625}, {"start": 3752.12, "end": 3752.32, "word": " demo", "probability": 0.7021484375}, {"start": 3752.32, "end": 3752.68, "word": " جان", "probability": 0.641357421875}, {"start": 3752.68, "end": 3754.3, "word": " له", "probability": 0.818359375}, {"start": 3754.3, "end": 3754.6, "word": " و", "probability": 0.68359375}, {"start": 3754.6, "end": 3754.82, "word": " أعطيكم", "probability": 0.6865478515625}, {"start": 3754.82, "end": 3754.92, "word": " الله", "probability": 0.466796875}, {"start": 3754.92, "end": 3755.22, "word": " عافية", "probability": 0.7607421875}, {"start": 3755.22, "end": 3755.76, "word": " نكمل", "probability": 0.7705891927083334}, {"start": 3755.76, "end": 3756.02, "word": " المرة", "probability": 0.947265625}, {"start": 3756.02, "end": 3756.16, "word": " اللي", "probability": 0.716064453125}, {"start": 3756.16, "end": 3756.3, "word": " جاي", "probability": 0.74560546875}, {"start": 3756.3, "end": 3756.4, "word": " ان", "probability": 0.77392578125}, {"start": 3756.4, "end": 3756.6, "word": " شاء", "probability": 0.934814453125}, {"start": 3756.6, "end": 3756.66, "word": " الله", "probability": 0.95361328125}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3757.10475, "duration_after_vad": 3561.0324999999825}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/_HzUlOTxQ18.srt b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/_HzUlOTxQ18.srt
new file mode 100644
index 0000000000000000000000000000000000000000..4fc1b8dc00d2e5c72e7fa328d2322278075b71cd
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/_HzUlOTxQ18.srt
@@ -0,0 +1,2006 @@
+1
+00:00:20,860 --> 00:00:22,860
+بسم الله والحمد لله والصلاة والسلام على رسول الله
+
+2
+00:00:22,860 --> 00:00:25,140
+اليوم إن شاء الله تعالى هنبدأ بشابتر جديد
+
+3
+00:00:25,140 --> 00:00:29,880
+هيكون ألطف من الشباتر السابقة، هنتكلم فيه على الـ
+
+4
+00:00:29,880 --> 00:00:35,300
+graph theory ونشوف أهميتها وتطبيقاتها، بداية بدي أقول
+
+5
+00:00:35,300 --> 00:00:39,720
+أنا سألت: "graph شو دخلها؟" يعني إيش يعني graph عادة؟
+
+6
+00:00:39,720 --> 00:00:43,260
+الشباب لما أتكلم على graph، أتكلم عليه كرسمة خريطة،
+
+7
+00:00:43,260 --> 00:00:46,120
+مجموعة من النقاط والخطوط اللي بينها، مجموعة من
+
+8
+00:00:46,120 --> 00:00:50,380
+النقاط والخطوط اللي بينها. وين تستخدم؟ في الـ
+
+9
+00:00:50,380 --> 00:00:56,440
+computer networking، computer network لما بنوصل
+
+10
+00:00:56,440 --> 00:01:01,300
+شبكة كمبيوتر، بتكلم على مجموعة من النقاط و
+
+11
+00:01:01,300 --> 00:01:04,860
+الخطوط اللي بينها، كل نقطة بتمثل computer، والخط
+
+12
+00:01:04,860 --> 00:01:08,140
+اللي بينهم هو الاتصال اللي موجود ما بين الجهازين.
+
+13
+00:01:08,140 --> 00:01:14,550
+بتكلم على الـ railways، خطوط السكة الحديد، شبكة
+
+14
+00:01:14,550 --> 00:01:20,110
+القطارات، تمام. graph، graph وإن كان يرى، إحنا بنرمز
+
+15
+00:01:20,110 --> 00:01:26,630
+أن المحطة هي النقطة، والخط اللي بينها، تمام، الخط
+
+16
+00:01:26,630 --> 00:01:30,270
+الواصل ما بين المحطات، آه، يعني هي فعلياً إحنا لما
+
+17
+00:01:30,270 --> 00:01:35,190
+بنجي في شبكة الكمبيوتر، بنحط مجموعة من النقاط و
+
+18
+00:01:35,190 --> 00:01:40,710
+بنوصل ما بين النقاط هذه بشكل أو بآخر،  بناءً على
+
+19
+00:01:40,710 --> 00:01:43,800
+إمكانية التوصيل اللي موجودة، لكن لما بتكلم في الـ
+
+20
+00:01:43,800 --> 00:01:45,820
+railways بقول والله هذه النقطة الأولى اللي هي
+
+21
+00:01:45,820 --> 00:01:49,460
+المحطة، بعض
+
+22
+00:01:49,460 --> 00:01:54,640
+المحطات، ممكن تصير فيها تفريعات، حسب ما يكون عندي نقطة
+
+23
+00:01:54,640 --> 00:02:00,280
+مركزية، وأنا من خلالها بصير أتكلم على التفريعات في
+
+24
+00:02:00,280 --> 00:02:06,660
+سكة الحديد. لما بتكلم على الـ maps، الخرائط، لما بتكلم
+
+25
+00:02:06,660 --> 00:02:14,340
+على الخرائط، في الخرائط الآن الطرق والمدن، النقاط هي
+
+26
+00:02:14,340 --> 00:02:20,700
+المدن أو المفترقات، والنقاط والخطوط هي الطرق
+
+27
+00:02:20,700 --> 00:02:24,340
+الموجودة بين النقاط أو المدن اللي موجودة عندي.
+
+28
+00:02:24,340 --> 00:02:28,680
+فالتطبيقات تبع الـ computer أو الـ graphs كثيرة جداً.
+
+29
+00:02:28,680 --> 00:02:32,920
+يعني لو درست شبكات، هتخدمك، لو اهتممت في موضوع design
+
+30
+00:02:32,920 --> 00:02:37,200
+زي ما جوجل ماب أو map quest أو ما شابه، كلها بتعتمد على
+
+31
+00:02:37,200 --> 00:02:42,840
+موضوع الصورة، في الآخر أنت بتشوف الخريطة صورة، والـ
+
+32
+00:02:42,840 --> 00:02:46,460
+graph تبعك يمثل بمجموعة من النقاط والخطوط اللي
+
+33
+00:02:46,460 --> 00:02:50,600
+بينهم، هنشوف كيف نمثله ك... أو ندخله لبرنامجنا أو
+
+34
+00:02:50,600 --> 00:02:54,360
+ما شابه. أنا وإحنا من ناحية الرياضيات بهمنا نفهم
+
+35
+00:02:54,360 --> 00:02:59,820
+أن الـ graph هو عبارة عن زوج مرتب، pair، بيحتوي على
+
+36
+00:02:59,820 --> 00:03:05,490
+عنصرين V وE، واتفقنا في الزوج المرتب، العنصر الأول
+
+37
+00:03:05,490 --> 00:03:11,730
+أو الترتيب مهم، الـ V هي عبارة عن مجموعة، أي V
+
+38
+00:03:11,730 --> 00:03:15,610
+عبارة عن مجموعتين، الـ V هي عبارة عن non-empty set،
+
+39
+00:03:15,610 --> 00:03:20,910
+مجموعة النقاط، مش لازم تكون فارغة، يعني مش لازم تكون
+
+40
+00:03:20,910 --> 00:03:26,570
+فارغة، كمجموعة على الأقل فيها عنصر واحد، and each
+
+41
+00:03:26,570 --> 00:03:32,530
+element في الـ E، كل عنصر في الـ E هو عبارة عن two
+
+42
+00:03:33,670 --> 00:03:39,250
+distinct elements of V، وكل عنصر في الـ E هو عبارة
+
+43
+00:03:39,250 --> 00:03:45,750
+عن عنصرين مختلفين من عناصر الـ V، عشان أوضح الكلام
+
+44
+00:03:45,750 --> 00:03:51,930
+هذا، لو أنا جيت وقلت: هاي
+
+45
+00:03:51,930 --> 00:04:00,130
+الـ graph هي A، B، C، وهاي الـ D، لأن الـ graph هذا أنا
+
+46
+00:04:00,130 --> 00:04:06,260
+بدأ بمخطط زوج مرتب، بروح أقول الـ graph هذي يمثل بزوج
+
+47
+00:04:06,260 --> 00:04:16,640
+مرتب V و E، إيش الـ V؟ تساوي {A, B, C, D}
+
+48
+00:04:16,640 --> 00:04:20,060
+{A, B, C, D}
+
+49
+00:04:20,060 --> 00:04:25,860
+مجموعة النقاط، non-empty set، أقل graph، أقل
+
+50
+00:04:25,860 --> 00:04:31,060
+graph ممكن إحنا نتكلم عليه اللي
+
+51
+00:04:31,060 --> 00:04:36,050
+فيه النقطة X هذه لحالها، هذا الـ graph من زوج مرتب
+
+52
+00:04:36,050 --> 00:04:44,270
+المجموعة {X} ومجموعة  الـ edges Φ، ولا لأ؟ لأ، هذه هي
+
+53
+00:04:44,270 --> 00:04:48,670
+مفهوم الـ definition، non-empty V هي مش فاضية، لكن
+
+54
+00:04:48,670 --> 00:04:52,050
+الـ E ممكن تكون فاضية، فهذا يكون أقل graph موجود
+
+55
+00:04:52,050 --> 00:04:59,910
+عندي، وهي نقطة واحدة، وإذا نكمل هذه الرسمة، الـ E هي
+
+56
+00:04:59,910 --> 00:05:05,540
+عبارة عن، كل element فيها عبارة عن two distinct
+
+57
+00:05:05,540 --> 00:05:10,460
+elements in V، عنصرين مختلفين مع بعض، هي مجموعة
+
+58
+00:05:10,460 --> 00:05:16,060
+الجسور، الجسور الموجودة بين مين ومين؟ {A, B}، هذه {A, B}،
+
+59
+00:05:16,060 --> 00:05:23,780
+العنصر الأول في المجموعة {A, B}، العنصر الثاني {B, C}.
+
+60
+00:05:26,720 --> 00:05:30,360
+مافيش غيرهم، هاي الجسرين اللي موجودات، هو لما قال لي
+
+61
+00:05:30,360 --> 00:05:35,520
+each element of E is a set of two distinct elements،
+
+62
+00:05:35,520 --> 00:05:39,040
+هو عبارة عن مجموعة من عنصرين مختلفين، أنا مثلت
+
+63
+00:05:39,040 --> 00:05:44,220
+المجموعة هي {a, b}، فيك تمثلهم كمجموعة ثانية فرعية،
+
+64
+00:05:44,220 --> 00:05:47,020
+ماعنديش مشكلة في الموضوع، بس لازم يكون الـ element
+
+65
+00:05:47,020 --> 00:05:51,580
+مختلفين عشان نتكلم على graph، لأن هذا التمثيل أسهل
+
+66
+00:05:51,580 --> 00:05:55,200
+لما أنا بكتب {A, B} دلالة على الجسر اللي موجود ما بين
+
+67
+00:05:56,780 --> 00:06:02,080
+النقطتين، هو نفس الجسر لو أنا كتبته {C, B} أو {B, A}.
+
+68
+00:06:02,080 --> 00:06:09,360
+يعني ما ينفعش أكتبه مرة {A, B} والمرة الثانية أكتبه {B,
+
+69
+00:06:09,360 --> 00:06:13,940
+A}، لأن هذه  مجموعة غير مرتبة، وعادة لما
+
+70
+00:06:13,940 --> 00:06:18,160
+بتكلم على طريق، أنا بتكلم two direction، موجود من A
+
+71
+00:06:18,160 --> 00:06:23,610
+لـ B هو نفس الـ connection من B لـ A، هذا هو التعريف لـ
+
+72
+00:06:23,610 --> 00:06:28,590
+graph اللي إحنا هنتعامل معاه من ناحية رياضيات، الـ
+
+73
+00:06:28,590 --> 00:06:32,630
+elements of V بنسميها الـ vertices، النقاط اللي هي A
+
+74
+00:06:32,630 --> 00:06:38,610
+وB وC وD اللي كتبناهم قبل شوية، والـ elements of E
+
+75
+00:06:38,610 --> 00:06:43,630
+لاحظت كتبناهم unordered pairs، يعني مش أزواج مرتبة،
+
+76
+00:06:43,630 --> 00:06:46,630
+وهم أزواج، نعم، لكنهم غير مرتبة، يعني ما تفرقش مين
+
+77
+00:06:46,630 --> 00:06:53,920
+يتقدم عن مين، هتمثل edges، vertices و edges، أو vertex
+
+78
+00:06:53,920 --> 00:07:00,460
+و edge، تمام، الآن
+
+79
+00:07:00,460 --> 00:07:05,040
+لما بآجي بقول: إيه، قلنا مكتوبين كمجموعة، صح؟ قبل
+
+80
+00:07:05,040 --> 00:07:13,260
+شوية رسمناهم، قلنا لازم الـ V والـ W يكونوا مختلفين و
+
+81
+00:07:13,260 --> 00:07:18,560
+بيربطوا، أو بمعنى آخر أن الـ edge E هذا بيربط النقطتين
+
+82
+00:07:19,790 --> 00:07:23,750
+V و W مع
+
+83
+00:07:23,750 --> 00:07:28,190
+بعض، incident،
+
+84
+00:07:28,190 --> 00:07:33,870
+مرتبطات مع بعض، يعني بقول إن V و W are incident
+
+85
+00:07:33,870 --> 00:07:40,030
+with the edge VW، معمول يهم join من خلال الـ edge
+
+86
+00:07:40,030 --> 00:07:45,410
+اللي موجودة عندها. لما بيكون في عندي نقطتين موجودين
+
+87
+00:07:45,410 --> 00:07:51,590
+على طرفين الجسر، بنقول عنهم نقاط متجاورة، adjacent
+
+88
+00:07:51,590 --> 00:07:56,830
+vertices، نقاط
+
+89
+00:07:56,830 --> 00:08:03,650
+متجاورة، الآن في الرسم هذه A
+
+90
+00:08:03,650 --> 00:08:09,610
+و B، وB و C، A و B متجاورات، وB و C متجاورات، لكن A و
+
+91
+00:08:09,610 --> 00:08:15,350
+D لا، A و C غير متجاورات كذلك، وبالتالي لما يكون عند
+
+92
+00:08:15,350 --> 00:08:22,330
+جسر ما بين نقطتين، بقول إن النقطتين متجاورتين، الجسور
+
+93
+00:08:22,330 --> 00:08:27,410
+متجاورة لما جسرين يلتقيان في نفس النقطة.
+
+94
+00:08:29,910 --> 00:08:34,790
+الآن {A, B} و {B, C} هذي جسور متجاورة، ولأنهم التقوا
+
+95
+00:08:34,790 --> 00:08:41,390
+أين؟ ولو كان في عندي نقطة أو في جسر من B لـ D، بيكون
+
+96
+00:08:41,390 --> 00:08:50,030
+B و D كـ vertices متجاورين، كذلك {A, B} و {B, D} و {B, C}
+
+97
+00:08:50,030 --> 00:08:54,050
+جسور متجاورة، لأنهم التقوا كلهم على نفس النقطة.
+
+98
+00:08:59,610 --> 00:09:06,150
+الآن، عدد الجسور الـ incident في النقطة X، أو عدد
+
+99
+00:09:06,150 --> 00:09:11,270
+الجسور الملتقية أو الواصلة للنقطة X، بنسميها الـ
+
+100
+00:09:11,270 --> 00:09:15,610
+degree تبعتها، رتبتها، رتبة النقطة تقاس أو تقدر
+
+101
+00:09:15,610 --> 00:09:19,730
+بعدد الجسور المتصلة بالنقطة، يعني الآن، رتبة A  يا
+
+102
+00:09:19,730 --> 00:09:26,050
+جماعة الشباب؟ واحد، كم edge متصل بالـ A؟ واحد، كم edge
+
+103
+00:09:26,050 --> 00:09:30,290
+متصل بالـ B؟ واحد، كم edge متصل بالـ C؟ واحد، كم edge
+
+104
+00:09:30,290 --> 00:09:34,510
+متصل بالـ B؟ ثلاثة، بالتالي الـ degree تبع الـ B؟
+
+105
+00:09:34,510 --> 00:09:39,390
+ثلاثة، الآن في الرسمة الأولانية ما كانش فيه  اتصال مع الـ D،
+
+106
+00:09:39,390 --> 00:09:45,490
+حذا كانت لحالها، هيك الـ degree تبع الـ D  جديش؟ صفر.
+
+107
+00:09:45,490 --> 00:09:49,150
+الـ degree تبع الـ D صفر، وبقول عنها isolated point،
+
+108
+00:09:49,150 --> 00:09:57,300
+نقطة معزولة، وبالتالي بنقول عنه الـ vertex odd vertex،
+
+109
+00:09:57,300 --> 00:10:02,320
+أو even vertex، بدايةً عن degree تبعته، لو كانت odd،
+
+110
+00:10:02,320 --> 00:10:07,020
+بقول عنه odd، يعني الـ A is odd vertex، odd يعني أن
+
+111
+00:10:07,020 --> 00:10:10,800
+الـ degree تبعته odd، ممكن واحد، ممكن ثلاثة، الله أعلم،
+
+112
+00:10:10,800 --> 00:10:16,980
+والـ B is even vertex، يعني الـ degree تبعته عدد
+
+113
+00:10:16,980 --> 00:10:17,400
+زوجي.
+
+114
+00:10:20,860 --> 00:10:24,460
+تعالى نشوف الـ graph اللي موجود عندي هنا، الـ graph
+
+115
+00:10:24,460 --> 00:10:31,300
+هذا كان vertex عليه 6، طبعاً لو أنا بدي أكثر، وإحنا
+
+116
+00:10:31,300 --> 00:10:35,460
+هأقول الـ G = (V,
+
+117
+00:10:35,460 --> 00:10:44,400
+E)، والـ V هذا تساوي {V1, V2, V3, V4,
+
+118
+00:10:44,480 --> 00:10:46,380
+V5, V6}
+
+119
+00:10:56,860 --> 00:11:01,800
+أقول E هي عبارة عن مجموعة الجسور اللي موجودة عندي،
+
+120
+00:11:01,800 --> 00:11:14,020
+هان الـ connections: {V1, V4}, {V2, V5}, {V1, V6}, {V4, V5}, {V5, V6}
+
+121
+00:11:14,020 --> 00:11:18,000
+وين؟
+
+122
+00:11:18,000 --> 00:11:23,930
+لأ، مش موجود، مش موجود، شوف النقطة اللي في النص، لاحظ
+
+123
+00:11:23,930 --> 00:11:26,710
+...لاحظ...أنا ما حسبت الـ...هي...ما حسبت الـ case
+
+124
+00:11:26,710 --> 00:11:33,330
+أنه هذا لو فيه نقطة هان، كان سؤالنا نفسنا أكثر، مش
+
+125
+00:11:33,330 --> 00:11:36,350
+كثير، واحد إن أنا...أنا أتخيل لو عندي فيه هان V7،
+
+126
+00:11:36,350 --> 00:11:41,390
+صح، في عندي واحد، اثنين، ثلاثة، أربعة، لأن الجسر واقع ما
+
+127
+00:11:41,390 --> 00:11:46,570
+بين نقطتين، الجسر دائماً واقع ما بين نقطتين، وبالتالي
+
+128
+00:11:46,570 --> 00:11:49,690
+أنا ما بديش أغير حسب النقاط اللي موجودة عندي هان.
+
+129
+00:11:51,060 --> 00:11:58,920
+وبالتالي الـ graph تبعي هذا هيمثله صح، V3 الـ
+
+130
+00:11:58,920 --> 00:12:04,320
+degree تبعتها صفر، isolated point، نقطة منعزلة، عن الـ
+
+131
+00:12:04,320 --> 00:12:07,980
+graph اللي موجود عندها، فيه شغل مهم جداً يا شباب هذا
+
+132
+00:12:07,980 --> 00:12:11,180
+الـ graph هو نفسه لو أنا اجيت رسمته هيك.
+
+133
+00:12:23,540 --> 00:12:32,420
+هذه أربعة، هذه خمسة، هذه اثنين، هذه ستة، وهذه ثلاثة.
+
+134
+00:12:32,420 --> 00:12:37,220
+هذا
+
+135
+00:12:37,220 --> 00:12:42,140
+نفس الـ graph، نفس الـ graph مع اختلاف الـ direction،
+
+136
+00:12:42,140 --> 00:12:45,240
+لأن النقاط هي نفسها، مع اختلاف الـ direction، اختلاف
+
+137
+00:12:45,240 --> 00:12:50,100
+الشكل، اختلاف الشكل، وهنشوف لاحقاً أن كيف ممكن أنا
+
+138
+00:12:50,100 --> 00:12:52,540
+أتعامل مع الـ graph اللي بالشكل هذا، كيف أعرف أن الـ
+
+139
+00:12:52,540 --> 00:12:55,460
+graph هذا يطابق الـ graph هذا، أو هل في خصائص من الـ
+
+140
+00:12:55,460 --> 00:12:57,500
+two graphs عشان أقول إن هما الاثنين هم نفس
+
+141
+00:12:57,500 --> 00:13:04,310
+الشكل ولا لأ، أنت عشان الـ A والـ V والـ K هي واحدة، لأن
+
+142
+00:13:04,310 --> 00:13:07,370
+المفروض بحيث تقارن، تعمل مقارنة ما بين النقاط
+
+143
+00:13:07,370 --> 00:13:10,990
+والنقاط الثانية والجسور والجسور الثانية، بناء على
+
+144
+00:13:10,990 --> 00:13:13,650
+تعريف النقاط اللي أنت اخترته، فهنشوفها لاحقاً يا
+
+145
+00:13:13,650 --> 00:13:18,770
+رامي، بس الفكرة أن هذا الـ graph هو graph مطابق
+
+146
+00:13:18,770 --> 00:13:23,790
+تماماً، يعني لو أنا كتبت الـ V والـ E، هتطلع نفسهم، الـ
+
+147
+00:13:23,790 --> 00:13:27,850
+V والـ E هتطلع نفسهم، تمام؟ وبالتالي بيقول عنهم
+
+148
+00:13:27,850 --> 00:13:31,950
+isomorphic graphs، وهنشوفها لاحقاً إن شاء الله تعالى.
+
+149
+00:13:31,950 --> 00:13:39,780
+طيب، الآن في عندي شغلة غالباً موجودة في التطبيقات أو
+
+150
+00:13:39,780 --> 00:13:43,120
+في الحياة، لكن في الـ definition الأصلي تبع الـ graph
+
+151
+00:13:43,120 --> 00:13:47,420
+مالهاش تعريف، مالهاش وجود، خصوصاً...خصوصاً لما أجينا
+
+152
+00:13:47,420 --> 00:13:50,800
+...اتكلمنا على المجموعات، أنت ملاحظ من البداية أنا
+
+153
+00:13:50,800 --> 00:13:54,970
+صرت الآن وكأنه مجموع...موضوع الـ graph شمل الـ
+
+154
+00:13:54,970 --> 00:13:59,450
+relation والمجموعات، لأنه قال لي إن هذه مجموعة وهذه
+
+155
+00:13:59,450 --> 00:14:02,990
+مجموعة، والاثنين موجودين في عبارة عن زوج مرتب، وزوج
+
+156
+00:14:02,990 --> 00:14:08,570
+مرتب، يعني relation، ولا لأ؟ الآن حصل، لما قال لي الـ
+
+157
+00:14:08,570 --> 00:14:13,650
+vertices مجموعات، يعني مافيش تكرار، تمام، ولما قال
+
+158
+00:14:13,650 --> 00:14:17,790
+لي الـ edges مجموعات، برضه مافيش تكرار للـ element، و
+
+159
+00:14:17,790 --> 00:14:25,610
+لا لأ، تمام. طيب، في حالة زي هذه، E1 وE2 هو عبارة عن
+
+160
+00:14:25,610 --> 00:14:31,230
+جسر...هو عبارة عن جسرين مختلفين موجودين بين V1 و
+
+161
+00:14:31,230 --> 00:14:34,870
+V2، طب في الـ representation تبعك الـ graph الأصلية
+
+162
+00:14:34,870 --> 00:14:42,190
+ما ينفعش آجي أقول والله أنا الـ E عندي تساوي {V1, V2}
+
+163
+00:14:42,190 --> 00:14:50,090
+كما {V1, V2}، لأن هذا بيتنافى مع تعريف المجموعات، و
+
+164
+00:14:50,090 --> 00:14:55,150
+بالتالي هذا إيش ممكن تساوي؟ يجب أن تعد واحد، لكن في
+
+165
+00:14:55,150 --> 00:15:00,290
+الواقع هو اثنين، طيب ما يأتي، هذا أصبح الـ
+
+166
+00:15:00,290 --> 00:15:03,850
+definition تبع الـ graph لا ينطبق عليه، عشان هيك
+
+167
+00:15:03,850 --> 00:15:08,590
+سامعون، الشغل اسمها بي سيدو graph، pseudo-graph، هو
+
+168
+00:15:08,590 --> 00:15:13,730
+graph مع بعض التعديلات أو بعض التجاوزات للـ
+
+169
+00:15:13,730 --> 00:15:16,810
+definition، الـ pseudo-graph هو عبارة عن graph
+
+170
+00:15:16,810 --> 00:15
+
+223
+00:19:48,850 --> 00:19:52,570
+لاحظ أنني لا يهمني الـ direction كل ما يهمني
+
+224
+00:19:52,570 --> 00:19:57,370
+أنني أخذت النقاط وأخذت الجسور التي فعلياً موجودة
+
+225
+00:19:57,370 --> 00:20:06,810
+ما بين النقاط، يعني الآن لو أنني أجئت عملت هكذا V1
+
+226
+00:20:06,810 --> 00:20:10,550
+وV2، هل هذا الـ graph subset
+
+227
+00:20:13,580 --> 00:20:21,700
+هل هذا الـ graph subset؟ subset V1 وV2 كمجموعة هل
+
+228
+00:20:21,700 --> 00:20:27,460
+هي subset من V؟ آه subset الآن، مجموعة الجسور V1 V2
+
+229
+00:20:27,460 --> 00:20:30,420
+جسر واحد في element واحد، هل هي subset من أيه؟
+
+230
+00:20:30,420 --> 00:20:33,780
+subset من أيه؟ معناته هذا subgraph من هذا، هاي
+
+231
+00:20:33,780 --> 00:20:37,600
+المعيار الوحيد الذي عندي، تمام؟ لا يهمني الـ direction
+
+232
+00:20:37,600 --> 00:20:42,500
+كل ما يهمني النقاط موجودة والجسور موجودة، أقول
+
+233
+00:20:42,500 --> 00:20:48,180
+عنه subset، وبالتالي هاي في عندي different subset V4
+
+234
+00:20:48,180 --> 00:20:57,640
+V3 V6 V7 موجودين، هل الـ V subset V4، V3 موجود؟
+
+235
+00:20:57,640 --> 00:21:07,360
+آه موجود، هايه طيب، و ثلاثه وستة، آه هايه موجود 6 و7
+
+236
+00:21:07,360 --> 00:21:10,180
+موجود، يعني هذه الرسمة التي نحن نتكلم عليها
+
+237
+00:21:10,180 --> 00:21:13,420
+قاعدين نلاحظ كيف الـ representation تختلف؟
+
+238
+00:21:13,420 --> 00:21:17,740
+ماليش دخل بشكلها، الآن أنت وجدت قابط أو مقابط، مش
+
+239
+00:21:17,740 --> 00:21:21,580
+مرحلتنا نحن نتكلم على الـ subset، المعيار تبعي أفحص
+
+240
+00:21:21,580 --> 00:21:26,160
+أن مجموعة الجسور ومجموعة النقاط مجموعات جزئية من
+
+241
+00:21:26,160 --> 00:21:32,920
+الجسور والنقاط التي موجودة على الـ graph الأصلي، لو
+
+242
+00:21:32,920 --> 00:21:37,280
+أنا أخذت هذين معاً، أخذته هكذا as one
+
+243
+00:21:37,280 --> 00:21:44,880
+graph، هل هو subset؟ V2, V3, V6, V7، subset الـ V's
+
+244
+00:21:44,880 --> 00:21:52,740
+طب الآن الجسور V2 و V3 موجودة هنا، V6, V7 موجودة هنا،
+
+245
+00:21:52,740 --> 00:21:58,120
+معناته هذا أيضاً إيش؟ subset، طيب،
+
+246
+00:21:58,120 --> 00:21:59,300
+لو أنا اتجهت هكذا يا شباب
+
+247
+00:22:09,410 --> 00:22:16,290
+لِحَالِها هكذا، أيوة
+
+248
+00:22:16,290 --> 00:22:22,210
+هل الـ graph هذا subset أم لا؟ كم واحداً يقول
+
+249
+00:22:22,210 --> 00:22:29,250
+subset؟ واحد، اثنين، ثلاثة، أربعة، خمسة، ستة،
+
+250
+00:22:29,250 --> 00:22:35,530
+واحدة، سأحدد اثنين، طيب، تعالَ احسبْ حساباً بسيطاً
+
+251
+00:22:35,530 --> 00:22:40,950
+جداً، اكتب لي هذا as كزوج مرتب هكذا، ماذا ستقول؟ ستقول
+
+252
+00:22:40,950 --> 00:22:51,530
+G V خمسة و Φ، صح؟ هل هذه subset من الـ V؟ آه
+
+253
+00:22:51,530 --> 00:22:57,590
+subset، طب و الـ Φ subset من الـ E؟ آه subset، معناته
+
+254
+00:22:57,590 --> 00:22:59,590
+الـ graph هذا subset
+
+255
+00:23:03,400 --> 00:23:09,040
+بالفترة، تمام؟ يعني أقل vertex أو أقل graph هو عبارة
+
+256
+00:23:09,040 --> 00:23:13,900
+عن graph من نقطة واحدة، ودائماً تبحث عن وقت الـ
+
+257
+00:23:13,900 --> 00:23:18,460
+subset، ممتاز، طيب الآن لدي مصطلح جديد اسمه الـ
+
+258
+00:23:18,460 --> 00:23:23,600
+complete graph، ما هو الـ complete graph؟ هو عبارة عن
+
+259
+00:23:23,600 --> 00:23:30,240
+graph كل vertex فيه متصل بكل الـ vertices الأخرى
+
+260
+00:23:33,850 --> 00:23:39,890
+يعني الآن كل نقطة فيه متصلة بكل النقاط، الآن لو أنا
+
+261
+00:23:39,890 --> 00:23:48,750
+افترضت graph بالشكل هذا V1 و V2، V1 و V2، وفيه
+
+262
+00:23:48,750 --> 00:23:53,970
+بينهما جسر، هل هذا complete graph؟ الـ definition
+
+263
+00:23:53,970 --> 00:24:00,730
+كانت تقول أن كل vertex، كل نقطة مرتبطة بكل النقاط
+
+264
+00:24:00,730 --> 00:24:06,430
+الموجودة، هذا في نقطتين فقط، مرتبطتين ببعضهما،
+
+265
+00:24:06,430 --> 00:24:12,270
+ممتاز؟
+
+266
+00:24:12,270 --> 00:24:17,090
+Complete
+
+267
+00:24:17,090 --> 00:24:26,530
+graph، واحد واثنين وثلاثة، واحد متصل مع اثنين و
+
+268
+00:24:26,530 --> 00:24:30,650
+ثلاثة، واثنين متصل مع واحد وثلاثة، وثلاثة متصل مع
+
+269
+00:24:30,650 --> 00:24:33,850
+واحد واثنين، معناته كل نقطة متصلة بكل النقاط
+
+270
+00:24:33,850 --> 00:24:37,150
+الأخرى
+
+271
+00:24:37,150 --> 00:24:43,210
+هكذا
+
+272
+00:24:43,210 --> 00:24:49,990
+مش complete graph، هكذا
+
+273
+00:24:49,990 --> 00:24:55,830
+صار complete graph، مصبوط؟ وفيك تتخيل كلما زاد
+
+274
+00:24:55,830 --> 00:25:00,270
+عدد اللقاءات، ماذا سيزيد؟ سيزيد عدد الجسور في الـ
+
+275
+00:25:00,270 --> 00:25:04,250
+complete graph، تمام، هذا فيه شغل مهم، خلينا نقوله من
+
+276
+00:25:04,250 --> 00:25:08,770
+الآن، لو طلعنا في الـ complete graph، كم الـ degree
+
+277
+00:25:08,770 --> 00:25:13,490
+كم قيمة الـ degree لكل complete graph؟ يعني عادةً
+
+278
+00:25:13,490 --> 00:25:19,320
+نرمز، لو نحن يا شباب، بالـ K، اختصاراً لكامل، أو رمز
+
+279
+00:25:19,320 --> 00:25:24,120
+لكامل، واحد يقول نسميها الـ C K كمان؟ والـ N عدد الـ
+
+280
+00:25:24,120 --> 00:25:34,160
+vertices، يعني هذا كده قيمته؟ K2، هذا K3، هذا K4
+
+281
+00:25:34,160 --> 00:25:38,220
+ممتاز، الـ K أكثر من الزاوية الثلاثين أكثر؟ الزاوية
+
+282
+00:25:38,220 --> 00:25:41,300
+الثلاثين؟
+
+283
+00:25:41,300 --> 00:25:46,190
+طب الزاوية 180 يا صاحبي، والزاوية هنا خمسة وأربعين
+
+284
+00:25:46,190 --> 00:25:49,630
+فهمت؟ الزاوية هنا ثلاثة وثلاثون وثلاثة وعشرة
+
+285
+00:25:49,630 --> 00:25:56,730
+ما لها علاقة بالزاوية، ما لها علاقة بالزاوية، الـ
+
+286
+00:25:56,730 --> 00:26:01,070
+K، أنا مش جاهز، أقول أنا complete، الـ K ترمز لـ
+
+287
+00:26:01,070 --> 00:26:05,350
+complete graph، والـ N التي تحتها تمثل عدد النقاط
+
+288
+00:26:05,350 --> 00:26:11,800
+التي موجودة في الـ graph، أيه، الآن هل أقدر أستفيد
+
+289
+00:26:11,800 --> 00:26:16,300
+أنا أو أحصل على قيمة الـ degree لكل الـ vertex من
+
+290
+00:26:16,300 --> 00:26:21,680
+خلال الـ K؟ يعني لو أنا سألتك، كم الـ degree لـ V
+
+291
+00:26:21,680 --> 00:26:27,720
+واحد؟ واحد، كم الـ degree لـ V اثنين؟ واحد، ما
+
+292
+00:26:27,720 --> 00:26:32,900
+علاقتها بالاثنين؟ نقص واحد في الـ K، ثلاثة، كم الـ
+
+293
+00:26:32,900 --> 00:26:40,940
+degree لواحد؟ اثنين، degree لاثنين ثلاثة، ثلاثة
+
+294
+00:26:40,940 --> 00:26:43,160
+ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة
+
+295
+00:26:43,160 --> 00:26:43,180
+ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة
+
+296
+00:26:43,180 --> 00:26:44,640
+ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة
+
+297
+00:26:44,640 --> 00:26:45,680
+ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة
+
+298
+00:26:45,680 --> 00:26:46,760
+ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة
+
+299
+00:26:46,760 --> 00:26:49,280
+ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة
+
+300
+00:26:49,280 --> 00:27:03,880
+ثلاثة ثلاثة ثلاثة ثلاثة تلا
+
+301
+00:27:04,320 --> 00:27:07,800
+والنقطة هذه ستكون متصلة بكل النقاط الأخرى، أيامه
+
+302
+00:27:07,800 --> 00:27:12,280
+ستكون متصلة بالنقص واحد من النقاط، أو بنقص متصلة
+
+303
+00:27:12,280 --> 00:27:16,500
+بالنقص واحد من الجسور، التي هي تمثل الـ degree، تمام
+
+304
+00:27:16,500 --> 00:27:22,500
+بقي لدينا شغل أخير في الـ complete graph، لو كان
+
+305
+00:27:22,500 --> 00:27:26,520
+عندي graph بالشكل هذا، هل هو complete graph؟
+
+306
+00:27:30,240 --> 00:27:32,260
+هناك من يقول complete graph، والآخر يقول
+
+307
+00:27:32,260 --> 00:27:39,520
+طبعاً كل نقطة متصلة بنفسها، لغاية متصلة بنفسها، متصلة
+
+308
+00:27:39,520 --> 00:27:44,780
+وبالتالي أنا أتحدث، جالس، عن complete graph، complete
+
+309
+00:27:44,780 --> 00:27:51,580
+graph، وبالتالي هذا K واحد، تعالَ طبق عليه قانون الـ
+
+310
+00:27:51,580 --> 00:27:56,980
+degree، طبق عليه قانون الـ degree، صفر
+
+311
+00:27:59,030 --> 00:28:02,030
+ممتاز، يعني complete graph، ويُطبّق عليه كل شروط الـ
+
+312
+00:28:02,030 --> 00:28:17,490
+complete graph 100%، في
+
+313
+00:28:17,490 --> 00:28:23,030
+عندي graph اسمه، يُقال عنه bipartite graph، bipartite
+
+314
+00:28:23,030 --> 00:28:25,790
+graph، هو عبارة عن partition  دي  graph، الـ graph
+
+315
+00:28:25,790 --> 00:28:29,680
+جُسِّمَ من النصف، مش جُسِّمَ الـ graph، أنا من النصف فصلته
+
+316
+00:28:29,680 --> 00:28:36,280
+يعني تأتي لتقول والله زي ما رأينا قبل قليل V2 V3
+
+317
+00:28:36,280 --> 00:28:45,060
+V6 و V7، لأنني فصلته هكذا، سميّتُه partitioned graph
+
+318
+00:28:45,060 --> 00:28:50,560
+الـ bipartite graph له خصائص معينة، الـ bipartite
+
+319
+00:28:50,560 --> 00:28:55,440
+graph هو عبارة عن graph أقدر أجسم الـ vertices
+
+320
+00:28:55,440 --> 00:29:01,660
+تبعه لـ two disjoint sets، يعني الجسم تبعنا أو الـ
+
+321
+00:29:01,660 --> 00:29:06,420
+partitioning  يجب أن يكون على اثنين، على النقاط الـ
+
+322
+00:29:06,420 --> 00:29:11,840
+bipartite graph هو عبارة عن graph أُجَرِّبُ أفصلُ أو أجسم
+
+323
+00:29:11,840 --> 00:29:14,620
+المجموعة، مجموعة النقاط تبعته، الـ vertices
+
+324
+00:29:14,620 --> 00:29:20,200
+لمجموعتين مختلفتين، التقاطع بينهما Φ، disjoint
+
+325
+00:29:20,200 --> 00:29:29,160
+بحيث أن كل vertex في المجموعة الأولى متصل بعناصر
+
+326
+00:29:29,160 --> 00:29:33,000
+المجموعة الثانية، وعناصر المجموعة الواحدة ما بينها
+
+327
+00:29:33,000 --> 00:29:39,440
+لا يوجد اتصال، أعيد ثانية أو نأخذ مثالاً، جاهز؟ جاهز؟ الآن
+
+328
+00:29:39,440 --> 00:29:50,160
+لو أنا أعطيت هكذا، سأقول A, B, C كـ vertices، الآن الـ
+
+329
+00:29:50,160 --> 00:30:00,260
+graph هذا الممثل بالمجموعتين A وB وC، والـ E
+
+330
+00:30:00,260 --> 00:30:09,100
+الجسور AB و BC، 100%، الآن أقدر أقول عن الـ graph
+
+331
+00:30:09,100 --> 00:30:13,940
+هذا bipartite graph، إذا قدرت أجسم المجموعة الـ
+
+332
+00:30:13,940 --> 00:30:19,780
+vertices لمجموعتين، بحيث أن الـ connections فقط
+
+333
+00:30:19,780 --> 00:30:23,460
+موجودة بين عناصر المجموعتين، عناصر المجموعة الواحدة
+
+334
+00:30:23,460 --> 00:30:29,400
+ما بينها connections، الآن تعالَ نفكر في الحالة
+
+335
+00:30:29,400 --> 00:30:32,540
+الوحيدة التي ممكن أن تُصلِحَ معي أن أحكم الـ B في
+
+336
+00:30:32,540 --> 00:30:39,180
+مجموعة، والـ A و C في مجموعة أخرى، أصلح؟
+
+337
+00:30:39,180 --> 00:30:45,880
+الآن الـ V التي عندي هنا، هذه
+
+338
+00:30:45,880 --> 00:30:55,830
+تساوي الـ B لحالها اتحاد A و C، الآن استطعت أن أجسم
+
+339
+00:30:55,830 --> 00:31:00,350
+الـ V هذه إلى مجموعتين disjoint، التقاطع بينهما Φ
+
+340
+00:31:00,350 --> 00:31:04,550
+لأستطيع أن أقول كامل الـ definition تبعي صحيح،
+
+341
+00:31:04,550 --> 00:31:08,890
+أقول عنه هذا bipartite graph، يجب أن أحصل على أن
+
+342
+00:31:08,890 --> 00:31:11,890
+عناصر المجموعة الواحدة يجب أن تكون غير متصلة ببعضها،
+
+343
+00:31:11,890 --> 00:31:15,430
+المجموعة الأولى ليست فيها إلا عنصر واحد، مريحة،
+
+344
+00:31:15,430 --> 00:31:22,230
+المجموعة الثانية فيها A و C متصلتان ببعضهما؟ لا، والاتصال
+
+345
+00:31:22,230 --> 00:31:25,070
+فقط موجود بين من ومن، بين المجموعة الأولى
+
+346
+00:31:25,070 --> 00:31:29,230
+والمجموعة الثانية، يعني bipartite graph عبارة عن
+
+347
+00:31:29,230 --> 00:31:33,690
+bipartite graph، طيب، لو أنا جئت لـ graph بالشكل
+
+348
+00:31:33,690 --> 00:31:38,930
+هذا V1
+
+349
+00:31:38,930 --> 00:31:44,490
+و V2، هل هو bipartite graph؟
+
+350
+00:31:47,770 --> 00:31:57,270
+طيب، أنا أريد أن أقول أن الـ V تساوي V1 اتحاد الـ V2
+
+351
+00:31:57,270 --> 00:32:02,830
+وعناصر المجموعة الواحدة غير متصلة ببعضها، صحيح أم
+
+352
+00:32:02,830 --> 00:32:08,710
+غير صحيح؟ صحيح؟ ما من جسور؟ من جسور في عناصر المجموعة
+
+353
+00:32:08,710 --> 00:32:13,610
+الواحدة؟ ما من جسور، مصبوط؟ وعناصر المجموعتين، أو
+
+354
+00:32:13,610 --> 00:32:18,460
+الجسور ممتدة ما بين عناصر المجموعتين، صحيح؟ وقلتُ لكَ
+
+355
+00:32:18,460 --> 00:32:21,660
+هذا bipartite graph، أمثالك أو شبابك الـ bipartite
+
+356
+00:32:21,660 --> 00:32:27,820
+graph، بتخيل أنّهُ نهر وعلى ضفتي النهر، أو على
+
+357
+00:32:27,820 --> 00:32:31,360
+ضفتي النهر موجودات ونريد أن نصنع جسراً، نريد أن نصنع
+
+358
+00:32:31,360 --> 00:32:35,640
+جسراً، الجسر أين نصنعهُ نحن؟ نصنعه فوق النهر؟ و
+
+359
+00:32:35,640 --> 00:32:39,280
+لا نصنعه على ضفة؟ يجب أن يمر فوق النهر، فوق
+
+360
+00:32:39,280 --> 00:32:44,530
+النهر، الآن إذا استطعتُ أنا أفصل المجموعة التابعة، عناصرها
+
+361
+00:32:44,530 --> 00:32:49,530
+مختلفة بحيث أن الـ connections فقط تكون كجسر من
+
+362
+00:32:49,530 --> 00:32:52,550
+عنصر النقطة الأولى والثانية، أنا أكون bipartite
+
+363
+00:32:52,550 --> 00:32:59,970
+graph، هذا الكلام يُصحّح تماماً، V1 و V2، عندنا نقطة اثنتان
+
+364
+00:32:59,970 --> 00:33:04,690
+فقط، وبالتالي أقدر أعتبر هذا bipartite graph، bi
+
+365
+00:33:04,690 --> 00:33:12,570
+partite graph، تعالَ نشوف الرسمة، هذا bipartite graph
+
+366
+00:33:16,990 --> 00:33:22,010
+ربك عليك وأنتَ يجب أن تتعلم من علم ربك، لأنه لم يتركك
+
+367
+00:33:22,010 --> 00:33:25,650
+جاهلاً، ولم يتركك هكذا، الآن هذا الـ definition موجود
+
+368
+00:33:25,650 --> 00:33:31,330
+بين يديك، الـ definition موجود بين يديك، هل هذا الـ
+
+369
+00:33:31,330 --> 00:33:35,550
+graph bipartite graph؟ الفكرة كانت تأتي بأنني أريد
+
+370
+00:33:35,550 --> 00:33:40,710
+أخذ النقاط، أجسمها لمجموعتين، عناصر المجموعة
+
+371
+00:33:40,710 --> 00:33:45,410
+الواحدة، وما بينها اتصال، هؤلاء
+
+372
+00:33:45,410 --> 00:33:50,520
+عليها ست نقاط، أنتَ تريد حتى لو كان واحد وأربعة، واحد
+
+373
+00:33:50,520 --> 00:33:55,260
+وخمسة، ما من مشكلة لديك، لم نضع حدّاً يا شباب على
+
+374
+00:33:55,260 --> 00:33:59,100
+عدد عناصر المجموعة، عندما أريد أجسمها هنا، صحيح؟ نحن
+
+375
+00:33:59,100 --> 00:34:02,160
+قلنا فقط أجسمها لمجموعتين، ولم نقل أن المجموعتين
+
+376
+00:34:02,160 --> 00:34:05,500
+المتساويتين، لم نضع عليهما أي شرط، فقط أجسمها إلى
+
+377
+00:34:05,500 --> 00:34:08,620
+مجموعتين،
+
+378
+00:34:08,620 --> 00:34:13,910
+لم يقل أحد، عناصر المجموعة الواحدة، ما بينها
+
+379
+00:34:13,910 --> 00:34:17,310
+connection، لأنه ما من جدوى يا شباب، تمام، مرّة أخرى يا شباب
+
+380
+00:34:17,310 --> 00:34:22,310
+افترض أن هذا هو النهر، هذا
+
+381
+00:34:22,310 --> 00:34:26,730
+الضفة الأولى، وهذه الضفة الثانية، الضفة الأولى، و
+
+382
+00:34:26,730 --> 00:34:32,130
+الضفة الثانية، تمام؟ الآن لو أنتَ جئتَ بنيتَ جسراً هنا،
+
+383
+00:34:32,130 --> 00:34:38,350
+منطق؟
+
+384
+00:34:38,350 --> 00:34:43,260
+المهندس الذي يريد أن يبني جسراً كهذا، يريد أن يمر به، أولا؟
+
+385
+00:34:43,260 --> 00:34:46,980
+لماذا؟ لأنه يُضيع المال في المكان الخاطئ، نحن لسنا
+
+386
+00:34:46,980 --> 00:34:52,140
+بحاجة لما... الجسم يجب أن يكون فوق
+
+387
+00:34:52,140 --> 00:34:55,960
+النهر ليحقق الفائدة منه، الآن عندما أنتَ
+
+388
+00:34:55,960 --> 00:35:00,500
+تفكر في bipartite graph بالشكل المنطقي
+
+389
+00:35:00,500 --> 00:35:06,160
+هذا، الآن، هل أقدر أنا أجسم الـ graph هذا؟ آه، بكل
+
+390
+00:35:06,160 --> 00:35:10,780
+بساطة، يُجسَّمُ هذه المجموعة الأولى وهذه المجموعات
+
+391
+00:35:10,780 --> 00:35:16,740
+الثانية، ولم يقل لي أحد أنه يجب أن يكون الجسم متساوياً
+
+392
+00:35:16,740 --> 00:35:20,700
+بل المهم الـ connection يكون ما بين عناصر
+
+393
+00:35:20,700 --> 00:35:24,540
+المجموعتين، طب أنا لو قصرتُ ست مجموعات، كل مجموعة
+
+394
+00:35:24,540 --> 00:35:28,800
+لا يوجد بينها جسور، اصبر، اصبر، اصبر، اصبر،
+
+395
+00:35:28,800 --> 00:35:29,860
+اصبر، اصبر، اصبر، اصبر، اصبر
+
+445
+00:39:33,010 --> 00:39:34,730
+كمان كمان كمان كمان كمان كمان كمان كمان كمان كمان
+
+446
+00:39:34,730 --> 00:39:39,870
+كمان كمان كمان كمان كمان كمان كمان كمان
+
+447
+00:39:39,870 --> 00:39:45,550
+كمان كمان كمان كمان كمان كمان كمان كمان كمان كمان
+
+448
+00:39:45,550 --> 00:39:48,990
+كمان
+
+449
+00:39:50,410 --> 00:39:58,410
+Complete bipartite graph اتنين تلاتة هذه
+
+450
+00:39:58,410 --> 00:40:08,670
+المجموعة الأولى V1 وهذه V2 وكل
+
+451
+00:40:08,670 --> 00:40:13,290
+element أو كل vertex في الأولى متصل بالتلاتة
+
+452
+00:40:13,290 --> 00:40:15,150
+الموجودين في الـ vertex في المجموعة الثانية
+
+453
+00:40:17,930 --> 00:40:24,330
+والعكس صحيح والعكس صحيح طيب .. الآن لو أنا سألتك
+
+454
+00:40:24,330 --> 00:40:27,550
+نفس السؤال اللي تكلمنا عنه في الـ complete graph الـ
+
+455
+00:40:27,550 --> 00:40:32,510
+degree .. الـ degree تبعت الـ complete graph
+
+456
+00:40:32,510 --> 00:40:39,990
+vertices  جداش هتكون؟ مجسومة لـ نصين الأولى
+
+457
+00:40:39,990 --> 00:40:43,190
+الـ
+
+458
+00:40:43,190 --> 00:40:49,450
+degree تبعتها n،  والتانية الـ degree تبعتها M يعني
+
+459
+00:40:49,450 --> 00:40:53,150
+بين جثين الـ degree تبعت عناصر المجموعة الأولى
+
+460
+00:40:53,150 --> 00:40:56,530
+اتنين، إذا سألتك الـ degree اللي فيه واحد جداش هنا؟
+
+461
+00:40:56,530 --> 00:40:59,550
+يا شباب اتنين، قلنا الـ degree هي عبارة عن عدد
+
+462
+00:40:59,550 --> 00:41:04,190
+الأساور المتصلة في النقطة، و الـ degree اللي فيه واحدة
+
+463
+00:41:04,190 --> 00:41:07,250
+فيه اتنين واحد واحد واحد واحد واحد واحد واحد واحد
+
+464
+00:41:07,250 --> 00:41:11,390
+واحد واحد واحد واحد واحد واحد واحد واحد
+
+465
+00:41:11,390 --> 00:41:12,450
+واحد واحد واحد واحد واحد واحد واحد واحد واحد واحد
+
+466
+00:41:12,450 --> 00:41:15,010
+واحد واحد واحد واحد واحد، والـ degree عناصر المجموعة
+
+467
+00:41:15,010 --> 00:41:20,430
+التانية واحد، شاجلبنا؟ و هم مخلصنا؟ ماجعب شاجلبهم بس
+
+468
+00:41:20,430 --> 00:41:29,050
+لازم تفهمليش إنك شاجلبهم، ماجعب، طيب تعالي هنا من a
+
+469
+00:41:29,050 --> 00:41:40,690
+b c d e جداش الـ degree بتاعت a ايه؟ رتبة a جداش؟ تلاتة، ايش
+
+470
+00:41:40,690 --> 00:41:45,850
+علاج بتهيأل؟ الارتباط تم لمن؟ للمجموعة الأولى، صح؟
+
+471
+00:41:45,850 --> 00:41:50,370
+فالـ degree تبعتها، الـ degree لكل عناصر المجموعة
+
+472
+00:41:50,370 --> 00:41:55,390
+الأولى تساوي عدد عناصر المجموعة الثانية لأن كل
+
+473
+00:41:55,390 --> 00:41:59,670
+عنصر في المجموعة الأولى مرتبط بكل عناصر المجموعة
+
+474
+00:41:59,670 --> 00:42:03,850
+الثانية وبالتالي في دي صور على كل عناصرها، نعرف الـ
+
+475
+00:42:03,850 --> 00:42:08,160
+degree بنفس العدد، والعكس صحيح، أنا أعرف إنك فهمت بس
+
+476
+00:42:08,160 --> 00:42:12,960
+بتكملها خلاص يعني، لإن أنا بتكلم مش معاك لحالك الآن
+
+477
+00:42:12,960 --> 00:42:18,760
+نفس الكلام عناصر المجموعة الثانية، الـ degree لكل
+
+478
+00:42:18,760 --> 00:42:23,560
+واحد فيهم اتنين، ليش؟ لإن كل .. لازم يكون مرتبط بكل
+
+479
+00:42:23,560 --> 00:42:28,720
+عناصر المجموعة الأولى، كيف
+
+480
+00:42:28,720 --> 00:42:32,620
+تقلبها يعني؟ لأ، صح، ليش هو المشكلة في الموضوع الآن
+
+481
+00:42:32,620 --> 00:42:40,130
+أسميلكم، بقول لو كتبت K تلاتة اتنين، مش مشكلة .. نفس
+
+482
+00:42:40,130 --> 00:42:44,610
+الحكاية .. مش مشكلة .. بس الفكرة إنك تعملي هاي
+
+483
+00:42:44,610 --> 00:42:51,870
+واحدة و هاي الثانية .. هد هي نفسها تلاتة .. لاحظ يا
+
+484
+00:42:51,870 --> 00:42:54,750
+شباب، التلاتة والتلاتة هي عبارة عن cardinality
+
+485
+00:42:54,750 --> 00:42:58,490
+للعناصر المجموعات .. بس .. و الـ K بتقول إن عناصر
+
+486
+00:42:58,490 --> 00:43:00,590
+المجموعة الأولى مرتبطة مع كل عناصر المجموعة
+
+487
+00:43:00,590 --> 00:43:07,500
+الثانية .. و العكس صحيح .. ممتاز .. اللي بعده، هي
+
+488
+00:43:07,500 --> 00:43:13,120
+Complete Bipartite Graph تلاتة في تلاتة
+
+489
+00:43:13,120 --> 00:43:19,360
+مالهم؟
+
+490
+00:43:19,360 --> 00:43:23,920
+اه، بتبطل لو هال .. لو هال فيه بيصير واحد بطل
+
+491
+00:43:23,920 --> 00:43:30,320
+Bipartite Graph لأن
+
+492
+00:43:30,320 --> 00:43:33,220
+مش حاجة تقدر تفصلهم، طيب
+
+493
+00:43:34,370 --> 00:43:42,110
+الآن في الـ graph أو في الـ pseudograph، حافظ
+
+494
+00:43:42,110 --> 00:43:49,670
+مجموع رتب النقاط .. ايش رتب النقاط يا شباب؟ الـ
+
+495
+00:43:49,670 --> 00:43:54,230
+degree هي عدد الجسور المرتبطة بالنقطة .. لو جمعتهم
+
+496
+00:43:54,230 --> 00:44:01,410
+كلهم، هيكون عبارة عن ضعف عدد الجسور الموجودة ..
+
+497
+00:44:01,410 --> 00:44:02,350
+في الـ graph
+
+498
+00:44:06,720 --> 00:44:14,580
+هي graph، الـ graph هذا complete graph صح؟ طيب قداش
+
+499
+00:44:14,580 --> 00:44:22,300
+الـ degree تبعته لكل نقطة؟ 2، طيب مجموعهم؟ حرام
+
+500
+00:44:22,300 --> 00:44:25,160
+عليك، مجموع الـ degree، أنا قاعد بقولك للـ vertices
+
+501
+00:44:25,160 --> 00:44:29,880
+هذا الـ degree اتنين، و هذا الـ degree اتنين، و هذا الـ
+
+502
+00:44:29,880 --> 00:44:41,420
+degree اتنين، ستة، تساوي اتنين في عدد الجسور، عدد
+
+503
+00:44:41,420 --> 00:44:47,480
+الجسور جداش يا شباب هنا؟ واحد اتنين تلاتة، تمام؟ تلاتة
+
+504
+00:44:47,480 --> 00:44:51,300
+في المية، لا
+
+505
+00:44:51,300 --> 00:45:00,320
+مش لازم، هاي الـ graph هذا مش complete graph، قعد يا
+
+506
+00:45:00,320 --> 00:45:02,960
+باشا، الـ degree له واحد
+
+507
+00:45:06,020 --> 00:45:09,440
+اتنين تلاتة اتنين تلاتة اتنين تلاتة اتنين تلاتة اتنين
+
+508
+00:45:09,440 --> 00:45:12,220
+تلاتة اتنين تلاتة اتنين تلاتة اتنين تلاتة اتنين تلاتة
+
+509
+00:45:12,220 --> 00:45:15,240
+اتنين تلاتة اتنين تلاتة اتنين تلاتة اتنين تلاتة اتنين
+
+510
+00:45:15,240 --> 00:45:16,360
+تلاتة اتنين تلاتة اتنين تلاتة اتنين تلاتة اتنين تلاتة
+
+511
+00:45:16,360 --> 00:45:18,520
+اتنين تلاتة اتنين تلاتة اتنين تلاتة اتنين تلاتة اتنين
+
+512
+00:45:18,520 --> 00:45:23,500
+تلاتة اتنين تلاتة اتنين تلاتة اتنين تلاتة اتنين تلاتة
+
+513
+00:45:23,500 --> 00:45:33,940
+اتنين تلاتة اتنين تلاتة اتنين تلاتة اتنين تلاتة اتنين
+
+514
+00:45:33,940 --> 00:45:39,780
+تلاتة، تمام؟ عشان كده قلنا لك هو سواء كان graph أو
+
+515
+00:45:39,780 --> 00:45:43,280
+pseudograph، complete graph أو incomplete graph
+
+516
+00:45:43,280 --> 00:46:00,220
+مش هتجدش مكان القانون هتطبق عليه 100%، تمام؟ جالي
+
+517
+00:46:00,220 --> 00:46:05,640
+هتضرب عدد الجسور في الـ Complete bipartite graph
+
+518
+00:46:05,640 --> 00:46:13,860
+تلاتة و ستة، ترسموه .. ممتاز .. واحد .. اتنين ..
+
+519
+00:46:13,860 --> 00:46:20,720
+تلاتة .. واحد .. اتنين .. تلاتة .. أربعة .. خمسة ..
+
+520
+00:46:20,720 --> 00:46:29,900
+ستة، بندق السادس، احنا عادل .. ماشي، فلنوصيها أبداً
+
+521
+00:46:29,900 --> 00:46:35,000
+.. لما قلت ارسم، أنا قاعد بقولك حطلي عدد الجسور
+
+522
+00:46:35,000 --> 00:46:42,860
+عشان بتعرف واحد يا
+
+523
+00:46:42,860 --> 00:46:47,200
+عيني عليك، هيبقى أسميلكم من أول ويك تقاش، وأقولك الله
+
+524
+00:46:47,200 --> 00:46:52,420
+يجيبك يا قلتي، نروح بالمناسبة، أنا ما قلتلكش ارسم
+
+525
+00:46:52,420 --> 00:46:55,780
+أنت اللي .. أنت اللي بيبقى ترسم، أنا ما قلتش لازم
+
+526
+00:46:55,780 --> 00:46:59,240
+ترسم، بتلعب
+
+527
+00:46:59,240 --> 00:46:59,740
+كده، ايش؟
+
+528
+00:47:07,510 --> 00:47:13,010
+الآن أصلي، صاحبي ماتفكرش ترسم، لأن لو أنا روحت و
+
+529
+00:47:13,010 --> 00:47:14,610
+قلتلك عشرة في تسعة
+
+530
+00:47:19,000 --> 00:47:22,460
+مش هتخلص، لو قلتلك أنا خريطة حقيقية، the
+
+531
+00:47:22,460 --> 00:47:26,300
+incomplete bipartite graph عليها المجموعة الأولى
+
+532
+00:47:26,300 --> 00:47:30,300
+خمسين vertex، والثانية مائة وسبعين، إيش بقى ترسم؟
+
+533
+00:47:30,300 --> 00:47:33,660
+هذا الكلام مش موضوع، هرسم شوية من دماغك، خالص، ايش
+
+534
+00:47:33,660 --> 00:47:39,020
+الحل؟ الحل تفهم التركيبة اللي موجودة عندها،
+
+535
+00:47:39,020 --> 00:47:46,240
+القانون كان بيقول لي الـ summation of degrees يساوي
+
+536
+00:47:46,240 --> 00:47:51,640
+ضعف عدد الجسور، مصبوط؟ بقدر أنا أجيب مجموع الـ
+
+537
+00:47:51,640 --> 00:47:56,080
+degrees؟ أنا بقدر أجيبها، الآن complete .. بدي
+
+538
+00:47:56,080 --> 00:47:59,900
+أستفيد من هنا يا شباب، هو بيقول complete bipartite
+
+539
+00:47:59,900 --> 00:48:04,840
+graph، يعني كل عنصر في المجموعة الأولى، الرتبة تبعه
+
+540
+00:48:04,840 --> 00:48:09,560
+كده إيش؟ ستة، ستة، لإن أنا مرتبط بكل عنصر المجموعة
+
+541
+00:48:09,560 --> 00:48:13,220
+الثانية، معناته الـ summation هذه، الـ summation للـ
+
+542
+00:48:13,220 --> 00:48:18,180
+degree للـ vertices تساوي تلت .. تلت .. تلت عناصر
+
+543
+00:48:18,180 --> 00:48:21,320
+في المجموعة الأولى، كل واحد الـ degree تبعتها ستة
+
+544
+00:48:21,320 --> 00:48:30,140
+ستة زائد، ما خلصناش، المجموعة الثانية فيها ست عناصر
+
+545
+00:48:30,140 --> 00:48:35,500
+الـ degree تبعت كل واحد فيهم تلاتة، هذا الكلام ما
+
+546
+00:48:35,500 --> 00:48:39,280
+جبتهوش من عندي يا شباب، جبته من .. من مفهوم الـ K
+
+547
+00:48:40,930 --> 00:48:46,650
+تلاتة،  تماطعش، تماطعش، ستة و تلاتين،  ماتوا الستة
+
+548
+00:48:46,650 --> 00:48:52,610
+و تلاتين هذه تساوي ضعف عدد الجسور، ماتوا عدد الجسور
+
+549
+00:48:52,610 --> 00:48:55,810
+تساوي
+
+550
+00:48:55,810 --> 00:49:01,010
+تماطعش الجسر بنفع
+
+551
+00:49:01,010 --> 00:49:04,070
+لو قلتلك
+
+552
+00:49:07,880 --> 00:49:13,600
+كمبليت جراف تمانية، كيف
+
+553
+00:49:13,600 --> 00:49:17,800
+مافيش جسور؟
+
+554
+00:49:17,800 --> 00:49:22,640
+كيف مافيش جسور؟ هذا كمبليت جراف مش كمبليت مش by
+
+555
+00:49:22,640 --> 00:49:27,760
+parted، كمبليت جراف، جراف من تمان نقاط، كل نقطة
+
+556
+00:49:27,760 --> 00:49:32,230
+مرتبطة بسبع نقاط تانية،  ده اللي أنت ما جد حل ف أنت
+
+557
+00:49:32,230 --> 00:49:35,790
+ماتفكرش إن أنا بس بده آخده أقرب زبط ما أكل، لأن هذا
+
+558
+00:49:35,790 --> 00:49:40,270
+by part، و فعلياً لو ضربته أنت هتحصل 100% همجد
+
+559
+00:49:40,270 --> 00:49:49,610
+السؤال نفسه هذا، بيبنى نغيره تمام؟ وحقها
+
+560
+00:49:49,610 --> 00:49:55,450
+كتسعة مثلاً، تسعة في تمانية ايه؟ تسعة في تمانية ايه؟
+
+561
+00:49:55,450 --> 00:49:55,850
+ايه؟ تسعة في تمانية ايه؟ تسعة في تمانية ايه؟ تسعة
+
+562
+00:49:55,850 --> 00:50:00,450
+في تمانية ايه؟ تسعة في تمانية ايه؟ تسعة في تمانللـ
+
+563
+00:50:00,450 --> 00:50:04,810
+degree للـ vertices تساوي كم vertex عندك؟ تسعة
+
+564
+00:50:04,810 --> 00:50:09,870
+vertices، مصبوط، الـ degree لكل واحد فيهم تمانية
+
+565
+00:50:09,870 --> 00:50:18,050
+تساوي اتنين وسبعين، واتنين وسبعين بتساوي ضعف في
+
+566
+00:50:18,050 --> 00:50:22,870
+عدد الجسور، ملاك
+
+567
+00:50:22,870 --> 00:50:24,450
+عدد الجسور الموجود عندي
+
+568
+00:50:29,400 --> 00:50:43,500
+كداش؟ سبعة و تلاتين، تمام يا شباب؟ الحمد لله، طيب
+
+569
+00:50:43,500 --> 00:50:49,820
+degree sequence، الاخر
+
+570
+00:50:49,820 --> 00:50:55,020
+شغل، لا تجلجي معايا، degree sequence، الآن بما إنه الـ
+
+571
+00:50:55,020 --> 00:51:00,710
+graph، أي مكان رسمته أو أي مكان شكله، وبقدر أنا أجيب
+
+572
+00:51:00,710 --> 00:51:04,630
+الـ degree لكل vertex، وقولنا هي الـ degree هي عبارة
+
+573
+00:51:04,630 --> 00:51:09,150
+عن عدد الجسور المرتبطة بالنقطة، مظبوط؟ تمام، الـ
+
+574
+00:51:09,150 --> 00:51:16,090
+graph هذا لو خليني إليه جاهز، هيك الـ
+
+575
+00:51:16,090 --> 00:51:22,340
+degree اللي فيه واحد جداش ايش؟ تلاتة تلاتة تلاتة
+
+576
+00:51:22,340 --> 00:51:24,800
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+577
+00:51:24,800 --> 00:51:27,500
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+578
+00:51:27,500 --> 00:51:30,420
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+579
+00:51:30,420 --> 00:51:33,720
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+580
+00:51:33,720 --> 00:51:36,860
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+581
+00:51:36,860 --> 00:51:42,000
+تلاتة تلاتة تلاتة تلاتة تلاتة
+
+582
+00:51:44,680 --> 00:51:50,660
+من الـ degrees بتبدأ من الرتبة الأعلى للرتبة الأقل
+
+583
+00:51:50,660 --> 00:51:55,040
+من الرتبة الأعلى للرتبة الأقل، أو بين قوسين بترتب
+
+584
+00:51:55,040 --> 00:52:00,300
+الرتب اللي لو عندك ترتيب تنازلي، فبيصير أربعة الـ
+
+585
+00:52:00,300 --> 00:52:05,600
+degree sequence، أربعة تلاتة اتنين واحد، كأرقام
+
+586
+00:52:09,530 --> 00:52:13,210
+عشان الترتيب التنازلي، هيها أنت بيقوم، هي الـ sequence
+
+587
+00:52:13,210 --> 00:52:17,610
+هي الـ sequence بحيث إنك تتأكد إن دي واحد، إذا تكون
+
+588
+00:52:17,610 --> 00:52:20,650
+أكبر أو تساوي، أكبر أو تساوي، طيب في الـ graph اللي
+
+589
+00:52:20,650 --> 00:52:27,610
+زي هذا يا شباب، هكذا لو
+
+590
+00:52:27,610 --> 00:52:33,870
+صارت فيه hand graph بالشكل هذا، هيصير فوق تلاتة و
+
+591
+00:52:33,870 --> 00:52:34,590
+أنا أربعة
+
+592
+00:52:38,370 --> 00:52:43,830
+أربعة أربعة تلاتة واحد، الأربعة اللي بتاعتني مهناش
+
+593
+00:52:43,830 --> 00:52:47,810
+لإن أنا بتكلم على إقامة الـ degree sequence هي
+
+594
+00:52:47,810 --> 00:52:53,090
+عبارة عن مجموعة الرتب مرتبة ترتيب تنازلي، الآن هذه
+
+595
+00:52:53,090 --> 00:52:58,030
+أربعة وهذه أربعة، مابتفرجش معايا أنا في الآخر
+
+596
+00:52:58,030 --> 00:53:05,640
+هرتبها، هقول أربعة أربعة تلاتة واحد، مش اتنين، مصبوط؟
+
+597
+00:53:05,640 --> 00:53:08,760
+وبالتالي هذه الـ degree sequence اللي موجودة عندها
+
+598
+00:53:08,760 --> 00:53:12,920
+المحيط .. وبناء عليه فيه الأقل من والأصغر أكبر من
+
+599
+00:53:12,920 --> 00:53:16,600
+أو يساوي، عفواً، تمام يا شباب؟ هذه إحنا بنسميها
+
+600
+00:53:16,600 --> 00:53:20,220
+degree sequence للـ graph، بنسميها degree sequence
+
+601
+00:53:20,220 --> 00:53:24,300
+للـ graph، ونخلص موضوع الـ isomorphism بنبدأ فيه
+
+602
+00:53:24,300 --> 00:53:26,880
+المحاضرة الجاية إن شاء الله تعالى، في أي سؤال يا
+
+603
+00:53:26,880 --> 00:53:30,400
+شباب؟ تمام؟ الله يعطيكم العافية
diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/_HzUlOTxQ18_raw.json b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/_HzUlOTxQ18_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..e9f3bd3867abee0ce797dc5c2db7d5df021e5965
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/_HzUlOTxQ18_raw.json
@@ -0,0 +1 @@
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اين؟ و لو كان في ندي نقطة او في جسر من b ل d بيكون b و d ك vertices متجاورين كذلك a,b و b,d و b,c جسور متجاورة لأنهم التقوا كلهم على نفس النقطة", "tokens": [6027, 7649, 257, 11, 65, 4032, 272, 11, 66, 8032, 8848, 1829, 10874, 3794, 13063, 44650, 7435, 995, 13063, 3660, 4032, 5296, 33456, 16095, 16712, 4587, 14407, 1975, 9957, 22807, 4032, 45164, 25961, 8978, 8717, 16254, 8717, 47432, 3660, 1975, 2407, 8978, 10874, 3794, 2288, 9154, 272, 5296, 274, 4724, 1829, 30544, 272, 4032, 274, 9122, 6509, 1473, 44650, 7435, 995, 13063, 9957, 9122, 8848, 23275, 257, 11, 65, 4032, 272, 11, 67, 4032, 272, 11, 66, 10874, 3794, 13063, 44650, 7435, 995, 13063, 3660, 5296, 33456, 16095, 16712, 4587, 14407, 28242, 16095, 15844, 8717, 36178, 28239, 47432, 3660], "avg_logprob": -0.24390624359250068, "compression_ratio": 1.8176470588235294, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 509.91, "end": 510.29, "word": "الان", "probability": 0.607177734375}, {"start": 510.29, "end": 510.99, 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1116.17, "word": " graph", "probability": 0.84765625}, {"start": 1116.17, "end": 1117.39, "word": " مجموعة", "probability": 0.96318359375}, {"start": 1117.39, "end": 1117.85, "word": " النقاط", "probability": 0.9373372395833334}, {"start": 1117.85, "end": 1118.47, "word": " طبعته", "probability": 0.9327392578125}, {"start": 1118.47, "end": 1119.17, "word": " مجموعة", "probability": 0.92607421875}, {"start": 1119.17, "end": 1119.75, "word": " جزئية", "probability": 0.9345703125}, {"start": 1119.75, "end": 1119.99, "word": " من", "probability": 0.9765625}, {"start": 1119.99, "end": 1120.53, "word": " ..", "probability": 0.179931640625}, {"start": 1120.53, "end": 1121.81, "word": " من", "probability": 0.83740234375}, {"start": 1121.81, "end": 1122.19, "word": " مجموعة", "probability": 0.9638671875}, {"start": 1122.19, "end": 1122.35, "word": " الـ", "probability": 0.728515625}, {"start": 1122.35, "end": 1122.47, "word": " V", "probability": 0.7724609375}, {"start": 1122.47, "end": 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116268, "start": 1133.64, "end": 1162.68, "text": "لو قلت لك هاتلي graph او هاتلي subset سميه G1 تمام؟ بكل بساطة انا ممكن اروح اخد V1 V2 V3 هي المجموعة V1 V2 V3 كمة و الجسور اللي ما بينهم في مجموعة تانية V1 V2 و V2", "tokens": [1211, 2407, 12174, 1211, 2655, 5296, 4117, 8032, 9307, 20292, 4295, 1975, 2407, 8032, 9307, 20292, 25993, 8608, 2304, 1829, 3224, 460, 16, 46811, 10943, 22807, 4724, 28820, 4724, 3794, 41193, 3660, 1975, 8315, 3714, 43020, 1975, 32887, 5016, 1975, 9778, 3215, 691, 16, 691, 17, 691, 18, 39896, 9673, 7435, 2304, 2407, 27884, 691, 16, 691, 17, 691, 18, 9122, 2304, 3660, 4032, 25724, 3794, 13063, 13672, 1829, 19446, 49374, 16095, 8978, 3714, 7435, 2304, 2407, 27884, 6055, 7649, 10632, 691, 16, 691, 17, 4032, 691, 17], "avg_logprob": -0.1987359496984589, "compression_ratio": 1.4913294797687862, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1133.64, "end": 1133.88, "word": "لو", "probability": 0.835693359375}, {"start": 1133.88, "end": 1134.12, "word": 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"word": " انا", "probability": 0.86279296875}, {"start": 1142.92, "end": 1143.16, "word": " ممكن", "probability": 0.991455078125}, {"start": 1143.16, "end": 1143.44, "word": " اروح", "probability": 0.9246419270833334}, {"start": 1143.44, "end": 1143.98, "word": " اخد", "probability": 0.9029947916666666}, {"start": 1143.98, "end": 1145.02, "word": " V1", "probability": 0.869140625}, {"start": 1145.02, "end": 1145.66, "word": " V2", "probability": 0.787841796875}, {"start": 1145.66, "end": 1146.92, "word": " V3", "probability": 0.975341796875}, {"start": 1146.92, "end": 1147.6, "word": " هي", "probability": 0.40380859375}, {"start": 1147.6, "end": 1148.06, "word": " المجموعة", "probability": 0.907421875}, {"start": 1148.06, "end": 1149.1, "word": " V1", "probability": 0.927490234375}, {"start": 1149.1, "end": 1150.54, "word": " V2", "probability": 0.97509765625}, {"start": 1150.54, "end": 1152.7, "word": " V3", "probability": 0.990234375}, {"start": 1152.7, "end": 1154.06, "word": " كمة", "probability": 0.5966796875}, {"start": 1154.06, "end": 1154.56, "word": " و", "probability": 0.381103515625}, {"start": 1154.56, "end": 1155.02, "word": " الجسور", "probability": 0.7750651041666666}, {"start": 1155.02, "end": 1155.18, "word": " اللي", "probability": 0.947509765625}, {"start": 1155.18, "end": 1155.32, "word": " ما", "probability": 0.76904296875}, {"start": 1155.32, "end": 1155.8, "word": " بينهم", "probability": 0.99072265625}, {"start": 1155.8, "end": 1156.12, "word": " في", "probability": 0.9208984375}, {"start": 1156.12, "end": 1156.52, "word": " مجموعة", "probability": 0.86943359375}, {"start": 1156.52, "end": 1157.0, "word": " تانية", "probability": 0.9949544270833334}, {"start": 1157.0, "end": 1158.82, "word": " V1", "probability": 0.974609375}, {"start": 1158.82, "end": 1160.78, "word": " V2", "probability": 0.82421875}, {"start": 1160.78, "end": 1162.0, "word": " و", "probability": 0.65234375}, {"start": 1162.0, "end": 1162.68, "word": " V2", "probability": 0.901123046875}], "temperature": 1.0}, {"id": 43, "seek": 117927, "start": 1164.43, "end": 1179.27, "text": "V3 مظبوط؟ خلصنا هذا ال graph بمثل subset من ال graph اللي موجود عندها بناء على إيش؟ بناء على إن ال vertices set هي subset من ال main set", "tokens": [53, 18, 3714, 19913, 3555, 2407, 9566, 22807, 16490, 1211, 9381, 8315, 23758, 2423, 4295, 4724, 2304, 12984, 1211, 25993, 9154, 2423, 4295, 13672, 1829, 3714, 29245, 23328, 43242, 11296, 44945, 16606, 15844, 11933, 1829, 8592, 22807, 44945, 16606, 15844, 36145, 2423, 32053, 992, 39896, 25993, 9154, 2423, 2135, 992], "avg_logprob": -0.38388479574053896, "compression_ratio": 1.4326241134751774, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 1164.4299999999998, "end": 1165.1499999999999, "word": "V3", "probability": 0.400146484375}, {"start": 1165.1499999999999, "end": 1165.87, "word": " مظبوط؟", "probability": 0.6910603841145834}, {"start": 1165.87, "end": 1166.41, "word": " خلصنا", "probability": 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V6, V7، subset ال V's طب الآن الجثور V2 و V3 موجود هيه V6, V7 موجود هيه، معناته هذا برضه إيش؟ subset طيب، لو أنا اتجهت هيك الشباب", "tokens": [3224, 3215, 12610, 2423, 9307, 1863, 9957, 20449, 45030, 11242, 5551, 9778, 3215, 2655, 3224, 8032, 4117, 15730, 382, 472, 4295, 8032, 1211, 31439, 25993, 22807, 691, 17, 11, 691, 18, 11, 691, 21, 11, 691, 22, 12399, 25993, 2423, 691, 311, 23032, 3555, 6024, 48506, 25724, 12984, 13063, 691, 17, 4032, 691, 18, 3714, 29245, 23328, 8032, 1829, 3224, 691, 21, 11, 691, 22, 3714, 29245, 23328, 39896, 3224, 12399, 20449, 8315, 47395, 23758, 4724, 43042, 3224, 11933, 1829, 8592, 22807, 25993, 23032, 1829, 3555, 12399, 45164, 41850, 1975, 2655, 7435, 3224, 2655, 39896, 4117, 25124, 3555, 16758], "avg_logprob": -0.39031249165534976, "compression_ratio": 1.49, "no_speech_prob": 0.0, "words": [{"start": 1294.7, "end": 1295.02, "word": "هدول", "probability": 0.709228515625}, {"start": 1295.02, "end": 1295.38, "word": " الاتنين", "probability": 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لو", "probability": 0.97216796875}, {"start": 1318.32, "end": 1318.5, "word": " أنا", "probability": 0.82177734375}, {"start": 1318.5, "end": 1318.78, "word": " اتجهت", "probability": 0.7046875}, {"start": 1318.78, "end": 1318.94, "word": " هيك", "probability": 0.63330078125}, {"start": 1318.94, "end": 1319.3, "word": " الشباب", "probability": 0.9775390625}], "temperature": 1.0}, {"id": 49, "seek": 135087, "start": 1329.41, "end": 1350.87, "text": "لحالها هيك، أيوة هل ال graph هذا subset ولا مش subset؟ كم واحد يقول subset؟ واحد، اتنين، تلاتة، اربعة، خمسة، ستة، واحدة راح تحديد تنتين", "tokens": [1211, 5016, 6027, 11296, 39896, 4117, 12399, 36632, 2407, 3660, 8032, 1211, 2423, 4295, 23758, 25993, 49429, 37893, 25993, 22807, 9122, 2304, 36764, 24401, 7251, 39648, 25993, 22807, 36764, 24401, 12399, 1975, 2655, 1863, 9957, 12399, 6055, 1211, 9307, 3660, 12399, 1975, 25513, 27884, 12399, 16490, 2304, 3794, 3660, 12399, 8608, 2655, 3660, 12399, 36764, 24401, 3660, 12602, 39319, 6055, 5016, 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2278.32, "word": " المجموعة", "probability": 0.892431640625}, {"start": 2278.32, "end": 2278.78, "word": " التانية", "probability": 0.95458984375}, {"start": 2278.78, "end": 2279.4, "word": " والعكس", "probability": 0.8365478515625}, {"start": 2279.4, "end": 2280.06, "word": " صحيح", "probability": 0.9927978515625}, {"start": 2280.06, "end": 2280.88, "word": " فبصي", "probability": 0.807861328125}, {"start": 2280.88, "end": 2281.02, "word": " غير", "probability": 0.474609375}, {"start": 2281.02, "end": 2281.52, "word": " عبارة", "probability": 0.75640869140625}, {"start": 2281.52, "end": 2281.66, "word": " عن", "probability": 0.99169921875}, {"start": 2281.66, "end": 2282.5, "word": " full", "probability": 0.81494140625}, {"start": 2282.5, "end": 2283.12, "word": " bipartite", "probability": 0.982666015625}, {"start": 2283.12, "end": 2283.42, "word": " graph", "probability": 0.97705078125}, {"start": 2283.42, "end": 2283.8, "word": " يعني", "probability": 0.875}, {"start": 2283.8, "end": 2284.52, "word": " لو", "probability": 0.8701171875}, {"start": 2284.52, "end": 2284.72, "word": " انا", "probability": 0.770751953125}, {"start": 2284.72, "end": 2285.02, "word": " اديت", "probability": 0.7486979166666666}, {"start": 2285.02, "end": 2285.38, "word": " هيك", "probability": 0.859619140625}], "temperature": 1.0}, {"id": 83, "seek": 230776, "start": 2288.86, "end": 2307.76, "text": "على الرصم الأولى تبعتنا هذا by bipartite graph صح؟ اه by bipartite graph حطينا V1 و V2 و V3 اول مثال شرحناه by bipartite graph الان لو دججت في ال graph هذا", "tokens": [3615, 23942, 34892, 9381, 2304, 16247, 12610, 7578, 6055, 3555, 34268, 8315, 23758, 538, 28741, 642, 4295, 20328, 5016, 22807, 1975, 3224, 538, 28741, 642, 4295, 11331, 9566, 1829, 8315, 691, 16, 4032, 691, 17, 4032, 691, 18, 1975, 12610, 50113, 6027, 13412, 2288, 5016, 8315, 3224, 538, 28741, 642, 4295, 2423, 7649, 45164, 11778, 7435, 7435, 2655, 8978, 2423, 4295, 23758], "avg_logprob": -0.3020833238722786, 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sequence", "probability": 0.98193359375}, {"start": 3197.58, "end": 3198.14, "word": " لل", "probability": 0.8369140625}, {"start": 3198.14, "end": 3198.54, "word": " graph", "probability": 0.6865234375}, {"start": 3198.54, "end": 3199.36, "word": " بنسميها", "probability": 0.888916015625}, {"start": 3199.36, "end": 3199.56, "word": " degree", "probability": 0.99365234375}, {"start": 3199.56, "end": 3200.22, "word": " sequence", "probability": 0.98583984375}, {"start": 3200.22, "end": 3200.94, "word": " لل", "probability": 0.93603515625}, {"start": 3200.94, "end": 3201.32, "word": " graph", "probability": 0.93603515625}, {"start": 3201.32, "end": 3202.32, "word": " ونخل", "probability": 0.872802734375}, {"start": 3202.32, "end": 3202.64, "word": " موضوع", "probability": 0.8526611328125}, {"start": 3202.64, "end": 3202.76, "word": " ال", "probability": 0.912109375}, {"start": 3202.76, "end": 3203.52, "word": " isomorphism", "probability": 0.9138997395833334}, {"start": 3203.52, "end": 3204.12, "word": " بنبدأ", "probability": 0.781982421875}, {"start": 3204.12, "end": 3204.3, "word": " فيه", "probability": 0.970458984375}, {"start": 3204.3, "end": 3204.84, "word": " المحاضرة", "probability": 0.986328125}, {"start": 3204.84, "end": 3205.48, "word": " الجاية", "probability": 0.81103515625}, {"start": 3205.48, "end": 3205.6, "word": " ان", "probability": 0.54345703125}, {"start": 3205.6, "end": 3205.72, "word": " شاء", "probability": 0.9638671875}, {"start": 3205.72, "end": 3205.76, "word": " الله", "probability": 0.9462890625}, {"start": 3205.76, "end": 3206.1, "word": " تعالى", "probability": 0.96533203125}, {"start": 3206.1, "end": 3206.4, "word": " في", "probability": 0.57470703125}, {"start": 3206.4, "end": 3206.54, "word": " أي", "probability": 0.45849609375}, {"start": 3206.54, "end": 3206.8, "word": " سؤال", "probability": 0.9671223958333334}, {"start": 3206.8, "end": 3206.88, "word": " يا", "probability": 0.9775390625}, {"start": 3206.88, "end": 3207.34, "word": " شباب؟", "probability": 0.9755859375}, {"start": 3207.34, "end": 3209.18, "word": " تمام؟", "probability": 0.84814453125}, {"start": 3209.18, "end": 3209.88, "word": " الله", "probability": 0.92529296875}, {"start": 3209.88, "end": 3210.08, "word": " أتكلم", "probability": 0.392303466796875}, {"start": 3210.08, "end": 3210.4, "word": " عافية", "probability": 0.7874348958333334}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3210.5070625, "duration_after_vad": 3027.4743749999934}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/_HzUlOTxQ18_raw.srt b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/_HzUlOTxQ18_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..32bd921ee16218d8368a86183e39b97e5a0ce3dc
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/_HzUlOTxQ18_raw.srt
@@ -0,0 +1,2436 @@
+1
+00:00:20,860 --> 00:00:22,860
+بسم الله والحمد لله والصلاة والسلام علي رسول الله
+
+2
+00:00:22,860 --> 00:00:25,140
+اليوم إن شاء الله تبارك وتعالى هنبدأ ب شبتر جديد
+
+3
+00:00:25,140 --> 00:00:29,880
+هيكون ألطف من الشباتريه السابقة هنتكلم فيه على ال
+
+4
+00:00:29,880 --> 00:00:35,300
+graph theory ونشوف أهميتها وتبتقاتها بداية بدي لو
+
+5
+00:00:35,300 --> 00:00:39,720
+أنا سألت graph شو دخلها؟ يعني إيش يعني graph عادة
+
+6
+00:00:39,720 --> 00:00:43,260
+الشباب لما أتكلم على graph أتكلم عليه رسمة خريطة
+
+7
+00:00:43,260 --> 00:00:46,120
+مجموعة من النقاط و الخطوط اللي بينها مجموعة من
+
+8
+00:00:46,120 --> 00:00:50,380
+النقاط و الخطوط اللي بينها وين تستخدم؟في ال
+
+9
+00:00:50,380 --> 00:00:56,440
+computer networking computer network لما بنوصل
+
+10
+00:00:56,440 --> 00:01:01,300
+شبكة شبكة computer بتكلم على مجموعة من النقاط و
+
+11
+00:01:01,300 --> 00:01:04,860
+الخطوط اللي بينها كل نقطة بتمثل computer و الخط
+
+12
+00:01:04,860 --> 00:01:08,140
+اللي بينهم الاتصال اللي موجود ما بين الجهازين
+
+13
+00:01:08,140 --> 00:01:14,550
+بتكلم على ال railways خطوط السكة الحديدشبكة
+
+14
+00:01:14,550 --> 00:01:20,110
+القطارات تمام graph graph وإن كان يران احنا بنرمز
+
+15
+00:01:20,110 --> 00:01:26,630
+ان المحطة هي النقطة والخط اللي بينها تمام الخط
+
+16
+00:01:26,630 --> 00:01:30,270
+الواصل ما بين المحطة اه يعني هي فعليا احنا لما
+
+17
+00:01:30,270 --> 00:01:35,190
+بنجي في شبكة الكمبيوتر بنحط مجموعة من النقاط و
+
+18
+00:01:35,190 --> 00:01:40,710
+بنوصل ما بين النقاط هذه بشكل او باخر ضد النظر على
+
+19
+00:01:40,710 --> 00:01:43,800
+قالية التوصيل اللي موجودةلكن لما بتكلم في ال
+
+20
+00:01:43,800 --> 00:01:45,820
+railways بقول والله هذه النقطة الأولى اللي هي
+
+21
+00:01:45,820 --> 00:01:49,460
+المحطة بعض
+
+22
+00:01:49,460 --> 00:01:54,640
+المحطات ممكن تصير فيها تفريعة حسب تكون عندي نقطة
+
+23
+00:01:54,640 --> 00:02:00,280
+مركزية وانا من خلالها بصير اتكلم على التفريعة في
+
+24
+00:02:00,280 --> 00:02:06,660
+سكة الحديد لما بتكلم على ال maps الخرائط لما بتكلم
+
+25
+00:02:06,660 --> 00:02:14,340
+على الخرائط في الخرائط الآن الطرق و المدنالنقاط هي
+
+26
+00:02:14,340 --> 00:02:20,700
+المدن او المفترجات و النقاط و الخطوط هي الطرق
+
+27
+00:02:20,700 --> 00:02:24,340
+الموجودة بين النقاط او المدن اللي موجودة عندى
+
+28
+00:02:24,340 --> 00:02:28,680
+فالتطبيقات تبع ال computer او ال graphs كتيرة جدا
+
+29
+00:02:28,680 --> 00:02:32,920
+يعنى لو درست شبكات هتخدمك لو تهتمت في موضوع design
+
+30
+00:02:32,920 --> 00:02:37,200
+زى ما جوجل ماب او مابسمي او مشابق كلها بتعتمد على
+
+31
+00:02:37,200 --> 00:02:42,840
+موضوع الصورة في الآخر انت بتشوف الخريطة صورةوالـ
+
+32
+00:02:42,840 --> 00:02:46,460
+graph تبعك يمثل بمجموعة من النقاط واليسور اللي
+
+33
+00:02:46,460 --> 00:02:50,600
+بينهم، هنشوف كيف نمثله ك .. أو ندخله لبرنامجنا او
+
+34
+00:02:50,600 --> 00:02:54,360
+ما شابه، انا و احنا من ناحية الرياضيات بهمنا نفهم
+
+35
+00:02:54,360 --> 00:02:59,820
+ان ال graph هو عبارة عن زوج مرتب، pair، بيحتوي على
+
+36
+00:02:59,820 --> 00:03:05,490
+عنصرين V وE، واتفقنا في الزوج المرتبالعنصر الأول
+
+37
+00:03:05,490 --> 00:03:11,730
+أو الترتيب المهم ال V هي عبارة عن مجموعة اي و V
+
+38
+00:03:11,730 --> 00:03:15,610
+عبارة عن مجموعتين ال V هي عبارة عن non-empty set
+
+39
+00:03:15,610 --> 00:03:20,910
+مجموعة النقاط مش لازم تكون فارقة يعني مش لازم تكون
+
+40
+00:03:20,910 --> 00:03:26,570
+فارقة كمجموعة على الأقل فيها عنصر واحد and each
+
+41
+00:03:26,570 --> 00:03:32,530
+element في ال E كل عنصر في ال E هو عبارة عن two
+
+42
+00:03:33,670 --> 00:03:39,250
+Distinct element of V وكل أنصر في الـ E هو عبارة
+
+43
+00:03:39,250 --> 00:03:45,750
+عن أنصرين مختلفين من أناصر الـ V عشان أوضح الكلام
+
+44
+00:03:45,750 --> 00:03:51,930
+هذا لو أنا جيت و قلت هاي
+
+45
+00:03:51,930 --> 00:04:00,130
+ال graph هي A B C و هاي ال D لأن ال graph هذا أنا
+
+46
+00:04:00,130 --> 00:04:06,260
+بدأ مخطط زوج مرتبهروح اقول ال graph هذي يمثل بزوج
+
+47
+00:04:06,260 --> 00:04:16,640
+مرتب V و E ايش ال V تساوي كمجموعة ABCD
+
+48
+00:04:16,640 --> 00:04:20,060
+ABCD
+
+49
+00:04:20,060 --> 00:04:25,860
+مجموعة النقاط non-empty set اقل ال graph اقل ال
+
+50
+00:04:25,860 --> 00:04:31,060
+graph ممكن احنا نتكلم عليه اللي
+
+51
+00:04:31,060 --> 00:04:36,050
+فيه النقطة X هذه لحالهاهذا الـ Graph من زوج مرتب
+
+52
+00:04:36,050 --> 00:04:44,270
+المجموعة X ومجموعة الديوزور Phi ولا لأ؟ لأ، هذه هي
+
+53
+00:04:44,270 --> 00:04:48,670
+مفهوم الـ Definition Non-Empty V هي مش فاضية لكن
+
+54
+00:04:48,670 --> 00:04:52,050
+الـ E ممكن تكون فاضية فهذا يكون أقل Graph موجود
+
+55
+00:04:52,050 --> 00:04:59,910
+عندي وهي مقطع واحدة وإذا نكمل هذه الرسمة الـ E هي
+
+56
+00:04:59,910 --> 00:05:05,540
+عبارة عنكل element فيها عبارة عن two distinct
+
+57
+00:05:05,540 --> 00:05:10,460
+elements in V، عنصرين مختلفين مع بعض، هي مجموعة
+
+58
+00:05:10,460 --> 00:05:16,060
+الجسور، الجسور الموجودة بين مين ومين؟ AB، هذه AB،
+
+59
+00:05:16,060 --> 00:05:23,780
+العنصر الأول في المجموعة AB، العنصر التاني BC
+
+60
+00:05:26,720 --> 00:05:30,360
+مافيش غيرهم هاي الجسرين اللي موجودات هو لما قاللي
+
+61
+00:05:30,360 --> 00:05:35,520
+each element of A a set of two distinct elements
+
+62
+00:05:35,520 --> 00:05:39,040
+هو عبارة عن مجموعة من عنصرين مختلفين انا مثلت
+
+63
+00:05:39,040 --> 00:05:44,220
+المجموعة هي a و b فيك تمثلهم كمجموعة تانية فرعية
+
+64
+00:05:44,220 --> 00:05:47,020
+ماعنديش مشكلة في الموضوع بس لازم يكون ال element
+
+65
+00:05:47,020 --> 00:05:51,580
+مختلفين عشان نتكلم على graph لان هذا التمثيل أسهل
+
+66
+00:05:51,580 --> 00:05:55,200
+لما انا بكتب ab دلالة على الجسر اللي موجود ما بين
+
+67
+00:05:56,780 --> 00:06:02,080
+النقطين هو نفس الجسد لو أنا كتبته C وB او B وA
+
+68
+00:06:02,080 --> 00:06:09,360
+يعني مانفعش اكتبه مرة A وB و المرة التانية اكتبه B
+
+69
+00:06:09,360 --> 00:06:13,940
+A لان هذه هي هذه ما لم اكتب زي مرتب و عادة لما
+
+70
+00:06:13,940 --> 00:06:18,160
+بتكلم على طريق انا بتكلم two direction موجود من A
+
+71
+00:06:18,160 --> 00:06:23,610
+لB هو نفس ال connection من B لAهذا هو التعريف لـ
+
+72
+00:06:23,610 --> 00:06:28,590
+Graph اللي احنا هتتعامل معاه من ناحية رياضيات ال
+
+73
+00:06:28,590 --> 00:06:32,630
+element of V بنسميها ال vertices النقاط اللي هي A
+
+74
+00:06:32,630 --> 00:06:38,610
+وB وC وD اللي كتبناهم قبل شوية و ال element of E
+
+75
+00:06:38,610 --> 00:06:43,630
+لاحظت كتبنالك unordered pairs يعني مش أزواج مرتبة
+
+76
+00:06:43,630 --> 00:06:46,630
+و هم أزواج نعم لكنهم غير مرتبة يعني ماتفرجش مين
+
+77
+00:06:46,630 --> 00:06:53,920
+يتقدم عن مين هيتمثلEdges Vertices وEdges او Vertex
+
+78
+00:06:53,920 --> 00:07:00,460
+و Edge تمام الان
+
+79
+00:07:00,460 --> 00:07:05,040
+لما باتي بقول ايه قلنا مكتوبهم كمجموعة مصبوط؟ قبل
+
+80
+00:07:05,040 --> 00:07:13,260
+شويه رسميهم قلنا لازم ال V و ال W كونوا مختلفين و
+
+81
+00:07:13,260 --> 00:07:18,560
+بيربطوا او بمعنى اخر ان الديسر E هذا بيربط النقطين
+
+82
+00:07:19,790 --> 00:07:23,750
+V و W مع
+
+83
+00:07:23,750 --> 00:07:28,190
+بعض Incident
+
+84
+00:07:28,190 --> 00:07:33,870
+مرتبطات مع بعض ان عندي بقول ان V و W are incident
+
+85
+00:07:33,870 --> 00:07:40,030
+with the edge VW معمول يهم join من خلال ال dessert
+
+86
+00:07:40,030 --> 00:07:45,410
+اللي موجودة عندها لما بكون في عندي مطبقين موجودين
+
+87
+00:07:45,410 --> 00:07:51,590
+علىبارفين الجسر بنقول عنهم نقاط متجاورة adjacent
+
+88
+00:07:51,590 --> 00:07:56,830
+vertex نقاط
+
+89
+00:07:56,830 --> 00:08:03,650
+متجاورة الان في الرسم هذه a
+
+90
+00:08:03,650 --> 00:08:09,610
+و bو B و C A و B متجاورات و B و C متجاورات لكن A و
+
+91
+00:08:09,610 --> 00:08:15,350
+D لأ A و C غير متجاورات كذلك وبالتالي لما يكون عند
+
+92
+00:08:15,350 --> 00:08:22,330
+جسر ما بين المقاطين يقول ان المقاط متجاورة الجسور
+
+93
+00:08:22,330 --> 00:08:27,410
+متجاورة لما جسرين يلتجوا في نفس النقطة
+
+94
+00:08:29,910 --> 00:08:34,790
+الان a,b و b,c هذي جسور متجاورة و لأنهم التقوا
+
+95
+00:08:34,790 --> 00:08:41,390
+اين؟ و لو كان في ندي نقطة او في جسر من b ل d بيكون
+
+96
+00:08:41,390 --> 00:08:50,030
+b و d ك vertices متجاورين كذلك a,b و b,d و b,c
+
+97
+00:08:50,030 --> 00:08:54,050
+جسور متجاورة لأنهم التقوا كلهم على نفس النقطة
+
+98
+00:08:59,610 --> 00:09:06,150
+الأن، عدد الجسور الـ Incident في النقطة X أو عدد
+
+99
+00:09:06,150 --> 00:09:11,270
+الجسور الملتقية أو الواصلة للنقطة X بنسميها الـ
+
+100
+00:09:11,270 --> 00:09:15,610
+Degree تبعتها، رتبتها، رتبة النقطة تقاس أو تقدر
+
+101
+00:09:15,610 --> 00:09:19,730
+بعدد الجسور المتصلة بالنقطة يعني الآن، رتبة ليه
+
+102
+00:09:19,730 --> 00:09:26,050
+جدّي الشباب؟واحد كم ديصر متصل بالـA؟ واحد كم ديصر
+
+103
+00:09:26,050 --> 00:09:30,290
+متصل بالـB؟ واحد كم ديصر متصل بالـC؟ واحد كم ديصر
+
+104
+00:09:30,290 --> 00:09:34,510
+متصل بالـB؟ تلاتة بالتالي ال degree تبع الـB؟
+
+105
+00:09:34,510 --> 00:09:39,390
+تلاتة الآن فالرسم الأولانية ماكانش في أنها مع الـD
+
+106
+00:09:39,390 --> 00:09:45,490
+حدا كانت لحالها هيك ال degree تبع الـD جديش؟ صفر
+
+107
+00:09:45,490 --> 00:09:49,150
+ال degree تبع الـD صفر وبقول عنها isolated point
+
+108
+00:09:49,150 --> 00:09:57,300
+نقطة معزولةوبالتالي بنقول عنه ال vertex odd vertex
+
+109
+00:09:57,300 --> 00:10:02,320
+او even vertex بداية عن degree تبعته، لو كانت odd
+
+110
+00:10:02,320 --> 00:10:07,020
+بقول عنه odd يعني ال a is odd vertex odd يعني ان
+
+111
+00:10:07,020 --> 00:10:10,800
+ال degree تبعته odd ممكن واحد ممكن تلاتة الله يعلم
+
+112
+00:10:10,800 --> 00:10:16,980
+و ال b is even vertex يعني ال degree تبعته عدد
+
+113
+00:10:16,980 --> 00:10:17,400
+زوجي
+
+114
+00:10:20,860 --> 00:10:24,460
+تعالى نشوف ال graph اللى موجود عندى هنا ال graph
+
+115
+00:10:24,460 --> 00:10:31,300
+هذا كان vertex عليه 6 طبعا لو انا بدى اكتر و احنا
+
+116
+00:10:31,300 --> 00:10:35,460
+هقول ال G V
+
+117
+00:10:35,460 --> 00:10:44,400
+و E و ال V هذا تساوي مجموعة الجسور V1, V2, V3, V4,
+
+118
+00:10:44,480 --> 00:10:46,380
+V5, V6
+
+119
+00:10:56,860 --> 00:11:01,800
+أقول E هي عبارة عن مجموعة الجسور اللي موجودة عندي
+
+120
+00:11:01,800 --> 00:11:14,020
+هان ال connections V1 V4 V2 V5 V1 V6 V4 V5 V5 V6
+
+121
+00:11:14,020 --> 00:11:18,000
+وين؟
+
+122
+00:11:18,000 --> 00:11:23,930
+لأ مش موجود مش موجود شاف النقطة اللي في النصلاحظ
+
+123
+00:11:23,930 --> 00:11:26,710
+.. لاحظ .. انا ما حسبت ال .. هي .. ما حسبت ال cash
+
+124
+00:11:26,710 --> 00:11:33,330
+انه هذا لو فيه نقطة هان كان سؤالنا نفسنا اكتر مش
+
+125
+00:11:33,330 --> 00:11:36,350
+كتار واحد ان انا .. انا اتخيل لو عندي فيه هان V7
+
+126
+00:11:36,350 --> 00:11:41,390
+صح في عندي واحد اتنين تلاتة اربع لان الجسر واقع ما
+
+127
+00:11:41,390 --> 00:11:46,570
+بين نقطتين الجسر دايما واقع ما بين نقطتين وبالتالي
+
+128
+00:11:46,570 --> 00:11:49,690
+انا مابديش اتغير حسب النقاط اللي موجودة عندي هان
+
+129
+00:11:51,060 --> 00:11:58,920
+وبالتالي ال graph تبعي هذا هيتمثله مصبوط V3 ال
+
+130
+00:11:58,920 --> 00:12:04,320
+degree تبعتها صفر isolated point نقطة منازلة عن ال
+
+131
+00:12:04,320 --> 00:12:07,980
+graph اللي موجود عندها في شغل مهم جدا يا شباب هذا
+
+132
+00:12:07,980 --> 00:12:11,180
+ال graph هو نفسه لو انا اجيت رسمته هيك
+
+133
+00:12:23,540 --> 00:12:32,420
+هذه أربعة هذه خمسة هذه اتنين هذه ستة وهذه تلاتة
+
+134
+00:12:32,420 --> 00:12:37,220
+هذا
+
+135
+00:12:37,220 --> 00:12:42,140
+نفس ال graphنفس ال graph مع اختلاف ال direction
+
+136
+00:12:42,140 --> 00:12:45,240
+لأن نقاط هي نفسها مع اختلاف ال direction اختلاف
+
+137
+00:12:45,240 --> 00:12:50,100
+الشكل اختلاف الشكل و هنشوف لاحقا ان كيف ممكن انا
+
+138
+00:12:50,100 --> 00:12:52,540
+اتعامل مع ال graph اللي بالشكل هذا كيف اعرف ان ال
+
+139
+00:12:52,540 --> 00:12:55,460
+graph هذا يطابق ال graph هذا او هل في خصائص من ال
+
+140
+00:12:55,460 --> 00:12:57,500
+two graphs عشان اقول ان هما دول التانين هم نفس
+
+141
+00:12:57,500 --> 00:13:04,310
+الشكل ولا لأ انت عشان ال a و ال v و k هي واحدلأن
+
+142
+00:13:04,310 --> 00:13:07,370
+المفروض بحيث تقارن تعمل مقارنة ما بين النقاط
+
+143
+00:13:07,370 --> 00:13:10,990
+والنقاط التانية والجسور والجسور التانية بناء على
+
+144
+00:13:10,990 --> 00:13:13,650
+تعريف النقاط اللي انت اخترته فهنشوفها لاحقا يا
+
+145
+00:13:13,650 --> 00:13:18,770
+رامي بس الفكرة ان هذا ال graph هو graph مطابق
+
+146
+00:13:18,770 --> 00:13:23,790
+تماما يعني لو انا كتبت ال V و ال E هتطلع نفسهم ال
+
+147
+00:13:23,790 --> 00:13:27,850
+V و ال E هتطلع نفسهم تمام؟ وبالتالي بيقول عنهم
+
+148
+00:13:27,850 --> 00:13:31,950
+isomorphic graphs هنشوفها لاحقا ان ش الله تعالى
+
+149
+00:13:31,950 --> 00:13:39,780
+طيبالآن في عندي شغلة غالبا موجودة في التطبيقات أو
+
+150
+00:13:39,780 --> 00:13:43,120
+في الحياة لكن في ال definition الأصلي تبع ال graph
+
+151
+00:13:43,120 --> 00:13:47,420
+مالهاش تعريف مالهاش وجود خصوصا .. خصوصا لما اجينا
+
+152
+00:13:47,420 --> 00:13:50,800
+.. اتكلمنا على المجموعات انت ملاحظ من البداية أنا
+
+153
+00:13:50,800 --> 00:13:54,970
+صرت الآن وكأنه مجموع .. موضوع ال graphشمل ال
+
+154
+00:13:54,970 --> 00:13:59,450
+relation والمجموعات لأنه قال لي إن هذه مجموعة وهذه
+
+155
+00:13:59,450 --> 00:14:02,990
+مجموعة والاتنين موجودين في عبارة عن زوج مرتب وزوج
+
+156
+00:14:02,990 --> 00:14:08,570
+مرتب يعني relation و لا لأ الآن حصل لما قال لي ال
+
+157
+00:14:08,570 --> 00:14:13,650
+vertices مجموعات يعني مافيش تكرار تمام و لما قال
+
+158
+00:14:13,650 --> 00:14:17,790
+لي ال edge مجموعات برضه مافيش تكرار لل element و
+
+159
+00:14:17,790 --> 00:14:25,610
+لا لأ تمام طيب في حالة زي هذه E1 و E2هو عبارة عن
+
+160
+00:14:25,610 --> 00:14:31,230
+جسر .. هو عبارة عن جسرين مختلفين موجودين بين V1 و
+
+161
+00:14:31,230 --> 00:14:34,870
+V2 طب في ال representation تبعك ال graph الأصلية
+
+162
+00:14:34,870 --> 00:14:42,190
+بينفعش أجي أقول والله أنا ال E عندي تساوي V1 V2
+
+163
+00:14:42,190 --> 00:14:50,090
+كما V1 V2 لأن هذا بتنافع مع تعريف المجموعات و
+
+164
+00:14:50,090 --> 00:14:55,150
+بالتالي هذا إيش ممكن تساوي؟يجب أن تعد واحد لكن في
+
+165
+00:14:55,150 --> 00:15:00,290
+الواقع هو اتنين طيب ما ياتوا هاد اصبح ال
+
+166
+00:15:00,290 --> 00:15:03,850
+definition تبع ال graph لا ينقلق عليه عشان هيك
+
+167
+00:15:03,850 --> 00:15:08,590
+سامون الشغل اسمها بي سيدو graph بي سيدو graph هو
+
+168
+00:15:08,590 --> 00:15:13,730
+graph مع بعض التعديلات او بعض التجاوزات لل
+
+169
+00:15:13,730 --> 00:15:16,810
+definition ال بي سيدو graph هو عبارة عن graph
+
+170
+00:15:16,810 --> 00:15:22,090
+بيحتوي على multi edge بين النقطتينيعني ممكن يكون
+
+171
+00:15:22,090 --> 00:15:24,410
+في عنده اكتر من جسر موجود بينهم و هدف ال
+
+172
+00:15:24,410 --> 00:15:27,690
+implementation او في الأمثلة اللي انا حكيتها واقع
+
+173
+00:15:27,690 --> 00:15:32,610
+لما بتكلم على شبكة الطرق على الخريطة ايش اللي يمنع
+
+174
+00:15:32,610 --> 00:15:36,070
+يكون بين مدينتنا اكتر من طريقة اكتر من طريقة مافيش
+
+175
+00:15:36,070 --> 00:15:41,670
+حاجة تمنع طيب هذه واحدة اتنين لو احنا اجينا جولة
+
+176
+00:15:42,470 --> 00:15:48,010
+الـ Lobe Edge الجسر الدوار على نفس الـ Vertex هو
+
+177
+00:15:48,010 --> 00:15:52,810
+لما عرف الجسر جال النقطين تبعوه للجسر لازم يكونوا
+
+178
+00:15:52,810 --> 00:15:58,390
+مختلفات Two distinct vertices طب بس هذا ال Lobe
+
+179
+00:15:58,390 --> 00:16:04,450
+Edge بيبدأ و بنتهي نفس المقطة عشان انا اوجده يعني
+
+180
+00:16:04,450 --> 00:16:07,710
+انا بتكلم على بيسيدوجراف يعني ال بيسيدوجراف هو
+
+181
+00:16:07,710 --> 00:16:14,410
+عبارة عن Graph بيسمح بوجود ال Lobeتمام؟ و ال
+
+182
+00:16:14,410 --> 00:16:17,650
+multiple edge بيسمح بوجود ال loops و ال multiple
+
+183
+00:16:17,650 --> 00:16:23,310
+edge ناقش الحالة يا شباب؟ طيب الآن في شغلة مهمة
+
+184
+00:16:23,310 --> 00:16:26,850
+جدا بما ان احنا اتكلمنا على ال degree بما ان احنا
+
+185
+00:16:26,850 --> 00:16:30,470
+اتكلمنا على ال degree الآن ال degree تبعت ال loop
+
+186
+00:16:30,470 --> 00:16:36,110
+بتزيد ال vertex او بتزيد ال degree تبعت ال vertex
+
+187
+00:16:36,110 --> 00:16:40,630
+عفوا بمقدارتنين لان احنا مش اتفقنا ايش هي ال
+
+188
+00:16:40,630 --> 00:16:45,110
+degree هي عبارة عن عدد ال connections اللي موجودة
+
+189
+00:16:45,110 --> 00:16:50,510
+و اين على النقطة بين النقطتين هيها لما اتينا هنا
+
+190
+00:16:50,510 --> 00:16:56,510
+للمقطة V2 هذي جدش عدد ال connections اللي عليها
+
+191
+00:16:56,510 --> 00:17:06,440
+تلاتة هذ V1 V2 V4 V1 طيب V3تعالى اعدى ال
+
+192
+00:17:06,440 --> 00:17:10,100
+connections اللى موجودة عليها الارهاي واحد هاي
+
+193
+00:17:10,100 --> 00:17:13,860
+اتنين الارفانية فيها كمان connection هاي تلاتة وفي
+
+194
+00:17:13,860 --> 00:17:16,760
+كمانها connection اربعة لأن ال loop ال connection
+
+195
+00:17:16,760 --> 00:17:20,280
+بتاعتها بتنين ال loop ال connection بتاعتها بتنين
+
+196
+00:17:20,280 --> 00:17:24,440
+طب الاتنين خانسة و خانسة؟ وينها؟ الاتنين اللى
+
+197
+00:17:24,440 --> 00:17:28,660
+مقطقطة مع ال V تلاتة من تحت من الدوريه من هين
+
+198
+00:17:28,660 --> 00:17:35,050
+عدتهم هاي واحد هاي اتنينهذه الكناتة هي أربعة عليها
+
+199
+00:17:35,050 --> 00:17:43,430
+أربعة نقاط اتصال الجسر اسمه E5 هذا مرتين بس و أنا
+
+200
+00:17:43,430 --> 00:17:45,790
+فعلا ما عديتهوش مرتين أنا عديت ال collections
+
+201
+00:17:45,790 --> 00:17:51,770
+تبعته يعني طرف الوصلة أو طرف الطريق موجود و مشبوك
+
+202
+00:17:51,770 --> 00:17:56,210
+وين على النقطة فسألتك النقطة هذه الموصولة بكم جسر؟
+
+203
+00:17:56,590 --> 00:18:05,970
+انت جيب تعد واحد اتنين تلات اربع انت جيب تعد واحد
+
+204
+00:18:05,970 --> 00:18:08,390
+اتنين تلات اربع اتنين تلات اربع اتنين تلات اربع
+
+205
+00:18:08,390 --> 00:18:08,390
+اتنين تلات اربع اتنين تلات اربع اتنين تلات اربع
+
+206
+00:18:08,390 --> 00:18:10,750
+اتنين تلات اربع اتنين تلات اربع اتنين تلات اربع
+
+207
+00:18:10,750 --> 00:18:12,110
+اتنين تلات اربع اتنين تلات اربع اتنين تلات اربع
+
+208
+00:18:12,110 --> 00:18:12,350
+اتنين تلات اربع اتنين تلات اربع اتنين تلات اربع
+
+209
+00:18:12,350 --> 00:18:15,650
+اتنين تلات اربع اتنين تلات اربع اتنين تلات اربع
+
+210
+00:18:15,650 --> 00:18:25,570
+اتنين تلات اربع اتنين
+
+211
+00:18:25,570 --> 00:18:33,950
+تلبين الـ V و الـ A لما أنا بتكلم على sub graph
+
+212
+00:18:33,950 --> 00:18:39,750
+بتكلم على graph مجموعة النقاط طبعته مجموعة جزئية
+
+213
+00:18:39,750 --> 00:18:45,050
+من .. من مجموعة الـ V اللي هندي و مجموعة الجسور
+
+214
+00:18:45,050 --> 00:18:49,350
+برضه عبارة عن subset من الـ A الآن هاي ال graph
+
+215
+00:18:49,350 --> 00:18:54,660
+اللي عندي هذا ال G على سبيل المثاللو قلت لك هاتلي
+
+216
+00:18:54,660 --> 00:19:00,460
+graph او هاتلي subset سميه G1 تمام؟
+
+217
+00:19:00,460 --> 00:19:08,060
+بكل بساطة انا ممكن اروح اخد V1 V2 V3 هي المجموعة
+
+218
+00:19:08,060 --> 00:19:16,520
+V1 V2 V3 كمة و الجسور اللي ما بينهم في مجموعة
+
+219
+00:19:16,520 --> 00:19:29,170
+تانية V1 V2 و V2V3 مظبوط؟ خلصنا هذا ال graph بمثل
+
+220
+00:19:29,170 --> 00:19:33,750
+subset من ال graph اللي موجود عندها بناء على إيش؟
+
+221
+00:19:33,750 --> 00:19:38,950
+بناء على إن ال vertices set هي subset من ال main
+
+222
+00:19:38,950 --> 00:19:44,710
+setو ال edge جسد مجموعة الجسور هي عبارة عن مجموعة
+
+223
+00:19:44,710 --> 00:19:48,850
+جزئية كذلك من مجموعة الجسور الرئيسية اللي عندي هنا
+
+224
+00:19:48,850 --> 00:19:52,570
+لاحظ ان انا مابيهمنيش ال direction كل اللي بيهمني
+
+225
+00:19:52,570 --> 00:19:57,370
+ان انا أخدت النقاط و أخدت الجسور اللي فعليا موجودة
+
+226
+00:19:57,370 --> 00:20:06,810
+ما بين النقاط يعني الآن لو انا اجيت اعملت هيك V1
+
+227
+00:20:06,810 --> 00:20:10,550
+و V2 هل هذا ال graph subset
+
+228
+00:20:13,580 --> 00:20:21,700
+هل هذا ال graph subset؟ subset V1 و V2 كمجموعة هل
+
+229
+00:20:21,700 --> 00:20:27,460
+هي subset من V؟ أه subset الآن مجموعة الجسور V1 V2
+
+230
+00:20:27,460 --> 00:20:30,420
+جسر واحد في element واحد هل هي subset من أيه؟
+
+231
+00:20:30,420 --> 00:20:33,780
+subset من أيه؟ معناته هذا sub graph من هذا هاي
+
+232
+00:20:33,780 --> 00:20:37,600
+المعيار الوحيد اللي عندي تمام؟ لا بهمني direction
+
+233
+00:20:37,600 --> 00:20:42,500
+كل اللي بهمني النقاط موجودة والجسور موجودة بقول
+
+234
+00:20:42,500 --> 00:20:48,180
+عنه subsetوبالتالي هاي في عندي different subset V4
+
+235
+00:20:48,180 --> 00:20:57,640
+V3 V6 V7 موجودين هاليوم ال V subset V4 V3 موجود؟
+
+236
+00:20:57,640 --> 00:21:07,360
+اه موجود هايه طيب و تلاتة و ستة اه هايه موجود6 و7
+
+237
+00:21:07,360 --> 00:21:10,180
+موجود يعني هذه الرسمية اللي احنا بتتكلم عليها
+
+238
+00:21:10,180 --> 00:21:13,420
+قاعدين لاحظ كيف ال representation تبقى تختلفت؟
+
+239
+00:21:13,420 --> 00:21:17,740
+ماليش دخل بشكلها الان انت جدت قابط او مقابط مش
+
+240
+00:21:17,740 --> 00:21:21,580
+مرحلتنا احنا بتتكلم على subset المعيار تبعي افحص
+
+241
+00:21:21,580 --> 00:21:26,160
+ان مجموعة الجسور ومجموعة النقاط مجموعات جزئية من
+
+242
+00:21:26,160 --> 00:21:32,920
+الجسور والنقاط اللي موجودة على ال graph الأصلي لو
+
+243
+00:21:32,920 --> 00:21:37,280
+أنا خدت هذاهدول الاتنين مع بعض أخدته هكذا as one
+
+244
+00:21:37,280 --> 00:21:44,880
+graph هل هو subset؟ V2, V3, V6, V7، subset ال V's
+
+245
+00:21:44,880 --> 00:21:52,740
+طب الآن الجثور V2 و V3 موجود هيه V6, V7 موجود هيه،
+
+246
+00:21:52,740 --> 00:21:58,120
+معناته هذا برضه إيش؟ subset طيب،
+
+247
+00:21:58,120 --> 00:21:59,300
+لو أنا اتجهت هيك الشباب
+
+248
+00:22:09,410 --> 00:22:16,290
+لحالها هيك، أيوة
+
+249
+00:22:16,290 --> 00:22:22,210
+هل ال graph هذا subset ولا مش subset؟ كم واحد يقول
+
+250
+00:22:22,210 --> 00:22:29,250
+subset؟ واحد، اتنين، تلاتة، اربعة، خمسة، ستة،
+
+251
+00:22:29,250 --> 00:22:35,530
+واحدة راح تحديد تنتينطيب، تعالى احسب حسبة بسيطة
+
+252
+00:22:35,530 --> 00:22:40,950
+جدا اكتبلي هذا as كسوج مرتب هك ايش هتقولي؟ هتقولي
+
+253
+00:22:40,950 --> 00:22:51,530
+G V خمسة و Phi صح؟ هل هذه subset من ال V؟ اه
+
+254
+00:22:51,530 --> 00:22:57,590
+subset طب و ال Phi subset من ال E؟ اه subset مهناة
+
+255
+00:22:57,590 --> 00:22:59,590
+ال graph هذا subset
+
+256
+00:23:03,400 --> 00:23:09,040
+بالفترة تمام يعني اقل vertex او اقل graph هو عبارة
+
+257
+00:23:09,040 --> 00:23:13,900
+عن graph من نقطة واحدة و دائما تبحث عن وقت ال
+
+258
+00:23:13,900 --> 00:23:18,460
+subset ممتاز طيب الان لدي مصطلح جديد اسمه ال
+
+259
+00:23:18,460 --> 00:23:23,600
+complete graph ايش ال complete graph هو عبارة عن
+
+260
+00:23:23,600 --> 00:23:30,240
+graph كل vertex فيه متصل في كل ال vertices داقية
+
+261
+00:23:33,850 --> 00:23:39,890
+يعني الان كل نقطة فيه متصلة بكل النقاط.الان لو انا
+
+262
+00:23:39,890 --> 00:23:48,750
+افترضت graph بالشكل هذا V1 و V2 V1 و V2 و فيه
+
+263
+00:23:48,750 --> 00:23:53,970
+بينهم جسر هل هذا complete graph؟ ال definition
+
+264
+00:23:53,970 --> 00:24:00,730
+كانت تالي ان كل vertex كل نقطة مرتبطة بكل النقاط
+
+265
+00:24:00,730 --> 00:24:06,430
+الموجودةهذا في نقطتين فقط، معينات المتصالات مع
+
+266
+00:24:06,430 --> 00:24:12,270
+بعض، ممتاز؟
+
+267
+00:24:12,270 --> 00:24:17,090
+Complete
+
+268
+00:24:17,090 --> 00:24:26,530
+graph، واحد و اتنينو تلاتة واحد متصل مع اتنين و
+
+269
+00:24:26,530 --> 00:24:30,650
+تلاتة و اتنين متصل مع واحد و تلاتة و تلاتة متصل مع
+
+270
+00:24:30,650 --> 00:24:33,850
+واحد و اتنين معناته كل نقطة متصلة بكل النقاط
+
+271
+00:24:33,850 --> 00:24:37,150
+التالية
+
+272
+00:24:37,150 --> 00:24:43,210
+هيك
+
+273
+00:24:43,210 --> 00:24:49,990
+مش complete graph هيك
+
+274
+00:24:49,990 --> 00:24:55,830
+صار complete graphمصبوط؟ و فيك تتخيل كل ما زادت
+
+275
+00:24:55,830 --> 00:25:00,270
+عدد اللقاءات، ايش هزيد؟ هزيد عدد الجثور في ال
+
+276
+00:25:00,270 --> 00:25:04,250
+complete graph تمام ده في شغل مهم خلينا نقولها من
+
+277
+00:25:04,250 --> 00:25:08,770
+الآن لو طلعت في ال complete graph جدش ال degree
+
+278
+00:25:08,770 --> 00:25:13,490
+جدش قيمة ال degree لكل complete graph يعني عادة
+
+279
+00:25:13,490 --> 00:25:19,320
+بنرمز لو احنا شباب بال Kاختصار لكمبليت أو رمز
+
+280
+00:25:19,320 --> 00:25:24,120
+لكمبليت واحد يقول نشم الـC K كمان؟ والـN عدد ال
+
+281
+00:25:24,120 --> 00:25:34,160
+vertices يعني هذا كده قيمته؟ K2 هذا K3 هذا K4
+
+282
+00:25:34,160 --> 00:25:38,220
+ممتاز الـK أكتر من الزاوية التالتين أكتر؟ الزاوية
+
+283
+00:25:38,220 --> 00:25:41,300
+التالتين؟
+
+284
+00:25:41,300 --> 00:25:46,190
+طب الزاوية 180 يا صاحبيوالزاوية هن خمسة واربعين
+
+285
+00:25:46,190 --> 00:25:49,630
+فح؟ الزاوية هن تلاتة و تلاتين و تلاتة و عشرة
+
+286
+00:25:49,630 --> 00:25:56,730
+مالعاش علاقة بالزاوية .. مالعاش علاقة بالزاوية ال
+
+287
+00:25:56,730 --> 00:26:01,070
+K .. انا مش جاهز بقول انا complete ال K ترمز ل
+
+288
+00:26:01,070 --> 00:26:05,350
+complete graph و ال N اللي تحتها بتمثل عدد النقاط
+
+289
+00:26:05,350 --> 00:26:11,800
+اللي موجودة في ال graph ايه .. الآنهل بقدر استفيد
+
+290
+00:26:11,800 --> 00:26:16,300
+انا او احصل على قيمة ال degree لكل ال vertex من
+
+291
+00:26:16,300 --> 00:26:21,680
+خلال ال K؟ يعني لو انا اسألتك جديش ال degree ل V
+
+292
+00:26:21,680 --> 00:26:27,720
+واحد؟ واحد جديش ال degree ل V اتنين؟ واحد شو
+
+293
+00:26:27,720 --> 00:26:32,900
+علاقتها بالتنين؟ نقص واحد في ال K تلاتة جديش ال
+
+294
+00:26:32,900 --> 00:26:40,940
+degree ل واحد؟ اتنينDegree لاتنين تارتة تلاتة
+
+295
+00:26:40,940 --> 00:26:43,160
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+296
+00:26:43,160 --> 00:26:43,180
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+297
+00:26:43,180 --> 00:26:44,640
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+298
+00:26:44,640 --> 00:26:45,680
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+299
+00:26:45,680 --> 00:26:46,760
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+300
+00:26:46,760 --> 00:26:49,280
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+301
+00:26:49,280 --> 00:27:03,880
+تلاتة تلاتة تلاتة تلاتة تل
+
+302
+00:27:04,320 --> 00:27:07,800
+والنقطة هذه هتكون متصلة بكل النقاط التالية أيامته
+
+303
+00:27:07,800 --> 00:27:12,280
+هتكون متصلة بالنقص واحد من النقاط او بين جثم متصلة
+
+304
+00:27:12,280 --> 00:27:16,500
+بالنقص واحد من الجثور اللي هي مثلة ال degree تمام
+
+305
+00:27:16,500 --> 00:27:22,500
+بقى لدينا شغل أخير في ال complete graph لو كان
+
+306
+00:27:22,500 --> 00:27:26,520
+عندي graph بالشكل هذا هل هو complete graph؟
+
+307
+00:27:30,240 --> 00:27:32,260
+هي في واحد بيقول complete graph هاي التاني بيقول
+
+308
+00:27:32,260 --> 00:27:39,520
+طبعا كل لقطة متصلة بنفسها لغاية متصلة بنفسها متصلة
+
+309
+00:27:39,520 --> 00:27:44,780
+وبالتالي أنا بتكلم جاعد complete graph complete
+
+310
+00:27:44,780 --> 00:27:51,580
+graph وبالتالي هذا K واحد تعالي تطبق عليه قانون ال
+
+311
+00:27:51,580 --> 00:27:56,980
+degree تطبق عليه قانون ال degree صفر
+
+312
+00:27:59,030 --> 00:28:02,030
+ممتاز يعني complete graph و بتطبق عليه كل شروط ال
+
+313
+00:28:02,030 --> 00:28:17,490
+complete graph 100% في
+
+314
+00:28:17,490 --> 00:28:23,030
+عندي graph اسم مقول عنه bipartite graph bipartite
+
+315
+00:28:23,030 --> 00:28:25,790
+graph هو عبارة عن partition دي graph ال graph
+
+316
+00:28:25,790 --> 00:28:29,680
+جسيته من النصبس مش جسد ال graph أنا من النصف فصلته
+
+317
+00:28:29,680 --> 00:28:36,280
+يعني تيجي تقولي والله زي ما شوفنا قبل شوية V2 V3
+
+318
+00:28:36,280 --> 00:28:45,060
+V6 و V7 عشان فصلته هيك سميت ويش partitioned graph
+
+319
+00:28:45,060 --> 00:28:50,560
+ال by parted graph له خصائص معينة ال by parted
+
+320
+00:28:50,560 --> 00:28:55,440
+graph هو عبارة ان graph بقدر أجسم ال vertices
+
+321
+00:28:55,440 --> 00:29:01,660
+تبعتهلـ two disjoint sets يعني الجسم تبعتنا أو الـ
+
+322
+00:29:01,660 --> 00:29:06,420
+partitioning بدي يكون على نين؟ على النقاط الـ
+
+323
+00:29:06,420 --> 00:29:11,840
+bipartite graph هو عبارة عن graph بجر أفصل أو أجسم
+
+324
+00:29:11,840 --> 00:29:14,620
+المجموعة .. مجموعة النقاط طبعته ال vertices
+
+325
+00:29:14,620 --> 00:29:20,200
+لمجموعتين مختلفتين التقابة بينهم five، disjoint
+
+326
+00:29:20,200 --> 00:29:29,160
+بحيث إن كل vertex في المجموعة الأولىمتصل بعناصر
+
+327
+00:29:29,160 --> 00:29:33,000
+المجموعة التانية وعناصر المجموعة الواحدة مافيش
+
+328
+00:29:33,000 --> 00:29:39,440
+بينهم اتصال اعيد تاني او ناخد مثال جابل جابل الان
+
+329
+00:29:39,440 --> 00:29:50,160
+لو انا اديت هيك هقولنا a,b,c ك vertices الان ال
+
+330
+00:29:50,160 --> 00:30:00,260
+graph هذا الممثل بالمجموعتين aو B و C و الـ E
+
+331
+00:30:00,260 --> 00:30:09,100
+الجسور AB و B و C 100% الآن بقدر أقول عن ال graph
+
+332
+00:30:09,100 --> 00:30:13,940
+هذا by parted graph إذا قدرت أجسم المجموعة ال
+
+333
+00:30:13,940 --> 00:30:19,780
+vertices لمجموعتين بحيث أن ال connections فقط
+
+334
+00:30:19,780 --> 00:30:23,460
+موجودة بين علاصر المجموعتين علاصر المجموعة الواحدة
+
+335
+00:30:23,460 --> 00:30:29,400
+مافيش بينهم connectionsالان تعالى نفكر فيها الحالة
+
+336
+00:30:29,400 --> 00:30:32,540
+الوحيدة اللى ممكن تظبط معايا ان احكم ال B في
+
+337
+00:30:32,540 --> 00:30:39,180
+مجموعة و ال A و C في مجموعة تانية اظبط؟
+
+338
+00:30:39,180 --> 00:30:45,880
+الان ال V اللى عندي هان هادي بدها
+
+339
+00:30:45,880 --> 00:30:55,830
+تساوي ال B لحالها اتحاد A و Cالآن استطعت أن أجسم
+
+340
+00:30:55,830 --> 00:31:00,350
+الـV هذه إلى مجموعتين disjoint التقابة بينهم فاي
+
+341
+00:31:00,350 --> 00:31:04,550
+عشان أستطيع أن أقول كامل الـdefinition تبعي صح
+
+342
+00:31:04,550 --> 00:31:08,890
+أقول عنه هذا bipartite graph بدي أتحص على أصل
+
+343
+00:31:08,890 --> 00:31:11,890
+المجموعة الواحدة لازم يكونوا غير متصيرين مع بعضهم
+
+344
+00:31:11,890 --> 00:31:15,430
+المجموعة الأولى ليست فيها غير أصل واحد مريحانة
+
+345
+00:31:15,430 --> 00:31:22,230
+المجموعة التانية فيها A وCمتصلات مع بعض؟ لأ واتصال
+
+346
+00:31:22,230 --> 00:31:25,070
+فقط موجود بين مين ومين، بين المجموعة الأولى
+
+347
+00:31:25,070 --> 00:31:29,230
+والمجموعة التانية، يعني بي بارتت ال graph عبارة عن
+
+348
+00:31:29,230 --> 00:31:33,690
+بي بارتت ال graph طيب، لو أنا جيت ل graph بالشكل
+
+349
+00:31:33,690 --> 00:31:38,930
+هذا V1
+
+350
+00:31:38,930 --> 00:31:44,490
+و V2 هل هو بي بارتت ال graph؟
+
+351
+00:31:47,770 --> 00:31:57,270
+طيب انا بدي اقول ان ال V تساوي V1 اتحاد ال V2
+
+352
+00:31:57,270 --> 00:32:02,830
+وعناصر المجموعة الواحدة غير متصلة مع بعضها صح ولا
+
+353
+00:32:02,830 --> 00:32:08,710
+مش صح؟ صح؟ مافيش جثور؟ في جثور بناصر المجموعة
+
+354
+00:32:08,710 --> 00:32:13,610
+الواحدة؟ مافيش جثور، مظبوط؟ وعناصر المجموعتين او
+
+355
+00:32:13,610 --> 00:32:18,460
+الجثور ممتدة ما بينعناصر المجموعتين صح؟ و قلتلها
+
+356
+00:32:18,460 --> 00:32:21,660
+ده by partigraph امثلك او شبّلك ال by partigraph
+
+357
+00:32:21,660 --> 00:32:27,820
+باشت تخيل انه في نهر و على ضفتين النهر او على
+
+358
+00:32:27,820 --> 00:32:31,360
+ضفتين النهر موجودات و بدنا نعمل جسر .. بدنا نعمل
+
+359
+00:32:31,360 --> 00:32:35,640
+جسر الجسر وين بنعملها احنا؟ بنعملها فوق النهر؟ و
+
+360
+00:32:35,640 --> 00:32:39,280
+لا بنعملها على ضفة؟ لازم ت move فوق النهر .. فوق
+
+361
+00:32:39,280 --> 00:32:44,530
+النهر الآن اذا قدرت انا افصل المجموعة تبعتيعصرها
+
+362
+00:32:44,530 --> 00:32:49,530
+مختلفة بحيث ان ال connections فقط تكون ك bridge من
+
+363
+00:32:49,530 --> 00:32:52,550
+عصر النقطة الأولى والتانية انا بكون by parted
+
+364
+00:32:52,550 --> 00:32:59,970
+graph هذا الكلام بيصبغى تماما V1 و V2 عندنا نقطة 2
+
+365
+00:32:59,970 --> 00:33:04,690
+بس وبالتالي بقدر اعتبر هذا by parted graph by
+
+366
+00:33:04,690 --> 00:33:12,570
+parted graph تعالى نشوف الرسم هاي by parted graph
+
+367
+00:33:16,990 --> 00:33:22,010
+ربك عليك وانت لازم تتعلم من علم ربك لانه ماترككش
+
+368
+00:33:22,010 --> 00:33:25,650
+جاهل و لا تركك هيك الان هاي ال definition موجود
+
+369
+00:33:25,650 --> 00:33:31,330
+بين إيديك ال definition موجود بين إيديك هل هذا ال
+
+370
+00:33:31,330 --> 00:33:35,550
+graph bipartite graph الفكرة كانت تالية ان انا بدي
+
+371
+00:33:35,550 --> 00:33:40,710
+أخد النقاط أجسمهم لمجموعتين على نصر المجموعة
+
+372
+00:33:40,710 --> 00:33:45,410
+الواحد ومافيش منهم اتصال هدولة
+
+373
+00:33:45,410 --> 00:33:50,520
+عليها 6 نقاطانت حابب حتى لو كان واحد و أربعة، واحد
+
+374
+00:33:50,520 --> 00:33:55,260
+و خمسة، مافي مشكلة عندك، ماحطناش limit يا شباب على
+
+375
+00:33:55,260 --> 00:33:59,100
+عدد عناصر المجموعة لما بده اجسمها هنا، صح؟ احنا
+
+376
+00:33:59,100 --> 00:34:02,160
+قلنا بس اجسمهم لمجموعتين، وماقلناش ان المجموعة تلك
+
+377
+00:34:02,160 --> 00:34:05,500
+المتساويات، ماحطناش عليهم اي شرط بس تجسمهم اليها
+
+378
+00:34:05,500 --> 00:34:08,620
+لمجموعتين،
+
+379
+00:34:08,620 --> 00:34:13,910
+ماحدش قال،على أسر المجموعة الواحدة مافيش
+
+380
+00:34:13,910 --> 00:34:17,310
+connection لأنه مافيش جدوى يا شباب تمام مرة شباب
+
+381
+00:34:17,310 --> 00:34:22,310
+افترض ان هذا هي النهر هي
+
+382
+00:34:22,310 --> 00:34:26,730
+البنك الأولى وهي البنك التانية الضفة الأولى و
+
+383
+00:34:26,730 --> 00:34:32,130
+الضفة التانية تمام؟ الان لو انت جيت بنيت جسر هان
+
+384
+00:34:32,130 --> 00:34:38,350
+منطق؟
+
+385
+00:34:38,350 --> 00:34:43,260
+المهندس اللى بده يبني جسر زي هيك بده طاخرولا لا؟
+
+386
+00:34:43,260 --> 00:34:46,980
+ليش؟ لأنه بيضيع الفلوس في المكان الصحيح احنا مش
+
+387
+00:34:46,980 --> 00:34:52,140
+بحاجة لما .. الجسم يجب أن يكون فوق
+
+388
+00:34:52,140 --> 00:34:55,960
+النهر عشان يحقق الفائدة اللي منه الآن لما انت
+
+389
+00:34:55,960 --> 00:35:00,500
+بتفكر في البيت بيقدر ال graph بتشتري بالشكل المنطق
+
+390
+00:35:00,500 --> 00:35:06,160
+هذا الآن هل بقدر انا اجسم ال graph هذا؟ اه بكل
+
+391
+00:35:06,160 --> 00:35:10,780
+بساطة بينجسم هذه المجموعة الأولى وهذه المجموعات
+
+392
+00:35:10,780 --> 00:35:16,740
+التانيةوماحدش قاللي والله انه لازم يكون الجسم قدم
+
+393
+00:35:16,740 --> 00:35:20,700
+بس المهم ال connection يكون ما بين عناصر
+
+394
+00:35:20,700 --> 00:35:24,540
+المجموعتين طب انا لو قصدي ست مجموعات، كل مجموعة
+
+395
+00:35:24,540 --> 00:35:28,800
+بيسيريش في بينها قصارى، اصبر، اصبر، اصبر، اصبر،
+
+396
+00:35:28,800 --> 00:35:29,860
+اصبر، اصبر، اصبر، اصبر، اصبر، اصبر، اصبر، اصبر،
+
+397
+00:35:29,860 --> 00:35:30,480
+اصبر، اصبر، اصبر، اصبر، اصبر، اصبر، اصبر، اصبر،
+
+398
+00:35:30,480 --> 00:35:30,700
+اصبر، اصبر، اصبر، اصبر، اصبر، اصبر، اصبر، اصبر،
+
+399
+00:35:30,700 --> 00:35:31,500
+اصبر، اصبر، اصبر، اصبر، اصبر، اصبر، اصبر، اصبر،
+
+400
+00:35:31,500 --> 00:35:39,840
+اصبر، اص
+
+401
+00:35:43,800 --> 00:35:49,880
+ماذا يقول هذا الشخص؟ ماذا يقول؟ اقسم المجموعة الـ
+
+402
+00:35:49,880 --> 00:35:53,560
+vertices لمجموعتين لم أقل اقسمهم لثلاثة انا وانا
+
+403
+00:35:53,560 --> 00:35:58,580
+قلت اقسمهم لاربعة لمجموعتين يكونوا disjoint تمام؟
+
+404
+00:35:58,580 --> 00:36:03,840
+تمام الجرافه ده لما انا رسمته هكذا انا عارف هذا
+
+405
+00:36:03,840 --> 00:36:08,800
+اللي عملك الربكة لما جسمته جسمته لمجموعتين لم
+
+406
+00:36:08,800 --> 00:36:12,140
+اجسمه لأكثر مظبوط؟
+
+407
+00:36:13,400 --> 00:36:19,120
+كمل الان وبالتالي هذا by partigraph هذا
+
+408
+00:36:19,120 --> 00:36:25,740
+by partigraph هذي
+
+409
+00:36:25,740 --> 00:36:34,080
+اتنين و تلاتة هذا نفسه شباب ممكن انا ارسمه هيك
+
+410
+00:36:34,080 --> 00:36:39,800
+by
+
+411
+00:36:39,800 --> 00:36:41,500
+partigraph ولا لا
+
+412
+00:36:46,270 --> 00:36:49,110
+مش مشكلة الفكرة كمان مرة انا بدى اقسم مجموعة
+
+413
+00:36:49,110 --> 00:36:53,830
+النقاط لمجموعات مختلفة مجموعتين مختلفتين disjoint
+
+414
+00:36:53,830 --> 00:36:59,110
+وعراصر المجموعة الواحدة مافيش منها connection هذا
+
+415
+00:36:59,110 --> 00:37:03,510
+الأخير ليش
+
+416
+00:37:03,510 --> 00:37:09,890
+لأ فكر كويس اطلع نفس الكلام كلنا بنتكلم على ال
+
+417
+00:37:09,890 --> 00:37:14,170
+graph الأخيروقولنا هل ال graph هذا bipartite graph
+
+418
+00:37:14,170 --> 00:37:19,210
+او bipartite graph جسمته لمجموعتين بحيث انه الجثور
+
+419
+00:37:19,210 --> 00:37:22,750
+فقط ممتدة بين عناصر المجموعة الأولى و عناصر
+
+420
+00:37:22,750 --> 00:37:26,530
+المجموعة التانية مافيش جثور ما بين عناصر المجموعة
+
+421
+00:37:26,530 --> 00:37:31,750
+الواحدة لسه ماتكلمش على ال complete يا أحمد نتكلم
+
+422
+00:37:31,750 --> 00:37:38,660
+على bipartite graph الان في ال bipartite graphفي
+
+423
+00:37:38,660 --> 00:37:42,900
+عندى graph اسمه complete bipartite graph complete
+
+424
+00:37:42,900 --> 00:37:47,860
+bipartite graph الفكرة فيه ان بعد ما أنا جسمت ال
+
+425
+00:37:47,860 --> 00:37:52,480
+graph هذا لمجموعتين ال vertices تبعته لجيت ان كل
+
+426
+00:37:52,480 --> 00:37:57,580
+vertex في المجموعة الأولى متصل في كل ال vertices
+
+427
+00:37:57,580 --> 00:38:01,020
+اللي في المجموعة التانية والعكس صحيح فبصي غير
+
+428
+00:38:01,020 --> 00:38:05,380
+عبارة عن full bipartite graph يعني لو انا اديت هيك
+
+429
+00:38:08,860 --> 00:38:15,860
+على الرصم الأولى تبعتنا هذا by bipartite graph صح؟
+
+430
+00:38:15,860 --> 00:38:23,260
+اه by bipartite graph حطينا V1 و V2 و V3 اول مثال
+
+431
+00:38:23,260 --> 00:38:27,380
+شرحناه by bipartite graph الان لو دججت في ال graph
+
+432
+00:38:27,380 --> 00:38:33,760
+هذاهلاجي ان ال graph هذا complete bipartite بمعنى
+
+433
+00:38:33,760 --> 00:38:38,580
+ان كل vertex في المجموعة الأولى متصل بكل ال
+
+434
+00:38:38,580 --> 00:38:42,120
+vertices في المجموعة التالية و العكس صحيح لأن
+
+435
+00:38:42,120 --> 00:38:47,560
+عناصر المجموعة الأولى مافيها V1 متصل مع V2 و V3
+
+436
+00:38:47,560 --> 00:38:50,660
+اللي هم عناصر المجموعة التالية عناصر المجموعة
+
+437
+00:38:50,660 --> 00:38:55,330
+التالية V2 و V3 و كل واحد فيهم متصلمع المجموعة
+
+438
+00:38:55,330 --> 00:38:57,810
+الأولى، مع كل العناصر في المجموعة الأولى بالتحديد
+
+439
+00:38:57,810 --> 00:39:02,910
+فهذا بنسميه Complete Bipartite وهكذا بنرمزله دائما
+
+440
+00:39:02,910 --> 00:39:07,870
+ناخد الـK يا شباب تحت ال Complete قبل شوية
+
+441
+00:39:07,870 --> 00:39:14,090
+وبنحطلها رقمين الرقم الأول والرقم التاني الآن حسب
+
+442
+00:39:14,090 --> 00:39:17,490
+المثال اللي عندي هان اللي هو رقم المجموعتين اللي
+
+443
+00:39:17,490 --> 00:39:22,110
+هي V1الـ Cardinality لـ V1 كُمَة والـ Cardinality
+
+444
+00:39:22,110 --> 00:39:27,430
+لـ V2 الأن سأقنعه كمان كمان كمان كمان كمان كمان
+
+445
+00:39:27,430 --> 00:39:33,010
+واحد و اتنين كمان كمان كمان كمان كمان كمان كمان
+
+446
+00:39:33,010 --> 00:39:34,730
+كمان كمان كمان كمان كمان كمان كمان كمان كمان كمان
+
+447
+00:39:34,730 --> 00:39:39,870
+كمان كمان كمان كمان كمان كمان كمان كمان
+
+448
+00:39:39,870 --> 00:39:45,550
+كمان كمان كمان كمان كمان كمان كمان كمان كمان كمان
+
+449
+00:39:45,550 --> 00:39:45,550
+كمان كمان كمان كمان كمان كمان كمان كمان كمان كمان
+
+450
+00:39:45,550 --> 00:39:45,550
+كمان كمان كمان كمان كمان كمان كمان كمان كمان كمان
+
+451
+00:39:45,550 --> 00:39:48,990
+كمان
+
+452
+00:39:50,410 --> 00:39:58,410
+Complete bipartite graph اتنين تلاتة هذه
+
+453
+00:39:58,410 --> 00:40:08,670
+المجموعة الأولى V1 وهذه V2 وكل
+
+454
+00:40:08,670 --> 00:40:13,290
+element أو كل vertex في الأولى متصل بالتلاتة
+
+455
+00:40:13,290 --> 00:40:15,150
+الموجودين في ال vertex في المجموعة التانية
+
+456
+00:40:17,930 --> 00:40:24,330
+والعكس صحيح والعكس صحيح طيب .. الآن لو أنا سألتك
+
+457
+00:40:24,330 --> 00:40:27,550
+نفس السؤال اللي ماتكلمناه عن ال complete graph ال
+
+458
+00:40:27,550 --> 00:40:32,510
+degree .. ال degree تبعت ال complete graph
+
+459
+00:40:32,510 --> 00:40:39,990
+vertices جداش هتكون مجسومة ل نصين الأولى
+
+460
+00:40:39,990 --> 00:40:43,190
+ال
+
+461
+00:40:43,190 --> 00:40:49,450
+degree تبعتها nوالتانية ال degree تبعتها M يعني
+
+462
+00:40:49,450 --> 00:40:53,150
+بين جثين ال degree تبعت عناصر المجموعة الأولى
+
+463
+00:40:53,150 --> 00:40:56,530
+اتنين إذا سألتك ال degree اللي فيه واحد جديش هنا
+
+464
+00:40:56,530 --> 00:40:59,550
+يا شباب اتنين قلنا ال degree هي عبارة عن عدد
+
+465
+00:40:59,550 --> 00:41:04,190
+اليسور المتصل في النقطة و ال degree اللي فيه واحدة
+
+466
+00:41:04,190 --> 00:41:07,250
+فيه اتنين واحد واحد واحد واحد واحد واحد واحد واحد
+
+467
+00:41:07,250 --> 00:41:11,390
+واحد واحد واحد واحد واحد واحد واحد واحد
+
+468
+00:41:11,390 --> 00:41:12,450
+واحد واحد واحد واحد واحد واحد واحد واحد واحد واحد
+
+469
+00:41:12,450 --> 00:41:15,010
+واحد واحد واحد واحد واحدو الدجريلة عناصر المجموعة
+
+470
+00:41:15,010 --> 00:41:20,430
+التالية واحد شاجلبنا و هم مخلصنا؟ ماجعب شاجلبهم بس
+
+471
+00:41:20,430 --> 00:41:29,050
+لازم تفهمليش انك شاجلبهم ماجعب طيب تعالي هنا من a
+
+472
+00:41:29,050 --> 00:41:40,690
+b c d e جدش الدجريلة ايه؟ رتبة a جدش؟ تلاتةأيش
+
+473
+00:41:40,690 --> 00:41:45,850
+علاج بتهيأل؟ الارتن تم لمن؟ للمجموعة الأولى، صح؟
+
+474
+00:41:45,850 --> 00:41:50,370
+فال degree تبعتها، ال degree لكل عناصر المجموعة
+
+475
+00:41:50,370 --> 00:41:55,390
+الأولى تساوي عدد عناصر المجموعة التانية لأن كل
+
+476
+00:41:55,390 --> 00:41:59,670
+عنصر في المجموعة الأولى مرتبط بكل عناصر المجموعة
+
+477
+00:41:59,670 --> 00:42:03,850
+التالية وبالتالي في دي صور على كل عناصرها، نعرف ال
+
+478
+00:42:03,850 --> 00:42:08,160
+degree بنفس العدد، والعكس صحيحأنا أعرف إنك فهمت بس
+
+479
+00:42:08,160 --> 00:42:12,960
+بتكملها خلاص يعني لإن أنا بتكلم مش معاك لحالك الان
+
+480
+00:42:12,960 --> 00:42:18,760
+نفس الكلام عناصر المجموعة التانية ال degree لكل
+
+481
+00:42:18,760 --> 00:42:23,560
+واحد فيهم اتنين ليش؟ لإن كل .. لازم يكون مرتبط بكل
+
+482
+00:42:23,560 --> 00:42:28,720
+عناصر المجموعة التانية كيف
+
+483
+00:42:28,720 --> 00:42:32,620
+تقلبها يعني؟ لأ صح ليش هو المشكلة في الموضوع الان
+
+484
+00:42:32,620 --> 00:42:40,130
+اسميلكم بقول لو كتبت K تلاتة اتنينمش مشكلة .. نفس
+
+485
+00:42:40,130 --> 00:42:44,610
+الحكاية .. مش مشكلة .. بس الفكرة أنك تعملي هاي
+
+486
+00:42:44,610 --> 00:42:51,870
+واحدة و هاي تنتين .. هد هي نفسها كتلاتة .. لاحظ يا
+
+487
+00:42:51,870 --> 00:42:54,750
+شباب التلاتة والتلال هي عبارة عن cardinality
+
+488
+00:42:54,750 --> 00:42:58,490
+العناصر المجموعات .. بس .. و ال K بتقول أن عناصر
+
+489
+00:42:58,490 --> 00:43:00,590
+المجموعة الأولى مرتبطة مع كل عناصر المجموعة
+
+490
+00:43:00,590 --> 00:43:07,500
+التانية .. و العكس صحيح .. ممتاز .. اللي بعدههي
+
+491
+00:43:07,500 --> 00:43:13,120
+Complete Bipartite Graph تلاتة في تلاتة
+
+492
+00:43:13,120 --> 00:43:19,360
+مالهم؟
+
+493
+00:43:19,360 --> 00:43:23,920
+اه بتبطل لو هال .. لو هال فيه بيصير واحد بطل
+
+494
+00:43:23,920 --> 00:43:30,320
+Bipartite Graph لأن
+
+495
+00:43:30,320 --> 00:43:33,220
+مش حاجة تقدر تفصلهم طيب
+
+496
+00:43:34,370 --> 00:43:42,110
+الان في ال graph او في ال pseudograph حافظ
+
+497
+00:43:42,110 --> 00:43:49,670
+جمع رتب النقاط .. ايش رتب النقاط يا شباب؟ ال
+
+498
+00:43:49,670 --> 00:43:54,230
+degree هي عدد الجسور المرتبطة بالنقطة .. لو جمعتهم
+
+499
+00:43:54,230 --> 00:44:01,410
+كلهما هيكون عبارة عن ضعف عدد الجسور الموجودة ..
+
+500
+00:44:01,410 --> 00:44:02,350
+هاي graph
+
+501
+00:44:06,720 --> 00:44:14,580
+هي graph ال graph هذا complete graph صح؟ طيب قدش
+
+502
+00:44:14,580 --> 00:44:22,300
+ال degree تبعته لكل نقطة؟ 2 طيب مجموعهم؟ حرام
+
+503
+00:44:22,300 --> 00:44:25,160
+عليك، مجموع ال degree أنا قاعد بقولك لل vertices
+
+504
+00:44:25,160 --> 00:44:29,880
+هذا ال degree اتنين و هذا ال degree اتنين و هذا ال
+
+505
+00:44:29,880 --> 00:44:41,420
+degree اتنين، ستةستة تساوي اتنين في عدد الجسور عدد
+
+506
+00:44:41,420 --> 00:44:47,480
+الجسور جدنا الشباب هنا واحد اتنين تلاتة تمام؟ تمية
+
+507
+00:44:47,480 --> 00:44:51,300
+المية لا
+
+508
+00:44:51,300 --> 00:45:00,320
+مش لازم هاي ال graph هذا مش complete graph قعد يا
+
+509
+00:45:00,320 --> 00:45:02,960
+باشا ال degree له واحد
+
+510
+00:45:06,020 --> 00:45:09,440
+تنين تلاتة تنين تلاتة تنين تلاتة تنين تلاتة تنين
+
+511
+00:45:09,440 --> 00:45:12,220
+تلاتة تنين تلاتة تنين تلاتة تنين تلاتة تنين تلاتة
+
+512
+00:45:12,220 --> 00:45:15,240
+تنين تلاتة تنين تلاتة تنين تلاتة تنين تلاتة تنين
+
+513
+00:45:15,240 --> 00:45:16,360
+تلاتة تنين تلاتة تنين تلاتة تنين تلاتة تنين تلاتة
+
+514
+00:45:16,360 --> 00:45:18,520
+تنين تلاتة تنين تلاتة تنين تلاتة تنين تلاتة تنين
+
+515
+00:45:18,520 --> 00:45:23,500
+تلاتة تنين تلاتة تنين تلاتة تنين تلاتة تنين تلاتة
+
+516
+00:45:23,500 --> 00:45:33,940
+تنين تلاتة تنين تلاتة تنين تلاتة تنين تلاتة تنين
+
+517
+00:45:33,940 --> 00:45:39,780
+تلاتةتمام؟ عشانك قلنا لك هو سواء كان graph أو
+
+518
+00:45:39,780 --> 00:45:43,280
+بيستيدو graph complete graph أو incomplete graph
+
+519
+00:45:43,280 --> 00:46:00,220
+مش هتجدش مكان القانون هتتبق عليه 100% تمام جالي
+
+520
+00:46:00,220 --> 00:46:05,640
+هتني عدد الجسورفي الـ Complete bipartite graph
+
+521
+00:46:05,640 --> 00:46:13,860
+تلاتة و ستة ترسموه .. ممتاز .. واحد .. اتنين ..
+
+522
+00:46:13,860 --> 00:46:20,720
+تلاتة .. واحد .. اتنين .. تلاتة .. اربع .. خمسة ..
+
+523
+00:46:20,720 --> 00:46:29,900
+اوى بندق السادس احنا عادل ..ماشي فلنوصيها أبدا
+
+524
+00:46:29,900 --> 00:46:35,000
+.. لما قلت شرسمهأنا قاعد بقولك حطلي عدد الجسور
+
+525
+00:46:35,000 --> 00:46:42,860
+عشان بتعرف واحد يا
+
+526
+00:46:42,860 --> 00:46:47,200
+عيني عليك هيبقى أسميلكم من أوليك تقاش و أقولك الله
+
+527
+00:46:47,200 --> 00:46:52,420
+يجيبك يا قولتي نروح بالمناسبة أنا ما قلتك كاش أرسم
+
+528
+00:46:52,420 --> 00:46:55,780
+انت اللي .. انت اللي بيبقى ترسم أنا ماقولتش لازم
+
+529
+00:46:55,780 --> 00:46:59,240
+ترسم بتلعب
+
+530
+00:46:59,240 --> 00:46:59,740
+كده إيش؟
+
+531
+00:47:07,510 --> 00:47:13,010
+الان اصلي صاحبي ماتفكرش ترسم لان لو انا روحت و
+
+532
+00:47:13,010 --> 00:47:14,610
+قلتلك عشرة فتسعة
+
+533
+00:47:19,000 --> 00:47:22,460
+مش هتخلص، لو قلتلك أنا خريبة حقيقية، the
+
+534
+00:47:22,460 --> 00:47:26,300
+incomplete bipartite graph عليها المجموعة الأولى
+
+535
+00:47:26,300 --> 00:47:30,300
+خمسين vertex والتاني مائة وسبعين، إيش بقى ترسم؟
+
+536
+00:47:30,300 --> 00:47:33,660
+هذا الكلام مش موضوع هرسم شويه من دماغك، خالص، إيش
+
+537
+00:47:33,660 --> 00:47:39,020
+الحل؟ الحل تفهم التركيبة اللي موجودة عندها،
+
+538
+00:47:39,020 --> 00:47:46,240
+القانون كان بيقولني ال summation of degrees يساوي
+
+539
+00:47:46,240 --> 00:47:51,640
+ضعف عدد الجسورمصبوط؟ بقدر انا اجيب مجموع ال
+
+540
+00:47:51,640 --> 00:47:56,080
+degrees؟ انا بقدر اجيبها، الان complete .. بدي
+
+541
+00:47:56,080 --> 00:47:59,900
+استفيد من هنا شباب، هو بيقول complete by parted
+
+542
+00:47:59,900 --> 00:48:04,840
+graph يعني كل أنصر في المجموعة الأولى، الرتبة تبعه
+
+543
+00:48:04,840 --> 00:48:09,560
+كده إيش؟ ستة، ستة، لإن أنا مرتبط بكل أنصر المجموعة
+
+544
+00:48:09,560 --> 00:48:13,220
+التانيةمعناته ال summation هذه ال summation لل
+
+545
+00:48:13,220 --> 00:48:18,180
+degree لل vertices تساوي تلت .. تلت .. تلت عناصر
+
+546
+00:48:18,180 --> 00:48:21,320
+في المجموعة الأولى كل واحد ال degree تبعتها ستة
+
+547
+00:48:21,320 --> 00:48:30,140
+ستة زائد ماخلصناش المجموعة التانية فيها ست عناصر
+
+548
+00:48:30,140 --> 00:48:35,500
+ال degree تبعت كل واحد فيهم تلاتة هذا الكلام ما
+
+549
+00:48:35,500 --> 00:48:39,280
+جبتهش من عندي يا شباب جبته من .. من مفهوم ال K
+
+550
+00:48:40,930 --> 00:48:46,650
+تلاتة تماطعش تماطعش ستة وتلاتين ماتوا الستة
+
+551
+00:48:46,650 --> 00:48:52,610
+وتلاتين هذه تساوي بقف عدد الجسور ماتوا عدد الجسور
+
+552
+00:48:52,610 --> 00:48:55,810
+تساوي
+
+553
+00:48:55,810 --> 00:49:01,010
+تماطعش الجسر بنفع
+
+554
+00:49:01,010 --> 00:49:04,070
+لو قلتلك
+
+555
+00:49:07,880 --> 00:49:13,600
+كمبليت جراف تمانية كيف
+
+556
+00:49:13,600 --> 00:49:17,800
+مافيش جسور؟
+
+557
+00:49:17,800 --> 00:49:22,640
+كيف مافيش جسور؟ هذا كومبليت جراف مش كومبليت مش by
+
+558
+00:49:22,640 --> 00:49:27,760
+parted كومبليت جراف جراف من تمان نقاط كل نقطة
+
+559
+00:49:27,760 --> 00:49:32,230
+مرتبطة بسبع نقاط تانياتهيك اللي انت ماجد حل فانت
+
+560
+00:49:32,230 --> 00:49:35,790
+ماتفكرش ان انا بس بده اخده اقرب زبط ما اكل لان هذا
+
+561
+00:49:35,790 --> 00:49:40,270
+by part و فعليا لو اضربته انت هتحصل 100% همجد
+
+562
+00:49:40,270 --> 00:49:49,610
+السؤال نفسه هذا بيبنى نغيره تمام؟ وحقها
+
+563
+00:49:49,610 --> 00:49:55,450
+كتسعة مثلا تسعة في تمانية ايه؟ تسعة في تمانية ايه؟
+
+564
+00:49:55,450 --> 00:49:55,450
+تسعة في تمانية ايه؟ تسعة في تمانية ايه؟ تسعة في
+
+565
+00:49:55,450 --> 00:49:55,450
+تمانية ايه؟ تسعة في تمانية ايه؟ تسعة في تمانية
+
+566
+00:49:55,450 --> 00:49:55,850
+ايه؟ تسعة في تمانية ايه؟ تسعة في تمانية ايه؟ تسعة
+
+567
+00:49:55,850 --> 00:50:00,450
+في تمانية ايه؟ تسعة في تمانية ايه؟ تسعة في تمانللـ
+
+568
+00:50:00,450 --> 00:50:04,810
+degree للـ vertices تساوي كم vertex عندك تسعة
+
+569
+00:50:04,810 --> 00:50:09,870
+vertices مصبوط ال degree لكل واحد فيهم تمانية
+
+570
+00:50:09,870 --> 00:50:18,050
+تساوي اتنين و سبعين و اتنين و سبعين بتساوي ضيق في
+
+571
+00:50:18,050 --> 00:50:22,870
+عدد الجسور ملاك
+
+572
+00:50:22,870 --> 00:50:24,450
+عدد الجسور الموجود عندى
+
+573
+00:50:29,400 --> 00:50:43,500
+كداش؟ سبتة و تلاتين تمام الشباب؟ الحمد لله طيب
+
+574
+00:50:43,500 --> 00:50:49,820
+degree sequence الاخر
+
+575
+00:50:49,820 --> 00:50:55,020
+شغل لا تجلجي معايا degree sequence الان بما انه ال
+
+576
+00:50:55,020 --> 00:51:00,710
+graphأي مكان رسمته أو أي مكان شكله و بقدر انا اجيب
+
+577
+00:51:00,710 --> 00:51:04,630
+ال degree لكل vertex و قولنا هي ال degree هي عبارة
+
+578
+00:51:04,630 --> 00:51:09,150
+عن هدد الجسور المرتبط على النقطة، مظبوط؟ تمام ال
+
+579
+00:51:09,150 --> 00:51:16,090
+graph هذا لو خليني اليه جهان هيك ال
+
+580
+00:51:16,090 --> 00:51:22,340
+degree اللي فيه واحد جد ايش؟تلاتة تلاتة تلاتة
+
+581
+00:51:22,340 --> 00:51:24,800
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+582
+00:51:24,800 --> 00:51:27,500
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+583
+00:51:27,500 --> 00:51:30,420
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+584
+00:51:30,420 --> 00:51:33,720
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+585
+00:51:33,720 --> 00:51:36,860
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+586
+00:51:36,860 --> 00:51:36,860
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+587
+00:51:36,860 --> 00:51:42,000
+تلاتة تلاتة تلاتة تلاتة تلاتة
+
+588
+00:51:44,680 --> 00:51:50,660
+من ال degrees بتبدأ من الرتبة الأعلى للرتبة الأقل
+
+589
+00:51:50,660 --> 00:51:55,040
+من الرتبة الأعلى للرتبة الأقل او بين قوسين بترتب
+
+590
+00:51:55,040 --> 00:52:00,300
+الرتب اللي لو عندك ترتيب تنازلي فبصير اربعة ال
+
+591
+00:52:00,300 --> 00:52:05,600
+degree sequence اربعة تلاتة نين واحد كارقام
+
+592
+00:52:09,530 --> 00:52:13,210
+عشان الترتيب التنازل هيها انت بيقوم هي ال sequence
+
+593
+00:52:13,210 --> 00:52:17,610
+هي ال sequence بحيث انك اتحقق ان دي واحد اذا تكون
+
+594
+00:52:17,610 --> 00:52:20,650
+اكبر او تساوي اكبر او تساوي طيب فى ال graph اللى
+
+595
+00:52:20,650 --> 00:52:27,610
+زى هذا شباب هك لو
+
+596
+00:52:27,610 --> 00:52:33,870
+صارت فيه hand graph بالشكل هذا هصير فوق تلاتة و
+
+597
+00:52:33,870 --> 00:52:34,590
+انا اربعة
+
+598
+00:52:38,370 --> 00:52:43,830
+أربعة أربعة تلاتة واحد الأربعة اللي بتاعتني مهناش
+
+599
+00:52:43,830 --> 00:52:47,810
+لإن أنا بتتكلم على أقامة ال degree sequence هي
+
+600
+00:52:47,810 --> 00:52:53,090
+عبارة عن مجموعة الرتب مرتبة ترتيب تنازلي الآن هذه
+
+601
+00:52:53,090 --> 00:52:58,030
+أربعة وهذه أربعة مابتفرجش معايا أنا في الآخر
+
+602
+00:52:58,030 --> 00:53:05,640
+هرتبها هقول أربعة أربعة تلاتة واحد مش اتنينمصبوط؟
+
+603
+00:53:05,640 --> 00:53:08,760
+وبالتالي هذه ال degree sequence اللي موجودة عندها
+
+604
+00:53:08,760 --> 00:53:12,920
+المحيط .. وبناء عليه فيه الأقل من و الأصغر أكبر من
+
+605
+00:53:12,920 --> 00:53:16,600
+أو يساوي عفوا تمام يا شباب؟ هذه احنا بنسميها
+
+606
+00:53:16,600 --> 00:53:20,220
+degree sequence لل graph بنسميها degree sequence
+
+607
+00:53:20,220 --> 00:53:24,300
+لل graph ونخل موضوع ال isomorphism بنبدأ فيه
+
+608
+00:53:24,300 --> 00:53:26,880
+المحاضرة الجاية ان شاء الله تعالى في أي سؤال يا
+
+609
+00:53:26,880 --> 00:53:30,400
+شباب؟ تمام؟ الله أتكلم عافية
+
diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/cD0ZBrc1468.srt b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/cD0ZBrc1468.srt
new file mode 100644
index 0000000000000000000000000000000000000000..99953348e8233d1105d68315488e14a669df93dc
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/cD0ZBrc1468.srt
@@ -0,0 +1,2045 @@
+
+1
+00:00:20,870 --> 00:00:22,850
+بسم الله والحمد لله والصلاة والسلام على رسول الله
+
+2
+00:00:22,850 --> 00:00:25,430
+.. مش أحلى صدري وأسر أمري وأحلى العقل تمالساني
+
+3
+00:00:25,430 --> 00:00:28,230
+أفقه قويفاليوم يا شباب إن شاء الله هنكمل في
+
+4
+00:00:28,230 --> 00:00:31,530
+chapter .. الـ chapter الثاني في الرياضيات المفصلة و
+
+5
+00:00:31,530 --> 00:00:34,810
+اللي بيتكلم عن الـ basic structures وهنكمل مع
+
+6
+00:00:34,810 --> 00:00:38,550
+المجموعات.. هنكمل مع المجموعات كنا حكينا أن
+
+7
+00:00:38,550 --> 00:00:41,810
+المجموعة هي عبارة عن unordered collection of
+
+8
+00:00:41,810 --> 00:00:46,330
+objects ولما اتكلمنا unordered عناصر غير مرتبة
+
+9
+00:00:46,330 --> 00:00:49,910
+يعني ترتيب العناصر لا يعني شيئاً وكل جملة مهمة
+
+10
+00:00:49,910 --> 00:00:54,690
+جداً، تكرار العنصر في المجموعة لا يعني شيئاً ولما
+
+11
+00:00:54,690 --> 00:00:57,150
+اتكلمنا على الـ contains معناته العلاقة بتصير بين
+
+12
+00:00:57,150 --> 00:00:59,670
+العنصر والمجموعة، العنصر اللي هو الـ object اللي
+
+13
+00:00:59,670 --> 00:01:03,950
+أنا بعده contains أو member of، بقول a is
+
+14
+00:01:03,950 --> 00:01:09,750
+member of الـ a، الـ a small as element is member of
+
+15
+00:01:09,750 --> 00:01:13,350
+الـ a، ولو كتش مش موجودة بقول is not a member of
+
+16
+00:01:13,350 --> 00:01:18,650
+الـ a، وقلنا Antemio لـ Antemio وعدّنا عناصر المجموعات
+
+17
+00:01:18,650 --> 00:01:22,870
+وقلنا في طريقة تمثيل المجموعات نوعين من تمثيل
+
+18
+00:01:22,870 --> 00:01:26,170
+المجموعات، الأولى سميناها الـ Roster Method وقلت أنا
+
+19
+00:01:26,170 --> 00:01:30,190
+بكتب الـ curly braces وبكتب عناصر المجموعة في
+
+20
+00:01:30,190 --> 00:01:35,110
+داخلهم مباشرة بشكل صريح، ولو عناصر المجموعة طويلة
+
+21
+00:01:35,110 --> 00:01:38,690
+وفيها sequence معين أو في جزء منها بنفهم وإحنا
+
+22
+00:01:38,690 --> 00:01:41,150
+بنعتمد على الشيء اللي سميناها الـ ellipses أو
+
+23
+00:01:41,150 --> 00:01:46,550
+النقاط مثلًا أقعد أكتب واحد اثنين ثلاثة وحط نقاط،
+
+24
+00:01:46,550 --> 00:01:50,690
+معناته يبقى الماشية إلى ما لا نهاية، لو حطيت 100،
+
+25
+00:01:50,690 --> 00:01:55,070
+معناته من واحد إلى مئة، 77 موجودة؟ آه موجودة، نابت
+
+26
+00:01:55,070 --> 00:01:58,410
+عنها ميم، الـEllipses ما بين الثلاثة لحد المئة
+
+27
+00:01:58,410 --> 00:02:03,830
+والصيغة الثانية في كتابة المجموعة كانت علاقة بالـ
+
+28
+00:02:03,830 --> 00:02:09,070
+Set Notation Builder، أقول إنها بتعتمد على أني أعرف
+
+29
+00:02:09,070 --> 00:02:13,730
+expression والـ expression هذا أديه وصف دقيق أحدد
+
+30
+00:02:13,730 --> 00:02:20,370
+إيش خصائصه بشكل واضح، مثل آجي أقول إن الـ X is an
+
+31
+00:02:20,370 --> 00:02:26,070
+odd positive integer less than عشرة، وبدي وصف صريح
+
+32
+00:02:26,070 --> 00:02:31,950
+واضح لعناصر المجموعة اللي عندي هنا، وانتقلنا بعد
+
+33
+00:02:31,950 --> 00:02:36,450
+هيك إلى المجموعات اللي عندنا، وقلنا في عندي شغل اسمها
+
+34
+00:02:36,450 --> 00:02:39,810
+الـ universal set وفي عندي الـ implicit الـ universal
+
+35
+00:02:39,810 --> 00:02:44,150
+set، هنفهمها دائماً من السياق أو تتعطى لنا بشكل واضح
+
+36
+00:02:44,150 --> 00:02:48,330
+لِمبادئي، بتكلم على مجموعة الـ integers في المثال
+
+37
+00:02:48,330 --> 00:02:52,890
+السابق، لما اتكلمنا x، x is an odd positive integer
+
+38
+00:02:52,890 --> 00:02:57,530
+less than 100 من الـ universal تبعتها كل الـ
+
+39
+00:02:57,530 --> 00:03:01,190
+integers لأن أنا بتكلم على integers في المقابل في
+
+40
+00:03:01,190 --> 00:03:05,750
+عندي الـ Empty Set، الـ Φ هو المجموعة الخالية اللي
+
+41
+00:03:05,750 --> 00:03:08,610
+مافيش فيها عناصر، وانتقلنا بعد هيك في المحاضرة
+
+42
+00:03:08,610 --> 00:03:11,970
+السابقة إلى الـ Set Equality عشان أقارن بين المجموعتين
+
+43
+00:03:11,970 --> 00:03:15,590
+هل في بينهم تساوي أو لأ، وقلت شرط التساوي اللي
+
+44
+00:03:15,590 --> 00:03:20,950
+عندي أنه لكل عنصر في المجموعة A هلاقي العنصر هذا
+
+45
+00:03:20,950 --> 00:03:27,020
+موجود في الـ B، وكل عنصر موجود في B هيكون موجود في A
+
+46
+00:03:27,020 --> 00:03:30,500
+وبالتالي الآن لو افترضت أن الـ A بيساوي واحد و
+
+47
+00:03:30,500 --> 00:03:34,620
+ثلاثة وخمسة، والـ B بيساوي ثلاثة وخمسة وواحد
+
+48
+00:03:34,620 --> 00:03:39,300
+متساويين، متساويين، نقول أن ترتيب العناصر لا يعني شيئاً
+
+49
+00:03:39,300 --> 00:03:42,100
+بالنسبة لنا، وبالتالي إذا أنا اتكرر العناصر لا يعني
+
+50
+00:03:42,100 --> 00:03:46,080
+شيئاً، فبالتالي هدول المجموعتين متساويات لأن كل عنصر
+
+51
+00:03:46,080 --> 00:03:48,820
+في A موجود في B والعكس صحيح
+
+52
+00:03:52,010 --> 00:03:54,950
+وانتقلنا بعد ذلك لتعريف الـ definition اسمه الـ
+
+53
+00:03:54,950 --> 00:03:58,190
+subset، المجموعة الجزئية، قلت لما أنا بتكلم على
+
+54
+00:03:58,190 --> 00:04:05,250
+مجموعة جزئية أنا عندي مجموعتين A وB باجي بقول
+
+55
+00:04:05,250 --> 00:04:08,950
+الـ A subset من B، مجموعة جزئية من الـ B لما آجي
+
+56
+00:04:08,950 --> 00:04:14,850
+كل عنصر في A موجود في B، for all X، X تنتمي إلى A
+
+57
+00:04:14,850 --> 00:04:20,930
+يؤدي إلى X تنتمي إلى B، وهذا سميّناها subset، بالمثال
+
+58
+00:04:20,930 --> 00:04:26,250
+السابق كانت الـ X واحد واثنين وثلاثة، هذه الـ P
+
+59
+00:04:26,250 --> 00:04:32,090
+بقدر آجي أقول أن الواحد واثنين مجموعة جزئية من
+
+60
+00:04:32,090 --> 00:04:35,650
+الدالة اللي عندها، وبتحب أذكرك في مثال ومهم جداً
+
+61
+00:04:35,650 --> 00:04:40,390
+للمثال هذا، لما اجينا قولنا الـ X بدها تساوي أو الـ A
+
+62
+00:04:40,390 --> 00:04:44,950
+تساوي X، والمجموعة X as element، هد المجموعة كم عنصر
+
+63
+00:04:44,950 --> 00:04:49,550
+فيها؟ اثنين، قلنا عشان يتحدد العلاقة ما بين الـ
+
+64
+00:04:49,550 --> 00:04:53,570
+ينتمي والـ subset وتكون دائماً صحيحة، اكتب كتانة
+
+65
+00:04:53,570 --> 00:04:59,450
+هال ينتمي A وهي subset من الـ A، subset يعني عبارة
+
+66
+00:04:59,450 --> 00:05:03,310
+عن مجموعة، والمطلوب منك في الفراغة هذا تاخد أحد
+
+67
+00:05:03,310 --> 00:05:08,050
+عناصر أو تاخد عناصر من عناصر المجموعة وتحطها لما
+
+68
+00:05:08,050 --> 00:05:13,040
+بتكلم عن ينتمي بتتكلم عن one element، صح؟ سواء تأخذ
+
+69
+00:05:13,040 --> 00:05:15,720
+الـ X كما هي أو العنصر الثاني كما هو.. لأن هنا
+
+70
+00:05:15,720 --> 00:05:19,160
+تأخذ عنصر من المجموعة وتجلبه هنا فتكون عملية اللي
+
+71
+00:05:19,160 --> 00:05:23,420
+ينتمي معك صحيحة 100% ولما تحافظ على الـ subset
+
+72
+00:05:23,420 --> 00:05:27,900
+تكون صحيحة، تشتغل نفس الكلام، تضع الأقواس subset و
+
+73
+00:05:27,900 --> 00:05:31,160
+تضع أي شيء تضعه في داخل من؟ في داخل الأقواس
+
+74
+00:05:31,160 --> 00:05:37,060
+وبالتالي ستحصل على الـ subset صحيحة برضه 100%، الآن
+
+75
+00:05:37,060 --> 00:05:41,400
+أنا في عندي الـ file هي عبارة عن subset من أي مجموعة
+
+76
+00:05:41,400 --> 00:05:45,770
+ثانية، وانتقلنا بعد ذلك لشغل اسمها الـ proper subset
+
+77
+00:05:45,770 --> 00:05:50,970
+إيش proper subset؟ أن المجموعة T أو المجموعة A هي
+
+78
+00:05:50,970 --> 00:05:57,250
+عبارة عن مجموعة جزئية من B لكنها غير مساوية لها، في
+
+79
+00:05:57,250 --> 00:05:59,990
+الـ subset اللي إحنا شفناها احتمال المساواة موجود
+
+80
+00:05:59,990 --> 00:06:05,410
+لأن كل المجموعات، نجيب نقول لكل عنصر في A هنجيب
+
+81
+00:06:05,410 --> 00:06:10,360
+موجود في الـ B، طب لو كان المجموعات متساويات، لو كانوا
+
+82
+00:06:10,360 --> 00:06:13,780
+المجموعتين متساويتين بتبدأ تُعتبر subset لأن كل عناصر
+
+83
+00:06:13,780 --> 00:06:16,820
+موجودة وبالتالي حققت الـ definition، مع الـ proper
+
+84
+00:06:16,820 --> 00:06:22,080
+subset، أضفنا جزئية جديدة على الـ definition and
+
+85
+00:06:22,080 --> 00:06:28,300
+there exist x، x تنتمي إلى b and الـ x لا تنتمي إلى
+
+86
+00:06:28,300 --> 00:06:33,060
+الـ a، وبهيك بصير أن أنا بتكلم على الـ proper subset
+
+87
+00:06:33,980 --> 00:06:38,460
+وانتقلنا وخلصنا محاضرتنا لأن وصلنا لـ Cardinality
+
+88
+00:06:38,460 --> 00:06:43,360
+اللي حنبدأ فيها باحتمال محاضرتنا اليوم، طيب، اليوم
+
+89
+00:06:43,360 --> 00:06:47,260
+بتكلم على الـ Cardinality، بتكلم على عدد عناصر
+
+90
+00:06:47,260 --> 00:06:54,080
+المجموعة، لما تكون المجموعة NDS بتحتوي على
+
+91
+00:06:54,080 --> 00:06:59,950
+Undistinct Element، إيش distinct؟ مختلفين، N distinct
+
+92
+00:06:59,950 --> 00:07:05,250
+elements عناصر مختلفة عددهم N، بقول عن الـ S is a
+
+93
+00:07:05,250 --> 00:07:11,410
+finite set، مجموعة منتهية، finite مجموعة منتهية، والـ
+
+94
+00:07:11,410 --> 00:07:16,470
+cardinality تبعتها تساوي N، عدد عناصرها N، يعني لو
+
+95
+00:07:16,470 --> 00:07:21,510
+كانت المجموعة S تبعتي بدها تساوي واحد وثلاثة و
+
+96
+00:07:21,510 --> 00:07:27,820
+واحد وأربعة أو خمسة، أيوة هذا التكرار لأ.. الآن
+
+97
+00:07:27,820 --> 00:07:30,940
+لاحظ لما أنا بسألك على الـ cardinality هي.. هي
+
+98
+00:07:30,940 --> 00:07:33,160
+رمز الـ cardinality اللي هي الـ absolute value تبع
+
+99
+00:07:33,160 --> 00:07:37,220
+الـ S بس بنسميها في المجموعات cardinality، عدد عناصر
+
+100
+00:07:37,220 --> 00:07:41,620
+المجموعة، عدد عناصر المجموعة S، قديش يا شباب؟ ثلاثة
+
+101
+00:07:41,620 --> 00:07:45,040
+ليش ما قلناش أربعة على الرغم أنه مكتوب عندها لأن
+
+102
+00:07:45,040 --> 00:07:47,880
+التكرار لا يعني شيئاً في المجموعة، وبالتالي أنا بتكلم
+
+103
+00:07:47,880 --> 00:07:54,180
+على ثلاثة عناصر في المجموعة اللي موجودة عندها، مثلًا
+
+104
+00:07:54,180 --> 00:07:57,960
+لو أنا قلت في عندي مجموعة السيارات مرسيديس، BMW، و
+
+105
+00:07:57,960 --> 00:08:04,000
+بورش، اتكلمت على المجموعة B فيها واحد واثنين وثلاثة
+
+106
+00:08:04,000 --> 00:08:09,560
+as a set، أربعة وخمسة as a set، ستة، لاحظوا الستة اثنين
+
+107
+00:08:09,560 --> 00:08:13,380
+وثلاثة، والستة، أربعة وخمسة عبارة عن elements في
+
+108
+00:08:13,380 --> 00:08:17,980
+المجموعة، وبالتالي واحد واثنين وثلاثة وأربعة فقط عناصر
+
+109
+00:08:17,980 --> 00:08:24,030
+الـ B، لو كانت الـ C تساوي الـ Φ، المجموعة الخالية، فاضية
+
+110
+00:08:24,030 --> 00:08:27,890
+مافيش ولا element، قديش عدد العناصر؟ صفر، ما بمش أقول
+
+111
+00:08:27,890 --> 00:08:30,650
+عدد العناصر مش موجود، لأ بتقول عنه صفر لأن دلوقتي
+
+112
+00:08:30,650 --> 00:08:37,290
+بتتكلم على رقم، بيه بتتكلم؟ هي عبارة عن مجموعة
+
+113
+00:08:37,290 --> 00:08:43,810
+بتحتوي على أربعة عناصر، من هم؟ الواحد والاثنين والثلاثة، هذه مجموعة، بس هالـ في الـ as element و
+
+114
+00:08:43,810 --> 00:08:47,910
+أربعة وخمسة وستة بتتكلم على أربعة عناصر موجودين في
+
+115
+00:08:47,910 --> 00:08:54,700
+المجموعة اللي عندها، لكن يا شباب لو أنا يا جماعة قلت لك
+
+116
+00:08:54,700 --> 00:08:59,780
+في اللحظة من اللحظات أن الـ definition تبعت
+
+117
+00:08:59,780 --> 00:09:01,920
+المجموعة تبعتي X حيث X تنتمي لـ natural number و X
+
+118
+00:09:01,920 --> 00:09:08,500
+أكبر أو يساوي 850، هل تقدر تجيب الـ cardinality
+
+119
+00:09:08,500 --> 00:09:12,000
+تبعتها؟ ليش؟ لأنه صار غير منتهي، infinite وبالتالي
+
+120
+00:09:18,240 --> 00:09:21,580
+وبالتالي لو جالك وقال لك اديني الـ cardinality
+
+121
+00:09:21,580 --> 00:09:26,160
+تبعتها بنقول أن الـ E هذه is infinite وبالتالي أنا
+
+122
+00:09:26,160 --> 00:09:29,780
+ما بقدر اتكلم على الـ cardinality أو عدد عناصر
+
+123
+00:09:29,780 --> 00:09:34,600
+المجموعة، لكن انتبه لو جيت قلت لك أن الـ S بده يساوي
+
+124
+00:09:34,600 --> 00:09:42,860
+X حيث X تنتمي للـ natural number and الـ X أقل أو
+
+125
+00:09:42,860 --> 00:09:47,040
+تساوي عشرة، عشرة
+
+126
+00:09:47,040 --> 00:09:52,680
+محصور، finite، واحد واثنين وثلاثة وأربعة وخمسة لحد
+
+127
+00:09:52,680 --> 00:09:57,120
+العشرة، ليش؟ لما تجنّب الكثرة، لاحظ لو اتبدلت معك
+
+128
+00:09:57,120 --> 00:10:02,840
+حالة real number كانت صارت infinite، كانت صارت معك
+
+129
+00:10:02,840 --> 00:10:08,840
+infinite، أو لو حتى سِبت الـ Z كانت ضلت infinite،
+
+130
+00:10:08,840 --> 00:10:11,860
+لماذا؟ لأنها تذهب باتجاه السالب إلى ما لا نهاية
+
+131
+00:10:11,860 --> 00:10:18,180
+وبالتالي، تعريف المجموعة دائماً بيلعب دور واضح في
+
+132
+00:10:18,180 --> 00:10:21,700
+تحديد عدد عناصرها أو تحديد الـ Cardinality تبعتها،
+
+133
+00:10:21,700 --> 00:10:27,600
+النقطة
+
+134
+00:10:27,600 --> 00:10:34,700
+اللي بعدها الـ Power Set، الـ Power Set هي عبارة عن
+
+135
+00:10:34,700 --> 00:10:40,240
+المجموعة التي تحتوي كل المجموعات الجزئية الممكنة
+
+136
+00:10:40,240 --> 00:10:48,680
+من الـ A، الآن لو أنا جيت افترضت أن الـ A بدها تساوي
+
+137
+00:10:48,680 --> 00:10:55,680
+A وB وC، وقلت لك اديني مجموعة جزئية
+
+138
+00:10:59,470 --> 00:11:08,750
+A وB أو A لحالها أو B لحالها أو C لحالها، B وC، A
+
+139
+00:11:08,750 --> 00:11:13,550
+و C، هتبدأ تخبز، بس لأ، أنا بقول لك في أكثر كمان، إيش
+
+140
+00:11:13,550 --> 00:11:18,970
+كمان؟ في الـ Φ وفي الـ A نفسها، A وB وC، طيب
+
+141
+00:11:18,970 --> 00:11:22,830
+هدول المجموعات الجزئية كلها، ياتهم عشان أنا أقدر
+
+142
+00:11:22,830 --> 00:11:26,630
+أحصرهم، لازم أعرف عددهم في الأول عشان أقول خلصت ولا
+
+143
+00:11:26,630 --> 00:11:32,390
+ما خلصتش، فلما أنا باجي بتكلم عن الـ power set بتكلم
+
+144
+00:11:32,390 --> 00:11:36,730
+الـ power set للـ A هي عبارة عن المجموعة التي تحتوي
+
+145
+00:11:36,730 --> 00:11:41,050
+كل المجموعات الجزئية الممكنة من الـ elements بتاعة
+
+146
+00:11:41,050 --> 00:11:48,010
+الـ A، الـ definition تبعتها، P of A، power set of A
+
+147
+00:11:48,010 --> 00:11:56,030
+تساوي الـ B as a set حيث الـ B subset من الـ A، دائماً
+
+148
+00:11:56,030 --> 00:12:00,390
+الـ power set عدد عناصرها يساوي اثنين أس الـ
+
+149
+00:12:00,390 --> 00:12:04,390
+cardinality تبعت الـ a، يعني الآن الـ a اللي عندي
+
+150
+00:12:04,390 --> 00:12:08,910
+أنجد فيها ثلاثة، اثنين أس ثلاثة، يعني أنا بتكلم
+
+151
+00:12:08,910 --> 00:12:13,850
+على ثمانية عناصر، عشان ثمانية.. مجموعة فيها ثمانية عناصر
+
+152
+00:12:13,850 --> 00:12:19,090
+كل عنصر منهم عبارة عن مجموعة، مجموعة فيها ثمانية
+
+153
+00:12:19,090 --> 00:12:23,570
+عناصر، كل عنصر فيهم عبارة عن مجموعة، مين هم؟ P of A
+
+154
+00:12:23,570 --> 00:12:28,390
+عشان تريح راسك دائماً اشتغل ضمن استراتيجية واحدة
+
+155
+00:12:28,390 --> 00:12:32,430
+وما بتتوهش فيها، اشتغل بالترتيب، الآن ابدأ من مجموعة
+
+156
+00:12:32,430 --> 00:12:35,730
+فيها عنصر، مجموعة فيها عنصرين، مجموعة فيها ثلاثة عناصر
+
+157
+00:12:35,730 --> 00:12:40,170
+تبدأ إيش تكبر، خليني أنا آخذ مثال أكبر شوية، D
+
+158
+00:12:40,170 --> 00:12:43,330
+على سبيل المثال، الآن الـ power set كان عنصر فيها
+
+159
+00:12:43,330 --> 00:12:49,500
+أربعة، اثنين أس أربعة، ستة عشر element، 16 element، عشان
+
+160
+00:12:49,500 --> 00:12:52,840
+لو.. لو طلبنا منك تجيب المجموعة على شو المفروض
+
+161
+00:12:52,840 --> 00:12:58,480
+تساوي، تذكرهم، إذا أنت بدك تشتغل تخمين هتكون سامحني
+
+162
+00:12:58,480 --> 00:13:02,000
+زي اللي مش شايف وقاعد بحسس في إيده، وأين الطريق
+
+163
+00:13:02,000 --> 00:13:05,680
+اللي أنا بدي إياها، هتخرج في الآخر أو هتخبط في حيط أو
+
+164
+00:13:05,680 --> 00:13:09,380
+هتجي عن الشباك، إلى آخرهم، في الآخر، خلينا نشتغل ضمن
+
+165
+00:13:09,380 --> 00:13:14,100
+استراتيجية بسيطة، ابدأ بالمجموعات الأصغر وأكبر أو
+
+166
+00:13:14,100 --> 00:13:18,260
+العكس، أنا بالنسبة لي بحب أبدأ هيك، A المجموعات اللي
+
+167
+00:13:18,260 --> 00:13:28,160
+فيها واحد، B وC وD، في غير هيك؟ مجموعات من عنصر
+
+168
+00:13:28,160 --> 00:13:35,160
+واحد؟ لأ، خلّي الـ Φ والمجموعة للأخر، بعد هيك عناصر من
+
+169
+00:13:35,160 --> 00:13:44,550
+مجموعات من عنصرين، A وB، A وC، A وD، بعدين B وC
+
+170
+00:13:44,550 --> 00:13:49,730
+إياك تقول B وA، ليش؟ لأن هي already موجودة، B
+
+223
+00:18:37,320 --> 00:18:40,190
+الـ Cartesian product هنا أنا بتكلم على Cartesian
+
+224
+00:18:40,190 --> 00:18:46,750
+product هل هتطلع أن زوج مرتب A و B بينما هن B و A
+
+225
+00:18:46,750 --> 00:18:52,070
+و هن A و B لا تساوي B و A وبالتالي المجموعتين الـ A
+
+226
+00:18:52,070 --> 00:18:57,970
+و الـ B لا تساوي B cross الـ A ما أتكلمش على dot
+
+227
+00:18:57,970 --> 00:19:01,090
+product الآن أنا بتكلم على Cartesian product بين
+
+228
+00:19:01,090 --> 00:19:08,610
+مجموعتين الآن X عشان تجيب الـ product صح تبدأ تشكل
+
+229
+00:19:08,610 --> 00:19:12,190
+أزواج مرتبة بتاخد العنصر الأول من المجموعة الأولى
+
+230
+00:19:12,190 --> 00:19:17,550
+وبتعمل اقتران مع كل العناصر في المجموعات الثانية X
+
+231
+00:19:17,550 --> 00:19:23,930
+و A, X و B, X و C بتاخد العنصر الثاني Y و A, Y و
+
+232
+00:19:23,930 --> 00:19:29,950
+B, Y و C لو أنت بدك تعمل product بين B و A, B
+
+233
+00:19:29,950 --> 00:19:39,630
+cross الـ A, Ax اي بيكس بيكس بيكس بيكس بيكس بيكس
+
+234
+00:19:39,630 --> 00:19:51,810
+بيكس بيكس بيكس بيكس بيكس بيكس بيكس
+
+235
+00:19:51,810 --> 00:19:53,730
+بيكس
+
+236
+00:19:58,750 --> 00:20:02,230
+أه إذا أنت بتتكلم على كيف السؤال فيه هو الهدف فيه
+
+237
+00:20:02,230 --> 00:20:05,650
+مش هدف السؤال باداته أنا بقولك اديني الـ Cartesian
+
+238
+00:20:05,650 --> 00:20:08,330
+product اضرب بين المجموعتين أو هاتلي الـ cross
+
+239
+00:20:08,330 --> 00:20:12,350
+product بين المجموعتين وهتكون بالشكل هذا .. هتكون
+
+240
+00:20:12,350 --> 00:20:16,570
+بالشكل هذا لكن هو فعلاً احنا بهمني التطبيق اللي
+
+241
+00:20:16,570 --> 00:20:20,590
+بعده يا أحمد أكثر ما بهمني وين بده يلزمني الآن هذا
+
+242
+00:20:20,590 --> 00:20:24,700
+الكلام بيلزمنا في الـ animation بيلزمنا في الـ design
+
+243
+00:20:24,700 --> 00:20:28,260
+بيلزمنا في أكثر من شغلة بيلزمنا بتحديد الموقع تبع
+
+244
+00:20:28,260 --> 00:20:33,040
+الشخص والموقع اللي بدنا ننقله وبالتالي بتصير الـ X
+
+245
+00:20:33,040 --> 00:20:37,760
+و الـ Y هدول عبارة عن position على الخريطة X و Y
+
+246
+00:20:37,760 --> 00:20:44,000
+تمام؟ وبالتالي أنا هذا الموقع غير هذا بصحيح؟ بس
+
+247
+00:20:44,000 --> 00:20:50,840
+طيب الآن
+
+248
+00:20:51,970 --> 00:20:57,270
+احنا شفنا الـ Sub notation builder و تعرّفنا عليه
+
+249
+00:20:57,270 --> 00:21:01,010
+quantifier سابقاً، مظبوط ولا لأ؟ لو أنا أجيب و
+
+250
+00:21:01,010 --> 00:21:07,310
+قلت لك، إيش بتعني هذه القيمة؟ أو هذه؟ في الأول
+
+251
+00:21:07,310 --> 00:21:12,610
+قيمتها true ولا false؟ وترجم لي إياها أو ترجم لي إياها و
+
+252
+00:21:12,610 --> 00:21:17,410
+قول لي true ولا false For all x تنتمي إلى R، x تربيع
+
+253
+00:21:17,410 --> 00:21:23,760
+أكبر أو تساوي صفر تربيع أي عدد حقيقي أكبر من صفر
+
+254
+00:21:23,760 --> 00:21:34,400
+true وجذر السالب واحد جذر السالب واحد أيوة شوف
+
+255
+00:21:34,400 --> 00:21:38,800
+أنت الآن أنا غشّشتك لما قلت لك جذر السالب واحد جذر
+
+256
+00:21:38,800 --> 00:21:43,180
+السالب واحد لا تنتمي للـ R عدد غير حقيقي عدد تخيلي
+
+257
+00:21:43,180 --> 00:21:47,200
+مش احنا متفقين من الأساس أن في عند القسمة على صفر
+
+258
+00:21:47,200 --> 00:21:51,840
+فيها مشكلة وعند السالب تحت الجذر كمان فيه مشكلة عدد
+
+259
+00:21:51,840 --> 00:21:54,840
+تخيلي وبالتالي هذه لا تنتمي إلى R هذه برّا اللعبة
+
+260
+00:21:54,840 --> 00:22:03,280
+خالص لا لا true هي true أي عدد حقيقي خذ أي عدد
+
+261
+00:22:03,280 --> 00:22:08,280
+حقيقي اربعة لأن فيه يساوي نبدأ من الصفر صفر ضرب
+
+262
+00:22:08,280 --> 00:22:18,410
+صفر صفر سالب واحد تربيع واحد نصف أو سالب نصف تربيع
+
+263
+00:22:18,410 --> 00:22:24,690
+ربع أكبر من صفر وبالتالي هذه القيمة true ولاحظ لو
+
+264
+00:22:24,690 --> 00:22:31,710
+أنا سألتك هذا الـ quantifier بيمثل مجموعة إيش
+
+265
+00:22:31,710 --> 00:22:36,630
+المجموعة اللي بيمثلها إيش بيمثلها كل الـ real
+
+266
+00:22:36,630 --> 00:22:41,620
+number كل الـ real number طيب تعال نشوف الـ
+
+267
+00:22:41,620 --> 00:22:47,680
+quantifier الثاني there exist x تنتمي إلى Z هناك x
+
+268
+00:22:47,680 --> 00:22:53,020
+واحدة على الأقل كعدد صحيح x تربيعها تساوي واحد true
+
+269
+00:22:53,020 --> 00:22:57,700
+واحد أو سالب واحد واحد منهم يكفينا وبالتالي
+
+270
+00:22:57,700 --> 00:23:02,440
+الثانية true طيب المجموعة هذه الأولى هذه تمثل كل
+
+271
+00:23:02,440 --> 00:23:04,520
+الـ R وهذه
+
+272
+00:23:08,070 --> 00:23:12,810
+-1 و 1 كمجموعات لاحظ هذا الـ quantifier كمثله أو
+
+273
+00:23:12,810 --> 00:23:16,890
+اكتبه كمجموعة وهذا اللي حكيناه سابقاً أنه ممكن أنا
+
+274
+00:23:16,890 --> 00:23:20,670
+أعرف أعرف المجموعة بناءً على predicate function و
+
+275
+00:23:20,670 --> 00:23:30,430
+quantifier لما
+
+276
+00:23:30,430 --> 00:23:33,850
+أتكلم على predicate function قلت لك predicate
+
+277
+00:23:33,850 --> 00:23:40,130
+function إيه دي قلت؟ B of X حيث X تربيع أكبر أو
+
+278
+00:23:40,130 --> 00:23:45,190
+تساوي صفر جدّيش
+
+279
+00:23:45,190 --> 00:23:50,350
+قيمتها true ولا false true ولا false ما بقدر أديها
+
+280
+00:23:50,350 --> 00:23:55,990
+قيمة لحد ما أعرف قيمة الـ X ما أبدّيش بقول لك أنا X of
+
+281
+00:23:55,990 --> 00:24:00,210
+إيش قيمة الـ X وينها
+
+282
+00:24:02,910 --> 00:24:06,670
+ما هو نوع الـ X؟ بتنتمي لأي عدد؟ يعني لو أنا جدّ
+
+283
+00:24:06,670 --> 00:24:15,550
+قلت لك P of سالب واحد العدد التخيلي أو الـ I هتصير
+
+284
+00:24:15,550 --> 00:24:19,210
+false، مظبوط ولا لأ؟ فالـ R هذه كلها مع الـ
+
+285
+00:24:19,210 --> 00:24:22,870
+predicate function أنا ما بقدر أديها قيمة لحد ما
+
+286
+00:24:22,870 --> 00:24:27,970
+أحدد قيمة الـ X بشكل صحيح، بشكل واضح أو أروح أتعامل
+
+287
+00:24:27,970 --> 00:24:33,960
+مع quantifier أقول for all .. عفواً .. أقول for all
+
+288
+00:24:33,960 --> 00:24:38,920
+x .. x تربيع أكبر .. وأحدد الـ universal domain
+
+289
+00:24:38,920 --> 00:24:42,920
+set .. مظبوط ولا لأ؟ أو أستخدم existential
+
+290
+00:24:42,920 --> 00:24:46,240
+quantifier وأقول there exists x بتحقق كده بعد
+
+291
+00:24:46,240 --> 00:24:49,660
+تعريف الـ domain وبالتالي .. هذا .. هيك .. الحالة
+
+292
+00:24:49,660 --> 00:24:54,700
+هيك .. أنا ما أقدرش أقيمها .. ولا لأ؟ لكن لو أنا أجيب
+
+293
+00:24:54,700 --> 00:25:00,780
+.. قلت لك الـ P of X .. P of X .. هي عبارة عن
+
+294
+00:25:00,780 --> 00:25:04,280
+المجموعة أو الـ Function اللي فيها الـ X تنتمي إلى
+
+295
+00:25:04,280 --> 00:25:09,120
+الـ D لمين؟ الـ Domain حددت لك Domain الآن B of X
+
+296
+00:25:09,120 --> 00:25:11,740
+عناصر .. بتقول هذه موجودة ولا مش موجودة بتقدر
+
+297
+00:25:11,740 --> 00:25:15,280
+تحدد عناصر المجموعة بشكل واضح تعال نشوف المثال
+
+298
+00:25:15,280 --> 00:25:21,140
+هذا بيجي بقول لي الـ domain تبع الـ function في
+
+299
+00:25:21,140 --> 00:25:27,640
+الأمثلة اللي جايه هي عبارة عن الـ integers Z تعال
+
+300
+00:25:27,640 --> 00:25:34,200
+و الـ domain Z الـ P of X الـ absolute value
+
+301
+00:25:34,200 --> 00:25:38,640
+للـ X يساوي واحد يعني أنا بجعل بتكلم على مجموعة
+
+302
+00:25:38,640 --> 00:25:43,920
+العناصر اللي فيها بتحقق المعادلة هذه إيش هي
+
+303
+00:25:43,920 --> 00:25:53,240
+المجموعة هذه؟ سالب واحد وواحد سالب واحد وواحد طيب
+
+304
+00:25:53,240 --> 00:26:00,490
+اللي بعديها Q of X is X تربيعها يساوي 2 X تربيع
+
+305
+00:26:00,490 --> 00:26:08,110
+تساوي 2 جذر الاثنين غلط عارف ليش؟ لأن جذر الاثنين
+
+306
+00:26:08,110 --> 00:26:13,490
+مش عدد صحيح اثنين وسالب اثنين غلط اثنين تربيع
+
+307
+00:26:13,490 --> 00:26:22,450
+أربعة وسالب اثنين تربيع أربعة غير معرف غلط مافيش
+
+308
+00:26:22,450 --> 00:26:27,280
+الشغل اسمه غير معرف هذا المقصود اللي في دماغك ..
+
+309
+00:26:27,280 --> 00:26:30,860
+المقصود اللي في دماغك والثانية تاخذ بالعالمين
+
+310
+00:26:30,860 --> 00:26:33,980
+واحدة اللي بيعرفوها أنا بالنسبة لي وغيري من المدرسين
+
+311
+00:26:33,980 --> 00:26:40,640
+اللي علاقة بليش بالمكتوب على ورقة والله
+
+312
+00:26:40,640 --> 00:26:43,720
+صدّقت اليوم اللي جينا ما تحاسب anyway تعال نشوف
+
+313
+00:26:43,720 --> 00:26:47,900
+المجموعة اللي بعدها R of X X أو الـ absolute value
+
+314
+00:26:47,900 --> 00:26:50,080
+للـ X تساوي X
+
+315
+00:26:53,270 --> 00:26:59,450
+أيوة، مين اللي بحكيها أنا؟ الـ Z الـ X الموجبة، كل
+
+316
+00:26:59,450 --> 00:27:05,250
+العناصر الـ
+
+317
+00:27:05,250 --> 00:27:09,750
+Z الموجبة فقط، عارف ليش؟ أيوة، لأن هو إيش قاعد
+
+318
+00:27:09,750 --> 00:27:15,570
+بيقول لي؟ بيقول لي الـ absolute تساوي القيمة، بس الـ
+
+319
+00:27:15,570 --> 00:27:20,840
+absolute لسالب واحد لا تساوي سالب واحد تساوي الواحد
+
+320
+00:27:20,840 --> 00:27:25,440
+وبالتالي أنا جا بتكلم على القيم الموجبة فقط الـ Z
+
+321
+00:27:25,440 --> 00:27:28,020
+plus بتكلم على الـ Z plus
+
+322
+00:27:37,650 --> 00:27:41,350
+لاحظ فعلياً هذه الـ predicate function مع الـ domain
+
+323
+00:27:41,350 --> 00:27:45,650
+مثّلت بالنسبة لي؟ عبارة عن مجموعات .. عبارة عن
+
+324
+00:27:45,650 --> 00:27:49,250
+مجموعات وهيك يكون الـ section الأول من الشابتر
+
+325
+00:27:49,250 --> 00:27:53,930
+الخلص الشابتر اللي خلص لأ يا حبيبي لسه الشابتر
+
+326
+00:27:53,930 --> 00:27:57,030
+الأول طيب
+
+327
+00:27:57,420 --> 00:28:00,480
+ننتقل لـ section الثاني اللي هو الـ set operations
+
+328
+00:28:00,480 --> 00:28:05,380
+العمليات على المجموعات العمليات على المجموعات كل
+
+329
+00:28:05,380 --> 00:28:09,460
+المحاضرة السابقة كانت بنعرف على إيه الشباب؟ بنعرف
+
+330
+00:28:09,460 --> 00:28:12,740
+المجموعة شو صفاتها؟ إيش يعني subset؟ إيش يعني
+
+331
+00:28:12,740 --> 00:28:17,760
+Cartesian؟ إيش power set؟ إلى آخره الآن بدنا
+
+332
+00:28:17,760 --> 00:28:22,930
+نتكلم على العمليات على المجموعات لما أتكلم على
+
+333
+00:28:22,930 --> 00:28:25,250
+العمليات على مجموعات شغلات بسيطة أقول لكم بتعرفوها
+
+334
+00:28:25,250 --> 00:28:30,350
+الاتحاد والتقاطع أو المكمل أو الاختلاف زمان عنهم
+
+335
+00:28:30,350 --> 00:28:34,290
+هلأ أنت بتتعرف عليهم وشوف أنت إيش بتعرف منهم طيب
+
+336
+00:28:34,290 --> 00:28:41,690
+لما أنا بتكلم على الاتحاد الـ union الاتحاد اتحاد
+
+337
+00:28:41,690 --> 00:28:48,150
+مجموعتين ينتج عنه مجموعة جديدة هيرجع الاتحاد A
+
+338
+00:28:48,150 --> 00:28:56,010
+union B يساوي الـ X حيث X تنتمي إلى الـ A أو الـ X
+
+339
+00:28:56,010 --> 00:29:01,290
+تنتمي إلى الـ B لو أنا أجيت هنا على السريع قلت لك A
+
+340
+00:29:01,290 --> 00:29:11,650
+بدأ تساوي واحد واثنين وثلاثة والـ B اثنين
+
+341
+00:29:11,650 --> 00:29:16,550
+وثلاثة وأربعة A
+
+342
+00:29:19,350 --> 00:29:24,910
+اتحاد الـ B يساوي المجموعة أول حاجة أول حاجة بدك
+
+343
+00:29:24,910 --> 00:29:29,950
+تفهم أن هنا شرط متى الشرط ده بيكون true لو كان
+
+344
+00:29:29,950 --> 00:29:32,690
+واحدة منهم على الأقل true طب لو كانت اثنين اثنين
+
+345
+00:29:32,690 --> 00:29:37,310
+true X تنتمي إلى A معناته أن أنت مغمض يا صاحبي و
+
+346
+00:29:37,310 --> 00:29:40,190
+تروح تقول واحد واثنين وثلاثة اللي هم عناصر الـ A
+
+347
+00:29:40,190 --> 00:29:46,570
+أصبت؟ بعد هيك بتروح لعناصر الـ B الاثنين موجودة؟
+
+348
+00:29:47,400 --> 00:29:50,580
+موجودة مافيش دي أكتبها مرة ثانية الثلاثة موجودة
+
+349
+00:29:50,580 --> 00:29:56,500
+مافيش دي أكتبها مرة ثانية الأربعة خلصنا معينة هاي
+
+350
+00:29:56,500 --> 00:30:03,380
+الاتحاد كل العناصر أحمد
+
+351
+00:30:03,380 --> 00:30:05,940
+بيقول ليش ما حطينا and تعال نشوف الـ and إيش بده ينتج
+
+352
+00:30:05,940 --> 00:30:10,740
+يا أحمد متى بيكون الـ and true لما كل الشرطين هدول
+
+353
+00:30:10,740 --> 00:30:17,240
+متحققين صح نجي للواحد الواحد تنتمي إلى A true تنتمي
+
+354
+00:30:17,240 --> 00:30:20,980
+إلى B false true and false false ميّر الواحد
+
+355
+00:30:20,980 --> 00:30:26,100
+الثاني تنتمي إلى الـ A true الثاني تنتمي إلى الـ B
+
+356
+00:30:26,100 --> 00:30:32,080
+true معناته اثنين صارت التقاطع ثلاثة تنتمي إلى الـ
+
+357
+00:30:32,080 --> 00:30:39,240
+A true تنتمي إلى الـ B هي ثلاثة الأربعة لا تنتمي
+
+358
+00:30:39,240 --> 00:30:43,480
+إلى الـ A false والـ X تنتمي إلى الـ B true أو
+
+359
+00:30:43,480 --> 00:30:44,700
+false؟ لا أعرف، لا أعرف، لا أعرف، لا أعرف، لا
+
+360
+00:30:44,700 --> 00:30:45,500
+أعرف، لا أعرف، لا أعرف، لا أعرف، لا أعرف، لا أعرف،
+
+361
+00:30:45,500 --> 00:30:45,800
+لا أعرف، لا أعرف، لا أعرف، لا أعرف، لا أعرف، لا
+
+362
+00:30:45,800 --> 00:30:46,640
+أعرف، لا أعرف، لا أعرف، لا أعرف، لا أعرف، لا أعرف،
+
+363
+00:30:46,640 --> 00:30:46,660
+لا أعرف، لا أعرف، لا أعرف، لا أعرف، لا أعرف، لا
+
+364
+00:30:46,660 --> 00:30:49,900
+أعرف، لا أعرف، لا أعرف، لا أعرف، لا أعرف، لا أعرف،
+
+365
+00:30:49,900 --> 00:30:58,860
+لا أعرف، لا أعرف، لا أعرف، لا أعرف، لا أعرف، لا
+
+366
+00:30:58,860 --> 00:31:05,960
+أعرف، لا أعرف، لا أعرف،
+
+367
+00:31:05,960 --> 00:31:16,680
+لا أعرف، لا أعرف واحد تنتمي إلى الـ A true واحد تنتمي
+
+368
+00:31:16,680 --> 00:31:20,660
+إلى الـ B false true or false true معناته واحد من
+
+369
+00:31:20,660 --> 00:31:26,100
+ضمن العناصر اثنين تنتمي إلى الـ A true اثنين تنتمي إلى
+
+370
+00:31:26,100 --> 00:31:31,720
+الـ B true true and true true ثلاثة زي الاثنين بنحط
+
+371
+00:31:31,720 --> 00:31:38,830
+الأربعة الأربعة تنتمي إلى الـ A false أو أربعة تنتمي
+
+372
+00:31:38,830 --> 00:31:43,270
+إلى الـ A إلى الـ B؟ true fourth or true؟ أربعة
+
+373
+00:31:43,270 --> 00:31:48,690
+تمام؟ وبالتالي هينا هيك خلصنا شفنا عمليتين خلال
+
+374
+00:31:48,690 --> 00:31:54,470
+one slide اتحاد وتقاطع أجازك
+
+375
+00:31:54,470 --> 00:31:58,670
+عشان اللي فوق؟ كويس عارف إذا كانت تقصد هيك كويس
+
+376
+00:31:58,670 --> 00:32:02,510
+في الـ definition على الأقل تقدر تتذكر هي all and
+
+377
+00:32:02,510 --> 00:32:07,190
+الإشارة لفوق لفوق يعني خلصنا فيه .. فيه .. فيه
+
+378
+00:32:07,190 --> 00:32:10,950
+logic في الموضوع تمام
+
+379
+00:32:10,950 --> 00:32:16,270
+وخلصنا من التقاطع والأولى تحت أكيد ما خلصنا عن
+
+380
+00:32:16,270 --> 00:32:20,030
+نفس الموال آه الأولى الشباب لو كانوا على أصل
+
+381
+00:32:20,030 --> 00:32:25,150
+المجموعتين مختلفين تماماً التقاطع بينهم يساوي فاي
+
+382
+00:32:25,150 --> 00:32:32,460
+يعني لو أنا أجيت قلت الـ B تساوي أربعة وخمسه وستة
+
+383
+00:32:32,460 --> 00:32:36,480
+حسب الـ definition تبع الاتحاد تصير في أن واحد
+
+384
+00:32:36,480 --> 00:32:43,640
+اثنين ثلاثة أربعة خمسة ستة في التقاطع هيكون فاي
+
+385
+00:32:43,640 --> 00:32:50,460
+التقاطع الـ B يساوي فاي وبنقول عنهم disjoint sets
+
+386
+00:32:50,460 --> 00:32:57,720
+بنقول عنهم disjoint sets مجموعات غير متداخلة أو
+
+387
+00:32:57,720 --> 00:32:58,520
+غير متقاطعة
+
+388
+00:33:04,210 --> 00:33:08,750
+طيب الـ difference الفرق لما بتكلم عن الـ difference
+
+389
+00:33:08,750 --> 00:33:15,270
+بتكلم على الفرق بين عناصر المجموعتين وعندي زي ما
+
+390
+00:33:15,270 --> 00:33:19,110
+احنا شفنا شباب سابقاً التبادل اللي عفواً أنتو الـ
+
+391
+00:33:19,110 --> 00:33:23,790
+and و الـ or عمليات إبدالية صح ولا لأ يعني a and الـ
+
+392
+00:33:23,790 --> 00:33:29,400
+b تساوي b and الـ a الاتحاد والتقاطع من العمليات
+
+393
+00:33:29,400 --> 00:33:33,620
+الإبدالية، لكن الـ Difference هام؟ لأ، لما أنا بأجيب
+
+394
+00:33:33,620 --> 00:33:38,600
+أقول الـ Difference بين مجموعتين A و B، بتكلم على
+
+395
+0
+
+445
+00:37:54,420 --> 00:37:56,360
+حصرليها
+
+446
+00:37:59,520 --> 00:38:10,060
+What is the complement of X أكبر من 70؟ عناصر
+
+447
+00:38:10,060 --> 00:38:16,360
+المجموعة A هي الـ A  الـ X  و الـ X أكبر من 70
+
+448
+00:38:16,360 --> 00:38:24,960
+يعني الـ A  71، 72، 73 لحد المية
+
+449
+00:38:27,790 --> 00:38:42,850
+الآن بقول يا ترى مكملة مكملة
+
+450
+00:38:42,850 --> 00:38:48,750
+مكملة  هَيقولك what is the complement of مكملة
+
+451
+00:38:48,750 --> 00:38:57,720
+الـ A من صفر لحد سبعين، اللي هي بين قسام الـ
+
+452
+00:38:57,720 --> 00:39:02,160
+universal set المية، من صفر لمية، بدنا نشيل منهم
+
+453
+00:39:02,160 --> 00:39:06,000
+العناصر الأكبر من سبعين، اللي هم واحد وسبعين و
+
+454
+00:39:06,000 --> 00:39:13,180
+اثنين وسبعين، الباقين هاي
+
+455
+00:39:13,180 --> 00:39:19,400
+مثال ثاني، لو أنا جيت قلت لك أن الـ A هي عبارة عن الـ
+
+456
+00:39:19,400 --> 00:39:24,230
+D للـ F، من الـ D للـ Z، عفواً. هذه الـ universal ... والـ
+
+457
+00:39:24,230 --> 00:39:28,590
+universal set كل الـ alphabetical set، حروف الأبجدية
+
+458
+00:39:28,590 --> 00:39:37,290
+الإنجليزية. الـ complement  الحروف الناقصة لأن
+
+459
+00:39:37,290 --> 00:39:39,630
+عليك بتصير... بتصير كل الـ alphabetical اللي هم الـ
+
+460
+00:39:39,630 --> 00:39:45,700
+26 حرف، لأقصى دول، مين بيضل؟ الـ ABC اللي هم الـ
+
+461
+00:39:45,700 --> 00:39:50,280
+difference المكملة هي المكملة شباب، تساوي الـ
+
+462
+00:39:50,280 --> 00:39:54,300
+universal set ناقص المجموعة نفسها. بإيش بتختلف الـ
+
+463
+00:39:54,300 --> 00:40:03,640
+universal set عن المجموعة؟ Symmetric
+
+464
+00:40:03,640 --> 00:40:13,640
+difference Symmetric
+
+465
+00:40:13,640 --> 00:40:17,900
+difference عندما أتكلم عن الـ Symmetric Difference
+
+466
+00:40:17,900 --> 00:40:25,940
+أتكلم عن مجموعة عناصرها عبارة عن اتحاد الاختلاف أو
+
+467
+00:40:25,940 --> 00:40:34,280
+عناصر الاختلاف بين المجموعتين، بالعناصر
+
+468
+00:40:34,280 --> 00:40:38,640
+... اتحاد العناصر المميزة لكل مجموعة. الـ
+
+469
+00:40:38,640 --> 00:40:43,960
+Asymmetric Difference مع الـ B تساوي A ناقص الـ B
+
+470
+00:40:43,960 --> 00:40:50,380
+اتحاد B ناقص الـ A. طيب لو أنا جيت قلت الـ A بدها
+
+471
+00:40:50,380 --> 00:40:54,920
+تساوي واحد، اثنين، وثلاثة، وقلت أن الـ B بدها تساوي
+
+472
+00:40:54,920 --> 00:41:00,820
+اثنين، ثلاثة، وأربعة. Asymmetric Difference الـ B
+
+473
+00:41:00,820 --> 00:41:03,940
+الـ
+
+474
+00:41:03,940 --> 00:41:11,280
+A ناقص الـ B، إيش تساوي؟ واحد. وأربعة. A ناقص الـ B
+
+475
+00:41:11,280 --> 00:41:16,200
+واحد، اتحاد B ناقص الـ A، أربعة
+
+476
+00:41:24,770 --> 00:41:33,790
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+477
+00:41:33,790 --> 00:41:34,210
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+478
+00:41:34,210 --> 00:41:36,170
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+479
+00:41:36,170 --> 00:41:37,190
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+480
+00:41:37,190 --> 00:41:37,490
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+481
+00:41:37,490 --> 00:41:37,770
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+482
+00:41:37,770 --> 00:41:42,570
+لأ لأ لأ لأ لأ لأ لأ لأ
+
+483
+00:41:42,570 --> 00:41:52,920
+بين قوسين، هي الفرق ما بين الاتحاد والتقاطع
+
+484
+00:41:52,920 --> 00:42:00,400
+إيش اتحادهم؟ واحد، اثنين، ثلاثة، أربعة. هي اتحادهم
+
+485
+00:42:00,400 --> 00:42:09,480
+ناقص التقاطع، اثنين وثلاثة، بتصفي واحد وأربعة. نفس
+
+486
+00:42:09,480 --> 00:42:11,920
+المعنى، واضحة الصورة هيك؟
+
+487
+00:42:14,890 --> 00:42:23,790
+عندنا مجموعة من القوانين، اللهم
+
+488
+00:42:23,790 --> 00:42:29,230
+علاقة بالـ logical اللي شفناه سابقاً، وبمفاهيمنا
+
+489
+00:42:29,230 --> 00:42:35,890
+للاتحاد، والتقاطع، والـ complement. الآن واحد اتحاد
+
+490
+00:42:35,890 --> 00:42:43,590
+و زي مجال العرعير، or، تقاطع، and، complement
+
+491
+00:42:45,670 --> 00:42:52,290
+نفي، تنتمي إلى A، ولا تنتمي إلى B، مظبوط ولا لأ؟ هو
+
+492
+00:42:52,290 --> 00:42:55,730
+الـ difference، في الآخر، هدول كانوا عندي... لما
+
+493
+00:42:55,730 --> 00:42:58,830
+اتكلمنا عن الـ logic، قدرنا نـ assemble منهم مجموعة من
+
+494
+00:42:58,830 --> 00:43:03,250
+القوانين. هتلاقي أن مجموعة القوانين هي تقريباً نفسها
+
+495
+00:43:03,250 --> 00:43:08,670
+من خلال الـ set operations اللي عندي. A اتحاد الـ Φ
+
+496
+00:43:08,670 --> 00:43:14,350
+A، ليش؟ لأن المجموعة الثانية فاضية، ما فيش فيها عناصر
+
+497
+00:43:15,910 --> 00:43:20,970
+A تقاطع الـ universal set، الـ universal set، A، لأن
+
+498
+00:43:20,970 --> 00:43:26,310
+الآن، إذا كانت الـ A هيها اثنين
+
+499
+00:43:26,310 --> 00:43:32,890
+أو بلاش A وB وC وD، هي تقول لنا أن الـ U هي كل
+
+500
+00:43:32,890 --> 00:43:43,470
+حروف الأبجدية، A، B لحد الـ Z. A تقاطع الـ U هيكون الـ
+
+501
+00:43:43,470 --> 00:43:47,550
+A، لما في الـ A، والـ B، والـ C، وهي بنسمي إحنا الـ
+
+502
+00:43:47,550 --> 00:43:51,290
+identity law
+
+503
+00:43:51,290 --> 00:43:57,390
+A اتحاد الـ universal set؟
+
+504
+00:43:57,390 --> 00:44:03,150
+A تقاطع الـ Φ؟ الـ Φ domination زي تماماً زي ما
+
+505
+00:44:03,150 --> 00:44:11,220
+قلنا، نقول A and False، إيش كانت النتيجة؟ False. A or
+
+506
+00:44:11,220 --> 00:44:16,080
+True، True domination، أو سيطرة للعناصر الموجودة
+
+507
+00:44:16,080 --> 00:44:23,220
+عندها. A اتحاد الـ A، تقاطع الـ A، كل العناصر الموجودة
+
+508
+00:44:23,220 --> 00:44:30,080
+مكملة المكملة ترجع لمجموعها نفسها، تماماً نفس النفي
+
+509
+00:44:30,080 --> 00:44:35,340
+إثبات A اتحاد الـ B يساوي B اتحاد الـ A، عملية
+
+510
+00:44:35,340 --> 00:44:37,460
+إبدالية، وكذلك التقاطع
+
+511
+00:44:40,170 --> 00:44:48,710
+عملية التجميع، A اتحاد B اتحاد C يساوي A اتحاد B
+
+512
+00:44:48,710 --> 00:44:55,530
+اتحاد C، تساوي A اتحاد (B اتحاد C). وكذلك
+
+513
+00:44:55,530 --> 00:44:58,470
+بتطبيقها على التقاطع، تماماً نفس الكلام اللي
+
+514
+00:44:58,470 --> 00:45:04,130
+بنطبقه على الـ and، الـ and is distributive، توزيع
+
+515
+00:45:04,130 --> 00:45:11,390
+أو خاصية التوزيع، A تقاطع (B اتحاد C) معناته A تقاطع
+
+516
+00:45:11,390 --> 00:45:17,510
+الـ B، اتحاد A تقاطع الـ C. وتوزيع الـ A للاتحاد، A
+
+517
+00:45:17,510 --> 00:45:24,410
+اتحاد (B تقاطع C)، تساوي (A اتحاد B) تقاطع (A
+
+518
+00:45:24,410 --> 00:45:35,070
+اتحاد C). دي مورغان قال، له صاحبنا، مكملة الاتحاد
+
+519
+00:45:35,070 --> 00:45:38,270
+تساوي تقاطع المكملات
+
+520
+00:45:40,530 --> 00:45:48,510
+تقريباً نفسها كمان مرة، مكملة الاتحاد تساوي تقاطع
+
+521
+00:45:48,510 --> 00:45:58,030
+المكملات، أو لا تقاطع المكملات تساوي اتحاد المكملات
+
+522
+00:45:58,030 --> 00:46:01,110
+أشرح
+
+523
+00:46:01,110 --> 00:46:05,390
+حاضر، مش هروح بالمثال، كمان هروح أثبت لك إياها، اصبر
+
+524
+00:46:05,390 --> 00:46:15,350
+A اتحاد B، أو A تقاطع B، A اتحاد A
+
+525
+00:46:15,350 --> 00:46:23,070
+تقاطع B، يساوي A.  الجزء المشتركة بين A و B هي
+
+526
+00:46:23,070 --> 00:46:27,950
+جزء من A، لما بروح بجمعهم مع A بظل A كلها
+
+527
+00:46:27,950 --> 00:46:34,830
+وكذلك التقاطع، A تقاطع (اتحاد B) هيديني
+
+528
+00:46:34,830 --> 00:46:35,690
+الـ A
+
+529
+00:46:38,210 --> 00:46:43,310
+A تقاطع، أو A اتحاد المكملة، كل الـ universal set، و
+
+530
+00:46:43,310 --> 00:46:51,990
+A تقاطع المكملة الأصل يساوي الـ Φ. أثبت
+
+531
+00:46:51,990 --> 00:46:55,670
+أن
+
+532
+00:46:55,670 --> 00:47:04,350
+(A اتحاد B) أو مكملة (A اتحاد B) تساوي مكملة A
+
+533
+00:47:04,350 --> 00:47:06,310
+أو مكملة الـ A تقاطع
+
+534
+00:47:09,280 --> 00:47:13,820
+عشان هو ما شاء الله عليكم، مكملة A تقاطع مكملة
+
+535
+00:47:13,820 --> 00:47:19,540
+B، ممتاز. البداية وين هتكون الشباب في الإثبات؟ هان
+
+536
+00:47:19,540 --> 00:47:26,080
+الشمال، بك، اتحولها إيش؟ بك اتحول فيها الآن الشباب
+
+537
+00:47:26,080 --> 00:47:31,000
+هان، الشغل اللي موجودة قدامك، الـ definition، إذا أنت
+
+538
+00:47:31,000 --> 00:47:35,800
+بتستحضر الـ definition صح، تمام؟ بتقدر تتكلم على أو
+
+539
+00:47:35,800 --> 00:47:39,580
+تشتق القانون هذا. لو أنا سألتك، إيش قانون الاتحاد؟
+
+540
+00:47:39,580 --> 00:47:47,000
+أنا بقول لك هيك، A اتحاد B يساوي المجموعة
+
+541
+00:47:47,000 --> 00:47:57,760
+العناصرها X، حيث X تنتمي إلى A أو X تنتمي إلى B
+
+542
+00:47:57,760 --> 00:48:06,330
+مظبوط؟ طيب لما أنا بقول المكملة لهذا، إيش يعني؟
+
+543
+00:48:06,330 --> 00:48:13,250
+يعني أنا جيت بأتكلم... هاي شوف المربع بمثل الـ
+
+544
+00:48:13,250 --> 00:48:19,090
+university، تمام؟ وهي A، وهي B، إذا... اتحاده
+
+545
+00:48:19,090 --> 00:48:22,730
+من كل المنطقة المظللة باللون الرمادي، صح؟ من اللي
+
+546
+00:48:22,730 --> 00:48:25,690
+بيبقى اللي عندي؟ بيبقى للمساحة اللي برا، أو
+
+547
+00:48:25,690 --> 00:48:29,490
+بين قوسين، هي العناصر التي لا تنتمي... لا تنتمي إلى
+
+548
+00:48:29,490 --> 00:48:31,790
+مين؟ إلى الاتحاد، صح؟
+
+549
+00:48:35,220 --> 00:48:40,280
+ماذا رأيكم بهذه؟ منيحة؟ لا تقول لي غلط بيه يا
+
+550
+00:48:40,280 --> 00:48:45,640
+صاحبي! الآن الـ X ليست تاني، هي نفي! يعني الـ X لا
+
+551
+00:48:45,640 --> 00:48:51,360
+تحقق الكلام هذا! الآن بدك تدخل النفي لجوة! بدك
+
+552
+00:48:51,360 --> 00:48:55,800
+تدخل النفي لجوة! وهذا يساوي! ما ينفعش تخليها برا!
+
+553
+00:48:58,780 --> 00:49:04,020
+عشان تتحول هذه، لا تساوي، أو لا تنتمي، and، ولا تنتمي
+
+554
+00:49:04,020 --> 00:49:09,520
+تتكلم عن تقاطعه، وبالتالي بروح بقول له هذه تساوي الـ
+
+555
+00:49:09,520 --> 00:49:13,600
+X، لا بت كاشن في الـ X، بت كاشن في الـ X، الـ X هي الـ
+
+556
+00:49:13,600 --> 00:49:20,170
+element، بدك تنفي صفتها، أو تغير في صفة الـ X، الـ X أو
+
+557
+00:49:20,170 --> 00:49:25,390
+هيك، نفي الـ X تنتمي إلى A أو... لسه خليها برا
+
+558
+00:49:25,390 --> 00:49:30,410
+X تنتمي إلى B، بس عشان نفصل كويسة الخطوات، هي
+
+559
+00:49:30,410 --> 00:49:34,310
+دخلت النفي، يعني أنت النفي بتعتمده مش للـ X، للـ
+
+560
+00:49:34,310 --> 00:49:37,390
+description تبعت X، للـ condition اللي بيوصف الـ
+
+561
+00:49:37,390 --> 00:49:47,560
+X، وعادة تساوي X... الآن نفي الـ X، لا تنتمي، الـ X لا
+
+562
+00:49:47,560 --> 00:49:56,100
+تنتمي إلى A، والـ or ستصبح and، الـ X لا تنتمي
+
+563
+00:49:56,100 --> 00:50:03,240
+إلى B. تعال نشوف المنطقة المظللة باللون الأزرق
+
+564
+00:50:03,240 --> 00:50:09,860
+إيش بتمثل هذه؟ المناطق التي لا تنتمي إلى A، وهي
+
+565
+00:50:09,860 --> 00:50:15,130
+بين قوسين، مكملة A بالنسبة للـ universe، مظبوط؟
+
+566
+00:50:15,130 --> 00:50:25,510
+مكملة A، X حيث X تنتمي لمكملة A. من أين أنا
+
+567
+00:50:25,510 --> 00:50:29,090
+جبتها؟ أما أننا اتفقنا أن هذه A، وهذه B، وهذه
+
+568
+00:50:29,090 --> 00:50:33,950
+الـ universe، شيلنا B، الآن هذه المنطقة المظللة
+
+569
+00:50:33,950 --> 00:50:38,350
+باللون الأزرق ماذا تتمثل لدي؟ تتمثل مكملة، أو مكملة
+
+570
+00:50:38,350 --> 00:50:42,810
+الـ A، يعني العناصر اللي ينتمي إليها لا ينتمي إلى
+
+571
+00:50:42,810 --> 00:50:48,360
+A. X لا تنتمي إلى A، معناته X تنتمي للمتمة
+
+572
+00:50:48,360 --> 00:50:56,140
+أو المكملة، and نفس الكلام بالـ B، معناته X تنتمي
+
+573
+00:50:56,140 --> 00:51:03,920
+لمكملة B. طيب صار في عندي X تنتمي، and X تنتمي
+
+574
+00:51:03,920 --> 00:51:11,980
+معناته تساوي مكملة A تقاطع مكملة B
+
+575
+00:51:14,960 --> 00:51:18,200
+أجيب الرسمة في الامتحان؟ لأ، هديعش في الإصلاح، علشان
+
+576
+00:51:18,200 --> 00:51:23,720
+أشرح لك إياها، بس نفس
+
+577
+00:51:23,720 --> 00:51:32,780
+الكلام
+
+578
+00:51:32,780 --> 00:51:38,000
+على اتحاد، أو على التقاطع، شغل بالكلام
+
+579
+00:51:42,700 --> 00:51:47,620
+بظبط؟ هو فاهمين شكله بالكلام، إيش
+
+580
+00:51:47,620 --> 00:51:53,160
+تعريف التقاطع؟ أن الـ X تنتمي إلى A، و الـ X تنتمي
+
+581
+00:51:53,160 --> 00:51:57,780
+إلى B. فالتقاطع نفس الكلام يا شباب، اللي قلناه، إيش
+
+582
+00:51:57,780 --> 00:52:04,760
+معنى التقاطع؟ أن الـ X... نفس الكلام... بدل... لاحظ
+
+583
+00:52:04,760 --> 00:52:07,260
+هذا الشيء اللي قلت لك، X لا تنتمي للتقاطع، شو هي
+
+584
+00:52:07,260 --> 00:52:13,530
+المكملة؟ تعريف التقاطع هي نفي، معناته X لا تنتمي
+
+585
+00:52:13,530 --> 00:52:18,130
+معناته صارت هذه اللي كانت مكملة، والآن صارت أرثر
+
+586
+00:52:18,130 --> 00:52:28,130
+بتكلم عن الاتحاد، أيوه
+
+587
+00:52:28,130 --> 00:52:35,070
+نفس الكلام السابق، أن X هيثو
+
+588
+00:52:35,070 --> 00:52:38,810
+مكملة، الـ X لا تنتمي
+
+589
+00:52:41,470 --> 00:52:50,390
+للـ A، تقاطع، تقاطع، تقاطع، تقاطع، تقاطع، تقاطع، تقاطع
+
+590
+00:52:50,390 --> 00:52:51,950
+تقاطع، تقاطع، تقاطع، تقاطع، تقاطع، تقاطع، تقاطع، تقاطع
+
+591
+00:52:51,950 --> 00:52:54,030
+تقاطع، تقاطع، تقاطع، تقاطع، تقاطع، تقاطع، تقاطع، تقاطع
+
+592
+00:52:54,030 --> 00:52:54,130
+تقاطع، تقاطع، تقاطع، تقاطع، تقاطع، تقاطع، تقاطع، تقاطع
+
+593
+00:52:54,130 --> 00:52:54,150
+تقاطع، تقاطع، تقاطع، تقاطع، تقاطع، تقاطع، تقاطع، تقاطع
+
+594
+00:52:54,150 --> 00:53:05,650
+تقاطع، تقاطع، تقاطع، تقاطع، تقاطع، تقاطع، تقاطع، تقاطع، ت
+
+595
+00:53:16,430 --> 00:53:21,290
+هو لازم كل مرة أنا أجيب الجطر لجطرة، جطرة؟ خلاص
+
+596
+00:53:21,290 --> 00:53:30,030
+يعني بقى كبرته، أه؟ وبالتالي، هيدي الـ definition
+
+597
+00:53:30,030 --> 00:53:33,150
+اللي موجود عندي الآن، إيش بقى اللي عندي أساوي؟ هقول
+
+598
+00:53:33,150 --> 00:53:39,350
+إن الـ X هذه تنتمي للمكملة، and الـ X تنتمي لمكملة الـ
+
+599
+00:53:39,350 --> 00:53:46,810
+B، and الـ X تنتمي لمكملة C. ماذا أستطيع أن أفعل
+
+600
+00:53:46,810 --> 00:53:56,430
+الآن؟ وزع الـ and، سيصبح X تنتمي لمكملة A، and
+
+601
+00:53:56,430 --> 00:54:07,210
+X تنتمي لمكملة B، الـ X تنتمي لمكملة A، and
+
+602
+00:54:07,210 --> 00:54:11,190
+X تنتمي لمكملة C
+
+603
+00:54:15,780 --> 00:54:24,600
+هذه، إيش؟ تقاطع المتمة A، تقاطع B، أو تقاطع
+
+604
+00:54:24,600 --> 00:54:30,440
+المتممات مرة ثانية أهو
+
+605
+00:54:30,440 --> 00:54:35,560
+أنا مشيت عشان أعيدها يا ربّي، هذه الخطوة  حوزية
+
+606
+00:54:35,560 --> 00:54:41,820
+logical، هل في عندي and، وفي عندي or، بوزعها
+
+607
+00:54:41,820 --> 00:54:51,760
+وتبقى الـ or ما بينهم. والقوس بتمثل الاتحاد،
+
+608
+00:54:51,760 --> 00:54:56,140
+بتمثل اتحاد،
+
+609
+00:54:56,140 --> 00:54:59,640
+إيش لما وصلنا؟
+
+610
+00:54:59,640 --> 00:55:04,420
+نفس هذه، الآن قلت لك دائماً في الإثبات حاول تشوف
+
+611
+00:55:04,420 --> 00:55:09,240
+هذه الصورة، هي هذه، يعني أنت بتتوزع مين؟ بتتوزع
+
+612
+00:55:09,240 --> 00:55:09,900
+لها؟
+
+61
\ No newline at end of file
diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/cD0ZBrc1468_postprocess.srt b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/cD0ZBrc1468_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..37eb8328b1cd797fad873aa9c0fa2be6a6c4b0fa
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/cD0ZBrc1468_postprocess.srt
@@ -0,0 +1,2596 @@
+1
+00:00:20,870 --> 00:00:22,850
+بسم الله والحمد لله والصلاة والسلام على رسول الله
+
+2
+00:00:22,850 --> 00:00:25,430
+.. مش أحلى صدري و أسر أمري و أحلى العقل تمالساني
+
+3
+00:00:25,430 --> 00:00:28,230
+أفقه قويفاليوم يا شباب ان شاء الله هنكمل في
+
+4
+00:00:28,230 --> 00:00:31,530
+chapter .. ال chapter التاني في الرياضات المفصلة و
+
+5
+00:00:31,530 --> 00:00:34,810
+اللي بيتكلم عن ال basic structures و هنكمل مع
+
+6
+00:00:34,810 --> 00:00:38,550
+المجموعات .. هنكمل مع المجموعات كنا حكينا ان
+
+7
+00:00:38,550 --> 00:00:41,810
+المجموعة هي عبارة عن unordered collection of
+
+8
+00:00:41,810 --> 00:00:46,330
+objects و لما اتكلمنا unordered عناصر غير مرتبة
+
+9
+00:00:46,330 --> 00:00:49,910
+يعني الترتيب العناصر لا يعني شيء و كل جملة مهمة
+
+10
+00:00:49,910 --> 00:00:54,690
+جدا تكرار العنصر في المجموعة لا يعني شيءو لما
+
+11
+00:00:54,690 --> 00:00:57,150
+اتكلمنا على ال contains معناته العلاقة بتصير بين
+
+12
+00:00:57,150 --> 00:00:59,670
+العنصر و المجموعة، العنصر اللي هو ال object اللي
+
+13
+00:00:59,670 --> 00:01:03,950
+انا بعده contains او member of، بقيتش بقول a is
+
+14
+00:01:03,950 --> 00:01:09,750
+member of ال a ال a small as element is member of
+
+15
+00:01:09,750 --> 00:01:13,350
+ال a، و لو كتش مش موجودة بقول is not a member of
+
+16
+00:01:13,350 --> 00:01:18,650
+ال aوقلنا Antemio لAntemio وعددنا عناصر المجموعات
+
+17
+00:01:18,650 --> 00:01:22,870
+وقلنا في طريقة تمثيل المجموعات أننا نوعين من تمثيل
+
+18
+00:01:22,870 --> 00:01:26,170
+المجموعات الأولى سمناها الـ Roster Method وقلت أنا
+
+19
+00:01:26,170 --> 00:01:30,190
+بكتب الـ curly braces و بكتب عناصر المجموعة في
+
+20
+00:01:30,190 --> 00:01:35,110
+داخلهم مباشرة بشكل صريح ولو عناصر المجموعة طويلة
+
+21
+00:01:35,110 --> 00:01:38,690
+وفيها sequence معين أو في جزء منها بنفهم وإحنا
+
+22
+00:01:38,690 --> 00:01:41,150
+بنعتمد على الشيء اللي سمناها الـ ellipses أو
+
+23
+00:01:41,150 --> 00:01:46,550
+النقاط مثلًا أقعد أكتب واحد اتنين تلاتةوحط نقاط،
+
+24
+00:01:46,550 --> 00:01:50,690
+معناته يبقى الماشية إلى ما لا نهاية، لو حطيت 100،
+
+25
+00:01:50,690 --> 00:01:55,070
+معناته من واحد إلى مية، 77 موجودة؟ أه موجودة، نابت
+
+26
+00:01:55,070 --> 00:01:58,410
+عنها ميم، الـEllipses ما بين التلاتة لحد المية
+
+27
+00:01:58,410 --> 00:02:03,830
+والصيغة التانية في كتابة المجموعة كانت علاقة بالـ
+
+28
+00:02:03,830 --> 00:02:09,070
+Set Notation Builderأقول إنها بتعتمد على أني أعرف
+
+29
+00:02:09,070 --> 00:02:13,730
+expression و ال expression هذا أديه وصف دقيق أحدد
+
+30
+00:02:13,730 --> 00:02:20,370
+إيش خصائصه بشكل واضح مثل آجي أقول إن ال X is an
+
+31
+00:02:20,370 --> 00:02:26,070
+odd positive integer less than عشرة و بدي وصف صريح
+
+32
+00:02:26,070 --> 00:02:31,950
+و واضح لعراصر المجموعة اللي عندي هناوانتقلنا بعد
+
+33
+00:02:31,950 --> 00:02:36,450
+هيكاد للمجموعات اللي عندنا وقلنا في عندي شغل اسمها
+
+34
+00:02:36,450 --> 00:02:39,810
+ال universal set وفي عندي ال implicit ال universal
+
+35
+00:02:39,810 --> 00:02:44,150
+set هنفهمها دائما من السياق او تتعطيلنا بشكل واضح
+
+36
+00:02:44,150 --> 00:02:48,330
+لمبادئي بتكلم على مجموعة ال integers في المثال
+
+37
+00:02:48,330 --> 00:02:52,890
+السابق لما اتكلمنا x, x is an odd positive integer
+
+38
+00:02:52,890 --> 00:02:57,530
+less than 100 من ال universal تبعتهاكل الـ
+
+39
+00:02:57,530 --> 00:03:01,190
+Integers لان انا بتكلم على Integers في المقابل في
+
+40
+00:03:01,190 --> 00:03:05,750
+عند الـ Empty Set الـ Phi هو المجموعة الخالية اللي
+
+41
+00:03:05,750 --> 00:03:08,610
+مافيش فيها عناصر وانتقلنا بعد هيكت في المحاضرة
+
+42
+00:03:08,610 --> 00:03:11,970
+السابقة للـ Set Equality عشان اقارن بين المجموعتين
+
+43
+00:03:11,970 --> 00:03:15,590
+هل في بينهم تساوي او لأ وقولت شرط التساوي اللي
+
+44
+00:03:15,590 --> 00:03:20,950
+عندي انه لكل عنصر في المجموعة A هلاقي العنصر هذا
+
+45
+00:03:20,950 --> 00:03:27,020
+موجود في الـ B وكل عنصر موجود في Bهيكون موجود في A
+
+46
+00:03:27,020 --> 00:03:30,500
+وبالتالي الآن لو افترضت ان ال A بيه تساوي واحد و
+
+47
+00:03:30,500 --> 00:03:34,620
+ثلاثة و خمسة و ال B بيه تساوي تلاتة و خمسة و واحد
+
+48
+00:03:34,620 --> 00:03:39,300
+متساويين متساويين تقولنا ترتيب العناصر لا يعني شيء
+
+49
+00:03:39,300 --> 00:03:42,100
+بالنسبة لنا وبالتالي اذا انا اتكرر العناصر لايعني
+
+50
+00:03:42,100 --> 00:03:46,080
+شيء فبالتالي هدول المجموعتين متساويات لأن كل عنصر
+
+51
+00:03:46,080 --> 00:03:48,820
+في A موجود في B و العكس صحيح
+
+52
+00:03:52,010 --> 00:03:54,950
+والتقلب بعد ذلك لتعريف الـ definition اسمه الـ
+
+53
+00:03:54,950 --> 00:03:58,190
+subset المجموعة الجزئية قلت لما أنا بتكلم على
+
+54
+00:03:58,190 --> 00:04:05,250
+مجموعة جزئية أنا فيها اندي مجموعتين A وB باجي بقول
+
+55
+00:04:05,250 --> 00:04:08,950
+الـ A subset من B مجموعة جزئية من الـ B لما لاجي
+
+56
+00:04:08,950 --> 00:04:14,850
+كل عنصر في A موجود في B for all X X تنتمي إلى A
+
+57
+00:04:14,850 --> 00:04:20,930
+يؤدي إلى X تنتمي إلى B وهذا سمنها subset بالمثال
+
+58
+00:04:20,930 --> 00:04:26,250
+السابقكانت الـ X واحد و اتنين و تلاتة هذه الـ P
+
+59
+00:04:26,250 --> 00:04:32,090
+بقدر اجي اقول ان الواحد و اتنين مجموعة جزئية من
+
+60
+00:04:32,090 --> 00:04:35,650
+الدالة اللي عندها و بتحب اذكرك في مثال و مهم جدا
+
+61
+00:04:35,650 --> 00:04:40,390
+لمثال هذا لما اجينا قولنا ال X بدها تساوي او ال A
+
+62
+00:04:40,390 --> 00:04:44,950
+تساوي Xوالمجموعة X as element هد المجموعة كام عنصر
+
+63
+00:04:44,950 --> 00:04:49,550
+فيها؟ اتنين قلنا عشان يتحدد العلاقة ما بين ال
+
+64
+00:04:49,550 --> 00:04:53,570
+ينتمي و ال subset و تكون دائما صحيحة اكتب كتانة
+
+65
+00:04:53,570 --> 00:04:59,450
+هال ينتمي A وهي subset من ال A subset يعني عبارة
+
+66
+00:04:59,450 --> 00:05:03,310
+عن مجموعة و المطلوب منك في الفراغة هدا تاخد احد
+
+67
+00:05:03,310 --> 00:05:08,050
+عناصر او تاخد عناصر من عناصر المجموعة و تحطها لما
+
+68
+00:05:08,050 --> 00:05:13,040
+بتكلم عن ينتمي بتتكلم عن one element صح؟سواء تأخذ
+
+69
+00:05:13,040 --> 00:05:15,720
+الـ X كما هي أو العنصر التاني كما هو .. لأن هنا
+
+70
+00:05:15,720 --> 00:05:19,160
+تأخذ عنصر من المجموعة و تجلبه هنا فتكون عملية اللي
+
+71
+00:05:19,160 --> 00:05:23,420
+ينتمي معاك صحيحة 100% و لما تحافظ على ال subset
+
+72
+00:05:23,420 --> 00:05:27,900
+تكون صحيحة تشتغل نفس الكلام تضع الأقواس subset و
+
+73
+00:05:27,900 --> 00:05:31,160
+تضع أي ألم تضعه في داخل من؟ في داخل الأقواس
+
+74
+00:05:31,160 --> 00:05:37,060
+وبالتالي ستحصل على ال subset صحيحة برضه 100% الآن
+
+75
+00:05:37,060 --> 00:05:41,400
+أنا في عند ال file هي عبارة عن subset من أي مجموعة
+
+76
+00:05:41,400 --> 00:05:45,770
+تانيةوانتقلنا بعد ذلك لشغل اسمها الـ proper subset
+
+77
+00:05:45,770 --> 00:05:50,970
+ايش proper subset؟ ان المجموعة T أو المجموعة A هي
+
+78
+00:05:50,970 --> 00:05:57,250
+عبارة عن مجموعة جزئية من B لكنها غير مساوية لها في
+
+79
+00:05:57,250 --> 00:05:59,990
+ال subset اللي احنا شفناها احتمال المساوية موجود
+
+80
+00:05:59,990 --> 00:06:05,410
+لأن كل المجموعات نجيب نقول لكل عنصر في A حد يجيب
+
+81
+00:06:05,410 --> 00:06:10,360
+موجود في ال B طب لو كان المجموعات متساوياتلو كانوا
+
+82
+00:06:10,360 --> 00:06:13,780
+المجموعات تانية تبدأ تُعتبر subset لأن كل أنصار
+
+83
+00:06:13,780 --> 00:06:16,820
+موجود وبالتالي حققت ال definition مع ال proper
+
+84
+00:06:16,820 --> 00:06:22,080
+subset أضفنا جزئية جديدة على ال definition and
+
+85
+00:06:22,080 --> 00:06:28,300
+there exist x, x تنتمي إلى b and ال x لا تنتمي إلى
+
+86
+00:06:28,300 --> 00:06:33,060
+ال a وبهك بصير ان انا بتكلم على ال proper subset
+
+87
+00:06:33,980 --> 00:06:38,460
+وانتقلنا وخلصنا محاضرتنا لأن وصلنا لـ Cardinality
+
+88
+00:06:38,460 --> 00:06:43,360
+اللي حنبدأ فيها باجهة محاضرتنا اليوم طيب، اليوم
+
+89
+00:06:43,360 --> 00:06:47,260
+بتكلم على الـ Cardinality بتكلم على عدد عناصر
+
+90
+00:06:47,260 --> 00:06:54,080
+المجموعة لما تكون المجموعة NDS بتحتوي على
+
+91
+00:06:54,080 --> 00:06:59,950
+Undistinct Element ايش distinct؟ مختلفينN distinct
+
+92
+00:06:59,950 --> 00:07:05,250
+elements عناصر مختلفة عددهم N بقول عن ال S is a
+
+93
+00:07:05,250 --> 00:07:11,410
+finite set مجموعة منتهية finite مجموعة منتهية و ال
+
+94
+00:07:11,410 --> 00:07:16,470
+cardinality تبعتها تساوي N عدد عناصرها N يعني لو
+
+95
+00:07:16,470 --> 00:07:21,510
+كانت المجموعة S تبعتي بدها تساوي واحد و تلاتة و
+
+96
+00:07:21,510 --> 00:07:27,820
+واحد و اربعة او خمسةأيوة هذه التكرار لأ .. الأن
+
+97
+00:07:27,820 --> 00:07:30,940
+لاحظ لما أنا باسألك على ال cardinality هي .. هي
+
+98
+00:07:30,940 --> 00:07:33,160
+رمز ال cardinality اللي هي ال absolute value تبع
+
+99
+00:07:33,160 --> 00:07:37,220
+ال S بس بنسميها في المجموعات cardinality عدد عناصر
+
+100
+00:07:37,220 --> 00:07:41,620
+المجموعة عدد عناصر المجموعة S جديش الشباب تلاتة
+
+101
+00:07:41,620 --> 00:07:45,040
+ليش مقولاش أربع على الرغم انه مكتوب عندها لأن
+
+102
+00:07:45,040 --> 00:07:47,880
+التكرار لا يعني شيء في المجموعة وبالتالي أنا بتكلم
+
+103
+00:07:47,880 --> 00:07:54,180
+على تلت عناصر في المجموعة اللي موجودة عندهامثلًا
+
+104
+00:07:54,180 --> 00:07:57,960
+لو أنا قلت في عندي مجموعة السيارات مرسيديوس BMW و
+
+105
+00:07:57,960 --> 00:08:04,000
+بورش اتكلمت على المجموعة B فيها واحد اتنين و تلاتة
+
+106
+00:08:04,000 --> 00:08:09,560
+as a set اربع و خمس as a set ستة لاحظوا الست اتنين
+
+107
+00:08:09,560 --> 00:08:13,380
+و تلاتة و الست اربع و خمس عبارة عن elements في
+
+108
+00:08:13,380 --> 00:08:17,980
+المجموعة وبالتالي واحد اتنين تلاتة اربع فقط عناصر
+
+109
+00:08:17,980 --> 00:08:24,030
+ال B لو كانت ال C تسوى الفاي المجموعة الخاليةفاضية
+
+110
+00:08:24,030 --> 00:08:27,890
+فاش ولا element جداش عدد العناصر صفر بمفهش اقول
+
+111
+00:08:27,890 --> 00:08:30,650
+عدد العناصر مش موجود لأ بتقول عنه صفر لان دلوقتي
+
+112
+00:08:30,650 --> 00:08:37,290
+بتتكلم على رقم بيه بتتكلم؟ هي عبارة عن مجموعة
+
+113
+00:08:37,290 --> 00:08:43,810
+بتحتوي على أربع عناصر من هم الواحد التاني و
+
+114
+00:08:43,810 --> 00:08:47,910
+التلاتة هذه مجموعة بس هال في البيئة as element و
+
+115
+00:08:47,910 --> 00:08:54,700
+أربع و خمسة و ستة بتتكلم على أربععناصر موجودين في
+
+116
+00:08:54,700 --> 00:08:59,780
+المجموعة اللي عندها لكن يا شباب لو انا يا جد قلتلك
+
+117
+00:08:59,780 --> 00:09:01,920
+في اللحظة من اللحظات ان ال definition تبعت
+
+118
+00:09:01,920 --> 00:09:08,500
+المجموعة تبعتي X حيث X تنتمي ل natural number و X
+
+119
+00:09:08,500 --> 00:09:12,000
+أكبر أو بسوء 850 هل تقدر تجيب ال cardinality
+
+120
+00:09:12,000 --> 00:09:17,280
+تبعتها؟ ليش؟ لأنه صار غير ممتع يانفينيت وبالتالي
+
+121
+00:09:18,240 --> 00:09:21,580
+وبالتالي لو جالك وقال لك اديني ال cardinality
+
+122
+00:09:21,580 --> 00:09:26,160
+تبعتها بنقول ان ال E هذي is infinite وبالتالي انا
+
+123
+00:09:26,160 --> 00:09:29,780
+مقدرش اتكلم على ال cardinality او عدد عناصر
+
+124
+00:09:29,780 --> 00:09:34,600
+المجموعة لكن امتبه لو اتيت قلتلك ان ال S بده تساوي
+
+125
+00:09:34,600 --> 00:09:42,860
+X حيث X تنتمي لل natural number and ال X اقل او
+
+126
+00:09:42,860 --> 00:09:47,040
+تساوي عشرة عشرة
+
+127
+00:09:47,040 --> 00:09:52,680
+محصرينفاي نايت واحد اتنين تلاتة اربع خمس لحد
+
+128
+00:09:52,680 --> 00:09:57,120
+العشرة ليش لما تجنبت الكثير لاحظ لو اتبدلت معاك
+
+129
+00:09:57,120 --> 00:10:02,840
+حالة real number كانت صارت infinite كانت صارت معاك
+
+130
+00:10:02,840 --> 00:10:08,840
+infiniteأو لو حتى سِبت الـ Z كانت ضالة Infinite،
+
+131
+00:10:08,840 --> 00:10:11,860
+لماذا؟ لأنها تذهب باتجاه السلب إلى ما لا نهاية
+
+132
+00:10:11,860 --> 00:10:18,180
+وبالتالي، تعريف المجموعة دائما بيلعب دور واضح في
+
+133
+00:10:18,180 --> 00:10:21,700
+تحديد عدد عناصرها أو تحديد الـ Cardinality تبعتها
+
+134
+00:10:21,700 --> 00:10:27,600
+النقطة
+
+135
+00:10:27,600 --> 00:10:34,700
+اللي بعدها الـ Power Setالـ Power Set هي عبارة عن
+
+136
+00:10:34,700 --> 00:10:40,240
+المجموعة التي تحتوي كل المجموعات الجزئية الممكنة
+
+137
+00:10:40,240 --> 00:10:48,680
+من الـ A الان لو انا اتيت فترضت ان ال A بدها تساوي
+
+138
+00:10:48,680 --> 00:10:55,680
+A وB وC وقلتلك اديني مجموعة جزئية
+
+139
+00:10:59,470 --> 00:11:08,750
+A و B او A لحالها او B لحالها او C لحالها B و C A
+
+140
+00:11:08,750 --> 00:11:13,550
+و C هتبدأ تخبز بس لأ انا بقولك فيه اكتر كمان ايش
+
+141
+00:11:13,550 --> 00:11:18,970
+كمان فيه ال five و فيه ال A نفسها A و B و C طيب
+
+142
+00:11:18,970 --> 00:11:22,830
+هدول المجموعات الجزئية كله ياتهم عشان انا اقدر
+
+143
+00:11:22,830 --> 00:11:26,630
+احصرهم لازم اعرف عددهم في الاول عشان اقول خلصت ولا
+
+144
+00:11:26,630 --> 00:11:32,390
+ماخلصتشفلما أنا باجي بتكلم عن ال power set بتكلم
+
+145
+00:11:32,390 --> 00:11:36,730
+ال power set لل A هي عبارة عن المجموعة التي تحتوي
+
+146
+00:11:36,730 --> 00:11:41,050
+كل المجموعات الجزئية الممكنة من ال element بتاعة
+
+147
+00:11:41,050 --> 00:11:48,010
+ال A ال definition تبعتها B of A power set of A
+
+148
+00:11:48,010 --> 00:11:56,030
+تساوي ال B as a set حيث ال B subset من ال Aدائما
+
+149
+00:11:56,030 --> 00:12:00,390
+ال power set عدد عناصرها يساوي اتنين أُس ال
+
+150
+00:12:00,390 --> 00:12:04,390
+cardinality كبعت ال a يعني الآن ال a اللي عندي
+
+151
+00:12:04,390 --> 00:12:08,910
+أنجد بيها شهر تلاتة اتنين أُس تلاتة يعني أنا بتكلم
+
+152
+00:12:08,910 --> 00:12:13,850
+على تمان عناصر عشان تمان .. مجموعة فيها تمان عناصر
+
+153
+00:12:13,850 --> 00:12:19,090
+كل عنصر منهم عبارة عن مجموعة مجموعة فيها تمان
+
+154
+00:12:19,090 --> 00:12:23,570
+عناصر كل عنصر فيهم عبارة عن مجموعة مين هم؟P of A
+
+155
+00:12:23,570 --> 00:12:28,390
+عشان تريح راسك دائما اشتغل ضمن استراتيجية واحدة
+
+156
+00:12:28,390 --> 00:12:32,430
+وما بتتوهش فيها اشتغل بالترتيب الان ابدأ من مجموعة
+
+157
+00:12:32,430 --> 00:12:35,730
+فيها عنصر مجموعة فيها عنصرين مجموعة فيها تلت عناصر
+
+158
+00:12:35,730 --> 00:12:40,170
+تبدأ ايش تكبر خليني انا اخد مثال اكبر ميادة شوية D
+
+159
+00:12:40,170 --> 00:12:43,330
+على سبيل المثال الان ال power set كان عنصر فيها
+
+160
+00:12:43,330 --> 00:12:49,500
+icon اتنين اص اربعة ستناشر element16 element عشان
+
+161
+00:12:49,500 --> 00:12:52,840
+لو .. لو طلبنا منك تجيب المجموعة على شو المفروض
+
+162
+00:12:52,840 --> 00:12:58,480
+تساوي تذكرهم إذا أنت بدك تشتغل تخمين هتكون سامحني
+
+163
+00:12:58,480 --> 00:13:02,000
+زي اللي مش شايف و قاعد بحسس في إيده و اين الطريق
+
+164
+00:13:02,000 --> 00:13:05,680
+اللي أنا بديها هتخرج في الآخر أو هتخبط في حيط أو
+
+165
+00:13:05,680 --> 00:13:09,380
+هتجي عن الشباك إلى آخرهم في الآخر هان اشتغل ضمري
+
+166
+00:13:09,380 --> 00:13:14,100
+استراتيجية بسيطة ابدأ بالمجموعات الأصغر و أكبرأو
+
+167
+00:13:14,100 --> 00:13:18,260
+العكس انا بالنسبة لي بحب ابدأ هك A المجموعات اللي
+
+168
+00:13:18,260 --> 00:13:28,160
+فيها واحد و B و C و D في غير هك؟ مجموعات من عنصر
+
+169
+00:13:28,160 --> 00:13:35,160
+واحد؟ لأ خل الفاي والمجموعة للاخر بعد هك عاصر من
+
+170
+00:13:35,160 --> 00:13:44,550
+مجموعات من عنصرين A B و A و C و A و Dبعدين بي و سي
+
+171
+00:13:44,550 --> 00:13:49,730
+إياك تقولي بي و إيه ليش لأن هي already موجودة بي و
+
+172
+00:13:49,730 --> 00:13:56,110
+سي و بي و دي و آخر حاجة سي و دي من عنصرين جداش
+
+173
+00:13:56,110 --> 00:13:59,510
+مجموعة العلاصر هذول هي أربعة و ست .. و أربعة و ست
+
+174
+00:13:59,510 --> 00:14:04,730
+عشرة الآن الجمعة اللي عندي من تلت علاصر المجموعات
+
+175
+00:14:04,730 --> 00:14:16,760
+اللي من تلت علاصر a و b و c و aو B و D .. A و C و
+
+176
+00:14:16,760 --> 00:14:24,960
+D .. و B و C و D .. هجديه صاروا هي عندي عشرة و هي
+
+177
+00:14:24,960 --> 00:14:27,460
+عندي اربعة اربع اتاش .. احنا قولنا العدل كله ستاش
+
+178
+00:14:27,460 --> 00:14:35,010
+.. الفايوالـ A نفسها اللي هي A B وC وD وبهيك أنت
+
+179
+00:14:35,010 --> 00:14:39,550
+بتحصر أو بتقدر تجيب كل ال subset من المجموعة هذي
+
+180
+00:14:39,550 --> 00:14:43,310
+طالما أنك حاولت تشتغل بالترتيب إذا أنت حاولت تشتغل
+
+181
+00:14:43,310 --> 00:14:48,550
+بالترتيب و بتصل بدها تشتغل كمان مرة تخمين هتجه أو
+
+182
+00:14:48,550 --> 00:14:49,250
+هتغلط فيها
+
+183
+00:14:54,000 --> 00:14:58,000
+أيش تعرف البواسطة؟ هي عبارة عن مجموعة تحتوي كل
+
+184
+00:14:58,000 --> 00:15:02,580
+المجموعات الجزئية الممكنة من الـA السؤال الـA
+
+185
+00:15:02,580 --> 00:15:08,220
+subset من الـA يا أحمد true ولا false؟ true يعني
+
+186
+00:15:08,220 --> 00:15:14,520
+لازم تكون موجودة فيها الفاي مش subset من الـA يعني
+
+187
+00:15:14,520 --> 00:15:17,440
+لازم تكون موجودة وبالتالي لازم تكون موجودة وإلا
+
+188
+00:15:17,440 --> 00:15:19,560
+مستحيل توصل لعدد 16
+
+189
+00:15:35,780 --> 00:15:41,740
+ده اول ما خلصنا المجموعات و ال power set في عندي
+
+190
+00:15:41,740 --> 00:15:45,940
+اول operation هطبقها على المجموعات اللي هي ال
+
+191
+00:15:45,940 --> 00:15:50,500
+Cartesian product او ال cross product ما بين
+
+192
+00:15:50,500 --> 00:15:53,980
+المجموعات بدي تفهم من البداية فيه ان في عندي شغل
+
+193
+00:15:53,980 --> 00:15:59,260
+اسمها ال table ال table مش مجموعة بتكلم عليه
+
+194
+00:15:59,260 --> 00:16:05,910
+مجموعة من العناصر لكن ترتيب العناصرمهم ومهم جدا
+
+195
+00:16:05,910 --> 00:16:14,970
+ترتيب العناصر مهم ومهم جدا وتكرار العنصر برضه مهم
+
+196
+00:16:14,970 --> 00:16:19,110
+بالنسبة لي لأنه لا يعني شيء التكرار التكرار له
+
+197
+00:16:19,110 --> 00:16:25,270
+قيمة ليش تكرار لأنه الآن في ال table في ال table
+
+198
+00:16:25,270 --> 00:16:30,660
+واحد وواحد هذا لا يسمى تكرارعارف ليش؟ لأن العنصر
+
+199
+00:16:30,660 --> 00:16:34,960
+هذا جاي من مجموعة مختلفة عن مجموعة العنصر التاني
+
+200
+00:16:34,960 --> 00:16:40,240
+وكل واحد بيمثل فيه شغلة مختلفة أبسط الأمور في الـ
+
+201
+00:16:40,240 --> 00:16:43,920
+Cartesian plane بتكلم إن العنصر الأول بيمثل ال X
+
+202
+00:16:43,920 --> 00:16:48,220
+axis و التالي بيمثل ال Y axis وبالتالي أنا بتكلم
+
+203
+00:16:48,220 --> 00:16:52,310
+إن القيمة هذه مختلفة تماماًالآية الـ tuple هدا
+
+204
+00:16:52,310 --> 00:16:56,210
+ممكن يكون n في n من العناصر ال tuple هدا ممكن يكون
+
+205
+00:16:56,210 --> 00:17:00,550
+في n من العناصر احنا بنختزل و دائما بنتكلم على
+
+206
+00:17:00,550 --> 00:17:04,590
+pair زوج مرتب بنسمي ordered pair ال tuple لما يكون
+
+207
+00:17:04,590 --> 00:17:09,730
+فيه عنصرين فقط او two tuple بنسميه ordered pair ال
+
+208
+00:17:09,730 --> 00:17:17,570
+ordered pair هدول a,b فيهم لا تساوي ال b,a ليش؟
+
+209
+00:17:17,570 --> 00:17:22,040
+لأنه كمان مرة أن العنصر ال element الأولبختلف من
+
+210
+00:17:22,040 --> 00:17:27,060
+مجموعة مختلفة عن العنصر التاني و هكذا إلا لو كانت
+
+211
+00:17:27,060 --> 00:17:32,680
+ال A تساوي ال B هنأشي تاني بصير الأمر anyway ال
+
+212
+00:17:32,680 --> 00:17:38,520
+Cartesian product هو عبارة عن المجموعة اللي بتحتوي
+
+213
+00:17:38,520 --> 00:17:44,860
+على الأزواج المرتبة A و B حيث ال A تنتمي إلى ال A
+
+214
+00:17:45,720 --> 00:17:51,420
+And الـ B تنتمي إلى الـ B طبعاً الـ A small اللي
+
+215
+00:17:51,420 --> 00:17:56,560
+هي العنصر الأول في الزوج المرتب بتنتمي للمجموعة A
+
+216
+00:17:56,560 --> 00:18:00,020
+و الـ B اللي هي العنصر التاني في الزوج المرتب
+
+217
+00:18:00,020 --> 00:18:07,180
+بتنتمي للمجموعة B بالمثال البسيط لو كان عندي أنا A
+
+218
+00:18:07,180 --> 00:18:13,400
+تساوي المجموعة فيها X و Y و الـ B تساوي A و B و C
+
+219
+00:18:15,600 --> 00:18:21,320
+الان اول ملاحظة بدنا نفهمها ان a cross ال b لا
+
+220
+00:18:21,320 --> 00:18:27,860
+تساوي b cross ال a ليش؟
+
+221
+00:18:27,860 --> 00:18:32,220
+ليش؟ ايوة لان الأزواج المرتبة اللي ناتي عن عملية
+
+222
+00:18:32,220 --> 00:18:37,320
+الضرب هتكون مختلفة اي ضرب، الضرب اللي عندنا بس مش
+
+223
+00:18:37,320 --> 00:18:40,190
+ال Cartesian productهنا أنا بتتكلم على Cartesian
+
+224
+00:18:40,190 --> 00:18:46,750
+product هل هتطلع أن زوج مرتب A و B بينما هن B و A
+
+225
+00:18:46,750 --> 00:18:52,070
+و هن A و B لا تساوي B و A وبالتالي المجمعتين ال A
+
+226
+00:18:52,070 --> 00:18:57,970
+cross ال B لا تساوي B cross ماتكلمش على dot
+
+227
+00:18:57,970 --> 00:19:01,090
+product الآن أنا بتكلم على Cartesian product بين
+
+228
+00:19:01,090 --> 00:19:08,610
+مجمعتين الآن Xعشان تجيب ال product صح تبدأ تشكل
+
+229
+00:19:08,610 --> 00:19:12,190
+أزواج مرتبة بتاخد العنصر الأول من المجموعة الأولى
+
+230
+00:19:12,190 --> 00:19:17,550
+وبتعمل اقتران مع كل العناصر في المجموعات التانية X
+
+231
+00:19:17,550 --> 00:19:23,930
+و A, X و B, X و C بتاخد العنصر التاني Y و A, Y و
+
+232
+00:19:23,930 --> 00:19:29,950
+B, Y و C لو أنت بدك تعمل product بين B و A, B
+
+233
+00:19:29,950 --> 00:19:39,630
+cross ال A, Axاي بيكس بيكس بيكس بيكس بيكس بيكس
+
+234
+00:19:39,630 --> 00:19:51,810
+بيكس بيكس بيكس بيكس بيكس بيكس بيكس
+
+235
+00:19:51,810 --> 00:19:53,730
+بيكس
+
+236
+00:19:58,750 --> 00:20:02,230
+أه اذا انت بتتكلم على كيف السؤال فيه هو الهدف فيه
+
+237
+00:20:02,230 --> 00:20:05,650
+مش هدف السؤال باداته انا بقولك اديني ال Cartesian
+
+238
+00:20:05,650 --> 00:20:08,330
+product اضرب بين المجموعتين او هاتلي ال cross
+
+239
+00:20:08,330 --> 00:20:12,350
+product بين المجموعتين وهتكون بالشكل هذا .. هتكون
+
+240
+00:20:12,350 --> 00:20:16,570
+بالشكل هذا لكن هو فعلا احنا بهمني التطبيق اللي
+
+241
+00:20:16,570 --> 00:20:20,590
+بعده يا أحمد اكتر ما بهمني وين بده يلزمني الآن هذا
+
+242
+00:20:20,590 --> 00:20:24,700
+الكلامبيلزمنا في ال animation بيلزمنا في ال design
+
+243
+00:20:24,700 --> 00:20:28,260
+بيلزمنا في أكتر من شغلة بيلزمنا بتحديد الموقع تبع
+
+244
+00:20:28,260 --> 00:20:33,040
+الشخص والموقع اللي بدنا نتقله وبالتالي بتصير ال X
+
+245
+00:20:33,040 --> 00:20:37,760
+و ال A هدول عبارة عن position على الخريطة X و Y
+
+246
+00:20:37,760 --> 00:20:44,000
+تمام؟ وبالتالي أنا هذا الموقع غير هذا بصبوط؟ بس
+
+247
+00:20:44,000 --> 00:20:50,840
+طيب الآن
+
+248
+00:20:51,970 --> 00:20:57,270
+أحنا شوفنا الـ Sub notation builder و تعرفنا عليه
+
+249
+00:20:57,270 --> 00:21:01,010
+quantifier سابقا، مظبوط ولا لأ؟ لو أنا أجيب و
+
+250
+00:21:01,010 --> 00:21:07,310
+قلتلك، إيش بتعني هذه القيمة؟ أو هذه؟ في الأول
+
+251
+00:21:07,310 --> 00:21:12,610
+قيمتها true ولا false؟ وترجمليها أو ترجمليها و
+
+252
+00:21:12,610 --> 00:21:17,410
+قولي true ولا false For all x تنتمي إلى R، x تربية
+
+253
+00:21:17,410 --> 00:21:23,760
+أكبر أو تساوي صفرتربيع أي عدد حقيقي أكبر من صفر
+
+254
+00:21:23,760 --> 00:21:34,400
+true و جدر السالب واحد جدر السالب واحد ايوة شوف
+
+255
+00:21:34,400 --> 00:21:38,800
+انت الآن انا غشتك لما قلت لك جدر السالب واحد جدر
+
+256
+00:21:38,800 --> 00:21:43,180
+السالب واحد لا تمتم لل R عدد غير حقيقي عدد تخيلي
+
+257
+00:21:43,180 --> 00:21:47,200
+مش احنا متفقين من الأساس ان في عند القسم على صفر
+
+258
+00:21:47,200 --> 00:21:51,840
+فيها مشكلةوعند السالب تحت الجدر كمان فيه مشكلة عدد
+
+259
+00:21:51,840 --> 00:21:54,840
+تخيلي وبالتالي هذه لا تنتمي إلى R هذه برا اللعبة
+
+260
+00:21:54,840 --> 00:22:03,280
+خالص لا لا true هي true اي عدد حقيقي خد اي عدد
+
+261
+00:22:03,280 --> 00:22:08,280
+حقيقي اربّه عشان فيه يساوي نبدأ من الصفر صفر ضرب
+
+262
+00:22:08,280 --> 00:22:18,410
+صفر صفر سالب واحدتربيع واحد نص او سالب نص تربيع
+
+263
+00:22:18,410 --> 00:22:24,690
+ربع اكبر من صفر وبالتالي هذا القيمة true ولاحظ لو
+
+264
+00:22:24,690 --> 00:22:31,710
+انا سألتك هذا ال quantifier بيمثلش مجموعة ايش
+
+265
+00:22:31,710 --> 00:22:36,630
+المجموعة اللي بيمثلها ايش بيمثلها كل ال real
+
+266
+00:22:36,630 --> 00:22:41,620
+number كل ال real numberطيب تعالى نشوف ال
+
+267
+00:22:41,620 --> 00:22:47,680
+quantifier التانى there exist x تنتمي إلى z هناك x
+
+268
+00:22:47,680 --> 00:22:53,020
+واحدة على الأقل كعدد صحيح x تربيها تساوي واحد true
+
+269
+00:22:53,020 --> 00:22:57,700
+واحد او سالب واحد واحد منهم بكفينا وبالتالي
+
+270
+00:22:57,700 --> 00:23:02,440
+التانية true طيب المجموعة هذه الأولى هذه مثلة كل
+
+271
+00:23:02,440 --> 00:23:04,520
+ال a وهذه
+
+272
+00:23:08,070 --> 00:23:12,810
+-1 و1 كمجموعات لاحظ هذا ال quantifier كمثله او
+
+273
+00:23:12,810 --> 00:23:16,890
+اكتبه كمجموعه وهذا اللي حكيناه سابقا انه ممكن انا
+
+274
+00:23:16,890 --> 00:23:20,670
+اعرف اعرف المجموعه بناء على predicate function و
+
+275
+00:23:20,670 --> 00:23:30,430
+quantifier لما
+
+276
+00:23:30,430 --> 00:23:33,850
+اتكلمني على predicate function قولت ل predicate
+
+277
+00:23:33,850 --> 00:23:40,130
+function ايه دي قولت؟B of X حيث X تربيع اكبر او
+
+278
+00:23:40,130 --> 00:23:45,190
+تساوي صفر جديش
+
+279
+00:23:45,190 --> 00:23:50,350
+قيمتها true ولا false true ولا false بقدرش اديها
+
+280
+00:23:50,350 --> 00:23:55,990
+قيمة لحد ما اعرف قيمة ال X لمبادشي بقولك انا X of
+
+281
+00:23:55,990 --> 00:24:00,210
+ايش قيمة ال X وينها
+
+282
+00:24:02,910 --> 00:24:06,670
+ما هو نوع الـ X؟ بتنتهي من أي عدد؟ يعني لو أنا جد
+
+283
+00:24:06,670 --> 00:24:15,550
+قلتلك بي of سالب واحد العدد التخيلي او الـ I هتصير
+
+284
+00:24:15,550 --> 00:24:19,210
+false، مظبوط ولا لأ؟ فالـ R هذه كلها مع ال
+
+285
+00:24:19,210 --> 00:24:22,870
+predicate function أنا ما بقدر أديها قيمة لحد ما
+
+286
+00:24:22,870 --> 00:24:27,970
+حدد قيمة الـ X بشكل صحيح، بشكل واضح أو أروح أتعامل
+
+287
+00:24:27,970 --> 00:24:33,960
+مع quantifierأقول for all .. عفوا .. أقول for all
+
+288
+00:24:33,960 --> 00:24:38,920
+x .. x تربيه أكبر .. و أحدد ال universal domain
+
+289
+00:24:38,920 --> 00:24:42,920
+set .. مظبوط ولا لأ؟ أو أستخدم existential
+
+290
+00:24:42,920 --> 00:24:46,240
+quantifier و أقول there exists x بتحقق كده بعد
+
+291
+00:24:46,240 --> 00:24:49,660
+تعريف ال domain وبالتالي .. هذا .. هيك .. الحالة
+
+292
+00:24:49,660 --> 00:24:54,700
+هيك .. أنا مقدرش أقيمها .. ولا لأ؟ لكن لو أنا أجيب
+
+293
+00:24:54,700 --> 00:25:00,780
+.. قلتلك ال P of X .. P of X ..هي عبارة عن
+
+294
+00:25:00,780 --> 00:25:04,280
+المجموعة أو الـ Function اللي فيها الـ X تنتمي إلى
+
+295
+00:25:04,280 --> 00:25:09,120
+الـ D لمين؟ الـ Domain حددتلك Domain الآن B of X
+
+296
+00:25:09,120 --> 00:25:11,740
+عناصر .. بتقول هذه موجودة و لا مش موجودة بتقدر
+
+297
+00:25:11,740 --> 00:25:15,280
+تحدد عناصر المجموعة بشكل واضح تعالى نشوف المثال
+
+298
+00:25:15,280 --> 00:25:21,140
+هذا بيجي بقوللي ال domain تبع ال function في
+
+299
+00:25:21,140 --> 00:25:27,640
+الأمثلة اللي جاية هي عبارة عن ال integers Z تعالى
+
+300
+00:25:27,640 --> 00:25:34,200
+B of Xوالـ domain Z الـ P of X الـ absolute value
+
+301
+00:25:34,200 --> 00:25:38,640
+للـ X يساوي واحد يعني أنا بجعل بتكلم على مجموعة
+
+302
+00:25:38,640 --> 00:25:43,920
+العناصر اللي فيها بتحقق المعادلة هذه إيش هي
+
+303
+00:25:43,920 --> 00:25:53,240
+المجموعة هذه؟ سالب واحد وواحد سالب واحد وواحد طيب
+
+304
+00:25:53,240 --> 00:26:00,490
+اللي بعديها Q of X is X تربيته ساوة اتنينX تربيه
+
+305
+00:26:00,490 --> 00:26:08,110
+تسوى اتنين جذر التنين غلط عارف ليش؟ لأن جذر التنين
+
+306
+00:26:08,110 --> 00:26:13,490
+مش عدد صحيح اتنين و سالب اتنين غلط اتنين تربيه
+
+307
+00:26:13,490 --> 00:26:22,450
+اربعة و سالب اتنين تربيه اربعة غير معروف غلط فيش
+
+308
+00:26:22,450 --> 00:26:27,280
+الشغل اسمه غير معروفهذا المقصود اللي في دماغك ..
+
+309
+00:26:27,280 --> 00:26:30,860
+المقصود اللي في دماغك والثانيه تاكره بالعالمين
+
+310
+00:26:30,860 --> 00:26:33,980
+وحده اللي بيعرفوه أنا بالنسبة لي وغيري من المدرسين
+
+311
+00:26:33,980 --> 00:26:40,640
+اللي علاقة بليش بالمكتوب على وردك والله
+
+312
+00:26:40,640 --> 00:26:43,720
+صدقت اليوم اللي جينا ماتحاسب anyway تعالى نشوف
+
+313
+00:26:43,720 --> 00:26:47,900
+المجموعة اللي بعدها R of X X او ال absolute value
+
+314
+00:26:47,900 --> 00:26:50,080
+لل X تساوي X
+
+315
+00:26:53,270 --> 00:26:59,450
+ايوة، مين اللي بحكيها انا؟ الـ Z الـ X الموجبة، كل
+
+316
+00:26:59,450 --> 00:27:05,250
+العراسة الـ
+
+317
+00:27:05,250 --> 00:27:09,750
+Z الموجبة فقط، عارف ليش؟ ايوة، لإن هو إيش قاعد
+
+318
+00:27:09,750 --> 00:27:15,570
+بيقولني؟ بيقوللي ال absolute تساوي القيمة، بس ال
+
+319
+00:27:15,570 --> 00:27:20,840
+absolute لسالب واحد لا تساوي سالب واحدتساوم الواحد
+
+320
+00:27:20,840 --> 00:27:25,440
+وبالتالي أنا جاعة بتكلم على القيم الموجرة فقط ال Z
+
+321
+00:27:25,440 --> 00:27:28,020
+plus بتكلم على ال Z plus
+
+322
+00:27:37,650 --> 00:27:41,350
+لاحظ فعليا هذه الـ predicate function مع ال domain
+
+323
+00:27:41,350 --> 00:27:45,650
+مثلت بالنسبة ليش؟ عبارة عن مجموعات .. عبارة عن
+
+324
+00:27:45,650 --> 00:27:49,250
+مجموعات وبهك يكون ال section الأول من الشابتر
+
+325
+00:27:49,250 --> 00:27:53,930
+الخلص الشابتر اللي خلص لأ يا حبيبي لسه الشابتر
+
+326
+00:27:53,930 --> 00:27:57,030
+الأول طيب
+
+327
+00:27:57,420 --> 00:28:00,480
+ننتقل لسكتشن التاني اللي هو الـ set operations
+
+328
+00:28:00,480 --> 00:28:05,380
+العمليات على المجموعات العمليات على المجموعات كل
+
+329
+00:28:05,380 --> 00:28:09,460
+المحاضرة السابقة كانت بنعرف على أيه الشباب؟ بنعرف
+
+330
+00:28:09,460 --> 00:28:12,740
+المجموعة شو صفاتها؟ إيش يعني subset؟ إيش يعني
+
+331
+00:28:12,740 --> 00:28:17,760
+Cartesian؟ إيش power set؟ إلى آخرين الآن بدنا
+
+332
+00:28:17,760 --> 00:28:22,930
+نتكلم على العمليات على المجموعاتلما أتكلم على
+
+333
+00:28:22,930 --> 00:28:25,250
+العمليات على مجموعات شغلات بسيطة أقولكوا بتعرفوها
+
+334
+00:28:25,250 --> 00:28:30,350
+الاتحاد والتقاط أو المكمل أو الاختلاف زمان عنهم
+
+335
+00:28:30,350 --> 00:28:34,290
+هلأ انت بتتعرف عليهم وشوف انت ايش بتعرف منهم طيب
+
+336
+00:28:34,290 --> 00:28:41,690
+لما أنا بتكلم على الاتحاد ال union الاتحاد اتحاد
+
+337
+00:28:41,690 --> 00:28:48,150
+مجموعتين ينتج عنه مجموعة جديدة هيرنز الاتحاد A
+
+338
+00:28:48,150 --> 00:28:56,010
+union B يساويال X حيث X تنتمي إلى ال A أو ال X
+
+339
+00:28:56,010 --> 00:29:01,290
+تنتمي إلى ال B لو أنا أجيت هنا على السريع قولتلك A
+
+340
+00:29:01,290 --> 00:29:11,650
+بدأ تساوي واحد و اتنين و تلاتة وال B اتنين
+
+341
+00:29:11,650 --> 00:29:16,550
+و تلاتة واربع A
+
+342
+00:29:19,350 --> 00:29:24,910
+اتحاد الـ B يساوي المجموعة اول حاجة اول حاجة بدك
+
+343
+00:29:24,910 --> 00:29:29,950
+تفهم ان هنا شرط متى الشرط ده بيكون true لو كان
+
+344
+00:29:29,950 --> 00:29:32,690
+واحدة منهم على الأقل true طب لو كانت اتين اتين
+
+345
+00:29:32,690 --> 00:29:37,310
+true X تنتمي الى A معناته ان انت مغمض يا صاحبي و
+
+346
+00:29:37,310 --> 00:29:40,190
+تروح تقولي واحد و اتنين و تلاتة اللي هم عناصر ال A
+
+347
+00:29:40,190 --> 00:29:46,570
+أصبت؟ بعد هيك بتروح لعناصر ال B التنين موجودة؟
+
+348
+00:29:47,400 --> 00:29:50,580
+موجودة مافيش دي اكتبها مرة تانية التلاتة موجودة
+
+349
+00:29:50,580 --> 00:29:56,500
+مافيش دي اكتبها مرة تانية الأربعة خلصنا معينة هاي
+
+350
+00:29:56,500 --> 00:30:03,380
+الاتحاد كل العناصر احمد
+
+351
+00:30:03,380 --> 00:30:05,940
+بيقول ليش محطينا and تعالى نشوف ال and ايش بده نتج
+
+352
+00:30:05,940 --> 00:30:10,740
+يا احمد متى بيكون ال and true لما كل الشرقين هدول
+
+353
+00:30:10,740 --> 00:30:17,240
+متحققين صح نجي للواحدالواحد تنتمي الى a true تنتمي
+
+354
+00:30:17,240 --> 00:30:20,980
+الى b false true and false false ميّر الواحد
+
+355
+00:30:20,980 --> 00:30:26,100
+التاني تنتمي الى ال a true تاني تنتمي الى ال b
+
+356
+00:30:26,100 --> 00:30:32,080
+true معناته اتنين صارت التقاطة تلاتة تنتمي الى ال
+
+357
+00:30:32,080 --> 00:30:39,240
+a true تنتمي الى ال b هي تلاتة الأربعة لا تنتمي
+
+358
+00:30:39,240 --> 00:30:43,480
+الى ال a false andالـ X تنتمي إلى الـ B true أو
+
+359
+00:30:43,480 --> 00:30:44,700
+false؟ لا أعرف، لا أعرف، لا أعرف، لا أعرف، لا
+
+360
+00:30:44,700 --> 00:30:45,500
+أعرف، لا أعرف، لا أعرف، لا أعرف، لا أعرف، لا أعرف،
+
+361
+00:30:45,500 --> 00:30:45,800
+لا أعرف، لا أعرف، لا أعرف، لا أعرف، لا أعرف، لا
+
+362
+00:30:45,800 --> 00:30:46,640
+أعرف، لا أعرف، لا أعرف، لا أعرف، لا أعرف، لا أعرف،
+
+363
+00:30:46,640 --> 00:30:46,660
+لا أعرف، لا أعرف، لا أعرف، لا أعرف، لا أعرف، لا
+
+364
+00:30:46,660 --> 00:30:49,900
+أعرف، لا أعرف، لا أعرف، لا أعرف، لا أعرف، لا أعرف،
+
+365
+00:30:49,900 --> 00:30:58,860
+لا أعرف، لا أعرف، لا أعرف، لا أعرف، لا أعرف، لا
+
+366
+00:30:58,860 --> 00:31:05,960
+أعرف، لا أعرف، لا أعرف،
+
+367
+00:31:05,960 --> 00:31:16,680
+لا أعرف، لا أعرفواحد تمتم إلى الـA true واحد تمتم
+
+368
+00:31:16,680 --> 00:31:20,660
+إلى الـB false true or false true معاتر واحد من
+
+369
+00:31:20,660 --> 00:31:26,100
+ضمن العناصر تنين تمتم إلى الـA true تنين تمتم إلى
+
+370
+00:31:26,100 --> 00:31:31,720
+الـB true true and true true تلاتة زي التنين بنجر
+
+371
+00:31:31,720 --> 00:31:38,830
+الأربعة الأربعة تمتم إلى الـA falseأو أربعة تنتمي
+
+372
+00:31:38,830 --> 00:31:43,270
+إلى الـA إلى الـB؟ true fourth or true؟ أربعة
+
+373
+00:31:43,270 --> 00:31:48,690
+تمام؟ وبالتالي هينا هيك خلصنا شوفت عمليتين خلال
+
+374
+00:31:48,690 --> 00:31:54,470
+one slide اتحاد و تقعبة أجازك
+
+375
+00:31:54,470 --> 00:31:58,670
+عشان اللي لفوق؟ كويس عارف إذا كانت تقصد هيك كويس
+
+376
+00:31:58,670 --> 00:32:02,510
+في ال definition على الأقل تقدر تتذكر هي all and
+
+377
+00:32:02,510 --> 00:32:07,190
+الإشارة لفوق لفوق يعني خلصنافيه .. فيه .. فيه
+
+378
+00:32:07,190 --> 00:32:10,950
+logic في الموال تمام
+
+379
+00:32:10,950 --> 00:32:16,270
+و خلصنا من التقاطة والأولى تحت أكيد ما خلصنا عن
+
+380
+00:32:16,270 --> 00:32:20,030
+نفس الموال آه الأولى الشباب لو كانوا على أصل
+
+381
+00:32:20,030 --> 00:32:25,150
+المجموعتين مختلفين تماما التقاطة بينهم يساوي فاي
+
+382
+00:32:25,150 --> 00:32:32,460
+يعني لو أنا أجيت قلت ال B تساويأربعة و خمسة و ستة
+
+383
+00:32:32,460 --> 00:32:36,480
+حسب ال definition تبع الاتحاد تصير في اني واحد
+
+384
+00:32:36,480 --> 00:32:43,640
+اتنين تلاتة اربع خمسة ستة في التقاطع هيكون فاي
+
+385
+00:32:43,640 --> 00:32:50,460
+التقاطع ال B يساوي فاين وبنقول عنهم disjoint sets
+
+386
+00:32:50,460 --> 00:32:57,720
+بنقول عنهم disjoint sets مجموعات غير متداخلة أو
+
+387
+00:32:57,720 --> 00:32:58,520
+غير متقاطعة
+
+388
+00:33:04,210 --> 00:33:08,750
+طيب ال difference الفرق لما بتكلم عن ال difference
+
+389
+00:33:08,750 --> 00:33:15,270
+بتكلم على الفرق بين علاصر المجموعتين وعندي زي ما
+
+390
+00:33:15,270 --> 00:33:19,110
+احنا شوفنا شباب سابقا التباقط اللي عفوا انتوا ال
+
+391
+00:33:19,110 --> 00:33:23,790
+and و ال or عمليات إبدالية صح ولا لأ يعني a and ال
+
+392
+00:33:23,790 --> 00:33:29,400
+b تساوي b and ال aالاتحاد والتقاطع من العمليات
+
+393
+00:33:29,400 --> 00:33:33,620
+الإبدالية، لكن الـDifference هام؟ لأ، لما أنا باجب
+
+394
+00:33:33,620 --> 00:33:38,600
+أقول الـDifference بين مجموعتين A وB، بتكلم على
+
+395
+00:33:38,600 --> 00:33:44,100
+الـElement اللي موجودة في Aومش موجودة في B يعني
+
+396
+00:33:44,100 --> 00:33:48,780
+بنجوسين بتكلم على العناصر المميزة لل A هذي لما
+
+397
+00:33:48,780 --> 00:33:53,200
+بقول مين ايه ال difference ال B او A نقص ال B لو
+
+398
+00:33:53,200 --> 00:33:58,480
+عكسنا الصورة B نقص ال A بتكلم على العناصر المميزة
+
+399
+00:33:58,480 --> 00:34:02,440
+لل B طبعا في الرسم اللي موجودة انها في ال Venn
+
+400
+00:34:02,440 --> 00:34:06,780
+Diagram اللي قدامنا واضح لو انا في عندي مشبوطين A
+
+401
+00:34:06,780 --> 00:34:11,810
+وBهذه العناصر المشتركة اللي جوا التقاطة و لا لأ
+
+402
+00:34:11,810 --> 00:34:16,610
+يعني لو انا افترض انه هنا A و هنا B و هنا C ال A
+
+403
+00:34:16,610 --> 00:34:23,310
+بتحتوي على A و B و ال B بتحتوي على B و C ال ال
+
+404
+00:34:23,310 --> 00:34:28,770
+مبادشي بقول ال A difference ال B A نقص ال B حسب ال
+
+405
+00:34:28,770 --> 00:34:35,050
+definition ان ال X تمتمي إلى A and ال X لا تمتمي
+
+406
+00:34:35,050 --> 00:34:39,260
+إلى B هذا الكلام فقط موجود معنينمع الـ A small
+
+407
+00:34:39,260 --> 00:34:42,800
+اللي هو العنصر اللي أنا كتبتهان وبالتالي لو أنا
+
+408
+00:34:42,800 --> 00:34:48,260
+قلت B ناقص ال A أو difference ال A العنصر اللي
+
+409
+00:34:48,260 --> 00:34:53,600
+موجود في B وغير موجود في ال A اللي هي ال C small
+
+410
+00:34:53,600 --> 00:34:57,620
+وبالتالي هاي اللي هي مجموعتين واللي احنا بنطلع منه
+
+411
+00:34:57,620 --> 00:35:01,560
+الآن ان ال A ناقص ال B او ال difference A
+
+412
+00:35:01,560 --> 00:35:05,800
+difference ال B لا يساوي B difference ال A او B
+
+413
+00:35:05,800 --> 00:35:06,960
+ناقص ال A
+
+414
+00:35:14,620 --> 00:35:20,120
+الـ Compliment المكملة ايش المكملة؟ هو المجموعة
+
+415
+00:35:20,120 --> 00:35:25,040
+المكملة؟ هي عبارة عن الـ Universal Set اللي بتمثل
+
+416
+00:35:25,040 --> 00:35:29,040
+بجيتي المجموعة اللي عندها لو انا اجيت قولتلك الـ A
+
+417
+00:35:29,040 --> 00:35:36,840
+تساوي واحد واثنين وتلاتة واربعة و سكتت يعني بتكلم
+
+418
+00:35:36,840 --> 00:35:40,920
+على مين يا شباب؟ بتكلم على أرقام واحد واثنين
+
+419
+00:35:40,920 --> 00:35:45,730
+وتلاتة واربعةما هي المجموعة الأكبر الـ Universal
+
+420
+00:35:45,730 --> 00:35:50,070
+تبعتها؟ إما بتكلم عن الـ Natural number، بتكلم عن
+
+421
+00:35:50,070 --> 00:35:53,470
+الـ Z، بتكلم عن الـ R، مظهر ولا لأ؟ الـ Complement
+
+422
+00:35:53,470 --> 00:35:59,510
+هي عبارة عن المجموعة هذه ماقص الأربعة هذول الـ
+
+423
+00:35:59,510 --> 00:36:03,930
+Complement أو المكملة هي عبارة عن المجموعة الكبيرة
+
+424
+00:36:03,930 --> 00:36:07,650
+اللي هنسميها اليوم الـ Universal set واللي غالبا
+
+425
+00:36:07,650 --> 00:36:12,910
+هتكون فهامة من ضمن السياق ما هذا المجموعةالموجودة
+
+426
+00:36:12,910 --> 00:36:16,270
+عندى هنا اجيب لك مثال لو انا جيت قلتلك مثال اخر بي
+
+427
+00:36:16,270 --> 00:36:23,430
+تساوي A وB وC الـ B كمجموعة تساوي المجموعة اللى
+
+428
+00:36:23,430 --> 00:36:28,330
+بتحتوي على حروف الأبجادية A وB وC مين المكملة
+
+429
+00:36:28,330 --> 00:36:35,390
+تبعتها؟ مين المكملة تبعتها؟ باقي حروف الأبجادية من
+
+430
+00:36:35,390 --> 00:36:41,550
+ورا نتكلم ما جيبته افهمته من السياق فما دي تساوي؟A
+
+431
+00:36:41,550 --> 00:36:47,450
+,B,C,D و E و F و
+
+432
+00:36:47,450 --> 00:36:52,710
+هكذا تمام؟ وبالتالي أنا بصير أتكلم على مجموعة
+
+433
+00:36:52,710 --> 00:37:00,350
+مكملة بأتكلم على مجموعة مكملة والمشكلة
+
+434
+00:37:00,350 --> 00:37:05,820
+في الموضوع .. والمشكلة في الموضوعإذا كنت بتتكلم عن
+
+435
+00:37:05,820 --> 00:37:08,980
+الـ integer أو عفوا على ال number الـ number اللي
+
+436
+00:37:08,980 --> 00:37:13,680
+بتكون أكبر أو تساوي أربعة أو أكبر من تلاتة صح؟ طيب
+
+437
+00:37:13,680 --> 00:37:19,640
+لو كنت بتتكلم على real number معناته أقل و أكبر و
+
+438
+00:37:19,640 --> 00:37:22,760
+اللي بينهم كمان بين الواحد والتنين و بين التلاتة
+
+439
+00:37:22,760 --> 00:37:27,740
+الكسور فانت بتتعرف فيها أن القيمة مش موجودة
+
+440
+00:37:29,300 --> 00:37:32,580
+وبالتالي المكملة هي عبارة عن ال X تنتمي لل
+
+441
+00:37:32,580 --> 00:37:39,180
+universal set وال X لا تنتمي إلى ال A بقول ال U
+
+442
+00:37:39,180 --> 00:37:43,580
+لاحظ حدد ليها بشكل واضح لأن بدون ما تعرف انت ال
+
+443
+00:37:43,580 --> 00:37:48,620
+universal set مش هتقدر تتكلم عليك مكملة is
+
+444
+00:37:48,620 --> 00:37:54,420
+positive integer less than 100 هي ال U تبعتنا
+
+445
+00:37:54,420 --> 00:37:56,360
+حصرليها
+
+446
+00:37:59,520 --> 00:38:10,060
+What is the complement of X أكبر من 70؟عناصر
+
+447
+00:38:10,060 --> 00:38:16,360
+المجموعة A هي الـA جلبك الـA الـX والـX أكبر من 70
+
+448
+00:38:16,360 --> 00:38:24,960
+يعني الـA الـA الـA 71 72 73 لحد المية
+
+449
+00:38:27,790 --> 00:38:42,850
+الان بقول ياتر مكملة مكملة
+
+450
+00:38:42,850 --> 00:38:48,750
+مكملة بدي هيقولك what is the complement of مكملة
+
+451
+00:38:48,750 --> 00:38:57,720
+ال ايه من صفر لحد سبعيناللي هي بين قسام الـ
+
+452
+00:38:57,720 --> 00:39:02,160
+universal set المية من صفر لمية بدنا نشيل منهم
+
+453
+00:39:02,160 --> 00:39:06,000
+العناصر الأكبر من سبعين اللي هم واحد و سبعين و
+
+454
+00:39:06,000 --> 00:39:13,180
+اتنين و سبعين الاخرين هاي
+
+455
+00:39:13,180 --> 00:39:19,400
+مثال تاني لو انا اجير قلتلك ان ال A هي عبارة من ال
+
+456
+00:39:19,400 --> 00:39:24,230
+D لل F من ال D لل Z عفواهذه الـ universal .. و ال
+
+457
+00:39:24,230 --> 00:39:28,590
+universal set كل ال alphabetical set حروف الأبجدية
+
+458
+00:39:28,590 --> 00:39:37,290
+الإنجليزية ال complement ABC الحروف النقصة لأن
+
+459
+00:39:37,290 --> 00:39:39,630
+عليك بتصير .. بتصير كل ال alphabetical اللي هم ال
+
+460
+00:39:39,630 --> 00:39:45,700
+26 حرف لأقصى دول مين بيضل؟ABC اللي هم ال
+
+461
+00:39:45,700 --> 00:39:50,280
+difference المكملة هي المكملة شباب تساوي ال
+
+462
+00:39:50,280 --> 00:39:54,300
+universal set نقص المجموعة نفسها بإيش بتختلف ال
+
+463
+00:39:54,300 --> 00:40:03,640
+universal set عن المجموعة Symmetric
+
+464
+00:40:03,640 --> 00:40:13,640
+difference Symmetric
+
+465
+00:40:13,640 --> 00:40:17,900
+differenceعندما أتكلم عن الـ Symmetric Difference
+
+466
+00:40:17,900 --> 00:40:25,940
+أتكلم عن مجموعة عناصرها عبارة عن اتحاد الاختلاف أو
+
+467
+00:40:25,940 --> 00:40:34,280
+عناصر الاختلاف بين المجموعتين بالعناصر
+
+468
+00:40:34,280 --> 00:40:38,640
+.. اتحاد العناصر المميز لكل مجموعةالـ Ed
+
+469
+00:40:38,640 --> 00:40:43,960
+Asymmetric Difference مع الـ B تساوي A minus الـ B
+
+470
+00:40:43,960 --> 00:40:50,380
+اتحاد B minus الـ A طيب لو أنا جيت قولت الـ A بدها
+
+471
+00:40:50,380 --> 00:40:54,920
+تساوي واحد واتنين وتلاتة وقلت ان الـ B بدها تساوي
+
+472
+00:40:54,920 --> 00:41:00,820
+اتنين وتلاتة واربعة Asymmetric Difference الـ B
+
+473
+00:41:00,820 --> 00:41:03,940
+الـ
+
+474
+00:41:03,940 --> 00:41:11,280
+A نقص الـ B ايش تساوي واحد واربعةا ناقص ال a بي
+
+475
+00:41:11,280 --> 00:41:16,200
+واحد اتحاد بي ناقص ال a اربع
+
+476
+00:41:24,770 --> 00:41:33,790
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+477
+00:41:33,790 --> 00:41:34,210
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+478
+00:41:34,210 --> 00:41:36,170
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+479
+00:41:36,170 --> 00:41:37,190
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+480
+00:41:37,190 --> 00:41:37,490
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+481
+00:41:37,490 --> 00:41:37,770
+لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ لأ
+
+482
+00:41:37,770 --> 00:41:42,570
+لأ لأ لأ لأ لأ لأ لأ لأ
+
+483
+00:41:42,570 --> 00:41:52,920
+لأ لأبينجوسين هي الفرق ما بين الاتحاد والتقاطق
+
+484
+00:41:52,920 --> 00:42:00,400
+ايش اتحادهم؟ واحد اتنين تلاتة اربعة هي اتحادهم
+
+485
+00:42:00,400 --> 00:42:09,480
+ناقص التقاطق اتنين و تلاتة بتصفي واحد واربعة نفس
+
+486
+00:42:09,480 --> 00:42:11,920
+المعنى واضحة الصورة هيك؟
+
+487
+00:42:14,890 --> 00:42:23,790
+عنا مجموعة من القوانين اللهم
+
+488
+00:42:23,790 --> 00:42:29,230
+علاقة بال logical اللي حنشوفناه سابقا و بمفاهمنا
+
+489
+00:42:29,230 --> 00:42:35,890
+للاتحاد و التقاطع و ال complement الان واحد اتحاد
+
+490
+00:42:35,890 --> 00:42:43,590
+و زي مجال العرعير or تقاطع and complement
+
+491
+00:42:45,670 --> 00:42:52,290
+نفي تنتمي إلى A ولا تنتمي إلى B مظلوك ولا لأ؟ هو
+
+492
+00:42:52,290 --> 00:42:55,730
+ال difference في الآخر هدولة كانت في عندي .. لما
+
+493
+00:42:55,730 --> 00:42:58,830
+اتكلمنا عن ال logic قدرنا نassemble منهم مجموعة من
+
+494
+00:42:58,830 --> 00:43:03,250
+القوانين هتلاقي ان مجموعة القوانين هي تقريبا نفسها
+
+495
+00:43:03,250 --> 00:43:08,670
+من خلال ال set operations اللي عندي A اتحاد الفاي
+
+496
+00:43:08,670 --> 00:43:14,350
+A ليش؟ لأن المجموعة التانية فاضية مافيش فيها عناصر
+
+497
+00:43:15,910 --> 00:43:20,970
+A تقاطع ال universe set ال universal set A لأن
+
+498
+00:43:20,970 --> 00:43:26,310
+الآن إذا كانت ال A هيها اتنين
+
+499
+00:43:26,310 --> 00:43:32,890
+او بلاش A و B و C و دي هي تقولنا أن ال U هي كل
+
+500
+00:43:32,890 --> 00:43:43,470
+حروف الأبجادية A B لحد ال Z A تقاطع ال Uهيكون الـ
+
+501
+00:43:43,470 --> 00:43:47,550
+A لما في الـ A و الـ B و الـ C وهي بنسمي احنا ال
+
+502
+00:43:47,550 --> 00:43:51,290
+identity law
+
+503
+00:43:51,290 --> 00:43:57,390
+ايه اتحاد ال universal set؟
+
+504
+00:43:57,390 --> 00:44:03,150
+ايه تقاطع الفي؟ الـ Phi Demonation زي تماما زي ما
+
+505
+00:44:03,150 --> 00:44:11,220
+قلنا نقول A and False ايش كانت النتيجة؟ FalseA or
+
+506
+00:44:11,220 --> 00:44:16,080
+true true domination أو سيطرة للعناصر الموجودة
+
+507
+00:44:16,080 --> 00:44:23,220
+عندها A اتحاد ال A اتقاط ال A كل العناصر الموجودة
+
+508
+00:44:23,220 --> 00:44:30,080
+مكملة المكملة ترجع لنجموعها نفسها تماما نفس النفي
+
+509
+00:44:30,080 --> 00:44:35,340
+اثبات A اتحاد ال B يساوي B اتحاد ال A عملية
+
+510
+00:44:35,340 --> 00:44:37,460
+ابدالية و كذلك التقاطة
+
+511
+00:44:40,170 --> 00:44:48,710
+عملية التجميع A اتحاد B اتحاد C يساوي A اتحاد B
+
+512
+00:44:48,710 --> 00:44:55,530
+اتحاد C تساوي A اتحاد B جوا الجوس اتحاد C وكذلك
+
+513
+00:44:55,530 --> 00:44:58,470
+بتطبيقها على التقاقع تماما نفس الكلام اللي
+
+514
+00:44:58,470 --> 00:45:04,130
+بنتطبقها على ال end ال end is distributive توزيع
+
+515
+00:45:04,130 --> 00:45:11,390
+او خاصية التوزيع A تقاقع B اتحاد Cمعناته A تقاطع
+
+516
+00:45:11,390 --> 00:45:17,510
+ال B اتحاد A تقاطع ال C وتوزيع ال A للاتحاد A
+
+517
+00:45:17,510 --> 00:45:24,410
+اتحاد ال B تقاطع ال C تساوي A اتحاد ال B تقاطع A
+
+518
+00:45:24,410 --> 00:45:35,070
+اتحاد ال C دي مورج قال له صاحبنا مكملة الاتحاد
+
+519
+00:45:35,070 --> 00:45:38,270
+تساوي تقاطع المكملات
+
+520
+00:45:40,530 --> 00:45:48,510
+قريبا نفسها كمان مرة مكملة الاتحاد تساوي تقاطع
+
+521
+00:45:48,510 --> 00:45:58,030
+المكملات او لا تقاطع المكملات تساوي اتحاد المكملات
+
+522
+00:45:58,030 --> 00:46:01,110
+هشرح
+
+523
+00:46:01,110 --> 00:46:05,390
+حاضر مش هروح بالمثال كمان هروح اثبتلك اياها اصبر
+
+524
+00:46:05,390 --> 00:46:15,350
+ايه اتحاد ال B او ايه اتحادA تقاطع الـB A اتحاد A
+
+525
+00:46:15,350 --> 00:46:23,070
+تقاطع الـB يساوي الـA العاصل المشتركة بين A وB هي
+
+526
+00:46:23,070 --> 00:46:27,950
+جزء من الـA لما بروح بجمعهم مع الـA بظل الـA كلها
+
+527
+00:46:27,950 --> 00:46:34,830
+كذلك التقاطع A تقاطع اتحاد الـB هديني
+
+528
+00:46:34,830 --> 00:46:35,690
+الـA
+
+529
+00:46:38,210 --> 00:46:43,310
+A تقاطع او A اتحاد المكملة كل الـ universal set و
+
+530
+00:46:43,310 --> 00:46:51,990
+A التقاطع المكملة الاصل يساوي الـ Phi اثبت
+
+531
+00:46:51,990 --> 00:46:55,670
+ان
+
+532
+00:46:55,670 --> 00:47:04,350
+A اتحاد الـ B او مكملة A اتحاد الـ B تساوي A
+
+533
+00:47:04,350 --> 00:47:06,310
+او مكملة الـ A تقاطع
+
+534
+00:47:09,280 --> 00:47:13,820
+عشان هو ما شاء الله عليكم مكملة الـA تقاطع مكملة
+
+535
+00:47:13,820 --> 00:47:19,540
+الـB ممتاز البداية وين هتكون الشباب في الإثبات هان
+
+536
+00:47:19,540 --> 00:47:26,080
+الشمال بك اتحولها ايش بك اتحول فيها الان الشباب
+
+537
+00:47:26,080 --> 00:47:31,000
+هان الشغل اللي موجودة قدامك ال definition اذا انت
+
+538
+00:47:31,000 --> 00:47:35,800
+بتستحضر ال definition صحتمام؟ بتقدر تتكلم على او
+
+539
+00:47:35,800 --> 00:47:39,580
+تشتق القانون هذا لو انا سألتك ايش قانون الاتحاد
+
+540
+00:47:39,580 --> 00:47:47,000
+انا بقولك هيك A اتحاد ال B يساوي المجموعة
+
+541
+00:47:47,000 --> 00:47:57,760
+العناصرها X حيث X تنتمي الى A او X تنتمي الى B
+
+542
+00:47:57,760 --> 00:48:06,330
+مظبوط؟ طيبلما أنا بقول المكملة لهذا، إيش يعني؟
+
+543
+00:48:06,330 --> 00:48:13,250
+يعني أنا جاعت بأتكلم .. هاي شوف المربع بمثل ال
+
+544
+00:48:13,250 --> 00:48:19,090
+university تمام؟ وهي ال A وهي ال B إذا .. اتحاده
+
+545
+00:48:19,090 --> 00:48:22,730
+من كل المنطقة المضاللة باللون الرمادي، صح؟ من اللي
+
+546
+00:48:22,730 --> 00:48:25,690
+بيبقى اللي عندى؟ بيبقى للمساحة اللي برا أو
+
+547
+00:48:25,690 --> 00:48:29,490
+بينجوسين هي العناصر التي لا تتمن .. لا تمتم إلى
+
+548
+00:48:29,490 --> 00:48:31,790
+مين؟ إلى الاتحاد، صح؟
+
+549
+00:48:35,220 --> 00:48:40,280
+ماذا رأيكوا بهذه؟ منيحة؟ لا تقوليش على غلط بيه يا
+
+550
+00:48:40,280 --> 00:48:45,640
+صاحبي! الآن ال X ليست تاني، هي نفي! يعني ال X لا
+
+551
+00:48:45,640 --> 00:48:51,360
+تحقق الكلام هذا! الآن بدك تدخل النفي لجوة! بدك
+
+552
+00:48:51,360 --> 00:48:55,800
+تدخل النفي لجوة! وهذا يساوي! مانفعش تخليها برا!
+
+553
+00:48:58,780 --> 00:49:04,020
+عشان تتحول هذه لا تساوي او لا تنتمي and و لا تنتمي
+
+554
+00:49:04,020 --> 00:49:09,520
+تتكلم عن اتقاطه وبالتالي بروح بقول له هذه تساوي ال
+
+555
+00:49:09,520 --> 00:49:13,600
+X لأ بت كاشن في ال X بتكاشن في ال X ال X هي ال
+
+556
+00:49:13,600 --> 00:49:20,170
+element بدك تنفي صفتها او تغير في صفة ال Xالـ X أو
+
+557
+00:49:20,170 --> 00:49:25,390
+هيك نفي الـ X تنتمي إلى الـ A أو .. لسه خليها برا
+
+558
+00:49:25,390 --> 00:49:30,410
+X تنتمي إلى الـ B بس عشان نفصل كويسه الخطوات هي
+
+559
+00:49:30,410 --> 00:49:34,310
+دخلت النفي يعني أنت النفي بتعتمده مش للـ X لل
+
+560
+00:49:34,310 --> 00:49:37,390
+description تبعت الـ X لل condition اللي بيوصف الـ
+
+561
+00:49:37,390 --> 00:49:47,560
+X وعادة تساوي X .. الآن نفي الـ X لا تنتميالـ X لا
+
+562
+00:49:47,560 --> 00:49:56,100
+تنتمي إلى الـ A والـ O ستصبح and الـ X لا تنتمي
+
+563
+00:49:56,100 --> 00:50:03,240
+إلى الـ B تعالى نشوف المنطقة المظلة باللون الأزرق
+
+564
+00:50:03,240 --> 00:50:09,860
+أيش بتمثل هذه؟ المناطق التي لا تنتمي إلى الـ A وهي
+
+565
+00:50:09,860 --> 00:50:15,130
+بين جوسين مكملة الـ A بالنسبة لل universityمصبوط؟
+
+566
+00:50:15,130 --> 00:50:25,510
+مكملة الـA X حيث الـX تنتمي لمكملة الـA من أين أنا
+
+567
+00:50:25,510 --> 00:50:29,090
+جبتها؟ أما أننا اتفاقنا أن هذه الـA وهذه الـB وهذه
+
+568
+00:50:29,090 --> 00:50:33,950
+الـUniversity شيلنا الـB الآن هذه المنطقة المضللة
+
+569
+00:50:33,950 --> 00:50:38,350
+باللون الأزرق ماذا تتمثل لدي؟ تتمثل مكملة أو مكملة
+
+570
+00:50:38,350 --> 00:50:42,810
+الـA يعني العوصر اللي ينتمي إليها لا ينتمي إلى
+
+571
+00:50:42,810 --> 00:50:48,360
+الـAX لا تنتمي إلى الـ A معناته X تنتمي إلى المتمة
+
+572
+00:50:48,360 --> 00:50:56,140
+أو المكملة and نفس الكلام بالـ B معناته X تنتمي
+
+573
+00:50:56,140 --> 00:51:03,920
+لمكملة الـ B طيب صار في عندي X تنتمي and X تنتمي
+
+574
+00:51:03,920 --> 00:51:11,980
+معناته تساوي A مكملة الـ A تقاطع مكملة الـ B
+
+575
+00:51:14,960 --> 00:51:18,200
+أجيب الرسمة في الامتحان؟ لأ هديعش في الإصلاح علشان
+
+576
+00:51:18,200 --> 00:51:23,720
+تشرحلك إيها بس نفس
+
+577
+00:51:23,720 --> 00:51:32,780
+الكلام
+
+578
+00:51:32,780 --> 00:51:38,000
+على اتحاد أو على التقاطة شجل بالكلام
+
+579
+00:51:42,700 --> 00:51:47,620
+بظبط؟ هو فاهمين شكله بالكلام ايش
+
+580
+00:51:47,620 --> 00:51:53,160
+تعريف التقاطق؟ ان ال X تنتمي الى ال A و ال X تنتمي
+
+581
+00:51:53,160 --> 00:51:57,780
+الى ال B فالتقاطق نفس الكلام يا شباب اللي قاله ايش
+
+582
+00:51:57,780 --> 00:52:04,760
+معنى التقاطق؟ ان ال X .. نفس الكلام .. بدل .. لاحظ
+
+583
+00:52:04,760 --> 00:52:07,260
+هذا الشيء اللي قلتلك X لا تنتمي للتقاطق، شو هي
+
+584
+00:52:07,260 --> 00:52:13,530
+المكملة؟ تعريف التقاطق هيهنفي معناته X لا تنتمي
+
+585
+00:52:13,530 --> 00:52:18,130
+معناته صارت هذه اللي كانت مكملة و الأن صارت ارثر
+
+586
+00:52:18,130 --> 00:52:28,130
+بتكلم عن الاتحاد ايوه
+
+587
+00:52:28,130 --> 00:52:35,070
+نفس الكلام السابق ان X هيثو
+
+588
+00:52:35,070 --> 00:52:38,810
+مكملة ال X لا تنتمي
+
+589
+00:52:41,470 --> 00:52:50,390
+لل A تقاطع تقاطع تقاطع تقاطع تقاطع تقاطع تقاطع
+
+590
+00:52:50,390 --> 00:52:51,950
+تقاطع تقاطع تقاطع تقاطع تقاطع تقاطع تقاطع تقاطع
+
+591
+00:52:51,950 --> 00:52:54,030
+تقاطع تقاطع تقاطع تقاطع تقاطع تقاطع تقاطع تقاطع
+
+592
+00:52:54,030 --> 00:52:54,130
+تقاطع تقاطع تقاطع تقاطع تقاطع تقاطع تقاطع تقاطع
+
+593
+00:52:54,130 --> 00:52:54,150
+تقاطع تقاطع تقاطع تقاطع تقاطع تقاطع تقاطع تقاطع
+
+594
+00:52:54,150 --> 00:53:05,650
+تقاطع تقاطع تقاطع تقاطع تقاطع تقاطع تقاطع تقاطع ت
+
+595
+00:53:16,430 --> 00:53:21,290
+هو لازم كل مرة انا اجيب الجطر ل الجطرة جطرة؟ خلاص
+
+596
+00:53:21,290 --> 00:53:30,030
+يعني بقى كبرته اه؟ وبالتالي هيدي ال definition
+
+597
+00:53:30,030 --> 00:53:33,150
+اللي موجود عندي الآن إيش بقى اللي عندي أساوي؟ هقول
+
+598
+00:53:33,150 --> 00:53:39,350
+إن ال X هذه تنتمي للمكملة and ال X تنتمي لمكملة ال
+
+599
+00:53:39,350 --> 00:53:46,810
+B are ال X تنتمي لمكملة ال Cماذا أستطيع أن أفعل
+
+600
+00:53:46,810 --> 00:53:56,430
+الآن؟ وزّق الـ and سيصبح X تنتمي لمتممة الـ A and
+
+601
+00:53:56,430 --> 00:54:07,210
+X تنتمي لمتممة الـ B الـ X تنتمي لمتممة الـ A and
+
+602
+00:54:07,210 --> 00:54:11,190
+X تنتمي لمتممة الـ C
+
+603
+00:54:15,780 --> 00:54:24,600
+هذه ايش تقاطع المتممة a تقاطع ال b او تقاطع
+
+604
+00:54:24,600 --> 00:54:30,440
+المتممات مرة تانية اهو
+
+605
+00:54:30,440 --> 00:54:35,560
+انا مشيت عشان اعيدها يا ربي هذا الخطوة حوزية
+
+606
+00:54:35,560 --> 00:54:41,820
+logical هل في عندي and و في عندي or بوزعها
+
+607
+00:54:41,820 --> 00:54:51,760
+وتبقى ال or ما بينهموالقرش بتمثل الاتحاد،
+
+608
+00:54:51,760 --> 00:54:56,140
+بتمثل اتحاد،
+
+609
+00:54:56,140 --> 00:54:59,640
+ايش لما نوصلنا؟
+
+610
+00:54:59,640 --> 00:55:04,420
+نفس هذه، الان قولتلك دائما في الاثبوت حاول تشوف
+
+611
+00:55:04,420 --> 00:55:09,240
+هذه الصورة، هي هذه، يعني انت بتتوزع مين؟ بتتوزع
+
+612
+00:55:09,240 --> 00:55:09,900
+ليها؟
+
+613
+00:55:21,290 --> 00:55:26,750
+إذا بدك تشتغل طريقة تانية اشرح سوى بناء على دي
+
+614
+00:55:26,750 --> 00:55:33,290
+مورجان اللي اثبتناه قبل شوية تمام؟
+
+615
+00:55:33,290 --> 00:55:39,630
+مكملة اتحاد هي عبارة عن تقاطة المكملات تبدلها
+
+616
+00:55:39,630 --> 00:55:45,850
+تقاطة المكملات صارت عندك هاي؟ ولا لا؟مكملة التقاطة
+
+617
+00:55:45,850 --> 00:55:52,610
+اتحاد المكملات عملية
+
+618
+00:55:52,610 --> 00:56:00,130
+ابدالية وخلصنا اجيب هذي ليش الخربطة هذي طيب الان
+
+619
+00:56:00,130 --> 00:56:03,930
+كمان مرة شباب بتكاش تعتمد على ال definition تبع
+
+620
+00:56:04,640 --> 00:56:08,920
+اللي ينتمي ولا ينتمي اشتغل على قانون دي مورجان
+
+621
+00:56:08,920 --> 00:56:12,980
+احنا قبل شوية اثبتناها دي مورجان والله الان احنا
+
+622
+00:56:12,980 --> 00:56:17,860
+قلنا كانت تالي A تقاطع B مكملة A تقاطع B اتحاد
+
+623
+00:56:17,860 --> 00:56:21,320
+المتممات او المكملات فتعالى اطبق نفس الكلام الآن
+
+624
+00:56:21,320 --> 00:56:24,320
+هى فيه اندي مكملة وفيه اندي اتحاد معناته تصير فيه
+
+625
+00:56:24,320 --> 00:56:31,720
+اندي مكملة ال A تقاطع مكملة ال B تقاطع ال C اطبق
+
+626
+00:56:31,720 --> 00:56:37,350
+نفس الكلام علىالـ B تقاطع الـ C معته هذا الـ A
+
+627
+00:56:37,350 --> 00:56:41,590
+بيتساوي تقاطع افتح الجزء زي ما هو مكملة الـ B و
+
+628
+00:56:41,590 --> 00:56:45,430
+مكملة الـ C و بينهم اتحاد كان الله بالسر عليهم
+
+629
+00:56:45,430 --> 00:56:50,930
+العملية عملية إيش إبدالية بس هذه هتهام و خلصنا هذه
+
+630
+00:56:50,930 --> 00:56:54,350
+أسهل أه ماشي الحل بس هذه ماجتش اللي غير بعد ما
+
+631
+00:56:54,350 --> 00:56:58,330
+انتهاش أثبتت هذه أنا حاولت أسقط نفس ال definition
+
+632
+00:56:58,330 --> 00:57:00,890
+أو اعتمادنا على ال definition في التعريف
+
+633
+00:57:11,410 --> 00:57:15,230
+لو كان في عندي مجموعة من الـ sets، مجموعة من
+
+634
+00:57:15,230 --> 00:57:23,470
+المجموعات، عددهم M، A1, A2, A3، الاتحاد تبعهم كلهم
+
+635
+00:57:24,220 --> 00:57:28,000
+يساوي الأولى، اتحاد التانى، اتحاد التالتة، اتحاد
+
+636
+00:57:28,000 --> 00:57:31,060
+الرابع إلى آخرها، وكذلك التقاطع، هذه عملية
+
+637
+00:57:31,060 --> 00:57:34,480
+الـGeneralization، ليس أننا قبل قليل اتفقنا أن
+
+638
+00:57:34,480 --> 00:57:38,300
+عملية الاتحاد هي عبارة عن عملية تجميعية، المصدر
+
+639
+00:57:38,300 --> 00:57:41,980
+لأ، وعملية التقاطع عبارة عن عملية تجميعية، نفس
+
+640
+00:57:41,980 --> 00:57:45,200
+الكلامها، لو كان هنا في عندي أن من المجموعات و
+
+641
+00:57:45,200 --> 00:57:49,480
+أعمل بينهم اتحاد،معناته انا بتكلم اتحاد المجموعة
+
+642
+00:57:49,480 --> 00:57:52,660
+الأولى مع التانية والناتج مع المجموعة التالتة
+
+643
+00:57:52,660 --> 00:57:55,120
+والناتج مع المجموعة الرابع والناتج مع الخمسة
+
+644
+00:57:55,120 --> 00:57:58,480
+وهاكذا او بين جثين الأولى اتحاد التانى اتحاد
+
+645
+00:57:58,480 --> 00:58:02,000
+التالتة اتحاد الرابع الخمسة ستة إلى حد الأن بس
+
+646
+00:58:02,000 --> 00:58:07,660
+ونفس الكلام بنسقط وين على التقاطع اللى موجود عندنا
+
+647
+00:58:07,660 --> 00:58:12,480
+وخلص ال section التانى وبهك بنكون خلصنا من
+
+648
+00:58:12,480 --> 00:58:15,980
+محاضرتنا اليوم في اي سؤال تانى شباب الله تكونوا
+
+649
+00:58:15,980 --> 00:58:16,280
+عافية
+
diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/cWgs8V-VhjE.srt b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/cWgs8V-VhjE.srt
new file mode 100644
index 0000000000000000000000000000000000000000..1d5c1b8e104c798352f3574f4ef1e7530a6d9fce
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/cWgs8V-VhjE.srt
@@ -0,0 +1,1364 @@
+1
+00:00:20,670 --> 00:00:24,070
+الحمد لله والصلاة والسلام على رسول الله إن البست
+
+2
+00:00:24,070 --> 00:00:31,010
+واحد ما بتغيرش البست ثابت ما بتغيرش واحد على طب
+
+3
+00:00:31,010 --> 00:00:35,610
+عشان تكون هذه واحد لازم تكون الـ output واحد واحد
+
+4
+00:00:35,610 --> 00:00:41,830
+مظبط لازم يكون المقام واحد طيب معناته أنا هبقى
+
+5
+00:00:41,830 --> 00:00:45,550
+أقول واحد على n طيب هان واحد على n
+
+6
+00:00:51,060 --> 00:00:57,740
+ما زال الـ Definition تمام جيتها واحد
+
+7
+00:00:57,740 --> 00:01:02,440
+على n غلط واحد على n غلط معناته خلاص بدك تبدأ
+
+8
+00:01:02,440 --> 00:01:06,780
+تدور على Definition يتناسب مع الثلاثة اللي فوق مع
+
+9
+00:01:06,780 --> 00:01:10,200
+هذه واللي جابلها يعني الواحد على n الآن غلط
+
+10
+00:01:10,200 --> 00:01:17,540
+فاكرش فيه انتهى أمره طيب ما ريش ممكن أنا أساوي أنت
+
+11
+00:01:17,540 --> 00:01:30,260
+تبيع نقص اثنين؟ أيوة طيب لو أنا جيت قلت كذا
+
+12
+00:01:30,260 --> 00:01:35,500
+طيب طيب تعال .. تعال نشوف احنا علاقة الـ index هذا
+
+13
+00:01:35,500 --> 00:01:40,160
+بالـ value الأربعة الثلاثة أو الأربعة إيش علاقتها
+
+14
+00:01:40,160 --> 00:01:45,560
+بالثلاثة؟ ثلاثة زائد واحد، مظبوط؟ طيب والتمانية
+
+15
+00:01:45,560 --> 00:01:47,980
+مع الأربعة؟
+
+16
+00:01:52,570 --> 00:01:56,830
+زائد أربعة لاحظت وبالتالي أنا مش هقدر أجيب ستة عشر
+
+17
+00:01:56,830 --> 00:02:02,570
+تساوي خمسة زائد أحد عشر وما فيش علاقة ثابتة أجيبها
+
+18
+00:02:02,570 --> 00:02:06,770
+بشكل مباشر ممتاز معناته أن هذا برضه التفكير بالشكل
+
+19
+00:02:06,770 --> 00:02:11,250
+هذا مش هيصبق معايا فلو أنا بدأت أفكر بالقصص طلع
+
+20
+00:02:11,250 --> 00:02:18,250
+بالأساس هان واحد اثنين أربعة ثمانية يعني هيك بين
+
+21
+00:02:18,250 --> 00:02:28,030
+قصين اثنين قص صفر اثنين قص واحد-2-3-4 يعني أن الـ
+
+22
+00:02:28,030 --> 00:02:31,810
+Definition تبع هذا هيك هي المقام اللي موجود عندي
+
+23
+00:02:31,810 --> 00:02:38,250
+هذا 1 2 وصفر 2
+
+24
+00:02:38,250 --> 00:02:45,910
+4 8 16 32 وبدأت أمشي بالـ Sequence كيف ممكن
+
+25
+00:02:45,910 --> 00:02:46,870
+أسوي أنا فيك أمر
+
+26
+00:02:54,000 --> 00:02:58,640
+أروح .. لو أنا أديت هيك وقلت له واحد على اثنين أس
+
+27
+00:02:58,640 --> 00:03:05,860
+n ناقص واحد وين المشكلة في الموضوع؟ اثنين أو واحد
+
+28
+00:03:05,860 --> 00:03:13,200
+على اثنين أس n ناقص واحد واحد ناقص واحد صفر وهي
+
+29
+00:03:13,200 --> 00:03:18,840
+دي واحد
+
+30
+00:03:18,840 --> 00:03:21,220
+على اثنين أس اثنين ناقص واحد
+
+31
+00:03:24,950 --> 00:03:28,810
+يعني بدون مبدأ من الصفر هي مباشرة مع الواحد انحلت
+
+32
+00:03:28,810 --> 00:03:37,490
+المشكلة اثنين أس ثلاثة ناقص واحد هذه واحد على
+
+33
+00:03:37,490 --> 00:03:42,710
+ثمانية اللي هي واحد على اثنين أس أربعة ناقص واحد
+
+34
+00:03:42,710 --> 00:03:47,810
+اللي هي اثنين أس ثلاثة واحد على ستة عشر بيتساوي واحد
+
+35
+00:03:47,810 --> 00:03:53,190
+على اثنين أس خمسة ناقص واحد وبالتالي هذه الـ
+
+36
+00:03:53,190 --> 00:03:55,830
+Definition تبعي معناته أنا بقدر أقوله a<sub>n</sub> بدها
+
+37
+00:03:55,830 --> 00:04:03,510
+تساوي واحد على اثنين أس m ناقص واحد والـ m أكبر أو
+
+38
+00:04:03,510 --> 00:04:09,290
+تساوي الواحد هل ممكن أحصل على Definition ثاني؟
+
+39
+00:04:09,290 --> 00:04:14,210
+أغير الـ index صفر
+
+40
+00:04:14,210 --> 00:04:20,810
+واحد اثنين ثلاثة أربعة معناته هتحصل عليها بشكل
+
+41
+00:04:20,810 --> 00:04:27,310
+مباشر واحد على اثنين
+
+42
+00:04:27,310 --> 00:04:32,550
+والصفر واحد على اثنين أس واحد واحد على اثنين أس
+
+43
+00:04:32,550 --> 00:04:36,650
+اثنين واحد على اثنين أس ثلاثة واحد على اثنين أس
+
+44
+00:04:36,650 --> 00:04:40,710
+أربعة معناته الـ a<sub>n</sub> تبعتي هي تساوي واحد على اثنين
+
+45
+00:04:40,710 --> 00:04:46,330
+أس n والـ n أكبر أو تساوي صفر وهي two definitions
+
+46
+00:04:46,330 --> 00:04:51,750
+لنفس الـ sequence اللي موجود عندك الآن
+
+47
+00:04:53,170 --> 00:04:58,570
+أيه يكون أسرع لذهنك تصلّه؟ قضية كتير بس في الآخر
+
+48
+00:04:58,570 --> 00:05:02,190
+.. في الآخر كونه هي sequence الأصل أنك تبني ..
+
+49
+00:05:02,190 --> 00:05:07,370
+تقدر تبنيها سواء كانت على واحد أو على صفر طيب، لو
+
+50
+00:05:07,370 --> 00:05:12,010
+أنت حسيت بديت من صفر ولا جيت سكرّت معاك، إيش تساوي؟
+
+51
+00:05:12,010 --> 00:05:15,270
+هو بدل الـ index من واحد ولو بديت من واحد و
+
+52
+00:05:15,270 --> 00:05:19,150
+سكّرت تبدأ .. لا جيت الشجّتان مسكرة، معناته مخك بده
+
+53
+00:05:19,150 --> 00:05:23,580
+يعمله formatting من جديد وتبدأ تفكر بالمسألة بشكل
+
+54
+00:05:23,580 --> 00:05:32,140
+مختلف تماما طيب لأن
+
+55
+00:05:32,140 --> 00:05:41,180
+لو إجا جالي لو إجا جالي في sequence arithmetic
+
+56
+00:05:41,180 --> 00:05:47,000
+sequence مثل
+
+57
+00:05:47,000 --> 00:05:50,680
+الـ sequence اثنين
+
+58
+00:05:50,680 --> 00:05:52,280
+أربعة
+
+59
+00:05:54,290 --> 00:05:57,030
+ستة ثمانية عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة
+
+60
+00:05:57,030 --> 00:05:57,470
+عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة
+
+61
+00:05:57,470 --> 00:05:57,670
+عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة
+
+62
+00:05:57,670 --> 00:06:02,870
+عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة
+
+63
+00:06:02,870 --> 00:06:02,910
+عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة
+
+64
+00:06:02,910 --> 00:06:06,630
+عشرة
+
+65
+00:06:06,630 --> 00:06:12,890
+عشرة عشرة عشرة عشرة
+
+66
+00:06:19,350 --> 00:06:22,250
+1 زائد 2 تساوي 3 أو تساوي ثلاثة ثلاثة ثلاثة ثلاثة
+
+67
+00:06:22,250 --> 00:06:26,170
+ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة
+
+68
+00:06:26,170 --> 00:06:31,970
+ثلاثة تساوي ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة
+
+69
+00:06:31,970 --> 00:06:34,970
+ثلاثة ثلاثة ثلاثة ثلاثة تساوي ثلاثة ثلاثة ثلاثة
+
+70
+00:06:34,970 --> 00:06:38,090
+ثلاثة تساوي ثلاثة ثلاثة ثلاثة ثلاثة تساوي ثلاثة
+
+71
+00:06:38,090 --> 00:06:48,460
+ثلاثة ثلاثة ثلاثة تساوي ثلاثة ثلاثة ثلاثة الـ N لـ
+
+72
+00:06:48,460 --> 00:06:52,100
+Index هيمشي Sequence إما صفر واحد اثنين ثلاثة إلى
+
+73
+00:06:52,100 --> 00:06:55,900
+ما لا نهاية أو واحد اثنين ثلاثة أربعة إلى ما لا نهاية
+
+74
+00:06:55,900 --> 00:06:59,520
+أنت دائماً تطلع في مين؟ في الأرقام اللي عندك إيش
+
+75
+00:06:59,520 --> 00:07:04,080
+الصيغة اللي عندي أنا دائماً في فرق اثنين بقدر
+
+76
+00:07:04,080 --> 00:07:09,560
+أقوله a<sub>n</sub> بيتساوي اثنين في n والـ n أكبر أو تساوي
+
+77
+00:07:09,560 --> 00:07:13,380
+صفر بصبر
+
+78
+00:07:13,380 --> 00:07:18,210
+شوية أنا كتبت أكبر أو تساوي صفر اثنين في الصفر صفر
+
+79
+00:07:18,210 --> 00:07:21,530
+لا تنتمي للـ sequence اللي موجودة عندها المسؤولة
+
+80
+00:07:21,530 --> 00:07:26,930
+لأ معناته التعريف تبعي بده يبدأ من واحد واحد في
+
+81
+00:07:26,930 --> 00:07:30,850
+اثنين أو اثنين في واحد اثنين اثنين في اثنين أربعة
+
+82
+00:07:30,850 --> 00:07:33,910
+اثنين في ثلاثة ستة معناته الـ definition هيك تبعي
+
+83
+00:07:33,910 --> 00:07:40,870
+صحيح مائة في المائة ما في مشكلة حل
+
+84
+00:07:40,870 --> 00:07:43,830
+الـ index هل بتقدر تحصل عليه في الـ natural number
+
+85
+00:07:43,830 --> 00:07:47,940
+أو في الـ z أو ماشي أبقى ما ش هتظبط الكلام أحمد الآن،
+
+86
+00:07:47,940 --> 00:07:50,340
+إحنا بنتكلم على sequence مجموعة من الأرقام
+
+87
+00:07:50,340 --> 00:07:55,720
+المتتالية، متتالية، من اسمها متتالية، الآن تبدأ
+
+88
+00:07:55,720 --> 00:08:04,100
+إيش؟ بدك رقم هم، لأ اسميكوا إيش بقول، بقول لو أنا
+
+89
+00:08:04,100 --> 00:08:05,400
+هذه بدي أبدأها من صفر
+
+90
+00:08:14,420 --> 00:08:18,740
+مش بتظبط معايا؟ أنا جاي أقول لك بتظبط؟ مش عارف .. هي
+
+91
+00:08:18,740 --> 00:08:23,200
+.. في الصفر .. عند الصفر تمام لكن عند الواحد أَدَّتْنِي
+
+92
+00:08:23,200 --> 00:08:26,140
+خمسة مئة وخلاص الـ definition فيه غلط مش هتظبط
+
+93
+00:08:26,140 --> 00:08:32,280
+الحال هيك إلا لو رحت أضفت صفر وأصبحت الآن أكبر
+
+94
+00:08:32,280 --> 00:08:35,300
+أو تساوي صفر بالشكل هذا بتضل العملية عندي عَش ..
+
+95
+00:08:35,300 --> 00:08:38,580
+صحيحة بصير هذا أول element في الـ sequence وممكن أن
+
+96
+00:08:38,580 --> 00:08:43,170
+الـ sequence عندي هيك صحيحة مئة في المائة طيب طبعاً حتى
+
+97
+00:08:43,170 --> 00:08:47,370
+على الـ definition الجديد أو أنا أجيت وقلت لك بدي
+
+98
+00:08:47,370 --> 00:08:55,970
+حاصل جمع أول خمس حدود بدي حاصل جمع أول خمس حدود شو
+
+99
+00:08:55,970 --> 00:09:01,910
+بيبقى تساوي؟ هتقول إيه؟ صفر .. اثنين .. ستة ..
+
+100
+00:09:01,910 --> 00:09:08,650
+اثنا عشر .. عشرين .. هاي أول خمس حدود صح؟
+
+101
+00:09:08,650 --> 00:09:09,890
+ممتاز .. طيب أول عشرة
+
+102
+00:09:13,350 --> 00:09:20,050
+مش هتخلص هيك، بدك تصير أنك تتمد على الـ summation،
+
+103
+00:09:20,050 --> 00:09:22,810
+والـ summation في عندي مجموعة من القوانين بكل
+
+104
+00:09:22,810 --> 00:09:35,410
+بساطة، القانون هي مجموع أول n terms، عشرة عشرة أول
+
+105
+00:09:35,410 --> 00:09:44,590
+مئـة مئة زائد أو مضروبة في أول element الـ a لأن الـ
+
+106
+00:09:44,590 --> 00:09:49,170
+a<sub>0</sub> ممكن تعمل لخمة لبعضكوا عشان الـ index المقصود
+
+107
+00:09:49,170 --> 00:09:57,670
+في الـ a<sub>0</sub> أول element زائد a<sub>n</sub> العنصر مش الأخير
+
+108
+00:09:58,620 --> 00:10:03,500
+العنصر العاشر أو العنصر المئة أو العنصر الخمسين
+
+109
+00:10:03,500 --> 00:10:08,680
+وهناك تنتبه وتنتبه كويس إذا الـ index بدي معاك من
+
+110
+00:10:08,680 --> 00:10:14,260
+صفر معناته العنصر العاشر بدي يكون تسعة أُصِبت؟ الـ
+
+111
+00:10:14,260 --> 00:10:18,580
+index تبعه تسعة وهذه المقصدات بتنتبه لها وبالتالي
+
+112
+00:10:18,580 --> 00:10:25,120
+المقصود بالـ a<sub>n</sub> هو العنصر الـ n على اثنين فابتدعي
+
+113
+00:10:25,120 --> 00:10:31,420
+أني آجي أطبق الكلام هذا الـ summation من الـ k أو من
+
+114
+00:10:31,420 --> 00:10:38,000
+الـ i أو الـ k equal zero للـ n طبعاً هال من zero للـ
+
+115
+00:10:38,000 --> 00:10:43,960
+n كم element صار n زائد واحد ليش بعد اللانهائي
+
+116
+00:10:43,960 --> 00:10:48,830
+الـ k من zero للـ n n زائد واحد انتبه فممكن أنت
+
+117
+00:10:48,830 --> 00:10:52,730
+القانون كمان يربكك أكثر المجموع الـ summation يساوي
+
+118
+00:10:52,730 --> 00:11:01,730
+هذه تعال نسقط الكلام هذا هم هي أول خمس أعداد أول
+
+119
+00:11:01,730 --> 00:11:07,790
+خمس أعداد مجموع أول خمس أعداد يساوي خمسة مضروبة في
+
+120
+00:11:07,790 --> 00:11:13,530
+أول element صفر زائد العنصر الخامس واحد اثنين
+
+121
+00:11:13,530 --> 00:11:20,610
+ثلاثة أربعة خمسة ثمانية على اثنين خمسة في ثمانية
+
+122
+00:11:20,610 --> 00:11:26,890
+أربعين على اثنين تساوي عشرين تمام الشباب كمان مرة
+
+123
+00:11:26,890 --> 00:11:34,130
+برجع وبأعد ثاني الـ a<sub>m</sub> ها دي هي العنصر اللي في
+
+124
+00:11:34,130 --> 00:11:37,850
+المنزلة m يعني لما أنا باجي بقول لك العنصر الأول عشر
+
+125
+00:11:37,850 --> 00:11:42,590
+عناصر هان باجي صدق العنصر العاشر لأ لو الـ index
+
+126
+00:11:42,590 --> 00:11:47,350
+تبعك بادي من صفر معناته هو العنصر التاسع بادي من
+
+127
+00:11:47,350 --> 00:11:50,350
+مئة أو عفواً بادي من واحد معناته هو العنصر
+
+128
+00:11:50,350 --> 00:11:55,870
+العاشر نفسه نعم أنا
+
+129
+00:11:55,870 --> 00:12:01,450
+إحنا قديته هي في الآخر صفر واحد اثنين ثلاثة أربعة لو
+
+130
+00:12:01,450 --> 00:12:05,250
+أنا سألتك يا رامي مش رامي برضه لو أنا سألتك إيش
+
+131
+00:12:05,250 --> 00:12:09,490
+ثاني عنصر في الـ sequence ثاني عنصر في الـ sequence
+
+132
+00:12:09,490 --> 00:12:13,290
+اثنين ثاني عنصر في الـ sequence اثنين على الرغم إنه
+
+133
+00:12:13,290 --> 00:12:17,570
+الـ index تبعه واحد خامس عنصر في الـ sequence ثمانية
+
+134
+00:12:17,570 --> 00:12:22,490
+ليش؟ لأن الـ index تبعك أنت الآن عند لما بدأت تشتغل
+
+135
+00:12:22,490 --> 00:12:26,660
+أنسى الـ sequence هيديك الـ index شوية قلت لك ومن
+
+136
+00:12:26,660 --> 00:12:29,220
+أصل الخامس في الـ sequence مباشرة هتقولي ثمانية
+
+137
+00:12:29,220 --> 00:12:35,860
+جديش الـ index تبعه حسب الـ sequence تبعتك بدأت من
+
+138
+00:12:35,860 --> 00:12:40,660
+صفر ولا بدأت من واحد الـ index تبعه حسب الـ sequence
+
+139
+00:12:40,660 --> 00:12:48,720
+اللي عندك تمام طيب لو أجينا قلنا arithmetic
+
+140
+00:12:48,720 --> 00:12:56,300
+sequence واحد اثنين ثلاثة أربعة خمسة إلى ما لا
+
+141
+00:12:56,300 --> 00:13:03,300
+نهاية arithmetic sequence ولا لأ الـ a فيها تساوي
+
+142
+00:13:03,300 --> 00:13:14,800
+واحد والـ d تساوي واحد ولا لأ صحّيك بقدر طيب تعال
+
+143
+00:13:14,800 --> 00:13:22,980
+لو أنا سألتك a<sub>n</sub> إيش بتساوي؟ a زائد n في d يعني
+
+144
+00:13:22,980 --> 00:13:31,080
+العنصر الخامس a<sub>5</sub> ماذا يساوي؟ واحد زائد خمسة في
+
+145
+00:13:31,080 --> 00:13:37,380
+واحد جديش الجواب إيه؟ ستة الجواب ستة معناته الـ
+
+146
+00:13:37,380 --> 00:13:42,180
+index تبعي في الـ sequence هذه جديش؟ صفر الـ index
+
+147
+00:13:42,180 --> 00:13:48,400
+تبعي في الـ sequence هذه صفر كمان مرة حلّقتي بقول لك
+
+148
+00:13:48,400 --> 00:13:53,920
+ليش صفر؟ كمان مرة الآن الـ sequence arithmetic
+
+149
+00:13:53,920 --> 00:13:59,740
+sequence arithmetic sequence متتابعة حسابية متتابعة
+
+150
+00:13:59,740 --> 00:14:05,020
+حسابية ليش؟ الفرق بين كل عنصرين متتاليين ثابت لو
+
+151
+00:14:05,020 --> 00:14:09,320
+واحد وبالتالي هي الـ a equal واحد والـ d equal واحد
+
+152
+00:14:09,320 --> 00:14:17,400
+الآن كتب الصيغة العامة تبعتها a<sub>n</sub> بدها تساوي a زائد
+
+153
+00:14:17,400 --> 00:14:24,150
+n في d n في d هذه هي الـ Definition، اللي هي لو أنا
+
+154
+00:14:24,150 --> 00:14:28,850
+دي اتسألتك عن العنصر الخامس a<sub>5</sub>، مقصودها دي
+
+155
+00:14:28,850 --> 00:14:33,850
+إيش؟ لو هيك لو أنا اتسألتك عن العنصر الخامس الـ a
+
+156
+00:14:33,850 --> 00:14:38,790
+العنصر الخامس، مباشرة يعني هتقدر لذهني أن الـ n
+
+157
+00:14:38,790 --> 00:14:45,230
+equal خمسة، معناته هاي واحد زائد خمسة في الـ d اللي
+
+158
+00:14:45,230 --> 00:14:50,080
+هي الواحد وده تساوي ستة بس الستة فعلياً العنصر
+
+159
+00:14:50,080 --> 00:14:56,020
+السادس إلا إلا في حالة واحدة الـ index تبقى إيش؟ بدأ
+
+160
+00:14:56,020 --> 00:15:01,340
+من صفر الـ index بدأ من صفر تمام وبالتالي بدأت أنت
+
+161
+00:15:01,340 --> 00:15:05,800
+بتجي لها أمر هي الـ definition تبقى الـ sequence هيك
+
+162
+00:15:05,800 --> 00:15:10,620
+والجيل اللي قلت لك ممكن أخليها برا ناقص واحد نعم
+
+163
+00:15:10,620 --> 00:15:18,260
+ممكن أخليها بره ناقص واحد تحطهم بره ناقص واحد يعني a
+
+164
+00:15:18,260 --> 00:15:25,320
+زائد m في d الكل ناقص واحد طيب
+
+165
+00:15:25,320 --> 00:15:32,440
+في الآخر هي حسابية طيب الآن اللي أنا بدي أوصلك إياه
+
+166
+00:15:32,440 --> 00:15:34,900
+هي الـ sequence وهي المواضيع من الـ sequence اللي
+
+167
+00:15:34,900 --> 00:15:41,760
+عندك وبقول لك اجمع لي أول خمس حدود منها اجمع لي أول
+
+168
+00:15:41,760 --> 00:15:44,060
+خمس حدود خمسة في
+
+169
+00:15:47,150 --> 00:15:58,210
+الحد الأول إيه؟ زائد الحد الخامس على اثنين
+
+170
+00:15:58,210 --> 00:16:02,130
+هاي
+
+171
+00:16:02,130 --> 00:16:04,910
+قدام الـ sequence موجودة خلها أنا بودّيك على
+
+172
+00:16:04,910 --> 00:16:09,010
+مشكلة أعوص من هيك الآن وهذا يساوي خمسة في ستة
+
+173
+00:16:09,010 --> 00:16:14,470
+ثلاثين على اثنين يساوي خمسة عشر لو جمعتهم خمسة عشر
+
+174
+00:16:18,780 --> 00:16:27,240
+first five terms هذا summation of الـ first five
+
+175
+00:16:27,240 --> 00:16:34,720
+terms طيب لو أنا أجيت قلت لك الـ summation of ال
+
+223
+00:20:59,690 --> 00:21:04,430
+الصفوف وعدد الأعمدة، يعني المصفوفة اللي قدامي في
+
+224
+00:21:04,430 --> 00:21:11,850
+المثال هذا عبارة عن ثلاث صفوف بنجدّم
+
+225
+00:21:11,850 --> 00:21:15,970
+عدد الصفوف ثلاثة في اثنين، في عدد الصفوف أو في عدد
+
+226
+00:21:15,970 --> 00:21:21,090
+الأعمدة اثنين. طيب، بنقول عن المصفوفة square matrix
+
+227
+00:21:22,940 --> 00:21:27,600
+لما بيكون عدد الصفوف يساوي عدد الأعمدة، بيكون عنها
+
+228
+00:21:27,600 --> 00:21:32,600
+مصفوفة مربعة. يعني مثل المصفوفة هذه، هذه مصفوفة
+
+229
+00:21:32,600 --> 00:21:37,080
+اثنين في اثنين: واحد، اثنين، ثلاثة، أربعة. وهذه مصفوفة
+
+230
+00:21:37,080 --> 00:21:42,340
+مربعة: واحد، اثنين، ثلاثة، أربعة، خمسة، ستة، سبعة، ثمانية،
+
+231
+00:21:42,340 --> 00:21:46,640
+تسعة. الأولى اللي فوق هذه اثنين في اثنين، وهذه ثلاثة
+
+232
+00:21:46,640 --> 00:21:50,380
+في ثلاثة square matrix. لازم يكون فيها عدد الصفوف
+
+233
+00:21:50,380 --> 00:21:55,620
+يساوي عدد الأعمدة. متى بقول عن مصفوفتين متساويتين؟
+
+234
+00:21:55,620 --> 00:21:59,860
+لما يكون كل element، أول حاجة لازم يكون له نفس
+
+235
+00:21:59,860 --> 00:22:05,200
+الحجم، نفس الحجم، وكل عنصر يساوي عنصر المقابل في
+
+236
+00:22:05,200 --> 00:22:09,140
+المصفوفة اللي موجودة عنده. ما فيش له صورة عنصر مقابل
+
+237
+00:22:09,140 --> 00:22:15,000
+له الآن.
+
+238
+00:22:15,000 --> 00:22:21,320
+الـ A هذه حجمها M في N، الصف الأول، الصف الثاني، الصف
+
+239
+00:22:21,320 --> 00:22:28,280
+الأم، أي واحد. يعني لو قلت لك: العنصر صف، ولو كانت
+
+240
+00:22:28,280 --> 00:22:35,040
+M في واحد، بيقول عنها عمود. عشان
+
+241
+00:22:35,040 --> 00:22:40,480
+أجمع مصفوفتين، لازم يكونوا نفس الحجم. احنا قبل شوية
+
+242
+00:22:40,480 --> 00:22:44,180
+قلت: عشان أقارن بين مصفوفتين من ناحية التساوي، لازم
+
+243
+00:22:44,180 --> 00:22:47,220
+يكونوا نفس الحجم. عشان أجمع مصفوفتين لازم يكونوا نفس
+
+244
+00:22:47,220 --> 00:22:55,160
+الحجم. الآن العنصر الجديد اللي هو الـ C، Cij،
+
+245
+00:22:55,160 --> 00:22:59,780
+طبعًا ناتج مصفوفة من نفس حجم المصفوفتين السابقتين،
+
+246
+00:22:59,780 --> 00:23:10,680
+يساوي الـ element IJ زائد الـ element Bij. بالتالي
+
+247
+00:23:10,680 --> 00:23:14,900
+الأربعة هذه تساوي الثلاثة
+
+248
+00:23:16,130 --> 00:23:20,450
+زائد الواحد. من وين هذا الكلام جبته؟ أنا الأربعة هذه
+
+249
+00:23:20,450 --> 00:23:26,310
+هي عبارة عن C11، مصبوط؟ وهي عبارة عن حاصل جمع
+
+250
+00:23:26,310 --> 00:23:34,630
+العنصرين A11 زائد B11. الآن هذا الثلاثة، أو هذا
+
+251
+00:23:34,630 --> 00:23:44,430
+العنصر، النقص ثلاثة. هذه عبارة عن C23، C23 هي
+
+252
+00:23:44,430 --> 00:23:55,290
+عبارة عن حاصل جمع B23 زائد A23. وهكذا، لو كانوا
+
+253
+00:23:55,290 --> 00:23:59,230
+المصفوفتين أحجامهم مختلفة، عملية الجمع ما بتضبطش
+
+254
+00:23:59,230 --> 00:24:08,110
+معاهم. تمام؟ ننتقل لعملية الضرب. طبعًا الموضوع سهل،
+
+255
+00:24:08,110 --> 00:24:14,630
+لأنّكم أخذتوها في الثانوية وقبل التوجيهي كمان. فتبدأ
+
+256
+00:24:14,630 --> 00:24:19,650
+تتكلم على المصَفّات من هاشر. طيب، ما ليش في رياضية
+
+257
+00:24:19,650 --> 00:24:23,450
+الوسائط أنا الآن؟ لأنّ عشان أضرب مصفوفتين في بعض،
+
+258
+00:24:23,450 --> 00:24:28,710
+عشان أضرب مصفوفتين في بعض، لازم يكون عدد أعمدة
+
+259
+00:24:28,710 --> 00:24:33,750
+الأولى يساوي عدد صفوف الثانية. يعني الآن لو
+
+260
+00:24:33,750 --> 00:24:39,310
+المصفوفة الأولى A عندي اثنين في ثلاثة، الـ B اللي
+
+261
+00:24:39,310 --> 00:24:44,990
+بدي أضربها فيها لازم تكون ثلاثة في أي حاجة، مثلًا
+
+262
+00:24:44,990 --> 00:24:52,790
+ثلاثة في أربعة. المصفوفة الناتج C هتكون عبارة عن
+
+263
+00:24:52,790 --> 00:24:59,710
+اثنين في أربعة. عملية
+
+264
+00:24:59,710 --> 00:25:07,250
+الضرب كيف؟ بالتمام، بتاخد الصف، الصف الأول، تضرب في
+
+265
+00:25:07,250 --> 00:25:12,110
+العمود الأول. لأ، شوية بس عشان نركز شوية في الضرب و
+
+266
+00:25:12,110 --> 00:25:17,830
+نتذكره صح. المصفوفة الناتج، إيش المفروض تكون؟ اثنين
+
+267
+00:25:17,830 --> 00:25:24,450
+في أربعة. هذه في المثال اللي عندي هنا، يعني فيها أنا
+
+268
+00:25:24,450 --> 00:25:26,650
+عندي صفين وأربعة أعمدة.
+
+269
+00:25:36,150 --> 00:25:41,930
+الآن العنصر هذا اللي جاي في الصف الأول، مين بيحدده؟
+
+270
+00:25:41,930 --> 00:25:46,970
+الصف الأول من المصفوفة، اللي حددت الصفوف، هكذا، قُدّت
+
+271
+00:25:46,970 --> 00:25:53,770
+صفوف المصفوفة C من صفوف A، مظبوط؟ وبالتالي… لما
+
+272
+00:25:53,770 --> 00:25:58,010
+تاخد الصف الأول… لما تاخد الصف الأول من الـ A،
+
+273
+00:25:58,010 --> 00:26:04,670
+معناته أنّك بتتكلم على ناتج في الصف الأول لـ C، مصبوط؟
+
+274
+00:26:04,670 --> 00:26:09,670
+طب، الصف الأول فيه أكتر من عمود، مين اللي بيحدده؟
+
+275
+00:26:09,670 --> 00:26:15,710
+العمود اللي اخترته من B. يعني هيك الصف الأول في
+
+276
+00:26:15,710 --> 00:26:21,430
+العمود الأول، بيعطينا الـ element، الصف الأول، العمود
+
+277
+00:26:21,430 --> 00:26:26,490
+الأول في مين؟ في C. الصف الأول في العمود الثاني
+
+278
+00:26:26,490 --> 00:26:31,580
+بيعطينا الـ element الثاني في الصف الناتج. واضح كلام
+
+279
+00:26:31,580 --> 00:26:35,840
+اللي أنا بقوله؟ يعني كل ما بتمسك صف من الـ A، بيكون
+
+280
+00:26:35,840 --> 00:26:40,420
+مقابل له صف من الـ C في الناتج، مقابل له صف من الـ C.
+
+281
+00:26:40,420 --> 00:26:44,820
+بتاخد الصف وبتضرب في كل عمود وبتجمع العناصر
+
+282
+00:26:44,820 --> 00:26:48,240
+اللي ما بينهم. يعني، وكأني جاهز، بقول لك: جيب الصف
+
+283
+00:26:48,240 --> 00:26:56,540
+هذا، مثلًا واحد، صفر، أربعة. اضرب كل عنصر بين جماله، و
+
+284
+00:26:56,540 --> 00:26:57,140
+اجمعهم.
+
+285
+00:27:00,200 --> 00:27:04,700
+أربعة في اثنين زائد صفر في واحد زائد ثلاثة، أربعة
+
+286
+00:27:04,700 --> 00:27:10,460
+في ثلاثة، أربعة، عشرة. هي الـ element. الآن خذ الصف
+
+287
+00:27:10,460 --> 00:27:15,840
+الأول في العمود الثاني كمان عشان تجيب لي الأربعة.
+
+288
+00:27:15,840 --> 00:27:20,360
+واحد في أربعة، أربعة. صفر في واحد، وأربعة في صفر،
+
+289
+00:27:20,360 --> 00:27:26,620
+أربعة. الآن يا صاحبي، إذا بدكش تعبيها صفوف، ممكن
+
+290
+00:27:26,620 --> 00:27:33,350
+تعبيها أعمدة. ممكن تعبيها عمود عمود. كيف بقى تساوي؟
+
+291
+00:27:33,350 --> 00:27:40,070
+هذه الصف الأول في العمود الأول، الثاني، أربعة، عشرة.
+
+292
+00:27:40,070 --> 00:27:45,750
+لما تنزل، تاخد الصف الثاني في العمود الأول، فهيا
+
+293
+00:27:45,750 --> 00:27:48,230
+أنت بقى بتعبي القيمة الثانية في العمود الأول في
+
+294
+00:27:48,230 --> 00:27:53,130
+النتائج، هذه ثمانية. اللي بعده،
+
+295
+00:27:55,990 --> 00:28:01,190
+هي سبعة، وهكذا. أنت عبي صف صف، أريح لك، أو بطريقة
+
+296
+00:28:01,190 --> 00:28:05,370
+اللي بتشوفها مناسبة، تمام؟ بطريقة اللي أنت متعود
+
+297
+00:28:05,370 --> 00:28:09,050
+عليها، اشتغل الصف الأول في العمود الأول، الصف الأول
+
+298
+00:28:09,050 --> 00:28:11,570
+في العمود الثاني، الصف الأول في العمود الثالث، وكل
+
+299
+00:28:11,570 --> 00:28:15,510
+حاجة، ما تخلص الصف الأول في الناتج، بتبدل الصف، و
+
+300
+00:28:15,510 --> 00:28:18,470
+بتبدل الصف في الـ… في الـ A، وبالتالي الصف في الـ
+
+301
+00:28:18,470 --> 00:28:25,090
+result. الأمر مش صعب ولا لا؟ في مشكلة بقى؟ تمام.
+
+302
+00:28:25,280 --> 00:28:32,840
+الصف I في العمود J، الأصلي، بيديني الـ element IJ.
+
+303
+00:28:32,840 --> 00:28:40,760
+الصف I في العمود J، الأصلي، بيديني الـ element IJ، حسب
+
+304
+00:28:40,760 --> 00:28:45,340
+القانون الموجود عندي تبع الضرب. تمام؟ هل الـ BA يساوي
+
+305
+00:28:45,340 --> 00:28:48,700
+AB؟
+
+306
+00:28:48,700 --> 00:28:55,640
+A، بدها تساوي واحد، واثنين، ثلاثة، أربعة. والـ B تساوي
+
+307
+00:28:55,640 --> 00:29:00,800
+أربعة، اثنين، أو بلاش واحد.
+
+308
+00:29:00,800 --> 00:29:10,980
+واحد، اثنين، اثنين. افترض أنّ هذه A، وهذه B. A ضرب الـ B،
+
+309
+00:29:10,980 --> 00:29:17,620
+إيش تساوي شباب؟ صفر، الأول في العمود الأول، واحد في
+
+310
+00:29:17,620 --> 00:29:22,860
+واحد زائد اثنين في اثنين، خمسة، برضه
+
+311
+00:29:22,860 --> 00:29:31,270
+كمان خمسة. الآن ثلاثة في واحد زائد ثمانية، إحدى عشر.
+
+312
+00:29:31,270 --> 00:29:38,890
+إحدى عشر. بقى، بي في أي بي،
+
+313
+00:29:38,890 --> 00:29:46,310
+في A، مش هتساوي. هتاخد الصف الأول وتضربه في العمود
+
+314
+00:29:46,310 --> 00:29:54,420
+الأول، هي الصف الأول، وهي العمود الأول. واحد في واحد زائد واحد
+
+315
+00:29:54,420 --> 00:30:02,660
+في ثلاثة، أربعة. بمجرّد أنّك شوفت الأربعة مباشرة، AB لا
+
+316
+00:30:02,660 --> 00:30:11,280
+تساوي BA. ليش؟ لأنّنا اتفقنا في المساواة، كل element
+
+317
+00:30:11,280 --> 00:30:15,080
+بدّه يساوي الـ element المقابل له في نفس الـ position.
+
+318
+00:30:15,080 --> 00:30:18,260
+هي الأربعة لا تساوي الخمسة. بس تعالى خلينا نكمل.
+
+319
+00:30:18,850 --> 00:30:23,630
+اثنين، بتساوي الـ identity matrix. إذا الناتج A ضرب
+
+320
+00:30:23,630 --> 00:30:30,990
+الـ B، إذا A ضرب الـ B يساوي B ضرب الـ A، معناته A
+
+321
+00:30:30,990 --> 00:30:35,910
+تساوي الـ B. هذا الاحتمال الأول، أو الـ B هي عبارة عن
+
+322
+00:30:35,910 --> 00:30:40,210
+الـ identity matrix. ما هي الـ identity matrix؟ هي
+
+323
+00:30:40,210 --> 00:30:46,070
+عبارة عن matrix، مصفوفة الوحدة، اللي كل عناصرها أصفار،
+
+324
+00:30:46,070 --> 00:30:51,530
+ما عدا القطر الرئيسي تساوي واحد. ما عدا عناصر
+
+325
+00:30:51,530 --> 00:30:57,650
+القطر الرئيسي تساوي واحد. وبالتالي مصفوفة الوحدة، هذه
+
+326
+00:30:57,650 --> 00:31:03,090
+لو ضربتها في أي مصفوفة، هتطلع المصفوفة نفسها. يعني
+
+327
+00:31:03,090 --> 00:31:10,770
+لو أنا جيت قلت: هيفي عندي مصفوفة واحد، اثنين، ثلاثة،
+
+328
+00:31:11,620 --> 00:31:15,640
+أربعة، خمسة، ستة. مصفوفة الوحدة اللي ممكن أضرب فيها
+
+329
+00:31:15,640 --> 00:31:21,040
+أنا، لازم تكون، يا شباب، واحد،
+
+330
+00:31:21,040 --> 00:31:26,820
+صفر، صفر، صفر، واحد، صفر، صفر، صفر، واحد. ليش هذا الكلام؟
+
+331
+00:31:26,820 --> 00:31:30,000
+لأنّه لازم يكون هذه اثنين في ثلاثة، هذه لازم تكون
+
+332
+00:31:30,000 --> 00:31:34,980
+ثلاثة في اثنين على الأقل، مصبوط؟ وبالتالي ثلاثة في
+
+333
+00:31:34,980 --> 00:31:41,540
+ثلاثة. إيش الـ result اللي، المصفوفة اللي هتطلع؟ اثنين في
+
+334
+00:31:41,540 --> 00:31:47,420
+ثلاثة. الصف الأول في العمود الأول، الصف الأول في
+
+335
+00:31:47,420 --> 00:31:53,660
+العمود الأول، واحد، اثنين، ثلاثة. الصف الأول في العمود
+
+336
+00:31:53,660 --> 00:31:58,360
+الثالث، اثنين. الصف الأول في العمود الثالث، ثلاثة. بعد هيك
+
+337
+00:31:58,360 --> 00:32:02,320
+الصف الأول في العمود الثالث، أربعة، خمسة، ستة.
+
+338
+00:32:02,320 --> 00:32:05,820
+وبالتالي المصفوفة، لما تضربها في الـ identity matrix،
+
+339
+00:32:05,820 --> 00:32:10,040
+مصفوفة الوحدة، تطلع نفسها. وكأنّ الـ identity matrix
+
+340
+00:32:10,040 --> 00:32:14,720
+هي المحايد ضربي تبع المصفوفات، بس بجتمع حجمها دائمًا.
+
+341
+00:32:14,720 --> 00:32:22,280
+الـ Transpose، مدوّر المصفوفة، أو مجلوب المصفوفة. ما هو
+
+342
+00:32:22,280 --> 00:32:27,560
+الـ Transpose؟ بتبدّل… بتبدّل صفوف المصفوفة لأعمدة،
+
+343
+00:32:27,560 --> 00:32:34,900
+أو بتبدّل الأعمدة لصفوف. طيب، الشباب، خليكم سامعين، يا
+
+344
+00:32:34,900 --> 00:32:41,200
+هان. الآن في الـ Transpose. الآن لو أنا افترضت
+
+345
+00:32:41,200 --> 00:32:48,080
+المصفوفة A هي عبارة عن M في M، إيش الـ Transpose،
+
+346
+00:32:48,080 --> 00:32:57,190
+مدوّر المصفوفة هذه؟ ماذا سيكون؟ سيكون M في M، لأنّ أنت
+
+347
+00:32:57,190 --> 00:33:03,730
+بدّلت صفوف المصفوفة لأعمدة، والأعمدة لصفوف. طيب،
+
+348
+00:33:03,730 --> 00:33:07,430
+وبالتالي،
+
+349
+00:33:07,430 --> 00:33:12,130
+لو كان بالمثال هذا، عندنا هي A؟ واحد، اثنين، ثلاثة،
+
+350
+00:33:12,130 --> 00:33:17,130
+أربعة، خمسة، ستة. هي عبارة عن مصفوفة اثنين في ثلاثة. الـ
+
+351
+00:33:17,130 --> 00:33:22,070
+transpose تبعها، بتكون ثلاثة في اثنين. الشيء المهم،
+
+352
+00:33:22,070 --> 00:33:27,810
+عندي الصف الأول بيكون العمود الأول، الصف الثاني
+
+353
+00:33:27,810 --> 00:33:33,330
+بيكون العمود الثاني. وبالتالي، بداية الصف هتكون هي
+
+354
+00:33:33,330 --> 00:33:37,090
+نفسها بداية العمود، عشان ما تخربطيش في الترتيب اللي
+
+355
+00:33:37,090 --> 00:33:42,450
+عناصر اللي عندنا. حكينا
+
+356
+00:33:42,450 --> 00:33:47,240
+على المصفوفة لما تكون square، وكل العناد… اه، okay.
+
+357
+00:33:47,240 --> 00:33:52,580
+بقول عن المصفوفة symmetric، أو متماثلة، لما يكون كل
+
+358
+00:33:52,580 --> 00:34:01,400
+element aij يساوي aji. إيش يعني؟ المصفوفة المتماثلة،
+
+359
+00:34:01,400 --> 00:34:06,840
+هي مصفوفة مربعة. إيش يعني مربعة؟ عدد صفوفها يساوي
+
+360
+00:34:06,840 --> 00:34:10,880
+عدد الأعمدة اللي فيها. بقول عنها المصفوفة متماثلة،
+
+361
+00:34:10,880 --> 00:34:20,140
+لما يكون كل element ij بدّه يساوي aji. الآن هذا العنصر، هذا
+
+362
+00:34:20,140 --> 00:34:26,880
+جدّه الـ position تبعه. طبعًا احنا الآن متماثلة، يعني،
+
+363
+00:34:26,880 --> 00:34:29,740
+أي واحد واحد، ما هي نفسها أي واحد واحد. في شوية
+
+364
+00:34:29,740 --> 00:34:33,020
+مشكلة. يعني، سيبني من عناصر القطر الرئيسي، بتكلم عن
+
+365
+00:34:33,020 --> 00:34:41,700
+العناصر الثانية. أنا، لأنّ هذا الـ element E3E1، عشان
+
+366
+00:34:41,700 --> 00:34:54,000
+تكون متماثلة المصفوفة، لازم يكون يساوي E1E3، أو
+
+367
+00:34:54,000 --> 00:34:58,660
+بين جسيمن، لو جسمت من النص وطبّقت المثلثين على بعض، كل
+
+368
+00:34:58,660 --> 00:35:02,720
+element هيكون مطابق للـ element المجاور له. الشرط
+
+369
+00:35:02,720 --> 00:35:09,710
+كمان مرة: كل element AIJ يساوي A JI. بنقول عنها
+
+370
+00:35:09,710 --> 00:35:14,330
+symmetric. بنقول عن المصفوفة 01 matrix، لو كانت كلها
+
+371
+00:35:14,330 --> 00:35:22,690
+عناصرها 01، أو بنقول عليها binary 01. مع الـ 01، صارت
+
+372
+00:35:22,690 --> 00:35:26,810
+binary الـ matrix. احنا قبل شوية شفنا جمع وضرب،
+
+373
+00:35:26,810 --> 00:35:32,350
+مظبوط؟ شفنا جمع وضرب. هل هنشوف join و meet؟ الـ join،
+
+374
+00:35:32,350 --> 00:35:36,750
+بقصد فيها الـ R، والـ
+
+375
+00:35:36,750 --> 00:35:41,930
+meet، بقصد فيها… مش لحمة… ميت، لحمة، ياك يا فالح!
+
+376
+00:35:41,930 --> 00:35:52,150
+… MEAT، ما يعني…
+
+377
+00:35:52,150 --> 00:35:54,030
+إنتوا أُسُود، ما شاء الله عليكوا، وما تفطّروش اللي غير
+
+378
+00:35:54,030 --> 00:35:59,030
+لحمة. عشان هيك، دائمًا أنا مصحصح معايا. طيب… هذه
+
+379
+00:35:59,030 --> 00:36:05,130
+المصفوفتين… هذه المصفوفتين A و B، هذول Zero و
+
+380
+00:36:05,130 --> 00:36:13,960
+One. الآن بدي أعمل بين A و B join. A و B join، شبكة، تساوي
+
+381
+00:36:13,960 --> 00:36:20,540
+كل element مع المُقابل، كل element بتعمل الـ R مع
+
+382
+00:36:20,540 --> 00:36:25,960
+المُقابل له، كل
+
+383
+00:36:25,960 --> 00:36:29,620
+element مع المُقابل. بدل ما جمعنا، بدل الجمع، بدأنا
+
+384
+00:36:29,620 --> 00:36:30,300
+نستخدم الـ R.
+
+385
+00:36:33,470 --> 00:36:37,870
+لازم الآن يا شباب، لازم يكون المصفوفتين نفس الحجم،
+
+386
+00:36:37,870 --> 00:36:41,970
+عشان أعمل بينهم join. لازم، زي ما اتكلمنا على الجمع،
+
+387
+00:36:41,970 --> 00:36:46,070
+والضرب، تمامًا، نفس المواصفات، لازم تنطبق عندنا، نفس
+
+388
+00:36:46,070 --> 00:36:50,950
+الجمع. نفس الجمع، إذا أنا بتكلم على الـ and والـ or،
+
diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/cWgs8V-VhjE_postprocess.srt b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/cWgs8V-VhjE_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..0b835771ca48fe54f794f0a536cdb4986a0f9150
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/cWgs8V-VhjE_postprocess.srt
@@ -0,0 +1,1620 @@
+1
+00:00:20,670 --> 00:00:24,070
+لأ الحمد لله الصلاة والسلام على رسول الله ان البست
+
+2
+00:00:24,070 --> 00:00:31,010
+واحد ما بتغيرش البست ثابت ما بتغيرش واحد على طب
+
+3
+00:00:31,010 --> 00:00:35,610
+عشان تكون هذه واحد لازم تكون ال output واحد واحد
+
+4
+00:00:35,610 --> 00:00:41,830
+مظبط لازم يكون المقام واحد طيب معناته انا هبقى
+
+5
+00:00:41,830 --> 00:00:45,550
+اقول واحد على n طيب هان واحد على n
+
+6
+00:00:51,060 --> 00:00:57,740
+ما زال الـ Definition تمام جيتها واحد
+
+7
+00:00:57,740 --> 00:01:02,440
+على أن غلط واحد على أن غلط معناته خلاص بدك تبدأ
+
+8
+00:01:02,440 --> 00:01:06,780
+تدور على Definition يتناسب مع التلاتة اللي فوق مع
+
+9
+00:01:06,780 --> 00:01:10,200
+هذه و اللي جابلها يعني الواحد على أن الآن غلط
+
+10
+00:01:10,200 --> 00:01:17,540
+فاكرش فيه انتهى أمره طيب ماريش ممكن أنا أساوي أنت
+
+11
+00:01:17,540 --> 00:01:30,260
+تبيع نقص اتنين؟ أيوةطيب لو انا جيت جولت كداش؟
+
+12
+00:01:30,260 --> 00:01:35,500
+طيب طيب تعال .. تعالى نشوف احنا علاقة ال index هذا
+
+13
+00:01:35,500 --> 00:01:40,160
+بال value الأربعة التلاتة او الأربعة ايش علاقتها
+
+14
+00:01:40,160 --> 00:01:45,560
+بالتلاتة؟ تلاتة زائد واحد، مظبوط؟ طيب و التمانية
+
+15
+00:01:45,560 --> 00:01:47,980
+مع الأربعة؟
+
+16
+00:01:52,570 --> 00:01:56,830
+زائد أربعة لاحظت وبالتالي أنا مش هقدر أجيب ستاش
+
+17
+00:01:56,830 --> 00:02:02,570
+تساوي خمسة زائد أحداشر ومافيش علاقة ثابتة أجيبها
+
+18
+00:02:02,570 --> 00:02:06,770
+بشكل مباشر ممتاز معناته أن هذا برضه التفكير بالشكل
+
+19
+00:02:06,770 --> 00:02:11,250
+هذا مش هيصبق معايا فلو أنا بدأت أفكر بالقصص طلع
+
+20
+00:02:11,250 --> 00:02:18,250
+بالأساس هان واحد اتنين اربعة تمانية يعني هيك بين
+
+21
+00:02:18,250 --> 00:02:28,030
+قصين اتنين قص صفر اتنين قص واحد-2-3-4 يعني أن الـ
+
+22
+00:02:28,030 --> 00:02:31,810
+Definition تبع هذا هيك هي المقام اللي موجود عندي
+
+23
+00:02:31,810 --> 00:02:38,250
+هذا 1 2 وصفر 2
+
+24
+00:02:38,250 --> 00:02:45,910
+4 8 16 2 أُص و بدأت أمشي بالـSequence كيف ممكن
+
+25
+00:02:45,910 --> 00:02:46,870
+أسوي أنا فيك أمر
+
+26
+00:02:54,000 --> 00:02:58,640
+أروح .. لو أنا أديت هيك و قلتله واحد على اتنين أس
+
+27
+00:02:58,640 --> 00:03:05,860
+ان ناقص واحد وين المشكلة في الموضوع؟ اتنين او واحد
+
+28
+00:03:05,860 --> 00:03:13,200
+على اتنين أس ان ناقص واحد واحد ناقص واحد صفر وهي
+
+29
+00:03:13,200 --> 00:03:18,840
+دي واحد
+
+30
+00:03:18,840 --> 00:03:21,220
+على اتنين أس اتنين ناقص واحد
+
+31
+00:03:24,950 --> 00:03:28,810
+يعني بدون مبدأ من الصفر هي مباشرة مع الواحد انحلت
+
+32
+00:03:28,810 --> 00:03:37,490
+المشكلة اتنين اص تلاتة ناقص واحد هذه واحد على
+
+33
+00:03:37,490 --> 00:03:42,710
+تمانية اللي هي واحد على اتنين اص اربع ناقص واحد
+
+34
+00:03:42,710 --> 00:03:47,810
+اللي هي اتنين اص تلاتة واحد على ستاش بيتساوي واحد
+
+35
+00:03:47,810 --> 00:03:53,190
+على اتنين اص خمسة ناقص واحدوبالتالي هذه الـ
+
+36
+00:03:53,190 --> 00:03:55,830
+Definition تبعي معناته انا بقدر أقوله An بدها
+
+37
+00:03:55,830 --> 00:04:03,510
+تساوي واحد على اتنين قص M ماقص واحد وال M أكبر أو
+
+38
+00:04:03,510 --> 00:04:09,290
+تساوي الواحد هل ممكن أحصل على Definition تاني؟
+
+39
+00:04:09,290 --> 00:04:14,210
+أغير ال index صفر
+
+40
+00:04:14,210 --> 00:04:20,810
+واحد اتنين تلاتة أربعة معناته هتحصل عليها بشكل
+
+41
+00:04:20,810 --> 00:04:27,310
+مباشرواحد على اتنين
+
+42
+00:04:27,310 --> 00:04:32,550
+والصفر واحد على اتنين اص واحد واحد على اتنين اص
+
+43
+00:04:32,550 --> 00:04:36,650
+اتنين واحد على اتنين اص تلاتة واحد على اتنين اص
+
+44
+00:04:36,650 --> 00:04:40,710
+اربعة مياته ال a n تبعتي هي تساوي واحد على اتنين
+
+45
+00:04:40,710 --> 00:04:46,330
+اص n و ال n أكبر او تساوي صفر وهي two definition
+
+46
+00:04:46,330 --> 00:04:51,750
+لنفس ال sequence اللي موجود عندك الآن
+
+47
+00:04:53,170 --> 00:04:58,570
+أيه يكون أسرع لذهنك تصلّه؟ قضية كتير بس في الآخر
+
+48
+00:04:58,570 --> 00:05:02,190
+.. في الآخر كونه هي sequence الأصل أنك تبني ..
+
+49
+00:05:02,190 --> 00:05:07,370
+تقدر تبنيها سواء كانت على واحد أو على صفر طيب، لو
+
+50
+00:05:07,370 --> 00:05:12,010
+أنت حسيت بديت من صفر ولاجيت سكّرت معاك، إيش تساوي؟
+
+51
+00:05:12,010 --> 00:05:15,270
+هو بدل ال-sin index من واحد ولو بديت من واحد و
+
+52
+00:05:15,270 --> 00:05:19,150
+سكّرت تبدأ .. لاجيت الشجتان مسكرة، معناته مخك بده
+
+53
+00:05:19,150 --> 00:05:23,580
+تعمله formatting من جديد و تبدأ تفكر بالمسألةبشكل
+
+54
+00:05:23,580 --> 00:05:32,140
+مختلف تماما طيب لأن
+
+55
+00:05:32,140 --> 00:05:41,180
+لو ايجا جالي لو ايجا جالي في sequence arithmetic
+
+56
+00:05:41,180 --> 00:05:47,000
+sequence مثل
+
+57
+00:05:47,000 --> 00:05:50,680
+ال sequence اتنين
+
+58
+00:05:50,680 --> 00:05:52,280
+اربعة
+
+59
+00:05:54,290 --> 00:05:57,030
+ستة تمانية عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة
+
+60
+00:05:57,030 --> 00:05:57,470
+عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة
+
+61
+00:05:57,470 --> 00:05:57,670
+عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة
+
+62
+00:05:57,670 --> 00:06:02,870
+عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة
+
+63
+00:06:02,870 --> 00:06:02,910
+عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة
+
+64
+00:06:02,910 --> 00:06:06,630
+عشرة
+
+65
+00:06:06,630 --> 00:06:12,890
+عشرة عشرة عشرة عشرة
+
+66
+00:06:19,350 --> 00:06:22,250
+1 زائد 2 تساوي 3 او تساوي ثلاثة ثلاثة ثلاثة ثلاثة
+
+67
+00:06:22,250 --> 00:06:26,170
+ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة
+
+68
+00:06:26,170 --> 00:06:31,970
+ثلاثة تساوي ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة تساوي
+
+69
+00:06:31,970 --> 00:06:34,970
+ثلاثة ثلاثة ثلاثة ثلاثة تساوي ثلاثة ثلاثة ثلاثة
+
+70
+00:06:34,970 --> 00:06:38,090
+ثلاثة تساوي ثلاثة ثلاثة ثلاثة ثلاثة تساوي ثلاثة
+
+71
+00:06:38,090 --> 00:06:48,460
+ثلاثة ثلاثة ثلاثة تساوي ثلاثة ثلاثة ثلاثالـ N لـ
+
+72
+00:06:48,460 --> 00:06:52,100
+Index هيمشي Sequence إما صفر واحد اتنين تلاتة إلى
+
+73
+00:06:52,100 --> 00:06:55,900
+مال نهاية أو واحد اتنين تلاتة أربع إلى مال نهاية
+
+74
+00:06:55,900 --> 00:06:59,520
+أنت دايماً تطلع في مين؟ في الأرقام اللي عندك إيش
+
+75
+00:06:59,520 --> 00:07:04,080
+الصيغة اللي عندي أنا دايماً في فرق اتنين بقدر
+
+76
+00:07:04,080 --> 00:07:09,560
+أقوله AN بيتساوي اتنين في N و ال N أكبر أو تساوي
+
+77
+00:07:09,560 --> 00:07:13,380
+صفر بصيصبر
+
+78
+00:07:13,380 --> 00:07:18,210
+شوية أنا كتبت أكبر أو تساوي صفر اتنين في الصفرصفر
+
+79
+00:07:18,210 --> 00:07:21,530
+لا تنتمي للـ sequence اللي موجودة عندها المسؤولة
+
+80
+00:07:21,530 --> 00:07:26,930
+لأ معناته التعريف تبعي بده يبدأ من واحد واحد في
+
+81
+00:07:26,930 --> 00:07:30,850
+اتنين او اتنين في واحد اتنين اتنين في اتنين اربعة
+
+82
+00:07:30,850 --> 00:07:33,910
+اتنين في تلاتة ستة معناته ال definition هيك تبعي
+
+83
+00:07:33,910 --> 00:07:40,870
+صحيح مائة في المائة مافي مشكلة حل
+
+84
+00:07:40,870 --> 00:07:43,830
+ال index هل بتقدر تحصل اليك في ال natural number
+
+85
+00:07:43,830 --> 00:07:47,940
+او في ال z او ماشي ابقىماش هتظبط الكلام أحمد الآن،
+
+86
+00:07:47,940 --> 00:07:50,340
+احنا بتكلمها على sequence مجموعة من الأرقام
+
+87
+00:07:50,340 --> 00:07:55,720
+المتتالية، متتالية، من اسمها متتالية، الآن تبدأ
+
+88
+00:07:55,720 --> 00:08:04,100
+ايش؟ بدك رقم هم، لأ اسميكوا إيش بقول، بقول لو أنا
+
+89
+00:08:04,100 --> 00:08:05,400
+هذه بدي أبدأها من صفر
+
+90
+00:08:14,420 --> 00:08:18,740
+مش بتظبط معايا؟ انا جاي أقولك بتظبط؟ مش عارف .. هي
+
+91
+00:08:18,740 --> 00:08:23,200
+.. في الصفر .. عند الصفر تمام لكن عند الواحد ادتني
+
+92
+00:08:23,200 --> 00:08:26,140
+خمسة ميات وخلاص ال definition فيه غلط مش هتظبط
+
+93
+00:08:26,140 --> 00:08:32,280
+الحال هيك إلا لو روحت أضافت صفر غام وضلت الأن أكبر
+
+94
+00:08:32,280 --> 00:08:35,300
+أو تساوي صفر بالشكل هذا بتضل العملية عندي عش ..
+
+95
+00:08:35,300 --> 00:08:38,580
+صحيحة بصير هذا أول element في ال sequence وممكن أن
+
+96
+00:08:38,580 --> 00:08:43,170
+ال sequence عند هيك صحيحة مئة في المئةطيب طبعا حتى
+
+97
+00:08:43,170 --> 00:08:47,370
+على ال definition الجديد او انا اتيت و قلتلك بدي
+
+98
+00:08:47,370 --> 00:08:55,970
+حاصل جمع اول خمس حدود بدي حاصل جمع اول خمس حدود شو
+
+99
+00:08:55,970 --> 00:09:01,910
+بيبقى تساوي؟ هتقول ايه؟ صفر .. اتنين .. ستة ..
+
+100
+00:09:01,910 --> 00:09:08,650
+اتناشر .. عشرين .. هاي اول خمس حدود صح؟
+
+101
+00:09:08,650 --> 00:09:09,890
+أمتاز .. طب اول عشرة
+
+102
+00:09:13,350 --> 00:09:20,050
+مش هتخلص هيك، بدك تصير أنك تتمد على الـSummation،
+
+103
+00:09:20,050 --> 00:09:22,810
+والـSummation في عندي مجموعة من القوانين بكل
+
+104
+00:09:22,810 --> 00:09:35,410
+بساطة، القانون هي مجموع أول N terms، عشرة عشرةأول
+
+105
+00:09:35,410 --> 00:09:44,590
+مية مية زائد او مضروبة فيه أول element ال a لأن ال
+
+106
+00:09:44,590 --> 00:09:49,170
+a صفر ممكن تعمل لخمة لبعضكوا عشان ال index المقصود
+
+107
+00:09:49,170 --> 00:09:57,670
+في ال a صفر أول element زائد an الانصر مش الأخير
+
+108
+00:09:58,620 --> 00:10:03,500
+العنصر العاشر أو العنصر المية أو العنصر الخمسين
+
+109
+00:10:03,500 --> 00:10:08,680
+وهناك تنتبه و تنتبه كويس إذا ال index بدي معاك من
+
+110
+00:10:08,680 --> 00:10:14,260
+صفر معناته العنصر العاشر بدي يكون تسعة أصبت؟ ال
+
+111
+00:10:14,260 --> 00:10:18,580
+index تبعته تسعة وهذه المقصدات بتنتبهله وبالتالي
+
+112
+00:10:18,580 --> 00:10:25,120
+المقصود بال A N هو العنصر ال Nعلى اتنين فابتدعي
+
+113
+00:10:25,120 --> 00:10:31,420
+اني اجي اطبق الكلام هذا ال summation من ال k او من
+
+114
+00:10:31,420 --> 00:10:38,000
+ال i او ال k equal zero ل ال n طبعا هال من zero ل
+
+115
+00:10:38,000 --> 00:10:43,960
+ال n كم element صار ن زائد واحد ليش بعد اللانهائي
+
+116
+00:10:43,960 --> 00:10:48,830
+ال k من zero ل nان زائد واحد انتبه فممكن انت
+
+117
+00:10:48,830 --> 00:10:52,730
+القانون كمان يربكك اكتر المجموع ال summation يساوي
+
+118
+00:10:52,730 --> 00:11:01,730
+هذه تعالى نسقط الكلام هذا هم هي اول خمس اعداد اول
+
+119
+00:11:01,730 --> 00:11:07,790
+خمس اعداد مجموع اول خمس اعداد يساوي خمسة مضروبة في
+
+120
+00:11:07,790 --> 00:11:13,530
+اول element صفر زائد الانصر الخامس واحد اتنين
+
+121
+00:11:13,530 --> 00:11:20,610
+تلاتة اربعة خمسة تمانيةعلى اتنين خمسة في تمانية
+
+122
+00:11:20,610 --> 00:11:26,890
+اربعين على اتنين تساوي عشرين تمام الشباب كمان مرة
+
+123
+00:11:26,890 --> 00:11:34,130
+برجع و باعد تاني ال am ها ديهي العنصر اللي في
+
+124
+00:11:34,130 --> 00:11:37,850
+المنزلة M يعني لما انا باجي بقولك العنصر الأول عشر
+
+125
+00:11:37,850 --> 00:11:42,590
+عناصر هانا باجي صدق العنصر العاشر لأ لو ال index
+
+126
+00:11:42,590 --> 00:11:47,350
+تبعك بادي من Zero معناته هو العنصر التاسع بادي من
+
+127
+00:11:47,350 --> 00:11:50,350
+مية او عفوا بادي من واحد معناته واحد من الكون
+
+128
+00:11:50,350 --> 00:11:55,870
+العاشر نفسه نعم انا
+
+129
+00:11:55,870 --> 00:12:01,450
+احنا قدته هي في الآخرصفر واحد اتنين تلاتة اربعة لو
+
+130
+00:12:01,450 --> 00:12:05,250
+انا سألتك يا رامي مش رامي برضه لو انا سألتك ايش
+
+131
+00:12:05,250 --> 00:12:09,490
+تاني عنصر في ال sequence تاني عنصر في ال sequence
+
+132
+00:12:09,490 --> 00:12:13,290
+اتنين تاني عنصر في ال sequence اتنين على الرغم انه
+
+133
+00:12:13,290 --> 00:12:17,570
+ال index تبعه واحد خامس عنصر في ال sequence تمانية
+
+134
+00:12:17,570 --> 00:12:22,490
+ليش لأن ال index تبعي انت الآن عند لما بدت تشتغل
+
+135
+00:12:22,490 --> 00:12:26,660
+انسال ال sequence هديهك ال index شويةقلت لك و من
+
+136
+00:12:26,660 --> 00:12:29,220
+أصل الخامس في ال sequence مباشرة هتقولي تمانية
+
+137
+00:12:29,220 --> 00:12:35,860
+جديش ال index تبعه حسب ال sequence تبعتك بدأت من
+
+138
+00:12:35,860 --> 00:12:40,660
+صفر ولا بدأت من واحد ال index تبعه حسب ال sequence
+
+139
+00:12:40,660 --> 00:12:48,720
+اللي عندك تمام طيب لو أجينا قولنا arithmetic
+
+140
+00:12:48,720 --> 00:12:56,300
+sequence واحد اتنين تلاتة أربعة خمسةالى ما لا
+
+141
+00:12:56,300 --> 00:13:03,300
+نهاية arithmetic sequence ولا لا ال A فيها تساوي
+
+142
+00:13:03,300 --> 00:13:14,800
+واحد وال D تساوي واحد ولا لا صحيك بقدر طيب تعالى
+
+143
+00:13:14,800 --> 00:13:22,980
+لو أنا سألتك A N ايش بتساوي A زائد N في D يعني
+
+144
+00:13:22,980 --> 00:13:31,080
+العنصر الخامس A خمسةماذا يساوي؟ واحد زائد خمسة في
+
+145
+00:13:31,080 --> 00:13:37,380
+واحد جديش الداني ايه؟ ستة الداني ستة معناته ال
+
+146
+00:13:37,380 --> 00:13:42,180
+index تبعي في ال sequence هذي جديش؟ صفر ال index
+
+147
+00:13:42,180 --> 00:13:48,400
+تبعي في ال sequence هذي صفر كمان مرة حلقتي بقولك
+
+148
+00:13:48,400 --> 00:13:53,920
+ليش صفر؟ كمان مرة الآن ال sequence arithmetic
+
+149
+00:13:53,920 --> 00:13:59,740
+sequencearithmetic sequence متتابعة حسابية متتابعة
+
+150
+00:13:59,740 --> 00:14:05,020
+حسابية ليش الفرق بين كل عنصرين متتاليين ثابت لو
+
+151
+00:14:05,020 --> 00:14:09,320
+واحد وبالتالي هي ال a equal واحد و ال d equal واحد
+
+152
+00:14:09,320 --> 00:14:17,400
+الان كتب الصيغة العامة تبعتها a n بدا تساوي a زائد
+
+153
+00:14:17,400 --> 00:14:24,150
+n في d n في dهذه هي الـ Definition، اللي هي لو أنا
+
+154
+00:14:24,150 --> 00:14:28,850
+دي اتسألتك عن العنصر الخامس A خمسة، مقصودها دي
+
+155
+00:14:28,850 --> 00:14:33,850
+إيش؟ لو هيك لو أنا اتسألتك عن العنصر الخامس الـ A
+
+156
+00:14:33,850 --> 00:14:38,790
+العنصر الخامس، مباشرة يعني هتقدر لذهني أن الـ N
+
+157
+00:14:38,790 --> 00:14:45,230
+equal خمسة، معناته هاي واحد زائد خمسة في الـD اللي
+
+158
+00:14:45,230 --> 00:14:50,080
+هي الواحدوده تساوي ستة بس الستة فعليا الانصار
+
+159
+00:14:50,080 --> 00:14:56,020
+السادس إلا إلا في حالة واحدة ال index تبقى إيش بدأ
+
+160
+00:14:56,020 --> 00:15:01,340
+من صفر ال index بدأ من صفر تمام و بالتالي بدأت أنت
+
+161
+00:15:01,340 --> 00:15:05,800
+بيجي لها أمر هي ال definition تبقى ال sequence هيك
+
+162
+00:15:05,800 --> 00:15:10,620
+و الجيل اللي قلتلك ممكن أخليها برا ناجس واحد نعم
+
+163
+00:15:10,620 --> 00:15:18,260
+ممكن أخليها برناجس واحد تحطهم برا ناجس واحديعني A
+
+164
+00:15:18,260 --> 00:15:25,320
+زائد M في D الكل ناجس واحد طيب
+
+165
+00:15:25,320 --> 00:15:32,440
+في الآخر هي حسابية طيب الآن اللي انا بده اوصلك هي
+
+166
+00:15:32,440 --> 00:15:34,900
+هي ال sequence و هي المواطيات من ال sequence اللي
+
+167
+00:15:34,900 --> 00:15:41,760
+عندك و بقولك اجمعلي أول خمس حدود منها اجمعلي أول
+
+168
+00:15:41,760 --> 00:15:44,060
+خمس حدود خمسة في
+
+169
+00:15:47,150 --> 00:15:58,210
+الحد الأول ايه؟ زائد الحد الخامس خمسة على اتنين
+
+170
+00:15:58,210 --> 00:16:02,130
+هاي
+
+171
+00:16:02,130 --> 00:16:04,910
+قدام ال sequence موجودة خلّالها أنا بودّيك على
+
+172
+00:16:04,910 --> 00:16:09,010
+مشكلة أعوص من هيك الآن و هذا تساوي خمسة بستة
+
+173
+00:16:09,010 --> 00:16:14,470
+تلاتين على اتنين يساوي خمستاشر لو جمعتهم خمستاشر
+
+174
+00:16:18,780 --> 00:16:27,240
+first five terms هذا summation of ال first five
+
+175
+00:16:27,240 --> 00:16:34,720
+terms طيب لو انا اديت قولتلك ال summation of ال
+
+176
+00:16:34,720 --> 00:16:40,700
+first twenty terms
+
+177
+00:16:40,700 --> 00:16:49,200
+الان مش هكون في عندك مشكلة عشرين واحد زائدعشرين
+
+178
+00:16:49,200 --> 00:16:55,540
+ايوة بناء على ايش انت بدأت هيك اد انه بدأ من واحد
+
+179
+00:16:55,540 --> 00:17:01,940
+وال difference عشرين عشرين
+
+180
+00:17:01,940 --> 00:17:10,960
+في واحد وعشرين على اتنين طيب الان مش
+
+181
+00:17:10,960 --> 00:17:14,960
+قضية كمان مرة زميلكوا بيقول لو بدأت من صفر احسن مش
+
+182
+00:17:14,960 --> 00:17:19,460
+قضية هتطلع معاكحسب إيش ال index تبعنا، اللي أنا ..
+
+183
+00:17:19,460 --> 00:17:22,500
+هاي ال sequence اللي عندي .. هاي ال sequence اللي
+
+184
+00:17:22,500 --> 00:17:27,860
+عندي حاطيكي إياها، لأن إذا أنت بدك تروح الرقم هذا،
+
+185
+00:17:27,860 --> 00:17:33,970
+انت مش متأكد إيش بدي يطلع معاك، تمام؟تشوف المعادلة
+
+186
+00:17:33,970 --> 00:17:37,770
+وتشوف الـ index وتدخل في التفاصيل زي ما قلنا اللي
+
+187
+00:17:37,770 --> 00:17:43,430
+بدهاش شغل أكتر يعني كمان مرة على A N تساوي N أو A
+
+188
+00:17:43,430 --> 00:17:50,610
+زائد N في D والـ N أكبر أو تساوي صفر الـ N أكبر أو
+
+189
+00:17:50,610 --> 00:17:57,710
+تساوي صفر مصبوطة هيك؟ أنا بسألك هاي الـ definition
+
+190
+00:17:57,710 --> 00:18:07,550
+صح؟ تديني واحد؟اللي بعدها ايوة
+
+191
+00:18:07,550 --> 00:18:13,190
+اتنين تلاتة
+
+192
+00:18:13,190 --> 00:18:24,250
+واحد زائد صفر واحد زائد واحد في واحد اتنين
+
+193
+00:18:24,250 --> 00:18:28,770
+ايوة صفر واحد اتنين تلاتة و انا في عندك دائما واحد
+
+194
+00:18:28,770 --> 00:18:35,370
+تساوي و هذه واحد هذه واحد هذه اتنينهذه ثلاثة أربعة
+
+195
+00:18:35,370 --> 00:18:37,590
+خمسة ستة مع تواعي ال definition تبعي ال sequence
+
+196
+00:18:37,590 --> 00:18:43,290
+عندي مش مشكلة وبالتالي بدك تمتع به دائما لل unterm
+
+197
+00:18:43,290 --> 00:18:46,890
+اللي بدك تشوفه طبعا على غرار القانون هذا في عندنا
+
+198
+00:18:46,890 --> 00:18:50,430
+مجموعة كمان من القوانين اللي لها علاقة بال other
+
+199
+00:18:50,430 --> 00:18:57,130
+sequences بال geometric sequence اللي همتكلم على
+
+200
+00:18:57,130 --> 00:19:05,730
+geometric sequence ar os k ar osK وبالتالي هتكون
+
+201
+00:19:05,730 --> 00:19:12,930
+AR أُس N زائد واحد ناقص A على R ناقص واحد وبالتالي
+
+202
+00:19:12,930 --> 00:19:19,850
+انت بتقدر المطلوب منك تحفظ هدول أول خمسة يعني
+
+203
+00:19:19,850 --> 00:19:26,370
+الواحدة بتاعة ال arithmetic وهدولة أربعة هذه
+
+204
+00:19:26,370 --> 00:19:33,360
+ماتنسهاش هذه واحدو هدول ايش؟ اربع .. ليش تحفظهم؟
+
+205
+00:19:33,360 --> 00:19:36,120
+لأنه لحد ال هيك اللي انا هطلب منك .. هقولك هي ال
+
+206
+00:19:36,120 --> 00:19:39,540
+sequence و روحتلي مجموع اول term الحدود تبعتها
+
+207
+00:19:39,540 --> 00:19:44,080
+عشان تقدر تجيبها بدك تتخيل الصيغة العامة تبعتها
+
+208
+00:19:44,080 --> 00:19:47,540
+كيف وبناء عليها تقدر تحدد ال summation
+
+209
+00:19:53,550 --> 00:19:56,170
+خلص ال section الخاص أو هذه الجزئية اللي انا بديها
+
+210
+00:19:56,170 --> 00:19:59,370
+من موضوع ال sequences ماخلصناش لسه فينا كمان
+
+211
+00:19:59,370 --> 00:20:03,750
+section بدنا نخلصه section بسيط زي هيك اربع اربع
+
+212
+00:20:03,750 --> 00:20:08,390
+خمس slide ال matrices
+
+213
+00:20:08,390 --> 00:20:15,470
+المظهوفات طيب
+
+214
+00:20:15,470 --> 00:20:21,510
+لان لما انا بتكلم عن المظهوفات برضه بتكلم على
+
+215
+00:20:21,510 --> 00:20:25,540
+discretestructure بتتكلم عن الـ discrete structure
+
+216
+00:20:25,540 --> 00:20:28,540
+لاحظ الشابتر كله بتتكلم عن الـ discrete structure
+
+217
+00:20:28,540 --> 00:20:34,580
+المجموعات الـ sets الـ functions جابني الماتريسيز
+
+218
+00:20:34,580 --> 00:20:39,220
+الـ sequences و هاي الماتريسيز او المصفوفات طيب
+
+219
+00:20:39,220 --> 00:20:42,160
+لان انا بتتكلم على matrix معناته انا بتتكلم على
+
+220
+00:20:42,160 --> 00:20:48,760
+rectangular array rectangular array و دائما ال
+
+221
+00:20:48,760 --> 00:20:50,420
+array هذه تحدد بعدد
+
+222
+00:20:52,970 --> 00:20:59,690
+الصفوف وعدد الأعمدة عدد
+
+223
+00:20:59,690 --> 00:21:04,430
+الصفوف وعدد الأعمدة يعني المصفوف اللي قدامي في
+
+224
+00:21:04,430 --> 00:21:11,850
+المثال هذا عبارة عن ثلاث صفوف بنجدم
+
+225
+00:21:11,850 --> 00:21:15,970
+عدد الصفوف تلاتة في اتنين في عدد الصفوف او في عدد
+
+226
+00:21:15,970 --> 00:21:21,090
+الأعمدة اتنين طيب بنقول عن المصفوفة square matrix
+
+227
+00:21:22,940 --> 00:21:27,600
+لما بيكون عدد الصفوف يساوي عدد الأعمدة بيكون عنها
+
+228
+00:21:27,600 --> 00:21:32,600
+مصفوفة مربعة يعني مثل المصفوفة هاي هذه مصفوفة
+
+229
+00:21:32,600 --> 00:21:37,080
+اتنين في اتنين واحد اتنين تلاتة اربعة وهذه مصفوفة
+
+230
+00:21:37,080 --> 00:21:42,340
+مربعة واحد اتنين تلاتة اربعة خمسة ستة سبعة تمانية
+
+231
+00:21:42,340 --> 00:21:46,640
+تسعة الأولى اللي فوق هذه اتنين في اتنين وهذه تلاتة
+
+232
+00:21:46,640 --> 00:21:50,380
+في تلاتة square matrix لازم يكون فيها عدد الصفوف
+
+233
+00:21:50,380 --> 00:21:55,620
+يساوي عدد الأعمدةمتى بقول عن مصفوفتين متساويتين؟
+
+234
+00:21:55,620 --> 00:21:59,860
+لما يكون كل element أول حاجة لازم يكون له نفس
+
+235
+00:21:59,860 --> 00:22:05,200
+الحجم نفس الحجم وكل عنصر يساوي عنصر المقابل في
+
+236
+00:22:05,200 --> 00:22:09,140
+المصفوفة اللي موجودة عنده مافيش له صورة عنصر مقابل
+
+237
+00:22:09,140 --> 00:22:15,000
+له الآن
+
+238
+00:22:15,000 --> 00:22:21,320
+الـA هذه حجمها M في Nالصف الأول الصف الثاني الصف
+
+239
+00:22:21,320 --> 00:22:28,280
+الأم اي واحد يعني لو قلت لك الانصار صف و لو كانت
+
+240
+00:22:28,280 --> 00:22:35,040
+ام في واحد بيقول عنها عمد عشان
+
+241
+00:22:35,040 --> 00:22:40,480
+أجمع مصرفين لازم يكونوا نفس الحجم احنا قبل شوية
+
+242
+00:22:40,480 --> 00:22:44,180
+قلت عشان أقارن بين مصرفين من ناحية التساوي لازم
+
+243
+00:22:44,180 --> 00:22:47,220
+يكونوا نفس الحجم عشان أجمع مصرفين لازم يكونوا نفس
+
+244
+00:22:47,220 --> 00:22:55,160
+الحجمبالآن العنصر الجديد اللي هو الـ C Cij
+
+245
+00:22:55,160 --> 00:22:59,780
+طبعا ناتج مصحوفة من نفس حجم المصوفتين السابقتين
+
+246
+00:22:59,780 --> 00:23:10,680
+يساوي ال element IJ زائد ال element Bij بالتالي
+
+247
+00:23:10,680 --> 00:23:14,900
+الأربعة هذه تساوي التلاتة
+
+248
+00:23:16,130 --> 00:23:20,450
+زائد الواحد من وين هذا الكلام جبته انا الاربعة هذه
+
+249
+00:23:20,450 --> 00:23:26,310
+هي عبارة عن C 11 مصبوط وهي عبارة عن حاصل جمع
+
+250
+00:23:26,310 --> 00:23:34,630
+العنصرين A11 زائد B11 الان هذا التلاتة او هذا
+
+251
+00:23:34,630 --> 00:23:44,430
+العنصر النقص تلاتة هذه عبارة عن CC2 3 C2 3 هي
+
+252
+00:23:44,430 --> 00:23:55,290
+عبارة عن حص الجامع B2 3 زائد A2 3 و هكذا لو كانوا
+
+253
+00:23:55,290 --> 00:23:59,230
+المصوفتين أحجامهم مختلفة عملية الجامع مابتفضبطش
+
+254
+00:23:59,230 --> 00:24:08,110
+معاهم تمام؟ ننتقل لعملية الضربطبعا الموضوع سهل
+
+255
+00:24:08,110 --> 00:24:14,630
+لأنكوا أخدتوه في الثانوية و قبل توجيهه كمان فتبدأ
+
+256
+00:24:14,630 --> 00:24:19,650
+تتكلم على المصطفات من هاشر طيب ماليش في رياضية
+
+257
+00:24:19,650 --> 00:24:23,450
+الوصائط أنا الآن؟لأن عشان أضرب مصفوفتين في بعض
+
+258
+00:24:23,450 --> 00:24:28,710
+عشان أضرب مصفوفتين في بعض لازم يكون عدد أعمدة
+
+259
+00:24:28,710 --> 00:24:33,750
+الأولى يساوي عدد صفوف الثانية يعني الآن لو
+
+260
+00:24:33,750 --> 00:24:39,310
+المصفوفة الأولى A عندي اتنين في تلاتة ال B اللي
+
+261
+00:24:39,310 --> 00:24:44,990
+بدي أضربها فيها لازم تكون تلاتة في أي حاجة مثلا
+
+262
+00:24:44,990 --> 00:24:52,790
+تلاتة في أربعة المصفوفة الناتج Cهتكون عبارة عن
+
+263
+00:24:52,790 --> 00:24:59,710
+اتنين في اربعة عملية
+
+264
+00:24:59,710 --> 00:25:07,250
+الضرب كيف بالتم تاخد الصف الصف الأول تضرب في
+
+265
+00:25:07,250 --> 00:25:12,110
+العمود الأول لأ شوية بس عشان نركز شوية في الضرب و
+
+266
+00:25:12,110 --> 00:25:17,830
+نتذكره صح المصفوفة الناتج ايش المفروض تكون اتنين
+
+267
+00:25:17,830 --> 00:25:24,450
+في اربعةهذه في المثال اللي عندي هنا يعني فيها أنا
+
+268
+00:25:24,450 --> 00:25:26,650
+عندي صفين وأربع أعمدان
+
+269
+00:25:36,150 --> 00:25:41,930
+الأن العنصر هذا اللي جاي في الصف الأول مين بيحدده؟
+
+270
+00:25:41,930 --> 00:25:46,970
+الصف الأول من المصوفة اللي حددت الصفوف هكذا قهدت
+
+271
+00:25:46,970 --> 00:25:53,770
+صفوف المصوفة C من صفوف A مظبوط؟ وبالتالي .. لما
+
+272
+00:25:53,770 --> 00:25:58,010
+تاخد الصف الأول .. لما تاخد الصف الأول من ال A
+
+273
+00:25:58,010 --> 00:26:04,670
+معناته أنك بتتكلم على ناتج في الصف الأول ل Cمصبوط؟
+
+274
+00:26:04,670 --> 00:26:09,670
+طب الصف الأول فيه أكتر من عمود مين اللي بحدده؟
+
+275
+00:26:09,670 --> 00:26:15,710
+العمود اللي اخترته من B يعني هيك الصف الأول في
+
+276
+00:26:15,710 --> 00:26:21,430
+العمود الأول بيعطينا ال element الصف الأول العمود
+
+277
+00:26:21,430 --> 00:26:26,490
+الأول في مين؟ في C الصف الأول في العمود التاني
+
+278
+00:26:26,490 --> 00:26:31,580
+بيعطينا ال element التاني في الصف الناتجواضح كلام
+
+279
+00:26:31,580 --> 00:26:35,840
+اللي أنا بقوله؟ يعني كل ما بتمسك صفر من الـA بيكون
+
+280
+00:26:35,840 --> 00:26:40,420
+مقابله صفر من الـC في النتج مقابله صفر من الـC
+
+281
+00:26:40,420 --> 00:26:44,820
+بتاخد الصفر و بتضرب في كل عمود و بتجمع العناصر
+
+282
+00:26:44,820 --> 00:26:48,240
+اللي ما بينهم يعني و كإني جاهز بقولك جيب الصفر
+
+283
+00:26:48,240 --> 00:26:56,540
+هالي مثلا واحد صفر أربعة اضرب كل عنصر بين جماله و
+
+284
+00:26:56,540 --> 00:26:57,140
+اجمعهم
+
+285
+00:27:00,200 --> 00:27:04,700
+أربعة في اتنين زائد صفر في واحد زائد تلاتة اربعة
+
+286
+00:27:04,700 --> 00:27:10,460
+في تلاتة اربع بعشر هي ال element الان خد الصف
+
+287
+00:27:10,460 --> 00:27:15,840
+الأول في العمود التاني كمان عشان تجيبني الاربعة
+
+288
+00:27:15,840 --> 00:27:20,360
+واحد في اربعة اربعة صفر في واحد واربعة في صفر
+
+289
+00:27:20,360 --> 00:27:26,620
+اربعة الان يا صاحبي اذا بدكش تعبيها صفوف ممكن
+
+290
+00:27:26,620 --> 00:27:33,350
+تعبيها اعمدانممكن تعبيها عمود عمود كيف بقى تساوي؟
+
+291
+00:27:33,350 --> 00:27:40,070
+هاي الصف الأول في العمود الأول الداني أربعة أعش
+
+292
+00:27:40,070 --> 00:27:45,750
+لما تنزل تاخد الصف التاني في العمود الأول فهليا
+
+293
+00:27:45,750 --> 00:27:48,230
+انت بقى بتعبي القيمة الثانية في العمود الأول في
+
+294
+00:27:48,230 --> 00:27:53,130
+الناتج هاي تمانية اللي بعده
+
+295
+00:27:55,990 --> 00:28:01,190
+هي سبعة و هكذا انت عبي صف صف اريح اليك او بطريقة
+
+296
+00:28:01,190 --> 00:28:05,370
+اللي بتشوفها مناسبة تمام؟ بطريقة اللي انت متعود
+
+297
+00:28:05,370 --> 00:28:09,050
+عليها اشتغل الصف الأول في العمود الأول الصف الأول
+
+298
+00:28:09,050 --> 00:28:11,570
+في العمود التاني الصف الأول في العمود التالت و كل
+
+299
+00:28:11,570 --> 00:28:15,510
+حاجة ما تخلص الصف الأول في الناتج بتبدل الصف و
+
+300
+00:28:15,510 --> 00:28:18,470
+بتبدل الصف في ال .. في ال a و بالتالي الصف في ال
+
+301
+00:28:18,470 --> 00:28:25,090
+result الأمر مش صعب ولا لا؟ في مشكلاش بقى؟ تمام
+
+302
+00:28:25,280 --> 00:28:32,840
+الصف I في العمود J الاصلي الديني ال element IJ
+
+303
+00:28:32,840 --> 00:28:40,760
+الصف I في العمود J الاصلي الديني ال element IJ حسب
+
+304
+00:28:40,760 --> 00:28:45,340
+القانون الموجود عندي تبع الدرب تمام هل ال BA يساوي
+
+305
+00:28:45,340 --> 00:28:48,700
+AB؟
+
+306
+00:28:48,700 --> 00:28:55,640
+A بدأ تساوي واحد و اتنين تلاتة اربعةوالـ B تساوي
+
+307
+00:28:55,640 --> 00:29:00,800
+اربعة اتنين او بلاش واحد
+
+308
+00:29:00,800 --> 00:29:10,980
+واحد اتنين اتنين افترض ان هذه A وهذه B A ضرب الـ B
+
+309
+00:29:10,980 --> 00:29:17,620
+ايش تساوي شباب صفر الأول في العمود الأول واحد في
+
+310
+00:29:17,620 --> 00:29:22,860
+واحد زيدي اتنين في اتنين خمسة برضه
+
+311
+00:29:22,860 --> 00:29:31,270
+كمان خمسةالان تلاتة في واحد زائد تمانية حداشر
+
+312
+00:29:31,270 --> 00:29:38,890
+حداشر بقى بي في ايه بي
+
+313
+00:29:38,890 --> 00:29:46,310
+في ايه مش هتساوي هتاخد الصف الأول وتضربه في العمود
+
+314
+00:29:46,310 --> 00:29:54,420
+الأول هي الصف الأول وهي العمود الأول1 في 1 زائد 1
+
+315
+00:29:54,420 --> 00:30:02,660
+في 3 أربعة بمجرد أنك شوفت الأربعة مباشرة A B لا
+
+316
+00:30:02,660 --> 00:30:11,280
+تساوي B A ليش؟ لأننا اتفقنا في المساواة كل element
+
+317
+00:30:11,280 --> 00:30:15,080
+بديه ساوي ال element المقابل له في نفس ال position
+
+318
+00:30:15,080 --> 00:30:18,260
+هي الأربعة لا تساوي الخمسة بس تعالى خلينا نكمل
+
+319
+00:30:18,850 --> 00:30:23,630
+اتنين بتساوي ال identity matrix إذا الناتج A ضرب
+
+320
+00:30:23,630 --> 00:30:30,990
+ال B إذا A ضرب ال B يساوي B ضرب ال A معناته A
+
+321
+00:30:30,990 --> 00:30:35,910
+تساوي ال B هذا الاحتمال الأول أو ال B هي عبارة عن
+
+322
+00:30:35,910 --> 00:30:40,210
+ال identity matrix ماهي ال identity matrix؟ هي
+
+323
+00:30:40,210 --> 00:30:46,070
+عبارة عن matrix مصفوفة الوحدةاللي كل عناصرها أسخار
+
+324
+00:30:46,070 --> 00:30:51,530
+ما يعدى القطر الرئيسي تساوي واحد ما يعدى عناصر
+
+325
+00:30:51,530 --> 00:30:57,650
+القطر الرئيسي تساوي واحد وبالتالي مصفوفة الوحدة ده
+
+326
+00:30:57,650 --> 00:31:03,090
+لو ضربتها في أي مصفوفة هتطلعش المصفوفة نفسها يعني
+
+327
+00:31:03,090 --> 00:31:10,770
+لو أنا جيت جولت هيفي عندي مصفوفة واحد اتنين تلاتة
+
+328
+00:31:11,620 --> 00:31:15,640
+أربعة خمسة ستة مصفوفة الوحدة اللي ممكن أضرب فيها
+
+329
+00:31:15,640 --> 00:31:21,040
+أنا لازم تكون جداش الشباب واحد
+
+330
+00:31:21,040 --> 00:31:26,820
+صفر صفر صفر واحد صفر صفر صفر واحد ليش هذا الكلام
+
+331
+00:31:26,820 --> 00:31:30,000
+لأنه لازم يكون هذي اتنين في تلاتة هذي لازم تكون
+
+332
+00:31:30,000 --> 00:31:34,980
+تلاتة في اتنين على الأقل مصبوط وبالتالي تلاتة في
+
+333
+00:31:34,980 --> 00:31:41,540
+تلاتة ايش ال result اللي مصفوفة اللي هتطلعإتنين في
+
+334
+00:31:41,540 --> 00:31:47,420
+تلاتة الصف الأول في العمود الأول الصف الأول في
+
+335
+00:31:47,420 --> 00:31:53,660
+العمود الأول واحد اتنين تلاتةالصف الأول في العمود
+
+336
+00:31:53,660 --> 00:31:58,360
+التالت 2 الصف الأول في العمود التالت ثلاثة بعد هيك
+
+337
+00:31:58,360 --> 00:32:02,320
+الصف الأول في العمود التالت أربعة خمسة ستة
+
+338
+00:32:02,320 --> 00:32:05,820
+وبالتالي المصفوفة لما تضربها في ال identity matrix
+
+339
+00:32:05,820 --> 00:32:10,040
+مصفوفة الوحدة تطلع نفسها وكأن ال identity matrix
+
+340
+00:32:10,040 --> 00:32:14,720
+هي المحادث ضربي تبع المصفوفات بس بجتمع حجمها دائما
+
+341
+00:32:14,720 --> 00:32:22,280
+ال Transpose مدور المصفوفة أو مجلوب المصفوفةما هو
+
+342
+00:32:22,280 --> 00:32:27,560
+الـ Transpose؟ بتبدل .. بتبدل صفوف المصفوفة لأعمدة
+
+343
+00:32:27,560 --> 00:32:34,900
+أو بتبدل الأعمدة لصفوف طيب الشباب خليكم بسمعاه يا
+
+344
+00:32:34,900 --> 00:32:41,200
+هان الان في ال Transpose الأن لو أنا افترضت
+
+345
+00:32:41,200 --> 00:32:48,080
+المصفوفة A هي عبارة عن M في M ايه ال Transpose
+
+346
+00:32:48,080 --> 00:32:57,190
+مدور المصفوفة هذه؟ماذا سيكون؟ سيكون M في M لأن انت
+
+347
+00:32:57,190 --> 00:33:03,730
+بدلت صفوف المصفوفة لأعمدة و لأعمدة لصفوف طيب
+
+348
+00:33:03,730 --> 00:33:07,430
+وبالتالي
+
+349
+00:33:07,430 --> 00:33:12,130
+لو كان بالمثال هذا عندنا هي ايه؟ واحد اتنين تلاتة
+
+350
+00:33:12,130 --> 00:33:17,130
+اربع خمسة ستة هي عبارة عن مصفوفة اتنين في تلاتة ال
+
+351
+00:33:17,130 --> 00:33:22,070
+transpose تبعتهابتكون تلاتة في اتنين الشرق المهم
+
+352
+00:33:22,070 --> 00:33:27,810
+عندي الصف الأول بيكون العمود الأول الصف الثاني
+
+353
+00:33:27,810 --> 00:33:33,330
+بيكون العمود التاني وبالتالي بداية الصف هتكون هي
+
+354
+00:33:33,330 --> 00:33:37,090
+نفسها بداية العمود عشان ما تخربطيش في الترتيب اللي
+
+355
+00:33:37,090 --> 00:33:42,450
+عناصر اللي عندنا حكينا
+
+356
+00:33:42,450 --> 00:33:47,240
+على المصوفة لما تكون squareوكل العناد .. اه okay
+
+357
+00:33:47,240 --> 00:33:52,580
+بقول عن المصفوفة symmetric او متماثلة لما يكون كل
+
+358
+00:33:52,580 --> 00:34:01,400
+element aij يساوي ajI ايش يعني؟ المصفوفة المتماثلة
+
+359
+00:34:01,400 --> 00:34:06,840
+هي مصفوفة مربعة ايش يعني مربعة؟ عدد صفوفها تساوي
+
+360
+00:34:06,840 --> 00:34:10,880
+عدد الأعمدة اللي فيها بقول عنها المصفوفة متماثلة
+
+361
+00:34:10,880 --> 00:34:20,140
+لما يكون كل element ijبدي يساوي جاي الانصار هذا
+
+362
+00:34:20,140 --> 00:34:26,880
+جداش ال position تبعه طبعا احنا الآن متماثلة يعني
+
+363
+00:34:26,880 --> 00:34:29,740
+اي واحد واحد ما هي نفسها اي واحد واحد في شوية
+
+364
+00:34:29,740 --> 00:34:33,020
+مشكلة يعني سيبني من عناصر القطر الرئيسي بتكلم عن
+
+365
+00:34:33,020 --> 00:34:41,700
+العناصر التاني انا لأن هذا ال elementE3E1 عشان
+
+366
+00:34:41,700 --> 00:34:54,000
+تكون متماثلة المصحوفة لازم يكون يساوي E1E3 او
+
+367
+00:34:54,000 --> 00:34:58,660
+بين جسيم لو جسمت من النص وطبقت المثلثين على بعض كل
+
+368
+00:34:58,660 --> 00:35:02,720
+element هيكون مطابق لل element المجاور له الشرط
+
+369
+00:35:02,720 --> 00:35:09,710
+كمان مرة كل element AIJ يساوي AJIبنقول عنها
+
+370
+00:35:09,710 --> 00:35:14,330
+symmetric بنقول عن المصفوفة 01 matrix لو كانت كلها
+
+371
+00:35:14,330 --> 00:35:22,690
+عناصرها 01 أو بنجوسين binary 01 مع ال 01 صارت
+
+372
+00:35:22,690 --> 00:35:26,810
+binary ال matrix احنا قبل شوية شوفنا جمع و ضرب
+
+373
+00:35:26,810 --> 00:35:32,350
+مصبوط شوفنا جمع و ضرب هل هنشوف join و meet ال join
+
+374
+00:35:32,350 --> 00:35:36,750
+بقصد فيها ال R و
+
+375
+00:35:36,750 --> 00:35:41,930
+ال meet بقصد فيهامش لحمة .. ميت لحمة ياك يا فالح
+
+376
+00:35:41,930 --> 00:35:52,150
+.. M E A T مايعني
+
+377
+00:35:52,150 --> 00:35:54,030
+انتوا أسود ما شاء الله عليكوا و ماتفطروش اللي غير
+
+378
+00:35:54,030 --> 00:35:59,030
+لحمة عشان هيك دايما أنا مصحى صحين معايا طيب .. هاي
+
+379
+00:35:59,030 --> 00:36:05,130
+المصفوفتين .. هاي المصفوفتين A و B هدولة Zero و
+
+380
+00:36:05,130 --> 00:36:13,960
+Oneالان بدى اعمل بين A وB جوين A وB جوين شبك تساوي
+
+381
+00:36:13,960 --> 00:36:20,540
+كل element مع المقابله كل element بتعمل ال R مع
+
+382
+00:36:20,540 --> 00:36:25,960
+المقابل له كل
+
+383
+00:36:25,960 --> 00:36:29,620
+element مع المقابله بدل ما جمعنا بدل الجمع بدأ
+
+384
+00:36:29,620 --> 00:36:30,300
+استخدم ال R
+
+385
+00:36:33,470 --> 00:36:37,870
+لازم الان يا شباب لازم يكون المصففتين نفس الحجم
+
+386
+00:36:37,870 --> 00:36:41,970
+عشان اعمل بينهم join لازم زي ما اتكلمنا على الجامع
+
+387
+00:36:41,970 --> 00:36:46,070
+و الدرب تماما نفس المواصفات لازم تنطبق عندنا نفس
+
+388
+00:36:46,070 --> 00:36:50,950
+الجامع نفس الجامع اذا انا بتكلم على ال and و ال or
+
+389
+00:36:50,950 --> 00:36:54,810
+ال meet و ال join لازم المصففات تكون من نفس الرتب
+
+390
+00:36:54,810 --> 00:36:58,290
+المصففات تبعتها تكون نفس الرتب لما بتكلم على ال
+
+391
+00:36:58,290 --> 00:37:08,810
+meet بتكلم على ال and1 and Zero Zero and واحد واحد
+
+392
+00:37:08,810 --> 00:37:14,190
+and Zero و هكذا مع كل answer مع المقابل بولين ال
+
+393
+00:37:14,190 --> 00:37:21,310
+product عشان ننهي في بولين ال product لازم يكون
+
+394
+00:37:21,310 --> 00:37:27,670
+عدد صفوف الأولى او عدد أعمدة التانية عفوا عدد
+
+395
+00:37:27,670 --> 00:37:31,430
+أعمدة الأولى يساوي صفوف التانية اللي هو شرط الدرب
+
+396
+00:37:33,000 --> 00:37:37,240
+بقول أنا product ضرب مش هتغير حاجة عندي و هستبدل
+
+397
+00:37:37,240 --> 00:37:42,020
+عملية الضرب اللي كنت سويها بال and و عملية الجمع
+
+398
+00:37:42,020 --> 00:37:47,660
+بال R يعني الآن هاخد الصف الأول في العمود الأول
+
+399
+00:37:47,660 --> 00:37:56,560
+كيف هيكون؟ واحد and الواحد R
+
+400
+00:37:58,110 --> 00:38:02,110
+صفر and الصفر هدولاش بيمثلوا .. هدولة بيمثلوا ال
+
+401
+00:38:02,110 --> 00:38:11,290
+element الأول في النتيجة مش صعبة والله بس هي نفس
+
+402
+00:38:11,290 --> 00:38:15,350
+الكلام .. نفس الكلام .. اذا انت فاهم الدرب بس كل
+
+403
+00:38:15,350 --> 00:38:21,270
+اللي بقولك استبدل الدرب ب and والجمع بال or وخلصنا
+
+404
+00:38:21,270 --> 00:38:24,310
+الله
+
+405
+00:38:24,310 --> 00:38:25,110
+يعطيك العافية خلاص
+
diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/cWgs8V-VhjE_raw.json b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/cWgs8V-VhjE_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..a39624de7061a6d7bc42b1105bdf69755fac1ace
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/cWgs8V-VhjE_raw.json
@@ -0,0 +1 @@
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"start": 141.87, "end": 166.87, "text": "-2-3-4 يعني أن الـ Definition تبع هذا هيك هي المقام اللي موجود عندي هذا 1 2 وصفر 2 4 8 16 2 أُص و بدأت أمشي بالـSequence كيف ممكن أسوي أنا فيك أمر", "tokens": [12, 17, 12, 18, 12, 19, 37495, 22653, 14739, 2423, 39184, 46245, 849, 6055, 3555, 3615, 23758, 39896, 4117, 39896, 9673, 4587, 10943, 13672, 1829, 3714, 29245, 23328, 43242, 1829, 23758, 502, 568, 4032, 9381, 5172, 2288, 568, 1017, 1649, 3165, 568, 5551, 10859, 9381, 4032, 47525, 10721, 2655, 5551, 2304, 8592, 1829, 20666, 39184, 10637, 358, 655, 9122, 33911, 3714, 43020, 5551, 3794, 45865, 41850, 8978, 4117, 5551, 29973], "avg_logprob": -0.4507042278706188, "compression_ratio": 1.3255813953488371, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 141.87, "end": 142.69, "word": "-2", "probability": 0.5184326171875}, {"start": 142.69, "end": 143.99, "word": "-3", "probability": 0.5758056640625}, {"start": 143.99, "end": 145.53, "word": "-4", "probability": 0.912353515625}, 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"start": 204.95, "end": 230.65, "text": "يعني بدون مبدأ من الصفر هي مباشرة مع الواحد انحلت المشكلة اتنين اص تلاتة ناقص واحد هذه واحد على تمانية اللي هي واحد على اتنين اص اربع ناقص واحد اللي هي اتنين اص تلاتة واحد على ستاش بيتساوي واحد على اتنين اص خمسة ناقص واحد", "tokens": [40228, 22653, 47525, 11536, 3714, 44510, 10721, 9154, 31767, 5172, 2288, 39896, 3714, 3555, 33599, 25720, 20449, 2423, 14407, 24401, 16472, 5016, 1211, 2655, 9673, 8592, 28820, 3660, 1975, 2655, 1863, 9957, 1975, 9381, 6055, 1211, 9307, 3660, 8717, 995, 4587, 9381, 36764, 24401, 29538, 36764, 24401, 15844, 46811, 7649, 10632, 13672, 1829, 39896, 36764, 24401, 15844, 1975, 2655, 1863, 9957, 1975, 9381, 1975, 25513, 3615, 8717, 995, 4587, 9381, 36764, 24401, 13672, 1829, 39896, 1975, 2655, 1863, 9957, 1975, 9381, 6055, 1211, 9307, 3660, 36764, 24401, 15844, 8608, 2655, 33599, 4724, 36081, 3794, 995, 45865, 36764, 24401, 15844, 1975, 2655, 1863, 9957, 1975, 9381, 16490, 2304, 3794, 3660, 8717, 995, 4587, 9381, 36764, 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طيب الآن اللي انا بده اوصلك هي هي ال sequence و هي المواطيات من ال sequence اللي عندك و بقولك اجمعلي أول خمس حدود منها اجمعلي أول خمس حدود خمسة في", "tokens": [40228, 22653, 316, 30767, 16373, 3215, 376, 8978, 413, 2423, 28820, 8717, 26108, 3794, 36764, 24401, 23032, 1829, 3555, 8978, 6024, 95, 34740, 39896, 11331, 3794, 16758, 10632, 23032, 1829, 3555, 6024, 48506, 13672, 1829, 1975, 8315, 47525, 3224, 1975, 2407, 36520, 4117, 39896, 39896, 2423, 8310, 4032, 39896, 9673, 14407, 9566, 1829, 9307, 9154, 2423, 8310, 13672, 1829, 43242, 4117, 4032, 4724, 39648, 4117, 1975, 7435, 2304, 3615, 20292, 5551, 12610, 16490, 2304, 3794, 11331, 3215, 23328, 9154, 11296, 1975, 7435, 2304, 3615, 20292, 5551, 12610, 16490, 2304, 3794, 11331, 3215, 23328, 16490, 2304, 3794, 3660, 8978], "avg_logprob": -0.2578914165496826, "compression_ratio": 1.8440860215053763, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 916.88, "end": 917.3, "word": "يعني", "probability": 0.865966796875}, {"start": 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واحد وعشرين على اتنين طيب الان مش قضية كمان مرة زميلكوا بيقول لو بدأت من صفر احسن مش قضية هتطلع معاك", "tokens": [3615, 8592, 16572, 1863, 1975, 1829, 2407, 3660, 44945, 16606, 15844, 1975, 1829, 8592, 16472, 2655, 47525, 10721, 2655, 39896, 4117, 1975, 3215, 16472, 3224, 47525, 10721, 9154, 36764, 24401, 16070, 2649, 6225, 46309, 9957, 6225, 46309, 9957, 8978, 36764, 24401, 4032, 3615, 46309, 9957, 15844, 1975, 2655, 1863, 9957, 23032, 1829, 3555, 2423, 7649, 37893, 12174, 11242, 10632, 9122, 2304, 7649, 3714, 25720, 30767, 2304, 26895, 4117, 14407, 4724, 1829, 39648, 45164, 47525, 10721, 2655, 9154, 20328, 5172, 2288, 1975, 5016, 3794, 1863, 37893, 12174, 11242, 10632, 8032, 2655, 9566, 1211, 3615, 20449, 995, 4117], "avg_logprob": -0.2622422778729311, "compression_ratio": 1.8, "no_speech_prob": 0.0, "words": [{"start": 1008.52, "end": 1009.2, "word": "عشرين", "probability": 0.736083984375}, {"start": 1009.2, "end": 1010.92, "word": " ايوة", "probability": 0.576507568359375}, 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{"start": 1245.24, "end": 1245.84, "word": " array", "probability": 0.96630859375}, {"start": 1245.84, "end": 1247.82, "word": " و", "probability": 0.7509765625}, {"start": 1247.82, "end": 1248.34, "word": " دائما", "probability": 0.87939453125}, {"start": 1248.34, "end": 1248.76, "word": " ال", "probability": 0.96875}, {"start": 1248.76, "end": 1249.02, "word": " array", "probability": 0.8955078125}, {"start": 1249.02, "end": 1249.3, "word": " هذه", "probability": 0.599609375}, {"start": 1249.3, "end": 1249.82, "word": " تحدد", "probability": 0.97216796875}, {"start": 1249.82, "end": 1250.42, "word": " بعدد", "probability": 0.7919921875}], "temperature": 1.0}, {"id": 45, "seek": 128108, "start": 1252.97, "end": 1281.09, "text": "الصفوف وعدد الأعمدة عدد الصفوف وعدد الأعمدة يعني المصفوف اللي قدامي في المثال هذا عبارة عن ثلاث صفوف بنجدم عدد الصفوف تلاتة في اتنين في عدد الصفوف او في عدد الأعمدة اتنين طيب بنقول عن المصفوفة square matrix", "tokens": [6027, 9381, 5172, 38688, 4032, 22488, 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"start": 1282.94, "end": 1312.32, "text": "لما بيكون عدد الصفوف يساوي عدد الأعمدة بيكون عنها مصفوفة مربعة يعني مثل المصفوفة هاي هذه مصفوفة اتنين في اتنين واحد اتنين تلاتة اربعة وهذه مصفوفة مربعة واحد اتنين تلاتة اربعة خمسة ستة سبعة تمانية تسعة الأولى اللي فوق هذه اتنين في اتنين وهذه تلاتة في تلاتة square matrix لازم يكون فيها عدد الصفوف يساوي عدد الأعمدة", "tokens": [1211, 15042, 4724, 1829, 30544, 6225, 3215, 3215, 31767, 5172, 38688, 7251, 3794, 995, 45865, 6225, 3215, 3215, 16247, 25957, 41891, 4724, 1829, 30544, 18871, 11296, 3714, 9381, 5172, 38688, 3660, 3714, 25513, 27884, 37495, 22653, 50113, 1211, 9673, 9381, 5172, 38688, 3660, 8032, 47302, 29538, 3714, 9381, 5172, 38688, 3660, 1975, 2655, 1863, 9957, 8978, 1975, 2655, 1863, 9957, 36764, 24401, 1975, 2655, 1863, 9957, 6055, 1211, 9307, 3660, 1975, 25513, 27884, 37037, 24192, 3714, 9381, 5172, 38688, 3660, 3714, 25513, 27884, 36764, 24401, 1975, 2655, 1863, 9957, 6055, 1211, 9307, 3660, 1975, 25513, 27884, 16490, 2304, 3794, 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"text": "واضح كلام اللي أنا بقوله؟ يعني كل ما بتمسك صفر من الـA بيكون مقابله صفر من الـC في النتج مقابله صفر من الـC بتاخد الصفر و بتضرب في كل عمود و بتجمع العناصر اللي ما بينهم يعني و كإني جاهز بقولك جيب الصفر هالي مثلا واحد صفر أربعة اضرب كل عنصر بين جماله و اجمعهم", "tokens": [2407, 46958, 5016, 28242, 10943, 13672, 1829, 41850, 4724, 39648, 3224, 22807, 37495, 22653, 28242, 19446, 39894, 2304, 3794, 4117, 20328, 5172, 2288, 9154, 2423, 39184, 32, 4724, 1829, 30544, 3714, 4587, 16758, 43761, 20328, 5172, 2288, 9154, 2423, 39184, 34, 8978, 2423, 29399, 7435, 3714, 4587, 16758, 43761, 20328, 5172, 2288, 9154, 2423, 39184, 34, 39894, 47283, 3215, 31767, 5172, 2288, 4032, 39894, 11242, 25513, 8978, 28242, 6225, 2304, 23328, 4032, 39894, 7435, 2304, 3615, 18863, 1863, 33546, 2288, 13672, 1829, 19446, 49374, 16095, 37495, 22653, 4032, 9122, 28814, 22653, 10874, 40294, 11622, 4724, 39648, 4117, 10874, 1829, 3555, 31767, 5172, 2288, 8032, 6027, 1829, 50113, 15040, 36764, 24401, 20328, 5172, 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/cWgs8V-VhjE_raw.srt b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/cWgs8V-VhjE_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..229752e5d26dd3ac5db6977c529c581bfca42579
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/cWgs8V-VhjE_raw.srt
@@ -0,0 +1,1628 @@
+1
+00:00:20,670 --> 00:00:24,070
+لأ الحمد لله الصلاة والسلام على رسول الله ان البست
+
+2
+00:00:24,070 --> 00:00:31,010
+واحد ما بتغيرش البست ثابت ما بتغيرش واحد على طب
+
+3
+00:00:31,010 --> 00:00:35,610
+عشان تكون هذه واحد لازم تكون ال output واحد واحد
+
+4
+00:00:35,610 --> 00:00:41,830
+مظبط لازم يكون المقام واحد طيب معناته انا هبقى
+
+5
+00:00:41,830 --> 00:00:45,550
+اقول واحد على n طيب هان واحد على n
+
+6
+00:00:51,060 --> 00:00:57,740
+ما زال الـ Definition تمام جيتها واحد
+
+7
+00:00:57,740 --> 00:01:02,440
+على أن غلط واحد على أن غلط معناته خلاص بدك تبدأ
+
+8
+00:01:02,440 --> 00:01:06,780
+تدور على Definition يتناسب مع التلاتة اللي فوق مع
+
+9
+00:01:06,780 --> 00:01:10,200
+هذه و اللي جابلها يعني الواحد على أن الآن غلط
+
+10
+00:01:10,200 --> 00:01:17,540
+فاكرش فيه انتهى أمره طيب ماريش ممكن أنا أساوي أنت
+
+11
+00:01:17,540 --> 00:01:30,260
+تبيع نقص اتنين؟ أيوةطيب لو انا جيت جولت كداش؟
+
+12
+00:01:30,260 --> 00:01:35,500
+طيب طيب تعال .. تعالى نشوف احنا علاقة ال index هذا
+
+13
+00:01:35,500 --> 00:01:40,160
+بال value الأربعة التلاتة او الأربعة ايش علاقتها
+
+14
+00:01:40,160 --> 00:01:45,560
+بالتلاتة؟ تلاتة زائد واحد، مظبوط؟ طيب و التمانية
+
+15
+00:01:45,560 --> 00:01:47,980
+مع الأربعة؟
+
+16
+00:01:52,570 --> 00:01:56,830
+زائد أربعة لاحظت وبالتالي أنا مش هقدر أجيب ستاش
+
+17
+00:01:56,830 --> 00:02:02,570
+تساوي خمسة زائد أحداشر ومافيش علاقة ثابتة أجيبها
+
+18
+00:02:02,570 --> 00:02:06,770
+بشكل مباشر ممتاز معناته أن هذا برضه التفكير بالشكل
+
+19
+00:02:06,770 --> 00:02:11,250
+هذا مش هيصبق معايا فلو أنا بدأت أفكر بالقصص طلع
+
+20
+00:02:11,250 --> 00:02:18,250
+بالأساس هان واحد اتنين اربعة تمانية يعني هيك بين
+
+21
+00:02:18,250 --> 00:02:28,030
+قصين اتنين قص صفر اتنين قص واحد-2-3-4 يعني أن الـ
+
+22
+00:02:28,030 --> 00:02:31,810
+Definition تبع هذا هيك هي المقام اللي موجود عندي
+
+23
+00:02:31,810 --> 00:02:38,250
+هذا 1 2 وصفر 2
+
+24
+00:02:38,250 --> 00:02:45,910
+4 8 16 2 أُص و بدأت أمشي بالـSequence كيف ممكن
+
+25
+00:02:45,910 --> 00:02:46,870
+أسوي أنا فيك أمر
+
+26
+00:02:54,000 --> 00:02:58,640
+أروح .. لو أنا أديت هيك و قلتله واحد على اتنين أس
+
+27
+00:02:58,640 --> 00:03:05,860
+ان ناقص واحد وين المشكلة في الموضوع؟ اتنين او واحد
+
+28
+00:03:05,860 --> 00:03:13,200
+على اتنين أس ان ناقص واحد واحد ناقص واحد صفر وهي
+
+29
+00:03:13,200 --> 00:03:18,840
+دي واحد
+
+30
+00:03:18,840 --> 00:03:21,220
+على اتنين أس اتنين ناقص واحد
+
+31
+00:03:24,950 --> 00:03:28,810
+يعني بدون مبدأ من الصفر هي مباشرة مع الواحد انحلت
+
+32
+00:03:28,810 --> 00:03:37,490
+المشكلة اتنين اص تلاتة ناقص واحد هذه واحد على
+
+33
+00:03:37,490 --> 00:03:42,710
+تمانية اللي هي واحد على اتنين اص اربع ناقص واحد
+
+34
+00:03:42,710 --> 00:03:47,810
+اللي هي اتنين اص تلاتة واحد على ستاش بيتساوي واحد
+
+35
+00:03:47,810 --> 00:03:53,190
+على اتنين اص خمسة ناقص واحدوبالتالي هذه الـ
+
+36
+00:03:53,190 --> 00:03:55,830
+Definition تبعي معناته انا بقدر أقوله An بدها
+
+37
+00:03:55,830 --> 00:04:03,510
+تساوي واحد على اتنين قص M ماقص واحد وال M أكبر أو
+
+38
+00:04:03,510 --> 00:04:09,290
+تساوي الواحد هل ممكن أحصل على Definition تاني؟
+
+39
+00:04:09,290 --> 00:04:14,210
+أغير ال index صفر
+
+40
+00:04:14,210 --> 00:04:20,810
+واحد اتنين تلاتة أربعة معناته هتحصل عليها بشكل
+
+41
+00:04:20,810 --> 00:04:27,310
+مباشرواحد على اتنين
+
+42
+00:04:27,310 --> 00:04:32,550
+والصفر واحد على اتنين اص واحد واحد على اتنين اص
+
+43
+00:04:32,550 --> 00:04:36,650
+اتنين واحد على اتنين اص تلاتة واحد على اتنين اص
+
+44
+00:04:36,650 --> 00:04:40,710
+اربعة مياته ال a n تبعتي هي تساوي واحد على اتنين
+
+45
+00:04:40,710 --> 00:04:46,330
+اص n و ال n أكبر او تساوي صفر وهي two definition
+
+46
+00:04:46,330 --> 00:04:51,750
+لنفس ال sequence اللي موجود عندك الآن
+
+47
+00:04:53,170 --> 00:04:58,570
+أيه يكون أسرع لذهنك تصلّه؟ قضية كتير بس في الآخر
+
+48
+00:04:58,570 --> 00:05:02,190
+.. في الآخر كونه هي sequence الأصل أنك تبني ..
+
+49
+00:05:02,190 --> 00:05:07,370
+تقدر تبنيها سواء كانت على واحد أو على صفر طيب، لو
+
+50
+00:05:07,370 --> 00:05:12,010
+أنت حسيت بديت من صفر ولاجيت سكّرت معاك، إيش تساوي؟
+
+51
+00:05:12,010 --> 00:05:15,270
+هو بدل ال-sin index من واحد ولو بديت من واحد و
+
+52
+00:05:15,270 --> 00:05:19,150
+سكّرت تبدأ .. لاجيت الشجتان مسكرة، معناته مخك بده
+
+53
+00:05:19,150 --> 00:05:23,580
+تعمله formatting من جديد و تبدأ تفكر بالمسألةبشكل
+
+54
+00:05:23,580 --> 00:05:32,140
+مختلف تماما طيب لأن
+
+55
+00:05:32,140 --> 00:05:41,180
+لو ايجا جالي لو ايجا جالي في sequence arithmetic
+
+56
+00:05:41,180 --> 00:05:47,000
+sequence مثل
+
+57
+00:05:47,000 --> 00:05:50,680
+ال sequence اتنين
+
+58
+00:05:50,680 --> 00:05:52,280
+اربعة
+
+59
+00:05:54,290 --> 00:05:57,030
+ستة تمانية عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة
+
+60
+00:05:57,030 --> 00:05:57,470
+عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة
+
+61
+00:05:57,470 --> 00:05:57,670
+عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة
+
+62
+00:05:57,670 --> 00:06:02,870
+عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة
+
+63
+00:06:02,870 --> 00:06:02,870
+عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة
+
+64
+00:06:02,870 --> 00:06:02,870
+عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة
+
+65
+00:06:02,870 --> 00:06:02,910
+عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة
+
+66
+00:06:02,910 --> 00:06:06,630
+عشرة
+
+67
+00:06:06,630 --> 00:06:12,890
+عشرة عشرة عشرة عشرة
+
+68
+00:06:19,350 --> 00:06:22,250
+1 زائد 2 تساوي 3 او تساوي ثلاثة ثلاثة ثلاثة ثلاثة
+
+69
+00:06:22,250 --> 00:06:26,170
+ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة
+
+70
+00:06:26,170 --> 00:06:31,970
+ثلاثة تساوي ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة تساوي
+
+71
+00:06:31,970 --> 00:06:34,970
+ثلاثة ثلاثة ثلاثة ثلاثة تساوي ثلاثة ثلاثة ثلاثة
+
+72
+00:06:34,970 --> 00:06:38,090
+ثلاثة تساوي ثلاثة ثلاثة ثلاثة ثلاثة تساوي ثلاثة
+
+73
+00:06:38,090 --> 00:06:48,460
+ثلاثة ثلاثة ثلاثة تساوي ثلاثة ثلاثة ثلاثالـ N لـ
+
+74
+00:06:48,460 --> 00:06:52,100
+Index هيمشي Sequence إما صفر واحد اتنين تلاتة إلى
+
+75
+00:06:52,100 --> 00:06:55,900
+مال نهاية أو واحد اتنين تلاتة أربع إلى مال نهاية
+
+76
+00:06:55,900 --> 00:06:59,520
+أنت دايماً تطلع في مين؟ في الأرقام اللي عندك إيش
+
+77
+00:06:59,520 --> 00:07:04,080
+الصيغة اللي عندي أنا دايماً في فرق اتنين بقدر
+
+78
+00:07:04,080 --> 00:07:09,560
+أقوله AN بيتساوي اتنين في N و ال N أكبر أو تساوي
+
+79
+00:07:09,560 --> 00:07:13,380
+صفر بصيصبر
+
+80
+00:07:13,380 --> 00:07:18,210
+شوية أنا كتبت أكبر أو تساوي صفر اتنين في الصفرصفر
+
+81
+00:07:18,210 --> 00:07:21,530
+لا تنتمي للـ sequence اللي موجودة عندها المسؤولة
+
+82
+00:07:21,530 --> 00:07:26,930
+لأ معناته التعريف تبعي بده يبدأ من واحد واحد في
+
+83
+00:07:26,930 --> 00:07:30,850
+اتنين او اتنين في واحد اتنين اتنين في اتنين اربعة
+
+84
+00:07:30,850 --> 00:07:33,910
+اتنين في تلاتة ستة معناته ال definition هيك تبعي
+
+85
+00:07:33,910 --> 00:07:40,870
+صحيح مائة في المائة مافي مشكلة حل
+
+86
+00:07:40,870 --> 00:07:43,830
+ال index هل بتقدر تحصل اليك في ال natural number
+
+87
+00:07:43,830 --> 00:07:47,940
+او في ال z او ماشي ابقىماش هتظبط الكلام أحمد الآن،
+
+88
+00:07:47,940 --> 00:07:50,340
+احنا بتكلمها على sequence مجموعة من الأرقام
+
+89
+00:07:50,340 --> 00:07:55,720
+المتتالية، متتالية، من اسمها متتالية، الآن تبدأ
+
+90
+00:07:55,720 --> 00:08:04,100
+ايش؟ بدك رقم هم، لأ اسميكوا إيش بقول، بقول لو أنا
+
+91
+00:08:04,100 --> 00:08:05,400
+هذه بدي أبدأها من صفر
+
+92
+00:08:14,420 --> 00:08:18,740
+مش بتظبط معايا؟ انا جاي أقولك بتظبط؟ مش عارف .. هي
+
+93
+00:08:18,740 --> 00:08:23,200
+.. في الصفر .. عند الصفر تمام لكن عند الواحد ادتني
+
+94
+00:08:23,200 --> 00:08:26,140
+خمسة ميات وخلاص ال definition فيه غلط مش هتظبط
+
+95
+00:08:26,140 --> 00:08:32,280
+الحال هيك إلا لو روحت أضافت صفر غام وضلت الأن أكبر
+
+96
+00:08:32,280 --> 00:08:35,300
+أو تساوي صفر بالشكل هذا بتضل العملية عندي عش ..
+
+97
+00:08:35,300 --> 00:08:38,580
+صحيحة بصير هذا أول element في ال sequence وممكن أن
+
+98
+00:08:38,580 --> 00:08:43,170
+ال sequence عند هيك صحيحة مئة في المئةطيب طبعا حتى
+
+99
+00:08:43,170 --> 00:08:47,370
+على ال definition الجديد او انا اتيت و قلتلك بدي
+
+100
+00:08:47,370 --> 00:08:55,970
+حاصل جمع اول خمس حدود بدي حاصل جمع اول خمس حدود شو
+
+101
+00:08:55,970 --> 00:09:01,910
+بيبقى تساوي؟ هتقول ايه؟ صفر .. اتنين .. ستة ..
+
+102
+00:09:01,910 --> 00:09:08,650
+اتناشر .. عشرين .. هاي اول خمس حدود صح؟
+
+103
+00:09:08,650 --> 00:09:09,890
+أمتاز .. طب اول عشرة
+
+104
+00:09:13,350 --> 00:09:20,050
+مش هتخلص هيك، بدك تصير أنك تتمد على الـSummation،
+
+105
+00:09:20,050 --> 00:09:22,810
+والـSummation في عندي مجموعة من القوانين بكل
+
+106
+00:09:22,810 --> 00:09:35,410
+بساطة، القانون هي مجموع أول N terms، عشرة عشرةأول
+
+107
+00:09:35,410 --> 00:09:44,590
+مية مية زائد او مضروبة فيه أول element ال a لأن ال
+
+108
+00:09:44,590 --> 00:09:49,170
+a صفر ممكن تعمل لخمة لبعضكوا عشان ال index المقصود
+
+109
+00:09:49,170 --> 00:09:57,670
+في ال a صفر أول element زائد an الانصر مش الأخير
+
+110
+00:09:58,620 --> 00:10:03,500
+العنصر العاشر أو العنصر المية أو العنصر الخمسين
+
+111
+00:10:03,500 --> 00:10:08,680
+وهناك تنتبه و تنتبه كويس إذا ال index بدي معاك من
+
+112
+00:10:08,680 --> 00:10:14,260
+صفر معناته العنصر العاشر بدي يكون تسعة أصبت؟ ال
+
+113
+00:10:14,260 --> 00:10:18,580
+index تبعته تسعة وهذه المقصدات بتنتبهله وبالتالي
+
+114
+00:10:18,580 --> 00:10:25,120
+المقصود بال A N هو العنصر ال Nعلى اتنين فابتدعي
+
+115
+00:10:25,120 --> 00:10:31,420
+اني اجي اطبق الكلام هذا ال summation من ال k او من
+
+116
+00:10:31,420 --> 00:10:38,000
+ال i او ال k equal zero ل ال n طبعا هال من zero ل
+
+117
+00:10:38,000 --> 00:10:43,960
+ال n كم element صار ن زائد واحد ليش بعد اللانهائي
+
+118
+00:10:43,960 --> 00:10:48,830
+ال k من zero ل nان زائد واحد انتبه فممكن انت
+
+119
+00:10:48,830 --> 00:10:52,730
+القانون كمان يربكك اكتر المجموع ال summation يساوي
+
+120
+00:10:52,730 --> 00:11:01,730
+هذه تعالى نسقط الكلام هذا هم هي اول خمس اعداد اول
+
+121
+00:11:01,730 --> 00:11:07,790
+خمس اعداد مجموع اول خمس اعداد يساوي خمسة مضروبة في
+
+122
+00:11:07,790 --> 00:11:13,530
+اول element صفر زائد الانصر الخامس واحد اتنين
+
+123
+00:11:13,530 --> 00:11:20,610
+تلاتة اربعة خمسة تمانيةعلى اتنين خمسة في تمانية
+
+124
+00:11:20,610 --> 00:11:26,890
+اربعين على اتنين تساوي عشرين تمام الشباب كمان مرة
+
+125
+00:11:26,890 --> 00:11:34,130
+برجع و باعد تاني ال am ها ديهي العنصر اللي في
+
+126
+00:11:34,130 --> 00:11:37,850
+المنزلة M يعني لما انا باجي بقولك العنصر الأول عشر
+
+127
+00:11:37,850 --> 00:11:42,590
+عناصر هانا باجي صدق العنصر العاشر لأ لو ال index
+
+128
+00:11:42,590 --> 00:11:47,350
+تبعك بادي من Zero معناته هو العنصر التاسع بادي من
+
+129
+00:11:47,350 --> 00:11:50,350
+مية او عفوا بادي من واحد معناته واحد من الكون
+
+130
+00:11:50,350 --> 00:11:55,870
+العاشر نفسه نعم انا
+
+131
+00:11:55,870 --> 00:12:01,450
+احنا قدته هي في الآخرصفر واحد اتنين تلاتة اربعة لو
+
+132
+00:12:01,450 --> 00:12:05,250
+انا سألتك يا رامي مش رامي برضه لو انا سألتك ايش
+
+133
+00:12:05,250 --> 00:12:09,490
+تاني عنصر في ال sequence تاني عنصر في ال sequence
+
+134
+00:12:09,490 --> 00:12:13,290
+اتنين تاني عنصر في ال sequence اتنين على الرغم انه
+
+135
+00:12:13,290 --> 00:12:17,570
+ال index تبعه واحد خامس عنصر في ال sequence تمانية
+
+136
+00:12:17,570 --> 00:12:22,490
+ليش لأن ال index تبعي انت الآن عند لما بدت تشتغل
+
+137
+00:12:22,490 --> 00:12:26,660
+انسال ال sequence هديهك ال index شويةقلت لك و من
+
+138
+00:12:26,660 --> 00:12:29,220
+أصل الخامس في ال sequence مباشرة هتقولي تمانية
+
+139
+00:12:29,220 --> 00:12:35,860
+جديش ال index تبعه حسب ال sequence تبعتك بدأت من
+
+140
+00:12:35,860 --> 00:12:40,660
+صفر ولا بدأت من واحد ال index تبعه حسب ال sequence
+
+141
+00:12:40,660 --> 00:12:48,720
+اللي عندك تمام طيب لو أجينا قولنا arithmetic
+
+142
+00:12:48,720 --> 00:12:56,300
+sequence واحد اتنين تلاتة أربعة خمسةالى ما لا
+
+143
+00:12:56,300 --> 00:13:03,300
+نهاية arithmetic sequence ولا لا ال A فيها تساوي
+
+144
+00:13:03,300 --> 00:13:14,800
+واحد وال D تساوي واحد ولا لا صحيك بقدر طيب تعالى
+
+145
+00:13:14,800 --> 00:13:22,980
+لو أنا سألتك A N ايش بتساوي A زائد N في D يعني
+
+146
+00:13:22,980 --> 00:13:31,080
+العنصر الخامس A خمسةماذا يساوي؟ واحد زائد خمسة في
+
+147
+00:13:31,080 --> 00:13:37,380
+واحد جديش الداني ايه؟ ستة الداني ستة معناته ال
+
+148
+00:13:37,380 --> 00:13:42,180
+index تبعي في ال sequence هذي جديش؟ صفر ال index
+
+149
+00:13:42,180 --> 00:13:48,400
+تبعي في ال sequence هذي صفر كمان مرة حلقتي بقولك
+
+150
+00:13:48,400 --> 00:13:53,920
+ليش صفر؟ كمان مرة الآن ال sequence arithmetic
+
+151
+00:13:53,920 --> 00:13:59,740
+sequencearithmetic sequence متتابعة حسابية متتابعة
+
+152
+00:13:59,740 --> 00:14:05,020
+حسابية ليش الفرق بين كل عنصرين متتاليين ثابت لو
+
+153
+00:14:05,020 --> 00:14:09,320
+واحد وبالتالي هي ال a equal واحد و ال d equal واحد
+
+154
+00:14:09,320 --> 00:14:17,400
+الان كتب الصيغة العامة تبعتها a n بدا تساوي a زائد
+
+155
+00:14:17,400 --> 00:14:24,150
+n في d n في dهذه هي الـ Definition، اللي هي لو أنا
+
+156
+00:14:24,150 --> 00:14:28,850
+دي اتسألتك عن العنصر الخامس A خمسة، مقصودها دي
+
+157
+00:14:28,850 --> 00:14:33,850
+إيش؟ لو هيك لو أنا اتسألتك عن العنصر الخامس الـ A
+
+158
+00:14:33,850 --> 00:14:38,790
+العنصر الخامس، مباشرة يعني هتقدر لذهني أن الـ N
+
+159
+00:14:38,790 --> 00:14:45,230
+equal خمسة، معناته هاي واحد زائد خمسة في الـD اللي
+
+160
+00:14:45,230 --> 00:14:50,080
+هي الواحدوده تساوي ستة بس الستة فعليا الانصار
+
+161
+00:14:50,080 --> 00:14:56,020
+السادس إلا إلا في حالة واحدة ال index تبقى إيش بدأ
+
+162
+00:14:56,020 --> 00:15:01,340
+من صفر ال index بدأ من صفر تمام و بالتالي بدأت أنت
+
+163
+00:15:01,340 --> 00:15:05,800
+بيجي لها أمر هي ال definition تبقى ال sequence هيك
+
+164
+00:15:05,800 --> 00:15:10,620
+و الجيل اللي قلتلك ممكن أخليها برا ناجس واحد نعم
+
+165
+00:15:10,620 --> 00:15:18,260
+ممكن أخليها برناجس واحد تحطهم برا ناجس واحديعني A
+
+166
+00:15:18,260 --> 00:15:25,320
+زائد M في D الكل ناجس واحد طيب
+
+167
+00:15:25,320 --> 00:15:32,440
+في الآخر هي حسابية طيب الآن اللي انا بده اوصلك هي
+
+168
+00:15:32,440 --> 00:15:34,900
+هي ال sequence و هي المواطيات من ال sequence اللي
+
+169
+00:15:34,900 --> 00:15:41,760
+عندك و بقولك اجمعلي أول خمس حدود منها اجمعلي أول
+
+170
+00:15:41,760 --> 00:15:44,060
+خمس حدود خمسة في
+
+171
+00:15:47,150 --> 00:15:58,210
+الحد الأول ايه؟ زائد الحد الخامس خمسة على اتنين
+
+172
+00:15:58,210 --> 00:16:02,130
+هاي
+
+173
+00:16:02,130 --> 00:16:04,910
+قدام ال sequence موجودة خلّالها أنا بودّيك على
+
+174
+00:16:04,910 --> 00:16:09,010
+مشكلة أعوص من هيك الآن و هذا تساوي خمسة بستة
+
+175
+00:16:09,010 --> 00:16:14,470
+تلاتين على اتنين يساوي خمستاشر لو جمعتهم خمستاشر
+
+176
+00:16:18,780 --> 00:16:27,240
+first five terms هذا summation of ال first five
+
+177
+00:16:27,240 --> 00:16:34,720
+terms طيب لو انا اديت قولتلك ال summation of ال
+
+178
+00:16:34,720 --> 00:16:40,700
+first twenty terms
+
+179
+00:16:40,700 --> 00:16:49,200
+الان مش هكون في عندك مشكلة عشرين واحد زائدعشرين
+
+180
+00:16:49,200 --> 00:16:55,540
+ايوة بناء على ايش انت بدأت هيك اد انه بدأ من واحد
+
+181
+00:16:55,540 --> 00:17:01,940
+وال difference عشرين عشرين
+
+182
+00:17:01,940 --> 00:17:10,960
+في واحد وعشرين على اتنين طيب الان مش
+
+183
+00:17:10,960 --> 00:17:14,960
+قضية كمان مرة زميلكوا بيقول لو بدأت من صفر احسن مش
+
+184
+00:17:14,960 --> 00:17:19,460
+قضية هتطلع معاكحسب إيش ال index تبعنا، اللي أنا ..
+
+185
+00:17:19,460 --> 00:17:22,500
+هاي ال sequence اللي عندي .. هاي ال sequence اللي
+
+186
+00:17:22,500 --> 00:17:27,860
+عندي حاطيكي إياها، لأن إذا أنت بدك تروح الرقم هذا،
+
+187
+00:17:27,860 --> 00:17:33,970
+انت مش متأكد إيش بدي يطلع معاك، تمام؟تشوف المعادلة
+
+188
+00:17:33,970 --> 00:17:37,770
+وتشوف الـ index وتدخل في التفاصيل زي ما قلنا اللي
+
+189
+00:17:37,770 --> 00:17:43,430
+بدهاش شغل أكتر يعني كمان مرة على A N تساوي N أو A
+
+190
+00:17:43,430 --> 00:17:50,610
+زائد N في D والـ N أكبر أو تساوي صفر الـ N أكبر أو
+
+191
+00:17:50,610 --> 00:17:57,710
+تساوي صفر مصبوطة هيك؟ أنا بسألك هاي الـ definition
+
+192
+00:17:57,710 --> 00:18:07,550
+صح؟ تديني واحد؟اللي بعدها ايوة
+
+193
+00:18:07,550 --> 00:18:13,190
+اتنين تلاتة
+
+194
+00:18:13,190 --> 00:18:24,250
+واحد زائد صفر واحد زائد واحد في واحد اتنين
+
+195
+00:18:24,250 --> 00:18:28,770
+ايوة صفر واحد اتنين تلاتة و انا في عندك دائما واحد
+
+196
+00:18:28,770 --> 00:18:35,370
+تساوي و هذه واحد هذه واحد هذه اتنينهذه ثلاثة أربعة
+
+197
+00:18:35,370 --> 00:18:37,590
+خمسة ستة مع تواعي ال definition تبعي ال sequence
+
+198
+00:18:37,590 --> 00:18:43,290
+عندي مش مشكلة وبالتالي بدك تمتع به دائما لل unterm
+
+199
+00:18:43,290 --> 00:18:46,890
+اللي بدك تشوفه طبعا على غرار القانون هذا في عندنا
+
+200
+00:18:46,890 --> 00:18:50,430
+مجموعة كمان من القوانين اللي لها علاقة بال other
+
+201
+00:18:50,430 --> 00:18:57,130
+sequences بال geometric sequence اللي همتكلم على
+
+202
+00:18:57,130 --> 00:19:05,730
+geometric sequence ar os k ar osK وبالتالي هتكون
+
+203
+00:19:05,730 --> 00:19:12,930
+AR أُس N زائد واحد ناقص A على R ناقص واحد وبالتالي
+
+204
+00:19:12,930 --> 00:19:19,850
+انت بتقدر المطلوب منك تحفظ هدول أول خمسة يعني
+
+205
+00:19:19,850 --> 00:19:26,370
+الواحدة بتاعة ال arithmetic وهدولة أربعة هذه
+
+206
+00:19:26,370 --> 00:19:33,360
+ماتنسهاش هذه واحدو هدول ايش؟ اربع .. ليش تحفظهم؟
+
+207
+00:19:33,360 --> 00:19:36,120
+لأنه لحد ال هيك اللي انا هطلب منك .. هقولك هي ال
+
+208
+00:19:36,120 --> 00:19:39,540
+sequence و روحتلي مجموع اول term الحدود تبعتها
+
+209
+00:19:39,540 --> 00:19:44,080
+عشان تقدر تجيبها بدك تتخيل الصيغة العامة تبعتها
+
+210
+00:19:44,080 --> 00:19:47,540
+كيف وبناء عليها تقدر تحدد ال summation
+
+211
+00:19:53,550 --> 00:19:56,170
+خلص ال section الخاص أو هذه الجزئية اللي انا بديها
+
+212
+00:19:56,170 --> 00:19:59,370
+من موضوع ال sequences ماخلصناش لسه فينا كمان
+
+213
+00:19:59,370 --> 00:20:03,750
+section بدنا نخلصه section بسيط زي هيك اربع اربع
+
+214
+00:20:03,750 --> 00:20:08,390
+خمس slide ال matrices
+
+215
+00:20:08,390 --> 00:20:15,470
+المظهوفات طيب
+
+216
+00:20:15,470 --> 00:20:21,510
+لان لما انا بتكلم عن المظهوفات برضه بتكلم على
+
+217
+00:20:21,510 --> 00:20:25,540
+discretestructure بتتكلم عن الـ discrete structure
+
+218
+00:20:25,540 --> 00:20:28,540
+لاحظ الشابتر كله بتتكلم عن الـ discrete structure
+
+219
+00:20:28,540 --> 00:20:34,580
+المجموعات الـ sets الـ functions جابني الماتريسيز
+
+220
+00:20:34,580 --> 00:20:39,220
+الـ sequences و هاي الماتريسيز او المصفوفات طيب
+
+221
+00:20:39,220 --> 00:20:42,160
+لان انا بتتكلم على matrix معناته انا بتتكلم على
+
+222
+00:20:42,160 --> 00:20:48,760
+rectangular array rectangular array و دائما ال
+
+223
+00:20:48,760 --> 00:20:50,420
+array هذه تحدد بعدد
+
+224
+00:20:52,970 --> 00:20:59,690
+الصفوف وعدد الأعمدة عدد
+
+225
+00:20:59,690 --> 00:21:04,430
+الصفوف وعدد الأعمدة يعني المصفوف اللي قدامي في
+
+226
+00:21:04,430 --> 00:21:11,850
+المثال هذا عبارة عن ثلاث صفوف بنجدم
+
+227
+00:21:11,850 --> 00:21:15,970
+عدد الصفوف تلاتة في اتنين في عدد الصفوف او في عدد
+
+228
+00:21:15,970 --> 00:21:21,090
+الأعمدة اتنين طيب بنقول عن المصفوفة square matrix
+
+229
+00:21:22,940 --> 00:21:27,600
+لما بيكون عدد الصفوف يساوي عدد الأعمدة بيكون عنها
+
+230
+00:21:27,600 --> 00:21:32,600
+مصفوفة مربعة يعني مثل المصفوفة هاي هذه مصفوفة
+
+231
+00:21:32,600 --> 00:21:37,080
+اتنين في اتنين واحد اتنين تلاتة اربعة وهذه مصفوفة
+
+232
+00:21:37,080 --> 00:21:42,340
+مربعة واحد اتنين تلاتة اربعة خمسة ستة سبعة تمانية
+
+233
+00:21:42,340 --> 00:21:46,640
+تسعة الأولى اللي فوق هذه اتنين في اتنين وهذه تلاتة
+
+234
+00:21:46,640 --> 00:21:50,380
+في تلاتة square matrix لازم يكون فيها عدد الصفوف
+
+235
+00:21:50,380 --> 00:21:55,620
+يساوي عدد الأعمدةمتى بقول عن مصفوفتين متساويتين؟
+
+236
+00:21:55,620 --> 00:21:59,860
+لما يكون كل element أول حاجة لازم يكون له نفس
+
+237
+00:21:59,860 --> 00:22:05,200
+الحجم نفس الحجم وكل عنصر يساوي عنصر المقابل في
+
+238
+00:22:05,200 --> 00:22:09,140
+المصفوفة اللي موجودة عنده مافيش له صورة عنصر مقابل
+
+239
+00:22:09,140 --> 00:22:15,000
+له الآن
+
+240
+00:22:15,000 --> 00:22:21,320
+الـA هذه حجمها M في Nالصف الأول الصف الثاني الصف
+
+241
+00:22:21,320 --> 00:22:28,280
+الأم اي واحد يعني لو قلت لك الانصار صف و لو كانت
+
+242
+00:22:28,280 --> 00:22:35,040
+ام في واحد بيقول عنها عمد عشان
+
+243
+00:22:35,040 --> 00:22:40,480
+أجمع مصرفين لازم يكونوا نفس الحجم احنا قبل شوية
+
+244
+00:22:40,480 --> 00:22:44,180
+قلت عشان أقارن بين مصرفين من ناحية التساوي لازم
+
+245
+00:22:44,180 --> 00:22:47,220
+يكونوا نفس الحجم عشان أجمع مصرفين لازم يكونوا نفس
+
+246
+00:22:47,220 --> 00:22:55,160
+الحجمبالآن العنصر الجديد اللي هو الـ C Cij
+
+247
+00:22:55,160 --> 00:22:59,780
+طبعا ناتج مصحوفة من نفس حجم المصوفتين السابقتين
+
+248
+00:22:59,780 --> 00:23:10,680
+يساوي ال element IJ زائد ال element Bij بالتالي
+
+249
+00:23:10,680 --> 00:23:14,900
+الأربعة هذه تساوي التلاتة
+
+250
+00:23:16,130 --> 00:23:20,450
+زائد الواحد من وين هذا الكلام جبته انا الاربعة هذه
+
+251
+00:23:20,450 --> 00:23:26,310
+هي عبارة عن C 11 مصبوط وهي عبارة عن حاصل جمع
+
+252
+00:23:26,310 --> 00:23:34,630
+العنصرين A11 زائد B11 الان هذا التلاتة او هذا
+
+253
+00:23:34,630 --> 00:23:44,430
+العنصر النقص تلاتة هذه عبارة عن CC2 3 C2 3 هي
+
+254
+00:23:44,430 --> 00:23:55,290
+عبارة عن حص الجامع B2 3 زائد A2 3 و هكذا لو كانوا
+
+255
+00:23:55,290 --> 00:23:59,230
+المصوفتين أحجامهم مختلفة عملية الجامع مابتفضبطش
+
+256
+00:23:59,230 --> 00:24:08,110
+معاهم تمام؟ ننتقل لعملية الضربطبعا الموضوع سهل
+
+257
+00:24:08,110 --> 00:24:14,630
+لأنكوا أخدتوه في الثانوية و قبل توجيهه كمان فتبدأ
+
+258
+00:24:14,630 --> 00:24:19,650
+تتكلم على المصطفات من هاشر طيب ماليش في رياضية
+
+259
+00:24:19,650 --> 00:24:23,450
+الوصائط أنا الآن؟لأن عشان أضرب مصفوفتين في بعض
+
+260
+00:24:23,450 --> 00:24:28,710
+عشان أضرب مصفوفتين في بعض لازم يكون عدد أعمدة
+
+261
+00:24:28,710 --> 00:24:33,750
+الأولى يساوي عدد صفوف الثانية يعني الآن لو
+
+262
+00:24:33,750 --> 00:24:39,310
+المصفوفة الأولى A عندي اتنين في تلاتة ال B اللي
+
+263
+00:24:39,310 --> 00:24:44,990
+بدي أضربها فيها لازم تكون تلاتة في أي حاجة مثلا
+
+264
+00:24:44,990 --> 00:24:52,790
+تلاتة في أربعة المصفوفة الناتج Cهتكون عبارة عن
+
+265
+00:24:52,790 --> 00:24:59,710
+اتنين في اربعة عملية
+
+266
+00:24:59,710 --> 00:25:07,250
+الضرب كيف بالتم تاخد الصف الصف الأول تضرب في
+
+267
+00:25:07,250 --> 00:25:12,110
+العمود الأول لأ شوية بس عشان نركز شوية في الضرب و
+
+268
+00:25:12,110 --> 00:25:17,830
+نتذكره صح المصفوفة الناتج ايش المفروض تكون اتنين
+
+269
+00:25:17,830 --> 00:25:24,450
+في اربعةهذه في المثال اللي عندي هنا يعني فيها أنا
+
+270
+00:25:24,450 --> 00:25:26,650
+عندي صفين وأربع أعمدان
+
+271
+00:25:36,150 --> 00:25:41,930
+الأن العنصر هذا اللي جاي في الصف الأول مين بيحدده؟
+
+272
+00:25:41,930 --> 00:25:46,970
+الصف الأول من المصوفة اللي حددت الصفوف هكذا قهدت
+
+273
+00:25:46,970 --> 00:25:53,770
+صفوف المصوفة C من صفوف A مظبوط؟ وبالتالي .. لما
+
+274
+00:25:53,770 --> 00:25:58,010
+تاخد الصف الأول .. لما تاخد الصف الأول من ال A
+
+275
+00:25:58,010 --> 00:26:04,670
+معناته أنك بتتكلم على ناتج في الصف الأول ل Cمصبوط؟
+
+276
+00:26:04,670 --> 00:26:09,670
+طب الصف الأول فيه أكتر من عمود مين اللي بحدده؟
+
+277
+00:26:09,670 --> 00:26:15,710
+العمود اللي اخترته من B يعني هيك الصف الأول في
+
+278
+00:26:15,710 --> 00:26:21,430
+العمود الأول بيعطينا ال element الصف الأول العمود
+
+279
+00:26:21,430 --> 00:26:26,490
+الأول في مين؟ في C الصف الأول في العمود التاني
+
+280
+00:26:26,490 --> 00:26:31,580
+بيعطينا ال element التاني في الصف الناتجواضح كلام
+
+281
+00:26:31,580 --> 00:26:35,840
+اللي أنا بقوله؟ يعني كل ما بتمسك صفر من الـA بيكون
+
+282
+00:26:35,840 --> 00:26:40,420
+مقابله صفر من الـC في النتج مقابله صفر من الـC
+
+283
+00:26:40,420 --> 00:26:44,820
+بتاخد الصفر و بتضرب في كل عمود و بتجمع العناصر
+
+284
+00:26:44,820 --> 00:26:48,240
+اللي ما بينهم يعني و كإني جاهز بقولك جيب الصفر
+
+285
+00:26:48,240 --> 00:26:56,540
+هالي مثلا واحد صفر أربعة اضرب كل عنصر بين جماله و
+
+286
+00:26:56,540 --> 00:26:57,140
+اجمعهم
+
+287
+00:27:00,200 --> 00:27:04,700
+أربعة في اتنين زائد صفر في واحد زائد تلاتة اربعة
+
+288
+00:27:04,700 --> 00:27:10,460
+في تلاتة اربع بعشر هي ال element الان خد الصف
+
+289
+00:27:10,460 --> 00:27:15,840
+الأول في العمود التاني كمان عشان تجيبني الاربعة
+
+290
+00:27:15,840 --> 00:27:20,360
+واحد في اربعة اربعة صفر في واحد واربعة في صفر
+
+291
+00:27:20,360 --> 00:27:26,620
+اربعة الان يا صاحبي اذا بدكش تعبيها صفوف ممكن
+
+292
+00:27:26,620 --> 00:27:33,350
+تعبيها اعمدانممكن تعبيها عمود عمود كيف بقى تساوي؟
+
+293
+00:27:33,350 --> 00:27:40,070
+هاي الصف الأول في العمود الأول الداني أربعة أعش
+
+294
+00:27:40,070 --> 00:27:45,750
+لما تنزل تاخد الصف التاني في العمود الأول فهليا
+
+295
+00:27:45,750 --> 00:27:48,230
+انت بقى بتعبي القيمة الثانية في العمود الأول في
+
+296
+00:27:48,230 --> 00:27:53,130
+الناتج هاي تمانية اللي بعده
+
+297
+00:27:55,990 --> 00:28:01,190
+هي سبعة و هكذا انت عبي صف صف اريح اليك او بطريقة
+
+298
+00:28:01,190 --> 00:28:05,370
+اللي بتشوفها مناسبة تمام؟ بطريقة اللي انت متعود
+
+299
+00:28:05,370 --> 00:28:09,050
+عليها اشتغل الصف الأول في العمود الأول الصف الأول
+
+300
+00:28:09,050 --> 00:28:11,570
+في العمود التاني الصف الأول في العمود التالت و كل
+
+301
+00:28:11,570 --> 00:28:15,510
+حاجة ما تخلص الصف الأول في الناتج بتبدل الصف و
+
+302
+00:28:15,510 --> 00:28:18,470
+بتبدل الصف في ال .. في ال a و بالتالي الصف في ال
+
+303
+00:28:18,470 --> 00:28:25,090
+result الأمر مش صعب ولا لا؟ في مشكلاش بقى؟ تمام
+
+304
+00:28:25,280 --> 00:28:32,840
+الصف I في العمود J الاصلي الديني ال element IJ
+
+305
+00:28:32,840 --> 00:28:40,760
+الصف I في العمود J الاصلي الديني ال element IJ حسب
+
+306
+00:28:40,760 --> 00:28:45,340
+القانون الموجود عندي تبع الدرب تمام هل ال BA يساوي
+
+307
+00:28:45,340 --> 00:28:48,700
+AB؟
+
+308
+00:28:48,700 --> 00:28:55,640
+A بدأ تساوي واحد و اتنين تلاتة اربعةوالـ B تساوي
+
+309
+00:28:55,640 --> 00:29:00,800
+اربعة اتنين او بلاش واحد
+
+310
+00:29:00,800 --> 00:29:10,980
+واحد اتنين اتنين افترض ان هذه A وهذه B A ضرب الـ B
+
+311
+00:29:10,980 --> 00:29:17,620
+ايش تساوي شباب صفر الأول في العمود الأول واحد في
+
+312
+00:29:17,620 --> 00:29:22,860
+واحد زيدي اتنين في اتنين خمسة برضه
+
+313
+00:29:22,860 --> 00:29:31,270
+كمان خمسةالان تلاتة في واحد زائد تمانية حداشر
+
+314
+00:29:31,270 --> 00:29:38,890
+حداشر بقى بي في ايه بي
+
+315
+00:29:38,890 --> 00:29:46,310
+في ايه مش هتساوي هتاخد الصف الأول وتضربه في العمود
+
+316
+00:29:46,310 --> 00:29:54,420
+الأول هي الصف الأول وهي العمود الأول1 في 1 زائد 1
+
+317
+00:29:54,420 --> 00:30:02,660
+في 3 أربعة بمجرد أنك شوفت الأربعة مباشرة A B لا
+
+318
+00:30:02,660 --> 00:30:11,280
+تساوي B A ليش؟ لأننا اتفقنا في المساواة كل element
+
+319
+00:30:11,280 --> 00:30:15,080
+بديه ساوي ال element المقابل له في نفس ال position
+
+320
+00:30:15,080 --> 00:30:18,260
+هي الأربعة لا تساوي الخمسة بس تعالى خلينا نكمل
+
+321
+00:30:18,850 --> 00:30:23,630
+اتنين بتساوي ال identity matrix إذا الناتج A ضرب
+
+322
+00:30:23,630 --> 00:30:30,990
+ال B إذا A ضرب ال B يساوي B ضرب ال A معناته A
+
+323
+00:30:30,990 --> 00:30:35,910
+تساوي ال B هذا الاحتمال الأول أو ال B هي عبارة عن
+
+324
+00:30:35,910 --> 00:30:40,210
+ال identity matrix ماهي ال identity matrix؟ هي
+
+325
+00:30:40,210 --> 00:30:46,070
+عبارة عن matrix مصفوفة الوحدةاللي كل عناصرها أسخار
+
+326
+00:30:46,070 --> 00:30:51,530
+ما يعدى القطر الرئيسي تساوي واحد ما يعدى عناصر
+
+327
+00:30:51,530 --> 00:30:57,650
+القطر الرئيسي تساوي واحد وبالتالي مصفوفة الوحدة ده
+
+328
+00:30:57,650 --> 00:31:03,090
+لو ضربتها في أي مصفوفة هتطلعش المصفوفة نفسها يعني
+
+329
+00:31:03,090 --> 00:31:10,770
+لو أنا جيت جولت هيفي عندي مصفوفة واحد اتنين تلاتة
+
+330
+00:31:11,620 --> 00:31:15,640
+أربعة خمسة ستة مصفوفة الوحدة اللي ممكن أضرب فيها
+
+331
+00:31:15,640 --> 00:31:21,040
+أنا لازم تكون جداش الشباب واحد
+
+332
+00:31:21,040 --> 00:31:26,820
+صفر صفر صفر واحد صفر صفر صفر واحد ليش هذا الكلام
+
+333
+00:31:26,820 --> 00:31:30,000
+لأنه لازم يكون هذي اتنين في تلاتة هذي لازم تكون
+
+334
+00:31:30,000 --> 00:31:34,980
+تلاتة في اتنين على الأقل مصبوط وبالتالي تلاتة في
+
+335
+00:31:34,980 --> 00:31:41,540
+تلاتة ايش ال result اللي مصفوفة اللي هتطلعإتنين في
+
+336
+00:31:41,540 --> 00:31:47,420
+تلاتة الصف الأول في العمود الأول الصف الأول في
+
+337
+00:31:47,420 --> 00:31:53,660
+العمود الأول واحد اتنين تلاتةالصف الأول في العمود
+
+338
+00:31:53,660 --> 00:31:58,360
+التالت 2 الصف الأول في العمود التالت ثلاثة بعد هيك
+
+339
+00:31:58,360 --> 00:32:02,320
+الصف الأول في العمود التالت أربعة خمسة ستة
+
+340
+00:32:02,320 --> 00:32:05,820
+وبالتالي المصفوفة لما تضربها في ال identity matrix
+
+341
+00:32:05,820 --> 00:32:10,040
+مصفوفة الوحدة تطلع نفسها وكأن ال identity matrix
+
+342
+00:32:10,040 --> 00:32:14,720
+هي المحادث ضربي تبع المصفوفات بس بجتمع حجمها دائما
+
+343
+00:32:14,720 --> 00:32:22,280
+ال Transpose مدور المصفوفة أو مجلوب المصفوفةما هو
+
+344
+00:32:22,280 --> 00:32:27,560
+الـ Transpose؟ بتبدل .. بتبدل صفوف المصفوفة لأعمدة
+
+345
+00:32:27,560 --> 00:32:34,900
+أو بتبدل الأعمدة لصفوف طيب الشباب خليكم بسمعاه يا
+
+346
+00:32:34,900 --> 00:32:41,200
+هان الان في ال Transpose الأن لو أنا افترضت
+
+347
+00:32:41,200 --> 00:32:48,080
+المصفوفة A هي عبارة عن M في M ايه ال Transpose
+
+348
+00:32:48,080 --> 00:32:57,190
+مدور المصفوفة هذه؟ماذا سيكون؟ سيكون M في M لأن انت
+
+349
+00:32:57,190 --> 00:33:03,730
+بدلت صفوف المصفوفة لأعمدة و لأعمدة لصفوف طيب
+
+350
+00:33:03,730 --> 00:33:07,430
+وبالتالي
+
+351
+00:33:07,430 --> 00:33:12,130
+لو كان بالمثال هذا عندنا هي ايه؟ واحد اتنين تلاتة
+
+352
+00:33:12,130 --> 00:33:17,130
+اربع خمسة ستة هي عبارة عن مصفوفة اتنين في تلاتة ال
+
+353
+00:33:17,130 --> 00:33:22,070
+transpose تبعتهابتكون تلاتة في اتنين الشرق المهم
+
+354
+00:33:22,070 --> 00:33:27,810
+عندي الصف الأول بيكون العمود الأول الصف الثاني
+
+355
+00:33:27,810 --> 00:33:33,330
+بيكون العمود التاني وبالتالي بداية الصف هتكون هي
+
+356
+00:33:33,330 --> 00:33:37,090
+نفسها بداية العمود عشان ما تخربطيش في الترتيب اللي
+
+357
+00:33:37,090 --> 00:33:42,450
+عناصر اللي عندنا حكينا
+
+358
+00:33:42,450 --> 00:33:47,240
+على المصوفة لما تكون squareوكل العناد .. اه okay
+
+359
+00:33:47,240 --> 00:33:52,580
+بقول عن المصفوفة symmetric او متماثلة لما يكون كل
+
+360
+00:33:52,580 --> 00:34:01,400
+element aij يساوي ajI ايش يعني؟ المصفوفة المتماثلة
+
+361
+00:34:01,400 --> 00:34:06,840
+هي مصفوفة مربعة ايش يعني مربعة؟ عدد صفوفها تساوي
+
+362
+00:34:06,840 --> 00:34:10,880
+عدد الأعمدة اللي فيها بقول عنها المصفوفة متماثلة
+
+363
+00:34:10,880 --> 00:34:20,140
+لما يكون كل element ijبدي يساوي جاي الانصار هذا
+
+364
+00:34:20,140 --> 00:34:26,880
+جداش ال position تبعه طبعا احنا الآن متماثلة يعني
+
+365
+00:34:26,880 --> 00:34:29,740
+اي واحد واحد ما هي نفسها اي واحد واحد في شوية
+
+366
+00:34:29,740 --> 00:34:33,020
+مشكلة يعني سيبني من عناصر القطر الرئيسي بتكلم عن
+
+367
+00:34:33,020 --> 00:34:41,700
+العناصر التاني انا لأن هذا ال elementE3E1 عشان
+
+368
+00:34:41,700 --> 00:34:54,000
+تكون متماثلة المصحوفة لازم يكون يساوي E1E3 او
+
+369
+00:34:54,000 --> 00:34:58,660
+بين جسيم لو جسمت من النص وطبقت المثلثين على بعض كل
+
+370
+00:34:58,660 --> 00:35:02,720
+element هيكون مطابق لل element المجاور له الشرط
+
+371
+00:35:02,720 --> 00:35:09,710
+كمان مرة كل element AIJ يساوي AJIبنقول عنها
+
+372
+00:35:09,710 --> 00:35:14,330
+symmetric بنقول عن المصفوفة 01 matrix لو كانت كلها
+
+373
+00:35:14,330 --> 00:35:22,690
+عناصرها 01 أو بنجوسين binary 01 مع ال 01 صارت
+
+374
+00:35:22,690 --> 00:35:26,810
+binary ال matrix احنا قبل شوية شوفنا جمع و ضرب
+
+375
+00:35:26,810 --> 00:35:32,350
+مصبوط شوفنا جمع و ضرب هل هنشوف join و meet ال join
+
+376
+00:35:32,350 --> 00:35:36,750
+بقصد فيها ال R و
+
+377
+00:35:36,750 --> 00:35:41,930
+ال meet بقصد فيهامش لحمة .. ميت لحمة ياك يا فالح
+
+378
+00:35:41,930 --> 00:35:52,150
+.. M E A T مايعني
+
+379
+00:35:52,150 --> 00:35:54,030
+انتوا أسود ما شاء الله عليكوا و ماتفطروش اللي غير
+
+380
+00:35:54,030 --> 00:35:59,030
+لحمة عشان هيك دايما أنا مصحى صحين معايا طيب .. هاي
+
+381
+00:35:59,030 --> 00:36:05,130
+المصفوفتين .. هاي المصفوفتين A و B هدولة Zero و
+
+382
+00:36:05,130 --> 00:36:13,960
+Oneالان بدى اعمل بين A وB جوين A وB جوين شبك تساوي
+
+383
+00:36:13,960 --> 00:36:20,540
+كل element مع المقابله كل element بتعمل ال R مع
+
+384
+00:36:20,540 --> 00:36:25,960
+المقابل له كل
+
+385
+00:36:25,960 --> 00:36:29,620
+element مع المقابله بدل ما جمعنا بدل الجمع بدأ
+
+386
+00:36:29,620 --> 00:36:30,300
+استخدم ال R
+
+387
+00:36:33,470 --> 00:36:37,870
+لازم الان يا شباب لازم يكون المصففتين نفس الحجم
+
+388
+00:36:37,870 --> 00:36:41,970
+عشان اعمل بينهم join لازم زي ما اتكلمنا على الجامع
+
+389
+00:36:41,970 --> 00:36:46,070
+و الدرب تماما نفس المواصفات لازم تنطبق عندنا نفس
+
+390
+00:36:46,070 --> 00:36:50,950
+الجامع نفس الجامع اذا انا بتكلم على ال and و ال or
+
+391
+00:36:50,950 --> 00:36:54,810
+ال meet و ال join لازم المصففات تكون من نفس الرتب
+
+392
+00:36:54,810 --> 00:36:58,290
+المصففات تبعتها تكون نفس الرتب لما بتكلم على ال
+
+393
+00:36:58,290 --> 00:37:08,810
+meet بتكلم على ال and1 and Zero Zero and واحد واحد
+
+394
+00:37:08,810 --> 00:37:14,190
+and Zero و هكذا مع كل answer مع المقابل بولين ال
+
+395
+00:37:14,190 --> 00:37:21,310
+product عشان ننهي في بولين ال product لازم يكون
+
+396
+00:37:21,310 --> 00:37:27,670
+عدد صفوف الأولى او عدد أعمدة التانية عفوا عدد
+
+397
+00:37:27,670 --> 00:37:31,430
+أعمدة الأولى يساوي صفوف التانية اللي هو شرط الدرب
+
+398
+00:37:33,000 --> 00:37:37,240
+بقول أنا product ضرب مش هتغير حاجة عندي و هستبدل
+
+399
+00:37:37,240 --> 00:37:42,020
+عملية الضرب اللي كنت سويها بال and و عملية الجمع
+
+400
+00:37:42,020 --> 00:37:47,660
+بال R يعني الآن هاخد الصف الأول في العمود الأول
+
+401
+00:37:47,660 --> 00:37:56,560
+كيف هيكون؟ واحد and الواحد R
+
+402
+00:37:58,110 --> 00:38:02,110
+صفر and الصفر هدولاش بيمثلوا .. هدولة بيمثلوا ال
+
+403
+00:38:02,110 --> 00:38:11,290
+element الأول في النتيجة مش صعبة والله بس هي نفس
+
+404
+00:38:11,290 --> 00:38:15,350
+الكلام .. نفس الكلام .. اذا انت فاهم الدرب بس كل
+
+405
+00:38:15,350 --> 00:38:21,270
+اللي بقولك استبدل الدرب ب and والجمع بال or وخلصنا
+
+406
+00:38:21,270 --> 00:38:24,310
+الله
+
+407
+00:38:24,310 --> 00:38:25,110
+يعطيك العافية خلاص
+
diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/gAlSRgSeIsQ_postprocess.srt b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/gAlSRgSeIsQ_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..d23699bcf512e6b8bcac442697e95ea921845e2d
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/gAlSRgSeIsQ_postprocess.srt
@@ -0,0 +1,2944 @@
+1
+00:00:21,280 --> 00:00:23,260
+نعوذ بالله السماعي العليم الشطراجي بسم الله الرحمن
+
+2
+00:00:23,260 --> 00:00:25,380
+الرحيم يا رب اشرحلي صدري و أثر أمري و أحنا علاقة
+
+3
+00:00:25,380 --> 00:00:28,100
+هم لساني أفقها قولين أهلا و سهلا يا شباب اليوم ان
+
+4
+00:00:28,100 --> 00:00:31,360
+شاء الله هنبلش بالمادة بشكل عملي أو بشكل فعلي
+
+5
+00:00:31,360 --> 00:00:33,240
+المرة الماضية اتكلمنا على ال syllabus أو وصف
+
+6
+00:00:33,240 --> 00:00:36,760
+المساق و اليوم هنبدأ مع chapter 1 و كنا أخدنا بعض
+
+7
+00:00:36,760 --> 00:00:41,120
+الملاحظات أو بعض الشغلات بشكل بسيط طبعا قولنا
+
+8
+00:00:41,120 --> 00:00:43,620
+المواضيع اللي هنغطيها في ال chapter هذا ال
+
+9
+00:00:43,620 --> 00:00:45,780
+propositional logic, propositional evaluations,
+
+10
+00:00:46,220 --> 00:00:49,020
+predicates and quantifiers, nested quantifiers و
+
+11
+00:00:49,020 --> 00:00:53,700
+rule of inferenceوبدأنا المحاضرة الماضية اندردش
+
+12
+00:00:53,700 --> 00:00:58,880
+وبشكل بسيط على الـ propositional logic وقولنا
+
+13
+00:00:58,880 --> 00:01:02,860
+أهمية ال logic إنها دائما بتديني أو بتحاول توضحلي
+
+14
+00:01:02,860 --> 00:01:07,690
+معاني ال mathematical statementsبتوضح لمعاني ال
+
+15
+00:01:07,690 --> 00:01:11,810
+mathematical statements وال rule هذه مهمتها جدا
+
+16
+00:01:11,810 --> 00:01:16,250
+الفرق بين ال valid و ال invalid conditions او ال
+
+17
+00:01:16,250 --> 00:01:19,370
+mathematical arguments يعني كلنا بنعرف في البرمجة
+
+18
+00:01:19,370 --> 00:01:25,650
+لما انا بيجي بقول why ال I أقل من عشرةطبعا هذه
+
+19
+00:01:25,650 --> 00:01:31,090
+بيسلقها دائما جملة I equal واحد او صفر ليش؟ عشان
+
+20
+00:01:31,090 --> 00:01:37,050
+تصير ال I عندى هذه معرفة و اقدر اخد decision او
+
+21
+00:01:37,050 --> 00:01:41,360
+قرار هى ال proposition هذه او ال rule هذهأو ال
+
+22
+00:01:41,360 --> 00:01:46,880
+condition هذا true أو false وبالتالي مهمة ال rules
+
+23
+00:01:46,880 --> 00:01:49,060
+أو ال logical rules أو ال proposition زي ما
+
+24
+00:01:49,060 --> 00:01:52,560
+هنسميها ان نفرق بين ال valid و ال invalid لما
+
+25
+00:01:52,560 --> 00:01:56,080
+نتكلم على valid فنتكلم على شغلة مقبولة invalid
+
+26
+00:01:56,080 --> 00:02:01,630
+شغلة غير مقبولةوطبعا قلنا أهمية الـ Logic إنه
+
+27
+00:02:01,630 --> 00:02:04,430
+مرتبطة بتطبيقات الحسوب و ال computer science و ال
+
+28
+00:02:04,430 --> 00:02:07,470
+computer engineering على مستوى computer circuits
+
+29
+00:02:07,470 --> 00:02:10,030
+أو الدوائر الإلكترونية بتتم استخدام ال digital
+
+30
+00:02:10,030 --> 00:02:13,850
+design كمادة أساسية بتعلموها عشان يبني عليها تصميم
+
+31
+00:02:13,850 --> 00:02:17,330
+دوائر إلكترونية وبقى هيك بالنسبة إلى على مستوى ال
+
+32
+00:02:17,330 --> 00:02:20,450
+computer كل ال constructions تبعتنا التعليمات
+
+33
+00:02:20,450 --> 00:02:24,330
+المكتوبة من خلال البرنامج هي لازم تخضع لتسلسل
+
+34
+00:02:24,330 --> 00:02:30,910
+منطقي في البرنامجوأول تعريف سنتعرفله نقول إن ال
+
+35
+00:02:30,910 --> 00:02:34,750
+logic system هو عبارة عن logic أو المنطق بعيدا عن
+
+36
+00:02:34,750 --> 00:02:38,310
+المسرحية تبع الزمان أنا بتتكلم إن ال logic system
+
+37
+00:02:38,310 --> 00:02:42,170
+هو .. أو ال logic هو عبارة عن system مبني على ال
+
+38
+00:02:42,170 --> 00:02:46,070
+proposition طيب بعيدا كمان عن الترجمة الحرفية
+
+39
+00:02:46,070 --> 00:02:49,070
+لكلمة proposition شو proposition ال proposition هو
+
+40
+00:02:49,070 --> 00:02:52,450
+عبارة عن statement بعد الآن نعمل narrowing
+
+41
+00:02:52,450 --> 00:02:57,210
+statement القيمة تبعتها إما trueأو false القيمة
+
+42
+00:02:57,210 --> 00:03:03,750
+تبعتها true او false هل ممكن تكون تنتين؟ لأ بمعنى
+
+43
+00:03:03,750 --> 00:03:08,250
+اخر اي statement بديها بقدر احكم على قيمتها true
+
+44
+00:03:08,250 --> 00:03:12,650
+او false فهي ترقى على مستوى ال proposition وال
+
+45
+00:03:12,650 --> 00:03:16,560
+statement هذهلأنه بيتكلم في التدرجات اللغة
+
+46
+00:03:16,560 --> 00:03:19,760
+الإنجليزية ال statement هذه هي عبارة عن sentence
+
+47
+00:03:19,760 --> 00:03:25,080
+أو phrase تمام بيقوللي بوصفلي شغلة أو بيخبرني عن
+
+48
+00:03:25,080 --> 00:03:28,520
+حقيقة احنا سابقا قولنا في المحاضرة الماضي لما انا
+
+49
+00:03:28,520 --> 00:03:31,320
+بدي اعمل describe الجمال اللي عندي اما جملة خبرية
+
+50
+00:03:31,320 --> 00:03:34,540
+او جملة وصية وهذه الجمل اللي انا بقدر اقيمها
+
+51
+00:03:34,540 --> 00:03:40,400
+واتكلم عليها بشكل واضحوبالتالي الـ proposition هو
+
+52
+00:03:40,400 --> 00:03:43,180
+عبارة عن statement بتاخد true أو false وال
+
+53
+00:03:43,180 --> 00:03:48,280
+statement هذه هي عبارة عن جملة خبرية أو جملة وصفية
+
+54
+00:03:48,280 --> 00:03:55,560
+تمام Jerusalem is the capital of Palestine القدس
+
+55
+00:03:55,560 --> 00:04:02,630
+عاصمة فلسطين جملةخبرية جملة خبرية وبالتالي قيمتها
+
+56
+00:04:02,630 --> 00:04:05,390
+بقدر احكم عليها true او false حاكما ان انا true
+
+57
+00:04:05,390 --> 00:04:08,490
+طبعا اياك تقول false في لحظة من لحظات وانا بسمعك
+
+58
+00:04:08,490 --> 00:04:14,570
+we see stars on day احنا بنشوف الجمهور في الشكارة
+
+59
+00:04:14,570 --> 00:04:19,350
+بعنا في الليل فبنشوفها في النهار مصبوط letter F
+
+60
+00:04:19,350 --> 00:04:24,130
+comes after G in English sequence برضه جملة خبرية
+
+61
+00:04:24,130 --> 00:04:28,690
+واحد زائد تلاتة تساوي أربعةبعرض جملة خبرية بقدر
+
+62
+00:04:28,690 --> 00:04:32,130
+أديها true أو false اتنين زي التلاتة تسوى أربعة
+
+63
+00:04:32,130 --> 00:04:35,230
+جملة خبرية بقدر أقيمها true أو false بناء على
+
+64
+00:04:35,230 --> 00:04:39,030
+معرفتي و ال knowledge اللي عندي لاحظ انه في كل ال
+
+65
+00:04:39,030 --> 00:04:43,410
+proposition هذه مافيش أي شغل غامضة لما اتكلمنا على
+
+66
+00:04:43,410 --> 00:04:47,630
+Jerusalem و اتكلمنا على فلسطين القدس و فلسطين
+
+67
+00:04:47,630 --> 00:04:54,510
+شغلتين معرفات و الكل بيعرفهم و ايه احناStars نجوم
+
+68
+00:04:54,510 --> 00:04:58,550
+معروفة والنهار معروف وبالتالي بقدر أقل الجملة هذه
+
+69
+00:04:58,550 --> 00:05:03,390
+كمارية مية في المية بقدر أقيمها ال F و ال G و
+
+70
+00:05:03,390 --> 00:05:05,810
+comes after كل الجملة هذه معنىها واضحة مائة في
+
+71
+00:05:05,810 --> 00:05:10,350
+المائة واحد زائد تلاتة ساوي فكل العناصر هذه لاحظ
+
+72
+00:05:10,350 --> 00:05:15,890
+مافيش فيها ولا شغلة مجهولة لكن تعالنشوف شغلات ممكن
+
+73
+00:05:15,890 --> 00:05:19,790
+ما تكونش proposition زي ال question لو أنا سألت اي
+
+74
+00:05:19,790 --> 00:05:26,630
+واحد فيكوا بقول هو قريه، بقول trueبقول له كيف
+
+75
+00:05:26,630 --> 00:05:33,390
+حالك؟ قولي true مش منطق الكلام، إيش كنت بتسأل؟ لأ
+
+76
+00:05:33,390 --> 00:05:37,430
+لأ الجملة الخبرية إما بتكون true أو false يعني
+
+77
+00:05:37,430 --> 00:05:39,970
+بتاخد واحدة من الاحتمالين، بتاخد قيمة من القيمتين،
+
+78
+00:05:39,970 --> 00:05:43,570
+بس مابتاخدش التنتين مع بعض يعني مثلا أجي أقولك إن
+
+79
+00:05:43,570 --> 00:05:49,010
+والله إحنا بنشوف الشمس بالليل جملة خبرية بس ال
+
+80
+00:05:49,010 --> 00:05:55,580
+value تبعتها false مافيش مجالطيب قلنا كمان مرة ال
+
+81
+00:05:55,580 --> 00:06:00,640
+question .. ال question مستحيل يكون proposition
+
+82
+00:06:00,640 --> 00:06:04,200
+ليش؟ لأنه مش هت .. مش هت .. يعني مش هتقدر تقيمه أو
+
+83
+00:06:04,200 --> 00:06:07,500
+تعمل evaluation واحد بيقولك جديش عمرك؟ جديش تسعيرت
+
+84
+00:06:07,500 --> 00:06:10,520
+مكالمة جوال أو مكالمة الوطنية؟ جديش احنا بعاد عن
+
+85
+00:06:10,520 --> 00:06:13,960
+انجام على الإسلامية؟ جديش انت في أي مستوى؟ مستحيل
+
+86
+00:06:13,960 --> 00:06:17,660
+يكون جوابك true أو false وإذا جوابتوا true أو
+
+87
+00:06:17,660 --> 00:06:21,380
+false معناه تطلعك برا ال logic خالص ال comments
+
+88
+00:06:22,780 --> 00:06:28,520
+الأوامر صح صح يا باشا حد بيقدر يقيمليها؟ مستحيل لو
+
+89
+00:06:28,520 --> 00:06:32,320
+قلتلك افتح الباب او اتفضل اطلع برا او تعال او خد
+
+90
+00:06:32,320 --> 00:06:36,580
+او كده كل ال comments هاي مستحيل تقدر تقضع ال
+
+91
+00:06:36,580 --> 00:06:43,250
+logical value كذلك الأمنيات اتكلم على ال wishesI
+
+92
+00:06:43,250 --> 00:06:46,530
+hope that I get A plus in Discrete Mathematics،
+
+93
+00:06:46,530 --> 00:06:50,970
+بتمنى أحصل علامة ممتاز، مع درجة الشرف، مرتبة الشرف
+
+94
+00:06:50,970 --> 00:06:55,250
+في الرياضات المفصلة، واش؟ أمية، بتقدر تقول true or
+
+95
+00:06:55,250 --> 00:06:59,850
+false عليها؟ لأ، بس في آخر الفصل الجملة دي هتتغير،
+
+96
+00:06:59,850 --> 00:07:03,430
+هتقول أنا حصلت على امتياز مع مرتبة الشرف في
+
+97
+00:07:03,430 --> 00:07:06,470
+الرياضات المفصلة، و أنا بقدر أقولك true or false
+
+98
+00:07:07,410 --> 00:07:11,270
+بتصير خبرية بالضبط بتصير الجملة خبرية happy new
+
+99
+00:07:11,270 --> 00:07:14,330
+year او happy birthday الى اخره من كل الأمنيات
+
+100
+00:07:14,330 --> 00:07:19,450
+تمام لأ تستطيع انك تقيمها تعالى نشوف مجموعة ال
+
+101
+00:07:19,450 --> 00:07:23,270
+proposition هاي شباب او مجموعة ال English
+
+102
+00:07:23,270 --> 00:07:26,810
+statements اذا قلت انا proposition من وقت حكمت
+
+103
+00:07:26,810 --> 00:07:29,570
+عليها كلها proposition ال English statements hello
+
+104
+00:07:29,570 --> 00:07:34,690
+how are you هل هذي proposition لأ لأ لأ هذي
+
+105
+00:07:34,690 --> 00:07:38,080
+questionطيب في هذه الجملة يا شباب و احنا قولنا
+
+106
+00:07:38,080 --> 00:07:47,700
+هتختلف لو انا قد قلتلك how are you is a
+
+107
+00:07:47,700 --> 00:07:55,900
+proposition ال
+
+108
+00:07:55,900 --> 00:08:01,260
+statement هذه كلها اللي جزء منها السؤال ايش معناها
+
+109
+00:08:01,260 --> 00:08:07,430
+ان هذه الجملة how are you is a propositionانت الان
+
+110
+00:08:07,430 --> 00:08:10,530
+بتقدر تقيمها ب true او false .. فالس .. فالس ..
+
+111
+00:08:10,530 --> 00:08:12,890
+فالس .. فالس .. فالس .. فالس .. فالس .. فالس ..
+
+112
+00:08:12,890 --> 00:08:18,910
+فالس .. فالس .. فالس .. فالس
+
+113
+00:08:18,910 --> 00:08:22,570
+.. فالس .. فالس .. فالس .. فالس .. فالس .. فالس ..
+
+114
+00:08:22,570 --> 00:08:22,630
+فالس .. فالس .. فالس .. فالس .. فالس .. فالس ..
+
+115
+00:08:22,630 --> 00:08:22,830
+فالس .. فالس .. فالس .. فالس .. فالس .. فالس ..
+
+116
+00:08:22,830 --> 00:08:25,690
+فالس .. فالس .. فالس .. فالس .. فالس .. فالس ..
+
+117
+00:08:25,690 --> 00:08:27,690
+فالس .. فالس .. فالس .. فالس .. فالس .. فالس ..
+
+118
+00:08:27,690 --> 00:08:35,090
+فالس .. فالس .. فالس .. فالس
+
+119
+00:08:36,420 --> 00:08:39,940
+true وبالتالي لكن تقدر تعمل evaluation تعلش تقدر
+
+120
+00:08:39,940 --> 00:08:46,580
+تعمل evaluation we و eat و rocks كلها كلمات معناها
+
+121
+00:08:46,580 --> 00:08:51,760
+واضح ومعروف وبالتالي مافيش إش فيها غايب عنها أحمد
+
+122
+00:08:51,760 --> 00:08:55,840
+taller than علي ال proposition لأن أحمد و علي
+
+123
+00:08:55,840 --> 00:09:00,340
+التنين المعروفين تمام؟ ممكن أختلف أنا وياك انت لا
+
+124
+00:09:00,340 --> 00:09:04,370
+شايفه أطولتمام؟ فتقولي والله لأ هو عادة بالبس من
+
+125
+00:09:04,370 --> 00:09:07,930
+ال .. ال cat .. شوهو .. وبالتالي ده ممكن يرفع طلعة
+
+126
+00:09:07,930 --> 00:09:11,170
+الصدر عشان هيك مبين لك هو أقوى من علي .. بس في
+
+127
+00:09:11,170 --> 00:09:15,750
+الآخر بنقدر نحكم ليش لأن أحمد و علي .. والصفة هذه
+
+128
+00:09:15,750 --> 00:09:19,110
+كمان واضحة بالنسبة لنا .. ده هان نشوف الرادع .. he
+
+129
+00:09:19,110 --> 00:09:24,530
+is a good student .. هان الشباب .. هان .. he ..
+
+130
+00:09:24,530 --> 00:09:29,350
+good .. student .. الان في عندي he ..بتقدر تحكم
+
+131
+00:09:29,350 --> 00:09:34,770
+عليها لو افترضنا بتكلم انا و راني اقول انت عارف يا
+
+132
+00:09:34,770 --> 00:09:40,550
+راني هو طالب دحيح بلغتكم مش هيك بتقوله بالدرجة
+
+133
+00:09:40,550 --> 00:09:44,250
+الاولى هل بتقدر تحكم على مين هو؟ بتقدر تقول two or
+
+134
+00:09:44,250 --> 00:09:48,590
+fours؟ لأ ليش؟ لأن انت مش عارف مين هو اللي بتتكلم
+
+135
+00:09:48,590 --> 00:09:52,010
+عليه وبالتالي أصبح في عند اللي هي هذه مجهولة مش
+
+136
+00:09:52,010 --> 00:09:57,060
+معروفة وبالتالي هذا ليسلأنه فيها مجهول و المجهول
+
+137
+00:09:57,060 --> 00:10:01,060
+هذا بيخلّي القيمة إما true أو false طيب إذا كنت
+
+138
+00:10:01,060 --> 00:10:04,980
+بتقول يا دكتور وي ما هذي الضمير و هذي الضمير بس
+
+139
+00:10:04,980 --> 00:10:09,260
+أنا بتتكلم نحن عن حالنا وبالتالي .. بالضبط و أنا
+
+140
+00:10:09,260 --> 00:10:13,100
+منهم وبالتالي المعنى واضح حالا ومعروفين من هؤلاء
+
+141
+00:10:13,100 --> 00:10:18,800
+الأشخاص بيننا هال؟ لأ please wake up it's not a
+
+142
+00:10:18,800 --> 00:10:23,480
+proposition it's command عمر خمساش ضرب زد أكبر أو
+
+143
+00:10:23,480 --> 00:10:29,900
+تساوي تلاتينProposition غلط فيها الـ Z مجهولة يعني
+
+144
+00:10:29,900 --> 00:10:32,760
+هذه تاخد .. ممكن تاخد قيمتين ممكن تاخد true أو
+
+145
+00:10:32,760 --> 00:10:35,940
+تاخد false بناء على قيمة الـ Z وكونوا قيمة الـ Z
+
+146
+00:10:35,940 --> 00:10:40,300
+مجهولة فماقدرش أديها قيمة ولا لأ؟ وبالتالي خلصنا
+
+147
+00:10:40,300 --> 00:10:45,030
+على خلاف ال condition هذا شبابالان لو انا في هذا
+
+148
+00:10:45,030 --> 00:10:47,450
+الـ statement هذي قلتلك بقدر اقول ان هذي
+
+149
+00:10:47,450 --> 00:10:50,870
+proposition؟ ال statement هذي why ال I أكبر عفوا
+
+150
+00:10:50,870 --> 00:10:53,910
+اقل من عشرة بقدر اقول ال proposition؟ اه بقدر لان
+
+151
+00:10:53,910 --> 00:10:58,270
+ال I already identified تم تعريف ال I مسبقا فضل
+
+152
+00:10:58,270 --> 00:11:02,750
+ايه؟
+
+153
+00:11:02,750 --> 00:11:08,470
+لأ و في كمان واحدة قبلها ان تكون جملة خبرية تاخد
+
+154
+00:11:08,470 --> 00:11:12,340
+true or false هذه الجملة شوف تاخدهذه true or
+
+155
+00:11:12,340 --> 00:11:16,280
+false؟ لأ لأ مجهولة مجهولة هذي يا إما true يا إما
+
+156
+00:11:16,280 --> 00:11:20,620
+false تمام اديه نقمتها الآن true or false مش هتقدر
+
+157
+00:11:20,620 --> 00:11:26,100
+لازم ت .. بالضبط إذا أنت حددت مين هو هذا فبالتالي
+
+158
+00:11:26,100 --> 00:11:33,500
+ممكن تتغير الجملة يعني هيك لو إجيت قولت أنا أحمد
+
+159
+00:11:33,500 --> 00:11:40,600
+is a cool man أو gentleman and
+
+160
+00:11:42,960 --> 00:11:49,320
+He is a good student يا راجل جنتل مؤدب تمام الان
+
+161
+00:11:49,320 --> 00:11:52,620
+هادث أصبحت proposition لأنه هذه مرتبطة تعرفت بمين؟
+
+162
+00:11:52,620 --> 00:11:56,900
+تعرفت بأحمد تم ربطها بمين؟ بأحمد وهذه الأمور بدك
+
+163
+00:11:56,900 --> 00:12:00,780
+تنتبه لها تنتبه لها بشكل كويس أثناء تقييم أو
+
+164
+00:12:00,780 --> 00:12:04,120
+evaluation لل statements اللي موجودة عندك واضح
+
+165
+00:12:04,120 --> 00:12:05,400
+الأمور لحظة شباب؟
+
+166
+00:12:25,060 --> 00:12:30,960
+الغريب ممكن يكون أغنى منك، صح؟ هذا ما تقول؟ ممكن
+
+167
+00:12:30,960 --> 00:12:33,680
+يكون أه، ممكن يكون لأ، تعتبر من مين هو ال stranger
+
+168
+00:12:33,680 --> 00:12:37,400
+اللي بتتكلم عليه؟ وبالتالي هذا ليس مو اقتراح، لأن
+
+169
+00:12:37,400 --> 00:12:41,280
+هذا البلد على مين؟ على مجهول، لكن اللي هو جد قلتلي
+
+170
+00:12:41,280 --> 00:12:46,460
+رامي أغنى منككل الناس بتصير تقول إما true يعني
+
+171
+00:12:46,460 --> 00:12:50,480
+بتقدر تدزم قيمة ال proposition هذه true أو false
+
+172
+00:12:50,480 --> 00:12:54,740
+بس في الحالة هذه لأ يمكن او يمكن لأ مصدق لا لأ
+
+173
+00:12:54,740 --> 00:12:58,080
+عشان هيكد بنبعد عن المجاهي الهادي أو بنخرجها من
+
+174
+00:12:58,080 --> 00:13:04,420
+خاصة من خاص ال proposition بالمناسبة شباب مافيش حد
+
+175
+00:13:04,420 --> 00:13:07,680
+بقدر يبني قرار على شغل مجهولة عشان هيك قلنا ال
+
+176
+00:13:07,680 --> 00:13:12,020
+proposition هو عبارة عن statementتلا fact بتديك
+
+177
+00:13:12,020 --> 00:13:16,760
+حقيقة أو بتوصف شيء حتى لو كان الوصف غلط انت بتقدر
+
+178
+00:13:16,760 --> 00:13:19,840
+تقرر و تقول هل هي true ولا false حتى لو كانت
+
+179
+00:13:19,840 --> 00:13:23,300
+الحقيقة هذه مغلوطة طبعا يعني مثلا نيوتن جيل فيه
+
+180
+00:13:23,300 --> 00:13:26,820
+السبب السقوط الأشياء وارتطانها في الأرض الجاذبية
+
+181
+00:13:26,820 --> 00:13:31,420
+حقيقة لكن ممكن تطلع ناس بعد فترة و تطلع ناس جابل
+
+182
+00:13:31,420 --> 00:13:34,160
+يقولك لا يا عم الله هذا الكلام غلط عشان الجاذبية
+
+183
+00:13:34,160 --> 00:13:38,920
+اللي كانت أسباب السبب السقوط مثلاوبالتالي لاحظ
+
+184
+00:13:38,920 --> 00:13:42,660
+نيوتن وجاذبية وسقوط كلها شغلات موضوع واضحة مافيش
+
+185
+00:13:42,660 --> 00:13:48,760
+فيها أي غمض طيب
+
+186
+00:13:48,760 --> 00:13:56,440
+لكن تعالى نشوف الجملة هذه بيجي واحد بيقولك أنا كذب
+
+187
+00:13:56,440 --> 00:13:59,560
+I
+
+188
+00:13:59,560 --> 00:14:04,500
+have always told lies واحد بيقول عن حاله كذب هل
+
+189
+00:14:04,500 --> 00:14:08,620
+بنقدر نعمل evaluation حقيقي للجملة هذه؟أيوة، ايش
+
+190
+00:14:08,620 --> 00:14:12,740
+بيقولوه؟ اه انا بقولك هذا الكلام خطأ لأنه إذا هو
+
+191
+00:14:12,740 --> 00:14:17,560
+جاء يقول عن حاله كذاب، تمام؟ بينفعش أنت تصدقه لأنه
+
+192
+00:14:17,560 --> 00:14:21,420
+إذا أنت صدقته، إيش يضمنك إنه في اللحظة هادي هو
+
+193
+00:14:21,420 --> 00:14:26,520
+جاعل يجذب عليك؟ تمام؟ وبالتالي هذه من الجمال اللي
+
+194
+00:14:26,520 --> 00:14:30,400
+فيها بعض ال confusing بعض الغموض مش واضحة أو فيها
+
+195
+00:14:30,400 --> 00:14:35,130
+بعض التناقض وبالتالي واحد يقول عن حاله كذابأسبجه
+
+196
+00:14:35,130 --> 00:14:39,090
+ولا أكذبه؟ إذا أنا كذبته و هو جاعت بيبقى بيبقى
+
+197
+00:14:39,090 --> 00:14:40,430
+بيبقى بيبقى بيبقى بيبقى بيبقى بيبقى بيبقى بيبقى
+
+198
+00:14:40,430 --> 00:14:41,110
+بيبقى بيبقى بيبقى بيبقى بيبقى بيبقى بيبقى بيبقى
+
+199
+00:14:41,110 --> 00:14:44,250
+بيبقى بيبقى بيبقى بيبقى بيبقى بيبقى بيبقى بيبقى
+
+200
+00:14:44,250 --> 00:14:45,030
+بيبقى بيبقى بيبقى بيبقى بيبقى بيبقى بيبقى بيبقى
+
+201
+00:14:45,030 --> 00:15:01,830
+بيبقى بيبقى بيبقى بيبقى بيبقى بيبقى
+
+202
+00:15:03,620 --> 00:15:08,960
+بتفرج لما أجي أقول فلان كذاب، فلان كذاب معناته أنك
+
+203
+00:15:08,960 --> 00:15:14,340
+تقدر تجزم على كلمتي هذه بناء على معرفتك بفلان،
+
+204
+00:15:14,340 --> 00:15:17,240
+تمام؟ لكن لما أنا باجي أقولك عن نفسي، الأمر شويه
+
+205
+00:15:17,240 --> 00:15:22,640
+هيش، هتكون confused طب قالتلي اللوجي بتاعك تلوجت
+
+206
+00:15:22,640 --> 00:15:24,740
+من فرق التحاد، precision ولا نظام؟
+
+207
+00:15:28,710 --> 00:15:32,550
+خلصنا معناته انا بتطلعها .. شوفوا يا شباب كمان مرة
+
+208
+00:15:32,550 --> 00:15:36,850
+دائما يكون معيارنا الأساسي ال proposition هو عبارة
+
+209
+00:15:36,850 --> 00:15:42,050
+عن جملة خبرية أو وصفية بقدر أجزم في قيمتها true أو
+
+210
+00:15:42,050 --> 00:15:42,350
+false
+
+211
+00:15:46,080 --> 00:15:49,180
+عادة في الـ Proposition هاي احنا بروح بنترجمها
+
+212
+00:15:49,180 --> 00:15:52,760
+عشان نتكلم الرياضيات الآن بنترجمها لمجموعة من
+
+213
+00:15:52,760 --> 00:15:58,200
+الرموز Q,R,A,B,C حسب انت ايش بتحتاجه و ال truth
+
+214
+00:15:58,200 --> 00:16:01,380
+value لل true بنرمزلها capital T و ال false
+
+215
+00:16:01,380 --> 00:16:06,700
+بنرمزلها capital F كلام بسيط و مافيش فيه اي حاجة
+
+216
+00:16:06,700 --> 00:16:10,220
+طيب
+
+217
+00:16:10,220 --> 00:16:14,380
+.. الآية ال compound proposition compound
+
+218
+00:16:14,380 --> 00:16:18,880
+propositionلو انا اجيت و قلتلك ايش شروع التسجيل في
+
+219
+00:16:18,880 --> 00:16:25,440
+الجامعة؟ تدفع الى 20 دولار، تكون معدلة من فوق 25
+
+220
+00:16:25,440 --> 00:16:28,900
+دولار .. شوف شوف ماديش نتكلم عن مقاسيك الآن و
+
+221
+00:16:28,900 --> 00:16:32,400
+الوضع الحالي السيء، لأ بنا نتكلم كلام بسيط، بالضبط
+
+222
+00:16:32,400 --> 00:16:37,020
+أول شرط للتسجيل في الجامعة تنجح في توجيهيإتنين،
+
+223
+00:16:37,020 --> 00:16:39,500
+اتجد مقالة بالتحق، بغض النظر عن جيبكوا عشرين دينار
+
+224
+00:16:39,500 --> 00:16:43,220
+ولا أكتر يا رامي، تمام؟ بعد هيك، بعد قبولك في
+
+225
+00:16:43,220 --> 00:16:46,160
+الجامعة، بصيب تتكلم عن تسجيل الفصلي، أنا كان
+
+226
+00:16:46,160 --> 00:16:48,940
+الكلام واضح، إيه الشروق التسجيل في الجامعة، إنك
+
+227
+00:16:48,940 --> 00:16:53,540
+تكون ناجح في توجيهي، إنك تكون ناجح في توجيهي، جايب
+
+228
+00:16:53,540 --> 00:16:58,240
+معدل فوق الـ65، و تدفع أو تتجد مقالة بالتحق، لاحظ
+
+229
+00:16:58,240 --> 00:17:04,240
+يا شباب، إن ضمن الكلام اللي أنا قلته هذا، تمام؟كم
+
+230
+00:17:04,240 --> 00:17:11,500
+proposition موجود؟ راني سجل في الجامعة true او
+
+231
+00:17:11,500 --> 00:17:19,440
+false؟ true بيعني ان راني حقق الشروط التلاتة وهنا
+
+232
+00:17:19,440 --> 00:17:23,980
+تصبح تسجيل في الجامعة compound proposition بمعنى
+
+233
+00:17:23,980 --> 00:17:28,280
+اخر هو تم تجميع مجموعة من ال small proposition او
+
+234
+00:17:28,280 --> 00:17:31,560
+ال simple proposition من أجل الوصول لل condition
+
+235
+00:17:31,560 --> 00:17:35,090
+العام اللي موجود عندناطبعا بتهيألي في نفس الشرق
+
+236
+00:17:35,090 --> 00:17:39,350
+موجود في كل مكان بيقولك ممنوع أقل طالب أقل من 17
+
+237
+00:17:39,350 --> 00:17:43,870
+سنة يسجل في الجامعة أحيانا في بعض الدول ممكن تعمل
+
+238
+00:17:43,870 --> 00:17:48,510
+اختبارات مستوى وتنقل الطالب من مستوى لمستوى آخر
+
+239
+00:17:48,510 --> 00:17:51,890
+يعني ممكن يخلص ثانوية عامة و أنا شوفت بعض الناس
+
+240
+00:17:51,890 --> 00:17:53,950
+خلصت ثانوية عامة و 15 سنة
+
+241
+00:17:57,550 --> 00:18:02,450
+خلصت ثانوية عامة تمام من خمس أشهر سنة خمس أشهر سنة
+
+242
+00:18:02,450 --> 00:18:07,090
+يعني انا انا اتكلم تالتة عدادي تاسع او عاشر تمام و
+
+243
+00:18:07,090 --> 00:18:10,030
+نجحت في الثانوية الآن قانون التعليم العالي وقف
+
+244
+00:18:10,030 --> 00:18:15,030
+حائل في موضوع التسجيل في الجامعة ليش؟ لأن شرط
+
+245
+00:18:15,030 --> 00:18:17,910
+التسجيل في الجامعة يكون مثلا سبعت عشر سنة وبالتالي
+
+246
+00:18:17,910 --> 00:18:23,550
+هذا الكلامما حققتش الشرق وبالتالي المحصلة الـ
+
+247
+00:18:23,550 --> 00:18:27,210
+compound proposition كانت نتيجته false طيب احنا في
+
+248
+00:18:27,210 --> 00:18:32,850
+الآخر ..بالتالي هنقدر نقول اي جملة رياضية هيتم
+
+249
+00:18:32,850 --> 00:18:37,230
+تركيبها من مجموعة .. مجمع او رابط من ال
+
+250
+00:18:37,230 --> 00:18:41,530
+proposition او اكتر مجموعة من ال proposition و ال
+
+251
+00:18:41,530 --> 00:18:44,190
+connections هذه او ال connectives هذه بنسميها ال
+
+252
+00:18:44,190 --> 00:18:50,410
+logical operators logical operatorsولمّا أتكلم عن
+
+253
+00:18:50,410 --> 00:18:55,750
+الـ Logical Operator كلنا بنعرف ان مافي و ال and و
+
+254
+00:18:55,750 --> 00:19:00,510
+ال or و ال XOR تمام؟ و معظمهم هدول اللي أنا ذكرتهم
+
+255
+00:19:00,510 --> 00:19:04,090
+هم متختم في المقدمة .. في المقدمة مصبوط؟ ال Logic
+
+256
+00:19:04,090 --> 00:19:10,370
+Gates و هم أساس التصميم المنطقي في ال computer
+
+257
+00:19:10,370 --> 00:19:13,350
+science و ال computer engineering هنضيف عليهم كمان
+
+258
+00:19:14,590 --> 00:19:17,770
+two operators ال implication if else و ال
+
+259
+00:19:17,770 --> 00:19:22,470
+biconditional و الشرط if and only if فهنبدأ نشوف
+
+260
+00:19:22,470 --> 00:19:28,310
+واحد واحد نبدأ مع إننا فيه أولا يا شباب بدنا ننتبه
+
+261
+00:19:28,310 --> 00:19:35,410
+على مصطلح مهم جدا unary و binary operator unary
+
+262
+00:19:35,410 --> 00:19:41,770
+يعني أحادي تطبق على قيمة واحدة تطبق على قيمة واحدة
+
+263
+00:19:41,770 --> 00:19:47,280
+و لما نشوف كلمة binaryمتكلم على قيمة او خلنا نقول
+
+264
+00:19:47,280 --> 00:19:50,940
+ال operator هذا بيحتاج ل two operands لازم يكون في
+
+265
+00:19:50,940 --> 00:19:53,900
+عندي قيمتين لازم يكون في عندي مدخلين لازم يكون في
+
+266
+00:19:53,900 --> 00:20:00,180
+عندي two operands تمام الآن في موضوع النفي او ال
+
+267
+00:20:00,180 --> 00:20:05,520
+negation او النقط سميها زي ما بدك انا المصطلح ان
+
+268
+00:20:05,520 --> 00:20:10,390
+ال proposition هذا عبارة عن unary propositionمفهوم
+
+269
+00:20:10,390 --> 00:20:14,290
+unary او binary فيه معنى يا شباب المعنى كانت تالي
+
+270
+00:20:14,290 --> 00:20:18,490
+unary معناته ان انا بتكلم على متغير واحد مظبوط
+
+271
+00:20:18,490 --> 00:20:23,970
+الاحتمالات تبعته جداش اتنين لان انا في اساس القيام
+
+272
+00:20:23,970 --> 00:20:27,950
+اللي عندى true او false هذا الاساس تبع النظام ال
+
+273
+00:20:27,950 --> 00:20:35,750
+binary مظبوط يعني اتنين اص واحد يساوي اتنينما هو
+
+274
+00:20:35,750 --> 00:20:39,210
+الواحد هذه؟ عدد المتغيرات اللي عندي عشان أعرف
+
+275
+00:20:39,210 --> 00:20:43,730
+كمحتمال للـ compound proposition هذا لازم ألا
+
+276
+00:20:43,730 --> 00:20:47,710
+أنتبه الحكاية الـ unary و ال binary في الحال اللي
+
+277
+00:20:47,710 --> 00:20:52,070
+عندي ال negation هي عبارة عن unary operator اتنين
+
+278
+00:20:52,070 --> 00:20:56,350
+أقصى واحد معناته اتنين القيمتين لازم تكون واحدة
+
+279
+00:20:56,350 --> 00:21:00,630
+true و واحدة false واحدة true و واحدة false
+
+280
+00:21:00,630 --> 00:21:08,190
+وبالتالي نفي الإثباتنفي و نفي النفي if bad يعني
+
+281
+00:21:08,190 --> 00:21:13,570
+not true false و not false true بتغير القيمة و
+
+282
+00:21:13,570 --> 00:21:16,730
+عادة بنسمي ال proposition هذا not ال بي أو بنقرأه
+
+283
+00:21:16,730 --> 00:21:23,890
+not بي not ال بي تمام لو أنا جد قلتلك ان ال بي هي
+
+284
+00:21:23,890 --> 00:21:28,630
+عبارة عن ال proposition بدي يساوي قيمته today is
+
+285
+00:21:28,630 --> 00:21:31,050
+Friday اليوم الجمعة false
+
+286
+00:21:33,550 --> 00:21:37,250
+انت عملتلي evaluation بالمناسبة هيك بناء على
+
+287
+00:21:37,250 --> 00:21:42,110
+معرفتك باليوم ان اليوم التلاتة و ال proposition
+
+288
+00:21:42,110 --> 00:21:45,930
+هدا بقولك ان اليوم يوم الجمعة فانت قدرت تحدد
+
+289
+00:21:45,930 --> 00:21:51,130
+القيمة تبعته ب false لكن مانفتهوش لو انا طلبت منك
+
+290
+00:21:51,130 --> 00:21:56,470
+حط لل نط بيه تبعته نط ال بيه اصلا كنت true هو عمل
+
+291
+00:21:56,470 --> 00:22:01,270
+evaluation و جالك false بصبوط كلامهأيوة وبالتالي
+
+292
+00:22:01,270 --> 00:22:05,350
+لما انا اتكلم الشباب على نافل ال proposition نقطة
+
+293
+00:22:05,350 --> 00:22:16,470
+بمعناته هي تساوي today is not Friday هينا
+
+294
+00:22:16,470 --> 00:22:20,730
+فيها طبعا انت لو قول today is a Tuesday كلامك صح
+
+295
+00:22:20,730 --> 00:22:25,010
+بس و هتقدر فعليا ان هذا false و هذا ال statement
+
+296
+00:22:25,010 --> 00:22:29,630
+صار true بس true اليوم و بكرا لأفعشان هي أفضل شغلة
+
+297
+00:22:29,630 --> 00:22:32,850
+لما تيجي تنفيها هناش تنفيها تنفيها is not Friday
+
+298
+00:22:32,850 --> 00:22:44,110
+طيب ناخد جملة أعقد شوية و احنا بنقولك علي walks at
+
+299
+00:22:44,110 --> 00:22:53,390
+least عشر كيلومتر today لاحظ انا مابقول cash علي
+
+300
+00:22:53,390 --> 00:22:55,970
+walks
+
+301
+00:22:57,890 --> 00:23:04,310
+10 كيلومتر اليوم الان لو أنا سألتك بدي أنفي الأولى
+
+302
+00:23:04,310 --> 00:23:08,350
+على فرض أن هذه R كيف بدي أنفيها؟ إيش نتيجة هيكون
+
+303
+00:23:08,350 --> 00:23:16,230
+الشباب؟ علي لا يمشي 10 كيلومتر لأن علي أما بيكون
+
+304
+00:23:16,230 --> 00:23:21,070
+ماشي أقل من عشرة أو أكتر من عشرة، و لا لأ؟ بصبت؟
+
+305
+00:23:21,070 --> 00:23:23,770
+يعني هي دي المفهومة هي كانت ال negation تبع ال R
+
+306
+00:23:23,770 --> 00:23:26,430
+نقطة R equal علي
+
+307
+00:23:29,630 --> 00:23:37,110
+ما يمشي عشرة كيلومتر ما مشيش عشرة كيلومتر النافي
+
+308
+00:23:37,110 --> 00:23:40,690
+تبعها بيحتبل أنه يكون ماشي أكتر من عشرة كيلومتر أو
+
+309
+00:23:40,690 --> 00:23:45,350
+ماشي أقل من عشرة كيلومتر لكن مع كلمة at least
+
+310
+00:23:45,350 --> 00:23:50,290
+اختلف ال proposition لأنه أقل ممكن أنه أقل فضل لما
+
+311
+00:23:50,290 --> 00:23:52,990
+بدأ فيها أنه ماكسما معالج بيمشي عشرة كيلومتر
+
+312
+00:23:54,120 --> 00:23:56,920
+maximum أقل من عشرة ماشية لأن هذه already العشرة
+
+313
+00:23:56,920 --> 00:24:01,680
+موجودة يعني احنا ليش بنقول هل ماشي على الأقل عشرة
+
+314
+00:24:01,680 --> 00:24:06,800
+كيلومتر يعني هو ماشي عشرة أو أكتر عشرة أو أكتر
+
+315
+00:24:06,800 --> 00:24:11,520
+نفيها إن هو ماشي أقل من عشرة كيلومتر مصدود أو لا؟
+
+316
+00:24:11,520 --> 00:24:14,260
+لأنه ال side التاني تبعه هيك أنت تخيل قاعد بقوله
+
+317
+00:24:14,260 --> 00:24:18,660
+أنا X اللي هي المسافة اللي مشيها عني أكبر أو تساوي
+
+318
+00:24:18,660 --> 00:24:26,990
+عشرة ان في ليها عكسها إن ال Xأقل من عشرة وبالتالي
+
+319
+00:24:26,990 --> 00:24:31,150
+مفهوم ال at least و ال at most هذا يجب أن ننتبه له
+
+320
+00:24:31,150 --> 00:24:35,570
+كويس في وهم لما أشوف ال proposition ما فيها عالي
+
+321
+00:24:35,570 --> 00:24:46,670
+walks less than عشر كيلومتر today تمام؟ P
+
+322
+00:24:46,670 --> 00:24:50,550
+all the student study discrete mathematics كل
+
+323
+00:24:50,550 --> 00:24:54,590
+الطلاب بدرس رياضيات منفصلة true؟
+
+324
+00:24:55,990 --> 00:24:59,730
+false إذا أنا بتكلم على كل طلاب الجامعة false وإذا
+
+325
+00:24:59,730 --> 00:25:03,670
+بتكلم على طلاب كلية التجارة للمعلومات true كل
+
+326
+00:25:03,670 --> 00:25:09,110
+الطلاب لازم يدرس هناك منفصلة أه كله بغض النظر إيش
+
+327
+00:25:09,110 --> 00:25:11,730
+ما تكون القيمة هذه بغض النظر عن ال domain اللي أنا
+
+328
+00:25:11,730 --> 00:25:15,390
+بطبقه فيها أو ال population اللي هطبقها عليه بدي
+
+329
+00:25:15,390 --> 00:25:27,730
+أنفيها الآن إيش عكس كل no one عكس الكللا واحد لا
+
+330
+00:25:27,730 --> 00:25:32,690
+واحد
+
+331
+00:25:32,690 --> 00:25:46,610
+لا واحد لا واحد لا واحد
+
+332
+00:25:46,610 --> 00:25:53,200
+لا واحد لا واحد لا واحد لا واحد لا واحد لا واحدأه
+
+333
+00:25:53,200 --> 00:25:59,420
+ماحدش درس .. لو أنا أجيت قولت most
+
+334
+00:25:59,420 --> 00:26:07,520
+of the students study
+
+335
+00:26:07,520 --> 00:26:11,240
+discrete mathematics most of the students إيشنا
+
+336
+00:26:11,240 --> 00:26:13,300
+فيها؟
+
+337
+00:26:17,830 --> 00:26:21,290
+أيوة يا شباب الان كمان مرة بنقول انا جاعة بقول
+
+338
+00:26:21,290 --> 00:26:27,550
+most of the student ماعظم ايش عكس معظم بعض some
+
+339
+00:26:27,550 --> 00:26:34,530
+some of the students ايوة بس تعالى نشوف الان لو
+
+340
+00:26:34,530 --> 00:26:42,210
+انا فرضنا انه هذه true هذه true كمان اصبر عليا انا
+
+341
+00:26:42,210 --> 00:26:46,350
+جاعة بقول some of the students
+
+342
+00:26:49,120 --> 00:26:54,380
+study discrete mathematics شو راكب هذه؟ إذا كانت
+
+343
+00:26:54,380 --> 00:26:58,320
+هذه true فالأصل إذا أنت بتقول إن هذه نفي تبعتها،
+
+344
+00:26:58,320 --> 00:27:01,160
+الأصل تكون قيمة هذه force لكن أنا جالس بقول لك
+
+345
+00:27:01,160 --> 00:27:06,620
+some of the student true
+
+346
+00:27:06,620 --> 00:27:11,200
+ومعناته أنا ما نفتهاش بالطريقة الصحيحةمعناته أنا
+
+347
+00:27:11,200 --> 00:27:15,340
+منافتهاش بطريقة صحية لأنه المفروض إذا كانت هذه
+
+348
+00:27:15,340 --> 00:27:19,440
+true مع النافي هذه تطلع false و لو كانت هذه false
+
+349
+00:27:19,440 --> 00:27:24,260
+تطلع لتحت true All
+
+350
+00:27:24,260 --> 00:27:30,820
+the students study
+
+351
+00:27:30,820 --> 00:27:33,780
+discrete mathematics
+
+352
+00:27:36,330 --> 00:27:41,130
+فتصير false أو none of the students study discrete
+
+353
+00:27:41,130 --> 00:27:48,890
+mathematics فانت ضروري جدا تفهم الجملة تمام؟تحاول
+
+354
+00:27:48,890 --> 00:27:52,970
+تشوف إيش الخيارات اللي قدامك في نفيها قبل ما تاخد
+
+355
+00:27:52,970 --> 00:27:56,430
+تقول إن هذا هو النفي النهائي تبعها لأنه واضح هي
+
+356
+00:27:56,430 --> 00:28:03,530
+عكس كل معظم القليل منهم تمام؟ لكن قوله التنتين نفس
+
+357
+00:28:03,530 --> 00:28:05,770
+القيمة وبالتالي هذا الكلام غلط في موضوع الـ
+
+358
+00:28:05,770 --> 00:28:09,310
+Proposition لأن إذا طبقت النفي الأصل أحصل على الـ
+
+359
+00:28:09,310 --> 00:28:12,690
+Negation تبعة الـ Value، بالضبط فانت بدك تنتبه و
+
+360
+00:28:12,690 --> 00:28:16,550
+تنتبه بشكل كويس لأن ما ليش نجل هيك مواضيع و نتكلم
+
+361
+00:28:16,550 --> 00:28:20,120
+أو نسألكهات ال negation تبع الجملة اللى موجودة
+
+362
+00:28:20,120 --> 00:28:26,800
+علينا نعم لو ماكنت انتحار مع الصورة الواحد كتب بدل
+
+363
+00:28:26,800 --> 00:28:30,980
+معنان all the students كتب all the students do not
+
+364
+00:28:30,980 --> 00:28:35,660
+study غالبا حسبلك إياها لإن كنت قايش دلوا واحد
+
+365
+00:28:35,660 --> 00:28:41,260
+قولت أكستها هان all the students doesn'tDon't
+
+366
+00:28:41,260 --> 00:28:46,600
+study انت نفيتها .. انت نفيتها لكن خلنا نقول ب ..
+
+367
+00:28:46,600 --> 00:28:51,640
+ب .. بطريقة غير رسمية فلأ احنا .. احنا من البداية
+
+368
+00:28:51,640 --> 00:28:53,600
+ده أقولك هذا الغبط ممكن تكفوهوش في الامتحانة ممكن
+
+369
+00:28:53,600 --> 00:28:57,500
+ممكن ممكن ممكن ممكن
+
+370
+00:28:57,500 --> 00:29:03,080
+ممكن ممكن ممكن
+
+371
+00:29:03,080 --> 00:29:06,060
+ممكن ممكن ممكن ممكن ممكن ممكن ممكن ممكن ممكن ممكن
+
+372
+00:29:06,060 --> 00:29:06,340
+ممكن ممكن ممكن ممكن ممكن ممكن ممكن ممكن ممكن ممكن
+
+373
+00:29:06,340 --> 00:29:08,280
+ممكن ممكن ممكن ممكن ممكن ممكن ممكن ممكن ممكن ممكن
+
+374
+00:29:08,280 --> 00:29:13,300
+مكن مكن مكن مكن مالان لو انا افترضت ان هذه قيمتها
+
+375
+00:29:13,300 --> 00:29:16,920
+true all the students in IT study discrete
+
+376
+00:29:16,920 --> 00:29:19,860
+mathematics بس الشوية مش تبرعليها هي هي هي هي هي
+
+377
+00:29:19,860 --> 00:29:20,660
+هي هي هي هي هي هي هي هي هي هي هي هي هي هي هي هي هي
+
+378
+00:29:20,660 --> 00:29:22,620
+هي هي هي هي هي هي هي هي هي هي هي هي هي هي هي هي هي
+
+379
+00:29:22,620 --> 00:29:25,120
+هي هي هي هي هي هي هي هي هي هي هي هي هي هي هي هي هي
+
+380
+00:29:25,120 --> 00:29:25,280
+هي هي هي هي هي هي هي هي هي هي هي هي هي هي هي هي هي
+
+381
+00:29:25,280 --> 00:29:28,520
+هي هي هي هي هي هي هي هي هي هي هي هي هي
+
+382
+00:29:28,520 --> 00:29:28,560
+هي هي هي هي هي هي هي هي هي هي هي هي هي هي هي هي هي
+
+383
+00:29:28,560 --> 00:29:28,600
+هي هي هي هي هي هي هي هي هي هي هي هي هي هي هي هي هي
+
+384
+00:29:28,600 --> 00:29:30,420
+هي هي هي هي هي هي هي هي هي هي هي هي هي هي هي هي هي
+
+385
+00:29:30,420 --> 00:29:33,100
+هي هي هي هي هي هي هي هي هي هي هي هي هي هي هي هي هي
+
+386
+00:29:37,160 --> 00:29:42,840
+ولو قلت انتهادي false تمام؟ ما يعني أطول تتمتع مع
+
+387
+00:29:42,840 --> 00:29:45,440
+النافذة حدثية ال true هي الأصل ويه اللي الشباب
+
+388
+00:29:45,440 --> 00:29:49,540
+بتفكر فيها؟ ماتيش تقول انا بدي أعمل not all the
+
+389
+00:29:49,540 --> 00:29:56,380
+student study discrete mathematics عكس الان فعليا
+
+390
+00:29:56,380 --> 00:30:00,520
+انت مابتنفيش كل الكلام هذا بتروح تقول some of the
+
+391
+00:30:00,520 --> 00:30:05,750
+student don't study discrete mathematicsعشان هي
+
+392
+00:30:05,750 --> 00:30:09,670
+كانت حاول اشتغل formal مع موضوع النفي بشكل كويس من
+
+393
+00:30:09,670 --> 00:30:13,730
+البداية احنا لسه على أول ال chapter أول الطريق
+
+394
+00:30:13,730 --> 00:30:20,010
+فالشغل بدهاش شوية تمرين ننتقل لل operator التاني
+
+395
+00:30:20,010 --> 00:30:26,110
+ال conjunction اللي هو ال and هو binary operator
+
+396
+00:30:26,110 --> 00:30:28,890
+ايش يعني binary operator يعني في عندي two operands
+
+397
+00:30:29,620 --> 00:30:33,620
+في عندى معاملية لازم يكونوا موجودين بجوار او على
+
+398
+00:30:33,620 --> 00:30:38,900
+يمين ويسار ال operators اللى موجود يعني عدد ال
+
+399
+00:30:38,900 --> 00:30:43,300
+base ده بقى اتنين true or false مع اتنين سوى اربعة
+
+400
+00:30:43,300 --> 00:30:47,920
+طيب وخلينا هنتكلم من هنا الان على بناء جدول
+
+401
+00:30:47,920 --> 00:30:50,660
+الاحتمالات هذا الجدول اللى انشطناه سابق انا شايف
+
+402
+00:30:50,660 --> 00:30:54,810
+اسمه جدول الاحتمالاتو طبعا كلكم بتعرفوه في المقدمة
+
+403
+00:30:54,810 --> 00:30:57,650
+بس الآن بدي أعيد مرة تانى كيف .. بناء على إيش أنا
+
+404
+00:30:57,650 --> 00:31:00,970
+بقى ابني الآن عدد الاحتمالات اللى موجودة عندى مع
+
+405
+00:31:00,970 --> 00:31:06,150
+two variable او أربعة كيف بدي أوزعهم؟ في عندى ال
+
+406
+00:31:06,150 --> 00:31:10,150
+first column اللى بمثل ال first operand وال second
+
+407
+00:31:10,150 --> 00:31:14,570
+operand ال first column وال second column الآن
+
+408
+00:31:14,570 --> 00:31:18,210
+عندك أربعة .. أربعة صفوف تنتمدهم يكونوا true
+
+409
+00:31:18,210 --> 00:31:24,240
+وتنتمدهم يكونوا false يعني أربعة على اتنينيساوى 2
+
+410
+00:31:24,240 --> 00:31:30,020
+هذا القيمة اللى جبتها تنتين true ورا بعض وتنتين
+
+411
+00:31:30,020 --> 00:31:33,600
+false ورا بعض الآن في العمود التانى بتاخد التنين
+
+412
+00:31:33,600 --> 00:31:36,400
+هادي و بتجسمها كمان مرة على تنين ليش بيجسم على
+
+413
+00:31:36,400 --> 00:31:38,520
+تنين يا شباب لإن القيمة اللى عندى التنتين يا إما
+
+414
+00:31:38,520 --> 00:31:42,980
+true يا إما false وبالتالي تنين على تنين واحد قيمة
+
+415
+00:31:42,980 --> 00:31:46,220
+true قيمة false شغل مهم برضه عشان روح أعيد تانى
+
+416
+00:31:46,220 --> 00:31:51,650
+درورى كل الأعمدة تبدأ بنفس البدايةإذا بدأت العمود
+
+417
+00:31:51,650 --> 00:31:56,310
+والأولى true كل الأعمدة تبدأ معاك بـ true بدأت بـ
+
+418
+00:31:56,310 --> 00:32:02,010
+false كل الأعمدة تبدأ بـ false تعالى جاي شوية و
+
+419
+00:32:02,010 --> 00:32:07,150
+ناخد كمان لو كان في عندى three operands تلاتة يعني
+
+420
+00:32:07,150 --> 00:32:16,650
+ال first column تسعة ال second column و ال third
+
+421
+00:32:16,650 --> 00:32:24,380
+column ال best twoأُس ثلاثة يساوي تمانية لأن عندي
+
+422
+00:32:24,380 --> 00:32:30,260
+تمان احتمالات تمانية
+
+423
+00:32:30,260 --> 00:32:35,180
+على اتنين اربعة يعني اندي اول اربعة true والاربعة
+
+424
+00:32:35,180 --> 00:32:39,260
+اللي وراهم false الآن في العمود التاني باخد
+
+425
+00:32:39,260 --> 00:32:44,520
+الأربعة و بجسمها على اتنين اتنين true و اتنين
+
+426
+00:32:44,520 --> 00:32:47,340
+false اتنين true و اتنين false لحد ما اخلص الجلول
+
+427
+00:32:48,690 --> 00:32:53,890
+باخد اتنين كمان مرة و بجسمها على اتنين واحد false
+
+428
+00:32:53,890 --> 00:32:57,090
+معناه قيمة قيمة true و false لحد ما اكمل العمود
+
+429
+00:32:57,090 --> 00:33:01,290
+هذا الكلام شباب بضمنك حتى لو كان جدول الاحتمالات
+
+430
+00:33:01,290 --> 00:33:06,290
+في عشر متغيرات بتقدر تشتغل انتياش و انت مرتاح يعني
+
+431
+00:33:06,290 --> 00:33:09,810
+تخيل عشان نبتداش تقول عشر متغيرات تتكلم عن خمسة
+
+432
+00:33:09,810 --> 00:33:14,470
+اتنين اقص خمسة اتنين و تلاتين العمود الأول صتناش
+
+433
+00:33:14,470 --> 00:33:18,950
+true و صتناش falseالعمود التاني تمانية true تمانية
+
+434
+00:33:18,950 --> 00:33:23,710
+false تمانية true تمانية false العمود التالت اربعة
+
+435
+00:33:23,710 --> 00:33:27,130
+true اربعة false اربعة true اربعة false اربعة true
+
+436
+00:33:27,130 --> 00:33:28,410
+اربعة false اربعة true اربعة false اربعة true
+
+437
+00:33:28,410 --> 00:33:32,990
+اربعة false حيث اتناشر اللي بعده اتنين اتنين true
+
+438
+00:33:32,990 --> 00:33:35,030
+اتنين false اتنين true اتنين false لحد ما تخلص
+
+439
+00:33:35,030 --> 00:33:39,670
+الجدول العمود الخامس واحد واحد واحد بهيك انت بتكون
+
+440
+00:33:39,670 --> 00:33:45,020
+جبت كل الاحتمالات بدون ما تعتمد على ذاكرتكليش؟
+
+441
+00:33:45,020 --> 00:33:48,120
+لأنه لما تقدر الاحتمالات شبه و تعتمد على الذاكرة
+
+442
+00:33:48,120 --> 00:33:52,780
+عشان تجيب ال combination تمام؟ ممكن تخطأ و تكرر
+
+443
+00:33:52,780 --> 00:33:57,020
+الصف و اذا انت اخطأت و كررت صف معناته انت ماجيبتش
+
+444
+00:33:57,020 --> 00:34:02,610
+جدول الاحتمالات كامل معناته الحكم علىبالنسبة لكم
+
+445
+00:34:02,610 --> 00:34:04,630
+الـ Compound و Proposition لك لن يكونوا صحيحين
+
+446
+00:34:04,630 --> 00:34:09,570
+لذلك مطلوب منك ترسم الجدول بشكل واضح طبعا احنا
+
+447
+00:34:09,570 --> 00:34:12,210
+الآن أصبناها بشكل سريع و هنعيده مرة و اتنين و
+
+448
+00:34:12,210 --> 00:34:16,610
+تلاتة طول ما احنا في الشفتر هذا طيب نرجع لـ
+
+449
+00:34:16,610 --> 00:34:19,450
+Logical Operator Conjunction اللي هو الـ AND
+
+450
+00:34:19,450 --> 00:34:22,730
+نرمزله
+
+451
+00:34:22,730 --> 00:34:31,840
+بالرمز هذا hat و بنسميه AND P AND Qالأولى
+
+452
+00:34:31,840 --> 00:34:36,740
+conjunction هدا بتكون قيمته true لو كان قيمة ال
+
+453
+00:34:36,740 --> 00:34:46,140
+two operands true لو
+
+454
+00:34:46,140 --> 00:34:50,020
+كانت قيمة ال two operands true يعني true and true
+
+455
+00:34:50,020 --> 00:34:56,520
+true true and false false false and true false
+
+456
+00:34:56,520 --> 00:34:58,460
+false and false false
+
+457
+00:35:03,260 --> 00:35:09,600
+All the operands are
+
+458
+00:35:09,600 --> 00:35:16,440
+true كل المعاملات الموجودة أو ال operands الموجودة
+
+459
+00:35:16,440 --> 00:35:21,400
+عندي لازم تكون true لو انا بدي أنفيها يعني هيك هيك
+
+460
+00:35:21,400 --> 00:35:26,620
+بديني true هذه true صح؟ مش هذي بتقدي ايه او بتديني
+
+461
+00:35:26,620 --> 00:35:32,490
+فوق بتديني true ببنفي هذي ال false متى بيكونNone
+
+462
+00:35:32,490 --> 00:35:38,150
+ولا واحد منهم؟ مش صحيح واحد على الأقل منهم يكون
+
+463
+00:35:38,150 --> 00:35:42,950
+false شوف انت قاعد تقول some or most أثبت؟ اذا انت
+
+464
+00:35:42,950 --> 00:35:49,170
+قلت most of the operands are true المهم كلهم بنعكس
+
+465
+00:35:49,170 --> 00:35:58,730
+عليهم most وبالتالي غلط مفهوش استخدم most at least
+
+466
+00:35:58,730 --> 00:36:05,180
+one operand is false يقل falseOkay او بتروح تقولي
+
+467
+00:36:05,180 --> 00:36:08,960
+some of the operands are false بعضهم يكون اياش
+
+468
+00:36:08,960 --> 00:36:12,560
+false معناته بتقدي نلاقي اياش لا false لاحظ كمان
+
+469
+00:36:12,560 --> 00:36:16,760
+مرة مفهوش اروح اقوله most of the operands are true
+
+470
+00:36:16,760 --> 00:36:21,860
+لإن ال most بتحتوي المعنى all يعني هي كمان اجي
+
+471
+00:36:21,860 --> 00:36:27,040
+اقول كل او معظم الشباب معظم الشباب نجحوا في المساك
+
+472
+00:36:28,530 --> 00:36:31,710
+ما لو كانوا كلهم نجحين، كلامي صح، لأ، ضربوا كلامي
+
+473
+00:36:31,710 --> 00:36:37,830
+صح، نصيحة لأ، لكن، بينفعش أستبدل all و must و
+
+474
+00:36:37,830 --> 00:36:44,890
+most، أنا إيش أقول هيك؟ All the students pass the
+
+475
+00:36:44,890 --> 00:36:47,270
+course، نجحوا في المساق، و أنا فعليا مش كلهم
+
+476
+00:36:47,270 --> 00:36:52,090
+نجحوا، لكن غالبيتهم، 90% منهم نجحوا، فبينفعش أقول
+
+477
+00:36:52,090 --> 00:36:55,370
+كل الطلاب نجحوا، بينفعش أدّعي، لازم أقول most of
+
+478
+00:36:55,370 --> 00:36:59,670
+the studentsباص otherwise بيكون ال composition أو
+
+479
+00:36:59,670 --> 00:37:06,750
+اللي بعرفه ال proposition تبعي خطأ طيب الان
+
+480
+00:37:06,750 --> 00:37:13,250
+لو احنا انتقلنا للجملة التالية و جالي افترض ان في
+
+481
+00:37:13,250 --> 00:37:16,830
+عندك two proposition بي and كيو بحيث ان ال بي
+
+482
+00:37:16,830 --> 00:37:21,370
+today is Friday وكيو
+
+483
+00:37:21,370 --> 00:37:27,560
+it is raining today بتشتي اليوم الدنيا بتمطرتمام؟
+
+484
+00:37:27,560 --> 00:37:30,520
+و بدى أروح أربطهم مع بعض أكوّن compound
+
+485
+00:37:30,520 --> 00:37:35,100
+proposition تمام؟ باعتماد على ال conjunction على
+
+486
+00:37:35,100 --> 00:37:42,220
+ال and إيش ماكنت تقول ليه؟ P and Q ليش أنا ماطلبتش
+
+487
+00:37:42,220 --> 00:37:47,010
+تنفيهاما طلبتش تنفيها انا جاعت بس بقولك اجمعلي
+
+488
+00:37:47,010 --> 00:37:49,290
+اياهم الاتنين مش احنا قولنا ال compound
+
+489
+00:37:49,290 --> 00:37:53,310
+proposition هو عبارة عن combination ما بين symbol
+
+490
+00:37:53,310 --> 00:37:55,930
+و proposition هاي ال symbol و ال proposition P and
+
+491
+00:37:55,930 --> 00:37:59,670
+Q هايهم تمام؟ و بدي استخدم ال conjunction الآن
+
+492
+00:37:59,670 --> 00:38:05,010
+شباب مابتدركاش تقولي تسوي false او تسوي true انا
+
+493
+00:38:05,010 --> 00:38:07,430
+جاعت بقولك اجمعلي proposition و مابهمنيش قيمته ده
+
+494
+00:38:07,430 --> 00:38:17,860
+الآن الان معناته today ايه؟is Friday and
+
+495
+00:38:17,860 --> 00:38:24,160
+it is raining today Running يجري، raining تمطر
+
+496
+00:38:24,160 --> 00:38:28,620
+Today
+
+497
+00:38:28,620 --> 00:38:33,500
+is Friday and it is raining today تمام؟ وبالتالي
+
+498
+00:38:33,500 --> 00:38:38,500
+هذه بدها تساوي ال B and Q يعني صار هذا عندي
+
+499
+00:38:38,500 --> 00:38:44,040
+compound proposition وأنابقدر أعمل منها باعتمادي
+
+500
+00:38:44,040 --> 00:38:47,940
+على ال proposition أو ال symbols الخاصة بال
+
+501
+00:38:47,940 --> 00:38:53,600
+proposition هي
+
+502
+00:38:53,600 --> 00:38:56,480
+أي سؤال حتى اللحظة يا شباب؟ أمور ماشية ان شاء
+
+503
+00:38:56,480 --> 00:39:03,280
+الله؟ تمام conjunction اللي نفس المثال disjunction
+
+504
+00:39:03,280 --> 00:39:10,420
+عفوا disjunction بتكلم على ال or برضه binary برضه
+
+505
+00:39:10,420 --> 00:39:16,490
+binary operatorالأن الـ disjunction اللي هو ال or
+
+506
+00:39:16,490 --> 00:39:27,590
+بتعطيني true لما يكون واحدة على الأقل at least one
+
+507
+00:39:27,590 --> 00:39:34,870
+operand is true على الأقل واحد من ال operand بيكون
+
+508
+00:39:34,870 --> 00:39:37,190
+true هذه بتساوي true
+
+509
+00:39:40,390 --> 00:39:50,870
+عكسها .. نفيها عفواً All the operands are false
+
+510
+00:39:50,870 --> 00:39:57,650
+شوفت كيف؟ عكس واحد على الأقل واحد مافيش على الأقل
+
+511
+00:39:57,650 --> 00:40:01,830
+واحدة، لكلهم تمام؟ ماينفعش أقول اتنين وماينفعش
+
+512
+00:40:01,830 --> 00:40:04,090
+أقول تلاتة وماينفعش أقول most لأنه برضه يُطبّق
+
+513
+00:40:04,090 --> 00:40:11,130
+عليهم على الأقل بظبط؟ لكن نفيها تماماً كلهمطيب
+
+514
+00:40:11,130 --> 00:40:16,070
+تعالى نشوفها at least one operand is true true or
+
+515
+00:40:16,070 --> 00:40:22,030
+true true true or false true false or true true
+
+516
+00:40:22,030 --> 00:40:29,890
+false false false all the operands are false لما
+
+517
+00:40:29,890 --> 00:40:35,030
+يقولوا كلهم false معناته بديني false شباب انتبه
+
+518
+00:40:35,030 --> 00:40:38,330
+لكلمة binary عشان كمان الشغل مانسهاش لما انا باجهي
+
+519
+00:40:38,330 --> 00:40:49,750
+بقول be andQ and R أو بعد يقول P or Q or R صار فيه
+
+520
+00:40:49,750 --> 00:40:55,170
+يعني ألف متغيرات كيبرا ساوي بدك تشتغل حسب
+
+521
+00:40:55,170 --> 00:40:57,810
+الأولويات اللي هتكلم عليها كمان شوية بس الأصل
+
+522
+00:40:57,810 --> 00:41:01,500
+العملية تنائيةمن ال binary يعني بطبق هذه وهذه في
+
+523
+00:41:01,500 --> 00:41:05,400
+الأول و بعدين بطبق لهم التاني و إذا أتكلم على
+
+524
+00:41:05,400 --> 00:41:09,060
+أولويات و العملية هان عملية تجميعية ممكن تطبق
+
+525
+00:41:09,060 --> 00:41:13,820
+للتاني P .. P .. Q and R و بعدين تطبق ال ب فيهم او
+
+526
+00:41:13,820 --> 00:41:20,120
+تعمل and وبالتالي ما زالت العملية binary طيب
+
+527
+00:41:20,120 --> 00:41:23,620
+على نفس المثال السابق تبع الجمعة و المطر لو بدى
+
+528
+00:41:23,620 --> 00:41:26,160
+استخدم ال disjunction كيف ممكن تنتهيهم أو عفوا
+
+529
+00:41:26,160 --> 00:41:27,180
+تربطهم مع بعض
+
+530
+00:41:31,730 --> 00:41:37,950
+D or Q إيش تساوي إذا كان ال P اليوم الجمعة و ال Q
+
+531
+00:41:37,950 --> 00:41:43,830
+اليوم قفيل مطر كل
+
+532
+00:41:43,830 --> 00:41:47,530
+بساطة بدك تكتب ال phrases زي ما هي today is Friday
+
+533
+00:41:47,530 --> 00:41:54,810
+or it is raining today يعني الآن احنا مهطلين في
+
+534
+00:41:54,810 --> 00:41:59,770
+إجازة السبب يا دنيا بتشتي اما اليوم الجمعة مافيش
+
+535
+00:41:59,770 --> 00:42:04,000
+غير هي المجالالخميس .. يا سيدي اعتبر حالنا في
+
+536
+00:42:04,000 --> 00:42:08,300
+المدرسة يعني .. كمان؟ وبالتالي المطلوب منك يا شباب
+
+537
+00:42:08,300 --> 00:42:11,240
+للوحلة الأولى .. للوحلة الأولى تكتب الجمال كما هي
+
+538
+00:42:11,240 --> 00:42:15,280
+على الـH مش هيكد و .. و مجرد أقعد أقولك
+
+539
+00:42:15,280 --> 00:42:22,380
+disjunction يعني R هي PRQ بكتب الـB و بحط الـR و
+
+540
+00:42:22,380 --> 00:42:26,260
+بكتب الـQ بطلع فيها بعد ذلك شوية بتروي هل في مجال
+
+541
+00:42:26,260 --> 00:42:29,980
+أصيغها بشكل ألطف؟ إذا في مجال بكتبها بشكل ألطف؟
+
+542
+00:42:29,980 --> 00:42:34,630
+مافيش شيءخلّيها زي ما هي نص خلصك تاخد العلامة
+
+543
+00:42:34,630 --> 00:42:38,070
+كاملة تاخد العلامة كاملة تاخد العلامة كاملة تاخد
+
+544
+00:42:38,070 --> 00:42:40,410
+العلامة كاملة تاخد العلامة كاملة تاخد العلامة
+
+545
+00:42:40,410 --> 00:42:43,830
+كاملة تاخد العلامة كاملة تاخد العلامة كاملة تاخد
+
+546
+00:42:43,830 --> 00:42:45,950
+العلامة كاملة تاخد العلامة كاملة تاخد العلامة
+
+547
+00:42:45,950 --> 00:42:46,490
+كاملة تاخد العلامة كاملة تاخد العلامة كاملة تاخد
+
+548
+00:42:46,490 --> 00:42:48,870
+العلامة كاملة تاخد العلامة كاملة تاخد العلامة
+
+549
+00:42:48,870 --> 00:42:49,490
+العلامة كاملة تاخد العلامة كاملة تاخد العلامة
+
+550
+00:42:49,490 --> 00:42:55,390
+كاملة تاخد العلامة كاملة تاخد
+
+551
+00:42:55,390 --> 00:43:00,710
+العلامة
+
+552
+00:43:00,710 --> 00:43:01,030
+كاملة تاخ
+
+553
+00:43:21,130 --> 00:43:27,850
+بالـ Exclusive OR بالـ XOR لازم واحد من الـ
+
+554
+00:43:27,850 --> 00:43:36,420
+operand على الأكثريكون true ال XR بتقول لي ال true
+
+555
+00:43:36,420 --> 00:43:53,600
+بحصل عليها if at most one operand is true لو
+
+556
+00:43:53,600 --> 00:44:00,240
+كان على الأكثر واحد من ال operand true بحصل عليه
+
+557
+00:44:02,180 --> 00:44:09,980
+true ايش يعني على الأكثر شباب يعني واحد واحد او
+
+558
+00:44:09,980 --> 00:44:18,260
+اتنين لأ تطلعش بال most طيب طب تعالى نفكر طب لو
+
+559
+00:44:18,260 --> 00:44:23,520
+كانوا التنين false التنين false لأن مافيش ولا واحد
+
+560
+00:44:23,520 --> 00:44:30,200
+منهم أصبح true يعني هيك احنا ممكن نصيحها if and
+
+561
+00:44:31,430 --> 00:44:40,330
+only if one operand is true هاي برضه صياغة تانية
+
+562
+00:44:40,330 --> 00:44:50,310
+الان نفيها لو انا بدي انفيها متى بتديني false none
+
+563
+00:44:50,310 --> 00:44:58,710
+of the operands is true الكلام صحيح بس هذا نص الحل
+
+564
+00:44:59,240 --> 00:45:02,240
+لو متشابهين إذا كانوا فوصة أو لو كانوا واحد .. لأن
+
+565
+00:45:02,240 --> 00:45:05,640
+لاحظ لو كانوا all وبالتالي لو بدك تقرر في عندك نفع
+
+566
+00:45:05,640 --> 00:45:11,240
+الجملة هذه هيعتمد على compound preposition هيك
+
+567
+00:45:11,240 --> 00:45:15,800
+none of the operands is true ولا واحد منهم true
+
+568
+00:45:15,800 --> 00:45:21,670
+andأر اند و لا ار انتبه خلّيها different هيك none
+
+569
+00:45:21,670 --> 00:45:25,390
+of the operand is are او are is false وبالتالي
+
+570
+00:45:25,390 --> 00:45:28,210
+حيكون في عندي or إذا كانت حتى الشرق الأول مش حد
+
+571
+00:45:28,210 --> 00:45:30,890
+يعني لو كانوا كلهم true مش هلاجي ولا واحد منهم
+
+572
+00:45:30,890 --> 00:45:35,170
+false و لو كانوا كلهم false ولا واحد منهم true هذه
+
+573
+00:45:35,170 --> 00:45:39,970
+الحالة اللي بتاع case اللي موجودة عندي كيف؟ طيب
+
+574
+00:45:39,970 --> 00:45:46,750
+الآن تعالي هان ار ار ار ار لو حكينا all of a brand
+
+575
+00:45:46,750 --> 00:45:52,680
+is trueما هو نفس الكلام اللي بنقوله .. نفس الكلام
+
+576
+00:45:52,680 --> 00:45:55,900
+اللي بنقوله .. بس بيؤكدنا على أن كله .. كل
+
+577
+00:45:55,900 --> 00:45:59,100
+الoperands .. لإن كمان مرة .. تبه معنا .. لإن
+
+578
+00:45:59,100 --> 00:46:06,400
+الشباب true .. it's all true .. الداني false ..
+
+579
+00:46:06,400 --> 00:46:11,000
+لما كانوا كلهم true .. الداني false .. و لما كانوا
+
+580
+00:46:11,000 --> 00:46:15,680
+كلهم false .. برضه ابني false .. يعني هيك .. all
+
+581
+00:46:15,680 --> 00:46:20,340
+the operands .. is it true .. lead to false ..all
+
+582
+00:46:20,340 --> 00:46:24,160
+the operands false lead to false معناته لو كان all
+
+583
+00:46:24,160 --> 00:46:29,940
+the operands are true او all the operands are
+
+584
+00:46:29,940 --> 00:46:36,660
+false معناته ناتج false تمام؟ وهذه عكس الجملة اللي
+
+585
+00:46:36,660 --> 00:46:43,740
+موجودة عندها نعم اروح اطبق عليها تبع المطر اكيد
+
+586
+00:46:43,740 --> 00:46:47,300
+هتظبط معاك تعالى بسم الله بقول لو بدنا نسقط عليها
+
+587
+00:46:47,300 --> 00:46:47,900
+مثل المطر
+
+588
+00:46:53,430 --> 00:47:02,710
+and today is Friday XR
+
+589
+00:47:02,710 --> 00:47:14,030
+it is raining today بتمطر اليوم عشان
+
+590
+00:47:14,030 --> 00:47:19,050
+تكون النتيجة هذه true لازم تكون واحدة من هدول فقط
+
+591
+00:47:19,050 --> 00:47:21,270
+false
+
+592
+00:47:22,510 --> 00:47:25,430
+واحدة من هدول فقط واحدة من هدول تكون true فقط
+
+593
+00:47:25,430 --> 00:47:28,970
+والتانية لازم تكون false ايوة يعني لازم تكون واحدة
+
+594
+00:47:28,970 --> 00:47:34,410
+false واحدة true واحدة false واحدة true ما هو نفسك
+
+595
+00:47:34,410 --> 00:47:41,290
+لا والله طيب انا بدي اسأل بقى انا جاهز بقول واحدة
+
+596
+00:47:41,290 --> 00:47:44,010
+false واحدة true ايش اللي بيفرج عن واحدة true
+
+597
+00:47:44,010 --> 00:47:44,670
+واحدة false
+
+598
+00:47:48,910 --> 00:47:52,370
+طيب و بالتالي مشاركة كويسة ماقاش الحل بس ماتحاولش
+
+599
+00:47:52,370 --> 00:47:56,490
+تخربطني يعني معاك تمام؟ و بالتالي عشان بال .. بال
+
+600
+00:47:56,490 --> 00:47:59,630
+.. ال exclusive or ال core الكهادة يكون ال true
+
+601
+00:47:59,630 --> 00:48:03,710
+لازم أنفي واحدة من التنتين و أحافظ على التانية
+
+602
+00:48:03,710 --> 00:48:08,530
+true يعني هيك بدي أضمن واحدة false و واحدة true
+
+603
+00:48:08,530 --> 00:48:19,320
+الأقل بما أن اليوم مش الجمعة isnt friday x oror it
+
+604
+00:48:19,320 --> 00:48:24,560
+is raining today طب بس مافيش مطار برا معناته false
+
+605
+00:48:24,560 --> 00:48:31,120
+و false معناته هتطلع معايا false إلا غير زي كان
+
+606
+00:48:31,120 --> 00:48:35,140
+بنستمطر الاسحاب اليوم يطلع طيارة هيك ترش شوية املح
+
+607
+00:48:35,140 --> 00:48:38,960
+على الاسحاب و بتنزل المطار أقولك أسمته باستمطار
+
+608
+00:48:38,960 --> 00:48:43,980
+السحاب؟أمطار صناعية وليس صناعية صناعية لأن في بعض
+
+609
+00:48:43,980 --> 00:48:48,560
+الدول اللي بيكون عندهم الغيوم فعليا محملة .. محملة
+
+610
+00:48:48,560 --> 00:48:51,620
+بالمطر بشكل ضخم يعني بتشوف الغيوم بتشوفه أسود أسود
+
+611
+00:48:51,620 --> 00:48:56,620
+لكن مهيئات ان يسقط المطر من البرد مش موجود فاش
+
+612
+00:48:56,620 --> 00:49:01,160
+بروح بسهولة بروح و بطلع بطيرات ضخمة زي ال B52 على
+
+613
+00:49:01,160 --> 00:49:05,940
+سبيل المثال بطلع فوق .. فوق السحاب و ببدأ يرش ملح
+
+614
+00:49:07,390 --> 00:49:13,230
+إيش الملح بيساوي؟ بيعمل على تجميع قطرات الميّن ..
+
+615
+00:49:13,230 --> 00:49:18,450
+بتتجل فبتنزل .. بتتجل فبتنزل .. هذا بالسمدوس ..
+
+616
+00:49:18,450 --> 00:49:25,710
+تمقار .. السحاب .. عقول كافرة .. لأ بالعكس .. مش
+
+617
+00:49:25,710 --> 00:49:27,630
+ضروري أن يكون عقول كافرة .. بالعكس هذا الكلام كثير
+
+618
+00:49:27,630 --> 00:49:29,890
+صحيح .. هو العقول الكافرة هي اللي بتنزل بالجيب
+
+619
+00:49:29,890 --> 00:49:33,970
+أصلا .. لأ لأ لأ .. عقول عقيبة .. مش صح .. لأ صح
+
+620
+00:49:33,970 --> 00:49:37,760
+..طيب .. انت .. ال .. ال .. كل ال .. الشغل تشيسوه
+
+621
+00:49:37,760 --> 00:49:41,900
+.. بس تشوف فعليا من .. من المعارض .. اللي بغض
+
+622
+00:49:41,900 --> 00:49:43,960
+النظر .. ماحكيش نعمله .. من .. من اللي جاب الفكرة
+
+623
+00:49:43,960 --> 00:49:46,060
+.. من اللي فكر .. الإنسان بغض النظر عن الإنسان ..
+
+624
+00:49:46,060 --> 00:49:48,020
+ان عرب بس .. طب انت ليش .. انت .. انت ليش decided
+
+625
+00:49:48,020 --> 00:49:51,760
+ان اللي فكر فيها إنسان غير مسلم؟ أكيد .. لأ .. لأ
+
+626
+00:49:51,760 --> 00:49:53,600
+.. لأ .. لأ .. لأ .. لأ .. لأ .. لأ .. لأ .. لأ ..
+
+627
+00:49:53,600 --> 00:49:54,960
+لأ .. لأ .. لأ .. لأ .. لأ .. لأ .. لأ .. لأ .. لأ
+
+628
+00:49:54,960 --> 00:49:55,380
+.. لأ .. لأ .. لأ .. لأ .. لأ .. لأ .. لأ .. لأ ..
+
+629
+00:49:55,380 --> 00:50:01,000
+لأ .. لأ .. لأ
+
+630
+00:50:01,000 --> 00:50:03,840
+.. لأ
+
+631
+00:50:06,570 --> 00:50:09,630
+طيب، هبنحاولش ننكر حاجة يا رامي، القدر ما احنا
+
+632
+00:50:09,630 --> 00:50:13,350
+بنحاوله فعليا أن نتكلم على واقع، طبعا، الآن صحيح
+
+633
+00:50:13,350 --> 00:50:17,530
+الوضع العالم العربي للأسف مذري، ماحدش بنكر، هذا لا
+
+634
+00:50:17,530 --> 00:50:22,290
+يمنع اللي في ناس عباقرا وموجودين، طبعا، و هو عربي
+
+635
+00:50:22,290 --> 00:50:25,790
+و من أصل عربي ولكن اللي جا فيه حاضنة في الدول
+
+636
+00:50:25,790 --> 00:50:31,540
+الأجنبية اتبنتهطبعا؟ يعني أنا قابلت مرة professor
+
+637
+00:50:31,540 --> 00:50:35,220
+مصري كان بتزوّد .. الجامعة بتزوّد المختبر تبعه و
+
+638
+00:50:35,220 --> 00:50:39,680
+بتجيه مشاريع في المختبر تبعه بعشرين مليون دولار،
+
+639
+00:50:39,680 --> 00:50:42,340
+بتدفعله فلوس، بتتكلم اللي وياه، بيقوللي ان الله
+
+640
+00:50:42,340 --> 00:50:45,560
+وروح يتعالى مصر، والله و بيصير اللي اللي .. اللي
+
+641
+00:50:45,560 --> 00:50:50,150
+الولد ييبقى .. ييبقى اللي معايشه قعمياماشي الحال،
+
+642
+00:50:50,150 --> 00:50:55,590
+هي مسلم وعربي تمام؟ ولقى فيه ناس تتبنى و بتنتج لكن
+
+643
+00:50:55,590 --> 00:50:59,750
+بغض النظر في الآخر الإنتاج اللى لما بيطلع للإعلام
+
+644
+00:50:59,750 --> 00:51:03,770
+بيطلع الجامعة الفلانية في الدولة الفلانية اخترعت
+
+645
+00:51:03,770 --> 00:51:09,650
+كده وبيذكروا اسمه وممكن لو اكرموا ويكتبوله مثلا
+
+646
+00:51:09,650 --> 00:51:14,570
+مصر الجنسية او ما شايفا ليكن طيب مش موضوعنا كمان
+
+647
+00:51:14,570 --> 00:51:20,830
+مرة عشان ما نجلبهاش سياسة ولا زيكتورياضياتلسه احنا
+
+648
+00:51:20,830 --> 00:51:27,150
+بطولين مشوارنا بناعوض التأخير طيب الان في عندي
+
+649
+00:51:27,150 --> 00:51:32,850
+implication implication اللي هو الـ implies أو
+
+650
+00:51:32,850 --> 00:51:38,150
+يقول إلى أو يؤدي إلى الان هده ال implication انت
+
+651
+00:51:38,150 --> 00:51:42,430
+غالبا ماشوفتهوش سابقا الان conditional statement
+
+652
+00:51:42,430 --> 00:51:48,930
+if statement if thenيعني if ال condition then
+
+653
+00:51:48,930 --> 00:51:52,850
+conclusion if ال hypothesis فرضية إذا تحققت
+
+654
+00:51:52,850 --> 00:51:59,630
+الفرضية then النتيجة بتتحقق عليها شرط وجواب الشرط
+
+655
+00:51:59,630 --> 00:52:04,990
+طيب لان تعالى نشوف متى ال implication هذا بيكون
+
+656
+00:52:04,990 --> 00:52:09,710
+true متى بتكون قيمة ال implication صحيحة لو كانت
+
+657
+00:52:09,710 --> 00:52:14,640
+ال true تقول إلى true يعني هيكإن الـ condition
+
+658
+00:52:14,640 --> 00:52:19,220
+تبعي كان قيمته true وإدى إن المحصلة أو ال
+
+659
+00:52:19,220 --> 00:52:23,400
+conclusion كانت true فالمنطق بيقول إن العملية هذا
+
+660
+00:52:23,400 --> 00:52:27,680
+منطقية سليمة يعني هيك اللي أداري الصح يقود إلى
+
+661
+00:52:27,680 --> 00:52:34,620
+نتيجة صح إذا كنت تدرس تنجح بالمحصلة كلام منطق فال
+
+662
+00:52:34,620 --> 00:52:38,220
+conclusion هذه أو ال implication هذه صحيحة 100%
+
+663
+00:52:38,220 --> 00:52:45,660
+true تقول إلى falseانت انجحت او عفوا اندرست
+
+664
+00:52:45,660 --> 00:52:50,080
+وماانجحتش فى شغل غلط فى الموضوع وبالتالي هذه من
+
+665
+00:52:50,080 --> 00:52:55,460
+ناحية منطق مرفوضة مدرستش
+
+666
+00:52:55,460 --> 00:53:00,660
+وانجحت ماشي الحال هى مش منطقية بس على النفس
+
+667
+00:53:00,660 --> 00:53:04,980
+الدكتور صدبك انجحت بالمصاد البوش رفعك الى اخره من
+
+668
+00:53:04,980 --> 00:53:10,790
+الشغلات اللى بتعرفوها كويسةمثلا .. درستش .. ماعرفش
+
+669
+00:53:10,790 --> 00:53:13,430
+أقولك .. من الشغلات اللي أنتوا بتعرفوها كويس ..
+
+670
+00:53:13,430 --> 00:53:20,670
+false implies false .. مادرستش .. و ماانجحتش ..
+
+671
+00:53:20,670 --> 00:53:23,750
+طبيعية جدا .. طبيعية جدا .. لاحظ الحالة الوحيدة
+
+672
+00:53:23,750 --> 00:53:27,930
+اللي مش طبيعية .. أنه أنت أخدت بالأسباب و ماكنتش
+
+673
+00:53:27,930 --> 00:53:31,690
+النتيجة صحية .. هل بيكون في الشغلة غلط .. وبالتالي
+
+674
+00:53:31,690 --> 00:53:35,950
+الشغلة مش منطقيها .. الحاجة على الدكتور .. بينكوا
+
+675
+00:53:35,950 --> 00:53:42,460
+بينوا عجابه ..واضح الأمور يا شباب؟ الان بنرمزهم P
+
+676
+00:53:42,460 --> 00:53:50,040
+implies Q هاي ال implication الان P بمثابة ال
+
+677
+00:53:50,040 --> 00:53:55,320
+hypothesis الفرضية و ال Q بمثابة ال conclusion او
+
+678
+00:53:55,320 --> 00:53:59,560
+النتيجة طيب ..الها هذه أسامي كتيرة
+
+679
+00:54:06,580 --> 00:54:10,840
+وتُكتب بصياغات مختلفة كلها تؤدي نفس المعنى if ال
+
+680
+00:54:10,840 --> 00:54:15,960
+بي then كيو يعني هيك لو انا افترضت ان ال بي ان
+
+681
+00:54:15,960 --> 00:54:22,780
+اليوم الجمعة و كيو بدأ لعب كورة if today is a
+
+682
+00:54:22,780 --> 00:54:28,360
+Friday then I'll play football
+
+683
+00:54:32,630 --> 00:54:37,210
+برضه في الكتابة ممكن اكتبها if today is Friday كمه
+
+684
+00:54:37,210 --> 00:54:44,130
+بدون مكتوب then I play football B is sufficient
+
+685
+00:54:44,130 --> 00:54:51,890
+for الـ B كافية من أجل أصل الـ Q ال hypothesis
+
+686
+00:54:51,890 --> 00:54:56,890
+الفرضية تبعتي كافية انها توصلني لمين لل conclusion
+
+687
+00:54:56,890 --> 00:55:06,470
+او للنتيجة today is FridayIt is sufficient to play
+
+688
+00:55:06,470 --> 00:55:10,310
+football يعني خلاص مكفين إنه اليوم الجمعة عشان
+
+689
+00:55:10,310 --> 00:55:17,130
+ألعب كرة يعني أنا في إجازة الـQFAB تمام؟ أنا جاهز
+
+690
+00:55:17,130 --> 00:55:21,270
+أتكلم لشباب هذه الصياغات ممكن تظهر من خلالها ال
+
+691
+00:55:21,270 --> 00:55:27,070
+implication تعالى نشوف هذه الـQFAB و الـQNB معناهم
+
+692
+00:55:27,070 --> 00:55:34,140
+إنه الـQ هذه هتتحقق أو هتكون trueإذا تحقق الـ
+
+693
+00:55:34,140 --> 00:55:37,100
+sharp بين قصين أصبحت الـ hypothesis هي الجامعة في
+
+694
+00:55:37,100 --> 00:55:40,760
+نهاية الجملة a necessary condition for B is a Q
+
+695
+00:55:40,760 --> 00:55:49,680
+الـ sharp اللي هيترتب على ال B اللي هو ال Q الـ Q
+
+696
+00:55:49,680 --> 00:55:55,980
+unless نقطة ال B الـ Q unless نقطة ال B معناته إن
+
+697
+00:55:55,980 --> 00:56:01,240
+الـ Q هذه مش هتتحقق إلا لو تحققت ال B لاحظ unless
+
+698
+00:56:01,240 --> 00:56:06,790
+نفيو نفي نفي نفي اثبات وبالتالي ال Q مش هتتحقق الا
+
+699
+00:56:06,790 --> 00:56:10,770
+غير لو اتحققت ال B الاخره من الجمال اللى موجوده
+
+700
+00:56:10,770 --> 00:56:17,530
+عندنا ناخدنا لتنتين بس أنا بأنصحك حاول اقراهم اك
+
+701
+00:56:17,530 --> 00:56:21,150
+مرة و اتنين و تلاتة و عشرة عشان لو جت واحده في
+
+702
+00:56:21,150 --> 00:56:25,210
+الامتحان تمام فالصح و غلط ممكن ييجوا وبالتالي انت
+
+703
+00:56:25,210 --> 00:56:27,690
+ممكن ايش تجيبها بشكل كويس
+
+704
+00:56:31,150 --> 00:56:37,010
+لتل بي علي studies discrete mathematics و ال Q علي
+
+705
+00:56:37,010 --> 00:56:42,130
+will get a good grade و بدنا نكتبها على صيغة if
+
+706
+00:56:42,130 --> 00:56:45,890
+then if
+
+707
+00:56:45,890 --> 00:56:50,410
+علي studies discrete mathematics لو علي درس
+
+708
+00:56:50,410 --> 00:56:56,610
+رياضيات منفصلة ممكن تحط كمه علي will و مكان الكمه
+
+709
+00:56:56,610 --> 00:57:03,870
+تكتب then علي will كلام صحعلي سيحصل
+
+710
+00:57:03,870 --> 00:57:11,110
+على جد جد لو درس رياضيات مفصلة لو درس رياضيات
+
+711
+00:57:11,110 --> 00:57:11,770
+مفصلة
+
+712
+00:57:18,770 --> 00:57:22,910
+إذا كان علي الأولى يدرس ديكريت ماتماتيكس فهو سيحصل
+
+713
+00:57:22,910 --> 00:57:26,910
+على درجة جيدة علي سيحصل على درجة جيدة عندما يدرس
+
+714
+00:57:26,910 --> 00:57:31,150
+ديكريت ماتماتيكس علي سيحصل على درجة جيدة إلا إذا
+
+715
+00:57:31,150 --> 00:57:37,210
+لم يدرس ديكريت ماتماتيكس كل هذه الصياغات السابقة
+
+716
+00:57:37,210 --> 00:57:45,730
+في موضوع ال implication أنا في عندي ال converse
+
+717
+00:57:45,730 --> 00:57:52,450
+العكس تبعتها عكسالـ B implies Q و Q implies B الـ
+
+718
+00:57:52,450 --> 00:58:00,830
+Contrapositive كمصطلح لـ B نط Q نط Q implies نط ال
+
+719
+00:58:00,830 --> 00:58:05,810
+B نط ال B او نط .. عفوا نط Q implies نط ال B ال
+
+720
+00:58:05,810 --> 00:58:10,670
+inverse تبعت ال B implies Q نفيها كلها نط B
+
+721
+00:58:10,670 --> 00:58:16,750
+implies نط Q بالمناسبة ال Contrapositive هذههذه
+
+722
+00:58:16,750 --> 00:58:22,510
+وهذه متكافئات متساويات يعني لو عملنا truth table
+
+723
+00:58:22,510 --> 00:58:29,130
+لتنتين هحصل ان التنتين لهم نفس القيمة اعيدهم ال
+
+724
+00:58:29,130 --> 00:58:38,490
+convers يعني انا بقول B تؤدي الى Q بدي تجلبها Q
+
+725
+00:58:38,490 --> 00:58:44,800
+تؤدي الى B الان ال contrapositiveالعكس الصحيح
+
+726
+00:58:44,800 --> 00:58:50,660
+تبعها، كأنني بدي أقول عكسها الصحيح، وين هو؟ تمام؟
+
+727
+00:58:50,660 --> 00:58:55,300
+بدي تلفها وتنفيها، يعني بين جثين، إذا ما تحققتش
+
+728
+00:58:55,300 --> 00:59:02,960
+الـQ، معناته ما تحققتش الـP، يعني إذا أنت ما جيبتش
+
+729
+00:59:02,960 --> 00:59:10,100
+علامة، معناته أنت مادرستش، مصبوط؟الـ Inverse
+
+730
+00:59:10,100 --> 00:59:14,500
+معكوسها إذا كنت أنا بقول B تقول إلى Q أو تؤدي إلى
+
+731
+00:59:14,500 --> 00:59:24,680
+Q، الـ Inverse تبعتها نطل بي تقول إلى نطل Q، لأ لو
+
+732
+00:59:24,680 --> 00:59:31,490
+طلع على المعادلة بالأحمر، مش نفس المعنىبس اذا انت
+
+733
+00:59:31,490 --> 00:59:35,230
+بتتكلم جاعة هيها المفهوم المعكوس تبعتها هيه ال
+
+734
+00:59:35,230 --> 00:59:38,830
+contrapositive هيها و ال inverse كذلك طيب عشان ما
+
+735
+00:59:38,830 --> 00:59:42,450
+لو كنت نتقل لمحاضرة تانية هنجف لليوم الحين فيه ضال
+
+736
+00:59:42,450 --> 00:59:44,490
+تقريبا كام slide في الشاب في السنة
+
diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/gAlSRgSeIsQ_raw.json b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/gAlSRgSeIsQ_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..bb283d0e02e85bd385c3d268d609b9a82b2d0ce0
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/gAlSRgSeIsQ_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 5004, "start": 21.28, "end": 50.04, "text": "نعوذ بالله السماعي العليم الشطراجي بسم الله الرحمن الرحيم يا رب اشرحلي صدري و أثر أمري و أحنا علاقة هم لساني أفقها قولين أهلا و سهلا يا شباب اليوم ان شاء الله هنبلش بالمادة بشكل عملي أو بشكل فعلي المرة الماضية اتكلمنا على ال syllabus أو وصف المساق و اليوم هنبدأ مع chapter 1 و كنا أخدنا بعض الملاحظات أو بعض الشغلات بشكل بسيط طبعا قولنا المواضيع اللي هنغطيها في ال chapter هذا ال propositional logic, propositional evaluations, predicates and quantifiers, nested quantifiers و rule of inference", "tokens": [1863, 3615, 2407, 8848, 20666, 43761, 21136, 15042, 3615, 1829, 18863, 20292, 2304, 25124, 9566, 2288, 26108, 1829, 4724, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 35186, 12602, 3555, 1975, 46309, 5016, 20292, 20328, 3215, 16572, 4032, 5551, 49115, 5551, 29973, 1829, 4032, 5551, 5016, 8315, 11203, 995, 28671, 8032, 2304, 5296, 3794, 7649, 1829, 5551, 5172, 4587, 11296, 12174, 12610, 9957, 5551, 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{"start": 38.52, "end": 39.62, "word": " بشكل", "probability": 0.9900716145833334}, {"start": 39.62, "end": 40.2, "word": " بسيط", "probability": 0.997314453125}, {"start": 40.2, "end": 40.86, "word": " طبعا", "probability": 0.94091796875}, {"start": 40.86, "end": 41.12, "word": " قولنا", "probability": 0.7040201822916666}, {"start": 41.12, "end": 41.5, "word": " المواضيع", "probability": 0.78857421875}, {"start": 41.5, "end": 41.6, "word": " اللي", "probability": 0.919921875}, {"start": 41.6, "end": 42.16, "word": " هنغطيها", "probability": 0.98974609375}, {"start": 42.16, "end": 42.3, "word": " في", "probability": 0.96923828125}, {"start": 42.3, "end": 42.38, "word": " ال", "probability": 0.689453125}, {"start": 42.38, "end": 42.6, "word": " chapter", "probability": 0.927734375}, {"start": 42.6, "end": 42.98, "word": " هذا", "probability": 0.8388671875}, {"start": 42.98, "end": 43.62, "word": " ال", "probability": 0.36669921875}, {"start": 43.62, "end": 44.16, "word": " 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"probability": 0.88818359375}], "temperature": 1.0}, {"id": 2, "seek": 6554, "start": 51.08, "end": 65.54, "text": "وبدأنا المحاضرة الماضية اندردش وبشكل بسيط على الـ propositional logic وقولنا أهمية ال logic إنها دائما بتديني أو بتحاول توضحلي معاني ال mathematical statements", "tokens": [37746, 3215, 10721, 8315, 9673, 5016, 46958, 25720, 9673, 46958, 10632, 16472, 3215, 2288, 3215, 8592, 46599, 8592, 28820, 4724, 3794, 1829, 9566, 15844, 2423, 39184, 7532, 2628, 9952, 4032, 39648, 8315, 5551, 16095, 10632, 2423, 9952, 36145, 11296, 11778, 16373, 15042, 39894, 3215, 9957, 1829, 34051, 39894, 5016, 995, 12610, 6055, 2407, 11242, 5016, 20292, 20449, 7649, 1829, 2423, 18894, 12363], "avg_logprob": -0.28546626889516435, "compression_ratio": 1.4619883040935673, "no_speech_prob": 0.0, "words": [{"start": 51.08, "end": 51.78, "word": "وبدأنا", "probability": 0.72869873046875}, {"start": 51.78, "end": 52.6, "word": " المحاضرة", "probability": 0.963623046875}, {"start": 52.6, "end": 53.1, "word": " الماضية", "probability": 0.9811197916666666}, {"start": 53.1, "end": 53.7, "word": " اندردش", "probability": 0.793896484375}, {"start": 53.7, "end": 54.08, "word": " وبشكل", "probability": 0.8359375}, {"start": 54.08, "end": 54.6, "word": " بسيط", "probability": 0.9971923828125}, {"start": 54.6, "end": 55.12, "word": " على", "probability": 0.79931640625}, {"start": 55.12, "end": 57.54, "word": " الـ", "probability": 0.4073486328125}, {"start": 57.54, "end": 58.12, "word": " propositional", "probability": 0.664794921875}, {"start": 58.12, "end": 58.5, "word": " logic", "probability": 0.95947265625}, {"start": 58.5, "end": 58.88, "word": " وقولنا", "probability": 0.390869140625}, {"start": 58.88, "end": 59.38, "word": " أهمية", "probability": 0.9265950520833334}, {"start": 59.38, "end": 59.52, "word": " ال", "probability": 0.91357421875}, {"start": 59.52, "end": 59.74, "word": " logic", "probability": 0.54833984375}, {"start": 59.74, "end": 60.1, "word": " إنها", "probability": 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بيجي بقول why ال I أقل من عشرة", "tokens": [3555, 2655, 2407, 11242, 5016, 32767, 3615, 7649, 1829, 2423, 18894, 12363, 16070, 4978, 29538, 3714, 16095, 2655, 11296, 10874, 28259, 27188, 2288, 4587, 49374, 2423, 7363, 4032, 2423, 34702, 4487, 1975, 2407, 2423, 18894, 12869, 37495, 22653, 28242, 8315, 44945, 3615, 28480, 8978, 2423, 26890, 2304, 7435, 3660, 5296, 15042, 1975, 8315, 4724, 1829, 7435, 1829, 4724, 39648, 983, 2423, 286, 5551, 4587, 1211, 9154, 6225, 8592, 25720], "avg_logprob": -0.24017857291868755, "compression_ratio": 1.4948979591836735, "no_speech_prob": 0.0, "words": [{"start": 66.33, "end": 66.77, "word": "بتوضح", "probability": 0.83115234375}, {"start": 66.77, "end": 67.39, "word": " لمعاني", "probability": 0.8843994140625}, {"start": 67.39, "end": 67.69, "word": " ال", "probability": 0.75537109375}, {"start": 67.69, "end": 68.05, "word": " mathematical", "probability": 0.1275634765625}, {"start": 68.05, "end": 69.33, "word": " statements", "probability": 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conditions", "probability": 0.84619140625}, {"start": 75.79, "end": 76.03, "word": " او", "probability": 0.88720703125}, {"start": 76.03, "end": 76.25, "word": " ال", "probability": 0.43017578125}, {"start": 76.25, "end": 76.47, "word": " mathematical", "probability": 0.57958984375}, {"start": 76.47, "end": 77.23, "word": " arguments", "probability": 0.79345703125}, {"start": 77.23, "end": 77.89, "word": " يعني", "probability": 0.83544921875}, {"start": 77.89, "end": 78.45, "word": " كلنا", "probability": 0.7841796875}, {"start": 78.45, "end": 78.79, "word": " بنعرف", "probability": 0.89404296875}, {"start": 78.79, "end": 78.89, "word": " في", "probability": 0.876953125}, {"start": 78.89, "end": 79.37, "word": " البرمجة", "probability": 0.8830078125}, {"start": 79.37, "end": 79.57, "word": " لما", "probability": 0.823974609375}, {"start": 79.57, "end": 79.73, "word": " انا", "probability": 0.749755859375}, {"start": 79.73, "end": 80.01, "word": " بيجي", "probability": 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"probability": 0.9148763020833334}, {"start": 95.97, "end": 96.61, "word": " decision", "probability": 0.90234375}, {"start": 96.61, "end": 97.05, "word": " او", "probability": 0.9248046875}, {"start": 97.05, "end": 97.57, "word": " قرار", "probability": 0.9874674479166666}, {"start": 97.57, "end": 98.23, "word": " هى", "probability": 0.61962890625}, {"start": 98.23, "end": 98.51, "word": " ال", "probability": 0.7109375}, {"start": 98.51, "end": 98.91, "word": " proposition", "probability": 0.77197265625}, {"start": 98.91, "end": 99.41, "word": " هذه", "probability": 0.298583984375}, {"start": 99.41, "end": 99.59, "word": " او", "probability": 0.95654296875}, {"start": 99.59, "end": 99.67, "word": " ال", "probability": 0.9306640625}, {"start": 99.67, "end": 99.85, "word": " rule", "probability": 0.85791015625}, {"start": 99.85, "end": 100.21, "word": " هذه", "probability": 0.52880859375}], "temperature": 1.0}, {"id": 5, "seek": 11814, "start": 100.96, "end": 118.14, "text": "أو ال condition هذا true أو false وبالتالي مهمة ال rules أو ال logical rules أو ال proposition زي ما هنسميها ان نفرق بين ال valid و ال invalid لما نتكلم على valid فنتكلم على شغلة مقبولة invalid شغلة غير مقبولة", "tokens": [10721, 2407, 2423, 4188, 23758, 2074, 34051, 7908, 46599, 6027, 2655, 6027, 1829, 3714, 16095, 3660, 2423, 4474, 34051, 2423, 14978, 4474, 34051, 2423, 24830, 30767, 1829, 19446, 8032, 1863, 38251, 1829, 11296, 16472, 8717, 5172, 2288, 4587, 49374, 2423, 7363, 4032, 2423, 34702, 5296, 15042, 8717, 2655, 4117, 19528, 15844, 7363, 6156, 29399, 4117, 19528, 15844, 13412, 17082, 37977, 3714, 4587, 3555, 12610, 3660, 34702, 13412, 17082, 37977, 32771, 13546, 3714, 4587, 3555, 12610, 3660], "avg_logprob": -0.17055601036393797, "compression_ratio": 1.7206703910614525, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 100.96, "end": 101.26, "word": "أو", "probability": 0.756103515625}, {"start": 101.26, "end": 101.36, "word": " ال", "probability": 0.552734375}, 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rules", "probability": 0.87060546875}, {"start": 107.94, "end": 108.1, "word": " أو", "probability": 0.853515625}, {"start": 108.1, "end": 108.22, "word": " ال", "probability": 0.93798828125}, {"start": 108.22, "end": 108.62, "word": " proposition", "probability": 0.73291015625}, {"start": 108.62, "end": 109.0, "word": " زي", "probability": 0.8671875}, {"start": 109.0, "end": 109.06, "word": " ما", "probability": 0.9609375}, {"start": 109.06, "end": 109.66, "word": " هنسميها", "probability": 0.85283203125}, {"start": 109.66, "end": 110.16, "word": " ان", "probability": 0.4755859375}, {"start": 110.16, "end": 110.62, "word": " نفرق", "probability": 0.926025390625}, {"start": 110.62, "end": 110.82, "word": " بين", "probability": 0.97802734375}, {"start": 110.82, "end": 110.96, "word": " ال", "probability": 0.9169921875}, {"start": 110.96, "end": 111.24, "word": " valid", "probability": 0.98876953125}, {"start": 111.24, "end": 111.46, "word": " و", "probability": 0.73779296875}, {"start": 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عندي لازم تكون true لو انا بدي أنفيها يعني هيك هيك بديني true هذه true صح؟ مش هذي بتقدي ايه او بتديني فوق بتديني true ببنفي هذي ال false متى بيكون", "tokens": [7868, 264, 2208, 2967, 366, 2074, 28242, 9673, 3615, 10943, 1211, 9307, 9673, 29245, 23328, 3660, 34051, 2423, 2208, 2967, 9673, 29245, 23328, 3660, 43242, 1829, 5296, 31377, 2304, 6055, 30544, 2074, 45164, 1975, 8315, 4724, 16254, 14739, 41185, 11296, 37495, 22653, 39896, 4117, 39896, 4117, 4724, 16254, 22653, 2074, 29538, 2074, 20328, 5016, 22807, 37893, 8032, 8848, 1829, 39894, 4587, 16254, 1975, 1829, 3224, 1975, 2407, 39894, 3215, 9957, 1829, 6156, 30543, 39894, 3215, 9957, 1829, 2074, 4724, 3555, 1863, 41185, 8032, 8848, 1829, 2423, 7908, 44650, 7578, 4724, 1829, 30544], "avg_logprob": -0.3015793074843704, "compression_ratio": 1.764102564102564, "no_speech_prob": 0.0, "words": [{"start": 2103.2599999999998, "end": 2104.06, "word": "All", "probability": 0.27978515625}, {"start": 2104.06, "end": 2104.86, "word": " the", 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{"id": 91, "seek": 240861, "start": 2380.39, "end": 2408.61, "text": "عكسها .. نفيها عفواً All the operands are false شوفت كيف؟ عكس واحد على الأقل واحد مافيش على الأقل واحدة، لكلهم تمام؟ ماينفعش أقول اتنين وماينفعش أقول تلاتة وماينفعش أقول most لأنه برضه يُطبّق عليهم على الأقل بظبط؟ لكن نفيها تماماً كلهم", "tokens": [3615, 4117, 3794, 11296, 4386, 8717, 41185, 11296, 6225, 5172, 14407, 14111, 1057, 264, 2208, 2967, 366, 7908, 13412, 38688, 2655, 9122, 33911, 22807, 6225, 4117, 3794, 36764, 24401, 15844, 16247, 4587, 1211, 36764, 24401, 19446, 41185, 8592, 15844, 16247, 4587, 1211, 36764, 24401, 3660, 12399, 5296, 28820, 16095, 46811, 10943, 22807, 19446, 9957, 5172, 3615, 8592, 5551, 39648, 1975, 2655, 1863, 9957, 4032, 15042, 9957, 5172, 3615, 8592, 5551, 39648, 6055, 1211, 9307, 3660, 4032, 15042, 9957, 5172, 3615, 8592, 5551, 39648, 881, 5296, 33456, 3224, 4724, 43042, 3224, 7251, 10859, 9566, 3555, 11703, 4587, 25894, 16095, 15844, 16247, 4587, 1211, 4724, 19913, 3555, 9566, 22807, 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"temperature": 1.0}, {"id": 93, "seek": 245875, "start": 2440.83, "end": 2458.75, "text": "Q and R أو بعد يقول P or Q or R صار فيه يعني ألف متغيرات كيبرا ساوي بدك تشتغل حسب الأولويات اللي هتكلم عليها كمان شوية بس الأصل العملية تنائية", "tokens": [48, 293, 497, 34051, 39182, 7251, 39648, 430, 420, 1249, 420, 497, 20328, 9640, 8978, 3224, 37495, 22653, 5551, 46538, 44650, 17082, 13546, 9307, 9122, 1829, 3555, 23557, 8608, 995, 45865, 47525, 4117, 6055, 8592, 2655, 17082, 1211, 11331, 35457, 16247, 12610, 45865, 9307, 13672, 1829, 8032, 2655, 4117, 19528, 25894, 11296, 9122, 2304, 7649, 13412, 2407, 10632, 4724, 3794, 16247, 36520, 18863, 42213, 10632, 6055, 1863, 16373, 10632], "avg_logprob": -0.29598215307508197, "compression_ratio": 1.4938271604938271, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 2440.83, "end": 2441.13, "word": "Q", "probability": 0.129150390625}, {"start": 2441.13, "end": 2441.97, "word": " and", "probability": 0.5380859375}, {"start": 2441.97, 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P .. 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"text": "إذا كان علي الأولى يدرس ديكريت ماتماتيكس فهو سيحصل على درجة جيدة علي سيحصل على درجة جيدة عندما يدرس ديكريت ماتماتيكس علي سيحصل على درجة جيدة إلا إذا لم يدرس ديكريت ماتماتيكس كل هذه الصياغات السابقة في موضوع ال implication أنا في عندي ال converse العكس تبعتها عكس", "tokens": [28814, 15730, 25961, 25894, 2423, 10721, 12610, 7578, 7251, 3215, 2288, 3794, 11778, 1829, 4117, 16572, 2655, 3714, 9307, 2304, 9307, 1829, 4117, 3794, 6156, 3224, 2407, 8608, 1829, 5016, 36520, 15844, 11778, 47341, 3660, 10874, 25708, 3660, 25894, 8608, 1829, 5016, 36520, 15844, 11778, 47341, 3660, 10874, 25708, 3660, 43242, 15042, 7251, 3215, 2288, 3794, 11778, 1829, 4117, 16572, 2655, 3714, 9307, 2304, 9307, 1829, 4117, 3794, 25894, 8608, 1829, 5016, 36520, 15844, 11778, 47341, 3660, 10874, 25708, 3660, 11933, 15040, 11933, 15730, 32767, 7251, 3215, 2288, 3794, 11778, 1829, 4117, 16572, 2655, 3714, 9307, 2304, 9307, 1829, 4117, 3794, 28242, 29538, 31767, 1829, 5718, 118, 9307, 21136, 16758, 28671, 8978, 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{"start": 3579.21, "end": 3579.47, "word": " نتقل", "probability": 0.7559814453125}, {"start": 3579.47, "end": 3579.93, "word": " لمحاضرة", "probability": 0.9189453125}, {"start": 3579.93, "end": 3580.35, "word": " تانية", "probability": 0.9679361979166666}, {"start": 3580.35, "end": 3581.05, "word": " هنجف", "probability": 0.6461181640625}, {"start": 3581.05, "end": 3581.39, "word": " لليوم", "probability": 0.7754720052083334}, {"start": 3581.39, "end": 3581.75, "word": " الحين", "probability": 0.5616455078125}, {"start": 3581.75, "end": 3582.23, "word": " فيه", "probability": 0.881103515625}, {"start": 3582.23, "end": 3582.45, "word": " ضال", "probability": 0.761474609375}, {"start": 3582.45, "end": 3582.89, "word": " تقريبا", "probability": 0.95205078125}, {"start": 3582.89, "end": 3583.29, "word": " كام", "probability": 0.884765625}, {"start": 3583.29, "end": 3583.65, "word": " slide", "probability": 0.82666015625}, {"start": 3583.65, "end": 3583.83, "word": " في", "probability": 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/jA9RTJkdbkc.srt b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/jA9RTJkdbkc.srt
new file mode 100644
index 0000000000000000000000000000000000000000..d9dbdb6b10a87f5788e75ea449dad53cc231b445
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/jA9RTJkdbkc.srt
@@ -0,0 +1,1969 @@
+1
+00:00:20,970 --> 00:00:22,910
+طيب الشباب، بسم الله والحمد لله والصلاة والسلام على
+
+2
+00:00:22,910 --> 00:00:25,430
+رسول الله، اليوم إن شاء الله هناخد two sections
+
+3
+00:00:25,430 --> 00:00:31,690
+خفاف ضراف، ونختم فيهم الـ chapter تبع الـ integers و
+
+4
+00:00:31,690 --> 00:00:35,430
+الـ primes. في البداية، الـ section الأولى اللي هو
+
+5
+00:00:35,430 --> 00:00:40,410
+أربعة تلاتة، هنتكلم فيه عن الـ primes والـ greatest
+
+6
+00:00:40,410 --> 00:00:43,070
+common divisor والـ least common multiple.
+
+7
+00:00:45,410 --> 00:00:52,450
+قبل ما أتكلم فيه، عندي الأعداد الأولية، يعني الـ section
+
+8
+00:00:52,450 --> 00:00:54,470
+أو الـ chapter بتتكلم عن الأعداد الأولية بشكل عام.
+
+9
+00:00:54,470 --> 00:01:01,350
+الأعداد الأولية هي عبارة عن كل عدد يقبل القسمة على
+
+10
+00:01:01,350 --> 00:01:04,510
+نفسه فقط، لا يقبل القسمة إلا على نفسه والواحد. هو كل
+
+11
+00:01:04,510 --> 00:01:07,270
+الأعداد بتقبل القسمة على نفسها، فخلاص إحنا بنقول
+
+12
+00:01:07,270 --> 00:01:10,410
+العدد الأولي هو عبارة عن كل عدد لا يقبل القسمة إلا
+
+13
+00:01:10,410 --> 00:01:11,490
+على نفسه.
+
+14
+00:01:14,370 --> 00:01:18,330
+مثالات مراجعة لشغلات إحنا المفروض بنعرفها من
+
+15
+00:01:18,330 --> 00:01:22,930
+وإحنا صغار، اللي هي إيش خاصية القسمة؟ إحنا بداية الـ
+
+16
+00:01:22,930 --> 00:01:25,910
+chapter كنا بنتكلم على الأعداد وخاصية القسمة اللي
+
+17
+00:01:25,910 --> 00:01:32,170
+موجودة. أقول لك التالي: لو كان أنا في عندي integer a
+
+18
+00:01:32,170 --> 00:01:41,910
+يقسم الـ b، معناته إن الـ b بتساوي quotient  في الـ a.  كمية مضروبة في الـ a
+
+19
+00:01:41,910 --> 00:01:46,710
+عفواً، في الـ a كمية مضروبة في الـ a.
+
+20
+00:01:46,710 --> 00:01:51,950
+ولو كانت الـ b لا تقبل القسمة على الـ a، معناته أنا
+
+21
+00:01:51,950 --> 00:01:57,690
+بقدر أكتب الـ b على صورة quotient مضروبة في
+
+22
+00:01:57,690 --> 00:02:01,830
+الـ a اللي هي divisor زائد الـ remainder، والـ
+
+23
+00:02:01,830 --> 00:02:06,590
+remainder هذا بيكون محصور ما بين الصفر والـ divisor
+
+24
+00:02:06,590 --> 00:02:11,480
+اللي هي الـ a، والـ divisor اللي هي الـ A. طبعاً هذا
+
+25
+00:02:11,480 --> 00:02:15,720
+الكلام لما الـ B تقبل القسمة على الـ A، أو الـ
+
+26
+00:02:15,720 --> 00:02:19,200
+A تقسم الـ B. هذا الكلام اللي إحنا قلناه المرة
+
+27
+00:02:19,200 --> 00:02:22,900
+الماضية. وبدأنا مع الأعداد الأولية، قلنا إن العدد
+
+28
+00:02:22,900 --> 00:02:26,920
+الأولى هو كل عدد لا يقبل القسمة إلا على نفسه، يعني
+
+29
+00:02:26,920 --> 00:02:31,340
+مالوش أي divisor، بقدرش اكتبه بالصورة هذه. العدد
+
+30
+00:02:31,340 --> 00:02:35,540
+الأولى بقدرش اكتبه بالصورة اللي موجودة عندنا فوق.
+
+31
+00:02:36,780 --> 00:02:42,980
+طيب، لو أنا جيت… أقول لك التالي: إنه عشان أفحص العدد
+
+32
+00:02:42,980 --> 00:02:46,400
+بيقبل قسمة أو لا يقبل قسمة، نراجع مع بعض على السريع.
+
+33
+00:02:46,400 --> 00:02:52,240
+لو أنا كتبت أي رقم، وليكن على سبيل المثال 1735،
+
+34
+00:02:52,240 --> 00:02:58,720
+و الرقم الثاني 2024،
+
+35
+00:02:58,720 --> 00:03:05,020
+201 مثلاً، ودي أسئلة نفسية. الرقم الأول
+
+36
+00:03:05,020 --> 00:03:11,510
+بيقبل القسمة على اتنين؟ لأ. ليش جاوبت لأ؟ لأن خانة الآحاد
+
+37
+00:03:11,510 --> 00:03:18,310
+هي least significant digit، خمسة. لا تقبل القسمة على اتنين لو
+
+38
+00:03:18,310 --> 00:03:23,750
+كان القيمة زوجية، والصفر من ضمن الأعداد الزوجية.
+
+39
+00:03:23,750 --> 00:03:30,270
+تمام. بيقبل القسمة على تلاتة؟ شرط القسمة على تلاتة إنك
+
+40
+00:03:30,270 --> 00:03:35,330
+تجمع الـ digits اللي موجودة، مجموعهم إذا بيقبل
+
+41
+00:03:35,330 --> 00:03:38,730
+القسمة على ثلاثة، معناته أنا بتكلم قسمة على ثلاثة.
+
+42
+00:03:38,730 --> 00:03:43,550
+خمسة وثلاثة ثمانية، سبعة، خمسة عشر، واحد، ثمانية عشر.
+
+43
+00:03:43,550 --> 00:03:48,490
+ستة عشر. ستة عشر على ثلاثة لا يقبل القسمة على ثلاثة، معناته
+
+44
+00:03:48,490 --> 00:03:52,310
+لا يقبل القسمة على ثلاثة. اللي بعده 2024،
+
+45
+00:03:52,310 --> 00:03:57,480
+لا يقبل القسمة على ثلاثة. 201 زي صفر،
+
+46
+00:03:57,480 --> 00:04:01,840
+زي واحد، ثلاثة تقبل القسمة على ثلاثة، معناته الـ 201
+
+47
+00:04:01,840 --> 00:04:06,540
+يقبل القسمة على ثلاثة، تمام؟ هذه الشغلات إحنا نحاول
+
+48
+00:04:06,540 --> 00:04:10,940
+أن نذكرها بشكل سريع. في موضوع القسمة على أربعة، بدي
+
+49
+00:04:10,940 --> 00:04:15,460
+آخد الـ two least significant digits، يعني خانة الآحاد
+
+50
+00:04:15,460 --> 00:04:20,580
+والعشرات مع بعض، اللي بنسميهم هيك. إذا الرقمين هدول
+
+51
+00:04:20,580 --> 00:04:25,820
+مع بعض بيقبلوا القسمة على الأربعة، فالرقم الكلي بيقبل
+
+52
+00:04:25,820 --> 00:04:29,360
+القسمة على… على أربعة. طيب 35 تقبل
+
+53
+00:04:29,360 --> 00:04:32,600
+القسمة على أربعة؟ لأ، طبعاً. هذا بدأ يعتمد على حفظ
+
+54
+00:04:32,600 --> 00:04:37,480
+الجداول، عشان بشكل سريع أقدر آخد القرار. طيب 24
+
+55
+00:04:37,480 --> 00:04:42,480
+بتقبل القسمة على أربعة؟ أيوة.  شوف أنت عارف…
+
+56
+00:04:42,480 --> 00:04:46,840
+الـ 24 تقبل القسمة على أربعة، يعني 24 بدها
+
+57
+00:04:46,840 --> 00:04:53,410
+تساوي quantity مضروبة في الأربعة، زائد الـ
+
+58
+00:04:53,410 --> 00:04:59,190
+remainder. الـ quantity اللي عندك هيقدر قيمتها صفر
+
+59
+00:04:59,190 --> 00:05:05,050
+صفر، والـ remainder اتنين، معناته لا يقبل القسمة على
+
+60
+00:05:05,050 --> 00:05:10,410
+أربعة. أو بمعنى آخر، الاتنين ليست من مضاعفات الأربعة.
+
+61
+00:05:10,410 --> 00:05:16,380
+تمام. الواحد يقبل القسمة على أربعة؟ لأ. اللي بعرف
+
+62
+00:05:16,380 --> 00:05:20,060
+القسمة على خمسة، بقول إن العدد بيقبل القسمة
+
+63
+00:05:20,060 --> 00:05:23,360
+على خمسة لو كانت الآحاد اللي هي least significant
+
+64
+00:05:23,360 --> 00:05:28,120
+digit بيقبل صفر أو خمسة. صفر أو خمسة، يعني 1735،
+
+65
+00:05:28,120 --> 00:05:30,000
+35،  1735.
+
+66
+00:05:30,000 --> 00:05:33,580
+تقبل القسمة على خمسة، والأرقام الثانية لأ. فالموضوع
+
+67
+00:05:33,580 --> 00:05:37,920
+القسمة على ستة: إذا كان الرقم يقبل القسمة على تلاتة، و
+
+68
+00:05:37,920 --> 00:05:43,200
+يقبل القسمة على اتنين، فبيقبل القسمة على 6. في موضوع
+
+69
+00:05:43,200 --> 00:05:49,420
+القسمة على 7، شوية العملية بدها شرح بسيط، لكن الفكرة
+
+70
+00:05:49,420 --> 00:05:52,220
+فيها كالتالي: خلينا نبدأ بالرقم الأسهل اللي هو 201.
+
+71
+00:05:52,220 --> 00:05:56,140
+الفكرة فيها كالتالي: هتاخد الرقم هذا وتقسمه لخانتين،
+
+72
+00:05:56,690 --> 00:06:00,770
+الخانة الأولى فيها الآحاد لحاله، تمام؟ وباقي الرقم
+
+73
+00:06:00,770 --> 00:06:05,770
+لحاله، يعني في الميتين هذه. هنقول عشرين، نخص منها
+
+74
+00:06:05,770 --> 00:06:10,030
+الاثنين مضروبة في الواحد اللي هي خانة الآحاد اللي
+
+75
+00:06:10,030 --> 00:06:17,150
+عندك. عشرين ناقص اتنين ثمانية عشر. لا تقبل القسمة على
+
+76
+00:06:17,150 --> 00:06:20,980
+سبعة، معناته 201 لا تقبل القسمة على سبعة. إذا
+
+77
+00:06:20,980 --> 00:06:23,200
+أنت مش عارف بالجد ولا مش قادر تحكم في موضوع
+
+78
+00:06:23,200 --> 00:06:28,320
+الثمانية عشر، تمام؟ كمان مرة، باخد أقول له: واحد ناقص
+
+79
+00:06:28,320 --> 00:06:39,780
+اتنين في ثمانية، ناقص خمسة عشر، تمام؟ وبالتالي أنت
+
+80
+00:06:39,780 --> 00:06:43,340
+المفروض توصل لهدا في الخطوة السابقة. لا يقبل القسمة على
+
+81
+00:06:43,340 --> 00:06:48,840
+سبعة. العدد اللي بعده 202، عشرين ناقص
+
+82
+00:06:48,840 --> 00:06:55,630
+اتنين في اثنين، ستة عشر. ستة عشر لا تقبل القسمة على سبعة، معناته 202
+
+83
+00:06:55,630 --> 00:07:02,550
+لا يقبل القسمة على سبعة. اللي بعده 1735،
+
+84
+00:07:02,550 --> 00:07:09,230
+-2 × 5، 163.
+
+85
+00:07:09,230 --> 00:07:19,150
+163 و 35، الآن،  بعرفش إيش بدك تقول. كمان مرة، 16 - 2 × 3 =10
+
+86
+00:07:20,980 --> 00:07:26,300
+عشرة ناقص، أو 16 ناقص ستة، عشرة. العشرة لا تقبل القسمة
+
+87
+00:07:26,300 --> 00:07:31,880
+على سبعة، معناته الـ 1735 لا يقبل القسمة على سبعة. مع
+
+88
+00:07:31,880 --> 00:07:36,720
+إنّ للوحدة الأولى بتشوف الـ 35، امتى بيقول تقبل القسمة
+
+89
+00:07:36,720 --> 00:07:41,260
+على سبعة، لكن الرقم هذا لا يقبل القسمة على سبعة، تمام؟
+
+90
+00:07:41,260 --> 00:07:46,800
+يا شباب، مثلاً،
+
+91
+00:07:46,800 --> 00:07:53,800
+لو أنا جيت قلت لك 7742، يقبل القسمة
+
+92
+00:07:53,800 --> 00:07:59,160
+على سبعة ولا لأ؟ مش عارف، بدك تشتغل نفس العملية.
+
+93
+00:07:59,160 --> 00:08:09,960
+774 ناقص اتنين في اثنين، 770.
+
+94
+00:08:09,960 --> 00:08:17,140
+هاش تقبل القسمة ولا لأ؟ مش متأكد. 770 ناقص
+
+95
+00:08:17,140 --> 00:08:25,400
+اتنين في صفر، 770. 770 تقبل القسمة ولا لأ؟ وبالتالي
+
+96
+00:08:25,400 --> 00:08:32,020
+الرقم الكل هذا يقبل القسمة على 7. في موضوع القسمة
+
+97
+00:08:32,020 --> 00:08:37,200
+على 8، بدك تاخد أول three digits اللي هم least
+
+98
+00:08:37,200 --> 00:08:41,760
+significant digits وتجسم قسمة مطولة على 8 عشان
+
+99
+00:08:41,760 --> 00:08:51,680
+تقدر تتكلم في الموضوع. 201 على 8… 20 على 8… أيوة…
+
+100
+00:08:51,680 --> 00:08:59,080
+اثنين… ستة… أربعة… اثنين…
+
+101
+00:08:59,080 --> 00:09:02,920
+ستة… أربعة… اثنين… ستة… أربعة…
+
+102
+00:09:02,920 --> 00:09:05,440
+اثنين… ستة… أربعة… اثنين… ستة… أربعة…
+
+103
+00:09:05,440 --> 00:09:08,740
+اثنين… ستة… أربعة… اثنين… ستة…
+
+104
+00:09:08,740 --> 00:09:09,360
+أربعة… اثنين… ستة… أربعة… اثنين… ستة…
+
+105
+00:09:09,360 --> 00:09:09,780
+ستة… أربعة… اثنين… ستة… أربعة…
+
+106
+00:09:09,780 --> 00:09:16,630
+اثنين… ستة… أربعة… اثنين… ستة… أربعة… اثنين…
+
+107
+00:09:16,630 --> 00:09:17,870
+أربعة… اثنين… أربعة… اثنين… أربعة… اثنين… أربعة…
+
+108
+00:09:17,870 --> 00:09:18,130
+اثنين… أربعة… اثنين… أربعة… اثنين… أربعة… اثنين…
+
+109
+00:09:18,130 --> 00:09:21,650
+أربعة… اثنين… أربعة… اثنين… أربعة… اثنين… أربعة…
+
+110
+00:09:21,650 --> 00:09:24,790
+اثنين…
+
+111
+00:09:24,790 --> 00:09:29,830
+أربعة… اثنين… أربعة… اثنين… أربعة… اثنين… أربعة…
+
+112
+00:09:29,830 --> 00:09:31,650
+اثنين… أربعة… اثنين… أربعة… اثنين… أربعة… اثنين…
+
+113
+00:09:31,650 --> 00:09:33,130
+أربعة… اثنين… أربعة… اثنين… أربعة… اثنين… أربعة…
+
+114
+00:09:33,130 --> 00:09:44,730
+اثنين… أربعة… اثنين… أربعة… اثنين… أربعة…
+
+115
+00:09:45,650 --> 00:09:52,570
+نزلنا الخمسة الأخيرة. خمسة وخمسين… ستة…
+
+116
+00:09:52,570 --> 00:10:00,130
+أو سبعة. ستة وخمسين، ماضبطتش. بقت ستة وتلاتين وأربعين، وجدنا عندها سبعة، فيه remainder، التالي ألف
+
+117
+00:10:00,130 --> 00:10:06,090
+وسبع مية وخمسة وتلاتين. الأكبر قسمة على ثمانية…
+
+118
+00:10:06,090 --> 00:10:08,190
+العدد الأخير 7742 على ثمانية…
+
+120
+00:10:32,840 --> 00:10:38,600
+أربعة وسبعين. سبعين وسبعين وسبعين وسبعين و
+
+121
+00:10:45,070 --> 00:10:49,410
+الأربعة الآن. نزلنا الأربعة، هيها. هنجي الدور الاثنين.
+
+122
+00:10:49,410 --> 00:10:56,650
+62، سبعة الباقي.
+
+123
+00:10:58,490 --> 00:11:01,250
+ستة مع تولي واحد من الأرقام هذه بيقبل القسمة على
+
+124
+00:11:01,250 --> 00:11:06,010
+ثمانية. يعني فعلياً بتحس إن القسمة على ثمانية مزعجة
+
+125
+00:11:06,010 --> 00:11:11,430
+أكثر من القسمة على سبعة، و… لا. طيب، فالقسمة على
+
+126
+00:11:11,430 --> 00:11:16,470
+تسعة: لو كان مجموع الـ digits زي التلاتة بيقبل القسمة
+
+127
+00:11:16,470 --> 00:11:19,970
+على تلاتة أو تسعة، فالعدد كله بيقبل القسمة على تسعة.
+
+128
+00:11:19,970 --> 00:11:24,150
+تمام. وبالتالي، هذه المراجعة مهمة جداً نذكرها، و
+
+129
+00:11:24,150 --> 00:11:27,480
+نحفظها عشان إيه؟ لك ولأولادك ولحبايبك إن شاء الله.
+
+130
+00:11:27,480 --> 00:11:36,360
+تعال لاحقاً لما تعلمهم حساب، تعرف تعلمهم حساب قبل
+
+131
+00:11:36,360 --> 00:11:39,420
+ما تكون أستاذ شاطر. بيبقى دورك كويس، دورك دور أمهم.
+
+132
+00:11:39,420 --> 00:11:44,960
+إن شاء الله مستقبلاً. طيب، الآن: كل العدد الأولي هو
+
+133
+00:11:44,960 --> 00:11:50,440
+عبارة عن كل عدد لا يقبل القسمة إلا على نفسه. لا يقبل
+
+134
+00:11:50,440 --> 00:11:54,880
+القسمة إلا على نفسه، والعدد اللي له divisors نسميه
+
+135
+00:11:54,880 --> 00:11:59,340
+composite، عكس prime. composite. الآن، لو أنا جيت
+
+136
+00:11:59,340 --> 00:12:07,860
+قلت 17، يا شباب، عدد أولي؟ أيوة. بتقدر بكل بساطة تفحص
+
+137
+00:12:07,860 --> 00:12:10,320
+كل الأعداد اللي قبله. بتبتدي القسمة الأول على واحد
+
+138
+00:12:10,320 --> 00:12:15,340
+منهم، فهو عدد أولي. لكن كل ما بيكبر العدد بتصير عملية
+
+139
+00:12:15,340 --> 00:12:19,660
+القسمة إيش؟ تصعب. يعني مثلاً، لو سألك 101 الآن، هل هي
+
+140
+00:12:19,660 --> 00:12:24,880
+عدد أولي؟ أيوة. بدك تبدأ تفكر فيها بنفس المنطقة. آه في
+
+141
+00:12:24,880 --> 00:12:30,540
+عندي نظرية بسيطة جداً بتقول: العدد المركب، العدد
+
+142
+00:12:30,540 --> 00:12:38,100
+المركب لازم تلاقيله divisor أقل من جذره، تمام؟ العدد
+
+143
+00:12:38,100 --> 00:12:43,120
+المركب بتلاقي له جذر أو بتلاقي له divisor أقل من
+
+144
+00:12:43,120 --> 00:12:47,420
+جذره. إيش يعني؟ بدك تاخد الـ 101، وتاخد الـ 17، و
+
+145
+00:12:47,420 --> 00:12:54,160
+تحطهم تحت الجذر. جذر الـ 17 تقريباً كده يا شباب؟
+
+146
+00:12:54,160 --> 00:13:04,610
+تقريباً 4. سيبنا خلاص 4. وجذر 101 تقريباً 10. الآن خذ
+
+147
+00:13:04,610 --> 00:13:10,610
+الـ 17 هذه وقسمها من واحد للـ أربعة، وقسم الـ 101 على الأرقام من
+
+148
+00:13:10,610 --> 00:13:15,150
+اثنين لحد العشرة. إذا ما وجدتش
+
+149
+00:13:15,150 --> 00:13:20,510
+ولا divisor له، هذا العدد عبارة عن عدد أولي.
+
+150
+00:13:20,510 --> 00:13:24,950
+الـ 17 لا يقبل القسمة على اتنين، ولا يقبل القسمة على
+
+151
+00:13:24,950 --> 00:13:30,330
+ثلاثة، ولا يقبل القسمة على أربعة، فهو prime. 101 لا يقبل
+
+152
+00:13:30,330 --> 00:13:35,570
+القسمة على 2، لا يقبل القسمة على 3، لا يقبل القسمة على 4، ولا
+
+153
+00:13:35,570 --> 00:13:40,730
+يقبل القسمة على 5، ولا 6، ومش بس هيك كمان هتلاقيه له
+
+154
+00:13:40,730 --> 00:13:44,590
+prime divisor. وبالتالي، ممكن تتكلم بس عن الـ primes
+
+155
+00:13:44,590 --> 00:13:49,070
+اللي هي… اللي موجودة في أقل من… أقل من الجذر.
+
+156
+00:13:49,070 --> 00:13:52,620
+يعني في 101، مش بالضرورة أن تفحص كل العشرة أرقام من
+
+157
+00:13:52,620 --> 00:13:55,940
+الاثنين للعشرة. لأ، خذ بس الـ prime numbers اللي هم
+
+158
+00:13:55,940 --> 00:14:00,480
+بنقول: اثنين، وثلاثة، وخمسة، وسبعة. اثنين، وثلاثة، وخمسة، وسبعة. الآن، 101 لا يقبل القسمة على اثنين، لا يقبل
+
+159
+00:14:00,480 --> 00:14:04,480
+القسمة على ثلاثة، لا يقبل خمسة، ولا يقبل القسمة على سبعة.
+
+160
+00:14:04,480 --> 00:14:09,040
+فالعدد 101 prime. لكن تعال نشوف لو اجيت
+
+161
+00:14:09,040 --> 00:14:13,100
+قلت 105 على سبيل المثال.
+
+162
+00:14:13,100 --> 00:14:15,560
+تمام؟ واضحة زي الشمس. أنت هتقول بيقبل القسمة… هذا
+
+163
+00:14:20,290 --> 00:14:23,630
+تمام؟ واضحة زي الشمس. أنت هتقول بيقبل القسمة… هذا
+
+164
+00:14:23,630 --> 00:14:26,230
+composite. بيقبل القسمة على خمسة، وبيقبل القسمة على
+
+165
+00:14:26,230 --> 00:14:30,210
+ثلاثة كمان، لأن مجموع
+
+223
+00:19:16,230 --> 00:19:19,490
+التلاتة والتلاتة تعالى نشوف عددين ثانيات لو على
+
+224
+00:19:19,490 --> 00:19:26,830
+سبيل المثال قولنا الـ 18 و 27 و بدّي ال greatest
+
+225
+00:19:26,830 --> 00:19:34,970
+common divisor بينهم الأن بدي أحللهم 18 بيتساوة 2
+
+226
+00:19:34,970 --> 00:19:43,430
+في 9 اللي هي 3 في 3 بصبت؟ طيب و 27 بدي أحللها هي 3
+
+227
+00:19:43,430 --> 00:19:48,020
+في 9، والتسعة كومبوزيت معناته تلاتة في تلاتة مين
+
+228
+00:19:48,020 --> 00:19:52,680
+القطاعة صار يا شباب تلاتة
+
+229
+00:19:52,680 --> 00:19:57,400
+في تلاتة، القاطعة أيوة تسعة، الآن بقولش أنه ميكبلوش
+
+230
+00:19:57,400 --> 00:20:00,320
+الجسم على تلاتة، لأ دي أكبر الجسم على تلاتة بس
+
+231
+00:20:00,320 --> 00:20:05,820
+القاسم المشترك الأكبر يعني أكبر عدد العددين هدولة
+
+232
+00:20:05,820 --> 00:20:09,460
+اللي جسم عليه اللي هو مين؟ التسعة، التسعة
+
+233
+00:20:09,460 --> 00:20:15,910
+و27 على تسعة مظبوط، و 18 على 9 برضه مظبوط لأن 9
+
+234
+00:20:15,910 --> 00:20:19,950
+divisor لـ 18، و 9 divisor لـ .. لكن ماقدرش أجي أقول
+
+235
+00:20:19,950 --> 00:20:26,510
+6 divisor لـ 27، ماقدرش أقول 10 divisor أو 12، أنتَ
+
+236
+00:20:26,510 --> 00:20:30,730
+دايماً حلل رقم لـ composite .. composite حلله
+
+237
+00:20:30,730 --> 00:20:34,470
+لمجموعة ضرب الأعداد الأولية، وخُذ تقاطعه اللي بينهم
+
+238
+00:20:34,470 --> 00:20:39,190
+واحد دي مقياس رقمين يا شباب، عشان نجرب على أرقام
+
+239
+00:20:39,190 --> 00:20:39,550
+تانية
+
+240
+00:20:43,090 --> 00:20:53,830
+جدّاش؟ تلاتعشَر وأربع وعشرين .. واحد .. ليش؟ اسميه
+
+241
+00:20:53,830 --> 00:20:57,810
+greatest common divisor بين التلاتعشَر والأربع
+
+242
+00:20:57,810 --> 00:21:03,530
+وعشرين .. التلاتعشَر عبارة عن تلاتعشَر، والأربع وعشرين
+
+243
+00:21:03,530 --> 00:21:09,510
+هي عبارة عن اتنين في اتناشَر، بصبت؟ والاتناشَر هي
+
+244
+00:21:09,510 --> 00:21:14,390
+عبارة عن اتنين في ستة، والستة هي عبارة عن اتنين في
+
+245
+00:21:14,390 --> 00:21:20,850
+تلاتة، في تقاطع بينهم؟ لما لو كتبت لك أنا واحد هنا،
+
+246
+00:21:20,850 --> 00:21:24,730
+لأ فيه يا صاحبي، فيه الواحد هذا اللي هو المحايد
+
+247
+00:21:24,730 --> 00:21:28,030
+الضربي موجود في المعادلة التانية، فالتقاطع بينهم
+
+248
+00:21:28,030 --> 00:21:33,820
+واحد، الـ greatest common divisor واحد، اختار عددين
+
+249
+00:21:33,820 --> 00:21:41,060
+two composite numbers ستة و ثمانِية عشر، ال greatest
+
+250
+00:21:41,060 --> 00:21:49,660
+common divisor ستة، صحيح
+
+251
+00:21:49,660 --> 00:21:54,020
+ال greatest common divisor بين الستة والثمانِية عشر
+
+252
+00:21:54,020 --> 00:21:58,760
+الستة تساوي اتنين في تلاتة، الثمانِية عشر
+
+253
+00:22:01,120 --> 00:22:06,040
+تساوي اتنين في تسعة اللي هي تلاتة في تلاتة، وين
+
+254
+00:22:06,040 --> 00:22:09,260
+التقاطع بينهم معناته اللي greatest common
+
+255
+00:22:09,260 --> 00:22:16,100
+divisor بين الستة والثمانِية عشر ستة، ستة و عشرين
+
+256
+00:22:16,100 --> 00:22:25,000
+ستة و عشرين
+
+257
+00:22:25,000 --> 00:22:30,720
+أيوه، اتنين في ثمانية، اتنين في أربعة، اتنين في اتنين
+
+258
+00:22:30,720 --> 00:22:33,340
+والاتنين واتنين واتنين والاتنين والاتنين
+
+259
+00:22:33,340 --> 00:22:38,820
+والاتنين والاتنين والاتنين والاتنين والاتنين
+
+260
+00:22:38,820 --> 00:22:42,280
+والاتنين والاتنين والاتنين والاتنين والاتنين
+
+261
+00:22:42,280 --> 00:22:42,440
+والاتنين والاتنين والاتنين والاتنين والاتنين
+
+262
+00:22:42,440 --> 00:22:42,480
+والاتنين والاتنين والاتنين والاتنين والاتنين
+
+263
+00:22:42,480 --> 00:22:42,620
+والاتنين والاتنين والاتنين والاتنين والاتنين
+
+264
+00:22:42,620 --> 00:22:42,780
+والاتنين والاتنين والاتنين والاتنين والاتنين
+
+265
+00:22:42,780 --> 00:22:42,800
+والاتنين والاتنين والاتنين والاتنين والاتنين
+
+266
+00:22:42,800 --> 00:22:54,540
+والاتنين والـ
+
+267
+00:22:56,980 --> 00:23:03,540
+نفس الفكرة، و ليش هيفرج معك تحللهم ل جسم اتنين، لاحظوا
+
+268
+00:23:03,540 --> 00:23:08,560
+أنه ممكن أنتَ عشان تختصر تكتب قصص، ما فيش لديك مشكلة
+
+269
+00:23:08,560 --> 00:23:13,140
+في الموضوع، لكن كل ما فرضتها بيكون أسهل لك، إيش عشان
+
+270
+00:23:13,140 --> 00:23:17,280
+تضمن العناصر اللي موجودة عندك، الآن هادِ التقاطع
+
+271
+00:23:17,280 --> 00:23:23,240
+وين موجودة يا شباب؟ هاي التقاطع تلاتة
+
+272
+00:23:23,240 --> 00:23:27,930
+واحدة و سبعة و سبعة، معناته اتنين و اتنين ضرب تلاتة
+
+273
+00:23:27,930 --> 00:23:31,850
+ضرب سبعة هو اللي جالِ greatest common divisor لِ 24 و
+
+274
+00:23:31,850 --> 00:23:36,950
+عشرين في سبعة، تمام؟
+
+275
+00:23:36,950 --> 00:23:41,990
+الآن لو كان في عندي رقمين زي ما قلت أنتَ قبل شوية
+
+276
+00:23:41,990 --> 00:23:49,350
+تلاتعشَر وأربع وعشرين، تلاتعشَر وأربع وعشرين، 1 prime
+
+277
+00:23:49,350 --> 00:23:53,890
+أو 1، لا، أو بين جثتين أي عددين غير أوليين، طبعاً الـ a
+
+278
+00:23:53,890 --> 00:23:56,110
+لو قلت لك الـ greatest common divisor بين أي two
+
+279
+00:23:56,110 --> 00:24:01,110
+primes واحد، الـ greatest common divisor بين أي
+
+280
+00:24:01,110 --> 00:24:06,710
+prime أو أي composite برضه واحد، مضبوط إلا لو كان
+
+281
+00:24:06,710 --> 00:24:12,350
+قلت لك الـ greatest common divisor ما بين التلاتة
+
+282
+00:24:12,350 --> 00:24:13,770
+و 33
+
+283
+00:24:17,940 --> 00:24:22,100
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+284
+00:24:22,100 --> 00:24:23,240
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+285
+00:24:23,240 --> 00:24:26,700
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+286
+00:24:26,700 --> 00:24:28,400
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+287
+00:24:28,400 --> 00:24:31,660
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+288
+00:24:31,660 --> 00:24:33,140
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+289
+00:24:33,140 --> 00:24:36,220
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+290
+00:24:38,570 --> 00:24:43,050
+بتتمتع بشكل كويس وما تستعجلش، two primes مع بعض، الـ
+
+291
+00:24:43,050 --> 00:24:46,050
+greatest common divisor بينهم واحد، مش هتلاقي تعمل
+
+292
+00:24:46,050 --> 00:24:50,070
+اشتراك لغير القسم، اشتراك لغير الواحد، لأن هناك بعض
+
+293
+00:24:50,070 --> 00:24:54,190
+الأعداد علاقتهم مع بعضهم زي الـ prime مع بعضهم
+
+294
+00:24:54,190 --> 00:24:57,850
+relatively prime بنسميهم، يعني لو احنا أخدنا الـ 15
+
+295
+00:24:57,850 --> 00:25:03,570
+composite صح؟ وأخدنا الـ 18، أو بلاش الـ 16
+
+296
+00:25:03,570 --> 00:25:07,930
+composite، الـ greatest common divisor بينهم جدّ إيش؟
+
+297
+00:25:09,420 --> 00:25:13,940
+الـ 16 و 15، الـ greatest common divisor بينهم واحد
+
+298
+00:25:13,940 --> 00:25:18,940
+تعالى أورجيك الـ greatest .. الـ greatest common
+
+299
+00:25:18,940 --> 00:25:24,140
+divisor ما بين الخمستاشر والستاشر عشان الكلام اللي
+
+300
+00:25:24,140 --> 00:25:30,320
+قبل ما قلته، خمستاشر بتساوي تلاتة في خمسة، وستاشر
+
+301
+00:25:30,320 --> 00:25:38,140
+اتنين في اتنين في اتنين في اتنين، الآن التقاطع بين
+
+302
+00:25:38,140 --> 00:25:42,940
+الأمير موجود في الواحد، وبالتالي greatest common
+
+303
+00:25:42,940 --> 00:25:47,040
+divisor بينهم واحد، بيقول عن الخمستاشر والستاشر
+
+304
+00:25:47,040 --> 00:25:54,420
+relatively primes، علاقتهم مع بعض زي علاقة الـ two
+
+305
+00:25:54,420 --> 00:25:58,500
+primes
+
+306
+00:25:58,500 --> 00:26:01,460
+مع بعض، الـ greatest common divisor يساوي واحد
+
+307
+00:26:05,750 --> 00:26:14,110
+لو أتينا على سبيل المثال، بقولنا الخمستاشرة وستاشرة
+
+308
+00:26:14,110 --> 00:26:21,050
+و .. و عشرين .. و عشرين .. في عندك الأربع، لأ ستة و
+
+309
+00:26:21,050 --> 00:26:27,590
+عشرين فيه حتكون اتنين، لأ مش هتظبط، عشرة، سبعة عشر، واحد
+
+310
+00:26:27,590 --> 00:26:32,150
+و عشرين، آه لازم يكون في هذا الـ number prime لأنه
+
+311
+00:26:32,150 --> 00:26:33,570
+كان في عندي تلت أعداد زي هذه
+
+312
+00:26:37,310 --> 00:26:42,150
+تمام؟ إيش بنقول احنا عنهم؟ Relatively Primes، الآن
+
+313
+00:26:42,150 --> 00:26:45,970
+عشرة و سبعة عشر، عشرة و واحد و عشرين و سبعة عشر و واحد
+
+314
+00:26:45,970 --> 00:26:50,890
+و عشرين، تنساش أنه هادِ عدد أولي، الآن هدول واحد
+
+315
+00:26:50,890 --> 00:26:53,890
+أولي، واحد فردي وواحد زوجي، طبيعي الفرق بينهم أو الـ
+
+316
+00:26:53,890 --> 00:26:57,310
+greatest common divisor هيكون واحد، واحد و عشرين و
+
+317
+00:26:57,310 --> 00:27:01,530
+سبعة عشر، واحد و عشرين وعشرة، نفس الكلام، الآن لو أنا
+
+318
+00:27:01,530 --> 00:27:07,000
+جيت مثلاً هدول مع بعض، ما أقدرش أقرنهم كلهم مع بعضهم
+
+319
+00:27:07,000 --> 00:27:11,180
+فإيش بروح باخدهم؟ اتنين اتنين، فبقول عنهم pairwise
+
+320
+00:27:11,180 --> 00:27:15,940
+يعني لما أخدتهم كل اتنين مع بعض، علاقتهم relatively
+
+321
+00:27:15,940 --> 00:27:18,920
+primes، لكن تعشوا في عشرة سبعة عشر اتنين وعشرين
+
+322
+00:27:18,920 --> 00:27:23,620
+ما أقدرش أقول عنهم pairwise relatively prime، يعني
+
+323
+00:27:23,620 --> 00:27:28,860
+pair يعني اتنين، 10 و 17 relatively prime، 17 و 22
+
+324
+00:27:28,860 --> 00:27:33,100
+relatively prime، لكن 10 و 22 لأ، الـ greatest common
+
+325
+00:27:33,100 --> 00:27:36,660
+divisor اتنين، فما أقدرش أقول عليهم relatively primes
+
+326
+00:27:36,660 --> 00:27:39,440
+مش كتير مهمة المعلومة هذه، لكن في الآخر لو قلت
+
+327
+00:27:39,440 --> 00:27:42,820
+بتكلم على مجموعة أعداد، طيب بدنا ننتقل في موضوع
+
+328
+00:27:42,820 --> 00:27:48,640
+التحليل نفسه للـ least common multiple، لما بتكلم
+
+329
+00:27:48,640 --> 00:27:55,250
+على الـ least common multiple، بتكلم أنا على أصغر عدد
+
+330
+00:27:55,250 --> 00:28:01,230
+.. أصغر عدد يقبل القسمة على الرقمين المقيادين إليك
+
+331
+00:28:01,230 --> 00:28:04,450
+عكس تماماً .. كنت بس أرجع بشوي على الـ greatest ..
+
+332
+00:28:04,450 --> 00:28:09,250
+common divisor، أكبر قاسم مشترك .. اللي أنا
+
+333
+00:28:09,250 --> 00:28:13,830
+جاءت بدور على أقل مضاعف مشترك، الـ least common
+
+334
+00:28:13,830 --> 00:28:17,370
+multiple، نرجع للأمثلة .. إيش أول مثال كتبناه احنا؟
+
+335
+00:28:18,180 --> 00:28:21,260
+الـ greatest common divisor، ولا حد بكتب ورايا مش
+
+336
+00:28:21,260 --> 00:28:24,440
+مشكلة، بنشوف الأمثلة اللي موجودة عندنا، ثمانِية عشر و
+
+337
+00:28:24,440 --> 00:28:29,900
+قداش؟ ثمانِية عشر وخمستاشر؟ لكن الـ greatest أو الـ
+
+338
+00:28:29,900 --> 00:28:36,780
+least common multiple بين الخمستاشر والثمانِية عشر الآن
+
+339
+00:28:36,780 --> 00:28:42,980
+بدك تحللهم لـ numbers بنفس الفكرة، خمستاشر بدها
+
+340
+00:28:42,980 --> 00:28:47,240
+تساوي تلاتة في خمسة، ثمانِية عشر
+
+341
+00:28:50,190 --> 00:28:58,130
+اتنين في تسعة، تلاتة في تلاتة، الـ least common
+
+342
+00:28:58,130 --> 00:29:02,250
+multiple يساوي الاتحاد ما بين المجموعتين هدول
+
+343
+00:29:02,250 --> 00:29:10,070
+اتحاد المجموعتين، إيش اتحادهم؟ اتنين في تلاتة في
+
+344
+00:29:10,070 --> 00:29:17,450
+تلاتة في خمسة، يعني الآن بدك تروح .. بدك تروح تلغي
+
+345
+00:29:17,450 --> 00:29:21,390
+التقابل ما بين التنتين، وتحتفظ بالباقية تضربهم كله
+
+346
+00:29:21,390 --> 00:29:25,430
+في بعض، هادِ وهادِ بتقابلوا في إيش؟ في تلاتة، فبدك تلغي
+
+347
+00:29:25,430 --> 00:29:29,630
+واحدة من التلاتات هدول، خلاص واحدة، فبتصير عندك
+
+348
+00:29:29,630 --> 00:29:35,090
+اتنين في تلاتة في تلاتة في خمسة، لأن الصفر عندك
+
+349
+00:29:35,090 --> 00:29:40,710
+تلاتين، حذفتي إيش؟ في الاتحاد أنتَ بتحذف التنتين ولا
+
+350
+00:29:40,710 --> 00:29:45,830
+بتحذف واحدة؟ خلاص إن ده هي التلاتة من هذه الأصل في
+
+351
+00:29:45,830 --> 00:29:49,710
+الاتحاد، إن أنا بجمع كل العناصر صح؟ والعناصر المكررة
+
+352
+00:29:49,710 --> 00:29:53,990
+أنا ما بديش إياها، بستغني عنصر واحدة منه، ف أنا اجيت
+
+353
+00:29:53,990 --> 00:29:59,650
+التلاتة هذه المكررة، آه مكررة، لغيت صورة ثانية، آخذ
+
+354
+00:29:59,650 --> 00:30:04,450
+كتابي، يعني أنا أجيت كتابة، أنا كتبت يساوي تلاتة ضرب
+
+355
+00:30:04,450 --> 00:30:09,700
+خمسة، بارد التلاتة الموجودة سابقاً أو لا، بارد التلاتة
+
+356
+00:30:09,700 --> 00:30:13,000
+الموجودة سابقاً، أو موجودة، ما بديش إياها، فإني لغاية
+
+357
+00:30:13,000 --> 00:30:16,940
+أجبّال هذه، بل في عندي مية في الآخر، بارد تلاتة ف أنا
+
+358
+00:30:16,940 --> 00:30:21,280
+روحت كنت مرتبهم مباشرة، اتنين في تلاتة في تلاتة في
+
+359
+00:30:21,280 --> 00:30:28,500
+خمسة، الآن أصغر عدد يقبل القسمة على التنين مع بعض هو
+
+360
+00:30:28,500 --> 00:30:36,840
+عبارة عن العدد هذا، تسعون، في خمسة وتسعين، أصغر عدد
+
+361
+00:30:36,840 --> 00:30:41,380
+يقبل القسمة على الخمستاشر ويقبل القسمة على الثمانِية عشر
+
+362
+00:30:41,380 --> 00:30:48,520
+هو عبارة عن تسعين، طيب
+
+363
+00:30:48,520 --> 00:30:53,740
+ناخذ كمان مثال، ناخذ
+
+364
+00:30:53,740 --> 00:31:01,060
+الستاشر وسبعة، أو بلاش ستاشر وأربع وعشرين، ستاشر أربع
+
+365
+00:31:01,060 --> 00:31:08,610
+وعشرين، اللي بدي الـ least common multiple لـ 16 و 24
+
+366
+00:31:08,610 --> 00:31:15,590
+16، 2x2x2x2
+
+367
+00:31:15,590 --> 00:31:27,110
+بصبوط، 24 إيش تساوي؟ 2x12، 2x2x2x3
+
+368
+00:31:27,110 --> 00:31:31,010
+2x2x2x3
+
+369
+00:31:31,300 --> 00:31:34,920
+في تلاتة، يمكن تكون الأساس هنا في الاتحاد أسهل لك
+
+370
+00:31:34,920 --> 00:31:42,740
+لأن عندي هان اتنين أقصى أربعة، أربعة، أربعة، هان
+
+371
+00:31:42,740 --> 00:31:51,060
+اتنين، أقصى تلاتة، ضرب تلاتة، تمام، اتحادهم
+
+372
+00:32:00,440 --> 00:32:07,060
+16 في 3، ليش؟ ليش؟ لأن هذه اتنين أس ثلاثة، هي عبارة
+
+373
+00:32:07,060 --> 00:32:11,380
+اتنين أس أربعة، تساوي اتنين أس ثلاثة ضرب اتنين
+
+374
+00:32:11,380 --> 00:32:17,820
+وهذه اتنين أس ثلاثة ضرب،  أنا غلطت غير أنا؟ آه
+
+375
+00:32:17,820 --> 00:32:22,300
+غلطت، تفهم؟ الآن، الحاجة تساوي، لا ما غلطتش
+
+376
+00:32:26,680 --> 00:32:29,680
+تنقص أربعة، المفروض آه تنقص أربعة، صح، الآن تساوي
+
+377
+00:32:29,680 --> 00:32:35,040
+الآن حطّ واحدة من الاتنين، اتنين هدول بس بتصير
+
+378
+00:32:35,040 --> 00:32:39,660
+تلاتة، اتنين أس تلاتة ضرب اتنين ضرب تلاتة، ليه اتنين
+
+379
+00:32:39,660 --> 00:32:46,780
+أقصى أربعة ضرب تلاتة، ستة وأربعين وتلاتة، تمام يا شباب، هاي
+
+380
+00:32:46,780 --> 00:32:52,440
+بالمثال اللي إحنا شفناه سابقاً، كيف؟
+
+381
+00:32:54,310 --> 00:32:58,410
+آه طبيعي، لازم .. مو أنتَ بتدور على عدد بدّه يقبل
+
+382
+00:32:58,410 --> 00:33:02,290
+القسمة على التنين هدول، فلازم يكون أكبر منهم، فلازم
+
+383
+00:33:02,290 --> 00:33:07,530
+يكون أكبر منهم أو يساوي على الأقل أكبر واحد فيهم
+
+384
+00:33:07,530 --> 00:33:11,370
+يعني لو أنا دي قلت لك بدي الـ least common multiple
+
+385
+00:33:11,370 --> 00:33:17,790
+ما بين الستة والثمانِية عشر، ستة وثمانِية عشر، إيش حتقول إيه؟
+
+386
+00:33:17,790 --> 00:33:24,340
+الستة تساوي اتنين في تلاتة، ثمانِية عشر اتنين في تلاتة في
+
+387
+00:33:24,340 --> 00:33:30,880
+تلاتة، اعمل اتحاد بينهم، تلاتة
+
+388
+00:33:30,880 --> 00:33:37,640
+في تلاتة في تلاتة، اعمل اتحاد بينهم، تلاتة في تلاتة
+
+389
+00:33:37
+
+445
+00:37:51,000 --> 00:37:53,960
+تمام اللي كان بده إياها فعرف أنه في خاين في الموضوع
+
+446
+00:37:53,960 --> 00:38:00,320
+فقرر أنه يعتمد يكتب الرسالة بشكل مخفي، تشفير إيش
+
+447
+00:38:00,320 --> 00:38:05,780
+يعني تشفير كريبتوجرافي، أنه يكتب نص، المعنى ماحدش
+
+448
+00:38:05,780 --> 00:38:09,540
+يعرفه غير المرسل والمستقبل.. جملة اتفاقية عشان
+
+449
+00:38:09,540 --> 00:38:15,560
+يعرف يرجع الناس لأصلها، فكرة الفكرة أنه يعتمد على
+
+450
+00:38:15,560 --> 00:38:18,940
+باقي القسمة.. باقي القسمة يا شباب.. كم character
+
+451
+00:38:18,940 --> 00:38:23,800
+عندي بالأجهزة الإنجليزية أنا؟ 26.. 26 character
+
+452
+00:38:23,800 --> 00:38:29,720
+تمام؟ الآن باخد الـ character لـ plain text وبضيف له
+
+453
+00:38:29,720 --> 00:38:33,440
+الـ key، الـ key هي عبارة عن مقدار الـ shift اللي بده
+
+454
+00:38:33,440 --> 00:38:39,860
+يصير على الدائرة اللي موجودة عندها، يعني الآن لو
+
+455
+00:38:39,860 --> 00:38:43,180
+أنا بدي ألغي الصورة بس هذه هيك شوية وأروح أعمل
+
+456
+00:38:43,180 --> 00:38:51,310
+rotate لهذه، لأ، بديش لهذه كلها ل.. برضه لم أكلمها
+
+457
+00:38:51,310 --> 00:39:02,750
+مرة لأ، بتلف لحالها، أيوة باللي
+
+458
+00:39:02,750 --> 00:39:07,610
+أنا عملته، أنا باللفة هذه عملت شغلة بسيطة جدا، قلت
+
+459
+00:39:07,610 --> 00:39:11,930
+كل character بدي أستبدله، أو الـ key، مقدار الـ key
+
+460
+00:39:11,930 --> 00:39:17,410
+تبعتي اثنين، كل الـ key تبعتي اثنين، يعني تخيل أن أنا
+
+461
+00:39:17,410 --> 00:39:26,220
+صرت بدي أدور على كلمة War Book، كتاب الحرب مثلاً، إيش
+
+462
+00:39:26,220 --> 00:39:31,060
+الفكرة، لاحظ أن حسب اللي أنا سويته هنا أن كل حرف
+
+463
+00:39:31,060 --> 00:39:37,440
+بيقدم خطوتين، يعني الـ a بدي أعمل له replacement بالـ c، و
+
+464
+00:39:37,440 --> 00:39:41,340
+هكذا، يعني مقدار الـ key تبعتي اثنين، تعالوا نشوف
+
+465
+00:39:41,340 --> 00:39:45,310
+في جدوة، آخر لو هذا بيحمل معادلة الحروف، يعني الـ key
+
+466
+00:39:45,310 --> 00:39:51,530
+صارت قيمتها اثنين، الـ W إيش صارت؟ إيش صارت؟ ثلاثة و
+
+467
+00:39:51,530 --> 00:39:57,490
+عشرين، هاي الـ W زاد اثنين، خمسة وعشرين، مضبوط؟ خمسة
+
+468
+00:39:57,490 --> 00:40:00,010
+وعشرين، اه، okay، مش هتظبط بس خليني أغير الـ key كمان
+
+469
+00:40:00,010 --> 00:40:03,570
+شوية عشان أوريك إيش فائدة باقي القسمة، بس بدي أزيد
+
+470
+00:40:03,570 --> 00:40:08,020
+الـ key بدل الاثنين تصير خمسة، تمام؟ ثلاثة وعشرين
+
+471
+00:40:08,020 --> 00:40:14,240
+زائد خمسة، ثمانية وعشرين، ثمانية وعشرين، مض.. مض
+
+472
+00:40:14,240 --> 00:40:21,180
+الـ 26، مش هتطلع، اثنين، مش هتديني بي
+
+473
+00:40:21,180 --> 00:40:34,100
+تمام؟ الـ a، الـ a واحد، زائد خمسة، ستة، اف، الآن
+
+474
+00:40:35,580 --> 00:40:44,160
+الـ R ثمانية، زائد خمسة، ثلاثة وعشرين، الـ
+
+475
+00:40:44,160 --> 00:40:54,080
+B اثنين، زائد خمسة، سبعة، الـ O خمسة عشر
+
+476
+00:40:54,080 --> 00:41:06,810
+وخمسة، عشرين، الـ K أحد عشر، زائد خمسة، ستة عشر، كتبت
+
+477
+00:41:06,810 --> 00:41:13,790
+الرسالة بالشكل اللي موجود عندي هنا، فالآن لما شاف
+
+478
+00:41:13,790 --> 00:41:19,330
+الـ.. الـ.. الـ intruder اللي في الطريق هذا، طلع في
+
+479
+00:41:19,330 --> 00:41:24,230
+الرسالة، قال أن هذا ليه الملك، مكتوبة بلغة لكن اللغة
+
+480
+00:41:24,230 --> 00:41:30,070
+مش مفهومة، لأن مين اللي بيفهمها؟ اللي بيعرف الـ key
+
+481
+00:41:30,070 --> 00:41:34,110
+المستقبل، اللي بيعرف أن هذا الـ text بده يعمل له عملية
+
+482
+00:41:34,110 --> 00:41:38,970
+عكسية، بدنا نعمل له عملية عكسية، إيش هي العملية
+
+483
+00:41:38,970 --> 00:41:43,950
+العكسية؟ نفس الكلام، بدك تطرح خمسة، مقدار الـ key بدك
+
+484
+00:41:43,950 --> 00:41:49,630
+تطرحه من قيمة الـ character وتعمل modulo على 26، مضبوط؟
+
+485
+00:41:49,630 --> 00:41:54,510
+فبتيجي الآن بي.. يعني الآن بدك تعمل عملية عكسية،
+
+486
+00:41:54,510 --> 00:42:02,500
+الآن الـ cypher نطرح الـ key، modulo الـ 26، هكذا تصير P
+
+487
+00:42:02,500 --> 00:42:08,120
+اختصار لـ plain text، نص مجرد، C اختصار لـ cipher text،
+
+488
+00:42:08,120 --> 00:42:12,120
+اللي هو النص المشفر أو المخفي، الآن P إيش قيمته يا
+
+489
+00:42:12,120 --> 00:42:17,260
+شباب؟ اثنين، اثنين ناقص خمسة، اثنين ناقص خمسة، كده؟
+
+490
+00:42:17,260 --> 00:42:25,840
+سالب ثلاثة، تساوي شغل مضروبة في الستة والعشرين
+
+491
+00:42:25,840 --> 00:42:28,440
+زائد الـ remainder، الـ remainder لازم يبقى positive،
+
+492
+00:42:30,870 --> 00:42:36,470
+في سالب واحد، أو سالب ثلاثة وعشرين، مئة بالمئة، هيك
+
+493
+00:42:36,470 --> 00:42:40,390
+مين؟ الثلاثة.. يعني الـ reminder، هو باقي القسمة
+
+494
+00:42:40,390 --> 00:42:46,130
+مضبوط، جدّيش؟ ثلاثة وعشرين، الباقي راح لمين؟ راح للـ W
+
+495
+00:42:46,130 --> 00:42:49,810
+للتلاتة
+
+496
+00:42:49,810 --> 00:42:59,230
+وعشرين، الـ F ستة، أخذنا منها خمسة، واحد، إيه؟ الـ W ثلاثة
+
+497
+00:42:59,230 --> 00:43:06,190
+وعشرين، أخذنا منها خمسة، ثمانية عشر، الـ G سبعة، أخذنا
+
+498
+00:43:06,190 --> 00:43:12,630
+منها خمسة، راحت للاتنين، T عشرين، أخذنا منها خمسة
+
+499
+00:43:12,630 --> 00:43:19,890
+خمسة عشر، P ستة عشر، أخذنا منها خمسة، راحت لأحد عشر، رجعنا
+
+500
+00:43:19,890 --> 00:43:24,560
+بالكلمة، الـ War Book، واحد بيقول: ليه في المحاضرة
+
+501
+00:43:24,560 --> 00:43:27,240
+السابقة؟ طب ما هو يا دكتور، لما بتكون الرسالة كبيرة
+
+502
+00:43:27,240 --> 00:43:29,780
+شوية، وبتخلص الحرف قبل ما أترجم الرسالة وأرجعها
+
+503
+00:43:29,780 --> 00:43:35,400
+لأصلها، كانت الحلقات هذه، أو الدائرتين هذه هي
+
+504
+00:43:35,400 --> 00:43:39,040
+المفتاح، ما كانش.. يعني هو الفكرة، نعم، إنبنت عليها
+
+505
+00:43:39,040 --> 00:43:42,540
+من ناحية الرياضيات، بس التطبيق تبعها كان بالشكل
+
+506
+00:43:42,540 --> 00:43:46,280
+هذا، خليني بس عشان أحركه لخمسة، يعني الـ A جدّيش صارت
+
+507
+00:43:46,280 --> 00:43:50,840
+شباب؟ جاب شوية خمسة، يعني بتصير ستة، مضبوط، الستة اللي
+
+508
+00:43:50,840 --> 00:43:51,860
+هي F
+
+509
+00:43:55,900 --> 00:44:01,220
+صح الكلام؟ shift
+
+510
+00:44:01,220 --> 00:44:06,900
+of خمسة لأ
+
+511
+00:44:06,900 --> 00:44:11,380
+في شغل خربطها شكلي، لأن هيدي War Book.. War Book..
+
+512
+00:44:11,380 --> 00:44:15,500
+اه، كان المفروض ألف اللي جوا، anyway، كان لازم أفكر
+
+513
+00:44:15,500 --> 00:44:19,760
+ألف اللي جوا، مش ألف اللي برا، anyway، في الآخر ما كانش
+
+514
+00:44:19,760 --> 00:44:23,320
+هو بيعتمد على الحسبة، بقله، هايه مقداري key خمسة،
+
+515
+00:44:23,320 --> 00:44:28,080
+بلفه، بصير إيش؟ كل نص بياخد الـ character المقابل له،
+
+516
+00:44:28,080 --> 00:44:31,580
+بشكل سريع، وبالتالي أنت بتحصل على النص، يعني لو
+
+517
+00:44:31,580 --> 00:44:34,880
+بالوضع الحالي، هاي الـ key، هاي الـ.. الآن، وقولنا لك
+
+518
+00:44:34,880 --> 00:44:40,820
+بدنا نأخذ الـ War Book عندي هنا، مش إحنا.. إحنا
+
+519
+00:44:40,820 --> 00:44:50,190
+قلنا War Book، هاه، هايها W، الـ A.. الـ.. الـ.. الـ
+
+520
+00:44:50,190 --> 00:44:50,470
+..الـ..الـ..الـ..الـ..الـ..الـ..الـ..الـ
+
+521
+00:44:50,470 --> 00:44:50,990
+الـ..الـ..الـ..الـ..الـ..الـ..الـ..الـ
+
+522
+00:44:50,990 --> 00:44:51,630
+..الـ..الـ..الـ..الـ..الـ..الـ..الـ..الـ
+
+523
+00:44:51,630 --> 00:44:51,670
+..الـ..الـ..الـ..الـ..الـ..الـ..الـ..الـ
+
+524
+00:44:51,670 --> 00:44:51,850
+..الـ..الـ..الـ..الـ..الـ..الـ..الـ..الـ
+
+525
+00:44:51,850 --> 00:44:51,990
+..الـ..الـ..الـ..الـ..الـ..الـ..الـ..الـ
+
+526
+00:44:51,990 --> 00:44:52,290
+..الـ..الـ..الـ..الـ..الـ..الـ..الـ..الـ
+
+527
+00:44:52,290 --> 00:44:52,450
+..الـ..الـ..الـ..الـ..الـ..الـ..الـ..الـ
+
+528
+00:44:52,450 --> 00:44:53,470
+..الـ..الـ..الـ..الـ..الـ..الـ..الـ..الـ
+
+529
+00:44:53,470 --> 00:44:54,790
+..الـ..الـ..الـ..الـ..الـ..الـ..الـ..الـ
+
+530
+00:44:54,790 --> 00:44:59,990
+..الـ..الـ..الـ..الـ..الـ..الـ..الـ..الـ
+
+531
+00:44:59,990 --> 00:45:16,810
+..الـ..الـ..الـ..الـ..الـ..
+
+532
+00:45:21,290 --> 00:45:25,470
+مع الـ B، ففعلياً استخدامك للعجلة هاي، أو للقرصير هذول
+
+533
+00:45:25,470 --> 00:45:29,950
+أسهل من أن يعتمد على النص اللي موجود، ففعلياً لو
+
+534
+00:45:29,950 --> 00:45:33,970
+دورت على الـ.. على الـ net أو على جوجل، في الـ
+
+535
+00:45:33,970 --> 00:45:39,080
+images، وقلت له: القيصر،  كانت موجودة.. لأ، 26
+
+536
+00:45:39,080 --> 00:45:43,080
+character نفسها، والحلقة أو الدائرة اللي في الوسط
+
+537
+00:45:43,080 --> 00:45:47,340
+هذه عليها إيش؟ عليها قابض بسيط عشان تقدر تلف، و
+
+538
+00:45:47,340 --> 00:45:51,100
+بالتالي عملية التشفير هتكون إيش؟ أسرع من أن إحنا
+
+539
+00:45:51,100 --> 00:45:54,160
+بنجد.. زي ما كنا نحكي قبل شوية، لكن فكرة فكرتها
+
+540
+00:45:54,160 --> 00:45:59,500
+فكرة حسابية، وnot the last 100%، تمام، طيب، لكن الفكرة
+
+541
+00:45:59,500 --> 00:46:05,100
+هذه يا شباب، أن العملية هذه قابلة للكسر، ماذا يعني
+
+542
+00:46:05,100 --> 00:46:09,280
+قابل للكسر؟ يعني أنا ممكن أجرب مرة واثنين وثلاثة
+
+543
+00:46:09,280 --> 00:46:15,560
+أصل الـ key، وخصوصاً إذا عرفنا أن في بعض الكلمات هي الـ
+
+544
+00:46:15,560 --> 00:46:20,440
+most frequent، مثل أكثر حرف بيتكرر في الكلمات في
+
+545
+00:46:20,440 --> 00:46:26,180
+الأبجدية الإنجليزية، حرف الـ E، وأكثر كلمة ممكن
+
+546
+00:46:26,180 --> 00:46:27,300
+تتكرر، The
+
+547
+00:46:32,560 --> 00:46:39,460
+ماذا سيفعل؟ سيُبحث عن كلمات من ثلاث حروف وأكثر، ثلاث
+
+548
+00:46:39,460 --> 00:46:45,360
+حروف، يتكرر، يفترض أن هذا هو ذات، ويأخذ الحرف الأخير
+
+549
+00:46:45,360 --> 00:46:50,100
+الـ E، ويبحث عن الكلمة، بيساوي، ويرجّعها لأصلها، وبناءً
+
+550
+00:46:50,100 --> 00:46:56,440
+على الـ key اللي يحصل عليه، يصبح حلها، حلها طبعاً طول
+
+551
+00:46:56,440 --> 00:46:58,860
+عمرنا بدأنا من أنهم، تعلمنا security، هم تعلمنا
+
+552
+00:46:58,860 --> 00:47:05,210
+كتالوج في حرب مشتعلة ما بين الـ Intruder والـ
+
+553
+00:47:05,210 --> 00:47:10,490
+Defender، بين المهاجم والمدافع، وكل ما المدافع
+
+554
+00:47:10,490 --> 00:47:13,070
+بيبتكر خطّة جديدة وفكرة جديدة، المهاجم بيدور على
+
+555
+00:47:13,070 --> 00:47:20,490
+ثغرة، وبناءً على هيك، في حرب متزايدة، الناس اللي بتشتغل
+
+556
+00:47:20,490 --> 00:47:22,790
+في الـ Defender أو في الدفاع، إيش قالت؟ قالت okay،
+
+557
+00:47:22,790 --> 00:47:27,010
+ماشي، الحل، أول خطوة، رقم واحد، بدنا نشيل الـ spaces أو
+
+558
+00:47:27,010 --> 00:47:30,750
+بلش، أول ما بلشوا يفكروا، بطلنا نعتمد بس على الـ key
+
+559
+00:47:30,750 --> 00:47:34,350
+لحالها، بدنا نروح للكلمة، نجصها من النص، ونعملها
+
+560
+00:47:34,350 --> 00:47:40,430
+shuffling، يعني مثلاً كلمة Book هذه، تمام؟ أروح أجصها
+
+561
+00:47:40,430 --> 00:47:46,370
+من النص، تصير OKB0O، تمام؟ وبعدين أطبق عليها الـ
+
+562
+00:47:46,370 --> 00:47:51,840
+key تبعها، فهو لما طبق عليها الـ key برضه حصل على
+
+563
+00:47:51,840 --> 00:47:56,400
+كلمة مالهاش معنى، وبالتالي لازم يجيب، يعرف إن هي جُسّمت،
+
+564
+00:47:56,400 --> 00:47:58,760
+لكم، كم character، وإيش الترتيب، عشان يقدر يردها
+
+565
+00:47:58,760 --> 00:48:03,680
+لأصلها، واحد ثاني يفكر: جالك، يوكيه، يعني هو اعتمد على
+
+566
+00:48:03,680 --> 00:48:06,740
+حرف إيه؟ عشان يجيب الـ key، قبل ما أنا أروح أجسّم
+
+567
+00:48:06,740 --> 00:48:10,120
+الكلمات هذه، خصوصاً إنه ممكن أقع في مشكلة مع الكلمات
+
+568
+00:48:10,120 --> 00:48:13,960
+اللي من ثلاث حروف، ومن أربعة حروف، والكلام هذا، بدي أروح أشيل
+
+569
+00:48:13,960 --> 00:48:20,660
+spaces، شان الـ spaces، كانت كل نص، كلمة واحدة، حروف ملاصقة
+
+570
+00:48:20,660 --> 00:48:24,020
+مع بعض، بطل يقدر يخمن وين الـ، عشان يدور على الـ
+
+571
+00:48:24,020 --> 00:48:28,200
+most frequent، ومش بس فكرة حساوية، جالك: بدي آخذ كل
+
+572
+00:48:28,200 --> 00:48:32,540
+أربعة digits، أعتبرهم one block، وأجسّمهم من النص،
+
+573
+00:48:32,540 --> 00:48:37,560
+وأبدلهم، فأنت تخيل حجم التعقيد اللي صار، لكن أنا
+
+574
+00:48:37,560 --> 00:48:42,610
+بقول، برضه العملية برضه بتظل قابلة للكسر، خصوصاً إنه
+
+575
+00:48:42,610 --> 00:48:48,730
+زي ما قلنا، بيصير سباق سريع ما بين الشغلات من
+
+576
+00:48:48,730 --> 00:48:53,450
+أكثر الـ algorithms شهرة، اعتمدت على الـ modulus والـ
+
+577
+00:48:53,450 --> 00:49:01,450
+primes، الـ algorithm اسمه RSA، RSA اختصار لأسماء
+
+578
+00:49:01,450 --> 00:49:06,730
+أو اسمين من مجموعة من اليهود، الـ algorithm
+
+579
+00:49:06,730 --> 00:49:13,050
+أخذ فكرته من باقي القسمة، جالك بكل بساطة، أنت بتأخذ
+
+580
+00:49:13,050 --> 00:49:17,030
+إيه الـ character الآن، اللي هي الـ message تبعتك، الـ
+
+581
+00:49:17,030 --> 00:49:23,270
+plain text، وبترفعها لأسّ a، يعني بتأخذ حرف الـ a
+
+582
+00:49:23,270 --> 00:49:28,230
+مثلاً، وبترفع قيمته لأسّ كذا، أنا هعمل اللي بدي
+
+583
+00:49:28,230 --> 00:49:33,150
+أعمل generate للـ key، بترفعها لأسّ a، طب إيش الـ a جالك؟
+
+584
+00:49:33,150 --> 00:49:38,780
+الـ a هي عبارة عن حاصل، أو عبارة عن رقم relatively
+
+585
+00:49:38,780 --> 00:49:44,980
+prime مع B ناقص واحد، وQ ناقص واحد، إيش الـ Q والـ B
+
+586
+00:49:44,980 --> 00:49:50,920
+عبارة عن two big primes، وN بتمثل حاصل ضرب الـ
+
+587
+00:49:50,920 --> 00:49:54,460
+primes هذول، يعني هيك فكر كتالي، راح آخذ عددين
+
+588
+00:49:54,460 --> 00:49:58,780
+أوليين كبيرين، وليكن، وليكن، آخذ 13 و17 على سبيل
+
+589
+00:49:58,780 --> 00:50:06,940
+المثال، فراح أضربهم في بعض، وحصلت على الـ N، 13 في 17
+
+590
+00:50:06,940 --> 00:50:11,960
+جدّيش يا شباب؟ أنا
+
+591
+00:50:11,960 --> 00:50:16,800
+ما بعرفش، إلا أشتغل هيك، سبعة واثنين، تسعة
+
+592
+00:50:16,800 --> 00:50:21,800
+ثلاثة، واحد، واحد، اثنين، اثنين، مائتين وواحد وعشرين
+
+593
+00:50:21,800 --> 00:50:25,540
+فجالك أن المسألة اللي بدها تصير عندي، الـ character
+
+594
+00:50:25,540 --> 00:50:33,280
+الـ M، مرفوعة للأسّ مائتين وواحد وعشرين، مرفوعة لأسّ جدّيش الأسّ
+
+595
+00:50:33,280 --> 00:50:40,680
+أخذه، عبارة عن رقم relatively prime لمين؟ لـ
+
+596
+00:50:40,680 --> 00:50:45,720
+greatest common divisor واحد، بين الـ (P-1) والـ
+
+597
+00:50:45,720 --> 00:50:51,400
+(Q-1)، اثنا عشر ضرب ستة عشر، اثنا عشر في ستة عشر، كده
+
+598
+00:50:51,400 --> 00:50:56,020
+يا شباب؟
+
+599
+00:50:56,020 --> 00:51:01,960
+ماية
+
+600
+00:51:01,960 --> 00:51:07,500
+وتسعين، مية واثنين وتسعين، يعني مية وواحد و
+
+601
+00:51:07,500 --> 00:51:11,860
+تسعين، ومية واثنين وتسعين، relatively prime ولا
+
+602
+00:51:11,860 --> 00:51:16,700
+لأ، relatively prime، الـ greatest common divisor
+
+603
+00:51:16,700 --> 00:51:21,320
+بينهم واحد، فجالك: أنا بدي أرفع هذه للأسّ مية وواحد
+
+604
+00:51:21,320 --> 00:51:27,960
+و تسعين، عشان أحصل على character جديد
+
+605
+00:51:27,960 --> 00:51:34,770
+تيجي في النهاية، الفكرة وين؟ أنا بدي أقول لك أن هذا
+
+606
+00:51:34,770 --> 00:51:39,21
\ No newline at end of file
diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/jA9RTJkdbkc_raw.srt b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/jA9RTJkdbkc_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..c8d37bbcea37c4d205700a2a4c0d26d91496cd9d
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/jA9RTJkdbkc_raw.srt
@@ -0,0 +1,2548 @@
+1
+00:00:20,970 --> 00:00:22,910
+طيب الشباب بسم الله والحمد لله والصلاة والسلام علي
+
+2
+00:00:22,910 --> 00:00:25,430
+الرسول الله اليوم ان شاء الله هناخد two sections
+
+3
+00:00:25,430 --> 00:00:31,690
+خفاف ضراف ونختم فيهم ال chapter تبع ال integers و
+
+4
+00:00:31,690 --> 00:00:35,430
+ال primes في البداية ال section الأولة اللي هو
+
+5
+00:00:35,430 --> 00:00:40,410
+أربعة تلاتة هنتكلم فيه عن ال primes وال greatest
+
+6
+00:00:40,410 --> 00:00:43,070
+common divisor وال least common multiple
+
+7
+00:00:45,410 --> 00:00:52,450
+قبل ما أتكلم في عندي الأعداد الأولية يعني section
+
+8
+00:00:52,450 --> 00:00:54,470
+أو chapter بتتكلم عن الأعداد الأولية بشكل عام
+
+9
+00:00:54,470 --> 00:01:01,350
+الأعداد الأولى هو عبارة عن كل عدد يقبل قسمة على
+
+10
+00:01:01,350 --> 00:01:04,510
+نفسه لا يقبل قسمة إلا على نفسه والواحد هو كل
+
+11
+00:01:04,510 --> 00:01:07,270
+الأعداد بتقبل قسمة على نفسها فخلاص احنا بنقول
+
+12
+00:01:07,270 --> 00:01:10,410
+العدد الأولى هو عبارة عن كل عدد لا يقبل قسمة إلا
+
+13
+00:01:10,410 --> 00:01:11,490
+على نفسه
+
+14
+00:01:14,370 --> 00:01:18,330
+مثالات مراجعة لشغلات احنا المفروض بنعرفها من و
+
+15
+00:01:18,330 --> 00:01:22,930
+احنا صغار اللي هي ايش خاصية القسمة احنا بداية ال
+
+16
+00:01:22,930 --> 00:01:25,910
+chapter كنا بنتكلم على الاعداد و خاص القسمة اللي
+
+17
+00:01:25,910 --> 00:01:32,170
+موجودة اقولك التالي لو كان انا في عندي integer a
+
+18
+00:01:32,170 --> 00:01:41,910
+divide يقسم ال b معناته ان ال b بنهت ساويQuantum
+
+19
+00:01:41,910 --> 00:01:46,710
+equation quotient عفوا في ال a كمية مضروبة في ال a
+
+20
+00:01:46,710 --> 00:01:51,950
+ولو كانت ال b لا تقبل القسمة على ال a معناته انا
+
+21
+00:01:51,950 --> 00:01:57,690
+بقدر اكتب ال a او ال b على صورة quotient مضروبة في
+
+22
+00:01:57,690 --> 00:02:01,830
+ال a اللي هي divisor زائد ال remainder و ال
+
+23
+00:02:01,830 --> 00:02:06,590
+remainder هذا بيكون محصور ما بين الصفر وال divisor
+
+24
+00:02:06,590 --> 00:02:11,480
+اللي هي ال a وال divisor اللي هيالـ A طبعا هذا
+
+25
+00:02:11,480 --> 00:02:15,720
+الكلام بيقبل القسم ال B تقبل القسم على ال A أو ال
+
+26
+00:02:15,720 --> 00:02:19,200
+A تقسم ال B هذا الكلام اللي احنا قلناه المرة
+
+27
+00:02:19,200 --> 00:02:22,900
+الماضية وبدأنا مع الأعداد الأولية قلنا ان العدد
+
+28
+00:02:22,900 --> 00:02:26,920
+الأولي هو كل عدد لا يقبل القسم الا على نفسه يعني
+
+29
+00:02:26,920 --> 00:02:31,340
+مالوش اي divisor بقدرش اكتبه بالصورة هذه العدد
+
+30
+00:02:31,340 --> 00:02:35,540
+الأولي بقدرش اكتبه بالصورة اللي موجودة عندنا فوق
+
+31
+00:02:36,780 --> 00:02:42,980
+طيب لو انا جيت .. اقولك التالي انه عشان افحص العدد
+
+32
+00:02:42,980 --> 00:02:46,400
+بيقبل قسم او لا يقبل قسم الراجع مع بعض على السريع
+
+33
+00:02:46,400 --> 00:02:52,240
+لو انا كتبت اي رقم وليكن على سبيل المثال واحد سبعة
+
+34
+00:02:52,240 --> 00:02:58,720
+تلاتة خمسة و الرقم التاني اتنين صفر اتنين تالت
+
+35
+00:02:58,720 --> 00:03:05,020
+اتنين صفر واحد مثلا و دي سؤال نفسي الرقم الاول
+
+36
+00:03:05,020 --> 00:03:11,510
+بيقبل جسم على اتنينلأ ليش جوابت لأ؟ لأن خانة الأحد
+
+37
+00:03:11,510 --> 00:03:18,310
+هي least common digit خمسة تقبل الجسم على اتنين لو
+
+38
+00:03:18,310 --> 00:03:23,750
+كان القيمة زوجية و الصفر من ضمن الأعداد الزوجية
+
+39
+00:03:23,750 --> 00:03:30,270
+تمام بيقبل الجسم على تلاتة شرط الجسم على تلاتة انك
+
+40
+00:03:30,270 --> 00:03:35,330
+تجمع ال digits اللي موجوداتمحاصر الجمع اذا بيقبل
+
+41
+00:03:35,330 --> 00:03:38,730
+القسم على ثلاثة معناته انا بتكلم قسم على ثلاثة
+
+42
+00:03:38,730 --> 00:03:43,550
+خمسة و ثلاثة تمانية سبعة خمستاشر واحد تمانتاش
+
+43
+00:03:43,550 --> 00:03:48,490
+ستاشر ستاشر على ثلاثة لايقبل قسم على ثلاثة معناته
+
+44
+00:03:48,490 --> 00:03:52,310
+لايقبل قسم على ثلاثة اللي بعده اتنين صفر اتنين
+
+45
+00:03:52,310 --> 00:03:57,480
+اربع لايقبل قسم على ثلاثة متين و واحداتنين زي صفر
+
+46
+00:03:57,480 --> 00:04:01,840
+زي واحد ثلاثة تقبل القسم على ثلاثة معناته الـ 201
+
+47
+00:04:01,840 --> 00:04:06,540
+يقبل القسم على ثلاثة تمام؟ هذه الشغلات نحن نحاول
+
+48
+00:04:06,540 --> 00:04:10,940
+أن نذكرها بشكل سريع في موضوع القسم على أربعة بدي
+
+49
+00:04:10,940 --> 00:04:15,460
+أخد two least significant digits يعني خانة الأحد
+
+50
+00:04:15,460 --> 00:04:20,580
+والعشرات مع بعض اللي بنسميهم هيك إذا الرقمين هدول
+
+51
+00:04:20,580 --> 00:04:25,820
+مع بعض بيقبل القسم علىالاربعة فالرقم الكلي بيقبل
+
+52
+00:04:25,820 --> 00:04:29,360
+الجسم على .. على أربعة طيب خمسة و تلاتين تقبل
+
+53
+00:04:29,360 --> 00:04:32,600
+الجسم على أربعة؟ لأ طبعا هاد بدأ اعتمد على حفظ
+
+54
+00:04:32,600 --> 00:04:37,480
+الجداول عشان بشكل سريع أقدر أخد القرار طيب التنين
+
+55
+00:04:37,480 --> 00:04:42,480
+بتقبل الجسم على أربعة؟ لأ لأ التنين شوف انت عارف
+
+56
+00:04:42,480 --> 00:04:46,840
+.. التنين تقبل الجسم على أربعة يعني اتنين بدها
+
+57
+00:04:46,840 --> 00:04:53,410
+تساوي quantity كميةمضروبة في الأربعة زائد ال
+
+58
+00:04:53,410 --> 00:04:59,190
+remainder ال quantity اللي عندك هيقدرش قيمتها صفر
+
+59
+00:04:59,190 --> 00:05:05,050
+صفر وال remainder اتنين معناته لا يقبل قسم على
+
+60
+00:05:05,050 --> 00:05:10,410
+أربعة أو بين جثين الاتنين ليست من مضاعفات الأربعة
+
+61
+00:05:10,410 --> 00:05:16,380
+تمام الواحد يقبل قسم على أربعة لألأ اللي بعرف
+
+62
+00:05:16,380 --> 00:05:20,060
+القسمة على خمسة بقول إن الدليل عددها بيقبل قسمة
+
+63
+00:05:20,060 --> 00:05:23,360
+على خمسة لو كانت الإحات اللي هي least significant
+
+64
+00:05:23,360 --> 00:05:28,120
+digit بيقبل صفر أو خمسة صفر أو خمسة يعني السبعتاشر
+
+65
+00:05:28,120 --> 00:05:30,000
+خمسة و تلاتين إلى الألف و سبعمية خمسة و تلاتين
+
+66
+00:05:30,000 --> 00:05:33,580
+تقبل قسمة على خمسة و الأرقام التانية لأ فالموضوع
+
+67
+00:05:33,580 --> 00:05:37,920
+القسمة على ستة إذا كان الرقم يقبل قسمة على تلاتة و
+
+68
+00:05:37,920 --> 00:05:43,200
+يقبل قسمة على اتنين فبيقبل قسمة على6 في موضوع
+
+69
+00:05:43,200 --> 00:05:49,420
+القسمة على 7 شويه العملية بدها شعل بسيط لكن الفكرة
+
+70
+00:05:49,420 --> 00:05:52,220
+فيها كالتالي خلينا نبدأ بالرقم الأسهل اللي هو 201
+
+71
+00:05:52,220 --> 00:05:56,140
+الفكرة فيها كالتالي هتاخد الرقم هذا وتقسمه لخنتين
+
+72
+00:05:56,690 --> 00:06:00,770
+الخانة الأولى فيها الأحد لحاله تمام وباقي الرقم
+
+73
+00:06:00,770 --> 00:06:05,770
+لحاله يعني في الميتين هذه هنقول عشرين هجسته من
+
+74
+00:06:05,770 --> 00:06:10,030
+النص ناقص اتنين ضرب الواحد اللي هي خانة الأحد اللي
+
+75
+00:06:10,030 --> 00:06:17,150
+عندك عشرين ناقص اتنين تمانتاش لا تقبل القسم على
+
+76
+00:06:17,150 --> 00:06:20,980
+سبعة معناته اتنين وواحد لا تقبل القسم على سبعةإذا
+
+77
+00:06:20,980 --> 00:06:23,200
+انت مش عارف بالجد ولا مش جادر تحسن في موضوع
+
+78
+00:06:23,200 --> 00:06:28,320
+التمنتاش تمام؟ كمان مرة باخد قول له واحد ناقص
+
+79
+00:06:28,320 --> 00:06:39,780
+اتنين في تمانية ناقص خمس ناشت تمام؟ وبالتالة انت
+
+80
+00:06:39,780 --> 00:06:43,340
+المفروض وجه هدوى في الخطوة السابقة لا يقبل قسم على
+
+81
+00:06:43,340 --> 00:06:48,840
+سبعة العدد اللي بعده اتنين و اتنين عشرين ناقص
+
+82
+00:06:48,840 --> 00:06:55,630
+اتنينفى 2 16 16 لا تقبل قسم على سبعة المعناته 202
+
+83
+00:06:55,630 --> 00:07:02,550
+لا يقبل قسم على سبعة اللى بعده 173
+
+84
+00:07:02,550 --> 00:07:09,230
+-2x5 163
+
+85
+00:07:09,230 --> 00:07:19,150
+163 و 60 الان بعرفش بداش تقول كمان مرة 16-2x3
+
+86
+00:07:20,980 --> 00:07:26,300
+عشرة نقص او 16 نقص ستة عشرة العشرة لا تقبل القسم
+
+87
+00:07:26,300 --> 00:07:31,880
+على سبعة معناته ال 1735 لا يقبل القسم على سبعة مع
+
+88
+00:07:31,880 --> 00:07:36,720
+انه للوحلة الاولى بتشوف ال 35 امتى يقول تقبل القسم
+
+89
+00:07:36,720 --> 00:07:41,260
+على سبعة لكن الرقم هذا لا يقبل القسم على سبعة تمام
+
+90
+00:07:41,260 --> 00:07:46,800
+يا شباب مثلا
+
+91
+00:07:46,800 --> 00:07:53,800
+لو انا جاي قلتلك سبعة سبعةأربعة اتنين يقبل القسم
+
+92
+00:07:53,800 --> 00:07:59,160
+على سبعة ولا لأ؟ مش عارف، بدك تشتغل نفس العملية
+
+93
+00:07:59,160 --> 00:08:09,960
+سبعة سبعة أربعة ناقص اتنين في اتنين سبعة سبعة واحد
+
+94
+00:08:09,960 --> 00:08:17,140
+هاش تقبل القسم ولا لأ؟ مش متأكد سبعة سبعين ناقص
+
+95
+00:08:17,140 --> 00:08:25,400
+اتنين في صفر77 77 تقبل القسمة ولا لأ وبالتالي
+
+96
+00:08:25,400 --> 00:08:32,020
+الرقم الكل هذا يقبل القسمة على 7 في موضوع القسمة
+
+97
+00:08:32,020 --> 00:08:37,200
+على 8 بدك تاخد أول three digits اللي هم least
+
+98
+00:08:37,200 --> 00:08:41,760
+significant digits وتجسم قسمة مطولة على 8 عشان
+
+99
+00:08:41,760 --> 00:08:51,680
+تقدر تتكلم في الموضوع 201 201 على 8 20 على 8ايوة
+
+100
+00:08:51,680 --> 00:08:59,080
+.. اتنين .. ستاشت .. اربع .. اتنين
+
+101
+00:08:59,080 --> 00:09:02,920
+.. ستاشت .. اربع .. اتنين .. ستاشت .. اربع ..
+
+102
+00:09:02,920 --> 00:09:05,440
+اتنين .. ستاشت .. اربع .. اتنين .. ستاشت .. اربع
+
+103
+00:09:05,440 --> 00:09:08,740
+.. اتنين .. ستاشت .. اربع .. اتنين .. ستاشت ..
+
+104
+00:09:08,740 --> 00:09:09,360
+اربع .. اتنين .. ستاشت .. اربع .. اتنين .. ستاشت
+
+105
+00:09:09,360 --> 00:09:09,360
+.. اربع .. اتنين .. ستاشت .. اربع .. اتنين ..
+
+106
+00:09:09,360 --> 00:09:09,360
+ستاشت .. اربع .. اتنين .. ستاشت .. اربع .. اتنين
+
+107
+00:09:09,360 --> 00:09:09,780
+.. ستاشت .. اربع .. اتنين .. ستاشت .. اربع ..
+
+108
+00:09:09,780 --> 00:09:16,630
+اتنين .. ستاشت .. اربع .. اتنين .. ستاشتاربع اتنين
+
+109
+00:09:16,630 --> 00:09:17,870
+اربع اتنين اربع اتنين اربع اتنين اربع اتنين اربع
+
+110
+00:09:17,870 --> 00:09:18,130
+اتنين اربع اتنين اربع اتنين اربع اتنين اربع اتنين
+
+111
+00:09:18,130 --> 00:09:21,650
+اربع اتنين اربع اتنين اربع اتنين اربع اتنين اربع
+
+112
+00:09:21,650 --> 00:09:24,790
+اتنين
+
+113
+00:09:24,790 --> 00:09:29,830
+اربع اتنين اربع اتنين اربع اتنين اربع اتنين اربع
+
+114
+00:09:29,830 --> 00:09:31,650
+اتنين اربع اتنين اربع اتنين اربع اتنين اربع اتنين
+
+115
+00:09:31,650 --> 00:09:33,130
+اربع اتنين اربع اتنين اربع اتنين اربع اتنين اربع
+
+116
+00:09:33,130 --> 00:09:44,730
+اتنين اربع اتنين اربع اتنين اربع اتنين
+
+117
+00:09:45,650 --> 00:09:52,570
+نزلوا الخمسة الأخيرة خمسة و خمسين ستة
+
+118
+00:09:52,570 --> 00:10:00,130
+أو سبعة ستة و خمسين ماتصبتش بياتوا ستة تبانية و
+
+119
+00:10:00,130 --> 00:10:06,090
+أربعين و جدش عنده كان سبعة فيه remainder متالي ألف
+
+120
+00:10:06,090 --> 00:10:08,190
+و سبعة مية و خمسة و تلاتين الأكبر قسم على تمانية
+
+121
+00:10:08,190 --> 00:10:13,950
+العدد الأخير سبعة سبعة أربعة اتنين على تمانية
+
+122
+00:10:32,840 --> 00:10:38,600
+أربعة و سبعين و سبعين و سبعين و سبعين و سبعين و
+
+123
+00:10:38,600 --> 00:10:38,600
+سبعين و سبعين و سبعين و سبعين و سبعين و سبعين و
+
+124
+00:10:38,600 --> 00:10:38,600
+سبعين و سبعين و سبعين و سبعين و سبعين و سبعين و
+
+125
+00:10:38,600 --> 00:10:38,600
+سبعين و سبعين و سبعين و سبعين و سبعين و سبعين و
+
+126
+00:10:38,600 --> 00:10:38,600
+سبعين و سبعين و سبعين و سبعين و سبعين و سبعين
+
+127
+00:10:45,070 --> 00:10:49,410
+الاربعة الآن نزلها الاربعة هيها هنجي الدور التنين
+
+128
+00:10:49,410 --> 00:10:56,650
+62 سبعة الباقى
+
+129
+00:10:58,490 --> 00:11:01,250
+ستة مع تولى واحد من الأرقام هذه بيقبل القسمة على
+
+130
+00:11:01,250 --> 00:11:06,010
+تمانية يعني فعليا بتحس ان القسمة على تمانية مزعجة
+
+131
+00:11:06,010 --> 00:11:11,430
+اكتر من القسمة على سبعة و لا لا طيب فالقسمة على
+
+132
+00:11:11,430 --> 00:11:16,470
+كسعة لو كان مجموع الديكي زي التلاتة بيقبل القسمة
+
+133
+00:11:16,470 --> 00:11:19,970
+على تلاتة او تسعة فالعدد كله بيقبل القسمة على تسعة
+
+134
+00:11:19,970 --> 00:11:24,150
+تمام وبالتالي هذه المراجعة مهمة جدا نذكرها و
+
+135
+00:11:24,150 --> 00:11:27,480
+نحفظهاعشان إيه لك و لأولادك و لحبايبك ان شاء الله
+
+136
+00:11:27,480 --> 00:11:36,360
+تعالى لاحقا لما تعلمهم حساب تعرف تعلمهم حساب قبل
+
+137
+00:11:36,360 --> 00:11:39,420
+ما تكون أستاذ شاطر بيبقى دورك كويس دورك دور أمهم
+
+138
+00:11:39,420 --> 00:11:44,960
+ان شاء الله مستقبلا طيب الآن كل العدد الأولين هو
+
+139
+00:11:44,960 --> 00:11:50,440
+عبارة عن كل عدد لا يقبل القسم إلاعلى نفسه لا يكبر
+
+140
+00:11:50,440 --> 00:11:54,880
+القسم الا على نفسه و العدد اللى له device نسميه
+
+141
+00:11:54,880 --> 00:11:59,340
+composite عكس prime composite الان لو انا اتيت
+
+142
+00:11:59,340 --> 00:12:07,860
+قولت 17 شباب عدد اول ايه اول بتقدر كل بساطة تفحص
+
+143
+00:12:07,860 --> 00:12:10,320
+كل الاعداد اللى جابله بتبتدش القسم الاول على واحد
+
+144
+00:12:10,320 --> 00:12:15,340
+منهم فهو عدد اولى لكن كل ما بيكبر العددبتصير عملية
+
+145
+00:12:15,340 --> 00:12:19,660
+القسم ايش تصعب يعني مثلا لو سألك 101 الآن هل هي
+
+146
+00:12:19,660 --> 00:12:24,880
+عند اول ايه؟ بدك تبدأ تفكر فيها بنفس المنطقة اه في
+
+147
+00:12:24,880 --> 00:12:30,540
+عندى نظرية بسيطة جدا بتقول العدد المركب العدد
+
+148
+00:12:30,540 --> 00:12:38,100
+المركب لازم تلاقيله divisor اقل من جذرهتمام؟ العدد
+
+149
+00:12:38,100 --> 00:12:43,120
+المركّب بتلاقي له جذر او بتلاقي له divisor اقل من
+
+150
+00:12:43,120 --> 00:12:47,420
+جذره ايش يعني؟ بدك تاخد ال 101 و تاخد ال 17 و
+
+151
+00:12:47,420 --> 00:12:54,160
+تحطهم تحت الجذر جذر ال 17 تقريبا كده يا شرفا؟
+
+152
+00:12:54,160 --> 00:13:04,610
+تقريبا 4 سيبنا خلاص 4 و جذر 101 تقريبا 10الان خد
+
+153
+00:13:04,610 --> 00:13:10,610
+السبعة عشر هذه وقسمها من تمين للاربعة وقسم المية
+
+154
+00:13:10,610 --> 00:13:15,150
+واحد على الأرقام من اتنين لحد العشرة إذا ما وجدتش
+
+155
+00:13:15,150 --> 00:13:20,510
+ولا divisor مالته هذا العدد عبارة عن عدد أولي
+
+156
+00:13:20,510 --> 00:13:24,950
+السبعة عشر لا يقبل قسم على اتنين ولا يقبل قسم على
+
+157
+00:13:24,950 --> 00:13:30,330
+تلاتة ولا يقبل قسم على أربعة فهو prime101 لا يقبل
+
+158
+00:13:30,330 --> 00:13:35,570
+قسم على 2 لا يقبل قسم على 3 لا يقبل قسم على 4 ولا
+
+159
+00:13:35,570 --> 00:13:40,730
+يقبل قسم على 5 ولا 6 ومش بس هيك كمان هتلاقيه له
+
+160
+00:13:40,730 --> 00:13:44,590
+prime divisor وبالتالي ممكن تتكلم بس عن ال primes
+
+161
+00:13:44,590 --> 00:13:49,070
+اللي مين اللي موجودات في أقل من مين أقل من الجذر
+
+162
+00:13:49,070 --> 00:13:52,620
+يعني في 101 مش بالضرورة أن تفحص كل العشر أقاممن
+
+163
+00:13:52,620 --> 00:13:55,940
+التنين للعشرة لأ خد باسم ال prime number اللي هم
+
+164
+00:13:55,940 --> 00:14:00,480
+بنقول تنين و تلاتة و سبعة اتنين و تلاتة و خمسة و
+
+165
+00:14:00,480 --> 00:14:04,480
+سبعة الان مية و واحد لا يقبل قسم على اتنين لا يقبل
+
+166
+00:14:04,480 --> 00:14:09,040
+قسم على تلاتة لا يقبل خمسة ولا يقبل قسم على سبعة
+
+167
+00:14:09,040 --> 00:14:13,100
+فالعدد مية و واحد ال prime لكن تعالى نشوف لو اجت
+
+168
+00:14:13,100 --> 00:14:15,560
+قلت مية و خمسة على سبيل المثال
+
+169
+00:14:20,290 --> 00:14:23,630
+تمام؟ واضحة زي الشمس انت هتقول بيقبل القسمة .. هذا
+
+170
+00:14:23,630 --> 00:14:26,230
+composite بيقبل القسمة على خمسة و بيقبل القسمة على
+
+171
+00:14:26,230 --> 00:14:30,210
+ثلاثة كمان لأن مجموعة ال dead yeast تبعته ستة لكن
+
+172
+00:14:30,210 --> 00:14:33,450
+تعالى نشوف الطبق في القانون مية خمسة تقريبا الجذر
+
+173
+00:14:33,450 --> 00:14:37,950
+تبعتها عشرة ميلي برايمز اللي حكينا عليهم اتنين
+
+174
+00:14:37,950 --> 00:14:43,150
+تلاتة خمسة سبعة تقبل قسمة على ثمين لأ تقبل قسمة
+
+175
+00:14:43,150 --> 00:14:47,620
+على تلاتة برايم و بتقبل قسمة على خمسة برايمولا
+
+176
+00:14:47,620 --> 00:14:49,720
+فاكر بالكسمة على السبب بس خلصنا كمون انجلة one
+
+177
+00:14:49,720 --> 00:14:54,180
+divisor فهو composite number فهو composite number
+
+178
+00:14:54,180 --> 00:15:00,340
+طبعا هذا الكلام يا شباب وين بتبين هميته اللغية هذه
+
+179
+00:15:00,340 --> 00:15:05,740
+لاحظ احنا قبل شوية كنا بنتكلم لحد المية يعني انا
+
+180
+00:15:05,740 --> 00:15:09,700
+بدي افحص الرقم هذا لحد الميةقلت لك لأ بس خد جهره
+
+181
+00:15:09,700 --> 00:15:15,460
+تقريبا جلالها بنسبة 90% لأن المية صارت عشر أرقام
+
+182
+00:15:15,460 --> 00:15:19,700
+والعشر أرقام هدول كمان قلت لك بتنفيهم كلهم بس افحص
+
+183
+00:15:19,700 --> 00:15:22,980
+من الـprimes اللي موجودات من خلالهم وبالتالي انت
+
+184
+00:15:22,980 --> 00:15:27,000
+بتحصل على نتيجة سريعة ناهيك ان لو كبر الرقم انت
+
+185
+00:15:27,000 --> 00:15:29,380
+هتصرف تعتمد على ال calculator او تعتمد على
+
+186
+00:15:29,380 --> 00:15:34,180
+الكمبيوتر ان هو يقولك هذا العدد أولي او غير أولي
+
+187
+00:15:34,180 --> 00:15:42,400
+تمامبدنا ننتقل لنظرية بسيطة وبيقول فيها كالتالي ان
+
+188
+00:15:42,400 --> 00:15:46,560
+اي composite number زي ال 105 اللي كتبناها قبل
+
+189
+00:15:46,560 --> 00:15:50,140
+شوية composite
+
+190
+00:15:50,140 --> 00:15:54,440
+لانه بيجب الجسم على ثلاثة وبيجب الجسم على خمسة اي
+
+191
+00:15:54,440 --> 00:15:57,800
+composite number وناخد مثال أبسط منه اللي هو ال 18
+
+192
+00:15:57,800 --> 00:16:05,500
+على سبيل المثالأي number تكتب على صورة حاصل ضرب
+
+193
+00:16:05,500 --> 00:16:11,460
+مجموعة من الأعداد الأولية نبدأ بالـ18، ماذا يعني؟
+
+194
+00:16:11,460 --> 00:16:14,000
+تقدر تقول، جيب مجموعة من الأعداد الأولية، لو
+
+195
+00:16:14,000 --> 00:16:18,380
+ضربتهم في بعض بس أعداد أولية، بيكون حصلت على مين؟
+
+196
+00:16:18,380 --> 00:16:25,340
+على الـ18 الآن، كون العدد هذا زوجي جسم على 2، 2 في
+
+197
+00:16:25,340 --> 00:16:30,380
+9، بصبوت غير برايالـ 9 كومبوزيت و لا برايم؟
+
+198
+00:16:30,380 --> 00:16:37,700
+كومبوزيت حللها لـ 3x3 مهاته
+
+199
+00:16:37,700 --> 00:16:41,780
+كومبوزيت number قدرت أضربه على حاصل مجموعة أعداد
+
+200
+00:16:41,780 --> 00:16:47,700
+من الـ Primes تعالى نشوف ال 105 105 جسم على 5 ولا
+
+201
+00:16:47,700 --> 00:16:50,460
+جسم على 3 بالنسبالي في البداية؟ زي ما بدك، مش
+
+202
+00:16:50,460 --> 00:16:54,640
+قضية، 5 يسعى ما هتكون إلك هتكون جداش؟ 5 ضرب 21
+
+203
+00:16:57,240 --> 00:17:03,640
+مصبوط ال 21 كمزت حللها سبعة في تلاتة يعني انا ممكن
+
+204
+00:17:03,640 --> 00:17:09,880
+اعيد سياخته هيك اقول تلاتة في خمسة في سبعة عشان
+
+205
+00:17:09,880 --> 00:17:12,760
+بصياشي تكون دلني ايش الأرقام ولا انا عارف ترتيب
+
+206
+00:17:12,760 --> 00:17:17,300
+معين ولو دلت في الحالة السابق مافيش مشكلة خمسة ضرب
+
+207
+00:17:17,300 --> 00:17:21,690
+تلاتة ضرب سبعة مافيش عندك مشكلة في الموضوع مطلقاو
+
+208
+00:17:21,690 --> 00:17:25,090
+بالتالي اي composite number .. اي composite number
+
+209
+00:17:25,090 --> 00:17:30,270
+بتقدر تكتبه على صورة حاصل ضرب مجموعة من الprimes
+
+210
+00:17:30,270 --> 00:17:34,550
+number او حاصل ضرب مجموعة من الأعداد الأولية الآن
+
+211
+00:17:34,550 --> 00:17:44,430
+في عندي شغلة بنسميها ال greatest common divisor ال
+
+212
+00:17:44,430 --> 00:17:48,570
+greatest common divisor ايش يعني divisor؟ يعني
+
+213
+00:17:48,570 --> 00:17:53,280
+قاسمقاسم ال greatest common divisor هيزودك برقمين
+
+214
+00:17:53,280 --> 00:17:59,440
+و تجيب أكبر قاسم مشترك ما بين الثانين يعني الآن و
+
+215
+00:17:59,440 --> 00:18:08,080
+أنا جيت و حاطيت ال 105 هدول ال 18 و 105 مع بعض و
+
+216
+00:18:08,080 --> 00:18:13,440
+قولتلك تجيبي ال greatest common divisor لهم بس
+
+217
+00:18:13,440 --> 00:18:17,120
+أصبر شوية .. أصبر شوية التلاتة مش أكبر قاسم مشترك
+
+218
+00:18:17,120 --> 00:18:24,600
+لهم كيف؟مش ضروري يكون أولي هو لما سألي جالي ال
+
+219
+00:18:24,600 --> 00:18:30,520
+greatest common أكبر divisor التاني بيجبر الجسم
+
+220
+00:18:30,520 --> 00:18:35,200
+عليه عشان تجيب ال greatest common divisor بدك تحلل
+
+221
+00:18:35,200 --> 00:18:42,340
+الرقمين as prime product كمان اتحلللهم الخطوة
+
+222
+00:18:42,340 --> 00:18:46,300
+التانية اروح جيب ال intersection اعتبر ان هدول
+
+223
+00:18:46,300 --> 00:18:51,910
+المشبوطين اعداد sixودى ايش ال intersection بينهم؟
+
+224
+00:18:51,910 --> 00:18:57,590
+ايش اتقاطهم في المجموعتين هدول؟ في غير التلاتة؟ هى
+
+225
+00:18:57,590 --> 00:19:01,710
+هى .. هى التقاطة معناته ال greatest common divisor
+
+226
+00:19:01,710 --> 00:19:07,890
+يساوي تلاتة مش هتلاقي غير التلاتة بيجسم العددين
+
+227
+00:19:07,890 --> 00:19:11,970
+هدول مع بعض تمام؟
+
+228
+00:19:11,970 --> 00:19:16,230
+فلما نتكلم عن ال intersectionلنعيد تقاطة بس بين
+
+229
+00:19:16,230 --> 00:19:19,490
+التلاتة والتلاتة تعالى نشوف عددين ثانيات لو على
+
+230
+00:19:19,490 --> 00:19:26,830
+سبيل المثال قولنا الـ 18 و 27 و بدّي ال greatest
+
+231
+00:19:26,830 --> 00:19:34,970
+common divisor بينهم الأن بدي أحللهم 18 بيتساوة 2
+
+232
+00:19:34,970 --> 00:19:43,430
+في 9 اللي هي 3 في 3 بصبت؟ طيب و 27 بدي أحللها هي 3
+
+233
+00:19:43,430 --> 00:19:48,020
+في 9والتسعة كومبوزيت معناته تلاتة في تلاتة مين
+
+234
+00:19:48,020 --> 00:19:52,680
+التقاطة صار يا شباب تلاتة
+
+235
+00:19:52,680 --> 00:19:57,400
+في تلاتة التقاطة ايوة تسعة الان بقولش انه ميكبلوش
+
+236
+00:19:57,400 --> 00:20:00,320
+الجسم على تلاتة لأ دي اكبر الجسم على تلاتة بس
+
+237
+00:20:00,320 --> 00:20:05,820
+القاسم المشترك الاكبر يعني اكبر عدد العددين هدولة
+
+238
+00:20:05,820 --> 00:20:09,460
+الدي جسم عليه اللي هو مين التسعة التسعة سبعة
+
+239
+00:20:09,460 --> 00:20:15,910
+وعشرين على تسعةمظبوط و 18 على 9 برضه مظبوط لأن 9
+
+240
+00:20:15,910 --> 00:20:19,950
+divisor ل 18 و 9 divisor ل .. لكن ماقدرش أجي أقول
+
+241
+00:20:19,950 --> 00:20:26,510
+6 divisor ل 27 ماقدرش أقول 10 divisor او 12 انت
+
+242
+00:20:26,510 --> 00:20:30,730
+دايما حلل رقم ل composite .. composite حلله
+
+243
+00:20:30,730 --> 00:20:34,470
+لمجموعة ضرب الأعداد الأولية و خد اتقاطه اللي بينهم
+
+244
+00:20:34,470 --> 00:20:39,190
+واحد دي مقيا رقمين الشباب عشان نجرب على أرقام
+
+245
+00:20:39,190 --> 00:20:39,550
+تانية
+
+246
+00:20:43,090 --> 00:20:53,830
+جداش؟ تلاتبعش واربع وعشرين .. واحد .. ليش؟ اسميكوا
+
+247
+00:20:53,830 --> 00:20:57,810
+جالك ريتس كومون دي فيزور بين التلاتبعش والاربع
+
+248
+00:20:57,810 --> 00:21:03,530
+وعشرين .. التلاتبعش عبارة عن تلاتبعشوالاربع وعشرين
+
+249
+00:21:03,530 --> 00:21:09,510
+هي عبارة عن اتنين في اتناش، بصبت؟ والاتناش هي
+
+250
+00:21:09,510 --> 00:21:14,390
+عبارة عن اتنين في ستة، والستة هي عبارة عن اتنين في
+
+251
+00:21:14,390 --> 00:21:20,850
+تلاتة، في تقاطع بينهم؟ لما لو كتبتلك انا واحد هنا،
+
+252
+00:21:20,850 --> 00:21:24,730
+لأ فيه يا صاحبي، في الواحد هذا اللي هو المحايد
+
+253
+00:21:24,730 --> 00:21:28,030
+الضربي موجود في المعادلة التانية، فالتقاطع بينهم
+
+254
+00:21:28,030 --> 00:21:33,820
+واحدالـ greatest common divisor واحد اختار عددين
+
+255
+00:21:33,820 --> 00:21:41,060
+two composite numbers ستة و تمانتاش ال greatest
+
+256
+00:21:41,060 --> 00:21:49,660
+common divisor ستة صحيح
+
+257
+00:21:49,660 --> 00:21:54,020
+ال greatest common divisor بين الستة والتمانتاش
+
+258
+00:21:54,020 --> 00:21:58,760
+الستة تساوي اتنين في تلاتة التمانتاش
+
+259
+00:22:01,120 --> 00:22:06,040
+تساوي اتنين فى تسعة اللى هى تلاتة فى تلاتة وين
+
+260
+00:22:06,040 --> 00:22:09,260
+التقاضة بين رأيهم معناته اللى greatest common
+
+261
+00:22:09,260 --> 00:22:16,100
+divisor بين الستة والتمانتاش ستة ستاشتان وعشرين
+
+262
+00:22:16,100 --> 00:22:25,000
+ستاشتان
+
+263
+00:22:25,000 --> 00:22:30,720
+ايوا اتنين فى تمانيةتنين في أربعة، تنين في اتنين
+
+264
+00:22:30,720 --> 00:22:33,340
+والاتنين و اتنين و اتنين والاتنين والاتنين
+
+265
+00:22:33,340 --> 00:22:38,820
+والاتنين والاتنين والاتنين والاتنين والاتنين
+
+266
+00:22:38,820 --> 00:22:42,280
+والاتنين والاتنين والاتنين والاتنين والاتنين
+
+267
+00:22:42,280 --> 00:22:42,440
+والاتنين والاتنين والاتنين والاتنين والاتنين
+
+268
+00:22:42,440 --> 00:22:42,480
+والاتنين والاتنين والاتنين والاتنين والاتنين
+
+269
+00:22:42,480 --> 00:22:42,620
+والاتنين والاتنين والاتنين والاتنين والاتنين
+
+270
+00:22:42,620 --> 00:22:42,780
+والاتنين والاتنين والاتنين والاتنين والاتنين
+
+271
+00:22:42,780 --> 00:22:42,800
+والاتنين والاتنين والاتنين والاتنين والاتنين
+
+272
+00:22:42,800 --> 00:22:42,800
+والاتنين والاتنين والاتنين والاتنين والاتنين
+
+273
+00:22:42,800 --> 00:22:42,800
+والاتنين والاتنين والاتنين والاتنين والاتنين
+
+274
+00:22:42,800 --> 00:22:54,540
+والاتنين والات
+
+275
+00:22:56,980 --> 00:23:03,540
+نفس الفكرة وليش هيفرج معاك تحللهم جسم اتنين لاحظوا
+
+276
+00:23:03,540 --> 00:23:08,560
+انه ممكن انت عشان تختصر تكتب قصص مافيش لديك مشكلة
+
+277
+00:23:08,560 --> 00:23:13,140
+في الموضوع لكن كل ما فرضتها بيكون أسهل لك ايش عشان
+
+278
+00:23:13,140 --> 00:23:17,280
+تضمن العناصر اللي موجودة عندك الان هادر التقاطة
+
+279
+00:23:17,280 --> 00:23:23,240
+وين موجودة يا شباب هاي التقاطة تلاتة
+
+280
+00:23:23,240 --> 00:23:27,930
+واحدةو سبعة و سبعة معناته اتنين وس اتنين ضرب ثلاثة
+
+281
+00:23:27,930 --> 00:23:31,850
+ضرب سبعة هو اللي جال اس common divisor ليه اربع و
+
+282
+00:23:31,850 --> 00:23:36,950
+عشرين في سبعة تمام؟
+
+283
+00:23:36,950 --> 00:23:41,990
+الان لو كان في عندي رقمين زي ما قلت انت قبل شوية
+
+284
+00:23:41,990 --> 00:23:49,350
+تلتاش و اربعة و عشرين تلتاش و اربعة و عشرين1 prime
+
+285
+00:23:49,350 --> 00:23:53,890
+او 1 لا او بين جثين اي عددين غير اولين طبعا ال a
+
+286
+00:23:53,890 --> 00:23:56,110
+لو قلت لك ال greatest common divisor بين اي two
+
+287
+00:23:56,110 --> 00:24:01,110
+primes واحد ال greatest common divisor بين اي
+
+288
+00:24:01,110 --> 00:24:06,710
+prime او اي composite برضه واحد مصبوط الا لو كان
+
+289
+00:24:06,710 --> 00:24:12,350
+قلت لك ال greatest common divisor ما بين التلاتة
+
+290
+00:24:12,350 --> 00:24:13,770
+و33
+
+291
+00:24:17,940 --> 00:24:22,100
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+292
+00:24:22,100 --> 00:24:23,240
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+293
+00:24:23,240 --> 00:24:26,700
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+294
+00:24:26,700 --> 00:24:28,400
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+295
+00:24:28,400 --> 00:24:31,660
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+296
+00:24:31,660 --> 00:24:33,140
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+297
+00:24:33,140 --> 00:24:36,220
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+298
+00:24:38,570 --> 00:24:43,050
+بتتمتع بشكل كويس وما تستعجلش two primes مع بعض ال
+
+299
+00:24:43,050 --> 00:24:46,050
+greatest common divisor بينهم واحد مش هتلاجح اعمل
+
+300
+00:24:46,050 --> 00:24:50,070
+اشتراك لغير القسم اشتراك لغير الواحد لان هناك بعض
+
+301
+00:24:50,070 --> 00:24:54,190
+الاعداد علاقتهم مع بعضهم زي ال prime مع بعضهم
+
+302
+00:24:54,190 --> 00:24:57,850
+relatively prime بنسميهم يعني لو احنا أخدنا ال 15
+
+303
+00:24:57,850 --> 00:25:03,570
+composite صح؟ و أخدنا ال 18 او بلاش ال 16
+
+304
+00:25:03,570 --> 00:25:07,930
+composite ال greatest common divisor بينهم جد ايش؟
+
+305
+00:25:09,420 --> 00:25:13,940
+الـ 16 و 15 الـ greatest common divisor بينهم واحد
+
+306
+00:25:13,940 --> 00:25:18,940
+تعالى أورجيك ال greatest .. ال greatest common
+
+307
+00:25:18,940 --> 00:25:24,140
+divisor ما بين الخمستاش و الستاش عشان الكلام اللي
+
+308
+00:25:24,140 --> 00:25:30,320
+قبل ما قلتها خمستاش بتساوي تلاتة في خمسة و ستاش
+
+309
+00:25:30,320 --> 00:25:38,140
+اتنين في اتنين في اتنين في اتنينالان التقاط بين
+
+310
+00:25:38,140 --> 00:25:42,940
+الأمير موجود في الواحد وبالتالي greatest common
+
+311
+00:25:42,940 --> 00:25:47,040
+divisor بينهم واحد بيقول عن الخمساش والستاش
+
+312
+00:25:47,040 --> 00:25:54,420
+relatively primes علاقتهم مع بعض زي علاقة ال two
+
+313
+00:25:54,420 --> 00:25:58,500
+primes
+
+314
+00:25:58,500 --> 00:26:01,460
+مع بعض ال greatest common divisor يسوى واحد
+
+315
+00:26:05,750 --> 00:26:14,110
+لو أتينا على سبيل المثال بقولنا الخمستاشه و ستاشه
+
+316
+00:26:14,110 --> 00:26:21,050
+و .. و عشرين .. و عشرين .. في عندك الأربع لأ ستة و
+
+317
+00:26:21,050 --> 00:26:27,590
+عشرين فيه حتكون اتنين لأ مش هتظبط عشرة سبعتاش واحد
+
+318
+00:26:27,590 --> 00:26:32,150
+و عشرين اه لازم يكون في هذا ال number prime لأنه
+
+319
+00:26:32,150 --> 00:26:33,570
+كان في عندي تلت أعداد زي هذه
+
+320
+00:26:37,310 --> 00:26:42,150
+تمام؟ ايش بنقول احنا عنهم؟ Relatively Primes الان
+
+321
+00:26:42,150 --> 00:26:45,970
+عشرة و سبعتاش عشرة و واحد و عشرين و سبعتاش و واحد
+
+322
+00:26:45,970 --> 00:26:50,890
+و عشرين تنساش انه هادى عدد اولى الان هدول واحد
+
+323
+00:26:50,890 --> 00:26:53,890
+اولى واحد فردي و واحد زوجي طبيعى الفرق بينهم او ال
+
+324
+00:26:53,890 --> 00:26:57,310
+Greatest common divisor هيكون واحد و عشرين و
+
+325
+00:26:57,310 --> 00:27:01,530
+سبعتاش واحد و عشرين و عشرة نفس الكلام الان لو انا
+
+326
+00:27:01,530 --> 00:27:07,000
+جيت مثلاهذول مع بعض ماقدرش أقرنهم كلهم مع بعضهم
+
+327
+00:27:07,000 --> 00:27:11,180
+فإيش بروح باخدهم؟ اتنين اتنين فبقول عنهم pairwise
+
+328
+00:27:11,180 --> 00:27:15,940
+يعني لما أخدتوا كل اتنين مع بعض علقتهم relatively
+
+329
+00:27:15,940 --> 00:27:18,920
+primes لكن تعشوا في عشرة سبعتين عشر اتنين وعشرين
+
+330
+00:27:18,920 --> 00:27:23,620
+ماقدرش أقول عنهم pairwise relatively prime يعني
+
+331
+00:27:23,620 --> 00:27:28,860
+pair يعني اتنين10 و 17 relatively prime 17 و 22
+
+332
+00:27:28,860 --> 00:27:33,100
+relatively prime لكن 10 و 22 لأ ال greatest common
+
+333
+00:27:33,100 --> 00:27:36,660
+divisor اتنين فبقدرش اقول عليهم relatively primes
+
+334
+00:27:36,660 --> 00:27:39,440
+مش كتير مهمة المعلومة هذه لكن في الآخر لو قلت
+
+335
+00:27:39,440 --> 00:27:42,820
+بتكلم على مجموعة أعداد طيب بدنا ننتقل في موضوع
+
+336
+00:27:42,820 --> 00:27:48,640
+التحليل نفسه لل least common multiple لما بتكلم
+
+337
+00:27:48,640 --> 00:27:55,250
+على ال least common multiple بتكلم انا علىأصغر أدد
+
+338
+00:27:55,250 --> 00:28:01,230
+.. أصغر أدد يقبل القسمة على الرقمين المقياد إليك
+
+339
+00:28:01,230 --> 00:28:04,450
+عكس تماما .. هكونت بس أرجع بشوي على الجريم ..
+
+340
+00:28:04,450 --> 00:28:09,250
+greatest common divisor أكبر قرص مشترك .. اللي أنا
+
+341
+00:28:09,250 --> 00:28:13,830
+جاعة بدور على أقل مضاعف مشترك ال least common
+
+342
+00:28:13,830 --> 00:28:17,370
+multiple نرجع للأمثلة .. إيش أول مثال كتبناه احنا؟
+
+343
+00:28:18,180 --> 00:28:21,260
+الـ greatest common divisor ولا حد بكتب ورايا مش
+
+344
+00:28:21,260 --> 00:28:24,440
+مشكلة بنشوف الأمثلة اللي موجودة عندها تمانتاش و
+
+345
+00:28:24,440 --> 00:28:29,900
+كداش؟ تمانتاش و خمستاش؟ لكن ال greatest أو ال
+
+346
+00:28:29,900 --> 00:28:36,780
+least common multiple بين الخمستاش والتمانتاش الآن
+
+347
+00:28:36,780 --> 00:28:42,980
+بدك اتحلل تكمبز ال number بنفس الفكرة خمستاش بده
+
+348
+00:28:42,980 --> 00:28:47,240
+تساوي تلاتة في خمسة تمانتاش
+
+349
+00:28:50,190 --> 00:28:58,130
+اتنين في تسعة تلاتة في تلاتة ال least common
+
+350
+00:28:58,130 --> 00:29:02,250
+multiple يساوي الاتحاد ما بين المجموعتين هدول
+
+351
+00:29:02,250 --> 00:29:10,070
+اتحاد المجموعتين ايش اتحادهم؟ اتنين في تلاتة في
+
+352
+00:29:10,070 --> 00:29:17,450
+تلاتة في خمسةيعني الآن بدك تروح .. بدك تروح تلغي
+
+353
+00:29:17,450 --> 00:29:21,390
+التقابع ما بين التنتين و تحتفظ بالباقية تضربوا كله
+
+354
+00:29:21,390 --> 00:29:25,430
+في بعض هدى و هدى بتقابع في اين؟ في تلاتة فبدك تلغي
+
+355
+00:29:25,430 --> 00:29:29,630
+واحدة من التلاتات هدول خلاص واحدة فبتصير عندك
+
+356
+00:29:29,630 --> 00:29:35,090
+اتنين في تلاتة في تلاتة في خمسة لان الصفر عندك
+
+357
+00:29:35,090 --> 00:29:40,710
+تلاتينحذفتي ايش؟ في الاتحاد انت بتحذف التنتين ولا
+
+358
+00:29:40,710 --> 00:29:45,830
+بتحذف واحدة؟ خلاص ان ده هي التلاتة من هذه الاصل في
+
+359
+00:29:45,830 --> 00:29:49,710
+الاتحاد ان انا بجمع كل العناصر صح؟ والأنصر المكرر
+
+360
+00:29:49,710 --> 00:29:53,990
+انا مابديش هي بستغني أنصر واحدة منه فانا اجيت
+
+361
+00:29:53,990 --> 00:29:59,650
+التلاتة هذه المكررة اه مكررة لغيت صورة تان اخد
+
+362
+00:29:59,650 --> 00:30:04,450
+كتابي يعني انا اجيت كتابة انا كتال يساوي تلاتة ضرب
+
+363
+00:30:04,450 --> 00:30:09,700
+خمسةبارد التلاتة الموجودة سابقا او لا بارد التلاتة
+
+364
+00:30:09,700 --> 00:30:13,000
+الموجودة سابقا او موجودة مابديش اياها فادي لغاية
+
+365
+00:30:13,000 --> 00:30:16,940
+اجبال هذى بل في عند ميه في الآخر بارد تلاتة فانا
+
+366
+00:30:16,940 --> 00:30:21,280
+روحت كنت مرتبهم مباشرة اتنين في تلاتة في تلاتة في
+
+367
+00:30:21,280 --> 00:30:28,500
+خمسة الان اصغر عدد يقبل القسم على التنين مع بعض هو
+
+368
+00:30:28,500 --> 00:30:36,840
+عبارة عن العدد هذا تمنتعش في خمسة تسعينأصغر عدد
+
+369
+00:30:36,840 --> 00:30:41,380
+يقبل القسم على الخمستاش ويقبل القسم على التمنتاش
+
+370
+00:30:41,380 --> 00:30:48,520
+هو عمارة عن تسعين طيب
+
+371
+00:30:48,520 --> 00:30:53,740
+ناخد كمان مثال ناخد
+
+372
+00:30:53,740 --> 00:31:01,060
+الستاش وسبعة أو بلاء ستاش واربع وعشرين ستاش اربع
+
+373
+00:31:01,060 --> 00:31:08,610
+وعشريناللي بدي ال least common multiple ل 16 و 24
+
+374
+00:31:08,610 --> 00:31:15,590
+16 2x2x2x2
+
+375
+00:31:15,590 --> 00:31:27,110
+بصبوط 24 ايش تساوي 2x12 2x2x2x3
+
+376
+00:31:27,110 --> 00:31:31,010
+2x2x2x3
+
+377
+00:31:31,300 --> 00:31:34,920
+في تلاتة يمكن تكون الأساس هنا في الاتحاد أسهل لك
+
+378
+00:31:34,920 --> 00:31:42,740
+لأنش عندي هان اتنين أقصى أربعة اربعة اربعة هان
+
+379
+00:31:42,740 --> 00:31:51,060
+اتنين أقصى تلاتة برب تلاتة تمام اتحادهم
+
+380
+00:32:00,440 --> 00:32:07,060
+16 في 3 ليش؟ ليش؟ لأن هذه اتنين أس ثلاثة هي عبارة
+
+381
+00:32:07,060 --> 00:32:11,380
+اتنين أس أربعة تتساوي اتنين أس ثلاثة ضرب اتنين
+
+382
+00:32:11,380 --> 00:32:17,820
+وهذه اتنين أس ثلاثة ضرب شكل انا غلطت غير انا؟ اه
+
+383
+00:32:17,820 --> 00:32:22,300
+غلطت تفهم؟ الآن حاجة تساوي لا ماغلطتش
+
+384
+00:32:26,680 --> 00:32:29,680
+تنقص اربعة المفروض اه تنقص اربعة صح الان تساوي
+
+385
+00:32:29,680 --> 00:32:35,040
+الان حطيه واحدة من الاتنين اتنين هدول بس بتصير
+
+386
+00:32:35,040 --> 00:32:39,660
+تلاتة اتنين اص تلاتة ضرب اتنين ضرب تلاتة ليه اتنين
+
+387
+00:32:39,660 --> 00:32:46,780
+اقص اربعة ضرب تلاتة ستناشف تلاتة تمام يا شباب هاي
+
+388
+00:32:46,780 --> 00:32:52,440
+بالمثال اللي احنا شفناه سابقا كيف؟
+
+389
+00:32:54,310 --> 00:32:58,410
+أه طبيعي لازم .. مو انت بتدور على عدد بدي يقبل
+
+390
+00:32:58,410 --> 00:33:02,290
+الجسم على التنين هدول فلازم يكون أكبر منهم فلازم
+
+391
+00:33:02,290 --> 00:33:07,530
+يكون أكبر منهم أو يسوى على الأقل أكبر واحد فيهم
+
+392
+00:33:07,530 --> 00:33:11,370
+يعني لو أنا دي قلتلك بدي ال least common multiple
+
+393
+00:33:11,370 --> 00:33:17,790
+ما بين الستة والتمنتاش ستة و تمانتاش اش هتقول ايه؟
+
+394
+00:33:17,790 --> 00:33:24,340
+الستة تساوي اتنين في تلاتة تمانتاشتنين في تلاتة في
+
+395
+00:33:24,340 --> 00:33:30,880
+تلاتة اعمل اتحاد بينهم تلاتة
+
+396
+00:33:30,880 --> 00:33:37,640
+في تلاتة في تلاتة اعمل اتحاد بينهم تلاتة في تلاتة
+
+397
+00:33:37,640 --> 00:33:39,560
+في تلاتة اعمل اتحاد بينهم تلاتة في تلاتة في تلاتة
+
+398
+00:33:39,560 --> 00:33:41,900
+في تلاتة في تلاتة في تلاتة في تلاتة في تلاتة في
+
+399
+00:33:41,900 --> 00:33:41,900
+تلاتة في تلاتة في تلاتة في تلاتة في تلاتة في تلاتة
+
+400
+00:33:41,900 --> 00:33:42,080
+في تلاتة في تلاتة في تلاتة في تلاتة في تلاتة في
+
+401
+00:33:42,080 --> 00:33:42,340
+تلاتة في تلاتة في تلاتة في تلاتة في تلاتة في تلاتة
+
+402
+00:33:42,340 --> 00:33:44,440
+في تلاتة في تلاتة في تلاتة في تلاتة في تلاتة في
+
+403
+00:33:44,440 --> 00:33:50,020
+تلاتة في تلأن الاصل أنه يقبل القسمة على الاتنين
+
+404
+00:33:50,020 --> 00:33:56,860
+هدول و بعد ذول يكون عبارة عن divisors خلص
+
+405
+00:33:56,860 --> 00:33:59,940
+ال section اللي له علاقة بالـprimes و greatest
+
+406
+00:33:59,940 --> 00:34:03,380
+common divisor و least common multiple سهل مافيش
+
+407
+00:34:03,380 --> 00:34:07,280
+فيه أي مشكلة ال section اللي بعده بتكلم عن
+
+408
+00:34:07,280 --> 00:34:13,780
+كريبتوغرافي تشفير البيانات لطيف
+
+409
+00:34:16,610 --> 00:34:20,910
+لأ لطيف لطيف ماتقلقاش سهل اعتمادنا الكل فيه هيكون
+
+410
+00:34:20,910 --> 00:34:24,930
+على باق القسمة اعتمادنا الكل فيه هيكون على باق
+
+411
+00:34:24,930 --> 00:34:29,630
+القسمة بالمناسبة هذا عبارة عن تطبيق للموديلوس عن
+
+412
+00:34:29,630 --> 00:34:34,630
+تطبيق للموديلوس الان في ال cryptology اللي هو علم
+
+413
+00:34:34,630 --> 00:34:42,260
+التشفير شباب عندي تخصصينأو عندي two trends ال
+
+414
+00:34:42,260 --> 00:34:44,540
+trend الأول ال cryptography اللي احنا بدنا ندرسه
+
+415
+00:34:44,540 --> 00:34:50,200
+اليوم هو اخفاء النص في نص اخر يعني انا بدي اشفر
+
+416
+00:34:50,200 --> 00:34:52,800
+النص اخفيه و يظهر نص مختلفة و في عندي
+
+417
+00:34:52,800 --> 00:34:55,940
+Steganography اللي انا من خلاله باخف النص في داخل
+
+418
+00:34:55,940 --> 00:35:00,320
+الصورة كيف تاخف النص في داخل الصورة؟ كلكم بتعرفوا
+
+419
+00:35:00,320 --> 00:35:07,320
+ان الصورة هي عبارة عن مصفوفة من ال pixels للأ و
+
+420
+00:35:07,320 --> 00:35:17,050
+أبسطتركيبة لكل Pixel يمسك في اللوانة ايش بتطلع؟ كل
+
+421
+00:35:17,050 --> 00:35:26,290
+Pixel انتهان عبارة عن مركبة من تلت ألوان RGB أقل
+
+422
+00:35:26,290 --> 00:35:29,790
+شيء ومابديش اتكلم لا على ال alpha ولا على ال
+
+423
+00:35:29,790 --> 00:35:32,390
+transparency ولا على اش تاني بس بتكلم على أبسط
+
+424
+00:35:32,390 --> 00:35:37,530
+مركبة مركبة اللون ال RGBوهذا في الآخر هو عبارة عن
+
+425
+00:35:37,530 --> 00:35:42,390
+رقم مثل اللون اللي في كل خلية فكرة Steganography
+
+426
+00:35:42,390 --> 00:35:48,630
+أن أحول النص لأرقام
+
+427
+00:35:48,630 --> 00:35:53,070
+و أضيف الأرقام هذه على قيم الألوان اللي موجودة
+
+428
+00:35:53,070 --> 00:35:57,430
+عندها الآن القيم تبع الألوان في كل خلية تتراوح من
+
+429
+00:35:57,430 --> 00:36:05,630
+صفرلـ 255 يعني لما تكون هذه 255 و هذه صغيرة و هذه
+
+430
+00:36:05,630 --> 00:36:10,170
+صغيرة بيكون اللون أحمر تماما و يبدأ يبدل نفس
+
+431
+00:36:10,170 --> 00:36:14,110
+الكافية لما تبدأ تغير بالتدريج بتبدأ تحصل على
+
+432
+00:36:14,110 --> 00:36:19,990
+الألوان التانية اللي احناهذه الألوان الرئيسية اللي
+
+433
+00:36:19,990 --> 00:36:24,870
+عندي فكرتها بكل بساطة على سبيل المثال ال a small
+
+434
+00:36:24,870 --> 00:36:30,230
+قمتها في ال ask ازن 96 او 97 مش فاكر و ال a small
+
+435
+00:36:30,230 --> 00:36:31,650
+64
+
+436
+00:36:35,170 --> 00:36:38,750
+لأ صح ال a small أصغر قيمتها بال ask أكبر من ال a
+
+437
+00:36:38,750 --> 00:36:42,810
+capital مش قضية الفرق بينهم اتنين و تلاتين تمام؟
+
+438
+00:36:42,810 --> 00:36:46,850
+الأمر المهم بتجي لكل كلمة بتاخد character
+
+439
+00:36:46,850 --> 00:36:51,150
+character character و بتجيب ال value بتجيب ال
+
+440
+00:36:51,150 --> 00:36:55,150
+value تبعتها و بتروح تضيفها ع مين؟على قيمة اللون
+
+441
+00:36:55,150 --> 00:36:59,310
+الاصل الاصل ان الصورة هتتغير معالمها شوية لكن
+
+442
+00:36:59,310 --> 00:37:02,710
+هتظلم حافظة على الصورة يعني ممكن تحسها باهتة تحسها
+
+443
+00:37:02,710 --> 00:37:08,070
+مشوشة بس في الآخر اذا انت مش .. مش عارف ايش فيها
+
+444
+00:37:08,070 --> 00:37:10,610
+data خلاص مش هتفكر .. مش هتفكر اللي بقولها و أساسا
+
+445
+00:37:10,610 --> 00:37:14,350
+لو عرفت كمان ايش القيمة اللي انضافت وانضافت على اي
+
+446
+00:37:14,350 --> 00:37:18,010
+واحدة فيهم ولا انضافت على التلاتة انضافت كله ولا
+
+447
+00:37:18,010 --> 00:37:21,930
+خدفنا ال modulus هاي الشغل كان مختلف تماما احنا
+
+448
+00:37:21,930 --> 00:37:27,570
+هنشتغل على الأبسطاللي هي الـ hide text as text كيف
+
+449
+00:37:27,570 --> 00:37:33,630
+تخب النص بنص آخر هيتبدل النص بنص مختلف الفكرة فيه
+
+450
+00:37:33,630 --> 00:37:38,840
+كانت بسيطة ومنشأها بقول لما كان القيصروعنده الجيش
+
+451
+00:37:38,840 --> 00:37:42,620
+برا وحشعر انه في انقلابات كان يحاول يبعت للجيش انه
+
+452
+00:37:42,620 --> 00:37:47,500
+ارجع لل .. للحصن او ارجع للدولة لروما ماكنتش يصل
+
+453
+00:37:47,500 --> 00:37:51,000
+الرسالة او اذا كانت تصل كانت تصل بمعاني مختلفة
+
+454
+00:37:51,000 --> 00:37:53,960
+تمام اللي كان بدوياها فعرف انه في خاين في الموضوع
+
+455
+00:37:53,960 --> 00:38:00,320
+فقرر انه يعتمد يكتب الرسالة بشكل مخفي تشفير ايش
+
+456
+00:38:00,320 --> 00:38:05,780
+يعني تشفير كريبتوجرافي انه اكتب نصالمعنى ماحدش
+
+457
+00:38:05,780 --> 00:38:09,540
+يعرفه غير المرسل والمستقبل .. جملة اتفاقية عشان
+
+458
+00:38:09,540 --> 00:38:15,560
+يعرف يرجع الناس لأصله فكرت الفكرة أنه يعتمد على
+
+459
+00:38:15,560 --> 00:38:18,940
+باقي القسمة .. باقي القسمة يا شباب .. كم character
+
+460
+00:38:18,940 --> 00:38:23,800
+عندي بالأجهزة الإنجليزية أنا؟26 .. 26 character
+
+461
+00:38:23,800 --> 00:38:29,720
+تمام؟ الان باخد ال character ل plain text و بضيفه
+
+462
+00:38:29,720 --> 00:38:33,440
+key ال key هي عبارة عن مقدار ال shift اللي بده
+
+463
+00:38:33,440 --> 00:38:39,860
+يصير على الدائرة اللي موجودة عندها يعني الان لو
+
+464
+00:38:39,860 --> 00:38:43,180
+انا بدي ألغي الصورة بس هذه هيك شوية و اروح اعمل
+
+465
+00:38:43,180 --> 00:38:51,310
+rotate لهذه لأ بديش لهذه كلها ل ..برضه لم اكلمها
+
+466
+00:38:51,310 --> 00:39:02,750
+مرة لأ بتلف لحالها ايوة باللي
+
+467
+00:39:02,750 --> 00:39:07,610
+انا عملته انا باللفة هذه عملت شغله بسيطه جدا قولت
+
+468
+00:39:07,610 --> 00:39:11,930
+كل character بدي استبدله او ال key مقدار ال key
+
+469
+00:39:11,930 --> 00:39:17,410
+تبعتي اتنين كل ال key تبعتي اتنين يعني تخيل ان انا
+
+470
+00:39:17,410 --> 00:39:26,220
+صرت بدي ادور على كلمةWar Book كتاب الحرب مثلا ايش
+
+471
+00:39:26,220 --> 00:39:31,060
+الفكرة لاحظ ان حسب اللي انا سويته هنا ان كل حرف
+
+472
+00:39:31,060 --> 00:39:37,440
+قدم خطوطين يعني ال a بدي نعمله replacement بال c و
+
+473
+00:39:37,440 --> 00:39:41,340
+هكذا يعني مقدار ال key تبعت ايه اتنين تعالى نشوف
+
+474
+00:39:41,340 --> 00:39:45,310
+في جدوة اخرلو هذا بيحمل معاد الحروف يعني ال key
+
+475
+00:39:45,310 --> 00:39:51,530
+صارت قيمة اتنين ال W ايش غمتها؟ ايش غمتها؟ تلاتة و
+
+476
+00:39:51,530 --> 00:39:57,490
+عشرين هاي ال W زاد اتنين خمسة و عشرين مصبوط؟ خمسة
+
+477
+00:39:57,490 --> 00:40:00,010
+و عشرين اه okay مش هتظبط بس خليني اغير ال key كمان
+
+478
+00:40:00,010 --> 00:40:03,570
+شوية عشان اوريك ايش فاتت باقى القسمة بس بدي ازيد
+
+479
+00:40:03,570 --> 00:40:08,020
+ال key بدل التنين تصيب خمسةتمام؟ تلاتة و عشرين
+
+480
+00:40:08,020 --> 00:40:14,240
+زيادة خمسة تمانية و عشرين تمانية و عشرين مض مض
+
+481
+00:40:14,240 --> 00:40:21,180
+الستة و عشرين جانش هتطلع اتنين جانش هتديني بي
+
+482
+00:40:21,180 --> 00:40:34,100
+تمام؟ ال a ال a واحد زيادة خمسة ستة اف الآن
+
+483
+00:40:35,580 --> 00:40:44,160
+الـ R تمنتعش و خمسة تلاتة و عشرين ال
+
+484
+00:40:44,160 --> 00:40:54,080
+B دين و خمسة سبعة ال O خمستاشر
+
+485
+00:40:54,080 --> 00:41:06,810
+و خمسة عشرين ال K حداشر و خمسة ستة عشر Pكتبت
+
+486
+00:41:06,810 --> 00:41:13,790
+الرسالة بالشكل اللي موجود عندي هنا فالان لما مسيك
+
+487
+00:41:13,790 --> 00:41:19,330
+ال .. ال .. ال intruder اللي في الطريق هذا طلع في
+
+488
+00:41:19,330 --> 00:41:24,230
+الرسالة قال ان هذا ليه الملك مكتوبة بلغة لكن اللغة
+
+489
+00:41:24,230 --> 00:41:30,070
+مش مفهومة لأن مين اللي بيفهمها اللي بيعرف ال key
+
+490
+00:41:30,070 --> 00:41:34,110
+المستقبل اللي بيعرف ان هذا ال text بده يعمله عملي
+
+491
+00:41:34,110 --> 00:41:38,970
+ايشعكسية بدينا نعمله عملية عكسية ايش هي العملية
+
+492
+00:41:38,970 --> 00:41:43,950
+العكسية نفس الكلام بدك تطرح خمسة للمقار ال key بدك
+
+493
+00:41:43,950 --> 00:41:49,630
+تطرحه من قيمة ال character و تعمل مد على 26 مصبوط
+
+494
+00:41:49,630 --> 00:41:54,510
+فبتيجي الان بي .. يعني الان بدك تعمل عملية عكسية
+
+495
+00:41:54,510 --> 00:42:02,500
+الان ال cypher نطبص ال key مد ال 26هك هتصير P
+
+496
+00:42:02,500 --> 00:42:08,120
+اختصار ل plain text نص مجرد C اختصار لcipher text
+
+497
+00:42:08,120 --> 00:42:12,120
+اللي هو النص المشفر او المخفي الان P ايش قيمته يا
+
+498
+00:42:12,120 --> 00:42:17,260
+شباب؟ اتنين اتنين نقص خمسة اتنين نقص خمسة كده؟
+
+499
+00:42:17,260 --> 00:42:25,840
+سالب سالب ثلاثة تساوي شغل مضروبة في الست و عشرين
+
+500
+00:42:25,840 --> 00:42:28,440
+زائد ال remainder ال remainder لازم يبقى positive
+
+501
+00:42:30,870 --> 00:42:36,470
+فى سالب واحد او سالب تلاتة وعشرين مية فالمية هيك
+
+502
+00:42:36,470 --> 00:42:40,390
+مين التلاتة .. يعني ال reminder هيه بقى القسمة
+
+503
+00:42:40,390 --> 00:42:46,130
+مظبوط جديش تلاتة وعشرين البُك راحة لمين؟ راحة لل W
+
+504
+00:42:46,130 --> 00:42:49,810
+للتلاتة
+
+505
+00:42:49,810 --> 00:42:59,230
+وعشرين ال F ستة خدنا منها خمسة واحد ايه؟ال W تلاتة
+
+506
+00:42:59,230 --> 00:43:06,190
+و عشرين أخدنا منها خمسة تمانتاش ال G سبعة أخدنا
+
+507
+00:43:06,190 --> 00:43:12,630
+منها خمسة راحت للتنين T أشرين أخدنا منها خمسة
+
+508
+00:43:12,630 --> 00:43:19,890
+خمستاش P ستاش أخدنا منها خمسة راحت للحداش فرجعنا
+
+509
+00:43:19,890 --> 00:43:24,560
+بالكلمة ال book warواحد بيقول ليه في المحاضرة
+
+510
+00:43:24,560 --> 00:43:27,240
+السابقة طب ما هو يا دكتور لما بتكون الرسالة كبيرة
+
+511
+00:43:27,240 --> 00:43:29,780
+شوية و بتخلص الحرف قبل ما ترجمه الرسالة و أرجعها
+
+512
+00:43:29,780 --> 00:43:35,400
+لأصلها كانت الحلقات هذه او الدقابتين هذه هي
+
+513
+00:43:35,400 --> 00:43:39,040
+المفتاح ماكانش .. يعني هو الفكرة نعم انبنت عليها
+
+514
+00:43:39,040 --> 00:43:42,540
+من ناحية الريابويات بس التطبيق تبعها كان بالشكل
+
+515
+00:43:42,540 --> 00:43:46,280
+هذا خليني بس عشان أحركه لخمسة يعني ال ا جدش صارت
+
+516
+00:43:46,280 --> 00:43:50,840
+شباب جاب شوية خمسة يعني بتصير ستة مظبوط الست اللي
+
+517
+00:43:50,840 --> 00:43:51,860
+هي F
+
+518
+00:43:55,900 --> 00:44:01,220
+صح الكلام؟ shift
+
+519
+00:44:01,220 --> 00:44:06,900
+of خمسة لأ
+
+520
+00:44:06,900 --> 00:44:11,380
+في شغل خربطها شكلي لإن هدى book war .. war book ..
+
+521
+00:44:11,380 --> 00:44:15,500
+اه كان المفروض ألف اللى جوا anyway كان لازم أفكر
+
+522
+00:44:15,500 --> 00:44:19,760
+ألف اللى جوا مش ألف اللى براAnyway في الآخر ماكانش
+
+523
+00:44:19,760 --> 00:44:23,320
+هو بيعتمد على الحسبة بقاله هايه مقداري كيه خمسة
+
+524
+00:44:23,320 --> 00:44:28,080
+بلفه بصير إيش كل نص بياخد ال character المقابل له
+
+525
+00:44:28,080 --> 00:44:31,580
+بشكل سريع وبالتالي أنت بتحصل على النص يعني لو
+
+526
+00:44:31,580 --> 00:44:34,880
+بالوضع الحالي هاي ال key هاي ال .. الآن وقولنا لك
+
+527
+00:44:34,880 --> 00:44:40,820
+بدنا ناخد ال book war عندي هان مش احنا .. احنا
+
+528
+00:44:40,820 --> 00:44:50,190
+قولنا war book هاه هايها Wالـ A .. ال .. ال .. ال
+
+529
+00:44:50,190 --> 00:44:50,470
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+530
+00:44:50,470 --> 00:44:50,990
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+531
+00:44:50,990 --> 00:44:51,630
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+532
+00:44:51,630 --> 00:44:51,670
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+533
+00:44:51,670 --> 00:44:51,850
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+534
+00:44:51,850 --> 00:44:51,990
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+535
+00:44:51,990 --> 00:44:52,290
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+536
+00:44:52,290 --> 00:44:52,450
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+537
+00:44:52,450 --> 00:44:53,470
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+538
+00:44:53,470 --> 00:44:54,790
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+539
+00:44:54,790 --> 00:44:54,790
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+540
+00:44:54,790 --> 00:44:59,990
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+541
+00:44:59,990 --> 00:45:16,810
+.. ال .. ال .. ال .. ال .. ال ..
+
+542
+00:45:21,290 --> 00:45:25,470
+مع ال B ففعليا استخدامك للعجلة هاي او للقرصير هذول
+
+543
+00:45:25,470 --> 00:45:29,950
+اسهل من ان يعتمد على النص اللى موجود ففعليا لو
+
+544
+00:45:29,950 --> 00:45:33,970
+دورت على ال .. على ال net او على الجوجل في ال
+
+545
+00:45:33,970 --> 00:45:39,080
+images وقلتله القيصرسافر كي كانت موجودة .. لأ 26
+
+546
+00:45:39,080 --> 00:45:43,080
+character نفسها و الحلقة أو الدائرة اللي في الوسط
+
+547
+00:45:43,080 --> 00:45:47,340
+هذه عليها ايش؟ عليها قابض بسيط عشان تقدر يلف و
+
+548
+00:45:47,340 --> 00:45:51,100
+بالتالي عملية التشويح هتكون ايش؟ أسرع ما ان احنا
+
+549
+00:45:51,100 --> 00:45:54,160
+بنجد .. زي ما كنا نحسن قبل شوية لكن فكرة فكرتها
+
+550
+00:45:54,160 --> 00:45:59,500
+فكرة حساب و مو the last 100% تمام طيب لكن الفكرة
+
+551
+00:45:59,500 --> 00:46:05,100
+هذه يا شباب ان العملية هذه قابلة للكسرماذا يعني
+
+552
+00:46:05,100 --> 00:46:09,280
+قابل الكسر؟ يعني انا ممكن مجرب مرة و اتنين و تلاتة
+
+553
+00:46:09,280 --> 00:46:15,560
+بصل ال K و خصوصا اذا عرفنا ان في بعض الكلمات هي ال
+
+554
+00:46:15,560 --> 00:46:20,440
+most frequent مثل أكثر حرف بتكرر في الكلمات في
+
+555
+00:46:20,440 --> 00:46:26,180
+الأبجدية الإنجليزية حرف ال E و أكثر كلمة ممكن
+
+556
+00:46:26,180 --> 00:46:27,300
+تتكرر The
+
+557
+00:46:32,560 --> 00:46:39,460
+ماذا سيفعل؟ سيبحث عن كلمات من ثلاث حروف و أكثر تلت
+
+558
+00:46:39,460 --> 00:46:45,360
+حروف تكرره يفترض أن هذا هو ذات و يأخذ الحرف الأخير
+
+559
+00:46:45,360 --> 00:46:50,100
+الـ E و يبحث عن كلمة بيساوي و يرجّه لأصله و بناء
+
+560
+00:46:50,100 --> 00:46:56,440
+على ال key اللي يحصل عليه يصبح حلها حلها طبعا طول
+
+561
+00:46:56,440 --> 00:46:58,860
+عمرنا بدأنا من انهم اتعلمنا security هم اتعلمنا
+
+562
+00:46:58,860 --> 00:47:05,210
+كتالةفي حرب مشتعلة ما بين الـ Intruder و الـ
+
+563
+00:47:05,210 --> 00:47:10,490
+Defender بين المهاجم و المدافع و كل ما المدافع
+
+564
+00:47:10,490 --> 00:47:13,070
+بيبتكر خيطة جديدة و فكرة جديدة المهاجم بيدور عليه
+
+565
+00:47:13,070 --> 00:47:20,490
+اعلق و بناء على هيك في حرب متزايدةالناس اللي بتشغل
+
+566
+00:47:20,490 --> 00:47:22,790
+في ال defender او في الدفاع ايش جالت؟ جالت okay
+
+567
+00:47:22,790 --> 00:47:27,010
+ماشي الحل اول خطوة رقم واحد بدنا نشيل ال spaces او
+
+568
+00:47:27,010 --> 00:47:30,750
+بلاش اول ما بدوا يفكروا بطلنا نعتمد بس على ال key
+
+569
+00:47:30,750 --> 00:47:34,350
+لحالها بدنا نروح الكلمة نجصها من النص و نعملها
+
+570
+00:47:34,350 --> 00:47:40,430
+shuffling يعني مثلا كلمة book هذه تمام؟ اروح اجصها
+
+571
+00:47:40,430 --> 00:47:46,370
+من النص تصير OKOKBO تمام؟ و بعدين اطبق عليها ال
+
+572
+00:47:46,370 --> 00:47:51,840
+key تبعتهفهو لما طبق عليها ال key برضه حصل علي
+
+573
+00:47:51,840 --> 00:47:56,400
+كلمة مالهاش معنى وبالتالي لازم يجيب يعرف انها جسمت
+
+574
+00:47:56,400 --> 00:47:58,760
+لكم كم character واش الترتيب عشان يقدر يردها
+
+575
+00:47:58,760 --> 00:48:03,680
+لاصلها واحد تاني يفكر جالك يوكيه يعني هو اعتمد على
+
+576
+00:48:03,680 --> 00:48:06,740
+حرف ايه عشان يجيب ال key جبل ما انا اروح اجسم
+
+577
+00:48:06,740 --> 00:48:10,120
+الكلمات هذه خصوصا انه ممكن اجع في مشكلة مع الكلمات
+
+578
+00:48:10,120 --> 00:48:13,960
+اللي من تلات حروف ومن الحرق وكالاخره بدي اروح اشيل
+
+579
+00:48:13,960 --> 00:48:20,660
+spacesشانلي سميس كانت كل نص كلمه واحدة حروف ملازقة
+
+580
+00:48:20,660 --> 00:48:24,020
+مع بعض بطل يقدر يخمن وين الدا عشان يدور على ال
+
+581
+00:48:24,020 --> 00:48:28,200
+most frequent ومش بس فكرة حساوية جالك بدي أخد كل
+
+582
+00:48:28,200 --> 00:48:32,540
+أربعة digit أعتبرهم one block وأجسمهم من النص
+
+583
+00:48:32,540 --> 00:48:37,560
+وابدلهم فانت تخيل حجم التعقيد اللي صار لكن انا
+
+584
+00:48:37,560 --> 00:48:42,610
+بقول برضه العملية برضه بتظل قابلةللكسر خصوصا انه
+
+585
+00:48:42,610 --> 00:48:48,730
+زي ما قولنا تقوم السعر وسريع ما بين الشغلات من
+
+586
+00:48:48,730 --> 00:48:53,450
+اكثر ال algorithm شهرة الاعتمدت على ال modulus و
+
+587
+00:48:53,450 --> 00:49:01,450
+الprimes ال algorithm اسمه RSA RSA اختصار لاسماء
+
+588
+00:49:01,450 --> 00:49:06,730
+او اسم الثاني من المجموعة من اليهود ال algorithm
+
+589
+00:49:06,730 --> 00:49:13,050
+اخد فكرتهمن باق القسمة جالك بكل بساطة انت بتاخد
+
+590
+00:49:13,050 --> 00:49:17,030
+ايه ال character الان اللي هي ال message تبعتك ال
+
+591
+00:49:17,030 --> 00:49:23,270
+plain text و بترفعها لقص a يعني بتاخد حرف ال a
+
+592
+00:49:23,270 --> 00:49:28,230
+مثلا و بترفع قيمته لقص كذا انا هو عمال اللي بدي
+
+593
+00:49:28,230 --> 00:49:33,150
+اعمل generate ل key بترفعها لقص a طب ايش ال a جالك
+
+594
+00:49:33,150 --> 00:49:38,780
+ال a هي عبارة عن حاصلأو عبارة عن رقم relatively
+
+595
+00:49:38,780 --> 00:49:44,980
+prime مع B ناقص واحد و Q ناقص واحد ايش ال Q و ال B
+
+596
+00:49:44,980 --> 00:49:50,920
+عبارة عن two biggie primes و N بتمثل حصل ضرب ال
+
+597
+00:49:50,920 --> 00:49:54,460
+primes هدول يعني هيك فكر كتالي راح أخد عددين
+
+598
+00:49:54,460 --> 00:49:58,780
+أوليات كبار و ليكن و ليكن أخد 13 و 17 على سبيل
+
+599
+00:49:58,780 --> 00:50:06,940
+المثال فراح ضربهم في بعض و حصل على ال N13 فى 17
+
+600
+00:50:06,940 --> 00:50:11,960
+جديش الشباب انا
+
+601
+00:50:11,960 --> 00:50:16,800
+ماعرفش ان انا غير اشتغل هيك سبعة و اتنين تسعة
+
+602
+00:50:16,800 --> 00:50:21,800
+تلاتة واحد واحد اتنين اتنين مائتين واحد وعشرين
+
+603
+00:50:21,800 --> 00:50:25,540
+فجالك ان المسألة اللى بدها تصير عندى ال character
+
+604
+00:50:25,540 --> 00:50:33,280
+ال M مط المائتين واحد وعشرين مرفوعة لقص جديش القص
+
+605
+00:50:33,280 --> 00:50:40,680
+أخد عبارة عن رقمrelatively prime لمن؟ علاقته ل
+
+606
+00:50:40,680 --> 00:50:45,720
+greatest common divisor واحد بين ال I ال E ومين ال
+
+607
+00:50:45,720 --> 00:50:51,400
+P نقص واحد اتناش ضرب ستاش اتناش في ستاش كده
+
+608
+00:50:51,400 --> 00:50:56,020
+الشباب؟
+
+609
+00:50:56,020 --> 00:51:01,960
+مية
+
+610
+00:51:01,960 --> 00:51:07,500
+اتنين وتسعينمية اتنين و تسعين يعني مية و واحد و
+
+611
+00:51:07,500 --> 00:51:11,860
+تسعين و مية و اتنين و تسعين relatively prime ولا
+
+612
+00:51:11,860 --> 00:51:16,700
+لأ relatively prime ال greatest common divisor
+
+613
+00:51:16,700 --> 00:51:21,320
+بينهم واحد فجالك انا بدي ارفع هذه للقص مية و واحد
+
+614
+00:51:21,320 --> 00:51:27,960
+و تسعين عشان احصل على character جديد
+
+615
+00:51:27,960 --> 00:51:34,770
+تيجي في المتحالةالفكرة وين؟ انا بدي اقولك ان هذا
+
+616
+00:51:34,770 --> 00:51:39,210
+ال algorithm ضال فترة طويلة تمام؟ و هم بتكلموا ال
+
+617
+00:51:39,210 --> 00:51:42,930
+algorithm هذا غير قابل للكسر بالمناسبة ال
+
+618
+00:51:42,930 --> 00:51:46,170
+algorithm هذا في ال .. في أواخر الستينات او اول
+
+619
+00:51:46,170 --> 00:51:50,410
+السبعينات اللي اتكلموا عليه اذا انا مش غلطان تمام؟
+
+620
+00:51:51,950 --> 00:51:58,110
+الفكرة كانت أن حصولك للـ key هذا كان شيء مستحيل و
+
+621
+00:51:58,110 --> 00:52:00,810
+أعتقد أنه كان في 2000 دراسة بتتكلم بالجول كتاري
+
+622
+00:52:00,810 --> 00:52:03,570
+عشان تكسر في 2000 بتتكلم على بنتهم الأديسة
+
+623
+00:52:03,570 --> 00:52:07,190
+بالمناسبة عشان تقدر تحصل على ال key أو تقدر تعمل
+
+624
+00:52:07,190 --> 00:52:10,830
+estimation لل two primes اللي هم ال b و ال key و
+
+625
+00:52:10,830 --> 00:52:17,280
+هدولبدك مليون سنة الكمبيوتر بقى شغال عشان تقدر تصل
+
+626
+00:52:17,280 --> 00:52:20,360
+ل ال keys الموجودة خصوصا لما اتكلم على براين مش ..
+
+627
+00:52:20,360 --> 00:52:23,880
+مش من two digits اتكلم من خمسة و لا من سبعة digits
+
+628
+00:52:23,880 --> 00:52:27,260
+كانوا بتكلموا على ألف و أربع و عشرين bit ألف و
+
+629
+00:52:27,260 --> 00:52:30,720
+أربع و عشرين bit يعني انت بتتكلم على عدد بخن جدا
+
+630
+00:52:30,720 --> 00:52:36,340
+الان هذا الكلام مع تقدم الكمبيوترات بطل يعني صرا
+
+631
+00:52:36,340 --> 00:52:39,220
+صرا بده ساعة ساعتين عشان إيش تحطه على cluster
+
+632
+00:52:39,220 --> 00:52:44,250
+بتكون انت عيشكسرته ووصلت لـ key اللي موجود عندك بس
+
+633
+00:52:44,250 --> 00:52:48,150
+الفكرة وين انه فعليا استخدم باق القسمة استخدم الـ
+
+634
+00:52:48,150 --> 00:52:51,390
+primes يعني اهتمت بس العمليات الحسابية البسيطة
+
+635
+00:52:51,390 --> 00:52:58,190
+عشان يوصل او يوصل لعملية تشفير معقدة صعبة الكسر
+
+636
+00:52:58,190 --> 00:53:03,910
+وسلامتكم هيك ال chapter بكون خلص في اي سؤال يا
+
+637
+00:53:03,910 --> 00:53:07,830
+شباب في اي سؤال الله يعطيكوا العافية
+
diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/mnboMT4aXMw_postprocess.srt b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/mnboMT4aXMw_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..f76f8f47534d133734a1c43836e18cc41e553570
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/mnboMT4aXMw_postprocess.srt
@@ -0,0 +1,2276 @@
+1
+00:00:20,810 --> 00:00:22,710
+بسم الله والحمد لله والصلاة والسلام على رسول الله
+
+2
+00:00:22,710 --> 00:00:26,530
+طيب يا شباب اليوم ان شاء الله هنكمل في ال chapter
+
+3
+00:00:26,530 --> 00:00:30,250
+الأول وما زلنا محاضرة هاي ومحاضرة الجاية بحيث نكمل
+
+4
+00:00:30,250 --> 00:00:34,610
+بعض الشغلات اللي هي علاقة بال logic اليوم هنتكلم
+
+5
+00:00:34,610 --> 00:00:38,450
+على موضوع اسمه ال predicate و ال quantifiers في
+
+6
+00:00:38,450 --> 00:00:41,970
+الأول لو أنا بتتكلم على ترجمة predicate تمام
+
+7
+00:00:41,970 --> 00:00:46,570
+المسند ايش عن المسند؟هتقول الشيخ عليك مُصنَد
+
+8
+00:00:46,570 --> 00:00:50,070
+الإمام أحمد بقولك صح مُصنَد يعني فعليا أنا برجع
+
+9
+00:00:50,070 --> 00:00:56,850
+للشغل هادي برجع إله و quantifier من يُقيم أو يعطي
+
+10
+00:00:56,850 --> 00:00:59,830
+قيمة للشغل اللي موجودة عندها وبالتالي بتكلم على
+
+11
+00:00:59,830 --> 00:01:02,910
+تقييم ال proposition وبما إن وازلت أنا بتكلم على
+
+12
+00:01:02,910 --> 00:01:05,910
+propositional function أو بتكلم في ال proposition
+
+13
+00:01:05,910 --> 00:01:11,970
+فتنتقلهم عليها برضه بال logic تتذكر لما قلتلك X
+
+14
+00:01:11,970 --> 00:01:20,750
+أكبر أو تساوي تلاتةهل هذه proposition؟ هيك is a
+
+15
+00:01:20,750 --> 00:01:26,530
+proposition؟ هتقولي
+
+16
+00:01:26,530 --> 00:01:31,270
+اه ايش قيمته؟ يا true يا false يعني مش proposition
+
+17
+00:01:31,270 --> 00:01:36,810
+يا true يا false يعني مش proposition يا انت بتقولي
+
+18
+00:01:36,810 --> 00:01:39,710
+true او بتقولي false وبالتالي هذه not a
+
+19
+00:01:39,710 --> 00:01:45,150
+propositionليش؟ لأن الـ X عندي مجهولة و هرجع معاك
+
+20
+00:01:45,150 --> 00:01:48,810
+للأمثلة السابقة قلنا بالأمثلة السابقة لما قلنا
+
+21
+00:01:48,810 --> 00:01:51,970
+أحمد taller than علي is a proposition قلنا true or
+
+22
+00:01:51,970 --> 00:01:54,950
+false is a proposition لأن أحمد معروف و علي معروف
+
+23
+00:01:54,950 --> 00:01:59,310
+لكن لما جينا قلنا he is a good student قلنا is not
+
+24
+00:01:59,310 --> 00:02:03,830
+a proposition لأنه مجهولة بالنسبالنا مش محدد من هو
+
+25
+00:02:03,830 --> 00:02:07,710
+الشخص اللي بنتكلم عليه وبالتالي هذه ال statement
+
+26
+00:02:07,710 --> 00:02:13,170
+أصبحت مجهولةطيب بس في كتير من الأحيان هلاقي ان في
+
+27
+00:02:13,170 --> 00:02:15,990
+عندي compound proposition او propositional
+
+28
+00:02:15,990 --> 00:02:20,150
+function بتعتمد على شغل زي هيك هنشي خطوة خطوة نشوف
+
+29
+00:02:20,150 --> 00:02:25,390
+كيف الكلام بده يصير عندى في المحاضرة هاي طيب الأول
+
+30
+00:02:25,390 --> 00:02:28,750
+هو احنا جينا قولنا every computer كل جهاز computer
+
+31
+00:02:28,750 --> 00:02:34,510
+موجود في داخل الجامعة شغال بشكل كويس كمان؟ شغال
+
+32
+00:02:34,510 --> 00:02:39,230
+بشكل كويس تقدر تقولي true ولا false؟ false ليش؟
+
+33
+00:02:40,340 --> 00:02:42,800
+عشان هي مش شغالة، عشان فيها مشكلة في المختبر، هيك
+
+34
+00:02:42,800 --> 00:02:46,780
+ما كنت تقول صح؟ بقولك تقييمك صح، لكن المفهوم شغالة
+
+35
+00:02:46,780 --> 00:02:50,660
+ولي مش شغالة جدش هو صحيح بالنسبة لك، مش هنختلف، مش
+
+36
+00:02:50,660 --> 00:02:54,720
+هروح في تفاصيل كتير الآن، وبالتالي أنا فعليا مافيش
+
+37
+00:02:54,720 --> 00:02:59,940
+عندي أي rule عشان الـ propositional logic هذه أروح
+
+38
+00:02:59,940 --> 00:03:03,980
+أعمل conclude لل truth value تبعتها بالشكل هذاشغال
+
+39
+00:03:03,980 --> 00:03:07,320
+ولا مش شغال؟ يعني على الجهاز اللي قدامي لو كان مش
+
+40
+00:03:07,320 --> 00:03:11,840
+شغال أو مافيش عليه البرنامج اللي انا بدي إياه أو
+
+41
+00:03:11,840 --> 00:03:14,400
+مافيش الان اللي فيه مشكلة في ال wire .. في ال
+
+42
+00:03:14,400 --> 00:03:16,140
+wireless أو في ال connection .. ال network
+
+43
+00:03:16,140 --> 00:03:19,680
+connection تبعته أنا قولت عنه مش شغال لكنه فعليا
+
+44
+00:03:19,680 --> 00:03:23,180
+هذا ال role أو هذا الكلام اللي انت حكمت عليهغير
+
+45
+00:03:23,180 --> 00:03:27,520
+مكتوب وبالتالي هذه الجملة بالشكل هذا بدنا نفهى
+
+46
+00:03:27,520 --> 00:03:31,220
+عشان اقول والله true ولا false شو يعني مفهوم
+
+47
+00:03:31,220 --> 00:03:35,800
+functioning properly لازم تتحدد بشكل واضح عشان انا
+
+48
+00:03:35,800 --> 00:03:43,120
+اقدر احكم على هيك مسألة طيب الان لو اجيت بشكل اصغر
+
+49
+00:03:43,120 --> 00:03:47,320
+شوية ال computer اللي في قسم الرياضيات واسمه بي سي
+
+50
+00:03:47,320 --> 00:03:52,470
+تلاتة is functioning properlyبشتغل في شكل ال
+
+51
+00:03:52,470 --> 00:03:56,550
+answer بتتكلم عن جهاز واحد و حددتله حاله صحيح او
+
+52
+00:03:56,550 --> 00:03:59,870
+true or false في computer science department في ان
+
+53
+00:03:59,870 --> 00:04:04,470
+ال computer pc2 is under attack يعني ال under
+
+54
+00:04:04,470 --> 00:04:08,150
+attack في عندك في عليه virus او في حد عمل عليه
+
+55
+00:04:08,150 --> 00:04:12,590
+attack الان هدولة أصبحت أجهزة موجودة في ال
+
+56
+00:04:12,590 --> 00:04:14,910
+computer و زي ان انا عرفت هدولة التنتين بقبل اقول
+
+57
+00:04:14,910 --> 00:04:20,430
+على ال falseولا لا؟ ليش؟ لأنه على الأقل صار VIN دي
+
+58
+00:04:20,430 --> 00:04:26,970
+جهاز مش شغال بشكل كويس مش شغال بشكل كويس تمام الآن
+
+59
+00:04:26,970 --> 00:04:30,930
+هذه كمقدمة في المثال تعالى نشوف بالعنوان تبعنا
+
+60
+00:04:30,930 --> 00:04:36,810
+بالتفصيل ال predicate هي عبارة عن tool logical
+
+61
+00:04:36,810 --> 00:04:43,310
+tool بستخدمها في تفسير range واسع من ال statements
+
+62
+00:04:43,310 --> 00:04:51,660
+لما أنا باجي بقول الشباب Xأكبر او تساوي تلاتة و
+
+63
+00:04:51,660 --> 00:04:57,100
+جيت قلتلك ان ال X هذه تنتمي ل ال natural number
+
+64
+00:04:57,100 --> 00:05:02,480
+لعدد الطبيعية جديش عدد ال proposition اللي تم
+
+65
+00:05:02,480 --> 00:05:07,880
+إنشائها من خلال السطرين هدول جديش
+
+66
+00:05:07,880 --> 00:05:11,980
+عدد ال proposition اللي تم إنشائهم من خلال السطرين
+
+67
+00:05:11,980 --> 00:05:19,310
+هدول غير منتهياتكمان؟ و أصبح بقدر أحكم الآن على
+
+68
+00:05:19,310 --> 00:05:24,950
+قيمة ال X أكبر أو تساوي تلاتة لو قلتلك كل ال X
+
+69
+00:05:24,950 --> 00:05:28,430
+اللي في ال natural number أي عدد طبيعي فهو أكبر أو
+
+70
+00:05:28,430 --> 00:05:33,620
+يساوي تلاتةfalse ليش على الأقل هتقول في عندي
+
+71
+00:05:33,620 --> 00:05:36,760
+الواحد أقل من تلاتة مش أكبر أو أسوأ تلاتة أقل من
+
+72
+00:05:36,760 --> 00:05:40,820
+تلاتة والتنين كذلك ولأ وبالتالي صار لما كنت أتكلم
+
+73
+00:05:40,820 --> 00:05:45,260
+على predicates صرت على القيمة المسندة هذه أقدر أنا
+
+74
+00:05:45,260 --> 00:05:49,280
+أحكم إذا عرفت شغل أسمينها ال domain وهذا المقصود
+
+75
+00:05:49,280 --> 00:05:52,140
+بال wide range of statement يعني صرت أنا بال
+
+76
+00:05:52,140 --> 00:05:56,620
+statement الواحدةبتتعبر عن مجموعة من الكلمات
+
+77
+00:05:56,620 --> 00:06:01,080
+مجموعة كبيرة جدا من الـ proposition أو من الـ
+
+78
+00:06:01,080 --> 00:06:07,480
+logical statements الأمثلة X أكبر من ثلاثة X
+
+79
+00:06:07,480 --> 00:06:10,940
+بتساوي Y زائد ثلاثة X بتساوي Y زائد Z هدول في
+
+80
+00:06:10,940 --> 00:06:14,680
+المفهوم ال single proposition ولا واحد فيهم
+
+81
+00:06:14,680 --> 00:06:16,040
+proposition
+
+82
+00:06:17,950 --> 00:06:22,330
+لأنه مبنيات على مجهيل مبنيات على مجهيل وقلنا ال
+
+83
+00:06:22,330 --> 00:06:25,990
+proposition هي عبارة عن statement بتخبرني حقيقة و
+
+84
+00:06:25,990 --> 00:06:29,310
+الحقيقة بدها تكون فعلية و بقدرحكم عليها مباشرة
+
+85
+00:06:29,310 --> 00:06:35,590
+true or false بس هان لأ Computer
+
+86
+00:06:35,590 --> 00:06:40,150
+X is under attack مش ال proposition لأن ال X
+
+87
+00:06:40,150 --> 00:06:44,170
+مجهولة كذلك الآن
+
+88
+00:06:44,170 --> 00:06:51,420
+في كل الأمثلة هذه السابقةأنا في عندى جزئين في عندى
+
+89
+00:06:51,420 --> 00:06:54,980
+جزئين في المعادلة اللى هى المعادلة اللى طبعا هي ال
+
+90
+00:06:54,980 --> 00:06:59,660
+X أكبر من أو او عفوا X أكبر من 3 في عندى ال
+
+91
+00:06:59,660 --> 00:07:05,000
+variable اللى مفروض أنا بدي أقيمه وفي عندى ال
+
+92
+00:07:05,000 --> 00:07:08,100
+predicate اللى هى القيمة اللى أنا بدي أستند عليها
+
+93
+00:07:08,100 --> 00:07:12,520
+فى التقييم مصبوط ال predicate اللى هى أكبر او
+
+94
+00:07:12,520 --> 00:07:17,320
+متساوي او أكبر من 3ومعناته هي بتتكلم ان انا بدي
+
+95
+00:07:17,320 --> 00:07:22,180
+اقارن خاص ال subject هذا او ال variable مع الأكبر
+
+96
+00:07:22,180 --> 00:07:25,780
+من تلاتة يعني انت كيف بتحكم على المسألة هذه تاخد
+
+97
+00:07:25,780 --> 00:07:31,800
+قيمة X مظبوط و بتقارنها بتعملها logical يعني هيك
+
+98
+00:07:31,800 --> 00:07:35,200
+لو قولنا اتنين اتنين اكبر او تساوي تلاتة بيربوسش
+
+99
+00:07:35,200 --> 00:07:41,030
+هنا شبابالـ Proposition وقيمته False .. مظهور ولا
+
+100
+00:07:41,030 --> 00:07:44,390
+لا .. لكن لما X أكبر أو تساوي تلاتة .. it's not a
+
+101
+00:07:44,390 --> 00:07:48,530
+proposition .. مية لمية .. تلاتة أكبر أو تساوي
+
+102
+00:07:48,530 --> 00:07:52,430
+تلاتة .. Proposition وقيمته True .. Proposition
+
+103
+00:07:52,430 --> 00:07:57,610
+وقيمته True .. يساوي .. هذه إيش مفهومها .. عشان إن
+
+104
+00:07:57,610 --> 00:08:03,610
+ال X أو التلاتة أكبر من تلاتة أو التلاتة بدها
+
+105
+00:08:03,610 --> 00:08:09,290
+تساوي تلاتةلو قلنا هنا false وهنا true true or
+
+106
+00:08:09,290 --> 00:08:21,190
+false true تمام okay وبالتالي
+
+107
+00:08:21,190 --> 00:08:26,270
+صرت انا بتكلم ان ال statement هذه x is أكبر من
+
+108
+00:08:26,270 --> 00:08:31,020
+تلاتة بدي اقول هي عبارة عنfunction هي عبارة عن
+
+109
+00:08:31,020 --> 00:08:34,260
+function propositional function propositional
+
+110
+00:08:34,260 --> 00:08:37,580
+function شو يعني propositional function؟ يعني هذه
+
+111
+00:08:37,580 --> 00:08:40,760
+ال function بتعتمد على متغير و لما بتكلم على
+
+112
+00:08:40,760 --> 00:08:46,940
+function بيلزمني أعرف domain ال function في
+
+113
+00:08:46,940 --> 00:08:48,520
+الرياضيات أي function؟
+
+114
+00:08:56,880 --> 00:09:00,620
+بتاخد من ال domain لل target او لل range كمجموعة
+
+115
+00:09:00,620 --> 00:09:07,380
+مصغرة بتاخد كل عنصر في ال domain و بتحددله صورة في
+
+116
+00:09:07,380 --> 00:09:14,460
+ال range .. 6 .. هذا كمجموعات مظبوط ولا لا؟ تخيل
+
+117
+00:09:14,460 --> 00:09:20,220
+الآن لو انا قلت لك مثلا في المثال الأول X أكبر او
+
+118
+00:09:20,220 --> 00:09:26,960
+تساوي 3 والـ X تنتمي لل number naturalهذه الـ P of
+
+119
+00:09:26,960 --> 00:09:30,600
+X بيتساوي هذه الجملة والـ X تنتمي لـ Natural
+
+120
+00:09:30,600 --> 00:09:37,140
+number قيمتها true ولا false؟ false اه انت الآن
+
+121
+00:09:37,140 --> 00:09:41,180
+بتقول مش عارف ايش هي بس انا بقولك لأ معروفة ليش؟
+
+122
+00:09:41,180 --> 00:09:45,240
+لأن كوني انا حددتلك ان ال natural number معناته
+
+123
+00:09:45,240 --> 00:09:51,120
+هذا ال proposition قيمة الدالة هذه واحد اكبر او
+
+124
+00:09:51,120 --> 00:10:00,140
+تساوي تلاتة and اتنينأكبر أو تساوي تلاتة and تلاتة
+
+125
+00:10:00,140 --> 00:10:06,600
+أكبر أو تساوي تلاتة and إلى ما لا نهاية الان بما
+
+126
+00:10:06,600 --> 00:10:12,080
+أن الأولى false ضمنت الباقي false وبالتالي أقدر
+
+127
+00:10:12,080 --> 00:10:15,480
+أحكم على ال predicate تعالي و أنا غيرت ال domain
+
+128
+00:10:15,480 --> 00:10:18,700
+من ال natural number و روحت قلتلك في المجموعة صفر
+
+129
+00:10:18,700 --> 00:10:27,320
+واحد و اتنين ستصبح ال statement هذهtrue true او
+
+130
+00:10:27,320 --> 00:10:35,340
+false false صفر غيرناها تلاتة ستة وخمسة صارت ال
+
+131
+00:10:35,340 --> 00:10:38,340
+true وبالتالي القيم اللي في ال domain هي اللي
+
+132
+00:10:38,340 --> 00:10:42,680
+بتحكم الموضوع طيب في حالة زي هذه انا لسه عن ال
+
+133
+00:10:42,680 --> 00:10:48,320
+domain ماتكلمتش عليه هاي الدالة اللي عندي بقول ان
+
+134
+00:10:48,320 --> 00:10:53,120
+ال P of X ال predicate function X أكبر أو تساوي
+
+135
+00:10:53,120 --> 00:10:59,490
+تلاتةعشان انا اقدر احكم و اديك truth value لازم
+
+136
+00:10:59,490 --> 00:11:04,730
+اتحدد ليه قيمة ال X يعني لو انا جيت سؤالتك قيمة P
+
+137
+00:11:04,730 --> 00:11:12,420
+of واحد بلكن ترجمها يعني الواحدأكبر او تساوي تلاتة
+
+138
+00:11:12,420 --> 00:11:16,980
+وهذه قيمتها false تمام؟ لاحظ ان هذه ال statement
+
+139
+00:11:16,980 --> 00:11:20,700
+صارت او ال predicate function هذه صارت هي الأساس
+
+140
+00:11:20,700 --> 00:11:23,560
+عندى في التقييم في المرحلة الحالية بالضبط هي
+
+141
+00:11:23,560 --> 00:11:26,560
+القانون اللى انا بدى احكم عليه على العناصر تبعد X
+
+142
+00:11:26,560 --> 00:11:31,340
+بس بنرجع للأساس بدون ما تكون قيمة X واضحة عندى مش
+
+143
+00:11:31,340 --> 00:11:34,680
+حاضر احكم تمام؟ اذا انا بتصير not a proposition
+
+144
+00:11:37,720 --> 00:11:42,080
+طيب الان مجموعة القيم اللي بتمثلها X احنا اتفقنا
+
+145
+00:11:42,080 --> 00:11:44,380
+هي عبارة عن ال domain اللي هي مصطلح تاني في
+
+146
+00:11:44,380 --> 00:11:47,380
+الرياضات المنفصل اللي بنسميها Universe of
+
+147
+00:11:47,380 --> 00:11:52,380
+Discourse Universe of Discourse و أحيانا بنرمزلها
+
+148
+00:11:52,380 --> 00:11:56,860
+بال E و D لو كتبنا domain لو كتبنا Universe of
+
+149
+00:11:56,860 --> 00:11:59,320
+Discourse او Universe of Discourse افهم ان احنا
+
+150
+00:11:59,320 --> 00:12:05,160
+بنتكلم جاعد على ال domain طيبتعالى نشوف بالمثال
+
+151
+00:12:05,160 --> 00:12:14,360
+اللى موجود عندنا هنا بالـ slide P of X و X is an
+
+152
+00:12:14,360 --> 00:12:21,720
+odd integer X is an odd integer الآن بيبقى انه
+
+153
+00:12:21,720 --> 00:12:27,220
+مابتكلمش على domain بقدر اتكلم فقط علىقيمة واحدة ل
+
+154
+00:12:27,220 --> 00:12:33,240
+X بسألك P of أربعة ترجمتها هتصير أن الأربعة is an
+
+155
+00:12:33,240 --> 00:12:39,320
+odd integer true ولا false؟ false P of سبعة يعني
+
+156
+00:12:39,320 --> 00:12:43,860
+أن السبعة is an odd integer true تمانية P of
+
+157
+00:12:43,860 --> 00:12:48,140
+تمانية يعني تمانية is an odd integer false تسعة
+
+158
+00:12:48,140 --> 00:12:53,100
+تسعة is an odd integer irony true
+
+159
+00:12:55,620 --> 00:12:59,420
+عيد تاني؟ احنا
+
+160
+00:12:59,420 --> 00:13:02,480
+بنقول كمان مرة شباب في الـ propositional function
+
+161
+00:13:02,480 --> 00:13:08,640
+اللي هى P of X بقيمها بقيمها بناء على تعريف ال
+
+162
+00:13:08,640 --> 00:13:15,120
+function ثم قيمة X قيمة X اللي هى جزء من ال domain
+
+163
+00:13:15,120 --> 00:13:18,970
+الآن في المثال هذاأنا قاعد بقول ان الـ
+
+164
+00:13:18,970 --> 00:13:22,230
+propositional function بتقول ان ال X هذه اللي هي P
+
+165
+00:13:22,230 --> 00:13:27,150
+of X X هذه عبارة عن عدد فردي عبارة عن عدد فردي
+
+166
+00:13:27,150 --> 00:13:31,790
+فانا أجي اقول P of أربعة بين قوسين بدأت الترجم
+
+167
+00:13:31,790 --> 00:13:36,130
+الأربعة is عدد عبارة عن عدد فردي وبالتالي الصرفة
+
+168
+00:13:36,130 --> 00:13:39,250
+اللي بقدر أقول عليها false لكن السبعة P of سبعة
+
+169
+00:13:39,250 --> 00:13:43,010
+حسب ال predicate function اللي عندي هذه السبعة is
+
+170
+00:13:43,010 --> 00:13:48,880
+an odd integer true تمام؟هي كمان predicate
+
+171
+00:13:48,880 --> 00:13:52,920
+function تانية لكنها تعتمد على two variables بحيث
+
+172
+00:13:52,920 --> 00:13:58,720
+أن مجموعهم أكبر من خمسة
+
+173
+00:14:02,600 --> 00:14:07,880
+تتذكر لما كنا نكتب 2 زائد أربعة equal خمسة نقول
+
+174
+00:14:07,880 --> 00:14:12,000
+عليها proposition ولا لا وقيمته false ال
+
+175
+00:14:12,000 --> 00:14:16,460
+proposition وقيمته false طيب الآن بال function
+
+176
+00:14:16,460 --> 00:14:20,740
+بالشكل هذا ماقدرش أتكلم و هذه is not a proposition
+
+177
+00:14:20,740 --> 00:14:25,340
+ولا لا لأن فيها مجولين الآن لك لما أجي أقولك قيمة
+
+178
+00:14:25,340 --> 00:14:30,320
+x بتنين وقيمة y بتنينأتحدّى لك فأصبح عبارة عن
+
+179
+00:14:30,320 --> 00:14:35,920
+proposition و بقدر أديله قيمة الان Q of 2 و 2 يعني
+
+180
+00:14:35,920 --> 00:14:40,700
+2 زائد 2 لاحظ كل مرة العمالي بقى ترجم بشكل فعلى
+
+181
+00:14:40,700 --> 00:14:45,720
+المتغيرات اللى عندى لـ proposition عشان أقدر أحكم
+
+182
+00:14:45,720 --> 00:14:52,980
+على قيمته 2 زائد 2 أربعة أكبر من خمسة false
+
+183
+00:14:52,980 --> 00:14:58,690
+وبالتالي القيمة هناfalse تلاتة زائد اتنين اكبر من
+
+184
+00:14:58,690 --> 00:15:04,970
+خمسة false تلاتة زائد تلاتة اكبر من خمسة true
+
+185
+00:15:04,970 --> 00:15:14,810
+تلاتة زائد اربعة اكبر من خمسة true تعالى
+
+186
+00:15:14,810 --> 00:15:18,010
+نشوف المتغير هذا او ال proposal function او ال
+
+187
+00:15:18,010 --> 00:15:22,270
+prediction function التالية Z او اعفن ال R بتعتمد
+
+188
+00:15:22,270 --> 00:15:30,830
+علىX تلك المتغيرات X و Y و Z و العلاقة ما بينهم X
+
+189
+00:15:30,830 --> 00:15:37,210
+زائد Y هي تساوي Z كمان مرة يا شباب بمنطق بمنطق ال
+
+190
+00:15:37,210 --> 00:15:40,270
+proposition او لا هذا ال statement is not a
+
+191
+00:15:40,270 --> 00:15:44,350
+proposition لكن بمنطق الأرقام او ال values تبع ال
+
+192
+00:15:44,350 --> 00:15:51,370
+X و Y و Z بتصير proposition الان R of 1 و 2 و 3
+
+193
+00:15:52,200 --> 00:15:57,760
+ترجمتها ان واحد زائد اتنين تساوي تلاتة بالمناسبة
+
+194
+00:15:57,760 --> 00:16:02,000
+ينفعك تقول اتنين زائد تلاتة تساوي واحد تتبع
+
+195
+00:16:02,000 --> 00:16:06,180
+الترتيب اللي موجود تماما بمعنى اخر هتيجي تقولي
+
+196
+00:16:06,180 --> 00:16:09,260
+والله الواحد هي ال X للاقيه الخانة الأولى في ال
+
+197
+00:16:09,260 --> 00:16:13,960
+argument التاني هي ال Yوالتلاتة هي الـ Z و بتكتبهم
+
+198
+00:16:13,960 --> 00:16:18,560
+نفس صورة المعادلة اللى موجودة عندها و بالتالي صارت
+
+199
+00:16:18,560 --> 00:16:20,900
+ال quantifier او عفوا ال predicate function اللى
+
+200
+00:16:20,900 --> 00:16:23,880
+عندى هذا الواحد اتنين و تلاتة هي عبارة عن ال
+
+201
+00:16:23,880 --> 00:16:29,300
+proposition قيمته او يخبر بالحقيقة التالية واحد
+
+202
+00:16:29,300 --> 00:16:33,840
+زائد اتنين تساوي تلاتة ال truth value جديش تبعته
+
+203
+00:16:33,840 --> 00:16:40,060
+true ال truth value تبعته true R of صفر و صفر واحد
+
+204
+00:16:41,600 --> 00:16:51,540
+صفر زاد صفر يساوي واحد false طبعا ماشي الحال يعني
+
+205
+00:16:51,540 --> 00:16:56,840
+الآن كخطوة أولى بنقول أنه ال predicate function ال
+
+206
+00:16:56,840 --> 00:17:02,360
+قيمة تبعتها تتمد على ال arguments أو المتغيرات
+
+207
+00:17:02,360 --> 00:17:05,880
+اللى موجودة فيها لو أنا مقدرش أدى المتغيرات قيم
+
+208
+00:17:07,130 --> 00:17:11,410
+معناته بقدرش أديه هيش true or false وبالتالي بتبطئ
+
+209
+00:17:11,410 --> 00:17:19,270
+اللي عندي proposition لما
+
+210
+00:17:19,270 --> 00:17:23,430
+أنا باجي بتكلم عن ال quantifier الآن بدي أدي قيمة
+
+211
+00:17:23,430 --> 00:17:27,330
+مطلقة هيك نسميها لمين لل proposition ال function
+
+212
+00:17:27,330 --> 00:17:30,870
+اللي عندي بناء على مين؟ بناء على ال domain اللي
+
+213
+00:17:30,870 --> 00:17:33,670
+احنا بنتكلم عليه سابقا ال domain لم يكن معرف بشكل
+
+214
+00:17:33,670 --> 00:17:38,200
+واضحبس الآن لأ بدك تصير تعرف مين هو ال domain اللي
+
+215
+00:17:38,200 --> 00:17:44,080
+موجود عندك نرجع للمثال اللي كتبته الأول P of X X
+
+216
+00:17:44,080 --> 00:17:51,780
+أكبر أو تساوي تلاتة وال X تنتمي لل natural number
+
+217
+00:17:51,780 --> 00:17:57,660
+هذا الكلام انا حيحرفت ال domainوعرفت الـ predicate
+
+218
+00:17:57,660 --> 00:18:01,220
+function بقال في عندي شغلة واحدة في موضوع ال
+
+219
+00:18:01,220 --> 00:18:04,280
+quantifiers او في ال universal quantifier اما في
+
+220
+00:18:04,280 --> 00:18:08,900
+عندي for all او there exist عشان اقدر احكم على ال
+
+221
+00:18:08,900 --> 00:18:13,680
+statement هذه ككل الان في ال quantifiers في عندي
+
+222
+00:18:13,680 --> 00:18:22,160
+ال universal quantifier of b of x من ال b of x هي
+
+223
+00:18:23,180 --> 00:18:26,500
+ماذا يعني الـ Universal؟ بيقول الـ P of X is true
+
+224
+00:18:26,500 --> 00:18:32,000
+for all values of X in الـ D في الدمين يعني بين
+
+225
+00:18:32,000 --> 00:18:40,440
+قسمين for all X P of X is true ترجعها
+
+226
+00:18:40,440 --> 00:18:52,260
+دي مفهومها for all X in دمين in الـ D P of X is
+
+227
+00:18:52,260 --> 00:18:52,640
+true
+
+228
+00:18:55,280 --> 00:18:58,620
+هذه مفهومها الـ Universal Quantification أو الـ
+
+229
+00:18:58,620 --> 00:19:04,140
+Universal Quantifier وهذه رمزها For All X, B of X
+
+230
+00:19:04,140 --> 00:19:10,180
+For Any, Any, For All, For Every معناته كلهم بتقدي
+
+231
+00:19:10,180 --> 00:19:14,780
+نفس العبارة For All X طيب الآن بناء على الكلام
+
+232
+00:19:14,780 --> 00:19:19,120
+اللي فوق هيعرفت ال domain هي ال D و هيعرفت
+
+233
+00:19:19,120 --> 00:19:22,620
+predicate function شو وضع ال Universal Quantifiers
+
+234
+00:19:22,620 --> 00:19:27,840
+هذا true ولا false؟false ليش false؟ لأن على الأقل
+
+235
+00:19:27,840 --> 00:19:31,180
+هتلاقي واحد .. واحدة من الأمثلة دي بتقولك أن
+
+236
+00:19:31,180 --> 00:19:35,260
+المثال هذا مش صحيح الواحد ينتمي لل natural number
+
+237
+00:19:35,260 --> 00:19:41,860
+الواحد لا يحقق المعادلة هذه اللي هو أقل من التلاتة
+
+238
+00:19:41,860 --> 00:19:45,580
+كمان؟ لا يحقق المعادلة يعني الواحد أقل من التلاتة
+
+239
+00:19:45,580 --> 00:19:45,940
+اللي عندي
+
+240
+00:19:49,040 --> 00:19:53,300
+الـ Quantifier التاني اللي هو الـ Existential لما
+
+241
+00:19:53,300 --> 00:19:59,140
+أنا بتكلم على الأقل حلاجي واحد حقق المعادلة يعني
+
+242
+00:19:59,140 --> 00:20:02,480
+لو أنا في ال universal اتجهت وقلت كل الطلاب نجحوا
+
+243
+00:20:02,480 --> 00:20:09,040
+في المساق تمام؟ هذا الكلام true true ما لم اجد بين
+
+244
+00:20:09,040 --> 00:20:13,580
+الطلاب واحدرسم في المثال لو لقيت واحد فقط معياته
+
+245
+00:20:13,580 --> 00:20:16,700
+بتصير ال predicate ال universal هذا قيمته false
+
+246
+00:20:16,700 --> 00:20:20,260
+باجي بقول كل الطلاب اللي في القاعة هن بيعرفوا Java
+
+247
+00:20:20,260 --> 00:20:23,820
+الان
+
+248
+00:20:23,820 --> 00:20:27,020
+true or false حسب الان لو واحد قاللي بعرفش ايش
+
+249
+00:20:27,020 --> 00:20:29,960
+اسمك لو أحمد هان قاللي أنا بعرفش Java بعرف Python
+
+250
+00:20:30,910 --> 00:20:34,150
+تمام بتصير ال statement عندي false و من ال domain
+
+251
+00:20:34,150 --> 00:20:37,250
+اللي أنا بتكلم عليه مجموعة القلاب الموجودين حاليا
+
+252
+00:20:37,250 --> 00:20:41,070
+في المساقة أو في الغرفة اللي موجودة عندهم في ال
+
+253
+00:20:41,070 --> 00:20:49,730
+existential على الأقل هناك واحدة نقول
+
+254
+00:20:49,730 --> 00:20:57,830
+at least على الأقل there exist one
+
+255
+00:20:57,830 --> 00:21:06,820
+x such thatB of X is true على الأقل هناك طالب واحد
+
+256
+00:21:06,820 --> 00:21:11,220
+نجح في المساق أو على الأقل في طالب واحد رسم في
+
+257
+00:21:11,220 --> 00:21:15,660
+المساق في الحالة الأولى على الأقل في طالب واحد نجح
+
+258
+00:21:15,660 --> 00:21:20,560
+true والحالة التانية على الأقل هناك طالب واحد رسم
+
+259
+00:21:20,560 --> 00:21:26,360
+برضه true تمام؟ بتصير false لو انتفى الأمر بالمطلق
+
+260
+00:21:26,360 --> 00:21:33,840
+طيب باشي بقول okayهنا في واحدة بس من الغلط باجي
+
+261
+00:21:33,840 --> 00:21:39,800
+بقولها على الأقل هناك طالب في القاعة بيعرف Java
+
+262
+00:21:39,800 --> 00:21:49,300
+true على الأقل في واحد بتصير false متى؟ لما كلهم
+
+263
+00:21:49,300 --> 00:21:52,860
+بيعرفوش Java لما تصير .. لاحظ انت قاعد في ال
+
+264
+00:21:52,860 --> 00:21:57,460
+predicate function اللي موجود عندك تعالى نشوف
+
+265
+00:22:01,560 --> 00:22:06,040
+ناخد المثال هذا بقول خلّي ال B بتشير ل ال
+
+266
+00:22:06,040 --> 00:22:11,200
+predicate function او لل statement X أكبر من 3 يا
+
+267
+00:22:11,200 --> 00:22:14,740
+عمي وال
+
+268
+00:22:14,740 --> 00:22:18,780
+universe of discourse اللي هي ال domain ال set of
+
+269
+00:22:18,780 --> 00:22:25,620
+real numbers الاعداد الحقيقية يعني بين جثين P of X
+
+270
+00:22:25,620 --> 00:22:34,790
+هي عبارة عن X أكبر من 3والدمين ال real number ايش
+
+271
+00:22:34,790 --> 00:22:40,590
+بيقول يحط قيمة ايش؟ قيمة there exist b
+
+272
+00:22:40,590 --> 00:22:48,610
+of x there exist x b of x و
+
+273
+00:22:48,610 --> 00:22:54,640
+for all xB of X ايش يعني there exists X B of X
+
+274
+00:22:54,640 --> 00:22:59,500
+يعني هناك واحدة على الأقل من X تحقق المعادلة هذه
+
+275
+00:22:59,500 --> 00:23:07,000
+ايش قيمتها true ليش لأن الواحد الواحد احنا بدنا
+
+276
+00:23:07,000 --> 00:23:11,980
+أكبر معناته الأربعة تنتمي لل real number and
+
+277
+00:23:11,980 --> 00:23:21,140
+الأربعة أكبر من التلاتة true and true trueهذا هو
+
+278
+00:23:21,140 --> 00:23:24,640
+تفسير ال quantifiers بتصير بالشكل هذا تعالى نشوف
+
+279
+00:23:24,640 --> 00:23:29,600
+for all بقول
+
+280
+00:23:29,600 --> 00:23:35,380
+لي كل الأعداد الحقيقية أكبر أو تساوي تلاتة false
+
+281
+00:23:35,380 --> 00:23:45,180
+عند الواحد تنتمي لل real number and الواحد مش أكبر
+
+282
+00:23:45,180 --> 00:23:50,240
+من التلاتةمظبوط ولا لا؟ إيش يعني مش أكبر من تلاتة؟
+
+283
+00:23:50,240 --> 00:23:55,440
+يعني أصغر أو تساوي تلاتة بالمناسبة لو قولنا تلاتة
+
+284
+00:23:55,440 --> 00:24:00,620
+أكبر من تلاتة false تلاتة أكبر من تلاتة false
+
+285
+00:24:00,620 --> 00:24:05,960
+تمام؟ الأمور
+
+286
+00:24:05,960 --> 00:24:10,300
+تمام الشباب؟ أي
+
+287
+00:24:10,300 --> 00:24:15,260
+اي ايمعكوسة ولا مع بتنجان يا راجل خلّيك كويس هنا
+
+288
+00:24:15,260 --> 00:24:19,920
+طب يعني انت قولت هذه معكوسة وهذه مع أي شيء تنتهي
+
+289
+00:24:19,920 --> 00:24:25,360
+نقيق there exist there exist for all there exist
+
+290
+00:24:25,360 --> 00:24:31,080
+for all exist اعملها
+
+291
+00:24:31,080 --> 00:24:36,110
+reflectionvertical و لا horizontal reflection
+
+292
+00:24:36,110 --> 00:24:39,550
+الناس اللي أخذت رياضات و حوصبة رياضات للحوصبة
+
+293
+00:24:39,550 --> 00:24:43,270
+الرياضيات الوساطية المتعددة ال graphics reflection
+
+294
+00:24:43,270 --> 00:24:47,450
+reflection horizontal و لا vertical horizontal
+
+295
+00:24:47,450 --> 00:24:55,870
+horizontal و هذه الله يعطيكوا العافية يا شباب هذه
+
+296
+00:24:55,870 --> 00:24:59,430
+ال why وهذه النقطة لما صرها reflection
+
+297
+00:25:02,230 --> 00:25:06,190
+Horizontal Reflection لأن العكاس يكون حول ال Y
+
+298
+00:25:06,190 --> 00:25:10,510
+Axis الحمد
+
+299
+00:25:10,510 --> 00:25:15,830
+لله الحمد لله الحمد لله الحمد
+
+300
+00:25:15,830 --> 00:25:20,210
+لله الحمد
+
+301
+00:25:20,210 --> 00:25:21,390
+لله الحمد لله الحمد لله الحمد لله الحمد لله الحمد
+
+302
+00:25:21,390 --> 00:25:22,050
+لله الحمد لله الحمد لله الحمد لله الحمد لله الحمد
+
+303
+00:25:22,050 --> 00:25:23,030
+لله الحمد لله الحمد لله الحمد لله الحمد لله الحمد
+
+304
+00:25:23,030 --> 00:25:24,490
+لله الحمد لله الحمد لله الحمد لله الحمد لله الحمد
+
+305
+00:25:24,490 --> 00:25:30,470
+لله الحمد
+
+306
+00:25:33,950 --> 00:25:38,230
+Number اللي بيحكوا ورا الشباب و هيك نبري منهم واحد
+
+307
+00:25:38,230 --> 00:25:44,850
+زي الأسد و يترجملي او يحللليها Any real number is
+
+308
+00:25:44,850 --> 00:25:52,610
+a rational number true or
+
+309
+00:25:52,610 --> 00:25:56,750
+false اي
+
+310
+00:25:56,750 --> 00:26:03,670
+عدد حقيقي هو عبارة عن عدد نسبيأي عدب حقيقي هو
+
+311
+00:26:03,670 --> 00:26:07,490
+عبارة عن عدب نسبي true true true true true true
+
+312
+00:26:07,490 --> 00:26:09,190
+true true true true true true true true true true
+
+313
+00:26:09,190 --> 00:26:09,350
+true true true true true true true true true true
+
+314
+00:26:09,350 --> 00:26:09,410
+true true true true true true true true true true
+
+315
+00:26:09,410 --> 00:26:12,650
+true true true true true true true true true true
+
+316
+00:26:12,650 --> 00:26:18,070
+true true true true true true true true true true
+
+317
+00:26:18,070 --> 00:26:18,130
+true true true true true true true true true true
+
+318
+00:26:18,130 --> 00:26:18,250
+true true true true true true true true true true
+
+319
+00:26:18,250 --> 00:26:18,330
+true true true true true true true true true true
+
+320
+00:26:18,330 --> 00:26:27,870
+true true true true true
+
+321
+00:26:27,870 --> 00:26:32,570
+true true trueاللي ضافت للـ natural number الصفر و
+
+322
+00:26:32,570 --> 00:26:37,630
+الـ negative مظبوط بعدها صار في عند ال rational
+
+323
+00:26:37,630 --> 00:26:43,250
+اللي هي ال Q و قلنا في ال Q اللي هي تكتب على صورة
+
+324
+00:26:43,250 --> 00:26:48,610
+A على B بي و A بنتمي لل Z و ال B لاتساوي صفر مظبوط
+
+325
+00:26:48,610 --> 00:26:55,690
+A بي لاتساوي صفر و A و B تنتمي ل Z في مجموعة تانية
+
+326
+00:26:55,690 --> 00:27:00,080
+اسمها ال rationalالاعداد الغير نسبية وال number
+
+327
+00:27:00,080 --> 00:27:07,280
+الواقعي تجمعهم كلياتهم وبالتالي هذا الكلام false
+
+328
+00:27:07,280 --> 00:27:14,940
+تعالي نحوله ماهو P of X X
+
+329
+00:27:14,940 --> 00:27:22,330
+is rationalنمبر لحظة شوية انا لسه ما هتسأل cash
+
+330
+00:27:22,330 --> 00:27:26,270
+على ال universal جعب اتكلم هيه x is a rational
+
+331
+00:27:26,270 --> 00:27:33,030
+number او بين غسين x بتنتمي ل q اذا انت هتكتب pure
+
+332
+00:27:33,030 --> 00:27:40,030
+mathematics تمام؟ الان ايش ال domain تبعنا ال real
+
+333
+00:27:40,030 --> 00:27:43,910
+number اللي
+
+334
+00:27:43,910 --> 00:27:50,510
+هي بين غسين ال a ولا لا؟الان انا مش قاعد بقول
+
+335
+00:27:50,510 --> 00:28:00,470
+every او for any طبعا يعني for all x b of x لأي x
+
+336
+00:28:00,470 --> 00:28:05,290
+في ال domain ال x is true مش فاكرة حتى رجلناها توي
+
+337
+00:28:05,290 --> 00:28:11,370
+لكل x في ال domain ال x is true false قيمتها false
+
+338
+00:28:11,370 --> 00:28:16,470
+ليش؟ لأن عندي جذري التينين تنتمي لل range عفوا لل
+
+339
+00:28:16,470 --> 00:28:24,690
+domain اللي هي ال R andجذر الاتنين لا يتنتني لكيو
+
+340
+00:28:24,690 --> 00:28:28,090
+بصبوط
+
+341
+00:28:28,090 --> 00:28:33,490
+وبالتالي هي السبب اللي صارت عندي false لو جلبنا
+
+342
+00:28:33,490 --> 00:28:37,950
+المسألة لو جلبنا المسألة بحيث انه صارت ال domain
+
+343
+00:28:37,950 --> 00:28:43,430
+هي ال domain هي ال key و ال any rational number is
+
+344
+00:28:43,430 --> 00:28:48,640
+a real numbertrue any rational number is a real
+
+345
+00:28:48,640 --> 00:28:53,260
+number is true بس طبعا تحاول تترجمها بالشكل اللي
+
+346
+00:28:53,260 --> 00:28:57,180
+موجود عندها طبعا الخطوة اللي بعدها أو ننتقل
+
+347
+00:28:57,180 --> 00:29:13,380
+للمقبرة اللي بعدها راحظ
+
+348
+00:29:13,380 --> 00:29:20,490
+معاياالتعريفات اللي احنا شوفناها for all x بيكس
+
+349
+00:29:20,490 --> 00:29:27,110
+for all x بيكس بيكس بيكس is true for every x متى
+
+350
+00:29:27,110 --> 00:29:31,830
+بتصير false لو لجيت واحدة على الأقل كانت false
+
+351
+00:29:31,830 --> 00:29:37,310
+there exist x بيكس يعني على الأقل ال b of x هذي
+
+352
+00:29:37,310 --> 00:29:40,550
+true لواحدة منها متى بتكون false لما يكون كل
+
+353
+00:29:40,550 --> 00:29:42,410
+العناصر false
+
+354
+00:29:44,430 --> 00:29:47,050
+لما نتكلم عن الأولويات أو قبل ما نتكلم عن
+
+355
+00:29:47,050 --> 00:29:50,530
+الأولويات إذا نحن نتكلم عن الـ Predicate و الـ
+
+356
+00:29:50,530 --> 00:29:53,330
+Quantifiers ما زلنا نتكلم في الـ Proposition و في
+
+357
+00:29:53,330 --> 00:29:58,890
+الـ Logic فالـ and و ال or و ال not هيظلوا حاضرات
+
+358
+00:29:58,890 --> 00:30:02,970
+هنا as connectors و أنا عمال لما بترجم بكتب and
+
+359
+00:30:02,970 --> 00:30:07,310
+كده و لا لأ؟ طيب الآن لو أنا إجيت في لحظة من
+
+360
+00:30:07,310 --> 00:30:13,850
+اللحظات و شوفنا ال quantifier أو بالشكل هذاأو شفنا
+
+361
+00:30:13,850 --> 00:30:17,330
+الـ Predicate أو الـ Proposition بالشكل هذا ماذا
+
+362
+00:30:17,330 --> 00:30:24,970
+نقرأه؟ for all x be x or q of x هل لما نتكلم عن
+
+363
+00:30:24,970 --> 00:30:28,830
+الأولويات أولويات احنا دايما نقول الأولوية للأقواص
+
+364
+00:30:28,830 --> 00:30:34,250
+بعدين ال and ال or الله يعطيك الله عفو النفي
+
+365
+00:30:34,250 --> 00:30:40,610
+جابلها أقواص نفي and or مصبوط ولا لا؟ ال and him
+
+366
+00:30:40,610 --> 00:30:41,810
+بعدين ال implies
+
+367
+00:30:45,200 --> 00:30:48,680
+لحظة لا مفيش هندي أقواس لو كان في عندك ال
+
+368
+00:30:48,680 --> 00:30:54,660
+universal أو ال quantifiers بتاخد أولوية على ال or
+
+369
+00:30:54,660 --> 00:31:01,840
+و ال connectors التانيين يعني هذه ترجمتها for all
+
+370
+00:31:01,840 --> 00:31:13,500
+x P of X لحالها or Q of Xماذا يعني؟ يعني انا في
+
+371
+00:31:13,500 --> 00:31:17,580
+عندي universal quantifier تمام؟ بدي احل ال
+
+372
+00:31:17,580 --> 00:31:21,220
+universal quantifier لحاله و اجيب قيمة ال Q of X
+
+373
+00:31:21,220 --> 00:31:27,180
+لحالها تمام؟ و اعمل بينهم R طب فعليا هال Q of X
+
+374
+00:31:27,180 --> 00:31:32,020
+بالصورة الحالية هذه بقدر اديها قيمة؟ لأ لازم اما
+
+375
+00:31:32,020 --> 00:31:36,420
+ال X تاخد value او بتتحول ل quantifier بنفس المنطق
+
+376
+00:31:36,420 --> 00:31:43,330
+السابق طيب و لو انا جانب المثالالـ B of for all X
+
+377
+00:31:43,330 --> 00:31:49,390
+for all X لاحظ الأقواس و في داخل الأقواس B of X
+
+378
+00:31:49,390 --> 00:31:57,690
+and Q of X يعني الـ for all بتتوزع على التنتين ال
+
+379
+00:31:57,690 --> 00:32:04,210
+quantifier بتتوزع على التنتين فيما يتعلق بموضوع
+
+380
+00:32:04,210 --> 00:32:08,030
+اننا فيه فيما يتعلق بموضوع اننا فيه احنا عاملا كنا
+
+381
+00:32:08,030 --> 00:32:19,710
+بنتكلمبنقول كل الطلاب كذا لو كانت true و بده
+
+382
+00:32:19,710 --> 00:32:26,070
+أنفيها بدها تصير false عشان تصير هذا أحد الطلاب
+
+383
+00:32:26,070 --> 00:32:38,750
+على الأقل واحد من الطلاب لم كذا عشان تنفيها
+
+384
+00:32:40,640 --> 00:32:43,260
+وبالتالي انت بتصير تقوله على ال statement اللي
+
+385
+00:32:43,260 --> 00:32:46,620
+موجودة فوق وبالتالي لاحظ لما انا بأجي بتكلم على ال
+
+386
+00:32:46,620 --> 00:32:52,680
+negation لل quantifiers لما بقش أقول for all x
+
+387
+00:32:52,680 --> 00:33:00,260
+نفيها there exist نفي ال P of X على ما قال واحد
+
+388
+00:33:00,260 --> 00:33:05,680
+ماليش بقوله ال P of X كله طالب نجحالـ B of X
+
+389
+00:33:05,680 --> 00:33:08,960
+الطالب نجح لـ Quantifier سبعتها الـ Universal
+
+390
+00:33:08,960 --> 00:33:15,760
+Quantifier كل الطلاب نجحوا نفيها على الأقل واحد من
+
+391
+00:33:15,760 --> 00:33:22,960
+الطلاب لم ينجح ولا لأ وبالتالي نفي الـ Universal
+
+392
+00:33:22,960 --> 00:33:27,240
+Quantifier الـ for all هتصير there exist at least
+
+393
+00:33:27,240 --> 00:33:32,700
+one والنفي انتقل لمين للـ B of X يعني هكذا لو
+
+394
+00:33:32,700 --> 00:33:34,040
+أجينا بالمثال السابق
+
+395
+00:33:37,810 --> 00:33:45,550
+for all x be of x و ال x أكبر من تلاتة و ال domain
+
+396
+00:33:45,550 --> 00:33:51,630
+تسوى ال natural number أه
+
+397
+00:33:51,630 --> 00:33:59,390
+بدي أنفيها أيوة
+
+398
+00:33:59,390 --> 00:34:08,270
+على الأقل هناك x واحدة نفيالـ P of X مافي ال P of
+
+399
+00:34:08,270 --> 00:34:15,010
+X ايش ممكن تكون يا شباب اقل او تساوي تلاتة there
+
+400
+00:34:15,010 --> 00:34:22,590
+exist X such that ال X اقل او تساوي تلاتة واضح
+
+401
+00:34:22,590 --> 00:34:30,770
+الأمور يا شباب طيب طيب مثلا
+
+402
+00:34:30,770 --> 00:34:34,850
+للبرمجة كل الطلاب في ال class حاليا بيعرفوا Java
+
+403
+00:34:37,140 --> 00:34:42,040
+for all عكسها على الأقل هناك واحد اللي هو أحمد
+
+404
+00:34:42,040 --> 00:34:47,140
+بيعرفش ال java نجي
+
+405
+00:34:47,140 --> 00:34:54,540
+لتاني عكس there exist عكس there exist ايش عكسها
+
+406
+00:34:54,540 --> 00:34:59,480
+there exist بتصير for all و نفيه لأن هكذا قلنا على
+
+407
+00:34:59,480 --> 00:35:05,780
+الأقل هناك طالب واحد بيعرف javaكلهم بيعرفوش كلهم
+
+408
+00:35:05,780 --> 00:35:08,480
+يعني for all و بيعرفوش نفيه ال function اللي
+
+409
+00:35:08,480 --> 00:35:13,180
+موجودة عندها وبالتالي صرت أنا بتكلم على العناصر
+
+410
+00:35:13,180 --> 00:35:18,160
+على الأقل هناك طالب بيعرف Java ما هي تحصير النفيها
+
+411
+00:35:18,160 --> 00:35:24,360
+كل الطلاب اللي عنده في ال class بيعرفوش ال Java
+
+412
+00:35:24,360 --> 00:35:34,210
+تمام؟ كأن حد مش بيقول تمام مش مشكلةلما اتكلم على
+
+413
+00:35:34,210 --> 00:35:38,230
+الـ Negation دي
+
+414
+00:35:38,230 --> 00:35:44,450
+مورغان مرمى أنا سابقا صح؟ لما قولت انا بأنفي P and
+
+415
+00:35:44,450 --> 00:35:52,910
+Q هل يتكافئ نقطة P أو نقطة Q و العكس صحيح لما
+
+416
+00:35:52,910 --> 00:35:57,990
+بستخدم ال R نفس الكلام دي مورغان هو صاحب فكرة
+
+417
+00:35:57,990 --> 00:36:01,830
+النفي أو أثبت نظرية النفي للي ي predicate بحيث انه
+
+418
+00:36:01,830 --> 00:36:06,290
+الله يعدى من المورغانخلص .. خلص من زمان بدون ما
+
+419
+00:36:06,290 --> 00:36:10,330
+تدعي there exists نفيها for all وصارت انتقلت
+
+420
+00:36:10,330 --> 00:36:14,390
+النفلة لل predicate function المعرفة اللي موجودة
+
+421
+00:36:14,390 --> 00:36:20,150
+عندك for every b x is false معناته there is a x
+
+422
+00:36:20,150 --> 00:36:27,750
+for which b of x is true طيب دعونا نشوف الأمثلة
+
+423
+00:36:27,750 --> 00:36:28,270
+التالية
+
+424
+00:36:31,540 --> 00:36:35,480
+لو قد جينا قولنا لك جيب اللي ال negation سيبك مني
+
+425
+00:36:35,480 --> 00:36:43,600
+على ال slide هنا مش تمام X تربيع أكبر من X و ال
+
+426
+00:36:43,600 --> 00:36:50,100
+domain تبعتنا هيها ال R is universal يعني بين جثين
+
+427
+00:36:50,100 --> 00:36:56,260
+أنا بتكلم هي ال P of X و ال domain كل ال R الآن
+
+428
+00:36:56,260 --> 00:36:57,240
+بدي أنفي هذه
+
+429
+00:36:59,940 --> 00:37:04,600
+ايوة بدك توزع النفي هي النفي هان معناته هتصيب هدى
+
+430
+00:37:04,600 --> 00:37:10,900
+there exist x مظبوط
+
+431
+00:37:10,900 --> 00:37:21,140
+دخل النفي على ال X تربيع أكبر من X بدك
+
+432
+00:37:21,140 --> 00:37:25,720
+تغير الإشارة اتجاه الإشارة ال X أكبر معناته عكسها
+
+433
+00:37:25,720 --> 00:37:34,060
+أصغر أو يساوي معناته there existX أن X تربيع أصغر
+
+434
+00:37:34,060 --> 00:37:41,020
+أو يساوي X هيك
+
+435
+00:37:41,020 --> 00:37:46,420
+المسألة بيقول انفي ليها What are the negation؟ إيش
+
+436
+00:37:46,420 --> 00:37:51,540
+النفي؟ الفكرة وين؟ أننا بدنا نرسخ مفهوم توزيع
+
+437
+00:37:51,540 --> 00:37:56,660
+النفي على ال predicateو ال quantifier اللي عندى
+
+438
+00:37:56,660 --> 00:38:01,620
+بقولى من خلال ال real number كذلك as domain and
+
+439
+00:38:01,620 --> 00:38:08,320
+there exist x x تربيع بدها تساوي x true ولا لا
+
+440
+00:38:08,320 --> 00:38:11,380
+true الواحد واحد تربيع يساوي واحد الصفر تربيع
+
+441
+00:38:11,380 --> 00:38:17,200
+يساوي صفر طيب هذه true بدى أنفيها قولنا مع النفي
+
+442
+00:38:17,200 --> 00:38:22,340
+تبعتها هيك بتصير for all x
+
+443
+00:38:26,520 --> 00:38:30,700
+X تربيع بدها تساوي X هذه النفة أنا لسه ماوصلتش
+
+444
+00:38:30,700 --> 00:38:36,920
+المرحلة الأخيرة هذه بدها تصير for all X X تربيع لا
+
+445
+00:38:36,920 --> 00:38:46,360
+تساوي X و باللا تساوي شو معناها شوف for all X ان X
+
+446
+00:38:46,360 --> 00:38:54,020
+تربيع أكبر من X أو و لا and مستحيل
+
+447
+00:38:54,020 --> 00:38:54,540
+تكون and
+
+448
+00:38:59,480 --> 00:39:03,860
+المجلد الموجود مستحيل يكون قاعدين تمام وبالتالي
+
+449
+00:39:03,860 --> 00:39:08,280
+عند X تربية أكبر من X أو وطبعا واحدة منهم اللي
+
+450
+00:39:08,280 --> 00:39:13,780
+بتتحقق مستحيل تنتين يتحقق الأمور تمام يا شباب لحد
+
+451
+00:39:13,780 --> 00:39:15,640
+اللحظة تمام
+
+452
+00:39:32,760 --> 00:39:39,280
+تعالى نشوف المثال التالي بقول ال quantifiers
+
+453
+00:39:39,280 --> 00:39:42,740
+تستخدم في ال system specification اللي بيشتغل
+
+454
+00:39:42,740 --> 00:39:46,360
+بالجوال الشباب مبسوط معاه يضبه شكله جيه رسالة
+
+455
+00:39:46,360 --> 00:39:55,620
+أضحكته يعنى أه أبسط أطول every email larger
+
+456
+00:39:55,620 --> 00:40:01,300
+than one megabyte will be compressed
+
+457
+00:40:03,930 --> 00:40:09,830
+الان من استخدام ال quantifiers وضع rules أو تعريف
+
+458
+00:40:09,830 --> 00:40:13,870
+ال specification أو مطلبات النظام كانت تالب كتب
+
+459
+00:40:13,870 --> 00:40:17,730
+ليها every email message larger than one megabyte
+
+460
+00:40:17,730 --> 00:40:20,730
+will be compressed يعني النظام البريد ال .. البريد
+
+461
+00:40:20,730 --> 00:40:25,150
+الإلكتروني تبع المؤسسة هذه بده يضغط كل رسالة حجمها
+
+462
+00:40:25,150 --> 00:40:31,120
+أكبر من واحد ميجاعشان الناس ما تختلفش، الناس اللي
+
+463
+00:40:31,120 --> 00:40:35,200
+بتشتغل في تقوير البرمجة، ما تختلفش في تفسير الكلام
+
+464
+00:40:35,200 --> 00:40:41,120
+هذا، بننجل الكلام من لغة البشر لرموز الرياضيات
+
+465
+00:40:41,120 --> 00:40:46,020
+التي لا تحتمل التقويل للأسف
+
+466
+00:40:46,020 --> 00:40:51,200
+أه، بس هذا من المناسبة مش عربي، هذا انجليزي طيب،
+
+467
+00:40:51,200 --> 00:40:54,420
+ماشي الحل يا أحمد، الآن تقالد ينحل ال statement
+
+468
+00:40:54,420 --> 00:41:00,720
+تبعتنانشوف إيش فيها أولاً أولاً كلمة every إيش
+
+469
+00:41:00,720 --> 00:41:08,360
+يعني for all for all طيب مين العنصر أنا باشطل عليه
+
+470
+00:41:08,360 --> 00:41:13,760
+ال message ال message طيب الحجم كذلك ممكن يكون
+
+471
+00:41:13,760 --> 00:41:17,180
+متغير في المسألة دي ثابت خلّيني أثبته تمام لكن
+
+472
+00:41:17,180 --> 00:41:23,340
+ممكن احنا نكتب حالنا بشكل أكبر طيب يعني الآن ال X
+
+473
+00:41:25,110 --> 00:41:30,590
+عبارة عن إيش؟ Email Message و لا رسالة بالبريد
+
+474
+00:41:30,590 --> 00:41:37,930
+الإلكتروني B of X X
+
+475
+00:41:37,930 --> 00:41:49,820
+أكبر من 1 ميجا بايت أكبر أو تساوي ميجا بايتو ممكن
+
+476
+00:41:49,820 --> 00:41:53,160
+بما انه اتكلم على ال sending email اللي انا بدي
+
+477
+00:41:53,160 --> 00:41:57,720
+ابعتها ممكن اغير الاسم لأس .. مغضب نظر على الرموز،
+
+478
+00:41:57,720 --> 00:42:01,540
+تمام؟ أسأم .. أسأم .. أسأم .. أسأم .. أسأم .. أسأم
+
+479
+00:42:01,540 --> 00:42:02,520
+.. أسأم .. أسأم .. أسأم .. أسأم .. أسأم .. أسأم ..
+
+480
+00:42:02,520 --> 00:42:05,280
+أسأم .. أسأم .. أسأم .. أسأم .. أسأم .. أسأم ..
+
+481
+00:42:05,280 --> 00:42:05,960
+أسأم .. أسأم .. أسأم .. أسأم .. أسأم .. أسأم ..
+
+482
+00:42:05,960 --> 00:42:07,820
+أسأم .. أسأم .. أسأم .. أسأم .. أسأم .. أسأم ..
+
+483
+00:42:07,820 --> 00:42:15,560
+أسأم .. أسأم .. أسأم .. أسأم .. أس
+
+484
+00:42:21,750 --> 00:42:31,910
+x will be compressed طيب ال will be شوفت يعني هذه
+
+485
+00:42:31,910 --> 00:42:39,750
+حسب ال logic عندي ال will be implies
+
+486
+00:42:39,750 --> 00:42:44,530
+تقول وبالتالي في عندي another predicate function
+
+487
+00:42:44,530 --> 00:42:49,210
+انا اسميها c c
+
+488
+00:42:49,210 --> 00:42:57,200
+of xX is compressed
+
+489
+00:42:57,200 --> 00:43:07,600
+انضبط ولا لأ وبالتالي هيك باشر بقول for all X as
+
+490
+00:43:07,600 --> 00:43:17,440
+of X لأي رسالة هتقول علاش ان ال C of X
+
+491
+00:43:20,470 --> 00:43:23,870
+أحنا قلنا قبل شوية .. احنا قلنا قبل شوية ال
+
+492
+00:43:23,870 --> 00:43:28,290
+quantifier .. ال quantifier هذه بتاخد أولوية على
+
+493
+00:43:28,290 --> 00:43:31,290
+ال operators اللي احنا شفناهم اللي هي ال and و ال
+
+494
+00:43:31,290 --> 00:43:35,010
+or و ال not و ال .. و ال implies وبالتالي هي
+
+495
+00:43:35,010 --> 00:43:41,510
+الرسالة اللي عندها تمام؟ أصبحيك .. كل رسالة حققت
+
+496
+00:43:41,510 --> 00:43:46,830
+أن حجمها أكبر من واحد ميجا بايت الرسالة هذه لازم
+
+497
+00:43:46,830 --> 00:43:51,160
+تنبغط must be compressedX must be compressed او X
+
+498
+00:43:51,160 --> 00:43:56,200
+is compressed كمان الان في هذه ال specification
+
+499
+00:43:56,200 --> 00:44:01,620
+ممكن ناخد خطوة كمال باتجاه الأمام بحيث انه اذا انت
+
+500
+00:44:01,620 --> 00:44:07,120
+الواحد ميجا هادي ممكن تلعب فيها او تغير فيها تروح
+
+501
+00:44:07,120 --> 00:44:12,260
+تخيليها هي عبارة عن متغير تاني لمين؟ لل X بحيث انه
+
+502
+00:44:12,260 --> 00:44:22,890
+نقول S of X و Y و ال Yبتساوي ال size ال 1 ميجا
+
+503
+00:44:22,890 --> 00:44:27,430
+بايت او الحجم اللي انت بدك هيه بتصير في عندها ال S
+
+504
+00:44:27,430 --> 00:44:32,690
+of XY ال X أكبر من ال Y اللي ال message هذي ايش
+
+505
+00:44:32,690 --> 00:44:37,230
+بتصير فيها بدها تنضغط ال message هذي بدها تنضغط
+
+506
+00:44:37,230 --> 00:44:45,190
+طيب الامور تمام هى
+
+507
+00:44:45,190 --> 00:44:49,620
+عبارة عن another functionعبارة عن دالة كانية
+
+508
+00:44:49,620 --> 00:44:54,260
+اختصاريا compressed بس احنا لما جيه اللي هي الناتج
+
+509
+00:44:54,260 --> 00:44:58,360
+ناتج لكن will be كان لها معنى عندي اللي هي ال
+
+510
+00:44:58,360 --> 00:45:02,120
+employees فانا شقبت ال will be بس احتفظت منين بال
+
+511
+00:45:02,120 --> 00:45:07,720
+compression ال property وبالتالي انا الآن صرت انا
+
+512
+00:45:07,720 --> 00:45:13,240
+بقدر اكتب ال email تبعي بالشكل هذا بعد ما انا
+
+513
+00:45:13,240 --> 00:45:19,780
+فسرته وفسلته كل واحدة اش يعنيفبقدر اخد ال
+
+514
+00:45:19,780 --> 00:45:24,400
+specification دي بشكل صحيح طيب تعالى نشوف برضه ناس
+
+515
+00:45:24,400 --> 00:45:30,940
+هشيلهم اش قضية if a user is active ال if ايش يعني
+
+516
+00:45:30,940 --> 00:45:39,100
+ال if يعني في implies user is active نفس الشيء
+
+517
+00:45:39,100 --> 00:45:46,480
+المفعل تمام يعني ممكن انا قاعد يقول هذا P of X ال
+
+518
+00:45:46,480 --> 00:45:54,500
+Xis active مين X يقول user مصبوط او لا طيب at
+
+519
+00:45:54,500 --> 00:46:00,880
+least على الأقل واحد من ال network link will be
+
+520
+00:46:00,880 --> 00:46:04,480
+available يعني هيك اذا كان في واحد من ال user في
+
+521
+00:46:04,480 --> 00:46:09,180
+داخل الشبكة شغال او active معناته واحد من ال links
+
+522
+00:46:09,180 --> 00:46:16,360
+الآن موجود طيب معناته انا بدى اتكلم هانوين
+
+523
+00:46:19,140 --> 00:46:26,420
+At least إيش يعني؟ There exists مصبوط و ال link is
+
+524
+00:46:26,420 --> 00:46:31,100
+active و ال link is active خلّيني أقول هادي انعرف
+
+525
+00:46:31,100 --> 00:46:36,400
+ال function نسميها ال U as a user و ال L of X
+
+526
+00:46:36,400 --> 00:46:42,700
+بينفعش بينفعش تاخد X بتحتاخد variable تاني تمام
+
+527
+00:46:42,700 --> 00:46:47,850
+عشان تتفرضوا عن ال user ماتخربطش في الأمور linkال
+
+528
+00:46:47,850 --> 00:46:55,870
+link ايه او y مش مشكلة و ال y is available link
+
+529
+00:46:55,870 --> 00:47:04,510
+ايش بتصير ال function if ال
+
+530
+00:47:04,510 --> 00:47:09,110
+ux معناته
+
+531
+00:47:09,110 --> 00:47:23,320
+there exist y بتحققall of Y صحيك؟ صحيك؟ صح بس هذا
+
+532
+00:47:23,320 --> 00:47:28,700
+الكلام فيه صورة تانية كتبناها احنا سابقا اللي هي
+
+533
+00:47:28,700 --> 00:47:34,420
+إيش ال Contra positive نفد أول أو نفد تاني يقول
+
+534
+00:47:34,420 --> 00:47:38,300
+إلى أول بين جثين إذا واحد من ال connection تبعت
+
+535
+00:47:38,300 --> 00:47:42,560
+الشبكة الآن شغال معناته في عندي واحد من ال user is
+
+536
+00:47:42,560 --> 00:47:47,750
+activeوالمفروض الآن الناس كونوا عايش روحوا انت
+
+537
+00:47:47,750 --> 00:47:50,810
+مابتعرفش انه في user شغال انت لما بتطلع على جهاز
+
+538
+00:47:50,810 --> 00:47:55,090
+التحكم تبع الشبكة ال router مابتعرفش منه الشبكة بس
+
+539
+00:47:55,090 --> 00:48:00,630
+بتشوف ال link بديك click ولا لأ؟ بديك إشارة انه في
+
+540
+00:48:00,630 --> 00:48:06,250
+الخط هذا busy شغال فبالتالي إذا الخط شغال معناته
+
+541
+00:48:06,250 --> 00:48:10,930
+فيه end user بما ان ال F هذه بي implies Q كانت
+
+542
+00:48:10,930 --> 00:48:17,940
+تكافئ تمامانقطة Q تعني نقطة B يعني أنني أكتبها
+
+543
+00:48:17,940 --> 00:48:22,840
+بصورة ألطف تتعبر عن الوظيفة اللي هي لو كان عندي
+
+544
+00:48:22,840 --> 00:48:30,480
+user شغال معناته على الأقل في عندي Y و Y is active
+
+545
+00:48:30,480 --> 00:48:35,160
+هذا الحالة الأولى قصة هكذا لو ماكانش عندي ولا خط
+
+546
+00:48:35,160 --> 00:48:39,900
+active أو ولا خط available معناته
+
+547
+00:48:43,520 --> 00:48:54,240
+for all y not l of y link is available issue at
+
+548
+00:48:54,240 --> 00:48:58,740
+day not
+
+549
+00:48:58,740 --> 00:49:06,540
+u of x أو مافيش there exist x not
+
+550
+00:49:07,960 --> 00:49:13,060
+for all بيصير universal بيصير كل مافيش ولا حدا for
+
+551
+00:49:13,060 --> 00:49:19,060
+all x negation تبع ال U of X خربتكوا انا صح نعيد
+
+552
+00:49:19,060 --> 00:49:22,700
+تاني انا عمال بقولك هذا ال quantifier بعد ما
+
+553
+00:49:22,700 --> 00:49:28,500
+كتبناه بالصورة هذه احنا اللي هي ال F معناته انا
+
+554
+00:49:28,500 --> 00:49:31,080
+بقدر بقول بكتبه بصورة تانية لو حاولت ايش أساوي
+
+555
+00:49:31,080 --> 00:49:36,200
+أشجلبهمعشان أجلبهم القيامة كمان مرة هي ال
+
+556
+00:49:36,200 --> 00:49:39,720
+quantifier اللي عندي لو كان فيه عندي user active
+
+557
+00:49:39,720 --> 00:49:44,840
+if there exist b x b of x لو كان واحد شغال على
+
+558
+00:49:44,840 --> 00:49:48,720
+الأقل واحد شغال اوكي أنا مش كاتب هنا there exist
+
+559
+00:49:48,720 --> 00:49:51,920
+لو
+
+560
+00:49:51,920 --> 00:49:54,800
+كان واحد .. واحد شغال معاه فيه له link available
+
+561
+00:49:54,800 --> 00:49:59,260
+مصبوط فيه link متاح و هالشارك من خلاله تعالوا
+
+562
+00:49:59,260 --> 00:50:01,620
+نكتبها بالصورة التانية تبع ال contrapositive
+
+563
+00:50:04,420 --> 00:50:09,540
+إذا ما كل ال links مش شغالة معناته أنا بتأكد إنه
+
+564
+00:50:09,540 --> 00:50:14,480
+مافيش ولا user active معناته مافيش ولا user active
+
+565
+00:50:14,480 --> 00:50:20,200
+وبهك انتهينا من موضوع ال section لليوم في أي سؤال
+
+566
+00:50:20,200 --> 00:50:23,160
+يا شباب في الأمثلة الأخيرة؟ ماشي الحال في أي سؤال
+
+567
+00:50:23,160 --> 00:50:27,140
+يا شباب؟ فلس أنا بدي أكسي تكفي لحد اليوم عشان أظهر
+
+568
+00:50:27,140 --> 00:50:30,040
+في عنا برضه section بسيط للمحاضرة اللي جاية و نخلص
+
+569
+00:50:30,040 --> 00:50:31,860
+من ال chapter الأول الله عطيكوا العافية
+
diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/mnboMT4aXMw_raw.json b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/mnboMT4aXMw_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..94aaee561409bf0da84f1732a1fe4f15a968bb30
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/mnboMT4aXMw_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4485, "start": 20.81, "end": 44.85, "text": "بسم الله والحمد لله والصلاة والسلام على رسول الله طيب يا شباب اليوم ان شاء الله هنكمل في ال chapter الأول وما زلنا محاضرة هاي ومحاضرة الجاية بحيث نكمل بعض الشغلات اللي هي علاقة بال logic اليوم هنتكلم على موضوع اسمه ال predicate و ال quantifiers في الأول لو أنا بتتكلم على ترجمة predicate تمام المسند ايش عن المسند؟", "tokens": [3555, 38251, 21984, 16070, 35571, 3215, 24976, 3224, 16070, 9381, 15040, 3660, 16070, 3794, 37440, 15844, 12602, 3794, 12610, 21984, 23032, 1829, 3555, 35186, 13412, 3555, 16758, 45595, 20498, 16472, 13412, 16606, 21984, 8032, 1863, 24793, 1211, 8978, 2423, 7187, 16247, 12610, 4032, 15042, 30767, 1211, 8315, 3714, 5016, 46958, 25720, 8032, 47302, 4032, 2304, 5016, 46958, 25720, 25724, 995, 10632, 4724, 5016, 1829, 12984, 8717, 24793, 1211, 45030, 11242, 25124, 17082, 1211, 9307, 13672, 1829, 39896, 11203, 995, 28671, 20666, 9952, 45595, 20498, 8032, 29399, 4117, 19528, 15844, 3714, 2407, 11242, 45367, 24525, 2304, 3224, 2423, 3852, 8700, 4032, 2423, 4426, 23463, 8978, 16247, 12610, 45164, 41850, 39894, 2655, 4117, 19528, 15844, 6055, 47341, 46007, 3852, 8700, 46811, 10943, 9673, 3794, 41260, 1975, 1829, 8592, 18871, 9673, 3794, 41260, 22807], "avg_logprob": -0.19022253945921408, "compression_ratio": 1.9377289377289377, "no_speech_prob": 2.384185791015625e-07, "words": [{"start": 20.81, "end": 21.09, "word": "بسم", "probability": 0.755615234375}, {"start": 21.09, "end": 21.23, "word": " الله", "probability": 0.970703125}, {"start": 21.23, "end": 21.49, "word": " والحمد", "probability": 0.7916666666666666}, {"start": 21.49, "end": 21.63, "word": " لله", "probability": 0.957275390625}, {"start": 21.63, "end": 21.87, "word": " والصلاة", "probability": 0.8626708984375}, {"start": 21.87, "end": 22.17, "word": " والسلام", "probability": 0.9153645833333334}, {"start": 22.17, "end": 22.29, "word": " على", "probability": 0.435791015625}, {"start": 22.29, "end": 22.57, "word": " 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أحكم على ال predicate تعالي و أنا غيرت ال domain من ال natural number و روحت قلتلك في المجموعة صفر واحد و اتنين ستصبح ال statement هذه", "tokens": [10721, 4117, 26890, 34051, 6055, 3794, 995, 45865, 6055, 1211, 9307, 3660, 293, 6055, 1211, 9307, 3660, 5551, 4117, 26890, 34051, 6055, 3794, 995, 45865, 6055, 1211, 9307, 3660, 293, 30731, 19446, 20193, 8717, 11296, 10632, 2423, 7649, 4724, 15042, 14739, 16247, 12610, 7578, 7908, 48812, 27842, 2655, 29739, 995, 38436, 7908, 46599, 6027, 2655, 6027, 1829, 5551, 28543, 2288, 5551, 5016, 24793, 15844, 2423, 3852, 8700, 37279, 6027, 1829, 4032, 41850, 32771, 13546, 2655, 2423, 9274, 9154, 2423, 3303, 1230, 4032, 12602, 2407, 33753, 12174, 1211, 2655, 23275, 8978, 9673, 7435, 2304, 45367, 3660, 20328, 5172, 2288, 36764, 24401, 4032, 1975, 2655, 1863, 9957, 8608, 2655, 9381, 49628, 2423, 5629, 29538], "avg_logprob": -0.22912056889154214, "compression_ratio": 1.7272727272727273, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 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{"start": 615.78, "end": 616.08, "word": " natural", "probability": 0.78271484375}, {"start": 616.08, "end": 616.64, "word": " number", "probability": 0.97607421875}, {"start": 616.64, "end": 617.08, "word": " و", "probability": 0.8671875}, {"start": 617.08, "end": 617.26, "word": " روحت", "probability": 0.664794921875}, {"start": 617.26, "end": 617.64, "word": " قلتلك", "probability": 0.7877197265625}, {"start": 617.64, "end": 617.76, "word": " في", "probability": 0.9736328125}, {"start": 617.76, "end": 618.32, "word": " المجموعة", "probability": 0.8798828125}, {"start": 618.32, "end": 618.7, "word": " صفر", "probability": 0.9114583333333334}, {"start": 618.7, "end": 619.26, "word": " واحد", "probability": 0.816162109375}, {"start": 619.26, "end": 619.38, "word": " و", "probability": 0.94384765625}, {"start": 619.38, "end": 620.24, "word": " اتنين", "probability": 0.890380859375}, {"start": 620.24, "end": 622.94, "word": " ستصبح", "probability": 0.7442626953125}, {"start": 622.94, "end": 623.02, "word": " ال", "probability": 0.7470703125}, {"start": 623.02, "end": 623.38, "word": " statement", "probability": 0.91748046875}, {"start": 623.38, "end": 623.84, "word": " هذه", "probability": 0.53515625}], "temperature": 1.0}, {"id": 24, "seek": 65370, "start": 625.86, "end": 653.7, "text": "true true او false false صفر غيرناها تلاتة ستة وخمسة صارت ال true وبالتالي القيم اللي في ال domain هي اللي بتحكم الموضوع طيب في حالة زي هذه انا لسه عن ال domain ماتكلمتش عليه هاي الدالة اللي عندي بقول ان ال P of X ال predicate function X أكبر أو تساوي تلاتة", "tokens": [6903, 622, 2074, 1975, 2407, 7908, 7908, 20328, 5172, 2288, 32771, 13546, 8315, 11296, 6055, 1211, 9307, 3660, 8608, 2655, 3660, 4032, 9778, 2304, 3794, 3660, 20328, 9640, 2655, 2423, 2074, 46599, 6027, 2655, 6027, 1829, 25062, 32640, 13672, 1829, 8978, 2423, 9274, 39896, 13672, 1829, 39894, 5016, 24793, 9673, 2407, 11242, 45367, 23032, 1829, 3555, 8978, 11331, 6027, 3660, 30767, 1829, 29538, 1975, 8315, 5296, 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{"start": 642.68, "end": 642.84, "word": " domain", "probability": 0.99658203125}, {"start": 642.84, "end": 643.54, "word": " ماتكلمتش", "probability": 0.873779296875}, {"start": 643.54, "end": 643.84, "word": " عليه", "probability": 0.95703125}, {"start": 643.84, "end": 645.52, "word": " هاي", "probability": 0.5645751953125}, {"start": 645.52, "end": 645.9, "word": " الدالة", "probability": 0.8763020833333334}, {"start": 645.9, "end": 646.02, "word": " اللي", "probability": 0.96240234375}, {"start": 646.02, "end": 646.34, "word": " عندي", "probability": 0.7398681640625}, {"start": 646.34, "end": 648.18, "word": " بقول", "probability": 0.96484375}, {"start": 648.18, "end": 648.32, "word": " ان", "probability": 0.763671875}, {"start": 648.32, "end": 648.46, "word": " ال", "probability": 0.5283203125}, {"start": 648.46, "end": 648.58, "word": " P", "probability": 0.37939453125}, {"start": 648.58, "end": 648.8, "word": " of", "probability": 0.798828125}, {"start": 648.8, "end": 649.12, 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{"start": 658.19, "end": 658.71, "word": " value", "probability": 0.9921875}, {"start": 658.71, "end": 659.49, "word": " لازم", "probability": 0.91015625}, {"start": 659.49, "end": 660.07, "word": " اتحدد", "probability": 0.8463134765625}, {"start": 660.07, "end": 660.47, "word": " ليه", "probability": 0.705322265625}, {"start": 660.47, "end": 661.31, "word": " قيمة", "probability": 0.9860026041666666}, {"start": 661.31, "end": 661.41, "word": " ال", "probability": 0.76318359375}, {"start": 661.41, "end": 661.69, "word": " X", "probability": 0.64208984375}, {"start": 661.69, "end": 662.33, "word": " يعني", "probability": 0.796142578125}, {"start": 662.33, "end": 662.55, "word": " لو", "probability": 0.8447265625}, {"start": 662.55, "end": 662.71, "word": " انا", "probability": 0.751220703125}, {"start": 662.71, "end": 662.83, "word": " جيت", "probability": 0.735107421875}, {"start": 662.83, "end": 663.37, "word": " سؤالتك", "probability": 0.895703125}, {"start": 663.37, "end": 664.15, 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بتصير not a proposition", "tokens": [10721, 4117, 26890, 1975, 2407, 6055, 3794, 995, 45865, 6055, 1211, 9307, 3660, 37037, 24192, 12174, 32640, 2655, 11296, 7908, 46811, 10943, 22807, 20193, 5016, 19913, 16472, 29538, 2423, 5629, 20328, 9640, 2655, 1975, 2407, 2423, 3852, 8700, 2445, 29538, 20328, 9640, 2655, 39896, 16247, 3794, 32277, 43242, 7578, 8978, 16712, 38436, 32640, 8978, 9673, 2288, 5016, 37977, 21542, 6027, 10632, 20666, 11242, 3555, 9566, 39896, 25062, 7649, 11536, 13672, 7578, 1975, 8315, 47525, 7578, 1975, 5016, 24793, 47356, 15844, 18863, 1863, 33546, 2288, 6055, 3555, 22488, 1783, 4724, 3794, 44945, 47341, 3615, 24976, 10721, 3794, 32277, 47525, 11536, 19446, 6055, 30544, 12174, 32640, 3660, 1783, 4032, 46958, 5016, 3660, 43242, 7578, 37893, 11331, 46958, 2288, 1975, 5016, 24793, 46811, 10943, 22807, 1975, 15730, 1975, 8315, 39894, 9381, 13546, 406, 257, 24830], "avg_logprob": -0.24506578499213197, "compression_ratio": 1.806338028169014, "no_speech_prob": 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predicate بحيث انه الله يعدى من المورغان", "tokens": [1211, 15042, 1975, 2655, 4117, 19528, 15844, 2423, 39184, 19103, 399, 11778, 1829, 3714, 13063, 17082, 7649, 3714, 2288, 2304, 7578, 41850, 8608, 16758, 4587, 995, 20328, 5016, 22807, 5296, 15042, 12174, 12610, 2655, 1975, 8315, 4724, 33456, 41185, 430, 293, 1249, 8032, 1211, 7251, 2655, 4117, 31845, 19986, 8717, 47432, 3660, 430, 34051, 8717, 47432, 3660, 1249, 4032, 18863, 4117, 3794, 20328, 5016, 1829, 5016, 5296, 15042, 4724, 14851, 9778, 40448, 2423, 497, 8717, 36178, 2423, 28820, 10943, 11778, 1829, 3714, 13063, 17082, 7649, 31439, 20328, 39319, 3555, 6156, 4117, 25720, 28239, 41185, 34051, 5551, 12984, 3555, 2655, 8717, 19913, 2288, 10632, 28239, 41185, 5296, 20292, 7251, 3852, 8700, 4724, 5016, 1829, 12984, 16472, 3224, 21984, 7251, 22488, 7578, 9154, 9673, 13063, 17082, 7649], "avg_logprob": -0.26463294431330664, "compression_ratio": 1.6926229508196722, "no_speech_prob": 2.0265579223632812e-06, "words": [{"start": 2133.37, 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"word": " there", "probability": 0.818359375}, {"start": 2178.19, "end": 2179.19, "word": " is", "probability": 0.72216796875}, {"start": 2179.19, "end": 2179.51, "word": " a", "probability": 0.319091796875}, {"start": 2179.51, "end": 2180.15, "word": " x", "probability": 0.83154296875}, {"start": 2180.15, "end": 2180.93, "word": " for", "probability": 0.9580078125}, {"start": 2180.93, "end": 2181.29, "word": " which", "probability": 0.962890625}, {"start": 2181.29, "end": 2181.71, "word": " b", "probability": 0.8037109375}, {"start": 2181.71, "end": 2181.83, "word": " of", "probability": 0.79248046875}, {"start": 2181.83, "end": 2181.99, "word": " x", "probability": 0.94970703125}, {"start": 2181.99, "end": 2182.27, "word": " is", "probability": 0.93505859375}, {"start": 2182.27, "end": 2183.41, "word": " true", "probability": 0.9765625}, {"start": 2183.41, "end": 2184.45, "word": " طيب", "probability": 0.9563802083333334}, {"start": 2184.45, "end": 2184.75, "word": " دعونا", "probability": 0.500640869140625}, {"start": 2184.75, "end": 2185.09, "word": " نشوف", "probability": 0.99658203125}, {"start": 2185.09, "end": 2187.75, "word": " الأمثلة", "probability": 0.956787109375}, {"start": 2187.75, "end": 2188.27, "word": " التالية", "probability": 0.9905598958333334}], "temperature": 1.0}, {"id": 82, "seek": 221723, "start": 2191.54, "end": 2217.24, "text": "لو قد جينا قولنا لك جيب اللي ال negation سيبك مني على ال slide هنا مش تمام X تربيع أكبر من X و ال domain تبعتنا هيها ال R is universal يعني بين جثين أنا بتكلم هي ال P of X و ال domain كل ال R الآن بدي أنفي هذه", "tokens": [1211, 2407, 12174, 3215, 10874, 1829, 8315, 12174, 12610, 8315, 5296, 4117, 10874, 1829, 3555, 13672, 1829, 2423, 2485, 399, 8608, 1829, 3555, 4117, 9154, 1829, 15844, 2423, 4137, 34105, 37893, 46811, 10943, 1783, 6055, 25513, 40228, 5551, 4117, 26890, 9154, 1783, 4032, 2423, 9274, 6055, 3555, 34268, 8315, 39896, 11296, 2423, 497, 307, 11455, 37495, 22653, 49374, 10874, 12984, 9957, 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"probability": 0.6602783203125}, {"start": 2223.4, "end": 2224.08, "word": " معناته", "probability": 0.7801106770833334}, {"start": 2224.08, "end": 2224.42, "word": " هتصيب", "probability": 0.814501953125}, {"start": 2224.42, "end": 2224.6, "word": " هدى", "probability": 0.4654947916666667}, {"start": 2224.6, "end": 2224.8, "word": " there", "probability": 0.66845703125}, {"start": 2224.8, "end": 2225.28, "word": " exist", "probability": 0.62060546875}, {"start": 2225.28, "end": 2227.5, "word": " x", "probability": 0.47314453125}, {"start": 2227.5, "end": 2230.9, "word": " مظبوط", "probability": 0.7728759765625}, {"start": 2230.9, "end": 2232.4, "word": " دخل", "probability": 0.91064453125}, {"start": 2232.4, "end": 2232.84, "word": " النفي", "probability": 0.88623046875}, {"start": 2232.84, "end": 2235.04, "word": " على", "probability": 0.73388671875}, {"start": 2235.04, "end": 2235.22, "word": " ال", "probability": 0.92822265625}, {"start": 2235.22, "end": 2235.46, "word": " X", "probability": 0.5126953125}, {"start": 2235.46, "end": 2236.2, "word": " تربيع", "probability": 0.86328125}, {"start": 2236.2, "end": 2236.86, "word": " أكبر", "probability": 0.7733561197916666}, {"start": 2236.86, "end": 2237.04, "word": " من", "probability": 0.994140625}, {"start": 2237.04, "end": 2237.46, "word": " X", "probability": 0.95751953125}, {"start": 2237.46, "end": 2241.14, "word": " بدك", "probability": 0.88232421875}, {"start": 2241.14, "end": 2241.54, "word": " تغير", "probability": 0.9329427083333334}, {"start": 2241.54, "end": 2242.16, "word": " الإشارة", "probability": 0.86572265625}, {"start": 2242.16, "end": 2242.5, "word": " اتجاه", "probability": 0.815673828125}, {"start": 2242.5, "end": 2243.04, "word": " الإشارة", "probability": 0.978515625}, {"start": 2243.04, "end": 2243.24, "word": " ال", "probability": 0.912109375}, {"start": 2243.24, "end": 2243.46, "word": " X", "probability": 0.939453125}, {"start": 2243.46, "end": 2243.96, "word": " أكبر", "probability": 0.9786783854166666}, {"start": 2243.96, "end": 2245.08, "word": " معناته", "probability": 0.9690755208333334}, {"start": 2245.08, "end": 2245.72, "word": " عكسها", "probability": 0.9781494140625}, {"start": 2245.72, "end": 2247.32, "word": " أصغر", "probability": 0.965576171875}, {"start": 2247.32, "end": 2247.5, "word": " أو", "probability": 0.82421875}, {"start": 2247.5, "end": 2248.02, "word": " يساوي", "probability": 0.9600830078125}, {"start": 2248.02, "end": 2248.74, "word": " معناته", "probability": 0.9358723958333334}, {"start": 2248.74, "end": 2248.94, "word": " there", "probability": 0.87060546875}, {"start": 2248.94, "end": 2249.32, "word": " exist", "probability": 0.90771484375}], "temperature": 1.0}, {"id": 84, "seek": 227417, "start": 2250.2, "end": 2274.18, "text": "X أن X تربيع أصغر أو يساوي X هيك المسألة بيقول انفي ليها What are the negation؟ إيش النفي؟ الفكرة وين؟ أننا بدنا نرسخ مفهوم توزيع النفي على ال predicate", "tokens": [55, 14739, 1783, 6055, 2288, 21292, 3615, 5551, 9381, 17082, 2288, 34051, 7251, 3794, 995, 45865, 1783, 39896, 4117, 9673, 3794, 10721, 37977, 4724, 1829, 39648, 16472, 41185, 32239, 11296, 708, 366, 264, 2485, 399, 22807, 11933, 1829, 8592, 28239, 41185, 22807, 27188, 4117, 25720, 4032, 9957, 22807, 14739, 8315, 47525, 8315, 8717, 2288, 3794, 9778, 3714, 5172, 3224, 20498, 33427, 11622, 40228, 28239, 41185, 15844, 2423, 3852, 8700], "avg_logprob": -0.3937500089406967, "compression_ratio": 1.4080459770114941, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 2250.2, "end": 2250.72, "word": "X", "probability": 0.306640625}, {"start": 2250.72, "end": 2251.58, "word": " أن", "probability": 0.05926513671875}, {"start": 2251.58, "end": 2252.02, "word": " X", "probability": 0.8984375}, {"start": 2252.02, "end": 2253.3, "word": " تربيع", "probability": 0.8350830078125}, {"start": 2253.3, "end": 2254.06, "word": " أصغر", "probability": 0.9158935546875}, {"start": 2254.06, "end": 2254.22, "word": " أو", "probability": 0.93310546875}, {"start": 2254.22, "end": 2254.78, "word": " يساوي", "probability": 0.9515380859375}, {"start": 2254.78, "end": 2256.56, "word": " X", "probability": 0.884765625}, {"start": 2256.56, "end": 2261.02, "word": " هيك", "probability": 0.2942962646484375}, {"start": 2261.02, "end": 2261.3, "word": " المسألة", "probability": 0.827880859375}, {"start": 2261.3, "end": 2261.5, "word": " بيقول", "probability": 0.5301106770833334}, {"start": 2261.5, "end": 2261.78, "word": " انفي", "probability": 0.5}, {"start": 2261.78, "end": 2262.22, "word": " ليها", "probability": 0.6368408203125}, {"start": 2262.22, "end": 2264.28, "word": " What", "probability": 0.1756591796875}, {"start": 2264.28, "end": 2265.48, "word": " are", "probability": 0.90478515625}, {"start": 2265.48, "end": 2265.62, "word": " the", "probability": 0.87451171875}, {"start": 2265.62, "end": 2266.26, "word": " negation؟", "probability": 0.6961263020833334}, {"start": 2266.26, "end": 2266.42, "word": " إيش", "probability": 0.7567545572916666}, {"start": 2266.42, "end": 2267.6, "word": " النفي؟", "probability": 0.79833984375}, {"start": 2267.6, "end": 2269.02, "word": " الفكرة", "probability": 0.8448893229166666}, {"start": 2269.02, "end": 2269.54, "word": " وين؟", "probability": 0.7156575520833334}, {"start": 2269.54, "end": 2269.78, "word": " أننا", "probability": 0.5982666015625}, {"start": 2269.78, "end": 2269.96, "word": " بدنا", "probability": 0.689208984375}, {"start": 2269.96, "end": 2270.42, "word": " نرسخ", "probability": 0.70001220703125}, {"start": 2270.42, "end": 2270.88, "word": " مفهوم", "probability": 0.9583740234375}, {"start": 2270.88, "end": 2271.54, "word": " توزيع", "probability": 0.97607421875}, {"start": 2271.54, "end": 2272.74, "word": " النفي", "probability": 0.883056640625}, {"start": 2272.74, "end": 2273.08, "word": " على", "probability": 0.853515625}, {"start": 2273.08, "end": 2273.62, "word": " ال", "probability": 0.3935546875}, {"start": 2273.62, "end": 2274.18, "word": " predicate", "probability": 0.690673828125}], "temperature": 1.0}, {"id": 85, "seek": 230234, "start": 2275.02, "end": 2302.34, "text": "و ال quantifier اللي عندى بقولى من خلال ال real number كذلك as domain and there exist x x تربيع بدها تساوي x true ولا لا true الواحد واحد تربيع يساوي واحد الصفر تربيع يساوي صفر طيب هذه true بدى أنفيها قولنا مع النفي تبعتها هيك بتصير for all x", "tokens": [2407, 2423, 4426, 9902, 13672, 1829, 43242, 7578, 4724, 39648, 7578, 9154, 16490, 1211, 6027, 2423, 957, 1230, 9122, 8848, 23275, 382, 9274, 293, 456, 2514, 2031, 2031, 6055, 2288, 21292, 3615, 47525, 11296, 6055, 3794, 995, 45865, 2031, 2074, 49429, 20193, 2074, 2423, 14407, 24401, 36764, 24401, 6055, 2288, 21292, 3615, 7251, 3794, 995, 45865, 36764, 24401, 31767, 5172, 2288, 6055, 2288, 21292, 3615, 7251, 3794, 995, 45865, 20328, 5172, 2288, 23032, 1829, 3555, 29538, 2074, 47525, 7578, 14739, 41185, 11296, 12174, 12610, 8315, 20449, 28239, 41185, 6055, 3555, 34268, 11296, 39896, 4117, 39894, 9381, 13546, 337, 439, 2031], "avg_logprob": -0.27073019801980197, "compression_ratio": 1.6986301369863013, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2275.02, "end": 2275.22, "word": "و", "probability": 0.1729736328125}, {"start": 2275.22, "end": 2275.3, "word": " ال", "probability": 0.262939453125}, {"start": 2275.3, "end": 2276.0, "word": " quantifier", "probability": 0.7120361328125}, {"start": 2276.0, "end": 2276.3, "word": " اللي", "probability": 0.816650390625}, {"start": 2276.3, "end": 2276.66, "word": " عندى", "probability": 0.6563720703125}, {"start": 2276.66, "end": 2277.7, "word": " بقولى", "probability": 0.7506510416666666}, {"start": 2277.7, "end": 2278.52, "word": " من", "probability": 0.9541015625}, {"start": 2278.52, "end": 2278.86, "word": " خلال", "probability": 0.9921875}, {"start": 2278.86, "end": 2278.98, "word": " ال", "probability": 0.9296875}, {"start": 2278.98, "end": 2279.12, "word": " real", "probability": 0.6357421875}, {"start": 2279.12, "end": 2279.48, "word": " number", "probability": 0.98291015625}, {"start": 2279.48, "end": 2280.02, "word": " كذلك", "probability": 0.9788411458333334}, {"start": 2280.02, "end": 2280.62, "word": " as", "probability": 0.82763671875}, {"start": 2280.62, "end": 2281.0, "word": " domain", "probability": 0.90283203125}, {"start": 2281.0, "end": 2281.62, "word": " and", "probability": 0.54638671875}, {"start": 2281.62, "end": 2281.86, "word": " there", "probability": 0.84130859375}, {"start": 2281.86, "end": 2282.38, "word": " exist", "probability": 0.6337890625}, {"start": 2282.38, "end": 2282.9, "word": " x", "probability": 0.65283203125}, {"start": 2282.9, "end": 2283.88, "word": " x", "probability": 0.1683349609375}, {"start": 2283.88, "end": 2284.24, "word": " تربيع", "probability": 0.740478515625}, {"start": 2284.24, "end": 2284.4, "word": " بدها", "probability": 0.43548583984375}, {"start": 2284.4, "end": 2284.84, "word": " تساوي", "probability": 0.8782958984375}, {"start": 2284.84, "end": 2285.24, "word": " x", "probability": 0.84130859375}, {"start": 2285.24, "end": 2287.72, "word": " true", "probability": 0.84716796875}, {"start": 2287.72, "end": 2288.04, "word": " ولا", "probability": 0.70849609375}, {"start": 2288.04, "end": 2288.32, "word": " لا", "probability": 0.724609375}, {"start": 2288.32, "end": 2289.14, "word": " true", "probability": 0.71484375}, {"start": 2289.14, "end": 2289.58, "word": " الواحد", "probability": 0.81787109375}, {"start": 2289.58, "end": 2289.96, "word": " واحد", "probability": 0.7008056640625}, {"start": 2289.96, "end": 2290.3, "word": " تربيع", "probability": 0.979248046875}, {"start": 2290.3, "end": 2290.5, "word": " يساوي", "probability": 0.73370361328125}, {"start": 2290.5, "end": 2290.68, "word": " واحد", "probability": 0.992919921875}, {"start": 2290.68, "end": 2291.0, "word": " الصفر", "probability": 0.8245442708333334}, {"start": 2291.0, "end": 2291.38, "word": " تربيع", "probability": 0.9818115234375}, {"start": 2291.38, "end": 2291.76, "word": " يساوي", "probability": 0.972900390625}, {"start": 2291.76, "end": 2292.62, "word": " صفر", "probability": 0.98046875}, {"start": 2292.62, "end": 2293.38, "word": " طيب", "probability": 0.9742838541666666}, {"start": 2293.38, "end": 2293.76, "word": " هذه", "probability": 0.268310546875}, {"start": 2293.76, "end": 2294.06, "word": " true", "probability": 0.974609375}, {"start": 2294.06, "end": 2294.58, "word": " بدى", "probability": 0.63671875}, {"start": 2294.58, "end": 2295.22, "word": " أنفيها", "probability": 0.765625}, {"start": 2295.22, "end": 2296.34, "word": " قولنا", "probability": 0.6993815104166666}, {"start": 2296.34, "end": 2296.78, "word": " مع", "probability": 0.98583984375}, {"start": 2296.78, "end": 2297.2, "word": " النفي", "probability": 0.725830078125}, {"start": 2297.2, "end": 2297.86, "word": " تبعتها", "probability": 0.83056640625}, {"start": 2297.86, "end": 2298.52, "word": " هيك", "probability": 0.924072265625}, {"start": 2298.52, "end": 2299.54, "word": " بتصير", "probability": 0.9588216145833334}, {"start": 2299.54, "end": 2300.54, "word": " for", "probability": 0.95947265625}, {"start": 2300.54, "end": 2301.12, "word": " all", "probability": 0.95751953125}, {"start": 2301.12, "end": 2302.34, "word": " x", "probability": 0.9169921875}], "temperature": 1.0}, {"id": 86, "seek": 233454, "start": 2306.52, "end": 2334.54, "text": "X تربيع بدها تساوي X هذه النفة أنا لسه ماوصلتش المرحلة الأخيرة هذه بدها تصير for all X X تربيع لا تساوي X و باللا تساوي شو معناها شوف for all X ان X تربيع أكبر من X أو و لا and مستحيل تكون and", "tokens": [55, 6055, 2288, 21292, 3615, 47525, 11296, 6055, 3794, 995, 45865, 1783, 29538, 28239, 5172, 3660, 41850, 5296, 3794, 3224, 19446, 2407, 36520, 2655, 8592, 9673, 2288, 5016, 37977, 16247, 9778, 48923, 29538, 47525, 11296, 6055, 9381, 13546, 337, 439, 1783, 1783, 6055, 2288, 21292, 3615, 20193, 6055, 3794, 995, 45865, 1783, 4032, 20666, 15040, 6055, 3794, 995, 45865, 13412, 2407, 20449, 8315, 11296, 13412, 38688, 337, 439, 1783, 16472, 1783, 6055, 2288, 21292, 3615, 5551, 4117, 26890, 9154, 1783, 34051, 4032, 20193, 293, 3714, 14851, 5016, 26895, 6055, 30544, 293], "avg_logprob": -0.2921195551753044, "compression_ratio": 1.8362573099415205, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 2306.52, "end": 2306.86, "word": "X", "probability": 0.47265625}, {"start": 2306.86, "end": 2307.52, "word": " تربيع", "probability": 0.78863525390625}, {"start": 2307.52, "end": 2308.42, "word": " بدها", "probability": 0.29950714111328125}, {"start": 2308.42, "end": 2308.8, "word": " تساوي", "probability": 0.948974609375}, {"start": 2308.8, "end": 2309.1, "word": " X", "probability": 0.95751953125}, {"start": 2309.1, "end": 2309.3, "word": " هذه", "probability": 0.28759765625}, {"start": 2309.3, "end": 2309.58, "word": " النفة", "probability": 0.4611002604166667}, {"start": 2309.58, "end": 2309.7, "word": " أنا", "probability": 0.36962890625}, 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"probability": 0.93310546875}, {"start": 3027.26, "end": 3027.46, "word": " عنا", "probability": 0.59088134765625}, {"start": 3027.46, "end": 3027.7, "word": " برضه", "probability": 0.9596354166666666}, {"start": 3027.7, "end": 3028.1, "word": " section", "probability": 0.6640625}, {"start": 3028.1, "end": 3028.62, "word": " بسيط", "probability": 0.9947509765625}, {"start": 3028.62, "end": 3029.16, "word": " للمحاضرة", "probability": 0.94609375}, {"start": 3029.16, "end": 3029.32, "word": " اللي", "probability": 0.76708984375}, {"start": 3029.32, "end": 3029.6, "word": " جاية", "probability": 0.8933919270833334}, {"start": 3029.6, "end": 3029.8, "word": " و", "probability": 0.9755859375}, {"start": 3029.8, "end": 3030.04, "word": " نخلص", "probability": 0.9056396484375}, {"start": 3030.04, "end": 3030.18, "word": " من", "probability": 0.93798828125}, {"start": 3030.18, "end": 3030.22, "word": " ال", "probability": 0.60400390625}, {"start": 3030.22, "end": 3030.42, "word": " chapter", 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/mnboMT4aXMw_raw.srt b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/mnboMT4aXMw_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..18f6685ea159afab696e3b6686fb05c4a86e55a7
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/mnboMT4aXMw_raw.srt
@@ -0,0 +1,2336 @@
+1
+00:00:20,810 --> 00:00:22,710
+بسم الله والحمد لله والصلاة والسلام على رسول الله
+
+2
+00:00:22,710 --> 00:00:26,530
+طيب يا شباب اليوم ان شاء الله هنكمل في ال chapter
+
+3
+00:00:26,530 --> 00:00:30,250
+الأول وما زلنا محاضرة هاي ومحاضرة الجاية بحيث نكمل
+
+4
+00:00:30,250 --> 00:00:34,610
+بعض الشغلات اللي هي علاقة بال logic اليوم هنتكلم
+
+5
+00:00:34,610 --> 00:00:38,450
+على موضوع اسمه ال predicate و ال quantifiers في
+
+6
+00:00:38,450 --> 00:00:41,970
+الأول لو أنا بتتكلم على ترجمة predicate تمام
+
+7
+00:00:41,970 --> 00:00:46,570
+المسند ايش عن المسند؟هتقول الشيخ عليك مُصنَد
+
+8
+00:00:46,570 --> 00:00:50,070
+الإمام أحمد بقولك صح مُصنَد يعني فعليا أنا برجع
+
+9
+00:00:50,070 --> 00:00:56,850
+للشغل هادي برجع إله و quantifier من يُقيم أو يعطي
+
+10
+00:00:56,850 --> 00:00:59,830
+قيمة للشغل اللي موجودة عندها وبالتالي بتكلم على
+
+11
+00:00:59,830 --> 00:01:02,910
+تقييم ال proposition وبما إن وازلت أنا بتكلم على
+
+12
+00:01:02,910 --> 00:01:05,910
+propositional function أو بتكلم في ال proposition
+
+13
+00:01:05,910 --> 00:01:11,970
+فتنتقلهم عليها برضه بال logic تتذكر لما قلتلك X
+
+14
+00:01:11,970 --> 00:01:20,750
+أكبر أو تساوي تلاتةهل هذه proposition؟ هيك is a
+
+15
+00:01:20,750 --> 00:01:26,530
+proposition؟ هتقولي
+
+16
+00:01:26,530 --> 00:01:31,270
+اه ايش قيمته؟ يا true يا false يعني مش proposition
+
+17
+00:01:31,270 --> 00:01:36,810
+يا true يا false يعني مش proposition يا انت بتقولي
+
+18
+00:01:36,810 --> 00:01:39,710
+true او بتقولي false وبالتالي هذه not a
+
+19
+00:01:39,710 --> 00:01:45,150
+propositionليش؟ لأن الـ X عندي مجهولة و هرجع معاك
+
+20
+00:01:45,150 --> 00:01:48,810
+للأمثلة السابقة قلنا بالأمثلة السابقة لما قلنا
+
+21
+00:01:48,810 --> 00:01:51,970
+أحمد taller than علي is a proposition قلنا true or
+
+22
+00:01:51,970 --> 00:01:54,950
+false is a proposition لأن أحمد معروف و علي معروف
+
+23
+00:01:54,950 --> 00:01:59,310
+لكن لما جينا قلنا he is a good student قلنا is not
+
+24
+00:01:59,310 --> 00:02:03,830
+a proposition لأنه مجهولة بالنسبالنا مش محدد من هو
+
+25
+00:02:03,830 --> 00:02:07,710
+الشخص اللي بنتكلم عليه وبالتالي هذه ال statement
+
+26
+00:02:07,710 --> 00:02:13,170
+أصبحت مجهولةطيب بس في كتير من الأحيان هلاقي ان في
+
+27
+00:02:13,170 --> 00:02:15,990
+عندي compound proposition او propositional
+
+28
+00:02:15,990 --> 00:02:20,150
+function بتعتمد على شغل زي هيك هنشي خطوة خطوة نشوف
+
+29
+00:02:20,150 --> 00:02:25,390
+كيف الكلام بده يصير عندى في المحاضرة هاي طيب الأول
+
+30
+00:02:25,390 --> 00:02:28,750
+هو احنا جينا قولنا every computer كل جهاز computer
+
+31
+00:02:28,750 --> 00:02:34,510
+موجود في داخل الجامعة شغال بشكل كويس كمان؟ شغال
+
+32
+00:02:34,510 --> 00:02:39,230
+بشكل كويس تقدر تقولي true ولا false؟ false ليش؟
+
+33
+00:02:40,340 --> 00:02:42,800
+عشان هي مش شغالة، عشان فيها مشكلة في المختبر، هيك
+
+34
+00:02:42,800 --> 00:02:46,780
+ما كنت تقول صح؟ بقولك تقييمك صح، لكن المفهوم شغالة
+
+35
+00:02:46,780 --> 00:02:50,660
+ولي مش شغالة جدش هو صحيح بالنسبة لك، مش هنختلف، مش
+
+36
+00:02:50,660 --> 00:02:54,720
+هروح في تفاصيل كتير الآن، وبالتالي أنا فعليا مافيش
+
+37
+00:02:54,720 --> 00:02:59,940
+عندي أي rule عشان الـ propositional logic هذه أروح
+
+38
+00:02:59,940 --> 00:03:03,980
+أعمل conclude لل truth value تبعتها بالشكل هذاشغال
+
+39
+00:03:03,980 --> 00:03:07,320
+ولا مش شغال؟ يعني على الجهاز اللي قدامي لو كان مش
+
+40
+00:03:07,320 --> 00:03:11,840
+شغال أو مافيش عليه البرنامج اللي انا بدي إياه أو
+
+41
+00:03:11,840 --> 00:03:14,400
+مافيش الان اللي فيه مشكلة في ال wire .. في ال
+
+42
+00:03:14,400 --> 00:03:16,140
+wireless أو في ال connection .. ال network
+
+43
+00:03:16,140 --> 00:03:19,680
+connection تبعته أنا قولت عنه مش شغال لكنه فعليا
+
+44
+00:03:19,680 --> 00:03:23,180
+هذا ال role أو هذا الكلام اللي انت حكمت عليهغير
+
+45
+00:03:23,180 --> 00:03:27,520
+مكتوب وبالتالي هذه الجملة بالشكل هذا بدنا نفهى
+
+46
+00:03:27,520 --> 00:03:31,220
+عشان اقول والله true ولا false شو يعني مفهوم
+
+47
+00:03:31,220 --> 00:03:35,800
+functioning properly لازم تتحدد بشكل واضح عشان انا
+
+48
+00:03:35,800 --> 00:03:43,120
+اقدر احكم على هيك مسألة طيب الان لو اجيت بشكل اصغر
+
+49
+00:03:43,120 --> 00:03:47,320
+شوية ال computer اللي في قسم الرياضيات واسمه بي سي
+
+50
+00:03:47,320 --> 00:03:52,470
+تلاتة is functioning properlyبشتغل في شكل ال
+
+51
+00:03:52,470 --> 00:03:56,550
+answer بتتكلم عن جهاز واحد و حددتله حاله صحيح او
+
+52
+00:03:56,550 --> 00:03:59,870
+true or false في computer science department في ان
+
+53
+00:03:59,870 --> 00:04:04,470
+ال computer pc2 is under attack يعني ال under
+
+54
+00:04:04,470 --> 00:04:08,150
+attack في عندك في عليه virus او في حد عمل عليه
+
+55
+00:04:08,150 --> 00:04:12,590
+attack الان هدولة أصبحت أجهزة موجودة في ال
+
+56
+00:04:12,590 --> 00:04:14,910
+computer و زي ان انا عرفت هدولة التنتين بقبل اقول
+
+57
+00:04:14,910 --> 00:04:20,430
+على ال falseولا لا؟ ليش؟ لأنه على الأقل صار VIN دي
+
+58
+00:04:20,430 --> 00:04:26,970
+جهاز مش شغال بشكل كويس مش شغال بشكل كويس تمام الآن
+
+59
+00:04:26,970 --> 00:04:30,930
+هذه كمقدمة في المثال تعالى نشوف بالعنوان تبعنا
+
+60
+00:04:30,930 --> 00:04:36,810
+بالتفصيل ال predicate هي عبارة عن tool logical
+
+61
+00:04:36,810 --> 00:04:43,310
+tool بستخدمها في تفسير range واسع من ال statements
+
+62
+00:04:43,310 --> 00:04:51,660
+لما أنا باجي بقول الشباب Xأكبر او تساوي تلاتة و
+
+63
+00:04:51,660 --> 00:04:57,100
+جيت قلتلك ان ال X هذه تنتمي ل ال natural number
+
+64
+00:04:57,100 --> 00:05:02,480
+لعدد الطبيعية جديش عدد ال proposition اللي تم
+
+65
+00:05:02,480 --> 00:05:07,880
+إنشائها من خلال السطرين هدول جديش
+
+66
+00:05:07,880 --> 00:05:11,980
+عدد ال proposition اللي تم إنشائهم من خلال السطرين
+
+67
+00:05:11,980 --> 00:05:19,310
+هدول غير منتهياتكمان؟ و أصبح بقدر أحكم الآن على
+
+68
+00:05:19,310 --> 00:05:24,950
+قيمة ال X أكبر أو تساوي تلاتة لو قلتلك كل ال X
+
+69
+00:05:24,950 --> 00:05:28,430
+اللي في ال natural number أي عدد طبيعي فهو أكبر أو
+
+70
+00:05:28,430 --> 00:05:33,620
+يساوي تلاتةfalse ليش على الأقل هتقول في عندي
+
+71
+00:05:33,620 --> 00:05:36,760
+الواحد أقل من تلاتة مش أكبر أو أسوأ تلاتة أقل من
+
+72
+00:05:36,760 --> 00:05:40,820
+تلاتة والتنين كذلك ولأ وبالتالي صار لما كنت أتكلم
+
+73
+00:05:40,820 --> 00:05:45,260
+على predicates صرت على القيمة المسندة هذه أقدر أنا
+
+74
+00:05:45,260 --> 00:05:49,280
+أحكم إذا عرفت شغل أسمينها ال domain وهذا المقصود
+
+75
+00:05:49,280 --> 00:05:52,140
+بال wide range of statement يعني صرت أنا بال
+
+76
+00:05:52,140 --> 00:05:56,620
+statement الواحدةبتتعبر عن مجموعة من الكلمات
+
+77
+00:05:56,620 --> 00:06:01,080
+مجموعة كبيرة جدا من الـ proposition أو من الـ
+
+78
+00:06:01,080 --> 00:06:07,480
+logical statements الأمثلة X أكبر من ثلاثة X
+
+79
+00:06:07,480 --> 00:06:10,940
+بتساوي Y زائد ثلاثة X بتساوي Y زائد Z هدول في
+
+80
+00:06:10,940 --> 00:06:14,680
+المفهوم ال single proposition ولا واحد فيهم
+
+81
+00:06:14,680 --> 00:06:16,040
+proposition
+
+82
+00:06:17,950 --> 00:06:22,330
+لأنه مبنيات على مجهيل مبنيات على مجهيل وقلنا ال
+
+83
+00:06:22,330 --> 00:06:25,990
+proposition هي عبارة عن statement بتخبرني حقيقة و
+
+84
+00:06:25,990 --> 00:06:29,310
+الحقيقة بدها تكون فعلية و بقدرحكم عليها مباشرة
+
+85
+00:06:29,310 --> 00:06:35,590
+true or false بس هان لأ Computer
+
+86
+00:06:35,590 --> 00:06:40,150
+X is under attack مش ال proposition لأن ال X
+
+87
+00:06:40,150 --> 00:06:44,170
+مجهولة كذلك الآن
+
+88
+00:06:44,170 --> 00:06:51,420
+في كل الأمثلة هذه السابقةأنا في عندى جزئين في عندى
+
+89
+00:06:51,420 --> 00:06:54,980
+جزئين في المعادلة اللى هى المعادلة اللى طبعا هي ال
+
+90
+00:06:54,980 --> 00:06:59,660
+X أكبر من أو او عفوا X أكبر من 3 في عندى ال
+
+91
+00:06:59,660 --> 00:07:05,000
+variable اللى مفروض أنا بدي أقيمه وفي عندى ال
+
+92
+00:07:05,000 --> 00:07:08,100
+predicate اللى هى القيمة اللى أنا بدي أستند عليها
+
+93
+00:07:08,100 --> 00:07:12,520
+فى التقييم مصبوط ال predicate اللى هى أكبر او
+
+94
+00:07:12,520 --> 00:07:17,320
+متساوي او أكبر من 3ومعناته هي بتتكلم ان انا بدي
+
+95
+00:07:17,320 --> 00:07:22,180
+اقارن خاص ال subject هذا او ال variable مع الأكبر
+
+96
+00:07:22,180 --> 00:07:25,780
+من تلاتة يعني انت كيف بتحكم على المسألة هذه تاخد
+
+97
+00:07:25,780 --> 00:07:31,800
+قيمة X مظبوط و بتقارنها بتعملها logical يعني هيك
+
+98
+00:07:31,800 --> 00:07:35,200
+لو قولنا اتنين اتنين اكبر او تساوي تلاتة بيربوسش
+
+99
+00:07:35,200 --> 00:07:41,030
+هنا شبابالـ Proposition وقيمته False .. مظهور ولا
+
+100
+00:07:41,030 --> 00:07:44,390
+لا .. لكن لما X أكبر أو تساوي تلاتة .. it's not a
+
+101
+00:07:44,390 --> 00:07:48,530
+proposition .. مية لمية .. تلاتة أكبر أو تساوي
+
+102
+00:07:48,530 --> 00:07:52,430
+تلاتة .. Proposition وقيمته True .. Proposition
+
+103
+00:07:52,430 --> 00:07:57,610
+وقيمته True .. يساوي .. هذه إيش مفهومها .. عشان إن
+
+104
+00:07:57,610 --> 00:08:03,610
+ال X أو التلاتة أكبر من تلاتة أو التلاتة بدها
+
+105
+00:08:03,610 --> 00:08:09,290
+تساوي تلاتةلو قلنا هنا false وهنا true true or
+
+106
+00:08:09,290 --> 00:08:21,190
+false true تمام okay وبالتالي
+
+107
+00:08:21,190 --> 00:08:26,270
+صرت انا بتكلم ان ال statement هذه x is أكبر من
+
+108
+00:08:26,270 --> 00:08:31,020
+تلاتة بدي اقول هي عبارة عنfunction هي عبارة عن
+
+109
+00:08:31,020 --> 00:08:34,260
+function propositional function propositional
+
+110
+00:08:34,260 --> 00:08:37,580
+function شو يعني propositional function؟ يعني هذه
+
+111
+00:08:37,580 --> 00:08:40,760
+ال function بتعتمد على متغير و لما بتكلم على
+
+112
+00:08:40,760 --> 00:08:46,940
+function بيلزمني أعرف domain ال function في
+
+113
+00:08:46,940 --> 00:08:48,520
+الرياضيات أي function؟
+
+114
+00:08:56,880 --> 00:09:00,620
+بتاخد من ال domain لل target او لل range كمجموعة
+
+115
+00:09:00,620 --> 00:09:07,380
+مصغرة بتاخد كل عنصر في ال domain و بتحددله صورة في
+
+116
+00:09:07,380 --> 00:09:14,460
+ال range .. 6 .. هذا كمجموعات مظبوط ولا لا؟ تخيل
+
+117
+00:09:14,460 --> 00:09:20,220
+الآن لو انا قلت لك مثلا في المثال الأول X أكبر او
+
+118
+00:09:20,220 --> 00:09:26,960
+تساوي 3 والـ X تنتمي لل number naturalهذه الـ P of
+
+119
+00:09:26,960 --> 00:09:30,600
+X بيتساوي هذه الجملة والـ X تنتمي لـ Natural
+
+120
+00:09:30,600 --> 00:09:37,140
+number قيمتها true ولا false؟ false اه انت الآن
+
+121
+00:09:37,140 --> 00:09:41,180
+بتقول مش عارف ايش هي بس انا بقولك لأ معروفة ليش؟
+
+122
+00:09:41,180 --> 00:09:45,240
+لأن كوني انا حددتلك ان ال natural number معناته
+
+123
+00:09:45,240 --> 00:09:51,120
+هذا ال proposition قيمة الدالة هذه واحد اكبر او
+
+124
+00:09:51,120 --> 00:10:00,140
+تساوي تلاتة and اتنينأكبر أو تساوي تلاتة and تلاتة
+
+125
+00:10:00,140 --> 00:10:06,600
+أكبر أو تساوي تلاتة and إلى ما لا نهاية الان بما
+
+126
+00:10:06,600 --> 00:10:12,080
+أن الأولى false ضمنت الباقي false وبالتالي أقدر
+
+127
+00:10:12,080 --> 00:10:15,480
+أحكم على ال predicate تعالي و أنا غيرت ال domain
+
+128
+00:10:15,480 --> 00:10:18,700
+من ال natural number و روحت قلتلك في المجموعة صفر
+
+129
+00:10:18,700 --> 00:10:27,320
+واحد و اتنين ستصبح ال statement هذهtrue true او
+
+130
+00:10:27,320 --> 00:10:35,340
+false false صفر غيرناها تلاتة ستة وخمسة صارت ال
+
+131
+00:10:35,340 --> 00:10:38,340
+true وبالتالي القيم اللي في ال domain هي اللي
+
+132
+00:10:38,340 --> 00:10:42,680
+بتحكم الموضوع طيب في حالة زي هذه انا لسه عن ال
+
+133
+00:10:42,680 --> 00:10:48,320
+domain ماتكلمتش عليه هاي الدالة اللي عندي بقول ان
+
+134
+00:10:48,320 --> 00:10:53,120
+ال P of X ال predicate function X أكبر أو تساوي
+
+135
+00:10:53,120 --> 00:10:59,490
+تلاتةعشان انا اقدر احكم و اديك truth value لازم
+
+136
+00:10:59,490 --> 00:11:04,730
+اتحدد ليه قيمة ال X يعني لو انا جيت سؤالتك قيمة P
+
+137
+00:11:04,730 --> 00:11:12,420
+of واحد بلكن ترجمها يعني الواحدأكبر او تساوي تلاتة
+
+138
+00:11:12,420 --> 00:11:16,980
+وهذه قيمتها false تمام؟ لاحظ ان هذه ال statement
+
+139
+00:11:16,980 --> 00:11:20,700
+صارت او ال predicate function هذه صارت هي الأساس
+
+140
+00:11:20,700 --> 00:11:23,560
+عندى في التقييم في المرحلة الحالية بالضبط هي
+
+141
+00:11:23,560 --> 00:11:26,560
+القانون اللى انا بدى احكم عليه على العناصر تبعد X
+
+142
+00:11:26,560 --> 00:11:31,340
+بس بنرجع للأساس بدون ما تكون قيمة X واضحة عندى مش
+
+143
+00:11:31,340 --> 00:11:34,680
+حاضر احكم تمام؟ اذا انا بتصير not a proposition
+
+144
+00:11:37,720 --> 00:11:42,080
+طيب الان مجموعة القيم اللي بتمثلها X احنا اتفقنا
+
+145
+00:11:42,080 --> 00:11:44,380
+هي عبارة عن ال domain اللي هي مصطلح تاني في
+
+146
+00:11:44,380 --> 00:11:47,380
+الرياضات المنفصل اللي بنسميها Universe of
+
+147
+00:11:47,380 --> 00:11:52,380
+Discourse Universe of Discourse و أحيانا بنرمزلها
+
+148
+00:11:52,380 --> 00:11:56,860
+بال E و D لو كتبنا domain لو كتبنا Universe of
+
+149
+00:11:56,860 --> 00:11:59,320
+Discourse او Universe of Discourse افهم ان احنا
+
+150
+00:11:59,320 --> 00:12:05,160
+بنتكلم جاعد على ال domain طيبتعالى نشوف بالمثال
+
+151
+00:12:05,160 --> 00:12:14,360
+اللى موجود عندنا هنا بالـ slide P of X و X is an
+
+152
+00:12:14,360 --> 00:12:21,720
+odd integer X is an odd integer الآن بيبقى انه
+
+153
+00:12:21,720 --> 00:12:27,220
+مابتكلمش على domain بقدر اتكلم فقط علىقيمة واحدة ل
+
+154
+00:12:27,220 --> 00:12:33,240
+X بسألك P of أربعة ترجمتها هتصير أن الأربعة is an
+
+155
+00:12:33,240 --> 00:12:39,320
+odd integer true ولا false؟ false P of سبعة يعني
+
+156
+00:12:39,320 --> 00:12:43,860
+أن السبعة is an odd integer true تمانية P of
+
+157
+00:12:43,860 --> 00:12:48,140
+تمانية يعني تمانية is an odd integer false تسعة
+
+158
+00:12:48,140 --> 00:12:53,100
+تسعة is an odd integer irony true
+
+159
+00:12:55,620 --> 00:12:59,420
+عيد تاني؟ احنا
+
+160
+00:12:59,420 --> 00:13:02,480
+بنقول كمان مرة شباب في الـ propositional function
+
+161
+00:13:02,480 --> 00:13:08,640
+اللي هى P of X بقيمها بقيمها بناء على تعريف ال
+
+162
+00:13:08,640 --> 00:13:15,120
+function ثم قيمة X قيمة X اللي هى جزء من ال domain
+
+163
+00:13:15,120 --> 00:13:18,970
+الآن في المثال هذاأنا قاعد بقول ان الـ
+
+164
+00:13:18,970 --> 00:13:22,230
+propositional function بتقول ان ال X هذه اللي هي P
+
+165
+00:13:22,230 --> 00:13:27,150
+of X X هذه عبارة عن عدد فردي عبارة عن عدد فردي
+
+166
+00:13:27,150 --> 00:13:31,790
+فانا أجي اقول P of أربعة بين قوسين بدأت الترجم
+
+167
+00:13:31,790 --> 00:13:36,130
+الأربعة is عدد عبارة عن عدد فردي وبالتالي الصرفة
+
+168
+00:13:36,130 --> 00:13:39,250
+اللي بقدر أقول عليها false لكن السبعة P of سبعة
+
+169
+00:13:39,250 --> 00:13:43,010
+حسب ال predicate function اللي عندي هذه السبعة is
+
+170
+00:13:43,010 --> 00:13:48,880
+an odd integer true تمام؟هي كمان predicate
+
+171
+00:13:48,880 --> 00:13:52,920
+function تانية لكنها تعتمد على two variables بحيث
+
+172
+00:13:52,920 --> 00:13:58,720
+أن مجموعهم أكبر من خمسة
+
+173
+00:14:02,600 --> 00:14:07,880
+تتذكر لما كنا نكتب 2 زائد أربعة equal خمسة نقول
+
+174
+00:14:07,880 --> 00:14:12,000
+عليها proposition ولا لا وقيمته false ال
+
+175
+00:14:12,000 --> 00:14:16,460
+proposition وقيمته false طيب الآن بال function
+
+176
+00:14:16,460 --> 00:14:20,740
+بالشكل هذا ماقدرش أتكلم و هذه is not a proposition
+
+177
+00:14:20,740 --> 00:14:25,340
+ولا لا لأن فيها مجولين الآن لك لما أجي أقولك قيمة
+
+178
+00:14:25,340 --> 00:14:30,320
+x بتنين وقيمة y بتنينأتحدّى لك فأصبح عبارة عن
+
+179
+00:14:30,320 --> 00:14:35,920
+proposition و بقدر أديله قيمة الان Q of 2 و 2 يعني
+
+180
+00:14:35,920 --> 00:14:40,700
+2 زائد 2 لاحظ كل مرة العمالي بقى ترجم بشكل فعلى
+
+181
+00:14:40,700 --> 00:14:45,720
+المتغيرات اللى عندى لـ proposition عشان أقدر أحكم
+
+182
+00:14:45,720 --> 00:14:52,980
+على قيمته 2 زائد 2 أربعة أكبر من خمسة false
+
+183
+00:14:52,980 --> 00:14:58,690
+وبالتالي القيمة هناfalse تلاتة زائد اتنين اكبر من
+
+184
+00:14:58,690 --> 00:15:04,970
+خمسة false تلاتة زائد تلاتة اكبر من خمسة true
+
+185
+00:15:04,970 --> 00:15:14,810
+تلاتة زائد اربعة اكبر من خمسة true تعالى
+
+186
+00:15:14,810 --> 00:15:18,010
+نشوف المتغير هذا او ال proposal function او ال
+
+187
+00:15:18,010 --> 00:15:22,270
+prediction function التالية Z او اعفن ال R بتعتمد
+
+188
+00:15:22,270 --> 00:15:30,830
+علىX تلك المتغيرات X و Y و Z و العلاقة ما بينهم X
+
+189
+00:15:30,830 --> 00:15:37,210
+زائد Y هي تساوي Z كمان مرة يا شباب بمنطق بمنطق ال
+
+190
+00:15:37,210 --> 00:15:40,270
+proposition او لا هذا ال statement is not a
+
+191
+00:15:40,270 --> 00:15:44,350
+proposition لكن بمنطق الأرقام او ال values تبع ال
+
+192
+00:15:44,350 --> 00:15:51,370
+X و Y و Z بتصير proposition الان R of 1 و 2 و 3
+
+193
+00:15:52,200 --> 00:15:57,760
+ترجمتها ان واحد زائد اتنين تساوي تلاتة بالمناسبة
+
+194
+00:15:57,760 --> 00:16:02,000
+ينفعك تقول اتنين زائد تلاتة تساوي واحد تتبع
+
+195
+00:16:02,000 --> 00:16:06,180
+الترتيب اللي موجود تماما بمعنى اخر هتيجي تقولي
+
+196
+00:16:06,180 --> 00:16:09,260
+والله الواحد هي ال X للاقيه الخانة الأولى في ال
+
+197
+00:16:09,260 --> 00:16:13,960
+argument التاني هي ال Yوالتلاتة هي الـ Z و بتكتبهم
+
+198
+00:16:13,960 --> 00:16:18,560
+نفس صورة المعادلة اللى موجودة عندها و بالتالي صارت
+
+199
+00:16:18,560 --> 00:16:20,900
+ال quantifier او عفوا ال predicate function اللى
+
+200
+00:16:20,900 --> 00:16:23,880
+عندى هذا الواحد اتنين و تلاتة هي عبارة عن ال
+
+201
+00:16:23,880 --> 00:16:29,300
+proposition قيمته او يخبر بالحقيقة التالية واحد
+
+202
+00:16:29,300 --> 00:16:33,840
+زائد اتنين تساوي تلاتة ال truth value جديش تبعته
+
+203
+00:16:33,840 --> 00:16:40,060
+true ال truth value تبعته true R of صفر و صفر واحد
+
+204
+00:16:41,600 --> 00:16:51,540
+صفر زاد صفر يساوي واحد false طبعا ماشي الحال يعني
+
+205
+00:16:51,540 --> 00:16:56,840
+الآن كخطوة أولى بنقول أنه ال predicate function ال
+
+206
+00:16:56,840 --> 00:17:02,360
+قيمة تبعتها تتمد على ال arguments أو المتغيرات
+
+207
+00:17:02,360 --> 00:17:05,880
+اللى موجودة فيها لو أنا مقدرش أدى المتغيرات قيم
+
+208
+00:17:07,130 --> 00:17:11,410
+معناته بقدرش أديه هيش true or false وبالتالي بتبطئ
+
+209
+00:17:11,410 --> 00:17:19,270
+اللي عندي proposition لما
+
+210
+00:17:19,270 --> 00:17:23,430
+أنا باجي بتكلم عن ال quantifier الآن بدي أدي قيمة
+
+211
+00:17:23,430 --> 00:17:27,330
+مطلقة هيك نسميها لمين لل proposition ال function
+
+212
+00:17:27,330 --> 00:17:30,870
+اللي عندي بناء على مين؟ بناء على ال domain اللي
+
+213
+00:17:30,870 --> 00:17:33,670
+احنا بنتكلم عليه سابقا ال domain لم يكن معرف بشكل
+
+214
+00:17:33,670 --> 00:17:38,200
+واضحبس الآن لأ بدك تصير تعرف مين هو ال domain اللي
+
+215
+00:17:38,200 --> 00:17:44,080
+موجود عندك نرجع للمثال اللي كتبته الأول P of X X
+
+216
+00:17:44,080 --> 00:17:51,780
+أكبر أو تساوي تلاتة وال X تنتمي لل natural number
+
+217
+00:17:51,780 --> 00:17:57,660
+هذا الكلام انا حيحرفت ال domainوعرفت الـ predicate
+
+218
+00:17:57,660 --> 00:18:01,220
+function بقال في عندي شغلة واحدة في موضوع ال
+
+219
+00:18:01,220 --> 00:18:04,280
+quantifiers او في ال universal quantifier اما في
+
+220
+00:18:04,280 --> 00:18:08,900
+عندي for all او there exist عشان اقدر احكم على ال
+
+221
+00:18:08,900 --> 00:18:13,680
+statement هذه ككل الان في ال quantifiers في عندي
+
+222
+00:18:13,680 --> 00:18:22,160
+ال universal quantifier of b of x من ال b of x هي
+
+223
+00:18:23,180 --> 00:18:26,500
+ماذا يعني الـ Universal؟ بيقول الـ P of X is true
+
+224
+00:18:26,500 --> 00:18:32,000
+for all values of X in الـ D في الدمين يعني بين
+
+225
+00:18:32,000 --> 00:18:40,440
+قسمين for all X P of X is true ترجعها
+
+226
+00:18:40,440 --> 00:18:52,260
+دي مفهومها for all X in دمين in الـ D P of X is
+
+227
+00:18:52,260 --> 00:18:52,640
+true
+
+228
+00:18:55,280 --> 00:18:58,620
+هذه مفهومها الـ Universal Quantification أو الـ
+
+229
+00:18:58,620 --> 00:19:04,140
+Universal Quantifier وهذه رمزها For All X, B of X
+
+230
+00:19:04,140 --> 00:19:10,180
+For Any, Any, For All, For Every معناته كلهم بتقدي
+
+231
+00:19:10,180 --> 00:19:14,780
+نفس العبارة For All X طيب الآن بناء على الكلام
+
+232
+00:19:14,780 --> 00:19:19,120
+اللي فوق هيعرفت ال domain هي ال D و هيعرفت
+
+233
+00:19:19,120 --> 00:19:22,620
+predicate function شو وضع ال Universal Quantifiers
+
+234
+00:19:22,620 --> 00:19:27,840
+هذا true ولا false؟false ليش false؟ لأن على الأقل
+
+235
+00:19:27,840 --> 00:19:31,180
+هتلاقي واحد .. واحدة من الأمثلة دي بتقولك أن
+
+236
+00:19:31,180 --> 00:19:35,260
+المثال هذا مش صحيح الواحد ينتمي لل natural number
+
+237
+00:19:35,260 --> 00:19:41,860
+الواحد لا يحقق المعادلة هذه اللي هو أقل من التلاتة
+
+238
+00:19:41,860 --> 00:19:45,580
+كمان؟ لا يحقق المعادلة يعني الواحد أقل من التلاتة
+
+239
+00:19:45,580 --> 00:19:45,940
+اللي عندي
+
+240
+00:19:49,040 --> 00:19:53,300
+الـ Quantifier التاني اللي هو الـ Existential لما
+
+241
+00:19:53,300 --> 00:19:59,140
+أنا بتكلم على الأقل حلاجي واحد حقق المعادلة يعني
+
+242
+00:19:59,140 --> 00:20:02,480
+لو أنا في ال universal اتجهت وقلت كل الطلاب نجحوا
+
+243
+00:20:02,480 --> 00:20:09,040
+في المساق تمام؟ هذا الكلام true true ما لم اجد بين
+
+244
+00:20:09,040 --> 00:20:13,580
+الطلاب واحدرسم في المثال لو لقيت واحد فقط معياته
+
+245
+00:20:13,580 --> 00:20:16,700
+بتصير ال predicate ال universal هذا قيمته false
+
+246
+00:20:16,700 --> 00:20:20,260
+باجي بقول كل الطلاب اللي في القاعة هن بيعرفوا Java
+
+247
+00:20:20,260 --> 00:20:23,820
+الان
+
+248
+00:20:23,820 --> 00:20:27,020
+true or false حسب الان لو واحد قاللي بعرفش ايش
+
+249
+00:20:27,020 --> 00:20:29,960
+اسمك لو أحمد هان قاللي أنا بعرفش Java بعرف Python
+
+250
+00:20:30,910 --> 00:20:34,150
+تمام بتصير ال statement عندي false و من ال domain
+
+251
+00:20:34,150 --> 00:20:37,250
+اللي أنا بتكلم عليه مجموعة القلاب الموجودين حاليا
+
+252
+00:20:37,250 --> 00:20:41,070
+في المساقة أو في الغرفة اللي موجودة عندهم في ال
+
+253
+00:20:41,070 --> 00:20:49,730
+existential على الأقل هناك واحدة نقول
+
+254
+00:20:49,730 --> 00:20:57,830
+at least على الأقل there exist one
+
+255
+00:20:57,830 --> 00:21:06,820
+x such thatB of X is true على الأقل هناك طالب واحد
+
+256
+00:21:06,820 --> 00:21:11,220
+نجح في المساق أو على الأقل في طالب واحد رسم في
+
+257
+00:21:11,220 --> 00:21:15,660
+المساق في الحالة الأولى على الأقل في طالب واحد نجح
+
+258
+00:21:15,660 --> 00:21:20,560
+true والحالة التانية على الأقل هناك طالب واحد رسم
+
+259
+00:21:20,560 --> 00:21:26,360
+برضه true تمام؟ بتصير false لو انتفى الأمر بالمطلق
+
+260
+00:21:26,360 --> 00:21:33,840
+طيب باشي بقول okayهنا في واحدة بس من الغلط باجي
+
+261
+00:21:33,840 --> 00:21:39,800
+بقولها على الأقل هناك طالب في القاعة بيعرف Java
+
+262
+00:21:39,800 --> 00:21:49,300
+true على الأقل في واحد بتصير false متى؟ لما كلهم
+
+263
+00:21:49,300 --> 00:21:52,860
+بيعرفوش Java لما تصير .. لاحظ انت قاعد في ال
+
+264
+00:21:52,860 --> 00:21:57,460
+predicate function اللي موجود عندك تعالى نشوف
+
+265
+00:22:01,560 --> 00:22:06,040
+ناخد المثال هذا بقول خلّي ال B بتشير ل ال
+
+266
+00:22:06,040 --> 00:22:11,200
+predicate function او لل statement X أكبر من 3 يا
+
+267
+00:22:11,200 --> 00:22:14,740
+عمي وال
+
+268
+00:22:14,740 --> 00:22:18,780
+universe of discourse اللي هي ال domain ال set of
+
+269
+00:22:18,780 --> 00:22:25,620
+real numbers الاعداد الحقيقية يعني بين جثين P of X
+
+270
+00:22:25,620 --> 00:22:34,790
+هي عبارة عن X أكبر من 3والدمين ال real number ايش
+
+271
+00:22:34,790 --> 00:22:40,590
+بيقول يحط قيمة ايش؟ قيمة there exist b
+
+272
+00:22:40,590 --> 00:22:48,610
+of x there exist x b of x و
+
+273
+00:22:48,610 --> 00:22:54,640
+for all xB of X ايش يعني there exists X B of X
+
+274
+00:22:54,640 --> 00:22:59,500
+يعني هناك واحدة على الأقل من X تحقق المعادلة هذه
+
+275
+00:22:59,500 --> 00:23:07,000
+ايش قيمتها true ليش لأن الواحد الواحد احنا بدنا
+
+276
+00:23:07,000 --> 00:23:11,980
+أكبر معناته الأربعة تنتمي لل real number and
+
+277
+00:23:11,980 --> 00:23:21,140
+الأربعة أكبر من التلاتة true and true trueهذا هو
+
+278
+00:23:21,140 --> 00:23:24,640
+تفسير ال quantifiers بتصير بالشكل هذا تعالى نشوف
+
+279
+00:23:24,640 --> 00:23:29,600
+for all بقول
+
+280
+00:23:29,600 --> 00:23:35,380
+لي كل الأعداد الحقيقية أكبر أو تساوي تلاتة false
+
+281
+00:23:35,380 --> 00:23:45,180
+عند الواحد تنتمي لل real number and الواحد مش أكبر
+
+282
+00:23:45,180 --> 00:23:50,240
+من التلاتةمظبوط ولا لا؟ إيش يعني مش أكبر من تلاتة؟
+
+283
+00:23:50,240 --> 00:23:55,440
+يعني أصغر أو تساوي تلاتة بالمناسبة لو قولنا تلاتة
+
+284
+00:23:55,440 --> 00:24:00,620
+أكبر من تلاتة false تلاتة أكبر من تلاتة false
+
+285
+00:24:00,620 --> 00:24:05,960
+تمام؟ الأمور
+
+286
+00:24:05,960 --> 00:24:10,300
+تمام الشباب؟ أي
+
+287
+00:24:10,300 --> 00:24:15,260
+اي ايمعكوسة ولا مع بتنجان يا راجل خلّيك كويس هنا
+
+288
+00:24:15,260 --> 00:24:19,920
+طب يعني انت قولت هذه معكوسة وهذه مع أي شيء تنتهي
+
+289
+00:24:19,920 --> 00:24:25,360
+نقيق there exist there exist for all there exist
+
+290
+00:24:25,360 --> 00:24:31,080
+for all exist اعملها
+
+291
+00:24:31,080 --> 00:24:36,110
+reflectionvertical و لا horizontal reflection
+
+292
+00:24:36,110 --> 00:24:39,550
+الناس اللي أخذت رياضات و حوصبة رياضات للحوصبة
+
+293
+00:24:39,550 --> 00:24:43,270
+الرياضيات الوساطية المتعددة ال graphics reflection
+
+294
+00:24:43,270 --> 00:24:47,450
+reflection horizontal و لا vertical horizontal
+
+295
+00:24:47,450 --> 00:24:55,870
+horizontal و هذه الله يعطيكوا العافية يا شباب هذه
+
+296
+00:24:55,870 --> 00:24:59,430
+ال why وهذه النقطة لما صرها reflection
+
+297
+00:25:02,230 --> 00:25:06,190
+Horizontal Reflection لأن العكاس يكون حول ال Y
+
+298
+00:25:06,190 --> 00:25:10,510
+Axis الحمد
+
+299
+00:25:10,510 --> 00:25:15,830
+لله الحمد لله الحمد لله الحمد
+
+300
+00:25:15,830 --> 00:25:20,210
+لله الحمد
+
+301
+00:25:20,210 --> 00:25:21,390
+لله الحمد لله الحمد لله الحمد لله الحمد لله الحمد
+
+302
+00:25:21,390 --> 00:25:22,050
+لله الحمد لله الحمد لله الحمد لله الحمد لله الحمد
+
+303
+00:25:22,050 --> 00:25:23,030
+لله الحمد لله الحمد لله الحمد لله الحمد لله الحمد
+
+304
+00:25:23,030 --> 00:25:23,030
+لله الحمد لله الحمد لله الحمد لله الحمد لله الحمد
+
+305
+00:25:23,030 --> 00:25:23,030
+لله الحمد لله الحمد لله الحمد لله الحمد لله الحمد
+
+306
+00:25:23,030 --> 00:25:23,030
+لله الحمد لله الحمد لله الحمد لله الحمد لله الحمد
+
+307
+00:25:23,030 --> 00:25:24,490
+لله الحمد لله الحمد لله الحمد لله الحمد لله الحمد
+
+308
+00:25:24,490 --> 00:25:30,470
+لله الحمد
+
+309
+00:25:30,470 --> 00:25:30,470
+لل
+
+310
+00:25:33,950 --> 00:25:38,230
+Number اللي بيحكوا ورا الشباب و هيك نبري منهم واحد
+
+311
+00:25:38,230 --> 00:25:44,850
+زي الأسد و يترجملي او يحللليها Any real number is
+
+312
+00:25:44,850 --> 00:25:52,610
+a rational number true or
+
+313
+00:25:52,610 --> 00:25:56,750
+false اي
+
+314
+00:25:56,750 --> 00:26:03,670
+عدد حقيقي هو عبارة عن عدد نسبيأي عدب حقيقي هو
+
+315
+00:26:03,670 --> 00:26:07,490
+عبارة عن عدب نسبي true true true true true true
+
+316
+00:26:07,490 --> 00:26:09,190
+true true true true true true true true true true
+
+317
+00:26:09,190 --> 00:26:09,190
+true true true true true true true true true true
+
+318
+00:26:09,190 --> 00:26:09,350
+true true true true true true true true true true
+
+319
+00:26:09,350 --> 00:26:09,350
+true true true true true true true true true true
+
+320
+00:26:09,350 --> 00:26:09,410
+true true true true true true true true true true
+
+321
+00:26:09,410 --> 00:26:12,650
+true true true true true true true true true true
+
+322
+00:26:12,650 --> 00:26:18,070
+true true true true true true true true true true
+
+323
+00:26:18,070 --> 00:26:18,130
+true true true true true true true true true true
+
+324
+00:26:18,130 --> 00:26:18,250
+true true true true true true true true true true
+
+325
+00:26:18,250 --> 00:26:18,250
+true true true true true true true true true true
+
+326
+00:26:18,250 --> 00:26:18,250
+true true true true true true true true true true
+
+327
+00:26:18,250 --> 00:26:18,250
+true true true true true true true true true true
+
+328
+00:26:18,250 --> 00:26:18,330
+true true true true true true true true true true
+
+329
+00:26:18,330 --> 00:26:18,330
+true true true true true true true true true true
+
+330
+00:26:18,330 --> 00:26:18,330
+true true true true true true true true true true
+
+331
+00:26:18,330 --> 00:26:18,330
+true true true true true true true true true true
+
+332
+00:26:18,330 --> 00:26:18,330
+true true true true true true true true true true
+
+333
+00:26:18,330 --> 00:26:18,330
+true true true true true true true true true true
+
+334
+00:26:18,330 --> 00:26:18,330
+true true true true true true true true true true
+
+335
+00:26:18,330 --> 00:26:27,870
+true true true true true
+
+336
+00:26:27,870 --> 00:26:32,570
+true true trueاللي ضافت للـ natural number الصفر و
+
+337
+00:26:32,570 --> 00:26:37,630
+الـ negative مظبوط بعدها صار في عند ال rational
+
+338
+00:26:37,630 --> 00:26:43,250
+اللي هي ال Q و قلنا في ال Q اللي هي تكتب على صورة
+
+339
+00:26:43,250 --> 00:26:48,610
+A على B بي و A بنتمي لل Z و ال B لاتساوي صفر مظبوط
+
+340
+00:26:48,610 --> 00:26:55,690
+A بي لاتساوي صفر و A و B تنتمي ل Z في مجموعة تانية
+
+341
+00:26:55,690 --> 00:27:00,080
+اسمها ال rationalالاعداد الغير نسبية وال number
+
+342
+00:27:00,080 --> 00:27:07,280
+الواقعي تجمعهم كلياتهم وبالتالي هذا الكلام false
+
+343
+00:27:07,280 --> 00:27:14,940
+تعالي نحوله ماهو P of X X
+
+344
+00:27:14,940 --> 00:27:22,330
+is rationalنمبر لحظة شوية انا لسه ما هتسأل cash
+
+345
+00:27:22,330 --> 00:27:26,270
+على ال universal جعب اتكلم هيه x is a rational
+
+346
+00:27:26,270 --> 00:27:33,030
+number او بين غسين x بتنتمي ل q اذا انت هتكتب pure
+
+347
+00:27:33,030 --> 00:27:40,030
+mathematics تمام؟ الان ايش ال domain تبعنا ال real
+
+348
+00:27:40,030 --> 00:27:43,910
+number اللي
+
+349
+00:27:43,910 --> 00:27:50,510
+هي بين غسين ال a ولا لا؟الان انا مش قاعد بقول
+
+350
+00:27:50,510 --> 00:28:00,470
+every او for any طبعا يعني for all x b of x لأي x
+
+351
+00:28:00,470 --> 00:28:05,290
+في ال domain ال x is true مش فاكرة حتى رجلناها توي
+
+352
+00:28:05,290 --> 00:28:11,370
+لكل x في ال domain ال x is true false قيمتها false
+
+353
+00:28:11,370 --> 00:28:16,470
+ليش؟ لأن عندي جذري التينين تنتمي لل range عفوا لل
+
+354
+00:28:16,470 --> 00:28:24,690
+domain اللي هي ال R andجذر الاتنين لا يتنتني لكيو
+
+355
+00:28:24,690 --> 00:28:28,090
+بصبوط
+
+356
+00:28:28,090 --> 00:28:33,490
+وبالتالي هي السبب اللي صارت عندي false لو جلبنا
+
+357
+00:28:33,490 --> 00:28:37,950
+المسألة لو جلبنا المسألة بحيث انه صارت ال domain
+
+358
+00:28:37,950 --> 00:28:43,430
+هي ال domain هي ال key و ال any rational number is
+
+359
+00:28:43,430 --> 00:28:48,640
+a real numbertrue any rational number is a real
+
+360
+00:28:48,640 --> 00:28:53,260
+number is true بس طبعا تحاول تترجمها بالشكل اللي
+
+361
+00:28:53,260 --> 00:28:57,180
+موجود عندها طبعا الخطوة اللي بعدها أو ننتقل
+
+362
+00:28:57,180 --> 00:29:13,380
+للمقبرة اللي بعدها راحظ
+
+363
+00:29:13,380 --> 00:29:20,490
+معاياالتعريفات اللي احنا شوفناها for all x بيكس
+
+364
+00:29:20,490 --> 00:29:27,110
+for all x بيكس بيكس بيكس is true for every x متى
+
+365
+00:29:27,110 --> 00:29:31,830
+بتصير false لو لجيت واحدة على الأقل كانت false
+
+366
+00:29:31,830 --> 00:29:37,310
+there exist x بيكس يعني على الأقل ال b of x هذي
+
+367
+00:29:37,310 --> 00:29:40,550
+true لواحدة منها متى بتكون false لما يكون كل
+
+368
+00:29:40,550 --> 00:29:42,410
+العناصر false
+
+369
+00:29:44,430 --> 00:29:47,050
+لما نتكلم عن الأولويات أو قبل ما نتكلم عن
+
+370
+00:29:47,050 --> 00:29:50,530
+الأولويات إذا نحن نتكلم عن الـ Predicate و الـ
+
+371
+00:29:50,530 --> 00:29:53,330
+Quantifiers ما زلنا نتكلم في الـ Proposition و في
+
+372
+00:29:53,330 --> 00:29:58,890
+الـ Logic فالـ and و ال or و ال not هيظلوا حاضرات
+
+373
+00:29:58,890 --> 00:30:02,970
+هنا as connectors و أنا عمال لما بترجم بكتب and
+
+374
+00:30:02,970 --> 00:30:07,310
+كده و لا لأ؟ طيب الآن لو أنا إجيت في لحظة من
+
+375
+00:30:07,310 --> 00:30:13,850
+اللحظات و شوفنا ال quantifier أو بالشكل هذاأو شفنا
+
+376
+00:30:13,850 --> 00:30:17,330
+الـ Predicate أو الـ Proposition بالشكل هذا ماذا
+
+377
+00:30:17,330 --> 00:30:24,970
+نقرأه؟ for all x be x or q of x هل لما نتكلم عن
+
+378
+00:30:24,970 --> 00:30:28,830
+الأولويات أولويات احنا دايما نقول الأولوية للأقواص
+
+379
+00:30:28,830 --> 00:30:34,250
+بعدين ال and ال or الله يعطيك الله عفو النفي
+
+380
+00:30:34,250 --> 00:30:40,610
+جابلها أقواص نفي and or مصبوط ولا لا؟ ال and him
+
+381
+00:30:40,610 --> 00:30:41,810
+بعدين ال implies
+
+382
+00:30:45,200 --> 00:30:48,680
+لحظة لا مفيش هندي أقواس لو كان في عندك ال
+
+383
+00:30:48,680 --> 00:30:54,660
+universal أو ال quantifiers بتاخد أولوية على ال or
+
+384
+00:30:54,660 --> 00:31:01,840
+و ال connectors التانيين يعني هذه ترجمتها for all
+
+385
+00:31:01,840 --> 00:31:13,500
+x P of X لحالها or Q of Xماذا يعني؟ يعني انا في
+
+386
+00:31:13,500 --> 00:31:17,580
+عندي universal quantifier تمام؟ بدي احل ال
+
+387
+00:31:17,580 --> 00:31:21,220
+universal quantifier لحاله و اجيب قيمة ال Q of X
+
+388
+00:31:21,220 --> 00:31:27,180
+لحالها تمام؟ و اعمل بينهم R طب فعليا هال Q of X
+
+389
+00:31:27,180 --> 00:31:32,020
+بالصورة الحالية هذه بقدر اديها قيمة؟ لأ لازم اما
+
+390
+00:31:32,020 --> 00:31:36,420
+ال X تاخد value او بتتحول ل quantifier بنفس المنطق
+
+391
+00:31:36,420 --> 00:31:43,330
+السابق طيب و لو انا جانب المثالالـ B of for all X
+
+392
+00:31:43,330 --> 00:31:49,390
+for all X لاحظ الأقواس و في داخل الأقواس B of X
+
+393
+00:31:49,390 --> 00:31:57,690
+and Q of X يعني الـ for all بتتوزع على التنتين ال
+
+394
+00:31:57,690 --> 00:32:04,210
+quantifier بتتوزع على التنتين فيما يتعلق بموضوع
+
+395
+00:32:04,210 --> 00:32:08,030
+اننا فيه فيما يتعلق بموضوع اننا فيه احنا عاملا كنا
+
+396
+00:32:08,030 --> 00:32:19,710
+بنتكلمبنقول كل الطلاب كذا لو كانت true و بده
+
+397
+00:32:19,710 --> 00:32:26,070
+أنفيها بدها تصير false عشان تصير هذا أحد الطلاب
+
+398
+00:32:26,070 --> 00:32:38,750
+على الأقل واحد من الطلاب لم كذا عشان تنفيها
+
+399
+00:32:40,640 --> 00:32:43,260
+وبالتالي انت بتصير تقوله على ال statement اللي
+
+400
+00:32:43,260 --> 00:32:46,620
+موجودة فوق وبالتالي لاحظ لما انا بأجي بتكلم على ال
+
+401
+00:32:46,620 --> 00:32:52,680
+negation لل quantifiers لما بقش أقول for all x
+
+402
+00:32:52,680 --> 00:33:00,260
+نفيها there exist نفي ال P of X على ما قال واحد
+
+403
+00:33:00,260 --> 00:33:05,680
+ماليش بقوله ال P of X كله طالب نجحالـ B of X
+
+404
+00:33:05,680 --> 00:33:08,960
+الطالب نجح لـ Quantifier سبعتها الـ Universal
+
+405
+00:33:08,960 --> 00:33:15,760
+Quantifier كل الطلاب نجحوا نفيها على الأقل واحد من
+
+406
+00:33:15,760 --> 00:33:22,960
+الطلاب لم ينجح ولا لأ وبالتالي نفي الـ Universal
+
+407
+00:33:22,960 --> 00:33:27,240
+Quantifier الـ for all هتصير there exist at least
+
+408
+00:33:27,240 --> 00:33:32,700
+one والنفي انتقل لمين للـ B of X يعني هكذا لو
+
+409
+00:33:32,700 --> 00:33:34,040
+أجينا بالمثال السابق
+
+410
+00:33:37,810 --> 00:33:45,550
+for all x be of x و ال x أكبر من تلاتة و ال domain
+
+411
+00:33:45,550 --> 00:33:51,630
+تسوى ال natural number أه
+
+412
+00:33:51,630 --> 00:33:59,390
+بدي أنفيها أيوة
+
+413
+00:33:59,390 --> 00:34:08,270
+على الأقل هناك x واحدة نفيالـ P of X مافي ال P of
+
+414
+00:34:08,270 --> 00:34:15,010
+X ايش ممكن تكون يا شباب اقل او تساوي تلاتة there
+
+415
+00:34:15,010 --> 00:34:22,590
+exist X such that ال X اقل او تساوي تلاتة واضح
+
+416
+00:34:22,590 --> 00:34:30,770
+الأمور يا شباب طيب طيب مثلا
+
+417
+00:34:30,770 --> 00:34:34,850
+للبرمجة كل الطلاب في ال class حاليا بيعرفوا Java
+
+418
+00:34:37,140 --> 00:34:42,040
+for all عكسها على الأقل هناك واحد اللي هو أحمد
+
+419
+00:34:42,040 --> 00:34:47,140
+بيعرفش ال java نجي
+
+420
+00:34:47,140 --> 00:34:54,540
+لتاني عكس there exist عكس there exist ايش عكسها
+
+421
+00:34:54,540 --> 00:34:59,480
+there exist بتصير for all و نفيه لأن هكذا قلنا على
+
+422
+00:34:59,480 --> 00:35:05,780
+الأقل هناك طالب واحد بيعرف javaكلهم بيعرفوش كلهم
+
+423
+00:35:05,780 --> 00:35:08,480
+يعني for all و بيعرفوش نفيه ال function اللي
+
+424
+00:35:08,480 --> 00:35:13,180
+موجودة عندها وبالتالي صرت أنا بتكلم على العناصر
+
+425
+00:35:13,180 --> 00:35:18,160
+على الأقل هناك طالب بيعرف Java ما هي تحصير النفيها
+
+426
+00:35:18,160 --> 00:35:24,360
+كل الطلاب اللي عنده في ال class بيعرفوش ال Java
+
+427
+00:35:24,360 --> 00:35:34,210
+تمام؟ كأن حد مش بيقول تمام مش مشكلةلما اتكلم على
+
+428
+00:35:34,210 --> 00:35:38,230
+الـ Negation دي
+
+429
+00:35:38,230 --> 00:35:44,450
+مورغان مرمى أنا سابقا صح؟ لما قولت انا بأنفي P and
+
+430
+00:35:44,450 --> 00:35:52,910
+Q هل يتكافئ نقطة P أو نقطة Q و العكس صحيح لما
+
+431
+00:35:52,910 --> 00:35:57,990
+بستخدم ال R نفس الكلام دي مورغان هو صاحب فكرة
+
+432
+00:35:57,990 --> 00:36:01,830
+النفي أو أثبت نظرية النفي للي ي predicate بحيث انه
+
+433
+00:36:01,830 --> 00:36:06,290
+الله يعدى من المورغانخلص .. خلص من زمان بدون ما
+
+434
+00:36:06,290 --> 00:36:10,330
+تدعي there exists نفيها for all وصارت انتقلت
+
+435
+00:36:10,330 --> 00:36:14,390
+النفلة لل predicate function المعرفة اللي موجودة
+
+436
+00:36:14,390 --> 00:36:20,150
+عندك for every b x is false معناته there is a x
+
+437
+00:36:20,150 --> 00:36:27,750
+for which b of x is true طيب دعونا نشوف الأمثلة
+
+438
+00:36:27,750 --> 00:36:28,270
+التالية
+
+439
+00:36:31,540 --> 00:36:35,480
+لو قد جينا قولنا لك جيب اللي ال negation سيبك مني
+
+440
+00:36:35,480 --> 00:36:43,600
+على ال slide هنا مش تمام X تربيع أكبر من X و ال
+
+441
+00:36:43,600 --> 00:36:50,100
+domain تبعتنا هيها ال R is universal يعني بين جثين
+
+442
+00:36:50,100 --> 00:36:56,260
+أنا بتكلم هي ال P of X و ال domain كل ال R الآن
+
+443
+00:36:56,260 --> 00:36:57,240
+بدي أنفي هذه
+
+444
+00:36:59,940 --> 00:37:04,600
+ايوة بدك توزع النفي هي النفي هان معناته هتصيب هدى
+
+445
+00:37:04,600 --> 00:37:10,900
+there exist x مظبوط
+
+446
+00:37:10,900 --> 00:37:21,140
+دخل النفي على ال X تربيع أكبر من X بدك
+
+447
+00:37:21,140 --> 00:37:25,720
+تغير الإشارة اتجاه الإشارة ال X أكبر معناته عكسها
+
+448
+00:37:25,720 --> 00:37:34,060
+أصغر أو يساوي معناته there existX أن X تربيع أصغر
+
+449
+00:37:34,060 --> 00:37:41,020
+أو يساوي X هيك
+
+450
+00:37:41,020 --> 00:37:46,420
+المسألة بيقول انفي ليها What are the negation؟ إيش
+
+451
+00:37:46,420 --> 00:37:51,540
+النفي؟ الفكرة وين؟ أننا بدنا نرسخ مفهوم توزيع
+
+452
+00:37:51,540 --> 00:37:56,660
+النفي على ال predicateو ال quantifier اللي عندى
+
+453
+00:37:56,660 --> 00:38:01,620
+بقولى من خلال ال real number كذلك as domain and
+
+454
+00:38:01,620 --> 00:38:08,320
+there exist x x تربيع بدها تساوي x true ولا لا
+
+455
+00:38:08,320 --> 00:38:11,380
+true الواحد واحد تربيع يساوي واحد الصفر تربيع
+
+456
+00:38:11,380 --> 00:38:17,200
+يساوي صفر طيب هذه true بدى أنفيها قولنا مع النفي
+
+457
+00:38:17,200 --> 00:38:22,340
+تبعتها هيك بتصير for all x
+
+458
+00:38:26,520 --> 00:38:30,700
+X تربيع بدها تساوي X هذه النفة أنا لسه ماوصلتش
+
+459
+00:38:30,700 --> 00:38:36,920
+المرحلة الأخيرة هذه بدها تصير for all X X تربيع لا
+
+460
+00:38:36,920 --> 00:38:46,360
+تساوي X و باللا تساوي شو معناها شوف for all X ان X
+
+461
+00:38:46,360 --> 00:38:54,020
+تربيع أكبر من X أو و لا and مستحيل
+
+462
+00:38:54,020 --> 00:38:54,540
+تكون and
+
+463
+00:38:59,480 --> 00:39:03,860
+المجلد الموجود مستحيل يكون قاعدين تمام وبالتالي
+
+464
+00:39:03,860 --> 00:39:08,280
+عند X تربية أكبر من X أو وطبعا واحدة منهم اللي
+
+465
+00:39:08,280 --> 00:39:13,780
+بتتحقق مستحيل تنتين يتحقق الأمور تمام يا شباب لحد
+
+466
+00:39:13,780 --> 00:39:15,640
+اللحظة تمام
+
+467
+00:39:32,760 --> 00:39:39,280
+تعالى نشوف المثال التالي بقول ال quantifiers
+
+468
+00:39:39,280 --> 00:39:42,740
+تستخدم في ال system specification اللي بيشتغل
+
+469
+00:39:42,740 --> 00:39:46,360
+بالجوال الشباب مبسوط معاه يضبه شكله جيه رسالة
+
+470
+00:39:46,360 --> 00:39:55,620
+أضحكته يعنى أه أبسط أطول every email larger
+
+471
+00:39:55,620 --> 00:40:01,300
+than one megabyte will be compressed
+
+472
+00:40:03,930 --> 00:40:09,830
+الان من استخدام ال quantifiers وضع rules أو تعريف
+
+473
+00:40:09,830 --> 00:40:13,870
+ال specification أو مطلبات النظام كانت تالب كتب
+
+474
+00:40:13,870 --> 00:40:17,730
+ليها every email message larger than one megabyte
+
+475
+00:40:17,730 --> 00:40:20,730
+will be compressed يعني النظام البريد ال .. البريد
+
+476
+00:40:20,730 --> 00:40:25,150
+الإلكتروني تبع المؤسسة هذه بده يضغط كل رسالة حجمها
+
+477
+00:40:25,150 --> 00:40:31,120
+أكبر من واحد ميجاعشان الناس ما تختلفش، الناس اللي
+
+478
+00:40:31,120 --> 00:40:35,200
+بتشتغل في تقوير البرمجة، ما تختلفش في تفسير الكلام
+
+479
+00:40:35,200 --> 00:40:41,120
+هذا، بننجل الكلام من لغة البشر لرموز الرياضيات
+
+480
+00:40:41,120 --> 00:40:46,020
+التي لا تحتمل التقويل للأسف
+
+481
+00:40:46,020 --> 00:40:51,200
+أه، بس هذا من المناسبة مش عربي، هذا انجليزي طيب،
+
+482
+00:40:51,200 --> 00:40:54,420
+ماشي الحل يا أحمد، الآن تقالد ينحل ال statement
+
+483
+00:40:54,420 --> 00:41:00,720
+تبعتنانشوف إيش فيها أولاً أولاً كلمة every إيش
+
+484
+00:41:00,720 --> 00:41:08,360
+يعني for all for all طيب مين العنصر أنا باشطل عليه
+
+485
+00:41:08,360 --> 00:41:13,760
+ال message ال message طيب الحجم كذلك ممكن يكون
+
+486
+00:41:13,760 --> 00:41:17,180
+متغير في المسألة دي ثابت خلّيني أثبته تمام لكن
+
+487
+00:41:17,180 --> 00:41:23,340
+ممكن احنا نكتب حالنا بشكل أكبر طيب يعني الآن ال X
+
+488
+00:41:25,110 --> 00:41:30,590
+عبارة عن إيش؟ Email Message و لا رسالة بالبريد
+
+489
+00:41:30,590 --> 00:41:37,930
+الإلكتروني B of X X
+
+490
+00:41:37,930 --> 00:41:49,820
+أكبر من 1 ميجا بايت أكبر أو تساوي ميجا بايتو ممكن
+
+491
+00:41:49,820 --> 00:41:53,160
+بما انه اتكلم على ال sending email اللي انا بدي
+
+492
+00:41:53,160 --> 00:41:57,720
+ابعتها ممكن اغير الاسم لأس .. مغضب نظر على الرموز،
+
+493
+00:41:57,720 --> 00:42:01,540
+تمام؟ أسأم .. أسأم .. أسأم .. أسأم .. أسأم .. أسأم
+
+494
+00:42:01,540 --> 00:42:02,520
+.. أسأم .. أسأم .. أسأم .. أسأم .. أسأم .. أسأم ..
+
+495
+00:42:02,520 --> 00:42:05,280
+أسأم .. أسأم .. أسأم .. أسأم .. أسأم .. أسأم ..
+
+496
+00:42:05,280 --> 00:42:05,960
+أسأم .. أسأم .. أسأم .. أسأم .. أسأم .. أسأم ..
+
+497
+00:42:05,960 --> 00:42:07,820
+أسأم .. أسأم .. أسأم .. أسأم .. أسأم .. أسأم ..
+
+498
+00:42:07,820 --> 00:42:15,560
+أسأم .. أسأم .. أسأم .. أسأم .. أس
+
+499
+00:42:21,750 --> 00:42:31,910
+x will be compressed طيب ال will be شوفت يعني هذه
+
+500
+00:42:31,910 --> 00:42:39,750
+حسب ال logic عندي ال will be implies
+
+501
+00:42:39,750 --> 00:42:44,530
+تقول وبالتالي في عندي another predicate function
+
+502
+00:42:44,530 --> 00:42:49,210
+انا اسميها c c
+
+503
+00:42:49,210 --> 00:42:57,200
+of xX is compressed
+
+504
+00:42:57,200 --> 00:43:07,600
+انضبط ولا لأ وبالتالي هيك باشر بقول for all X as
+
+505
+00:43:07,600 --> 00:43:17,440
+of X لأي رسالة هتقول علاش ان ال C of X
+
+506
+00:43:20,470 --> 00:43:23,870
+أحنا قلنا قبل شوية .. احنا قلنا قبل شوية ال
+
+507
+00:43:23,870 --> 00:43:28,290
+quantifier .. ال quantifier هذه بتاخد أولوية على
+
+508
+00:43:28,290 --> 00:43:31,290
+ال operators اللي احنا شفناهم اللي هي ال and و ال
+
+509
+00:43:31,290 --> 00:43:35,010
+or و ال not و ال .. و ال implies وبالتالي هي
+
+510
+00:43:35,010 --> 00:43:41,510
+الرسالة اللي عندها تمام؟ أصبحيك .. كل رسالة حققت
+
+511
+00:43:41,510 --> 00:43:46,830
+أن حجمها أكبر من واحد ميجا بايت الرسالة هذه لازم
+
+512
+00:43:46,830 --> 00:43:51,160
+تنبغط must be compressedX must be compressed او X
+
+513
+00:43:51,160 --> 00:43:56,200
+is compressed كمان الان في هذه ال specification
+
+514
+00:43:56,200 --> 00:44:01,620
+ممكن ناخد خطوة كمال باتجاه الأمام بحيث انه اذا انت
+
+515
+00:44:01,620 --> 00:44:07,120
+الواحد ميجا هادي ممكن تلعب فيها او تغير فيها تروح
+
+516
+00:44:07,120 --> 00:44:12,260
+تخيليها هي عبارة عن متغير تاني لمين؟ لل X بحيث انه
+
+517
+00:44:12,260 --> 00:44:22,890
+نقول S of X و Y و ال Yبتساوي ال size ال 1 ميجا
+
+518
+00:44:22,890 --> 00:44:27,430
+بايت او الحجم اللي انت بدك هيه بتصير في عندها ال S
+
+519
+00:44:27,430 --> 00:44:32,690
+of XY ال X أكبر من ال Y اللي ال message هذي ايش
+
+520
+00:44:32,690 --> 00:44:37,230
+بتصير فيها بدها تنضغط ال message هذي بدها تنضغط
+
+521
+00:44:37,230 --> 00:44:45,190
+طيب الامور تمام هى
+
+522
+00:44:45,190 --> 00:44:49,620
+عبارة عن another functionعبارة عن دالة كانية
+
+523
+00:44:49,620 --> 00:44:54,260
+اختصاريا compressed بس احنا لما جيه اللي هي الناتج
+
+524
+00:44:54,260 --> 00:44:58,360
+ناتج لكن will be كان لها معنى عندي اللي هي ال
+
+525
+00:44:58,360 --> 00:45:02,120
+employees فانا شقبت ال will be بس احتفظت منين بال
+
+526
+00:45:02,120 --> 00:45:07,720
+compression ال property وبالتالي انا الآن صرت انا
+
+527
+00:45:07,720 --> 00:45:13,240
+بقدر اكتب ال email تبعي بالشكل هذا بعد ما انا
+
+528
+00:45:13,240 --> 00:45:19,780
+فسرته وفسلته كل واحدة اش يعنيفبقدر اخد ال
+
+529
+00:45:19,780 --> 00:45:24,400
+specification دي بشكل صحيح طيب تعالى نشوف برضه ناس
+
+530
+00:45:24,400 --> 00:45:30,940
+هشيلهم اش قضية if a user is active ال if ايش يعني
+
+531
+00:45:30,940 --> 00:45:39,100
+ال if يعني في implies user is active نفس الشيء
+
+532
+00:45:39,100 --> 00:45:46,480
+المفعل تمام يعني ممكن انا قاعد يقول هذا P of X ال
+
+533
+00:45:46,480 --> 00:45:54,500
+Xis active مين X يقول user مصبوط او لا طيب at
+
+534
+00:45:54,500 --> 00:46:00,880
+least على الأقل واحد من ال network link will be
+
+535
+00:46:00,880 --> 00:46:04,480
+available يعني هيك اذا كان في واحد من ال user في
+
+536
+00:46:04,480 --> 00:46:09,180
+داخل الشبكة شغال او active معناته واحد من ال links
+
+537
+00:46:09,180 --> 00:46:16,360
+الآن موجود طيب معناته انا بدى اتكلم هانوين
+
+538
+00:46:19,140 --> 00:46:26,420
+At least إيش يعني؟ There exists مصبوط و ال link is
+
+539
+00:46:26,420 --> 00:46:31,100
+active و ال link is active خلّيني أقول هادي انعرف
+
+540
+00:46:31,100 --> 00:46:36,400
+ال function نسميها ال U as a user و ال L of X
+
+541
+00:46:36,400 --> 00:46:42,700
+بينفعش بينفعش تاخد X بتحتاخد variable تاني تمام
+
+542
+00:46:42,700 --> 00:46:47,850
+عشان تتفرضوا عن ال user ماتخربطش في الأمور linkال
+
+543
+00:46:47,850 --> 00:46:55,870
+link ايه او y مش مشكلة و ال y is available link
+
+544
+00:46:55,870 --> 00:47:04,510
+ايش بتصير ال function if ال
+
+545
+00:47:04,510 --> 00:47:09,110
+ux معناته
+
+546
+00:47:09,110 --> 00:47:23,320
+there exist y بتحققall of Y صحيك؟ صحيك؟ صح بس هذا
+
+547
+00:47:23,320 --> 00:47:28,700
+الكلام فيه صورة تانية كتبناها احنا سابقا اللي هي
+
+548
+00:47:28,700 --> 00:47:34,420
+إيش ال Contra positive نفد أول أو نفد تاني يقول
+
+549
+00:47:34,420 --> 00:47:38,300
+إلى أول بين جثين إذا واحد من ال connection تبعت
+
+550
+00:47:38,300 --> 00:47:42,560
+الشبكة الآن شغال معناته في عندي واحد من ال user is
+
+551
+00:47:42,560 --> 00:47:47,750
+activeوالمفروض الآن الناس كونوا عايش روحوا انت
+
+552
+00:47:47,750 --> 00:47:50,810
+مابتعرفش انه في user شغال انت لما بتطلع على جهاز
+
+553
+00:47:50,810 --> 00:47:55,090
+التحكم تبع الشبكة ال router مابتعرفش منه الشبكة بس
+
+554
+00:47:55,090 --> 00:48:00,630
+بتشوف ال link بديك click ولا لأ؟ بديك إشارة انه في
+
+555
+00:48:00,630 --> 00:48:06,250
+الخط هذا busy شغال فبالتالي إذا الخط شغال معناته
+
+556
+00:48:06,250 --> 00:48:10,930
+فيه end user بما ان ال F هذه بي implies Q كانت
+
+557
+00:48:10,930 --> 00:48:17,940
+تكافئ تمامانقطة Q تعني نقطة B يعني أنني أكتبها
+
+558
+00:48:17,940 --> 00:48:22,840
+بصورة ألطف تتعبر عن الوظيفة اللي هي لو كان عندي
+
+559
+00:48:22,840 --> 00:48:30,480
+user شغال معناته على الأقل في عندي Y و Y is active
+
+560
+00:48:30,480 --> 00:48:35,160
+هذا الحالة الأولى قصة هكذا لو ماكانش عندي ولا خط
+
+561
+00:48:35,160 --> 00:48:39,900
+active أو ولا خط available معناته
+
+562
+00:48:43,520 --> 00:48:54,240
+for all y not l of y link is available issue at
+
+563
+00:48:54,240 --> 00:48:58,740
+day not
+
+564
+00:48:58,740 --> 00:49:06,540
+u of x أو مافيش there exist x not
+
+565
+00:49:07,960 --> 00:49:13,060
+for all بيصير universal بيصير كل مافيش ولا حدا for
+
+566
+00:49:13,060 --> 00:49:19,060
+all x negation تبع ال U of X خربتكوا انا صح نعيد
+
+567
+00:49:19,060 --> 00:49:22,700
+تاني انا عمال بقولك هذا ال quantifier بعد ما
+
+568
+00:49:22,700 --> 00:49:28,500
+كتبناه بالصورة هذه احنا اللي هي ال F معناته انا
+
+569
+00:49:28,500 --> 00:49:31,080
+بقدر بقول بكتبه بصورة تانية لو حاولت ايش أساوي
+
+570
+00:49:31,080 --> 00:49:36,200
+أشجلبهمعشان أجلبهم القيامة كمان مرة هي ال
+
+571
+00:49:36,200 --> 00:49:39,720
+quantifier اللي عندي لو كان فيه عندي user active
+
+572
+00:49:39,720 --> 00:49:44,840
+if there exist b x b of x لو كان واحد شغال على
+
+573
+00:49:44,840 --> 00:49:48,720
+الأقل واحد شغال اوكي أنا مش كاتب هنا there exist
+
+574
+00:49:48,720 --> 00:49:51,920
+لو
+
+575
+00:49:51,920 --> 00:49:54,800
+كان واحد .. واحد شغال معاه فيه له link available
+
+576
+00:49:54,800 --> 00:49:59,260
+مصبوط فيه link متاح و هالشارك من خلاله تعالوا
+
+577
+00:49:59,260 --> 00:50:01,620
+نكتبها بالصورة التانية تبع ال contrapositive
+
+578
+00:50:04,420 --> 00:50:09,540
+إذا ما كل ال links مش شغالة معناته أنا بتأكد إنه
+
+579
+00:50:09,540 --> 00:50:14,480
+مافيش ولا user active معناته مافيش ولا user active
+
+580
+00:50:14,480 --> 00:50:20,200
+وبهك انتهينا من موضوع ال section لليوم في أي سؤال
+
+581
+00:50:20,200 --> 00:50:23,160
+يا شباب في الأمثلة الأخيرة؟ ماشي الحال في أي سؤال
+
+582
+00:50:23,160 --> 00:50:27,140
+يا شباب؟ فلس أنا بدي أكسي تكفي لحد اليوم عشان أظهر
+
+583
+00:50:27,140 --> 00:50:30,040
+في عنا برضه section بسيط للمحاضرة اللي جاية و نخلص
+
+584
+00:50:30,040 --> 00:50:31,860
+من ال chapter الأول الله عطيكوا العافية
+
diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/pKrZGwbVnlc.srt b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/pKrZGwbVnlc.srt
new file mode 100644
index 0000000000000000000000000000000000000000..b58a0f9ce2ecc03913d176cb17c55df2a6a45f4b
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/pKrZGwbVnlc.srt
@@ -0,0 +1,1787 @@
+
+1
+00:00:21,040 --> 00:00:22,880
+بسم الله والحمد لله والصلاة والسلام على رسول
+
+2
+00:00:22,880 --> 00:00:26,900
+الله، اليوم إن شاء الله يا شباب، هنكمل في
+
+3
+00:00:26,900 --> 00:00:32,960
+mathematical proving بالإثبات الرياضي، لكن محاضرتنا
+
+4
+00:00:32,960 --> 00:00:35,520
+مش هتكون فيها… يعني هتكلم عن موضوع واحد جديد
+
+5
+00:00:35,520 --> 00:00:39,240
+اللي هو الإثبات بالتناقض، ومن ثم نحاول نحل مجموعة
+
+6
+00:00:39,240 --> 00:00:43,840
+من الأمثلة عشان نثبت موضوع الإثباتات السابقة، طبعاً
+
+7
+00:00:43,840 --> 00:00:47,240
+كنا إحنا الأسبوع الماضي بدأنا بالإثبات الرياضي، و
+
+8
+00:00:47,240 --> 00:00:51,190
+قلنا كالتالي: لأن معظم المسائل أو معظم النظريات اللي
+
+9
+00:00:51,190 --> 00:00:54,630
+بيطلب مننا نثبتها، هتلاقيها موجودة على صورة if
+
+10
+00:00:54,630 --> 00:01:00,110
+implied أو if then أو P implies Q، وأول نوع من
+
+11
+00:01:00,110 --> 00:01:03,930
+الإثبات الرياضي، قلنا: هروح أنا أفترض فيه الـ Q is
+
+12
+00:01:03,930 --> 00:01:10,050
+true، وجينا قلنا كالتالي: إحنا الأساس… الأساس أن
+
+13
+00:01:10,050 --> 00:01:13,950
+B implies Q، لو تحققت الـ hypothesis معناته الـ
+
+14
+00:01:13,950 --> 00:01:18,690
+conclusion هتكون عندي true، دائماً true، تقول الـ true
+
+15
+00:01:18,690 --> 00:01:24,970
+فبالمجمل هتكون عندي العملية كلها true،  أول طريقة
+
+16
+00:01:24,970 --> 00:01:29,930
+مُقررة للإثبات كانت الـ direct، إثبات المباشر، ومنها
+
+17
+00:01:29,930 --> 00:01:36,220
+أنا بعتمد على أو بفترض أن P is true، لما أفترض أن P
+
+18
+00:01:36,220 --> 00:01:40,280
+is true، هتوصلني أن الـ Q تتحقق عندي، وبالتالي أنا
+
+19
+00:01:40,280 --> 00:01:44,900
+بكون وصلت للمطلوب اللي موجود عندي، بمعنى آخر أنه في
+
+20
+00:01:44,900 --> 00:01:46,960
+النظرية اللي هتكون موجودة عندي أو المطلوب من
+
+21
+00:01:46,960 --> 00:01:51,790
+إثباتها، مطلوب إذا ما كانت مكتوبة بشكل مباشر if then،
+
+22
+00:01:51,790 --> 00:01:54,710
+معناته أنا بدي أكتبها if then، هذه خطوة رقم واحد،
+
+23
+00:01:54,710 --> 00:02:00,650
+وأروح أفترض أن الـ P is true، وبناءً على الـ P أحاول
+
+24
+00:02:00,650 --> 00:02:05,830
+أصل لمين؟ لـ Q، وطبعاً كلنا بنعرف نضرب ونجمع ونقول
+
+25
+00:02:05,830 --> 00:02:09,550
+العدد على اليمين واليمين واليسار، إشارة اللي يساوي، وها
+
+26
+00:02:09,550 --> 00:02:14,190
+كذا، وطبعاً كان بالمثال اللي عندنا الأسهل هي if الـ M
+
+27
+00:02:14,190 --> 00:02:17,810
+is odd then M is odd، بس من باب التذكير،
+
+28
+00:02:17,810 --> 00:02:26,620
+الآن هي الـ P وهذه الـ Q، الـ N، شو يعني الـ N is odd؟ و
+
+29
+00:02:26,620 --> 00:02:31,920
+أنا أخوك، واحد على واحد، هقول Assume الـ
+
+30
+00:02:31,920 --> 00:02:37,160
+P، خلاص، لو كنت بتديش كمان is it true، أنا بفترض أن
+
+31
+00:02:37,160 --> 00:02:42,700
+أنت جاي بتشتغل صح، Assume الـ P is true، يعني الـ N is
+
+32
+00:02:42,700 --> 00:02:50,450
+odd، مفهومها الـ N is…الخطوة التالية اللي هي الكلام
+
+33
+00:02:50,450 --> 00:02:55,690
+تجيب صورة الـ N كعدد فردي، اللي هي صورة 2K زائد
+
+34
+00:02:55,690 --> 00:03:00,770
+واحد، for some K تنتمي إلى Z، الخطوة رقم ثلاثة، بعد
+
+35
+00:03:00,770 --> 00:03:04,810
+هيك هو بيقول لك أن الـ N تربيع، معناته أنك تربّع الـ N
+
+36
+00:03:04,810 --> 00:03:12,490
+اللي عندك، وتمشي الخطوة التالية، تربّع الـ N تصير
+
+37
+00:03:12,490 --> 00:03:17,640
+2…أو N تربيع، بدها تساوي 2K زائد واحد، لكل
+
+38
+00:03:17,640 --> 00:03:23,060
+تربيع، بدها تساوي 4K تربيع زائد 4K زائد
+
+39
+00:03:23,060 --> 00:03:27,560
+واحد، لأن بأخذ عامل مشترك من هنا، 2 في
+
+40
+00:03:27,560 --> 00:03:33,180
+2K تربيع زائد 2K، لكل زائد واحد، وهذه
+
+41
+00:03:33,180 --> 00:03:39,800
+الصورة 2K، عفواً، وهذه الصورة صورة العدد
+
+42
+00:03:39,800 --> 00:03:48,660
+الفردي، odd integer، وبالتالي أنت وصلت لمين؟ للحل
+
+43
+00:03:48,660 --> 00:03:55,340
+اللي وصلت لـ Q، هذا بنسميه Direct Proof، بعض
+
+44
+00:03:55,340 --> 00:03:59,180
+المسائل…بعض المسائل هتحس أن الـ Direct Proof مش
+
+45
+00:03:59,180 --> 00:04:04,180
+هينفع معاها، خطوة فيها مش هتقدر توصل لنتيجة، طب إيش
+
+46
+00:04:04,180 --> 00:04:06,800
+بيكون الحل؟ بيكون الحل أن أنا أعتمد على الـ
+
+47
+00:04:06,800 --> 00:04:09,740
+Contrapositive تبعها، إيش الـ Contrapositive؟ إحنا
+
+48
+00:04:09,740 --> 00:04:18,000
+بنعرف أن الـ P implies Q تكافئ not Q implies not P،
+
+49
+00:04:18,000 --> 00:04:26,160
+وبالتالي إذا تحققت هذه المعادلة، صحيحة في هذه
+
+50
+00:04:26,160 --> 00:04:29,980
+المعادلة، سأفترض الـ Negation تبع الـ Q، سأقول
+
+51
+00:04:29,980 --> 00:04:34,260
+Assume not Q، ونفس الخطوات التي اتبعتها في الـ
+
+52
+00:04:34,260 --> 00:04:38,260
+Direct Proof، بس الفرق أن بدل ما أنا أفترض الـ P،
+
+53
+00:04:38,260 --> 00:04:43,580
+أفترضت أو اعتمدت على not Q، في حل من الأمثلة
+
+54
+00:04:43,580 --> 00:04:51,420
+اللي ممكن نشوفها بالشكل هذا، لما قال لي: 3N
+
+55
+00:04:51,420 --> 00:04:56,500
+زائد 2 is odd if الـ N…if الـ N، if الـ 3N
+
+56
+00:04:56,500 --> 00:05:03,900
+زائد 2 is odd، هي الـ P، معناته الـ N is odd، هي الـ
+
+57
+00:05:03,900 --> 00:05:07,580
+Q، الآن لو أنا فكرت أبدأ في الـ P في الـ direct proof،
+
+58
+00:05:07,580 --> 00:05:11,560
+هذا مش هيوصلني لنتيجة، مش هيوصلني لنتيجة، لأنها
+
+59
+00:05:11,560 --> 00:05:17,790
+complex، وبالتالي أنا بدي أحاول أشوف الأسهل، لو أنا
+
+60
+00:05:17,790 --> 00:05:23,850
+بدي أحولها بالـ contrapositive، ماذا أقول؟ if الـ N is
+
+61
+00:05:23,850 --> 00:05:27,610
+even، not Q،
+
+62
+00:05:27,610 --> 00:05:32,830
+then 3N زائد 2 is even، not P،
+
+63
+00:05:38,070 --> 00:05:42,450
+هذه النظرية هيك بيتصير، وأروح بقول له: assume not…
+
+64
+00:05:42,450 --> 00:05:48,510
+هذه إيش بتمثل؟ هذه نفي الـ Q، Assume not Q، حصل لمين؟
+
+65
+00:05:48,510 --> 00:05:51,970
+حصل لـ not P، وبالتالي حصلت على Contrapositive،
+
+66
+00:05:51,970 --> 00:05:56,870
+وبالتالي المعادلة اللي عندنا الأولى هتكون صحيحة في
+
+67
+00:05:56,870 --> 00:06:02,050
+الحالة هذه، هروح أقول له: assume not
+
+68
+00:06:02,050 --> 00:06:03,070
+Q is true،
+
+69
+00:06:07,500 --> 00:06:14,220
+ماذا يعني not Q is true؟ معناته N is not odd، بين
+
+70
+00:06:14,220 --> 00:06:20,820
+جوة سين هيكون even، فصورة الـ even، الـ N بيبقى تساوي
+
+71
+00:06:20,820 --> 00:06:28,420
+2K، وK تنتمي لـ Z، في قرصان K، الخطوة بعد هيك
+
+72
+00:06:28,420 --> 00:06:34,040
+3N زائد 2 تساوي
+
+73
+00:06:34,040 --> 00:06:42,070
+3 في 2K زائد 2، تساوي 6K زائد 2،
+
+74
+00:06:42,070 --> 00:06:47,610
+تساوي، آخذ الـ 2 عامل مشترك، 3K زائد واحد، هذه
+
+75
+00:06:47,610 --> 00:06:51,990
+integer، وهذه العدد عبارة عن is even integer،
+
+76
+00:06:51,990 --> 00:06:55,510
+contrapositive،
+
+77
+00:06:55,510 --> 00:07:03,150
+إلى آخره، تمام؟ أبدأ مع مين؟ مع الـ direct ولا مع
+
+78
+00:07:03,150 --> 00:07:09,590
+الـ contrapositive؟ الأصل أنك بدك تجرب وتتطلع في
+
+79
+00:07:09,590 --> 00:07:15,230
+المسألة بشكل كويس، أول خطوة أو أول جهد لازم تبذله
+
+80
+00:07:15,230 --> 00:07:22,030
+أنك تحدد الـ P ومن الـ Q في المسألة، عشان تمشي للـ
+
+81
+00:07:22,030 --> 00:07:25,390
+next step، الآن بقى إذا اتحددت P وQ، أنت صاحب
+
+82
+00:07:25,390 --> 00:07:31,750
+القرار، والتجربة هي أكثر نجاعة، ستمشي معاك مباشرة،
+
+83
+00:07:31,750 --> 00:07:36,210
+تمسك بيك وحالتك، وستأدي، وغالباً كل ما تلاقي P
+
+84
+00:07:36,210 --> 00:07:41,310
+complex، ستلاقي contrapositive وهو الحل،
+
+85
+00:07:41,310 --> 00:07:45,250
+كل ما تلاقي P complex، ستكون contrapositive، أنت
+
+86
+00:07:45,250 --> 00:07:50,470
+قارن، مين أسهل، P ولا Q؟ Q أسهل، يعني تقوم
+
+87
+00:07:50,470 --> 00:07:55,030
+باستخدام not Q، لن تبقى بسهولة بمكان اللي موجود
+
+88
+00:07:55,030 --> 00:08:00,110
+عندك، وبالتالي أنت لازم…يعني بدك تحاول وتجرب مرة
+
+89
+00:08:00,110 --> 00:08:03,490
+و اثنين وثلاثة لحد ما تصير أنت عايش صرف، عندك خبرة
+
+90
+00:08:03,490 --> 00:08:08,470
+في بناء أو في… بأي اتجاه أنا بدي أروح له، طيب النوع
+
+91
+00:08:08,470 --> 00:08:15,390
+الثالث من الإثبات في الـ…P implies Q، أحياناً مش
+
+92
+00:08:15,390 --> 00:08:18,430
+هيكون في اللي بنسميه إحنا بالتناقض، يعني لا جاية
+
+93
+00:08:18,430 --> 00:08:23,310
+معايا بالـ Direct Proof ولا جاية معايا بالـ
+
+94
+00:08:23,310 --> 00:08:26,890
+Contrapositive، في عندك طريقة ثالثة أو طريقة ثالثة
+
+95
+00:08:26,890 --> 00:08:31,410
+هم يسمّوها الـ Contradiction، إثبات بالتناقض، الإثبات
+
+96
+00:08:31,410 --> 00:08:38,230
+بالتناقض، إحنا كلنا بنعرف أن الـ P implies Q
+
+97
+00:08:38,230 --> 00:08:45,290
+equivalent to P or not Q، يعني لو تحققت واحدة من
+
+98
+00:08:45,290 --> 00:08:49,370
+الاثنين هدول، بتكون العملية إيش؟ الـ true، جالك الإثبات
+
+99
+00:08:49,370 --> 00:08:54,550
+بالتناقض كالتالي: إذا أنا روحت كالتالي، أخدت الموضوع
+
+100
+00:08:54,550 --> 00:08:59,790
+P وأخدت Q، ومش قادر أصل لواحدة منهم بالاتجاهين،
+
+101
+00:08:59,790 --> 00:09:03,350
+سواء كانت بالـ direct أو بالـ contrapositive، معناته
+
+102
+00:09:03,350 --> 00:09:08,910
+ممكن أنا أجرب أروح أفرض أن الـ P صحيحة والـ Q…
+
+103
+00:09:08,910 --> 00:09:11,430
+not Q صحيحة، يعني الـ Q…الـ Q false، يعني بدي
+
+104
+00:09:11,430 --> 00:09:15,870
+أقول أن النظرية دي مش صحيحة، وأجرب أشتغل مع الـ P and
+
+105
+00:09:15,870 --> 00:09:20,690
+الأسهل منهم، إذا حصلت على أي تناقض، معناته النظرية
+
+106
+00:09:20,690 --> 00:09:25,630
+الأصلية هي…هتكون صحيحة، كمان مرة أنت إيش عاملك؟
+
+107
+00:09:25,630 --> 00:09:29,810
+بتفترض أن الـ P is true والـ conclusion المحصلة
+
+108
+00:09:29,810 --> 00:09:34,470
+تبع النظرية Q is true، مضبوط؟ فأنت روحت وقلت له
+
+109
+00:09:34,470 --> 00:09:38,790
+false، قلت له أنك بتفترض أن الـ P is true والـ Q is
+
+110
+00:09:38,790 --> 00:09:44,860
+false، وأثناء الحل وصلت إن الـ false اللي أنت فرضتها
+
+111
+00:09:44,860 --> 00:09:52,940
+is false، نفي نفي يعني false، false، وكأنك تنفي إنك
+
+112
+00:09:52,940 --> 00:09:57,460
+تنفي، تمام؟ وبالتالي بتكون حصلت على شغل إيه اسمها؟
+
+113
+00:09:57,460 --> 00:10:01,720
+تطابق بين الفرضيات، طبعاً بدون ما تتطلع في…اسمي لك
+
+114
+00:10:01,720 --> 00:10:07,200
+يا غزال يا سويسي، خليك معايا هنا عشان تفهم إيش
+
+115
+00:10:07,200 --> 00:10:07,880
+المقصود بيه،
+
+116
+00:10:14,580 --> 00:10:22,660
+لو كان تربيع العدد فردي، فمعناته العدد لن يكون عندي
+
+117
+00:10:22,660 --> 00:10:38,210
+إيش؟ فردي، if الـ n تربيع is odd then الـ n is…أضعف
+
+118
+00:10:38,210 --> 00:10:42,930
+غزال أدم، يثبتها بإيش؟ Contra
+
+119
+00:10:42,930 --> 00:10:48,310
+positive، جاهز 100% معانا، بروح بقول له: assume not q،
+
+120
+00:10:48,310 --> 00:10:51,910
+يعني الـ n is even، الحاجة قبل شوية أثبتناها مضبوط،
+
+121
+00:10:51,910 --> 00:10:56,170
+ولا لأ؟ أو أثبتنا مثلها قريب منها، even وربع الـ even
+
+122
+00:10:56,170 --> 00:11:00,310
+في الآخر توصل، لكن أنا بدأت أستخدم معاها الإثبات
+
+123
+00:11:00,310 --> 00:11:01,790
+بالتناقض،
+
+124
+00:11:04,060 --> 00:11:07,340
+كمان مرة عشان الناس أصحابنا ما يتهوش، إيش يعني بـ
+
+125
+00:11:07,340 --> 00:11:13,780
+Contrapositive، بتجربة Contrapositive، proof by
+
+126
+00:11:13,780 --> 00:11:17,840
+contrapositive للمسألة،
+
+127
+00:11:17,840 --> 00:11:23,320
+هذه، هروح أقول له: assume not
+
+128
+00:11:23,320 --> 00:11:29,720
+q is true، إيش يعني not q is true؟ أن الـ N is not
+
+129
+00:11:29,720 --> 00:11:31,380
+odd،
+
+130
+00:11:32,870 --> 00:11:36,610
+even، هي المصدر اللي حللناه قبل شوية، اتفقنا الـ N
+
+131
+00:11:36,610 --> 00:11:42,410
+equal 2K، والـ K تنتمي إلى Z، وقاعد بدأنا من الـ N
+
+132
+00:11:42,410 --> 00:11:47,170
+تربيع، N تربيع بدها تساوي 2K كل تربيع، وبدها تساوي
+
+133
+00:11:47,170 --> 00:11:54,310
+4K تربيع، وبدها تساوي 2 في 2K تربيع، even
+
+134
+00:11:54,310 --> 00:11:58,170
+integer، contrapositive،
+
+135
+00:12:01,440 --> 00:12:07,580
+مضبوط؟ اللي هي دي بتمثل not P، خلص البرهان، هدف
+
+136
+00:12:07,580 --> 00:12:10,900
+الـ contrapositive، هدف الـ contrapositive صحيح مئة
+
+137
+00:12:10,900 --> 00:12:14,940
+في المئة، ما فيش عليه مشكلة، لأن بـ contradiction إيش
+
+138
+00:12:14,940 --> 00:12:21,500
+بدك تفترض أنت؟ بدك تقول: الـ P is it true؟ وand…
+
+139
+00:12:21,500 --> 00:12:25,080
+نه…بالضبط، والـ Q غلط…false، إيش…إذا…لما
+
+140
+00:12:25,080 --> 00:12:29,320
+تكون n is odd false، يعني الـ n is…even…even،
+
+141
+00:12:29,320 --> 00:12:31,860
+…فيه…ما فيش حاجة غير هيك، ولا لأ…بقيت هروح
+
+142
+00:12:31,860 --> 00:12:40,820
+أقول له: أنا أسيوم…أفترض الـ P and…not Q…مين
+
+143
+00:12:40,820 --> 00:12:47,040
+الـ P هيها؟ ومين الـ Q؟ هيها…أصبت؟
+
+144
+00:12:50,200 --> 00:12:59,800
+معناته الـ P أو الـ N تربيع is odd and الـ N is not
+
+145
+00:12:59,800 --> 00:13:04,080
+odd، اللي هي بين جثتين even، إن شاء الله يا شباب، ما
+
+146
+00:13:04,080 --> 00:13:06,460
+تكتبليش is not odd، ما عنديش مشكلة أنا في الموضوع،
+
+147
+00:13:06,460 --> 00:13:11,800
+اكتب لي مباشرة even، ما فيش مشكلة، يعني صار أنا فيه عندي
+
+148
+00:13:11,800 --> 00:13:15,780
+الـ N وكأنه موجبة 2 بين إيديا، أعتمد على مين
+
+149
+00:13:15,780 --> 00:13:19,860
+فيهم في الشغل؟ الـ N تربيع، أقول الـ N تربيع بدها
+
+150
+00:13:19,860 --> 00:13:23,280
+تساوي 2K زائد واحد، وآخذ الجذر، ولا أعتمد على
+
+151
+00:13:23,280 --> 00:13:27,660
+الأسهل اللي هي الـ N equal 2K، وأربعها، لأ، و
+
+152
+00:13:27,660 --> 00:13:30,660
+الله، بأربعها بعدها، هروح لخبرة تالية، هقول الـ N بدها
+
+153
+00:13:30,660 --> 00:13:37,340
+تساوي 2K، مضبوط؟ ليش هي is not odd، is not odd،
+
+154
+00:13:37,340 --> 00:13:42,510
+even، يعني 2K، لأن equal 2K، N تربيع، الخطوة اللي
+
+155
+00:13:42,510 --> 00:13:48,530
+بعدها، N تربيع بدها تساوي 4K تربيع، وتساوي 2 في 2K
+
+156
+00:13:48,530 --> 00:13:58,470
+تربيع، صح، even، وها دي even integer، not
+
+157
+00:13:58,470 --> 00:14:00,990
+odd، contradiction،
+
+158
+00:14:07,020 --> 00:14:14,960
+with،  ترقض معامل مع الفرضية and تربيع is odd، خلصنا
+
+159
+00:14:14,960 --> 00:14:19,400
+البرهان، إيش يعني؟ يعني لما بتكون الـ N تربيع is
+
+160
+00:14:19,400 --> 00:14:27,140
+odd، الـ N is odd، وهذا هو الإثبات بالترقض، إنك أنت
+
+161
+00:14:27,140 --> 00:14:30,760
+بتفرض حالتين وبتشتغل مع أي واحدة فيهم، مش مشكلة
+
+162
+00:14:30,760 --> 00:14:34,700
+عندك معامل، بلام أنك حققتهم في الفرضيات، يعني بتقدر
+
+163
+00:14:34,700 --> 00:14:39,000
+تعتمد عليهم زي ما بدك، وبتشي للاتجاه التالي لحد ما
+
+164
+00:14:39,000 --> 00:14:43,260
+توصل لأي تطابق، عشان هيك كتبنا لك هنا: assume P and
+
+165
+00:14:43,260 --> 00:14:48,460
+not Q، then deduce any contradiction، وحاول ابحث أو
+
+166
+00:14:48,460 --> 00:15:01,220
+أوجد عن أي تطابق موجود في المسألة اللي عندك، تمام،
+
+167
+00:15:01,220 --> 00:15:01,780
+مثال؟
+
+168
+00:15:14,740 --> 00:15:21,720
+وقول لي: لو كانت الـ M زائد
+
+223
+00:20:31,060 --> 00:20:35,200
+تروح تطلع على أسئلة الكتاب وتجرب لأن مش كل المسائل
+
+224
+00:20:35,200 --> 00:20:38,720
+جاياكي مجشرة بيقولك اتفضل يعني أنت أحياناً بتكون
+
+225
+00:20:38,720 --> 00:20:42,340
+عند ضيف أو تكون ضيف عند ناس، عفواً، بيقعد بيجشر لك
+
+226
+00:20:42,340 --> 00:20:45,080
+الموزة وبيقدملك إياها بكل احترام أو بيقعد بيجشر لك
+
+227
+00:20:45,080 --> 00:20:49,810
+التفاحة وبيقولك اتفضل، مصبوط؟ أيوة، أحياناً بتكون
+
+228
+00:20:49,810 --> 00:20:54,290
+كتر ما شافك وزورتك تيل خلال الفصل يا راني جرف منك
+
+229
+00:20:54,290 --> 00:20:58,450
+بقولك احمل هاي الـ بورتجانه وهاي السكينه، لأ احمل
+
+230
+00:20:58,450 --> 00:21:03,210
+الـ بورتجانه مش المادة، تمام؟ وبالتالي المطلوب أن
+
+231
+00:21:03,210 --> 00:21:09,490
+أنت إيش تبدأ تشتغل؟ تبدأ تشتغل، والأصل أنك تبدأ تعرف
+
+232
+00:21:09,490 --> 00:21:13,490
+لأنه كمان مرة مفتاح الحل في المسائل يا شباب إذا
+
+233
+00:21:13,490 --> 00:21:20,110
+ما كانتش موجودة F، و then أنت بدك إيش تبحث أو توجد الـ
+
+234
+00:21:20,110 --> 00:21:24,550
+F within هذي الـيك عشان تبدأ الحل، بتهيألي بعد هيك
+
+235
+00:21:24,550 --> 00:21:31,330
+حلت المسألة ولا شو رايكوا في دا حلها دا؟ يعني
+
+236
+00:21:31,330 --> 00:21:35,410
+إما بدها تساوي اتنين K زائد واحد، إن بدها تساوي
+
+237
+00:21:35,410 --> 00:21:42,640
+اتنين K، أنا ما بعرف ليش k زائد واحد غلط، لأنك أنت خدت
+
+238
+00:21:42,640 --> 00:21:46,540
+نفس الـ aim، أنتم جماعته لا نفسه، خد أي رقم تاني غير
+
+239
+00:21:46,540 --> 00:21:51,560
+الـ k، لو.. لو قلت نقص واحد، okay، بمشي الحل، بس في
+
+240
+00:21:51,560 --> 00:21:56,930
+الآخر خد different number، زائد H، اتنين H زائد واحد
+
+241
+00:21:56,930 --> 00:22:00,590
+واجمعهم واحصل على نتيجة ستكون صح، السؤال التاني
+
+242
+00:22:00,590 --> 00:22:03,370
+برضه استخدم الـ direct proof to show the sum of
+
+243
+00:22:03,370 --> 00:22:08,750
+even، عكسه كمان، مصبوط؟ ما لازِم تدخل فيه تلاتة، show
+
+244
+00:22:08,750 --> 00:22:20,250
+that the square of an even number is an even number، بدي
+
+245
+00:22:20,250 --> 00:22:30,140
+حد يصيغ لي إياها، F within، آه سويسي، قول، اتديني إياها، if و
+
+246
+00:22:30,140 --> 00:22:35,520
+then، أيوة
+
+247
+00:22:35,520 --> 00:22:41,720
+ممتاز، على الرغم أنه بدالك المسألة، the square زي
+
+248
+00:22:41,720 --> 00:22:45,700
+المجلة كان the sum، the square of an even number
+
+249
+00:22:45,700 --> 00:22:53,140
+يعني لو كانت الـ n is even، then، if الـ n is even
+
+250
+00:22:55,820 --> 00:23:01,320
+ذن الآن تربيعها is even، هذه صيغة المسألة اللي موجودة
+
+251
+00:23:01,320 --> 00:23:04,940
+عندك، وبالتالي أول ما تشوف مسألة زي هيك مش قادر
+
+252
+00:23:04,940 --> 00:23:09,160
+تمسك فيها، if و then، بدك تحاول توجد الـ if و الـ then
+
+253
+00:23:09,160 --> 00:23:15,340
+تبعاتها، المسألة هاي: show that the additive
+
+254
+00:23:15,340 --> 00:23:19,920
+inverse، المعكوس الجمعي، additive inverse، المعكوس
+
+255
+00:23:19,920 --> 00:23:26,200
+الجمعي، أو حطوط قياب انبوسين، الـ negative of an even
+
+256
+00:23:26,200 --> 00:23:30,840
+integer أو even number is an even number، using the
+
+257
+00:23:30,840 --> 00:23:39,400
+direct proof، كمان مرة بدنا واحد من السرحانين يحاول
+
+258
+00:23:39,400 --> 00:23:45,120
+يجيب اللي هي f و then the
+
+259
+00:23:45,120 --> 00:23:49,220
+additive inverse، المعكوس الجمعي، اللي هو بين جثين
+
+260
+00:23:49,220 --> 00:23:54,060
+حطوا لي كيان نيجاتيف للـ even number is even number
+
+261
+00:23:58,310 --> 00:24:08,410
+إذا الـ N هو نيجاتيف، إذا الـ N هو نيجاتيف، إذا الـ N
+
+262
+00:24:08,410 --> 00:24:14,110
+هو نيجاتيف، إذا الـ N هو نيجاتيف، إذا الـ N هو
+
+263
+00:24:14,110 --> 00:24:20,050
+نيجاتيف، إذا الـ
+
+264
+00:24:20,050 --> 00:24:23,030
+N هو نيجاتيف، إذا الـ N هو نيجاتيف، إذا الـ N هو
+
+265
+00:24:23,030 --> 00:24:26,390
+نيجاتيف، إذا الـ N هو نيجاتيف، إذا الـ N هو نيجاتيف،
+
+266
+00:24:26,390 --> 00:24:26,430
+هو نيجاتيف، إذا الـ N
+
+267
+00:24:33,060 --> 00:24:38,900
+لو كانت الـ N even، هيكون المعكوس الجمعي تبعها
+
+268
+00:24:38,900 --> 00:24:47,020
+ناقص N is even، هي show that the additive inverse
+
+269
+00:24:47,020 --> 00:24:53,040
+of an even integer، يعني المعكوس الجمعي للعدد
+
+270
+00:24:53,040 --> 00:25:02,040
+الزوجي، عدد زوجي، اتنين وسالب اتنين، مصبوط؟ هاي..
+
+271
+00:25:02,040 --> 00:25:07,960
+ما أبتهاش.. ما عكستش، لأ، أنا حاولت استخلص منها if و
+
+272
+00:25:07,960 --> 00:25:13,720
+then، هو إيش عمله؟ قاعد بيقول لي، تعالى نشوف بشكل عام
+
+273
+00:25:13,720 --> 00:25:20,140
+أنا مطلوب مني في المسألة هي أقول له if فراغ
+
+274
+00:25:21,920 --> 00:25:25,940
+then فراغ، أكتب على الشكل هذا، أفصلها، إيش قاعد هو
+
+275
+00:25:25,940 --> 00:25:31,800
+بيقولها؟ المعكوس الجمعي للعدد الزوجي، يعني إيش
+
+276
+00:25:31,800 --> 00:25:36,380
+المعطى إليك عدد زوجي، المعطى إليك العدد الزوجي
+
+277
+00:25:36,380 --> 00:25:40,300
+وقاعد بيقول لك أنه أثبت أن المعكوس الجمعي للعدد
+
+278
+00:25:40,300 --> 00:25:46,600
+الزوجي هو عبارة عن عدد زوجي، يعني هو back and is
+
+279
+00:25:46,600 --> 00:25:53,690
+even، وأثبت أن المعكوس الجمعي اللي هو سالب N is
+
+280
+00:25:53,690 --> 00:26:00,870
+even، طبعاً، بضبط، بس أنت عارف إيش هتروح تقول له؟ هتروح تقول
+
+281
+00:26:00,870 --> 00:26:11,370
+Assume B is true، صح؟ يعني N is even، هذا بيقود أن
+
+282
+00:26:11,370 --> 00:26:15,870
+الـ N equal اتنين K، و K تنتمي إلى Z، هذا لاحظ أنه
+
+283
+00:26:15,870 --> 00:26:20,230
+بتحس أنه أول سطرين بنكتبهم في البرهان وكأنهم نسخ
+
+284
+00:26:20,230 --> 00:26:23,650
+نحطه على مكان التصوير وبنضغط عليك تكتبهم حسب نوع
+
+285
+00:26:23,650 --> 00:26:27,930
+الإثبات اللي عندك، اتنين K زائد واحد أو اتنين K، عفواً
+
+286
+00:26:27,930 --> 00:26:34,830
+إيش هو بده من ايه؟ المعكوس الجمعي، هذا يؤدي أن سالب N
+
+287
+00:26:34,830 --> 00:26:40,550
+تساوي سالب واحد أو سالب واحد مضروبة في اتنين K
+
+288
+00:26:40,550 --> 00:26:47,110
+وتساوي سالب اتنين K، صح؟ وتساوي اتنين في سالب K، وهكذا
+
+289
+00:26:47,110 --> 00:26:53,430
+وتصير جوعانها even، يا خالد، آه، الفكرة أن دائماً
+
+290
+00:26:53,430 --> 00:26:57,630
+صورة عدد زوجي هي عبارة عن اتنين مضروبة في some
+
+291
+00:26:57,630 --> 00:27:02,260
+integer، هي التنين وهي الـ sum integer، لو أنت من
+
+292
+00:27:02,260 --> 00:27:05,580
+اللحظة هذه قلت لي أنا بصدقك وبقول مية مية كلامك
+
+293
+00:27:05,580 --> 00:27:09,740
+صح، بس الخطوة التالتة الأخيرة هذه عشان ما تتركش
+
+294
+00:27:09,740 --> 00:27:13,660
+مجال لأي حد، قلت لي هي التنين اللي حار يا عم، وهي الـ
+
+295
+00:27:13,660 --> 00:27:21,640
+integer اللي هو السالب K، ضربناها is even، خلصنا، خلص
+
+296
+00:27:21,640 --> 00:27:24,520
+البرهان، معناه سالب N is even
+
+297
+00:27:37,010 --> 00:27:45,690
+خمسة، مضيك F within، في خمسة، show that F، الـ N زائد
+
+298
+00:27:45,690 --> 00:27:55,150
+الـ M، and N زائد الـ B are even integers، هذا
+
+299
+00:27:55,150 --> 00:28:00,480
+الـ B، هذه الـ B كلها، تمام؟ where بقى بقول لك الـ M والـ
+
+300
+00:28:00,480 --> 00:28:02,940
+N are integers، أعداد صحيحة، يعني مش real number
+
+301
+00:28:02,940 --> 00:28:11,180
+then M زائد الـ B، وهذه Q، M زائد الـ N أفضل، M زائد الـ
+
+302
+00:28:11,180 --> 00:28:19,440
+B is even، اسكت يا أحمد، تسمعني صوتك، if الـ M زائد الـ
+
+303
+00:28:19,440 --> 00:28:25,200
+N and N زائد الـ B are even
+
+304
+00:28:28,050 --> 00:28:36,550
+then M زائد N is even، M زائد B، عفواً، هي المسألة اللي
+
+305
+00:28:36,550 --> 00:28:46,970
+بديك إياها، هو الـ N، الآن احنا نقول له assume
+
+306
+00:28:46,970 --> 00:28:47,550
+B is true
+
+307
+00:28:51,590 --> 00:28:55,450
+هل هو ضروري الـ direct تكون صح؟ ما بعرف، بدي أجرب وبناء
+
+308
+00:28:55,450 --> 00:29:01,330
+على تجربتي بعد خطوات اتنين بشوف كيف الوضع، M زائد
+
+309
+00:29:01,330 --> 00:29:05,430
+الـ N is even و
+
+310
+00:29:05,430 --> 00:29:13,330
+N زائد الـ B is even، هذا بيقود أن M زائد الـ N equal
+
+311
+00:29:13,330 --> 00:29:23,020
+2K، و N زائد الـ B equal 2H، for some K تنتمي إلى Z، و
+
+312
+00:29:23,020 --> 00:29:27,220
+for some H تنتمي إلى Z، for some K و H integers
+
+313
+00:29:27,220 --> 00:29:31,800
+تمام؟ بس هو في الطرف التاني إيش مستخدم هنا يا
+
+314
+00:29:31,800 --> 00:29:38,200
+شباب؟ M زائد الـ B، يعني الـ N مش في الحسبة، الـ N مش في
+
+315
+00:29:38,200 --> 00:29:43,020
+الحسبة، وكأنه بيقول خاصيتي التعدي هنا، حروح أنا بدي
+
+316
+00:29:43,020 --> 00:29:46,260
+أخذ الـ M لحالها وأخذ الـ B لحالها بناء على
+
+317
+00:29:46,260 --> 00:29:52,660
+المعادلة هذه، الـ M مش بده تساوي اتنين K ناقص الـ M والـ
+
+318
+00:29:52,660 --> 00:29:58,300
+B بده تساوي اتنين H، نقطة في الـ N، مصبوط؟ اجمعهم
+
+319
+00:29:58,300 --> 00:30:04,660
+الآن مع المعادلة، الخطوة اللي بعدها، M زائد B هو
+
+320
+00:30:04,660 --> 00:30:15,720
+المطلوب، يساوي اتنين H، اتنين K ناقص M زائد اتنين H
+
+321
+00:30:15,720 --> 00:30:26,920
+ناقص M، ناقص N، ناقص اتنين M، إيش تشيل؟ اتنين
+
+322
+00:30:26,920 --> 00:30:32,220
+K زائد اتنين H ناقص اتنين M، ويساوي اتنين عامل
+
+323
+00:30:32,220 --> 00:30:40,810
+مشترك، K زائد H ناقص M، اتنين مضروبة في some integer
+
+324
+00:30:40,810 --> 00:30:46,710
+even، خلصت
+
+325
+00:30:46,710 --> 00:30:53,230
+المسألة، direct، نعم، الـ M لحالها odd، صح؟ مين قال؟
+
+326
+00:30:53,230 --> 00:30:57,170
+مين قال؟ اتنين K ناقص واحد.. اتنين K ناقص واحد، وليه؟
+
+327
+00:30:57,170 --> 00:30:59,470
+وليه؟ و ليش؟ لأن افترضتها odd؟ لأنها ممكن تكون
+
+328
+00:30:59,470 --> 00:31:02,610
+even، اتنين زائد أربعة، ستة
+
+329
+00:31:04,600 --> 00:31:09,700
+بس اصبر، احنا ما لازِم في قيمة n، هو ذاك فرضيه، إيش هي
+
+330
+00:31:09,700 --> 00:31:15,980
+فرضيته أن الـ M زائد الـ N عبارة عن even، صح؟ يعني
+
+331
+00:31:15,980 --> 00:31:21,060
+أما الـ M.. حسب ما احنا بنقعد، M زائد N even يعني
+
+332
+00:31:21,060 --> 00:31:25,560
+يا إما التنين odd، يا إما التنين even، وبتاني ليش
+
+333
+00:31:25,560 --> 00:31:28,480
+دخل في هاللخمة أنا هاي؟ هو كل اللي قال لي إيه؟ إيه M
+
+334
+00:31:28,480 --> 00:31:32,920
+زائد N is even، معناته is even، معناته M زائد N يكتب
+
+335
+00:31:32,920 --> 00:31:37,690
+على صورة اتنين K، خلصت، وهو بده مني الـ N لحالها
+
+336
+00:31:37,690 --> 00:31:44,510
+فباخذ الـ N على الطرف التاني وخلصت، تطلع الـ N odd
+
+337
+00:31:44,510 --> 00:31:48,570
+تطلع even، أنا ما بيهمني، أنا كانت اللي بيهمني N
+
+338
+00:31:48,570 --> 00:31:52,150
+زائد الـ N اللي هي الـ even، وأنا حققت له إياها عشان
+
+339
+00:31:52,150 --> 00:31:55,630
+ايه، ما فيش داعي، دائماً احاول التفكير اللي أنت فكرت
+
+340
+00:31:55,630 --> 00:32:00,830
+فيه، صح، بس أنت وجعت وين؟ أنت افترضت أن هذي odd، إذا
+
+341
+00:32:00,830 --> 00:32:04,310
+هذي odd، لازم تكون الـ N is odd، بس في الآخر مجموعهم
+
+342
+00:32:04,310 --> 00:32:09,310
+even، ولو كانت هذه even، الـ N uneven، عشان يكون
+
+343
+00:32:09,310 --> 00:32:11,830
+مجموعهم even، فبالتالي ما ليش دخل في الموضوع أنا
+
+344
+00:32:11,830 --> 00:32:15,430
+يعني فبالتالي نمشي بالبرهان حسب المسألة اللي
+
+345
+00:32:15,430 --> 00:32:19,850
+موجودة عندي بالتدريج، نروح للـ contrapositive أو الـ
+
+346
+00:32:19,850 --> 00:32:23,450
+contradiction، ممكن نجيب حل، الـ contrapositive ممكن
+
+347
+00:32:23,450 --> 00:32:27,050
+نجيب حل، متوقع
+
+348
+00:32:27,050 --> 00:32:32,840
+أن الـ contrapositive توصلني لحل، إثبات، فاكر.. قبل ما
+
+349
+00:32:32,840 --> 00:32:38,780
+تجاوب، فاكر.. آه
+
+350
+00:32:38,780 --> 00:32:46,460
+يا عمر.. لأ.. ليش.. ما بعرف.. غيره.. سواركي
+
+351
+00:32:46,460 --> 00:32:50,960
+.. ممكن الـ contrapositive يوصلني لحل.. أنت
+
+352
+00:32:50,960 --> 00:32:56,080
+سواركي.. ما بيرجع لي فاك.. أنا بوصح لكم تدوش الجنسية
+
+353
+00:32:56,080 --> 00:33:04,780
+.. آه.. ممكن.. طيب أقول لكم شغلة، أنت تعالى تطلع
+
+354
+00:33:04,780 --> 00:33:11,940
+فيها هنا، بدوش عندي M و B، أصبت؟ والطرف التاني فيه
+
+355
+00:33:11,940 --> 00:33:15,960
+عندي N، طب الـ N اللي أنا بدأ أفرضها، شو بدأ أفرضها؟
+
+356
+00:33:15,960 --> 00:33:19,980
+بدأ أفرضها عدد زوجي ولا بدأ أفرضها عدد فردي؟ مش
+
+357
+00:33:19,980 --> 00:33:25,220
+عارف، وبالتالي الـ contrapositive ما بتمشيش معايا، لكن
+
+358
+00:33:25,220 --> 00:33:29,180
+الـ contradiction ممكن تصبط يا حمد؟ الـ
+
+359
+00:33:29,180 --> 00:33:34,720
+contradiction ممكن تصبط؟ ليش لأ؟ في الـ contradiction
+
+360
+00:33:34,720 --> 00:33:38,640
+أنا إيش بده أقول له؟ بده أقول له B and not the Q، وهذه
+
+361
+00:33:38,640 --> 00:33:42,520
+صورتها إيش؟ صورتها إيش؟ Odd، فلما تشتغل نفس الشغل
+
+362
+00:33:42,520 --> 00:33:51,360
+هذا، بس مع فرضية.. مع الفرضية أنها and not the Q
+
+363
+00:33:51,360 --> 00:33:58,860
+اللي هي M زائد B is not even، لبيّن جوسين Odd
+
+364
+00:33:59,390 --> 00:34:03,350
+Contradiction، بالتناقض، هتشتغل مع هدوء، تكتب نفس
+
+365
+00:34:03,350 --> 00:34:07,850
+الخطوات السابقة، هتوصل أن الـ M زي الـ B is even
+
+366
+00:34:07,850 --> 00:34:11,270
+Contradiction مع مين؟ مع الفرضية اللي موجودة عندي
+
+367
+00:34:11,270 --> 00:34:17,590
+السابقة كمان؟ وبالتالي هي بدالك تتبعها، انحلت، و
+
+368
+00:34:17,590 --> 00:34:23,610
+بالـ contradiction انحلت، أي حل اعتمد فيهم أي واحد أي
+
+369
+00:34:23,610 --> 00:34:28,330
+واحد اللي أنت تقدر تجيبه في الامتحان، طبعاً لو أنا
+
+370
+00:34:28,330 --> 00:34:33,290
+كنت بقول لك استخدم الـ contradiction، تمام؟ ورحت
+
+371
+00:34:33,290 --> 00:34:41,290
+تبتديها بالـ direct، بتاخد الـ big zero، آه، ما بقي له
+
+372
+00:34:41,290 --> 00:34:45,110
+اتعب، هذا إسمه عند المجاولين، أنا ما باخدش المجاولة، لأ
+
+373
+00:34:45,110 --> 00:34:51,670
+وبالتالي.. لأ، الكلمتين هدول يا سوستفان بيعنوا
+
+374
+00:34:51,670 --> 00:34:55,270
+أنك أنت فاهم إيش الطريقة اللي بتفرج هدى عن هدى
+
+375
+00:34:56,600 --> 00:35:00,300
+كمان؟ الآن في التاسع، عاشر، بقول لك إيش؟ استخدم الـ proof
+
+376
+00:35:00,300 --> 00:35:03,780
+by contradiction to prove that.. بيقول استخدم
+
+377
+00:35:03,780 --> 00:35:08,320
+الإثبات بالتناقض عشان تثبت أن حاصل جمع irrational
+
+378
+00:35:08,320 --> 00:35:17,760
+number and rational number is irrational، بس
+
+379
+00:35:17,760 --> 00:35:19,180
+المهم إيش الأولة وإيش التانية
+
+380
+00:35:30,010 --> 00:35:35,910
+بقول لك أثبت بالتناقض، use proof by contradiction
+
+381
+00:35:35,910 --> 00:35:40,230
+to prove that، عشان تثبت، the sum of an irrational
+
+382
+00:35:40,230 --> 00:35:45,470
+number and a rational number is irrational، سؤال تسعة
+
+383
+00:35:45,470 --> 00:35:48,830
+اللي هو أنا حاولت أكتبه بالخطة اللي ما فيش فوق هذا
+
+384
+00:35:48,830 --> 00:35:58,110
+تمام، الآن عشان تحله بدك تعمله if then، بي و كيو، if
+
+385
+00:35:58,110 --> 00:35:59,810
+then، if b then q
+
+386
+00:36:05,350 --> 00:36:19,650
+الـ M is rational and الـ M is irrational، then الـ M
+
+387
+00:36:19,650 --> 00:36:25,790
+زائد الـ N is irrational
+
+388
+00:36:25,79
+
+445
+00:42:49,650 --> 00:42:54,550
+نسبي؟ مصبوط؟ نص في جذر التنين.. جذر التنين على
+
+446
+00:42:54,550 --> 00:42:58,930
+اتنين برضه عدد غير نسبي وهكذا لأن شرط المقام
+
+447
+00:42:58,930 --> 00:43:01,590
+البسط والمقام يجب أن يكون يتملكا لمين؟ للأعداد
+
+448
+00:43:01,590 --> 00:43:05,810
+الصحيحة.. وبالتالي هذه بدها إثبات.. إيش استخدام
+
+449
+00:43:05,810 --> 00:43:09,710
+معاها؟ Contrapositive ولا Contradiction ولا
+
+450
+00:43:09,710 --> 00:43:13,170
+Direct؟ فكر فيها زي ما بدك.. احنا أيها؟ اختار
+
+451
+00:43:13,170 --> 00:43:19,140
+لناها هنا.. في تسعة.. احنا جمعناهم هنا.. بس في
+
+452
+00:43:19,140 --> 00:43:22,240
+السؤال ده عمال بيقول إيه؟ the product حاصل ضربهم
+
+453
+00:43:22,240 --> 00:43:26,760
+ومن هنا بتفهم إيش حاطط لك non-zero عشان لما بيبقى
+
+454
+00:43:26,760 --> 00:43:38,520
+تروح تجيب ما يطلعش المكان صفر معاك. طيب في 16
+
+455
+00:43:38,520 --> 00:43:45,060
+prove that if M and N are integers وحاصل ضربهم is
+
+456
+00:43:45,060 --> 00:43:45,440
+even
+
+457
+00:43:48,430 --> 00:43:55,590
+معناته واحد منهم is even. شو رأيك هو؟ أنا بقول لك لو
+
+458
+00:43:55,590 --> 00:44:01,410
+أخذنا أي عددين صحيحين وضربناهم في بعض وطلع الناتج
+
+459
+00:44:01,410 --> 00:44:07,150
+عدد زوجي فهذا يعني أن واحد منهم على الأقل هيكون
+
+460
+00:44:07,150 --> 00:44:12,510
+عدد زوجي. true true يعني أنك تثبتها يا باشا true
+
+461
+00:44:12,510 --> 00:44:17,700
+يعني أنك تثبتها بتقدم بإثبات رياضي لأن أنا بقول لك both
+
+462
+00:44:17,700 --> 00:44:24,720
+الآن كمان مرة، أقول لك إيش وبقول لك ستاش if  الـ M في N is even
+
+463
+00:44:24,720 --> 00:44:36,940
+then الـ M is even or الـ N is even أو لو كانوا
+
+464
+00:44:36,940 --> 00:44:43,880
+اتنين صح.  هاي الـ F والـ then Contradiction ولا
+
+465
+00:44:43,880 --> 00:44:45,520
+contrapositive ولا direct
+
+466
+00:44:48,500 --> 00:44:51,920
+الـ Direct عمرها ما بتجيب معاك نتيجة
+
+467
+00:44:51,920 --> 00:44:55,680
+Contrapositive أو Contradiction هدول اللي ممكن
+
+468
+00:44:55,680 --> 00:45:00,880
+يجيبوا معاك. ليش يا شباب؟ لأن هنا M وN is even يعني
+
+469
+00:45:00,880 --> 00:45:11,340
+كتير منكم هيقول ليه؟ M N equal 2K. M بدها تساوي 2K على N
+
+470
+00:45:11,340 --> 00:45:18,950
+ولو عملت لي هيك ما حدش بيضمن أن هذا ينتمي إلى Z. في حد
+
+471
+00:45:18,950 --> 00:45:24,450
+يضمن لنا هذا؟ لأ ممتاز. integer على integer مش
+
+472
+00:45:24,450 --> 00:45:29,530
+ضروري يكون integer. اتنين على أربعة، تلاتة على اتنين
+
+473
+00:45:29,530 --> 00:45:33,030
+مش ضروري يكون integer وبالتالي إذا هذه مش هذه مش
+
+474
+00:45:33,030 --> 00:45:37,230
+مضمونة. بالتالي الـ direct proof لقد مسكرة.
+
+475
+00:45:37,230 --> 00:45:46,130
+contrapositive بتصير و contradiction بتصير تمام؟
+
+476
+00:45:46,130 --> 00:45:54,220
+بتروح تقول assume نطق U يعني الـ M is odd and الـ M
+
+477
+00:45:54,220 --> 00:45:57,740
+is odd. اتنين K زائد واحد، اتنين H زائد واحد، و
+
+478
+00:45:57,740 --> 00:46:06,560
+تضربهم في بعض، هيطلع معاك إيه.. خطأ. هيطلع معاك odd
+
+479
+00:46:06,560 --> 00:46:14,060
+الأصل. اتنين K زائد واحد في اتنين H زائد
+
+480
+00:46:14,060 --> 00:46:25,220
+واحد. 4KH زائد 2K زائد 2H زائد واحد. هاخد هدول
+
+481
+00:46:25,220 --> 00:46:32,820
+عامل مشترك الاتنين. 2 في 2KH زائد K زائد H زائد واحد.
+
+482
+00:46:32,820 --> 00:46:39,480
+هذا odd. Contrapositive ولو افترضت أنت B and not Q
+
+483
+00:46:39,480 --> 00:46:47,050
+في الـ contradiction B is even ونقطة Q هيها مظبوط
+
+484
+00:46:47,050 --> 00:46:51,710
+يعني هدول odd هتحل نفس الحل هذا وفي الآخر هتقول
+
+485
+00:46:51,710 --> 00:46:55,810
+أنه هذا بتناقض أو contradiction. لأ، بس في الحالة
+
+486
+00:46:55,810 --> 00:46:59,790
+هذه احنا لما قلنا assume نقطة Q المفروض نقول هنا
+
+487
+00:46:59,790 --> 00:47:04,650
+Contra positive. ليش؟
+
+488
+00:47:04,650 --> 00:47:09,290
+اللي هي بين جسين نقطة الـ B، نقطة الـ B، نقطة Q وصلتني
+
+489
+00:47:09,290 --> 00:47:12,150
+لنقطة الـ B. 17
+
+490
+00:47:14,660 --> 00:47:19,180
+إذا الـ N هو Integer N is an integer بس بقول لك الـ N
+
+491
+00:47:19,180 --> 00:47:25,320
+is integer حتى الآن and الـ
+
+492
+00:47:25,320 --> 00:47:30,780
+N زائد خمسة is odd وكأنه بيقول لك if الـ N تكعيب زائد
+
+493
+00:47:30,780 --> 00:47:39,020
+الخمسة is odd then الـ N is even. جاهزة جاهزة يعني
+
+494
+00:47:39,020 --> 00:47:48,540
+قاعد أبديكي إياها. if N تكعيب زائد خمسة is odd then
+
+495
+00:47:48,540 --> 00:47:54,760
+N is even. وبيقول لك إما بتثبتها بالـ contrapositive أو
+
+496
+00:47:54,760 --> 00:47:58,760
+بالـ contradiction. أيوة.
+
+497
+00:47:58,760 --> 00:48:02,760
+أنا بدي اختار، أنا هختار واحدة عشان أحلها بواحدة
+
+498
+00:48:02,760 --> 00:48:04,600
+و الثانية عليك. خلاص ما بديش كلام يعني
+
+499
+00:48:04,600 --> 00:48:08,440
+contradiction or contraposition. position positive
+
+500
+00:48:08,440 --> 00:48:13,370
+مش فارقة كتير دي لبالك في المصطلح يعني. آه يا شباب، أنا
+
+501
+00:48:13,370 --> 00:48:24,530
+هحل واحدة بس، مش هحل الاتنين والله.
+
+502
+00:48:24,530 --> 00:48:27,550
+الاتنين ما بيفرجوا معاك ولا حاجة في الآخر، بس لأن في
+
+503
+00:48:27,550 --> 00:48:32,610
+كل الأحوال أنت بدك تفرض B ونفي Q صح؟ بس هذه تصير
+
+504
+00:48:32,610 --> 00:48:40,510
+نفي Q بدون الـ B وحاجة مش هتصل عكسها. طيب assume B
+
+505
+00:48:40,510 --> 00:48:41,530
+and
+
+506
+00:48:50,640 --> 00:49:00,740
+not even is not
+
+507
+00:49:00,740 --> 00:49:04,960
+even
+
+508
+00:49:04,960 --> 00:49:05,560
+يعني odd
+
+509
+00:49:12,280 --> 00:49:16,640
+يعني بين جثين odd. الخطوة اللي بعد هيك معناته n
+
+510
+00:49:16,640 --> 00:49:30,300
+تساوي 2k زائد 1، و الـ k تنتمي إلى Z. طيب بدك
+
+511
+00:49:30,300 --> 00:49:34,500
+تعتمد غير في المسألة اللي فوق. هذا يؤدي أن الـ n
+
+512
+00:49:34,500 --> 00:49:45,010
+تكعيب زائد 5 تساوي 2K زائد واحد لكل تكعيب زائد خمسة
+
+513
+00:49:45,010 --> 00:49:53,690
+وهذه تساوي 2K زائد واحد مضروبة في 4K تربيع زائد
+
+514
+00:49:53,690 --> 00:50:02,810
+6K زائد واحد صح؟ ليش عكس الإشارة؟ طب ما الإشارة
+
+515
+00:50:02,810 --> 00:50:07,990
+عندي موجبة من فوق زائد صح؟
+
+516
+00:50:08,360 --> 00:50:12,540
+أنت في السالب تحرك الإشارة وبعدين أنا روحت معاك
+
+517
+00:50:12,540 --> 00:50:20,600
+على شغل أسهل حتى لو كانت 2k-1 تكعيب عشان ما
+
+518
+00:50:20,600 --> 00:50:25,320
+أتخرطش في الإشارة. أنا إيش افترضتها؟ هي عبارة عن 2k
+
+519
+00:50:25,320 --> 00:50:31,800
+-1 في 2k-1 تربيع. حالة المربع حد لحاله. تربيع الأول
+
+520
+00:50:31,800 --> 00:50:34,860
+الأول
+
+521
+00:50:34,860 --> 00:50:39,210
+في التربيع الثاني، واحد زي الأول في الثاني في اتنين
+
+522
+00:50:39,210 --> 00:50:44,850
+ماقص 4K زائد واحد. وروحت ضربهم في بعض بالشكل
+
+523
+00:50:44,850 --> 00:50:49,390
+هذا. فأنا روحت لك على شغل أسهل ما أنا كنت، لأنه
+
+524
+00:50:49,390 --> 00:50:53,570
+متوقع ومتأكد أنه حصل فيه خربطة في الموضوع. حل
+
+525
+00:50:53,570 --> 00:50:59,890
+التكعيب خصوصا لما تكون الإشارات زي بعضها تساوي
+
+526
+00:50:59,890 --> 00:51:07,350
+8K التكعيب زائد زائد الخمسة. أنا ما عنديش الحل بس
+
+527
+00:51:07,350 --> 00:51:13,150
+برا عملت الضرب زائد 8K تربيع زائد 12K
+
+528
+00:51:13,150 --> 00:51:19,850
+زائد 4K تربيع زائد 4K زائد واحد زائد
+
+529
+00:51:19,850 --> 00:51:30,890
+خمسة. وهذه تساوي 8K تكعيب زائد
+
+530
+00:51:30,890 --> 00:51:35,960
+12K تربيع. هي 8 وأنا 4. اتماشى مع 12K تربيع زائد
+
+531
+00:51:35,960 --> 00:51:43,100
+6K زائد 6. خد الاتنين على المشترك تصير 2
+
+532
+00:51:43,100 --> 00:51:48,560
+مضروبة في 4K تكعيب زائد 6K تربيع
+
+533
+00:51:48,560 --> 00:51:56,320
+زائد 3K زائد 3. 2 في Integer even
+
+534
+00:51:56,320 --> 00:52:02,080
+معناته احنا حصلنا على contradiction لأن المفروض هذه
+
+535
+00:52:02,080 --> 00:52:08,580
+تكون إيش؟ Odd. طب في الـ Contrapositive هروح أنا
+
+536
+00:52:08,580 --> 00:52:13,340
+أقول له assume not Q هيها وهمشي معاها هيك أصلا مين
+
+537
+00:52:13,340 --> 00:52:18,160
+أن هذه عبارة عن even وهي not الـ B وبالتالي حصلت
+
+538
+00:52:18,160 --> 00:52:22,160
+على Contrapositive. تمام الأمور يا شباب؟ أعتقد..
+
+539
+00:52:22,160 --> 00:52:27,540
+أعتقد بعد هيك.. احنا بدلنا جهد كويس أنا وياكم
+
+540
+00:52:27,540 --> 00:52:31,530
+في الأمثلة ومع الأسئلة. المفروض أن ترجع على الأسئلة
+
+541
+00:52:31,530 --> 00:52:35,530
+هذه سواء حلتها أو ما حلتهاش وتبدأ تحلها عندك، ليش؟
+
+542
+00:52:35,530 --> 00:52:39,390
+على ورقة لأن هذه مفتاح حل أي سؤال لاحقا إن شاء
+
+543
+00:52:39,390 --> 00:52:42,010
+الله تبارك وتعالى. ماشي الحال يا شباب؟ في حد عنده
+
+544
+00:52:42,010 --> 00:52:44,390
+أي سؤال؟ في محاضرتنا الجاية هنتكلم عن الـ
+
+545
+00:52:44,390 --> 00:52:47,750
+mathematical induction. هنشرح الـ concept ونروح على
+
+546
+00:52:47,750 --> 00:52:50,470
+الـ section ونشوف الأسئلة اللي موجودة عليه ونختار
+
+547
+00:52:50,470 --> 00:52:54,990
+كام سؤال زي كده ونحلهم ونكون خلصنا الجزئية اللي
+
+548
+00:52:54,990 --> 00:52:57,430
+احنا حكيناها من البداية اللي هي البعض
+
+549
+00:52:57,430 --> 00:53:00,370
+الاستراتيجيات أنك تحاول تجسم الـ set اللي موجودة
+
+550
+00:53:00,370 --> 00:53:05,870
+عندك لما بيقول لك أن تربيع أكبر من صفر أو أكبر من n
+
+551
+00:53:05,870 --> 00:53:10,870
+لكل الأعداد الموجبة أو لكل الأعداد الصحيحة أو لكل
+
+552
+00:53:10,870 --> 00:53:15,290
+الأعداد الموجبة أو لكل الأعداد الصحيحة أو لكل
+
+553
+00:53:15,290 --> 00:53:17,890
+الأعداد الصحيحة أو لكل الأعداد الموجبة أو لكل
+
+554
+00:53:17,890 --> 00:53:18,310
+الأعداد الصحيحة أو لكل
+
+555
+00:53:18,310 --> 00:53:18,390
+الأعداد الصحيحة أو لكل
+
+556
+00:53:18,390 --> 00:53:19,930
+الأعداد الصحيحة أو لكل
+
+557
+00:53:19,930 --> 00:53:20,690
+الأعداد الصحيحة أو لكل ال
diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/pKrZGwbVnlc_postprocess.srt b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/pKrZGwbVnlc_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..2dcf5962942e6d08c837b3e420a94f59ecd9983d
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/pKrZGwbVnlc_postprocess.srt
@@ -0,0 +1,2228 @@
+1
+00:00:21,040 --> 00:00:22,880
+بسم الله و الحمد لله و الصلاة والسلام علي رسول
+
+2
+00:00:22,880 --> 00:00:26,900
+الله اليوم ان شاء الله شباب هنكمل في ال
+
+3
+00:00:26,900 --> 00:00:32,960
+mathematical proving بالإثبات الرياضي لكن محاضرتنا
+
+4
+00:00:32,960 --> 00:00:35,520
+مش هتكون فيها .. يعني هتكلم عن موضوع واحد جديد
+
+5
+00:00:35,520 --> 00:00:39,240
+اللي هو الإثبات بالتناقض و من ثم نحاول نحل مجموعة
+
+6
+00:00:39,240 --> 00:00:43,840
+من الأمثل عشان نثبت موضوع الإثباتات السابقة طبعا
+
+7
+00:00:43,840 --> 00:00:47,240
+كنا احنا الأسبوع الماضي بدأنا بالإثبات الرياضي و
+
+8
+00:00:47,240 --> 00:00:51,190
+قلنا كتالةلأن معظم المسائل أو معظم النظريات اللى
+
+9
+00:00:51,190 --> 00:00:54,630
+بيطلب مننا نثبتها هتلاقيها موجودة على صورة if
+
+10
+00:00:54,630 --> 00:01:00,110
+implied او if them او P implies Q وأول نوع من
+
+11
+00:01:00,110 --> 00:01:03,930
+اثبات الرياضي قولنا هروح انا افترض فيه ال Q is
+
+12
+00:01:03,930 --> 00:01:10,050
+true و جينا قولنا كتالي احنا الأساس .. الأساس انB
+
+13
+00:01:10,050 --> 00:01:13,950
+implies Q لو تحققت ال hypothesis معناته ال
+
+14
+00:01:13,950 --> 00:01:18,690
+conclusion هتكون عندي true دايما true تقول ال true
+
+15
+00:01:18,690 --> 00:01:24,970
+فبالمجمل هتكون عندي العملية كلها true الأول طريقة
+
+16
+00:01:24,970 --> 00:01:29,930
+مقرره الإثبات كانت ال direct إثبات المباشر و منها
+
+17
+00:01:29,930 --> 00:01:36,220
+انا بعتمد على او بفترض ان بي isTrue لما بفترض ان P
+
+18
+00:01:36,220 --> 00:01:40,280
+is true هتوصلني ان الـ Q تتحقق عندى و بالتالي انا
+
+19
+00:01:40,280 --> 00:01:44,900
+بكون وصلت للمطلوب اللى موجود عندى بمعنى اخر انه في
+
+20
+00:01:44,900 --> 00:01:46,960
+النظرية اللى هتكون موجودة عندى او المطلوب من
+
+21
+00:01:46,960 --> 00:01:51,790
+اثباتها مطلوب اذا ماكنتش مكتوبة بشكل مباشر Fthen
+
+22
+00:01:51,790 --> 00:01:54,710
+معناته انا بدى اكتبها if then هذا خطوة رقم واحد
+
+23
+00:01:54,710 --> 00:02:00,650
+واروح افترض ان ال B is true وبناء على ال B احاول
+
+24
+00:02:00,650 --> 00:02:05,830
+اصل لمين ل ال Q وطبعا كلنا بنعرف نضرب ونجمع ونقول
+
+25
+00:02:05,830 --> 00:02:09,550
+العدد علي اليمين ويمين ويسار اشارة ليه ساوي وها
+
+26
+00:02:09,550 --> 00:02:14,190
+كذا وطبعا كان بالمثال اللي عندنا الأسهل هي if ال M
+
+27
+00:02:14,190 --> 00:02:17,810
+is odd then and ترميه is odd بس من باب التذكير
+
+28
+00:02:17,810 --> 00:02:26,620
+الآن هي ال Bو هذه ال Q ال N شو يعني ال N is odd؟ و
+
+29
+00:02:26,620 --> 00:02:31,920
+انا اخوك واحد عن واحد هقول Assume ال
+
+30
+00:02:31,920 --> 00:02:37,160
+B خلاص لو كنت بتديش كمان is it true انا بفترض ان
+
+31
+00:02:37,160 --> 00:02:42,700
+انت جاي بتشتغل صح Assume ال B is true يعني ال N is
+
+32
+00:02:42,700 --> 00:02:50,450
+odd مفهومها ال N isالخطوة التالية اللي هي الكلام
+
+33
+00:02:50,450 --> 00:02:55,690
+تجيب صورة الان كعدد فردي اللي هي صورة اتنين K زائد
+
+34
+00:02:55,690 --> 00:03:00,770
+واحد for some K تنتمي الى Z الخطوة رقم تلاتة بعد
+
+35
+00:03:00,770 --> 00:03:04,810
+هيك هو بيقولك ان الان تربيع معناته انك تربع الان
+
+36
+00:03:04,810 --> 00:03:12,490
+اللي عندك وتمشي الخطوة التالية تربع الان تصير
+
+37
+00:03:12,490 --> 00:03:17,640
+اتنين او ان تربيعبدا تساوي اتنين كي زائد واحد لكل
+
+38
+00:03:17,640 --> 00:03:23,060
+تربيع بدا تساوي اربع كي تربيع زائد اربع كي زائد
+
+39
+00:03:23,060 --> 00:03:27,560
+واحد لان باخد عامل تاني عامل مشترك من هنا اتنين في
+
+40
+00:03:27,560 --> 00:03:33,180
+اتنين كي تربيع زائد اربع كي لكل زائد واحد وهذه
+
+41
+00:03:33,180 --> 00:03:39,800
+الصورة الاتنين كي عفوا وهذه الصورة صورة العدد
+
+42
+00:03:39,800 --> 00:03:48,660
+الفردي odd integerوبالتالي انت وصلت لمين؟ للحل
+
+43
+00:03:48,660 --> 00:03:55,340
+اللي وصلت ل Q هذا بنسميه Direct Proof بعض
+
+44
+00:03:55,340 --> 00:03:59,180
+المسائل .. بعض المسائل هتحس ان ال Direct Proof مش
+
+45
+00:03:59,180 --> 00:04:04,180
+هينشي معاها خطوة فيها مش هتقدر تمصل لنتيجة طب ايش
+
+46
+00:04:04,180 --> 00:04:06,800
+بيكون الحل؟ بيكون الحل ان انا اعتمد على ال
+
+47
+00:04:06,800 --> 00:04:09,740
+Contrapositive تبعتها ايش ال Contrapositive؟ احنا
+
+48
+00:04:09,740 --> 00:04:18,000
+بنعرف ان ال B implies Q تكافئنقطة Q تعني نقطة B
+
+49
+00:04:18,000 --> 00:04:26,160
+وبالتالي إذا تحققت هذه المعروفة صحيحة في هذه
+
+50
+00:04:26,160 --> 00:04:29,980
+المعروفة سأفترض الـ Negation تابعة الـ Q سأقول
+
+51
+00:04:29,980 --> 00:04:34,260
+Assume نقطة Q ونفس الخطوات التي اتبعتها في ال
+
+52
+00:04:34,260 --> 00:04:38,260
+Direct Proof بس الفرق أن بدل ما انا افترض الـ B
+
+53
+00:04:38,260 --> 00:04:43,580
+افترضت أو اعتمدت على نقطة Q في الحلو من الأمثلة
+
+54
+00:04:43,580 --> 00:04:51,420
+اللي ممكن نشوفها بالشكل هذا لما قال لي تلاتة N
+
+55
+00:04:51,420 --> 00:04:56,500
+زائد اتنين is odd if ال N .. if ال N if التلاتة N
+
+56
+00:04:56,500 --> 00:05:03,900
+زائد اتنين is odd هي ال B معناته ال N is odd هي ال
+
+57
+00:05:03,900 --> 00:05:07,580
+Q الآن لو أنا فكرت أبدأ في ال B في ال direct proof
+
+58
+00:05:07,580 --> 00:05:11,560
+هذا مش هتوصلني لنتيجة مش هتوصلني لنتيجة لأنها
+
+59
+00:05:11,560 --> 00:05:17,790
+complexبالتالي انا بدى احاول اشوف الاسهل لو انا
+
+60
+00:05:17,790 --> 00:05:23,850
+بدى احولها بال contrapositive ماذا هقول if ال N is
+
+61
+00:05:23,850 --> 00:05:27,610
+even نقطة
+
+62
+00:05:27,610 --> 00:05:32,830
+Q ثم تلاتة N زائد اتنين is even
+
+63
+00:05:38,070 --> 00:05:42,450
+هذه النظرية هيك بيتصير و بروح بقوله assume not ..
+
+64
+00:05:42,450 --> 00:05:48,510
+هذي إيش بتمثل؟ هذي نفي ال Q Assume not Q حصل لمين؟
+
+65
+00:05:48,510 --> 00:05:51,970
+حصل ل not B وبالتالي حصلت على Contra positive
+
+66
+00:05:51,970 --> 00:05:56,870
+وبالتالي المعادلة اللي عند الأولى هتكون صحيحة في
+
+67
+00:05:56,870 --> 00:06:02,050
+الحالة هذه هروح أقوله assume not
+
+68
+00:06:02,050 --> 00:06:03,070
+Q is true
+
+69
+00:06:07,500 --> 00:06:14,220
+ماذا يعني نقطة Q is true؟ معناته N is not odd بين
+
+70
+00:06:14,220 --> 00:06:20,820
+جو سين هيكون even فبصورة ال even ال N بيبقى تساوي
+
+71
+00:06:20,820 --> 00:06:28,420
+اتنين في K وK تنتمي لزد في قرصان K الخطوة بعد هيك
+
+72
+00:06:28,420 --> 00:06:34,040
+تلاتة N زائد اتنين تساوي
+
+73
+00:06:34,040 --> 00:06:42,070
+تلاتة في اتنين Kزائد اتنين تساوي ستة K زائد اتنين
+
+74
+00:06:42,070 --> 00:06:47,610
+تساوي خد التنين عامل مشترك تلاتة K زائد واحد هذه
+
+75
+00:06:47,610 --> 00:06:51,990
+integer وهذه العدد عبارة عن is even integer
+
+76
+00:06:51,990 --> 00:06:55,510
+contrapositive
+
+77
+00:06:55,510 --> 00:07:03,150
+إلى اخرها تمام؟ ابدأ مع مين؟ مع ال direct ولا مع
+
+78
+00:07:03,150 --> 00:07:09,590
+ال contrapositive؟الاصل انك بدك تجرب وتتطلع في
+
+79
+00:07:09,590 --> 00:07:15,230
+المسألة بشكل كويس اول خطوة او اول جهد لازم تبذله
+
+80
+00:07:15,230 --> 00:07:22,030
+انك تحدد من ال B و من ال Q في المسألة عشان تمشي لل
+
+81
+00:07:22,030 --> 00:07:25,390
+next step الآن بقى اذا اتحددت B و Q انت صاحب
+
+82
+00:07:25,390 --> 00:07:31,750
+القراروالتجربة هي اكتر نجاعة ستمشي معاك مباشرة
+
+83
+00:07:31,750 --> 00:07:36,210
+تمسك بيك وحالتك ستتأدي وغالبا كل ما تلاقي بيك
+
+84
+00:07:36,210 --> 00:07:41,310
+كومبليكس ستلاقي كومبليكس كونترا بوزيتيف وهو الحل
+
+85
+00:07:41,310 --> 00:07:45,250
+كل ما تلاقي بيك كومبليكس ستكون كونترا بوزيتيف انت
+
+86
+00:07:45,250 --> 00:07:50,470
+قارن مين أسهل بيك و لا كيو؟ كيو أسهل يعني تقوم
+
+87
+00:07:50,470 --> 00:07:55,030
+باستخدام نقطة كيو لن تبقى بسهولة بمكان اللي موجود
+
+88
+00:07:55,030 --> 00:08:00,110
+عندكوبالتالي انت لازم .. يعني بدك تحاول و تجرب مرة
+
+89
+00:08:00,110 --> 00:08:03,490
+و اتنين و تلاتة لحد ما تصير انت عايش صرف عندك خبرة
+
+90
+00:08:03,490 --> 00:08:08,470
+في بناء او في .. بأي اتجاه انا بدي اروحه طيب النوع
+
+91
+00:08:08,470 --> 00:08:15,390
+التالت من الاثبات في ال .. بي implies q أحيانا مش
+
+92
+00:08:15,390 --> 00:08:18,430
+هيكون في اللي بنسميه احنا بالتناقض يعني لا جاية
+
+93
+00:08:18,430 --> 00:08:23,310
+معايابالـ Direct Proof ولا جاية معايا بالـ
+
+94
+00:08:23,310 --> 00:08:26,890
+Contrapositive في عندك طريقة تالتة او طريقة تالتة
+
+95
+00:08:26,890 --> 00:08:31,410
+هم يسميها الـ Contradiction اثبات بالتناقض الاثبات
+
+96
+00:08:31,410 --> 00:08:38,230
+بالتناقض احنا كلنا بنعرف ان ال B implies Q
+
+97
+00:08:38,230 --> 00:08:45,290
+equivalent to B or not Q يعني لو تحققت واحدة من
+
+98
+00:08:45,290 --> 00:08:49,370
+التنتين هدول بتكون العملية إيش ال trueجالك الإثبات
+
+99
+00:08:49,370 --> 00:08:54,550
+للتناقض كالتالي إذا أنا روحت كالتالي أخدت الموضوع
+
+100
+00:08:54,550 --> 00:08:59,790
+P و أخدت Q و مش قادر أصل لواحدة منهم بالاتجاهين
+
+101
+00:08:59,790 --> 00:09:03,350
+سواء كانت بال direct أو بال contrapositive معناته
+
+102
+00:09:03,350 --> 00:09:08,910
+ممكن أنا أجرب أروح أفرض أن ال P صحيحة و ال Q ..
+
+103
+00:09:08,910 --> 00:09:11,430
+not ال Q صحيحة يعني ال Q .. ال Q false يعني بدي
+
+104
+00:09:11,430 --> 00:09:15,870
+أقول أن النظرية دي مش صحيحةوأجرب أشتغل مع ال band
+
+105
+00:09:15,870 --> 00:09:20,690
+الأسهل منهم إذا حصلت على أي تناقض معناته النظرية
+
+106
+00:09:20,690 --> 00:09:25,630
+الأصلية هيش هتكون صحيحة كمان مرة انت ايش عاملك
+
+107
+00:09:25,630 --> 00:09:29,810
+بتفترض ان ال B is true و ال conclusion المحصلة
+
+108
+00:09:29,810 --> 00:09:34,470
+تبعت النظرية ال Q is true مصبوط فانت روحت و قلتله
+
+109
+00:09:34,470 --> 00:09:38,790
+false قلتله انك بتفترض ان ال B is true و ال Q is
+
+110
+00:09:38,790 --> 00:09:44,860
+falseو أثناء الحل وصلت إن ال false اللي أنت فرضتها
+
+111
+00:09:44,860 --> 00:09:52,940
+is false نفي نفي يعني false false وكأنك تنفي إنك
+
+112
+00:09:52,940 --> 00:09:57,460
+ننفي تمام؟ وبالتالي بتكون حصلت على شغل إيه اسمها؟
+
+113
+00:09:57,460 --> 00:10:01,720
+طلاق بين الفرضيات طبعا بدون ما تتطلع في .. إسميلك
+
+114
+00:10:01,720 --> 00:10:07,200
+يا غزال يا سويسي خلّيك معايا هنا عشان تفهم إيش
+
+115
+00:10:07,200 --> 00:10:07,880
+المقصود بيه
+
+116
+00:10:14,580 --> 00:10:22,660
+لو كان تربيع العدد فردي فمعناته العدد لن يكون عندي
+
+117
+00:10:22,660 --> 00:10:38,210
+إيش فردي if ال n تربيع is odd then ال n isأضعف
+
+118
+00:10:38,210 --> 00:10:42,930
+غزال أدم يثبتها بإيش Contra
+
+119
+00:10:42,930 --> 00:10:48,310
+positive تجه 100% معانا بروح بقوله assume not q
+
+120
+00:10:48,310 --> 00:10:51,910
+يعني الأن is even الحاجة قبل شويه أثبتناها مصبوط
+
+121
+00:10:51,910 --> 00:10:56,170
+ولا لأ أو أثبتنا مثلها قريب منها even وربع ال even
+
+122
+00:10:56,170 --> 00:11:00,310
+في الآخر تصل لكن أنا بدأ أستخدم معاها الإثبات
+
+123
+00:11:00,310 --> 00:11:01,790
+بالتناقض
+
+124
+00:11:04,060 --> 00:11:07,340
+كمان مرة عشان الناس صحابنا ميتهوش ايش يعني ب
+
+125
+00:11:07,340 --> 00:11:13,780
+Contrapositive بتجربة Contrapositive proof by
+
+126
+00:11:13,780 --> 00:11:17,840
+contrapositive للمسألة
+
+127
+00:11:17,840 --> 00:11:23,320
+هذه هروح أقول له assume not
+
+128
+00:11:23,320 --> 00:11:29,720
+q is true ايش يعني not q is true ان ال N is not
+
+129
+00:11:29,720 --> 00:11:31,380
+odd
+
+130
+00:11:32,870 --> 00:11:36,610
+even هي المصدر اللي حللناه قبل شوية اتوا ال N
+
+131
+00:11:36,610 --> 00:11:42,410
+equal 2K و ال K تنتبي الى Z و قاعد بدوا من ال N
+
+132
+00:11:42,410 --> 00:11:47,170
+تربيع N تربيع بدها تساوي 2K كل تربيع و بدها تساوي
+
+133
+00:11:47,170 --> 00:11:54,310
+4K تربيع و بدها تساوي هاتين في 2K تربيع even
+
+134
+00:11:54,310 --> 00:11:58,170
+integer contrapositive
+
+135
+00:12:01,440 --> 00:12:07,580
+مظبوط؟ اللي هي دي بتمثل ات نط ال B خلص البرهان هدف
+
+136
+00:12:07,580 --> 00:12:10,900
+ال contrapositive هدف ال contrapositive صحيح مية
+
+137
+00:12:10,900 --> 00:12:14,940
+في المية مافيش عليه مشكلة لأن ب contradiction ايش
+
+138
+00:12:14,940 --> 00:12:21,500
+بدك تفترض انت؟ بدك تقول لل B is it true؟و and ..
+
+139
+00:12:21,500 --> 00:12:25,080
+نه .. بالضبط و ال Q غلط .. false إيش .. إذا .. لما
+
+140
+00:12:25,080 --> 00:12:29,320
+تكون n is odd false يعني ال n is .. even .. even
+
+141
+00:12:29,320 --> 00:12:31,860
+.. فيه .. فيش حاجة غير هيك و لا لأ .. بقيت هروح
+
+142
+00:12:31,860 --> 00:12:40,820
+أقوله أنا أسيوم .. افترض ال P and .. نقطة Q .. مين
+
+143
+00:12:40,820 --> 00:12:47,040
+ال P هيها؟ و مين ال Q؟ هيها .. أصبت؟
+
+144
+00:12:50,200 --> 00:12:59,800
+معناته ال B أو ال N تربيع is odd and ال N is not
+
+145
+00:12:59,800 --> 00:13:04,080
+odd اللي هي بين جثين even إن شاءت يا شباب ما
+
+146
+00:13:04,080 --> 00:13:06,460
+تكتبليش is not odd ماعنديش مشكلة أنا في الموضوع
+
+147
+00:13:06,460 --> 00:13:11,800
+كتبلي مباشرة even مافيش مشكلةيعني صار انا فيه عندى
+
+148
+00:13:11,800 --> 00:13:15,780
+الان وكأنه موقعيات اتنين بين ايديا اعتمد على مين
+
+149
+00:13:15,780 --> 00:13:19,860
+فيهم في الشغل الان تربيع اقول الان تربيع بيده
+
+150
+00:13:19,860 --> 00:13:23,280
+تساوي اتنين كساوية واحد واخد الجذر ولا اعتمد على
+
+151
+00:13:23,280 --> 00:13:27,660
+الأسهل اللى هى الان اكوال اتنين اك واربعها لأ و
+
+152
+00:13:27,660 --> 00:13:30,660
+الله بيربعها بعدها هروح لخبرة تالية هقول الان بيده
+
+153
+00:13:30,660 --> 00:13:37,340
+تساوي اتنين ك مصبوط ليش هي is not odd is not odd
+
+154
+00:13:37,340 --> 00:13:42,510
+even يعني2K لان equal 2K أن تربيع الخطوة اللي
+
+155
+00:13:42,510 --> 00:13:48,530
+بعدها أن تربيع بدها تساوي 4K تربيع ونتساوي 2 في 2K
+
+156
+00:13:48,530 --> 00:13:58,470
+تربيع صح even وها دي even integer not
+
+157
+00:13:58,470 --> 00:14:00,990
+odd contradiction
+
+158
+00:14:07,020 --> 00:14:14,960
+with ترقض معميل مع الفرضية and تربيع is odd خلصنا
+
+159
+00:14:14,960 --> 00:14:19,400
+البرهان إيش يعني؟ يعني لما بتكون ال and تربيع is
+
+160
+00:14:19,400 --> 00:14:27,140
+odd ال and is odd وهذا هو الإثبات بالترقض إنك أنت
+
+161
+00:14:27,140 --> 00:14:30,760
+بتفرض حالتين و بتشتغل مع أي واحدة فيهم مش مشكلة
+
+162
+00:14:30,760 --> 00:14:34,700
+عندك معميل بلام أنك حققتهم في الفرضيات يعني بتقدر
+
+163
+00:14:34,700 --> 00:14:39,000
+تعتمد عليهم زي ما بدكوبتمشي للاتجاه التالي لحد ما
+
+164
+00:14:39,000 --> 00:14:43,260
+تصل لأي طلاقط عشان هيك كتبنا لك هان assume P and
+
+165
+00:14:43,260 --> 00:14:48,460
+not Q then deduce any contradiction وحاول ابحث او
+
+166
+00:14:48,460 --> 00:15:01,220
+اوجد عن اي طلاقط موجود في المسألة اللي عندها تمام
+
+167
+00:15:01,220 --> 00:15:01,780
+مثال؟
+
+168
+00:15:14,740 --> 00:15:21,720
+وقول لي لو كانت ال M زائد ال N أقل من 89 هذي مثلت
+
+169
+00:15:21,720 --> 00:15:35,820
+مين؟ ال B ثم M أقل من 45 او ال N أقل من 45 ل Q و
+
+170
+00:15:35,820 --> 00:15:39,240
+بدنا نثبتها بال contradiction نثبتها بالتراقد تثبت
+
+171
+00:15:39,240 --> 00:15:41,100
+بالتراقد يعني assume
+
+172
+00:15:55,040 --> 00:16:06,260
+ممتاز ايش ال B ال M زائد ال M اكبر اصغر من 89 and
+
+173
+00:16:06,260 --> 00:16:09,860
+ال
+
+174
+00:16:09,860 --> 00:16:14,470
+and بدك تنفي تنساه بدك تنفي كل Q ال Mال M أكبر أو
+
+175
+00:16:14,470 --> 00:16:19,190
+تساوي خمسة و أربعين ال or بتصير and و ال M أكبر أو
+
+176
+00:16:19,190 --> 00:16:24,050
+تساوي خمسة و أربعين مظبوط؟ و بالتالي هقوله الآن ال
+
+177
+00:16:24,050 --> 00:16:33,230
+M أكبر أو تساوي خمسة و أربعين and ال M أكبر أو
+
+178
+00:16:33,230 --> 00:16:39,070
+تساوي خمسة و أربعين لاحظ
+
+179
+00:16:39,070 --> 00:16:43,740
+الفرضية تبعتك كم عنصر فيها موجودة الآنواحدة تنتين
+
+180
+00:16:43,740 --> 00:16:49,380
+تلاتة تستخدمين فيهم الأسهل لك اللي ممكن ياش تمشي
+
+181
+00:16:49,380 --> 00:16:51,860
+معاك في الحل لأن الأن دول الفرقويات التلاتة
+
+182
+00:16:51,860 --> 00:16:55,400
+الموجودة وانت مطلوب منك توجد اي تناقض مطلوب منك
+
+183
+00:16:55,400 --> 00:17:00,080
+توجد اي تناقض الان لو مسكت الأولى هذي مش حصل الحل
+
+184
+00:17:00,080 --> 00:17:04,380
+انا ولا لا؟ بدأ ادور علاقة بدأ امسك هذه او التانية
+
+185
+00:17:04,380 --> 00:17:09,740
+هوحى باللهيك ال M أكبر او تساوي
+
+186
+00:17:17,980 --> 00:17:23,440
+معناته M زائد M هتكون أكبر أو تساوي خمسة و أربعين
+
+187
+00:17:23,440 --> 00:17:28,560
+زائد ال N تصبر
+
+188
+00:17:28,560 --> 00:17:31,800
+ان اضافنا ال N على ال برافين عشان النساء اللي
+
+189
+00:17:31,800 --> 00:17:37,580
+اتبعها صحيحةطب احنا أساسا عندنا ال N أكبر من 45،
+
+190
+00:17:37,580 --> 00:17:42,080
+مصبوط؟ معناته بما أن ال N هذه أكبر من 45، معناته
+
+191
+00:17:42,080 --> 00:17:49,760
+حصي الجمع هذا أكبر أو تساوي 45 زاد ال 45، صح؟ اللي
+
+192
+00:17:49,760 --> 00:17:57,230
+هي 90وبخصيتي التعدي إذا كانت ال M أكبر من M من 45
+
+193
+00:17:57,230 --> 00:18:02,670
+زائد ال M و أكبر من 90 فهي هتكون M زائد M أكبر من
+
+194
+00:18:02,670 --> 00:18:10,050
+90 وهذا هيقدر أن M زائد M أكبر أو تساوي 90 هذا
+
+195
+00:18:10,050 --> 00:18:15,290
+بتناقض معنى Contradiction أنا وصلت ل Contradiction
+
+196
+00:18:20,510 --> 00:18:25,510
+ماذا يعني؟ يعني لما تكون ال M زائد ال M أقل من 89،
+
+197
+00:18:25,510 --> 00:18:30,170
+معناته ال M هتكون أقل من 45، أو يعني واحدة منهم
+
+198
+00:18:30,170 --> 00:18:34,610
+هتكون أقل من 45، هاي الإثبات بالتناقض، هتحس إنه
+
+199
+00:18:34,610 --> 00:18:38,770
+فعلا أن الأمر صار سهل و ممكن أنا أجيب حل و أوجد
+
+200
+00:18:38,770 --> 00:18:40,530
+منه برهان بكل بساطة
+
+201
+00:18:43,490 --> 00:18:46,930
+قبل أن ألتقى للموضوع التالي اللي هو ال
+
+202
+00:18:46,930 --> 00:18:49,530
+mathematical induction لكن أنا بدي أتركه للمحاضرة
+
+203
+00:18:49,530 --> 00:18:53,130
+الجاية و بدي أشوف أسئلة الكتاب يعني قبل ما أجي على
+
+204
+00:18:53,130 --> 00:18:59,510
+المحاضرة أخدت snapshot من أول تمنتاشر سؤال تقريبا
+
+205
+00:18:59,510 --> 00:19:04,850
+بدنا نحلهم مش مش حلهم كلهمبنتحاول ناخد بعضهم و
+
+206
+00:19:04,850 --> 00:19:08,470
+نشوف كيف ممكن احنا نحل نعتمد على direct نعتمد على
+
+207
+00:19:08,470 --> 00:19:12,170
+contrapositive نستخدم ال contradiction اي واحد من
+
+208
+00:19:12,170 --> 00:19:16,810
+الاثباتات انا اتبعهم طبعا هتلاقي انك بعض الأحيان
+
+209
+00:19:16,810 --> 00:19:22,770
+من الكتاب بيقولك استخدم كده تمام؟ و غالبا .. غالبا
+
+210
+00:19:22,770 --> 00:19:25,550
+في الامتحان اذا انا .. يعني انا ممكن طريقة انحلب
+
+211
+00:19:25,550 --> 00:19:29,950
+اكتر من شغله ممكن اقولك انا استخدمهكذا اذا كان انا
+
+212
+00:19:29,950 --> 00:19:32,810
+بدي اياها او ممكن يسيبك اياها مفتوحة معناته بتقدر
+
+213
+00:19:32,810 --> 00:19:37,930
+تحل مثلا ال contrapositive او الcontradiction طيب
+
+214
+00:19:37,930 --> 00:19:43,670
+direct proof ده هتشوف السؤال الأول بيقول استخدم ال
+
+215
+00:19:43,670 --> 00:19:47,510
+direct proof عشان تثبت جمع او حاصل جمع two odd
+
+216
+00:19:47,510 --> 00:19:55,090
+integers is even فيها if و then يا شباب انت اللي
+
+217
+00:19:55,090 --> 00:19:59,680
+بكي تركب ال if و then الآنمين ال B و مين ال Q في
+
+218
+00:19:59,680 --> 00:20:03,280
+المسألة؟ جيل بيقول لك show that the sum of two odd
+
+219
+00:20:03,280 --> 00:20:08,760
+integers لأ لأ اللي قد تقول two odd integers هي
+
+220
+00:20:08,760 --> 00:20:16,260
+المعطاه حصل جمعهم even يعني هتقول هيك if ال M and
+
+221
+00:20:16,260 --> 00:20:27,760
+ال N are odd then M زائد ال M iseven؟ ولا شو رأيك؟
+
+222
+00:20:27,760 --> 00:20:31,060
+لأن هيك صحيحة المسألة عشان هيك عشان هيك انت لازم
+
+223
+00:20:31,060 --> 00:20:35,200
+تروح تطلع على أسئلة الكتاب وتجرب لأن مش كل المسائل
+
+224
+00:20:35,200 --> 00:20:38,720
+جاياكي مجشرة بيقولك اتفضل يعني أنت أحيانا بتكون
+
+225
+00:20:38,720 --> 00:20:42,340
+عند ضيف أو تكون ضيف عند ناس عفوا بيقعد بيجشرلك
+
+226
+00:20:42,340 --> 00:20:45,080
+الموزة و بيقدملك إيها بكل احترام أو بيقعد بيجشرلك
+
+227
+00:20:45,080 --> 00:20:49,810
+التفاحة و بيقولك اتفضل مصبوط؟ أيوةأحياناً بتكون
+
+228
+00:20:49,810 --> 00:20:54,290
+كتر ما شافك وزورتك تيل خلال الفصل يا راني جرف منك
+
+229
+00:20:54,290 --> 00:20:58,450
+بقولك احمل هاي ال بورتجانه و هاي السكينه لأ احمل
+
+230
+00:20:58,450 --> 00:21:03,210
+ال بورتجانه مش المادة تمام؟ وبالتالي المطموع ان
+
+231
+00:21:03,210 --> 00:21:09,490
+انت ايش تبدأ تشتغل تبدأ تشتغل والاصل انك تبدأ تعرف
+
+232
+00:21:09,490 --> 00:21:13,490
+لانه كمان مرة مفتاح الحل في المسائل يا شباب اذا
+
+233
+00:21:13,490 --> 00:21:20,110
+ماكنتش موجودة F و Thenانت بدك ايش تبحث او توجد ال
+
+234
+00:21:20,110 --> 00:21:24,550
+F within هذي اليك عشان تبدأ الحل بتهيألي بعد هيك
+
+235
+00:21:24,550 --> 00:21:31,330
+حلت المسألة ولا شو رايكوا في دا حلها دا يعني
+
+236
+00:21:31,330 --> 00:21:35,410
+اما بدها تساوي اتنين K زائد واحد ان بدها تساوي
+
+237
+00:21:35,410 --> 00:21:42,640
+اتنين Kأنا ماعرف ليش k زال واحد غلط لإنك انت خدت
+
+238
+00:21:42,640 --> 00:21:46,540
+نفس الايم انتوا جماعته لا نفسه خد اي رقم تاني غير
+
+239
+00:21:46,540 --> 00:21:51,560
+ال k لو .. لو قلت نقص واحد okay بمشي الحل بس في
+
+240
+00:21:51,560 --> 00:21:56,930
+الآخر خد different numberزائد H اتنين H زائد واحد
+
+241
+00:21:56,930 --> 00:22:00,590
+و إجمعهم و أحصل على نتيجة ستكون صح السؤال التاني
+
+242
+00:22:00,590 --> 00:22:03,370
+برضه استخدم ال direct proof to show the sum of
+
+243
+00:22:03,370 --> 00:22:08,750
+even عكسه كماما، مصبوط؟ مالاش تدخل فيه تلاتة show
+
+244
+00:22:08,750 --> 00:22:20,250
+that the square of even number is even number بدي
+
+245
+00:22:20,250 --> 00:22:30,140
+حد يصيغليها F withinأه سويسي قول اتديني اها if و
+
+246
+00:22:30,140 --> 00:22:35,520
+then ايوه
+
+247
+00:22:35,520 --> 00:22:41,720
+ممتاز على الرغم انه بدالك المسألة the square زي
+
+248
+00:22:41,720 --> 00:22:45,700
+المجلة كان the sum the square of an even number
+
+249
+00:22:45,700 --> 00:22:53,140
+يعني لو كانت ال n is even then if ال n is even
+
+250
+00:22:55,820 --> 00:23:01,320
+ذن الآن ترميع is even هذه صيغة المسألة اللي موجودة
+
+251
+00:23:01,320 --> 00:23:04,940
+عندك وبالتالي أول ما تفشوف مسألة زي هيك مش قادر
+
+252
+00:23:04,940 --> 00:23:09,160
+تمسك فيها if و then بدك تحاول توجد ال if و ال then
+
+253
+00:23:09,160 --> 00:23:15,340
+تباعتها المسألة هاي أربعة show that the additive
+
+254
+00:23:15,340 --> 00:23:19,920
+inverse المعكوس الجامعي additive inverse المعكوس
+
+255
+00:23:19,920 --> 00:23:26,200
+الجامعي أو حطوط قياب انبوسين ال negativeof an even
+
+256
+00:23:26,200 --> 00:23:30,840
+integer او even number is even number using the
+
+257
+00:23:30,840 --> 00:23:39,400
+direct proof كمان مرة بدنا واحد من السرحانين يحاول
+
+258
+00:23:39,400 --> 00:23:45,120
+يجيب اللي هي f و then the
+
+259
+00:23:45,120 --> 00:23:49,220
+additive inverse المعكوس الجمعى اللي هو بين جثين
+
+260
+00:23:49,220 --> 00:23:54,060
+حطولا كيان نيجاتيف لل even number is even number
+
+261
+00:23:58,310 --> 00:24:08,410
+إذا ال N هو نيجاتيف، إذا ال N هو نيجاتيف، إذا ال N
+
+262
+00:24:08,410 --> 00:24:14,110
+هو نيجاتيف، إذا ال N هو نيجاتيف، إذا ال N هو
+
+263
+00:24:14,110 --> 00:24:20,050
+نيجاتيف، إذا ال
+
+264
+00:24:20,050 --> 00:24:23,030
+N هو نيجاتيف، إذا ال N هو نيجاتيف، إذا ال N هو
+
+265
+00:24:23,030 --> 00:24:26,390
+نيجاتيف، إذا ال N هو نيجاتيف، إذا ال N هو نيجاتيف،
+
+266
+00:24:26,390 --> 00:24:26,430
+هو نيجاتيف، إذا ال N
+
+267
+00:24:33,060 --> 00:24:38,900
+لو كانت ال N even هيكون المعكوس الجامعي تبقتها
+
+268
+00:24:38,900 --> 00:24:47,020
+ناقص ن is even هي show that the additive inverse
+
+269
+00:24:47,020 --> 00:24:53,040
+of an even integer يعني المعكوس الجامعي للعدد
+
+270
+00:24:53,040 --> 00:25:02,040
+الزوجي عدد زوجياتنين و سالم اتنين بصبوط هاي ..
+
+271
+00:25:02,040 --> 00:25:07,960
+ماتبتها .. ماعكستش لأ انا حاولت استخلص منها اف و
+
+272
+00:25:07,960 --> 00:25:13,720
+دل هو ايش عمله قاعد يقول ليه تعالى نشوف بشكل عام
+
+273
+00:25:13,720 --> 00:25:20,140
+انا مطلوب مني في المسألة هي اقول له اف فراغ
+
+274
+00:25:21,920 --> 00:25:25,940
+ثم فرح اكتب على الشكل هذا افصلها ايش قاعد هو
+
+275
+00:25:25,940 --> 00:25:31,800
+بيقولها المعكوس الجامعى للعدد الزوجى يعني ايش
+
+276
+00:25:31,800 --> 00:25:36,380
+المعطى اليك عدد الزوجى المعطى اليك العدد الزوجى
+
+277
+00:25:36,380 --> 00:25:40,300
+وقاعد بيقولك انه اثبت ان المعكوس الجامعى للعدد
+
+278
+00:25:40,300 --> 00:25:46,600
+الزوجى هو عبارة عن عدد زوجى يعني هو back and is
+
+279
+00:25:46,600 --> 00:25:53,690
+evenو اثبت ان المعكوس الجمعى اللى هو سالب N is
+
+280
+00:25:53,690 --> 00:26:00,870
+even طبعا بضبط بس انت عارفش هتروح تقوله هتروح تقول
+
+281
+00:26:00,870 --> 00:26:11,370
+Assume B is true صح يعني N isEVEN هذا بيقدر ان
+
+282
+00:26:11,370 --> 00:26:15,870
+الان equal اتنين K و K تان تانى الى Z هذا لاحظ انه
+
+283
+00:26:15,870 --> 00:26:20,230
+بتحس انه اول سطرين بنكتبهم في البرهان و كأنهم نسخ
+
+284
+00:26:20,230 --> 00:26:23,650
+نحطه على مكان التصوير و بنضغط عليك تكتبهم حسب نوع
+
+285
+00:26:23,650 --> 00:26:27,930
+الاثبات اللى عندك اتنين K زائد واحد او اتنين K عفر
+
+286
+00:26:27,930 --> 00:26:34,830
+اش هو بده من ايه؟المعكوس الجمعي هذا يؤدى ان سالب N
+
+287
+00:26:34,830 --> 00:26:40,550
+تساوي سالب واحد او سالب واحد مضروبة في اتنين K
+
+288
+00:26:40,550 --> 00:26:47,110
+وتساوي سالب اتنين K صح؟ وتساوي اتنين في سالب K وهك
+
+289
+00:26:47,110 --> 00:26:53,430
+و تصير جوعانها even يا خالد اه الفكرة ان دايما
+
+290
+00:26:53,430 --> 00:26:57,630
+صورة عدد الزوج هي عبارة عن اتنين مضروبة في some
+
+291
+00:26:57,630 --> 00:27:02,260
+integerهي التنين وهي الـ sum integer لو انت من
+
+292
+00:27:02,260 --> 00:27:05,580
+اللحظة هذه قلتلي انا بصدقك و بقول مية لمية كلامك
+
+293
+00:27:05,580 --> 00:27:09,740
+صح بس الخطوة التالتة الأخيرة هذه عشان ما تتركش
+
+294
+00:27:09,740 --> 00:27:13,660
+مجال لأي حد قلتلي هى التنين اللي حار يا عم وهي ال
+
+295
+00:27:13,660 --> 00:27:21,640
+integer اللي هو السالب K ضربناها is even خلصنا خلص
+
+296
+00:27:21,640 --> 00:27:24,520
+البرهان معته سالب N is even
+
+297
+00:27:37,010 --> 00:27:45,690
+خمسة مضيك F within في خمسة show that F ال N زائد
+
+298
+00:27:45,690 --> 00:27:55,150
+ال M and N زائد ال B are even integers هذا
+
+299
+00:27:55,150 --> 00:28:00,480
+ال Bهذه ال B كلها تمام؟ where بقى بقولك ال M و ال
+
+300
+00:28:00,480 --> 00:28:02,940
+N are integers أعداد صحيحة يعني مش real number
+
+301
+00:28:02,940 --> 00:28:11,180
+then M زائد ال B وهذه Q M زائد ال N افضل M زائد ال
+
+302
+00:28:11,180 --> 00:28:19,440
+B is even اسكت يا أحمد تسمعني صوتك if ال M زائد ال
+
+303
+00:28:19,440 --> 00:28:25,200
+N and N زائد ال B are even
+
+304
+00:28:28,050 --> 00:28:36,550
+ثم M زائد N is even M زائد B عفوا هى المسألة اللى
+
+305
+00:28:36,550 --> 00:28:46,970
+بديك إياها هو N الان احنا هقوله assume B
+
+306
+00:28:46,970 --> 00:28:47,550
+is true
+
+307
+00:28:51,590 --> 00:28:55,450
+هل هو ضروري الدارك تكون صح؟ ماعرفش بدي أجرب وبناء
+
+308
+00:28:55,450 --> 00:29:01,330
+على تجربتي بعد خطوات اتنين بشوف كيف الوضع M زائد
+
+309
+00:29:01,330 --> 00:29:05,430
+ال N is even و
+
+310
+00:29:05,430 --> 00:29:13,330
+N زائد ال B is even هذا بيقدر ان M زائد ال N equal
+
+311
+00:29:13,330 --> 00:29:23,020
+2K و N زائد ال B equal 2Hfor some K تنتمي إلى Z و
+
+312
+00:29:23,020 --> 00:29:27,220
+for some H تنتمي إلى Z for some K و H integers
+
+313
+00:29:27,220 --> 00:29:31,800
+تمام؟ بس هو في الطرف التاني إيش مستخدم هنا يا
+
+314
+00:29:31,800 --> 00:29:38,200
+شباب؟م زائد ال B يعني ال N مش في الحسبة ال N مش في
+
+315
+00:29:38,200 --> 00:29:43,020
+الحسبة و كأنه بيقول خاصيتي التعدي هنا حروح أنا بدي
+
+316
+00:29:43,020 --> 00:29:46,260
+أخد ال M لحالها و ياخد ال B لحالها بناء على
+
+317
+00:29:46,260 --> 00:29:52,660
+المعادلة هذه ال M مش بده تساوي اتنين K نقص ال M و
+
+318
+00:29:52,660 --> 00:29:58,300
+ال B بده تساوي اتنين H نقطة في ال N مصبوط اجمعهم
+
+319
+00:29:58,300 --> 00:30:04,660
+الآن مع المعادلة الخطوة اللي بعدهام زائد ب هو
+
+320
+00:30:04,660 --> 00:30:15,720
+المطلوب يساوي اتنين H اتنين K ناقص M زائد اتنين H
+
+321
+00:30:15,720 --> 00:30:26,920
+ناقص M ناجس M ناجس N ناجس اتنين M ايش تشيل؟ اتنين
+
+322
+00:30:26,920 --> 00:30:32,220
+K زائد اتنين H ناقص اتنين M ويساوي اتنين عامل
+
+323
+00:30:32,220 --> 00:30:40,810
+مشتركK زائد H نقص M اتنين مضبوطة في some integer
+
+324
+00:30:40,810 --> 00:30:46,710
+even خلصت
+
+325
+00:30:46,710 --> 00:30:53,230
+المسألة direct نعم ال M لحالها odd صح؟ مين قال؟
+
+326
+00:30:53,230 --> 00:30:57,170
+مين قال؟ اتنين K نقص واحد .. اتنين K نقصان و ليه؟
+
+327
+00:30:57,170 --> 00:30:59,470
+و ليه؟ و ليش لإن افترضتها نقد؟ لأنها ممكن تكون
+
+328
+00:30:59,470 --> 00:31:02,610
+even اتنين زائد أربعة ستة
+
+329
+00:31:04,600 --> 00:31:09,700
+بس اصبر احنا مالاش في قيمة n هو الذاك فرضيه ايش هي
+
+330
+00:31:09,700 --> 00:31:15,980
+فرضيته ان ال M زائد ال N عبارة عن even صح؟ يعني
+
+331
+00:31:15,980 --> 00:31:21,060
+اما ال M .. حسب ما احنا بنقعد M زائد N even يعني
+
+332
+00:31:21,060 --> 00:31:25,560
+يا اما التنين odd يا اما التنين even وبتاني ليش
+
+333
+00:31:25,560 --> 00:31:28,480
+دخل في هاللخمة أنا هاي؟ هو كل اللي قاللي ايه ايه M
+
+334
+00:31:28,480 --> 00:31:32,920
+زائد N is even معناته is even معناته M زائد N يكتب
+
+335
+00:31:32,920 --> 00:31:37,690
+على صورةأتنين K خلصت و هو بده مني ال N لحالها
+
+336
+00:31:37,690 --> 00:31:44,510
+فباخد ال N على الطرف التاني و خلصت تطلع ال N odd
+
+337
+00:31:44,510 --> 00:31:48,570
+تطلع even انا مابعننيش انا كانت اللي بيعنيني N
+
+338
+00:31:48,570 --> 00:31:52,150
+زائد ال N اللي هي ال even و انا حققتله إياها عشان
+
+339
+00:31:52,150 --> 00:31:55,630
+ايه مافيش داعي دايما احاول التفكير اللي انت فكرت
+
+340
+00:31:55,630 --> 00:32:00,830
+فيه صح بس انت وجعت وين انت افترضت ان هذي odd اذا
+
+341
+00:32:00,830 --> 00:32:04,310
+هذي odd لازم تكون ال N is oddبس في الآخر مجموعهم
+
+342
+00:32:04,310 --> 00:32:09,310
+even و لو كانت هذه even ال uneven عشان يكون
+
+343
+00:32:09,310 --> 00:32:11,830
+مجموعهم even فبالتالي ماليش دخل في الموضوع انا
+
+344
+00:32:11,830 --> 00:32:15,430
+يعني فبالتالي نمشي بالبرغام حسب المسألة اللي
+
+345
+00:32:15,430 --> 00:32:19,850
+موجودة عندي بالتدريج تتوجه ال contrapositive او ال
+
+346
+00:32:19,850 --> 00:32:23,450
+contradiction ممكن نجيب حل ال contrapositive ممكن
+
+347
+00:32:23,450 --> 00:32:27,050
+نجيب حل متوقع
+
+348
+00:32:27,050 --> 00:32:32,840
+ان ال contrapositive توصلي لحل اثباتفاكر .. قبل ما
+
+349
+00:32:32,840 --> 00:32:38,780
+تجاوب فاكر .. اه
+
+350
+00:32:38,780 --> 00:32:46,460
+يا عمر .. لأ .. ليش .. مش عارف .. غيره .. سواركي
+
+351
+00:32:46,460 --> 00:32:50,960
+.. ممكن ال contrapositive يوصلني لحال .. انت
+
+352
+00:32:50,960 --> 00:32:56,080
+سواركي .. مايرزعيل فاك .. انا بوصحكوا تدوش الجنسية
+
+353
+00:32:56,080 --> 00:33:04,780
+.. اه .. ممكن ..طيب اقولكوا شغلة انت تعالى تطلع
+
+354
+00:33:04,780 --> 00:33:11,940
+فيها هنا بدوش عندي M و B أصبت؟ و الطرف التاني فيه
+
+355
+00:33:11,940 --> 00:33:15,960
+عندي N طب ال N اللي انا بدأ افرضها شو بدأ افرضها؟
+
+356
+00:33:15,960 --> 00:33:19,980
+بدأ افرضها عدد زوجي ولا بدأ افرضها عدد فردي؟ مش
+
+357
+00:33:19,980 --> 00:33:25,220
+عارف وبالتالي ال contrapositive مابتمشيش معايا لكن
+
+358
+00:33:25,220 --> 00:33:29,180
+ال contradiction ممكن تصبط يا حمد؟ ال
+
+359
+00:33:29,180 --> 00:33:34,720
+contradiction ممكن تصبط؟ليش لأ؟ في الcontradiction
+
+360
+00:33:34,720 --> 00:33:38,640
+أنا إيش بده أقوله؟ بده أقوله B and not the Q وهذه
+
+361
+00:33:38,640 --> 00:33:42,520
+صورة هو إيه؟ صورة هي إيش؟ Odd فلما تشتغل نفس الشغل
+
+362
+00:33:42,520 --> 00:33:51,360
+هذا بس مع فرضية .. مع الفرضية أنها and not the Q
+
+363
+00:33:51,360 --> 00:33:58,860
+اللي هي M زائد B is not even لبين جوسين Odd
+
+364
+00:33:59,390 --> 00:34:03,350
+Contradiction بالتناقض هتشتغل مع هدوء تكتب نفس
+
+365
+00:34:03,350 --> 00:34:07,850
+الخطوات السابقة هتوصل ان ال M زي ال B is even
+
+366
+00:34:07,850 --> 00:34:11,270
+Contradiction مع مين؟ مع الفرضية اللى موجودة عندى
+
+367
+00:34:11,270 --> 00:34:17,590
+السابقة كمان؟ وبالتالي هي بدالك تتبعه في انحلت و
+
+368
+00:34:17,590 --> 00:34:23,610
+بالcontradiction انحلت اي حل اعتمد فيهم اي واحد اي
+
+369
+00:34:23,610 --> 00:34:28,330
+واحد اللى انت تقدر تجيبه في الامتحانطبعا لو انا
+
+370
+00:34:28,330 --> 00:34:33,290
+كنت بتقول لك استخدم ال contradiction تمام؟ و روحت
+
+371
+00:34:33,290 --> 00:34:41,290
+تبتليها بال direct بتاخد ال big zero اه مابقالله
+
+372
+00:34:41,290 --> 00:34:45,110
+اتعب هذا شسمه عند المجاولين انا ماخدش المجاولة لأ
+
+373
+00:34:45,110 --> 00:34:51,670
+و بالتالي .. لأ الكلامتين هدول يا سوستفان بيعنوا
+
+374
+00:34:51,670 --> 00:34:55,270
+انك انت فاهم ايش الطريقة اللي بتفرج هدى عن هدى
+
+375
+00:34:56,600 --> 00:35:00,300
+كمان؟ الان في التاسع عاش بقول ليه؟ استخدم ال proof
+
+376
+00:35:00,300 --> 00:35:03,780
+by contradiction to prove that .. بيقول استخدم
+
+377
+00:35:03,780 --> 00:35:08,320
+الأثبات بالتناقض عشان تثبت أن حاصل جامع irrational
+
+378
+00:35:08,320 --> 00:35:17,760
+number and rational number is irrational بس
+
+379
+00:35:17,760 --> 00:35:19,180
+المهم إيش الأولة و إيش التانية
+
+380
+00:35:30,010 --> 00:35:35,910
+بقول لك اثبت بالتناقض use proof by contradiction
+
+381
+00:35:35,910 --> 00:35:40,230
+to prove that عشان تثبت the sum of an irrational
+
+382
+00:35:40,230 --> 00:35:45,470
+number and rational number is irrational سؤال تسعة
+
+383
+00:35:45,470 --> 00:35:48,830
+اللي هو انا حاولت اكتبه بالخطة اللي مافيش فوق هذا
+
+384
+00:35:48,830 --> 00:35:58,110
+تمام الان عشان تحله بدك تعمله if then بي و كيو if
+
+385
+00:35:58,110 --> 00:35:59,810
+then if b then q
+
+386
+00:36:05,350 --> 00:36:19,650
+ال M is rational and ال M is irrational then ال M
+
+387
+00:36:19,650 --> 00:36:25,790
+زائد ال N is irrational
+
+388
+00:36:25,790 --> 00:36:31,070
+لأ
+
+389
+00:36:31,070 --> 00:36:37,210
+هو جايب يقولك شوفها مرة تانيةthe sum of an
+
+390
+00:36:37,210 --> 00:36:41,370
+irrational number and a rational number يعني واحد
+
+391
+00:36:41,370 --> 00:36:45,850
+rational واحد irrational اثبت انه حاصل جمعه
+
+392
+00:36:45,850 --> 00:36:53,350
+irrational irrational number طبعا كونه محدد لك
+
+393
+00:36:53,350 --> 00:37:01,190
+فانت مش هتتعب بالفرضية طيب الآن assume
+
+394
+00:37:06,570 --> 00:37:18,570
+B and not Q ايش يعني B؟ B M is rational و
+
+395
+00:37:18,570 --> 00:37:25,830
+هذا بيقدّي ان ال M equal A على B مصبوط A و B تنتمي
+
+396
+00:37:25,830 --> 00:37:30,470
+الى Z and ال B لا تسوى صفر هي تعريف ال rational
+
+397
+00:37:30,470 --> 00:37:34,110
+number M is rational تمام
+
+398
+00:37:35,610 --> 00:37:41,550
+الـ M is irrational و
+
+399
+00:37:41,550 --> 00:37:49,330
+لا Q و M زائد الـ N is rational
+
+400
+00:37:49,330 --> 00:37:56,830
+ايش يعني؟ برضه يُكتب على الصورة الفرضية
+
+401
+00:37:56,830 --> 00:38:01,850
+تبعتاش في الـ contradiction لا Q فالـ M زائد الـ N
+
+402
+00:38:05,110 --> 00:38:15,010
+يساوي X على Y X و Y تنتمي إلى Z و Y لا تساوي صفر و
+
+403
+00:38:15,010 --> 00:38:19,450
+حتى لو احنا ما كتبناهاش تمام الاصل تيجي لأنه خلاص
+
+404
+00:38:19,450 --> 00:38:23,790
+من تعريف rational تمام الخطوة اللي بعد هيك شو
+
+405
+00:38:23,790 --> 00:38:32,430
+بنسوي يا شباب؟ بدي اجمع ال M زائد ال N M زائد ال N
+
+406
+00:38:32,430 --> 00:38:44,200
+يساويA على B زائد ال N صح؟ يساوي X
+
+407
+00:38:44,200 --> 00:38:57,240
+على Y صح؟ بظهر؟ كمان هذا يؤدي ان ال N تساوي X على
+
+408
+00:38:57,240 --> 00:39:00,280
+Y لاقص A على B
+
+409
+00:39:06,700 --> 00:39:19,060
+يساوي واحد المقامات Y في B هتساوي B في X ناقص
+
+410
+00:39:19,060 --> 00:39:28,860
+Y في A أنا بقول هذا is rational ولا لا يا شباب؟
+
+411
+00:39:28,860 --> 00:39:38,880
+ليش rational؟ ليش rational؟ لأنهBX Integer YA
+
+412
+00:39:38,880 --> 00:39:44,220
+Integer حاصل ضرحهم Integer YB Integer و لا يساوي
+
+413
+00:39:44,220 --> 00:39:47,820
+صفر لأن ال Y لا تساوي صفر و ال B لا تساوي صفر يعني
+
+414
+00:39:47,820 --> 00:39:56,180
+أن ال N is rational وهذا Contradiction تناقض
+
+415
+00:39:56,180 --> 00:40:01,480
+لماذا؟ لأن أنا أعرف أن ال N is irrational لأن أعرف
+
+416
+00:40:01,480 --> 00:40:07,280
+أن ال N is irrationalوخلصنا معناته بنقدر نقول حاصل
+
+417
+00:40:07,280 --> 00:40:12,820
+جمع عدد rational عدد نسبي مع عدد غير نسبي بالكون
+
+418
+00:40:12,820 --> 00:40:13,600
+غير نسبي
+
+419
+00:40:41,300 --> 00:40:46,760
+في الـ 11 بقول لك prove or disprove اثبت او جيب
+
+420
+00:40:46,760 --> 00:40:51,000
+مثال او انفي طبعا لما تنفي تجيب مثال بيقول ان
+
+421
+00:40:51,000 --> 00:40:54,140
+الكلام هذا غير صحيح بيقول ان الكلام هذا غير صالح
+
+422
+00:40:54,140 --> 00:40:59,380
+اللي هو بتسميه counter example prove or disprove
+
+423
+00:40:59,380 --> 00:41:03,540
+that the product of two irrational numbers is
+
+424
+00:41:03,540 --> 00:41:08,340
+irrational حاصل ضرب اي عدد اي عددين غير نسبيين
+
+425
+00:41:08,340 --> 00:41:10,540
+بتديني عدد غير نسبي
+
+426
+00:41:15,930 --> 00:41:19,210
+بال contrapositive يعني انت بتقول ان الاهل الكلام
+
+427
+00:41:19,210 --> 00:41:23,870
+صحيح و بده اثبات بتقول
+
+428
+00:41:23,870 --> 00:41:31,110
+ان الكلام هذا صحيح و بده اثبات حاصل ضرب اي عددين
+
+429
+00:41:31,110 --> 00:41:37,450
+غير نسبيين بديني عدد غير نسبي بتعرفوا العدد الغير
+
+430
+00:41:37,450 --> 00:41:42,610
+نسبية انتوا؟ بتعرف ال by؟ بتعرف جذر التنين؟ هذه
+
+431
+00:41:42,610 --> 00:41:48,650
+عدد غير نسبيةأيوة هذا الكلام غير صحيح لو جربنا جذر
+
+432
+00:41:48,650 --> 00:41:54,150
+التنين في جذر التنين عدد نسبي في عدد غير نسبي في
+
+433
+00:41:54,150 --> 00:41:58,650
+عدد غير نسبي بيطلع تنين و التنين عدد نسبي طيب في
+
+434
+00:41:58,650 --> 00:42:02,470
+12 اما
+
+435
+00:42:02,470 --> 00:42:04,470
+هو انت الان روحت فانت جيها ال disapprove ال
+
+436
+00:42:04,470 --> 00:42:08,090
+disapprove بتقولهذا الكلام غير صحيح وهي counter
+
+437
+00:42:08,090 --> 00:42:13,110
+example جذر التنين يساوي 2 والتنين is rational
+
+438
+00:42:13,110 --> 00:42:17,870
+خلصنا في المسألة في التماعيش ماذا قاعد يقول؟ proof
+
+439
+00:42:17,870 --> 00:42:23,890
+or disproof the product of non rational number
+
+440
+00:42:23,890 --> 00:42:32,430
+يعني كل الإعداد المسبية معادل الصفرلو أخدت عدد
+
+441
+00:42:32,430 --> 00:42:36,010
+نسبي غير الصفر و ضربته في irrational بتديني
+
+442
+00:42:36,010 --> 00:42:41,270
+irrational number هذه true و بدها إثبات تمام؟ هذه
+
+443
+00:42:41,270 --> 00:42:45,230
+true و بدها إثبات ليش بدها إثبات؟ ليش true؟ لأن لو
+
+444
+00:42:45,230 --> 00:42:49,650
+ضربت اتنين في جزر التنين، اتنين جزر التنين عدد غير
+
+445
+00:42:49,650 --> 00:42:54,550
+نسبيمصبوط؟ نص في جذر التنين .. جذر التنين على
+
+446
+00:42:54,550 --> 00:42:58,930
+اتنين برضه عدد غير نسبي و هكذا لأن شرط المقام
+
+447
+00:42:58,930 --> 00:43:01,590
+البسط و المقام يجب يكون يتملوا لمين؟ للأعداد
+
+448
+00:43:01,590 --> 00:43:05,810
+الصحيحة .. و بالتالي هذه بدها إثبات .. إيش استخدام
+
+449
+00:43:05,810 --> 00:43:09,710
+معاها؟ Contrapositive ولا Contradiction ولا
+
+450
+00:43:09,710 --> 00:43:13,170
+Direct؟ فكر فيها زي ما بدك .. احنا أيها؟ اختح
+
+451
+00:43:13,170 --> 00:43:19,140
+لناها هان .. في تسعة .. احنا جمعناهم هان ..بس في
+
+452
+00:43:19,140 --> 00:43:22,240
+السؤال ده عمالش بيقول إيه؟ the product حاصل ضربهم
+
+453
+00:43:22,240 --> 00:43:26,760
+و من هنا بتفهم إيش حطلّك non-zero عشان لما بيبقى
+
+454
+00:43:26,760 --> 00:43:38,520
+تروح تجلب ماطلعش المكان صفر معاك طيب في 16
+
+455
+00:43:38,520 --> 00:43:45,060
+prove that if M and N are integers و حاصل ضربهم is
+
+456
+00:43:45,060 --> 00:43:45,440
+even
+
+457
+00:43:48,430 --> 00:43:55,590
+معناته واحد منهم is even شو رأيك هو؟ انا بقولك لو
+
+458
+00:43:55,590 --> 00:44:01,410
+أخدنا اي عددين صحيحين وضربناهم في بعض وطلع الناتج
+
+459
+00:44:01,410 --> 00:44:07,150
+عدد زوجي فهذا يعني ان واحد منهم على الأقل هيكون
+
+460
+00:44:07,150 --> 00:44:12,510
+عدد زوجي true true يعني انك تثبتها يا باشا true
+
+461
+00:44:12,510 --> 00:44:17,700
+يعني انك تثبت تتجدم بثبات رياضيلأن انا بقولك both
+
+462
+00:44:17,700 --> 00:44:24,720
+الان كمان مرة اش و بقولك ستاش if ال M في N is even
+
+463
+00:44:24,720 --> 00:44:36,940
+then ال N ال M is even or ال N is even او لو كانوا
+
+464
+00:44:36,940 --> 00:44:43,880
+اتنين صح هاي ال F و ال then contradiction ولا
+
+465
+00:44:43,880 --> 00:44:45,520
+contrapositive ولا direct
+
+466
+00:44:48,500 --> 00:44:51,920
+الـ Direct والعمرها بتجيب معاك نتيجة
+
+467
+00:44:51,920 --> 00:44:55,680
+Contrapositive او Contradiction هدول اللي ممكن
+
+468
+00:44:55,680 --> 00:45:00,880
+يجيبوا معاك ليش يا شباب لأن هنا M و N is even يعني
+
+469
+00:45:00,880 --> 00:45:11,340
+كتيرك هتقول ليه M N equal 2K M بدها تساوي 2K على N
+
+470
+00:45:11,340 --> 00:45:18,950
+ولو قمتلي هيك ماحدش بضمن ان هذا ينتمي الى Zفي حد
+
+471
+00:45:18,950 --> 00:45:24,450
+يفتيلنا فيه هذا؟ لأ ممتاز integer على integer مش
+
+472
+00:45:24,450 --> 00:45:29,530
+ضروري يكون integer اتنين على اربعة تلاتة على اتنين
+
+473
+00:45:29,530 --> 00:45:33,030
+مش ضروري يكون integer وبالتالي اذا هذه مش هذه مش
+
+474
+00:45:33,030 --> 00:45:37,230
+مضمونة بالتالي ال direct proof لقد مسكرة
+
+475
+00:45:37,230 --> 00:45:46,130
+contrapositive بتصير و contradiction بتصير تمام؟
+
+476
+00:45:46,130 --> 00:45:54,220
+بتروح تقولها assumeنطق U يعني ال M is odd and ال M
+
+477
+00:45:54,220 --> 00:45:57,740
+is odd اتنين K زائد واحد اتنين H زائد واحد و
+
+478
+00:45:57,740 --> 00:46:06,560
+تضربهم في بعض هتقل معاك ايه .. خطأ هتقل معاك odd
+
+479
+00:46:06,560 --> 00:46:14,060
+الأصل اتنين K اتنين K زائد واحد في اتنين H زائد
+
+480
+00:46:14,060 --> 00:46:25,220
+واحد2K اربع KH زائد 2K زائد 2H زائد واحد هلخد هدول
+
+481
+00:46:25,220 --> 00:46:32,820
+عامل مشترك التنين 2 في 2KH زائد K زائد H زائد واحد
+
+482
+00:46:32,820 --> 00:46:39,480
+هذا odd Contrapositive ولو افترضت انت B and not Q
+
+483
+00:46:39,480 --> 00:46:47,050
+في ال contradiction B is evenو نقطة Q هيها مظبوط
+
+484
+00:46:47,050 --> 00:46:51,710
+يعني هدولة odd هتحل نفس الحل هذا و في الآخر هتقول
+
+485
+00:46:51,710 --> 00:46:55,810
+إنه هذا بتناقض أو contradiction لأ بس في الحالة
+
+486
+00:46:55,810 --> 00:46:59,790
+هذه إحنا لما قولنا assume نقطة Q مفروض نقول هنا
+
+487
+00:46:59,790 --> 00:47:04,650
+Contra positive ليش؟
+
+488
+00:47:04,650 --> 00:47:09,290
+اللي هي بين جسين نقطة ال B نقطة ال B نقطة Q وصلتني
+
+489
+00:47:09,290 --> 00:47:12,150
+لنقطة ال B 17
+
+490
+00:47:14,660 --> 00:47:19,180
+إذا الـ N هو إنتجار N is an integer بس بقولك الـ N
+
+491
+00:47:19,180 --> 00:47:25,320
+is integer حتى الآن and ال
+
+492
+00:47:25,320 --> 00:47:30,780
+N زائد خمسة is odd وكأنه بقولك if ال N تكعيب زائد
+
+493
+00:47:30,780 --> 00:47:39,020
+الخمسة is odd then ال N is even جاهزة جاهزة يعني
+
+494
+00:47:39,020 --> 00:47:48,540
+قاعد أبديكيها if N تكعيب زائد خمسةis odd than and
+
+495
+00:47:48,540 --> 00:47:54,760
+is even و بيقولك اما بتثبتها بال contrapositive او
+
+496
+00:47:54,760 --> 00:47:58,760
+بالcontradiction ايوة
+
+497
+00:47:58,760 --> 00:48:02,760
+انا بدي اختار انا اختار الواحدة عشان احلها بواحدة
+
+498
+00:48:02,760 --> 00:48:04,600
+و التانية عليك خلاص مابديهاش كلام يعني
+
+499
+00:48:04,600 --> 00:48:08,440
+contradiction or contraposition position positive
+
+500
+00:48:08,440 --> 00:48:13,370
+مش فارقة كتير دي لبالك في المصطلح يعني اه شبابأنا
+
+501
+00:48:13,370 --> 00:48:24,530
+هحل واحدة بس مش هحل التنتين والله
+
+502
+00:48:24,530 --> 00:48:27,550
+التنتين ميفرجوا معاك ولا حاجة في الآخر بس لإن في
+
+503
+00:48:27,550 --> 00:48:32,610
+كل الأحوال انت بدك تفرض B ونبت Q صح؟ بس هذي تصير
+
+504
+00:48:32,610 --> 00:48:40,510
+نبت Q بدون ال B وحتين مش هيتصل عكسها طيب assume B
+
+505
+00:48:40,510 --> 00:48:41,530
+and
+
+506
+00:48:50,640 --> 00:49:00,740
+not even is not
+
+507
+00:49:00,740 --> 00:49:04,960
+even
+
+508
+00:49:04,960 --> 00:49:05,560
+يعني odd
+
+509
+00:49:12,280 --> 00:49:16,640
+يعني بين جثين odd الخطوة اللي بعد هيك مناته n
+
+510
+00:49:16,640 --> 00:49:30,300
+تساوي 2k زائد 1 و ال k تنتمي إلى z طيب بدك
+
+511
+00:49:30,300 --> 00:49:34,500
+اتعود غير في المسألة اللي فوق هذا يؤدي ان ال n
+
+512
+00:49:34,500 --> 00:49:45,010
+تكعيب زائد 5 تساوي2K زائد واحد لكل تكييب زائد خمسة
+
+513
+00:49:45,010 --> 00:49:53,690
+وهذه تساوي 2K زائد واحد مضروبة فيه 4K تربيع زائد
+
+514
+00:49:53,690 --> 00:50:02,810
+4K زائد واحد صح؟ ليش عكس الإشارة؟ طب ما الإشارة
+
+515
+00:50:02,810 --> 00:50:07,990
+عندي موجة بفوق زائد صح؟
+
+516
+00:50:08,360 --> 00:50:12,540
+أنت في السالب تحكز الإشارة وبعدين أنا روحت معاك
+
+517
+00:50:12,540 --> 00:50:20,600
+على شغل أسهل حتى لو كانت 2k-1 تكعيب عشان ما
+
+518
+00:50:20,600 --> 00:50:25,320
+اتخرطتش في الإشارة أنا ايش افترضتها هي عبارة عن 2k
+
+519
+00:50:25,320 --> 00:50:31,800
+-1 في 2k-1 تربيع حالة المربع حدا لحاله تربيع الأول
+
+520
+00:50:31,800 --> 00:50:34,860
+الأول
+
+521
+00:50:34,860 --> 00:50:39,210
+في التربيع التانيواحد زي الأول في التاني في اتنين
+
+522
+00:50:39,210 --> 00:50:44,850
+ماقص اربع K زائد واحد وروحت بدربهم في بعض بالشكل
+
+523
+00:50:44,850 --> 00:50:49,390
+هذا فانا روحت لك على شغل أسهل ما أنا كنتاش لأنه
+
+524
+00:50:49,390 --> 00:50:53,570
+متوقع ومتأكد انه حصلوا فيه خربطة في الموضوع حل
+
+525
+00:50:53,570 --> 00:50:59,890
+التكعيب خصوصا لما تكون الإشارات زي بعضها تساوي
+
+526
+00:50:59,890 --> 00:51:07,350
+تمانية K التكعيب زائدزائد الخمسة أنا ماعش الحل بس
+
+527
+00:51:07,350 --> 00:51:13,150
+برا عملت الضرب زائد تمانية ك تربيع زائد اتنين ك
+
+528
+00:51:13,150 --> 00:51:19,850
+زائد اربعة ك تربيع زائد اربعة ك زائد واحد زائد
+
+529
+00:51:19,850 --> 00:51:30,890
+خمسة وهذه تساوي تمانية ك تكعيب زائد
+
+530
+00:51:30,890 --> 00:51:35,960
+تربيع هي تمانية وانا اربعة اتماشىمعشر ك تربيع زائد
+
+531
+00:51:35,960 --> 00:51:43,100
+ستة ك زائد ستة خد التانين على المشترك تصير اتنين
+
+532
+00:51:43,100 --> 00:51:48,560
+مضغوبة في اربعة ك تربيع تكعيب زائد ستة ك تربيع
+
+533
+00:51:48,560 --> 00:51:56,320
+زائد تلاتة ك زائد تلاتة اتنين في انتجار even
+
+534
+00:51:56,320 --> 00:52:02,080
+معناته احنا حصلنا على contradictionلأن المفروض هذي
+
+535
+00:52:02,080 --> 00:52:08,580
+تكون إيش؟ Odd طب في الـ Contrapositive هروح أنا
+
+536
+00:52:08,580 --> 00:52:13,340
+أقول له assume not Q هيا و همشي معاها هيك أصلا مين
+
+537
+00:52:13,340 --> 00:52:18,160
+أن هذي عبارة عن even و هي not ال B وبالتالي حصلت
+
+538
+00:52:18,160 --> 00:52:22,160
+على Contrapositive تمام الأمور يا شباب؟ اعتقد ..
+
+539
+00:52:22,160 --> 00:52:27,540
+اعتقد بعد هيك .. احنا بدلنا جهد كويس أنا وجد داعمك
+
+540
+00:52:27,540 --> 00:52:31,530
+في الأمثلة و مع الأسئلةالمفروض ان ترجع على الأسئلة
+
+541
+00:52:31,530 --> 00:52:35,530
+هذه سواء حلتها او ماحلتهاش و تبدأ تحلها عندك عليش
+
+542
+00:52:35,530 --> 00:52:39,390
+على ورقة لان هذه مفتاح حل اي سؤال لاحقا ان شاء
+
+543
+00:52:39,390 --> 00:52:42,010
+الله تبارك وتعالى ماشي الحال يا شباب؟ فى حد عنده
+
+544
+00:52:42,010 --> 00:52:44,390
+اي سؤال في محاضرتنا الجاية هنتكلم عن ال
+
+545
+00:52:44,390 --> 00:52:47,750
+mathematical induction هنشرح ال concept ونروح على
+
+546
+00:52:47,750 --> 00:52:50,470
+ال section ونشوف الأسئلة اللى موجودة عليه ونختارنا
+
+547
+00:52:50,470 --> 00:52:54,990
+كام سؤال زى كده ونحلهم ونكون خلصنا الجزئيةاللي
+
+548
+00:52:54,990 --> 00:52:57,430
+احنا حكيناها من البداية اللي هي البعض
+
+549
+00:52:57,430 --> 00:53:00,370
+الاستراتيجيات انك تحاول تجسم ال set اللي موجودة
+
+550
+00:53:00,370 --> 00:53:05,870
+عندك لما بيقولك أن تربيع أكبر من صفر أو أكبر من أن
+
+551
+00:53:05,870 --> 00:53:10,870
+لكل الأعداد الموجبة أو لكل الأعداد الصحيحة او لكل
+
+552
+00:53:10,870 --> 00:53:15,290
+الأعداد الموجبة او لكل الأعداد الصحيحة او لكل
+
+553
+00:53:15,290 --> 00:53:17,890
+الأعداد الصحيحة او لكل الأعداد الموجبة او لكل
+
+554
+00:53:17,890 --> 00:53:18,310
+الأعداد الصحيحة او لكل الأعداد الصحيحة او لكل
+
+555
+00:53:18,310 --> 00:53:18,390
+الأعداد الصحيحة او لكل الأعداد الصحيحة او لكل
+
+556
+00:53:18,390 --> 00:53:19,930
+الأعداد الصحيحة او لكل الأعداد الصحيحة او لكل
+
+557
+00:53:19,930 --> 00:53:20,690
+الأعداد الصحيحة او لكل الأعد
+
diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/pKrZGwbVnlc_raw.json b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/pKrZGwbVnlc_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..1427cca9819cfaa28d1f16395538e9fabf119f68
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/pKrZGwbVnlc_raw.json
@@ -0,0 +1 @@
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"end": 305.28, "word": " لو", "probability": 0.97705078125}, {"start": 305.28, "end": 305.44, "word": " أنا", "probability": 0.6123046875}, {"start": 305.44, "end": 305.92, "word": " فكرت", "probability": 0.91357421875}, {"start": 305.92, "end": 306.28, "word": " أبدأ", "probability": 0.90380859375}, {"start": 306.28, "end": 306.38, "word": " في", "probability": 0.408935546875}, {"start": 306.38, "end": 306.46, "word": " ال", "probability": 0.96533203125}, {"start": 306.46, "end": 306.62, "word": " B", "probability": 0.697265625}, {"start": 306.62, "end": 306.78, "word": " في", "probability": 0.9453125}, {"start": 306.78, "end": 306.88, "word": " ال", "probability": 0.947265625}, {"start": 306.88, "end": 307.16, "word": " direct", "probability": 0.646484375}, {"start": 307.16, "end": 307.58, "word": " proof", "probability": 0.962890625}, {"start": 307.58, "end": 307.8, "word": " هذا", "probability": 0.42626953125}, {"start": 307.8, "end": 307.92, "word": " مش", "probability": 0.80078125}, {"start": 307.92, "end": 308.46, "word": " هتوصلني", "probability": 0.8548828125}, {"start": 308.46, "end": 309.04, "word": " لنتيجة", "probability": 0.969140625}, {"start": 309.04, "end": 310.5, "word": " مش", "probability": 0.9560546875}, {"start": 310.5, "end": 310.96, "word": " هتوصلني", "probability": 0.95205078125}, {"start": 310.96, "end": 311.3, "word": " لنتيجة", "probability": 0.98125}, {"start": 311.3, "end": 311.56, "word": " لأنها", "probability": 0.7469075520833334}, {"start": 311.56, "end": 311.88, "word": " complex", "probability": 0.5478515625}], "temperature": 1.0}, {"id": 12, "seek": 33283, "start": 314.37, "end": 332.83, "text": "بالتالي انا بدى احاول اشوف الاسهل لو انا بدى احولها بال contrapositive ماذا هقول if ال N is even نقطة Q ثم تلاتة N زائد اتنين is even", "tokens": [3555, 6027, 2655, 6027, 1829, 1975, 8315, 47525, 7578, 1975, 5016, 995, 12610, 1975, 8592, 38688, 2423, 32277, 3224, 1211, 45164, 1975, 8315, 47525, 7578, 1975, 5016, 12610, 11296, 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318.05, "word": " بدى", "probability": 0.837890625}, {"start": 318.05, "end": 318.61, "word": " احولها", "probability": 0.879150390625}, {"start": 318.61, "end": 318.99, "word": " بال", "probability": 0.55029296875}, {"start": 318.99, "end": 320.71, "word": " contrapositive", "probability": 0.7101898193359375}, {"start": 320.71, "end": 321.27, "word": " ماذا", "probability": 0.4590657552083333}, {"start": 321.27, "end": 321.51, "word": " هقول", "probability": 0.740478515625}, {"start": 321.51, "end": 321.93, "word": " if", "probability": 0.1953125}, {"start": 321.93, "end": 323.15, "word": " ال", "probability": 0.80419921875}, {"start": 323.15, "end": 323.43, "word": " N", "probability": 0.31494140625}, {"start": 323.43, "end": 323.85, "word": " is", "probability": 0.9208984375}, {"start": 323.85, "end": 324.43, "word": " even", "probability": 0.89208984375}, {"start": 324.43, "end": 327.61, "word": " نقطة", "probability": 0.69482421875}, {"start": 327.61, "end": 327.95, "word": " Q", 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في", "probability": 0.427978515625}, {"start": 395.3, "end": 395.68, "word": " اتنين", "probability": 0.9761962890625}, {"start": 395.68, "end": 395.98, "word": " K", "probability": 0.90087890625}], "temperature": 1.0}, {"id": 15, "seek": 42411, "start": 396.93, "end": 424.11, "text": "زائد اتنين تساوي ستة K زائد اتنين تساوي خد التنين عامل مشترك تلاتة K زائد واحد هذه integer وهذه العدد عبارة عن is even integer contrapositive إلى اخرها تمام؟ ابدأ مع مين؟ مع ال direct ولا مع ال contrapositive؟", "tokens": [11622, 16373, 3215, 1975, 2655, 1863, 9957, 6055, 3794, 995, 45865, 8608, 2655, 3660, 591, 30767, 16373, 3215, 1975, 2655, 1863, 9957, 6055, 3794, 995, 45865, 16490, 3215, 16712, 1863, 9957, 6225, 10943, 1211, 37893, 2655, 31747, 6055, 1211, 9307, 3660, 591, 30767, 16373, 3215, 36764, 24401, 29538, 24922, 37037, 24192, 18863, 3215, 3215, 6225, 3555, 9640, 3660, 18871, 307, 754, 24922, 660, 4007, 329, 2187, 30731, 1975, 34740, 11296, 46811, 10943, 22807, 1975, 44510, 10721, 20449, 3714, 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contrapositive هدف ال contrapositive صحيح مية في المية مافيش عليه مشكلة لأن ب contradiction ايش بدك تفترض انت؟ بدك تقول لل B is it true؟", "tokens": [2304, 19913, 3555, 2407, 9566, 22807, 13672, 1829, 39896, 11778, 1829, 39894, 2304, 12984, 1211, 1975, 2655, 8717, 9566, 2423, 363, 16490, 1211, 9381, 2423, 26890, 3224, 7649, 8032, 3215, 5172, 2423, 660, 4007, 329, 2187, 8032, 3215, 5172, 2423, 660, 4007, 329, 2187, 20328, 5016, 1829, 5016, 3714, 10632, 8978, 9673, 10632, 19446, 41185, 8592, 25894, 3224, 37893, 28820, 3660, 5296, 33456, 4724, 34937, 1975, 1829, 8592, 47525, 4117, 6055, 5172, 2655, 43042, 16472, 2655, 22807, 47525, 4117, 6055, 39648, 24976, 363, 307, 309, 2074, 22807], "avg_logprob": -0.2942116419700059, "compression_ratio": 1.553191489361702, "no_speech_prob": 2.1457672119140625e-06, "words": [{"start": 721.44, "end": 722.08, "word": "مظبوط؟", "probability": 0.7451578776041666}, {"start": 722.08, "end": 722.24, "word": " اللي", "probability": 0.642578125}, {"start": 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تساوي", "probability": 0.9591064453125}, {"start": 824.03, "end": 825.61, "word": " 4K", "probability": 0.8125}, {"start": 825.61, "end": 826.21, "word": " تربيع", "probability": 0.963623046875}, {"start": 826.21, "end": 827.15, "word": " ونتساوي", "probability": 0.7153523763020834}, {"start": 827.15, "end": 827.51, "word": " 2", "probability": 0.96875}, {"start": 827.51, "end": 828.05, "word": " في", "probability": 0.325927734375}, {"start": 828.05, "end": 828.53, "word": " 2K", "probability": 0.961669921875}, {"start": 828.53, "end": 829.09, "word": " تربيع", "probability": 0.980712890625}, {"start": 829.09, "end": 830.19, "word": " صح", "probability": 0.59197998046875}, {"start": 830.19, "end": 831.25, "word": " even", "probability": 0.3857421875}, {"start": 831.25, "end": 833.65, "word": " وها", "probability": 0.5201416015625}, {"start": 833.65, "end": 833.91, "word": " دي", "probability": 0.8681640625}, {"start": 833.91, "end": 834.91, "word": " even", "probability": 0.92919921875}, {"start": 834.91, "end": 835.41, "word": " integer", "probability": 0.479248046875}, {"start": 835.41, "end": 838.47, "word": " not", "probability": 0.57763671875}, {"start": 838.47, "end": 838.81, "word": " odd", "probability": 0.87451171875}, {"start": 838.81, "end": 840.99, "word": " contradiction", "probability": 0.92529296875}], "temperature": 1.0}, {"id": 32, "seek": 87608, "start": 847.02, "end": 876.08, "text": "with ترقض معميل مع الفرضية and تربيع is odd خلصنا البرهان إيش يعني؟ يعني لما بتكون ال and تربيع is odd ال and is odd وهذا هو الإثبات بالترقض إنك أنت بتفرض حالتين و بتشتغل مع أي واحدة فيهم مش مشكلة عندك معميل بلام أنك حققتهم في الفرضيات يعني بتقدر تعتمد عليهم زي ما بدك", "tokens": [11820, 6055, 2288, 4587, 11242, 20449, 2304, 26895, 20449, 27188, 43042, 10632, 293, 6055, 2288, 21292, 3615, 307, 7401, 16490, 1211, 9381, 8315, 2423, 26890, 3224, 7649, 11933, 1829, 8592, 37495, 22653, 22807, 37495, 22653, 5296, 15042, 39894, 30544, 2423, 293, 6055, 2288, 21292, 3615, 307, 7401, 2423, 293, 307, 7401, 37037, 15730, 31439, 33688, 12984, 3555, 9307, 20666, 2655, 2288, 4587, 11242, 36145, 4117, 14739, 2655, 39894, 5172, 43042, 11331, 6027, 2655, 9957, 4032, 39894, 8592, 2655, 17082, 1211, 20449, 36632, 36764, 24401, 3660, 8978, 16095, 37893, 37893, 28820, 3660, 43242, 4117, 20449, 2304, 26895, 4724, 1211, 10943, 14739, 4117, 11331, 4587, 38149, 16095, 8978, 27188, 43042, 1829, 9307, 37495, 22653, 39894, 28543, 2288, 6055, 34268, 2304, 3215, 25894, 16095, 30767, 1829, 19446, 47525, 4117], "avg_logprob": -0.18061024208707133, "compression_ratio": 1.853061224489796, "no_speech_prob": 2.980232238769531e-07, "words": [{"start": 847.02, "end": 847.5, "word": "with", "probability": 0.1611328125}, {"start": 847.5, "end": 848.54, "word": " ترقض", "probability": 0.6314697265625}, {"start": 848.54, "end": 849.0, "word": " معميل", "probability": 0.9104817708333334}, {"start": 849.0, "end": 849.54, "word": " مع", "probability": 0.80029296875}, {"start": 849.54, "end": 850.22, "word": " الفرضية", "probability": 0.9773763020833334}, {"start": 850.22, "end": 850.44, "word": " and", "probability": 0.54345703125}, {"start": 850.44, "end": 850.78, "word": " تربيع", "probability": 0.83203125}, {"start": 850.78, "end": 850.92, "word": " is", "probability": 0.430908203125}, {"start": 850.92, "end": 851.26, "word": " odd", "probability": 0.87890625}, {"start": 851.26, "end": 854.96, "word": " خلصنا", "probability": 0.791015625}, {"start": 854.96, "end": 855.4, "word": " البرهان", "probability": 0.8504638671875}, {"start": 855.4, "end": 856.26, "word": " إيش", "probability": 0.66827392578125}, {"start": 856.26, "end": 856.76, "word": " يعني؟", "probability": 0.8411458333333334}, {"start": 856.76, "end": 857.68, "word": " يعني", "probability": 0.880126953125}, {"start": 857.68, "end": 858.02, "word": " لما", "probability": 0.93701171875}, {"start": 858.02, "end": 858.46, "word": " بتكون", "probability": 0.920166015625}, {"start": 858.46, "end": 858.6, "word": " ال", "probability": 0.93212890625}, {"start": 858.6, "end": 858.82, "word": " and", "probability": 0.75244140625}, {"start": 858.82, "end": 859.22, "word": " تربيع", "probability": 0.949951171875}, {"start": 859.22, "end": 859.4, "word": " is", "probability": 0.958984375}, {"start": 859.4, "end": 859.84, "word": " odd", "probability": 0.9443359375}, {"start": 859.84, "end": 862.1, "word": " ال", "probability": 0.939453125}, {"start": 862.1, "end": 862.3, "word": " and", "probability": 0.82568359375}, {"start": 862.3, "end": 862.52, "word": " is", "probability": 0.84521484375}, {"start": 862.52, "end": 862.82, "word": " odd", "probability": 0.9423828125}, {"start": 862.82, "end": 864.26, "word": " وهذا", "probability": 0.79296875}, {"start": 864.26, "end": 864.44, "word": " هو", "probability": 0.9921875}, {"start": 864.44, "end": 865.12, "word": " الإثبات", "probability": 0.9271240234375}, {"start": 865.12, "end": 866.4, "word": " بالترقض", "probability": 0.9548828125}, {"start": 866.4, "end": 866.92, "word": " إنك", "probability": 0.740234375}, {"start": 866.92, "end": 867.14, "word": " أنت", "probability": 0.748779296875}, {"start": 867.14, "end": 867.6, "word": " بتفرض", "probability": 0.97607421875}, {"start": 867.6, "end": 868.24, "word": " حالتين", "probability": 0.9427490234375}, {"start": 868.24, "end": 868.88, "word": " و", "probability": 0.66162109375}, {"start": 868.88, "end": 869.36, "word": " بتشتغل", "probability": 0.928515625}, {"start": 869.36, "end": 869.52, "word": " مع", "probability": 0.9921875}, {"start": 869.52, "end": 869.72, "word": " أي", "probability": 0.802734375}, {"start": 869.72, "end": 870.1, "word": " واحدة", "probability": 0.98095703125}, {"start": 870.1, "end": 870.22, "word": " فيهم", "probability": 0.69482421875}, {"start": 870.22, "end": 870.4, "word": " مش", "probability": 0.771484375}, {"start": 870.4, "end": 870.76, "word": " مشكلة", "probability": 0.9716796875}, {"start": 870.76, "end": 870.98, "word": " عندك", "probability": 0.970458984375}, {"start": 870.98, "end": 871.32, "word": " معميل", "probability": 0.9651692708333334}, {"start": 871.32, "end": 872.42, "word": " بلام", "probability": 0.5940755208333334}, {"start": 872.42, "end": 872.64, "word": " أنك", "probability": 0.74560546875}, {"start": 872.64, "end": 873.02, "word": " حققتهم", "probability": 0.7735595703125}, {"start": 873.02, "end": 873.12, "word": " في", "probability": 0.9619140625}, {"start": 873.12, "end": 873.88, "word": " الفرضيات", "probability": 0.9368896484375}, {"start": 873.88, "end": 874.34, "word": " يعني", "probability": 0.971435546875}, {"start": 874.34, "end": 874.7, "word": " بتقدر", "probability": 0.92041015625}, {"start": 874.7, "end": 875.14, "word": " تعتمد", "probability": 0.96044921875}, {"start": 875.14, "end": 875.42, "word": " عليهم", "probability": 0.95556640625}, {"start": 875.42, "end": 875.6, "word": " زي", "probability": 0.988525390625}, {"start": 875.6, "end": 875.66, "word": " ما", "probability": 0.9462890625}, {"start": 875.66, "end": 876.08, "word": " بدك", "probability": 0.9443359375}], "temperature": 1.0}, {"id": 33, "seek": 90178, "start": 876.64, "end": 901.78, "text": "وبتمشي للاتجاه التالي لحد ما تصل لأي طلاقط عشان هيك كتبنا لك هان assume P and not Q then deduce any contradiction وحاول ابحث او اوجد عن اي طلاقط موجود في المسألة اللي عندها تمام مثال؟", "tokens": [37746, 39237, 8592, 1829, 24976, 9307, 7435, 40294, 16712, 6027, 1829, 5296, 24401, 19446, 6055, 36520, 5296, 10721, 1829, 23032, 15040, 4587, 9566, 6225, 8592, 7649, 39896, 4117, 9122, 2655, 3555, 8315, 5296, 4117, 8032, 7649, 6552, 430, 293, 406, 1249, 550, 4172, 4176, 604, 34937, 4032, 5016, 995, 12610, 1975, 49628, 12984, 1975, 2407, 1975, 29245, 3215, 18871, 1975, 1829, 23032, 15040, 4587, 9566, 3714, 29245, 23328, 8978, 9673, 3794, 10721, 37977, 13672, 1829, 43242, 11296, 46811, 10943, 50113, 6027, 22807], "avg_logprob": -0.23983434417161598, "compression_ratio": 1.4477611940298507, "no_speech_prob": 0.0, "words": [{"start": 876.64, "end": 877.56, "word": "وبتمشي", "probability": 0.781982421875}, {"start": 877.56, "end": 878.24, "word": " للاتجاه", "probability": 0.8974609375}, {"start": 878.24, "end": 878.58, "word": " التالي", "probability": 0.8170572916666666}, {"start": 878.58, "end": 878.9, "word": " لحد", "probability": 0.81982421875}, {"start": 878.9, "end": 879.0, "word": " ما", "probability": 0.982421875}, {"start": 879.0, "end": 879.3, "word": " تصل", "probability": 0.969970703125}, {"start": 879.3, "end": 879.68, "word": " لأي", "probability": 0.8943684895833334}, {"start": 879.68, "end": 880.36, "word": " طلاقط", "probability": 0.663818359375}, {"start": 880.36, "end": 880.98, "word": " عشان", "probability": 0.8406575520833334}, {"start": 880.98, "end": 881.22, "word": " هيك", "probability": 0.3505859375}, {"start": 881.22, "end": 881.56, "word": " كتبنا", "probability": 0.9698486328125}, {"start": 881.56, "end": 881.78, "word": " لك", "probability": 0.6087646484375}, {"start": 881.78, "end": 882.06, "word": " هان", "probability": 0.750732421875}, {"start": 882.06, "end": 882.74, "word": " assume", "probability": 0.60986328125}, {"start": 882.74, "end": 883.04, "word": " P", "probability": 0.281494140625}, {"start": 883.04, "end": 883.26, "word": " and", "probability": 0.91064453125}, {"start": 883.26, "end": 883.5, "word": " not", "probability": 0.88330078125}, {"start": 883.5, "end": 883.9, "word": " Q", "probability": 0.9736328125}, {"start": 883.9, "end": 884.7, "word": " then", "probability": 0.5009765625}, {"start": 884.7, "end": 885.72, "word": " deduce", "probability": 0.8974609375}, {"start": 885.72, "end": 886.2, "word": " any", "probability": 0.75830078125}, {"start": 886.2, "end": 887.04, "word": " contradiction", "probability": 0.9189453125}, {"start": 887.04, "end": 887.74, "word": " وحاول", "probability": 0.8162841796875}, {"start": 887.74, "end": 888.26, "word": " ابحث", "probability": 0.7738444010416666}, {"start": 888.26, "end": 888.46, "word": " او", "probability": 0.760009765625}, {"start": 888.46, "end": 888.94, "word": " اوجد", "probability": 0.7710774739583334}, {"start": 888.94, "end": 889.28, "word": " عن", "probability": 0.55224609375}, {"start": 889.28, "end": 889.48, "word": " اي", "probability": 0.7408447265625}, {"start": 889.48, "end": 889.96, "word": " طلاقط", "probability": 0.9449462890625}, {"start": 889.96, "end": 890.4, "word": " موجود", "probability": 0.9697265625}, {"start": 890.4, "end": 890.76, "word": " في", "probability": 0.91748046875}, {"start": 890.76, "end": 891.22, "word": " المسألة", "probability": 0.972900390625}, {"start": 891.22, "end": 891.54, "word": " اللي", "probability": 0.923583984375}, {"start": 891.54, "end": 891.88, "word": " عندها", "probability": 0.84375}, {"start": 891.88, "end": 901.22, "word": " تمام", "probability": 0.783203125}, {"start": 901.22, "end": 901.78, "word": " مثال؟", "probability": 0.8899739583333334}], "temperature": 1.0}, {"id": 34, "seek": 94110, "start": 914.74, "end": 941.1, "text": "وقول لي لو كانت ال M زائد ال N أقل من 89 هذي مثلت مين؟ ال B ثم M أقل من 45 او ال N أقل من 45 ل Q و بدنا نثبتها بال contradiction نثبتها بالتراقد تثبت بالتراقد يعني assume", "tokens": [2407, 39648, 32239, 45164, 25961, 2655, 2423, 376, 30767, 16373, 3215, 2423, 426, 5551, 4587, 1211, 9154, 31877, 8032, 8848, 1829, 50113, 1211, 2655, 3714, 9957, 22807, 2423, 363, 38637, 2304, 376, 5551, 4587, 1211, 9154, 6905, 1975, 2407, 2423, 426, 5551, 4587, 1211, 9154, 6905, 5296, 1249, 4032, 47525, 8315, 8717, 12984, 3555, 2655, 11296, 20666, 34937, 8717, 12984, 3555, 2655, 11296, 20666, 2655, 23557, 28543, 6055, 12984, 3555, 2655, 20666, 2655, 23557, 28543, 37495, 22653, 6552], "avg_logprob": -0.2899525391904614, "compression_ratio": 1.6011904761904763, "no_speech_prob": 0.0, "words": [{"start": 914.74, "end": 915.06, "word": "وقول", "probability": 0.3563232421875}, {"start": 915.06, "end": 915.18, "word": " لي", "probability": 0.385009765625}, {"start": 915.18, "end": 915.3, "word": " لو", "probability": 0.58544921875}, {"start": 915.3, "end": 915.84, "word": " كانت", "probability": 0.914794921875}, {"start": 915.84, "end": 916.12, "word": " ال", "probability": 0.7158203125}, {"start": 916.12, "end": 916.36, "word": " M", "probability": 0.447021484375}, {"start": 916.36, "end": 916.82, "word": " زائد", "probability": 0.8616536458333334}, {"start": 916.82, "end": 917.0, "word": " ال", "probability": 0.587890625}, {"start": 917.0, "end": 917.26, "word": " N", "probability": 0.57958984375}, {"start": 917.26, "end": 917.74, "word": " أقل", "probability": 0.9401041666666666}, {"start": 917.74, "end": 918.06, "word": " من", "probability": 0.99169921875}, {"start": 918.06, "end": 919.44, "word": " 89", "probability": 0.8154296875}, {"start": 919.44, "end": 921.3, "word": " هذي", "probability": 0.5476888020833334}, {"start": 921.3, "end": 921.72, "word": " مثلت", "probability": 0.8028971354166666}, {"start": 921.72, "end": 922.88, "word": " مين؟", "probability": 0.724365234375}, {"start": 922.88, "end": 923.62, "word": " ال", "probability": 0.85791015625}, {"start": 923.62, "end": 923.86, "word": " B", "probability": 0.7880859375}, {"start": 923.86, "end": 924.7, "word": " ثم", "probability": 0.4903564453125}, {"start": 924.7, "end": 926.56, "word": " M", "probability": 0.52490234375}, {"start": 926.56, "end": 926.92, "word": " أقل", "probability": 0.966796875}, {"start": 926.92, "end": 927.06, "word": " من", "probability": 0.99658203125}, {"start": 927.06, "end": 927.72, "word": " 45", "probability": 0.95751953125}, {"start": 927.72, "end": 928.88, "word": " او", "probability": 0.61578369140625}, {"start": 928.88, "end": 929.08, "word": " ال", "probability": 0.90673828125}, {"start": 929.08, "end": 929.3, "word": " N", "probability": 0.9599609375}, {"start": 929.3, "end": 929.72, "word": " أقل", "probability": 0.96630859375}, {"start": 929.72, "end": 929.86, "word": " من", "probability": 0.99755859375}, 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أجيب حل و أوجد منه برهان بكل بساطة", "tokens": [2304, 45636, 995, 37495, 22653, 22807, 37495, 22653, 5296, 15042, 6055, 30544, 2423, 376, 30767, 16373, 3215, 2423, 376, 5551, 4587, 1211, 9154, 31877, 12399, 20449, 8315, 47395, 2423, 376, 8032, 2655, 30544, 5551, 4587, 1211, 9154, 6905, 12399, 34051, 37495, 22653, 36764, 24401, 3660, 9154, 16095, 8032, 2655, 30544, 5551, 4587, 1211, 9154, 6905, 12399, 8032, 47302, 33688, 12984, 3555, 9307, 20666, 2655, 8315, 4587, 11242, 12399, 8032, 2655, 5016, 3794, 36145, 3224, 6156, 3615, 15040, 14739, 16247, 29973, 20328, 9640, 8608, 3224, 1211, 4032, 3714, 43020, 41850, 5551, 7435, 1829, 3555, 11331, 1211, 4032, 5551, 29245, 3215, 9154, 3224, 4724, 2288, 3224, 7649, 4724, 28820, 4724, 3794, 41193, 3660], "avg_logprob": -0.2403738901817373, "compression_ratio": 1.855, "no_speech_prob": 8.58306884765625e-06, "words": [{"start": 1100.51, "end": 1101.11, "word": "ماذا", "probability": 0.4873860677083333}, {"start": 1101.11, "end": 1101.51, "word": " 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{"start": 1716.83, "end": 1717.13, "word": " إياها", "probability": 0.6490885416666666}, {"start": 1717.13, "end": 1717.35, "word": " هو", "probability": 0.73974609375}, {"start": 1717.35, "end": 1717.59, "word": " N", "probability": 0.65771484375}, {"start": 1717.59, "end": 1720.17, "word": " الان", "probability": 0.624267578125}, {"start": 1720.17, "end": 1722.97, "word": " احنا", "probability": 0.43603515625}, {"start": 1722.97, "end": 1723.23, "word": " هقوله", "probability": 0.53564453125}, {"start": 1723.23, "end": 1723.73, "word": " assume", "probability": 0.859375}, {"start": 1723.73, "end": 1726.97, "word": " B", "probability": 0.37939453125}, {"start": 1726.97, "end": 1727.13, "word": " is", "probability": 0.8896484375}, {"start": 1727.13, "end": 1727.55, "word": " true", "probability": 0.958984375}], "temperature": 1.0}, {"id": 65, "seek": 175941, "start": 1731.59, "end": 1759.41, "text": "هل هو ضروري الدارك تكون صح؟ ماعرفش بدي أجرب وبناء على تجربتي بعد خطوات اتنين بشوف كيف الوضع M زائد ال N is even و N زائد ال B is even هذا بيقدر ان M زائد ال N equal 2K و N زائد ال B equal 2H", "tokens": [3224, 1211, 31439, 48812, 2288, 13063, 1829, 32748, 9640, 4117, 6055, 30544, 20328, 5016, 22807, 19446, 3615, 28480, 8592, 4724, 16254, 5551, 7435, 25513, 46599, 1863, 16606, 15844, 6055, 7435, 25513, 31371, 39182, 16490, 9566, 2407, 9307, 1975, 2655, 1863, 9957, 4724, 8592, 38688, 9122, 33911, 2423, 2407, 11242, 3615, 376, 30767, 16373, 3215, 2423, 426, 307, 754, 4032, 426, 30767, 16373, 3215, 2423, 363, 307, 754, 23758, 4724, 1829, 4587, 3215, 2288, 16472, 376, 30767, 16373, 3215, 2423, 426, 2681, 568, 42, 4032, 426, 30767, 16373, 3215, 2423, 363, 2681, 568, 39], "avg_logprob": -0.2401928259654248, "compression_ratio": 1.5957446808510638, "no_speech_prob": 0.0, "words": [{"start": 1731.59, "end": 1731.85, "word": "هل", "probability": 0.949462890625}, {"start": 1731.85, "end": 1732.01, "word": " هو", "probability": 0.41015625}, {"start": 1732.01, "end": 1732.47, 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" equal", "probability": 0.25048828125}, {"start": 1753.33, "end": 1754.09, "word": " 2K", "probability": 0.75732421875}, {"start": 1754.09, "end": 1755.59, "word": " و", "probability": 0.94580078125}, {"start": 1755.59, "end": 1755.91, "word": " N", "probability": 0.7802734375}, {"start": 1755.91, "end": 1756.47, "word": " زائد", "probability": 0.9518229166666666}, {"start": 1756.47, "end": 1756.67, "word": " ال", "probability": 0.9462890625}, {"start": 1756.67, "end": 1756.99, "word": " B", "probability": 0.974609375}, {"start": 1756.99, "end": 1757.77, "word": " equal", "probability": 0.87841796875}, {"start": 1757.77, "end": 1759.41, "word": " 2H", "probability": 0.819091796875}], "temperature": 1.0}, {"id": 66, "seek": 177228, "start": 1760.16, "end": 1772.28, "text": "for some K تنتمي إلى Z و for some H تنتمي إلى Z for some K و H integers تمام؟ بس هو في الطرف التاني إيش مستخدم هنا يا شباب؟", "tokens": [2994, 512, 591, 6055, 29399, 2304, 1829, 30731, 1176, 4032, 337, 512, 389, 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{"start": 2514.07, "end": 2514.15, "word": " في", "probability": 0.802734375}, {"start": 2514.15, "end": 2514.29, "word": " عدد", "probability": 0.9930013020833334}, {"start": 2514.29, "end": 2514.45, "word": " غير", "probability": 0.99658203125}, {"start": 2514.45, "end": 2514.73, "word": " نسبي", "probability": 0.9912109375}, {"start": 2514.73, "end": 2515.01, "word": " بيطلع", "probability": 0.7681640625}, {"start": 2515.01, "end": 2515.41, "word": " تنين", "probability": 0.86083984375}, {"start": 2515.41, "end": 2515.67, "word": " و", "probability": 0.50390625}, {"start": 2515.67, "end": 2516.01, "word": " التنين", "probability": 0.7379557291666666}, {"start": 2516.01, "end": 2516.51, "word": " عدد", "probability": 0.9905598958333334}, {"start": 2516.51, "end": 2517.97, "word": " نسبي", "probability": 0.9659830729166666}, {"start": 2517.97, "end": 2518.45, "word": " طيب", "probability": 0.8185221354166666}, {"start": 2518.45, "end": 2518.65, "word": " في", "probability": 0.55029296875}, {"start": 2518.65, "end": 2519.15, "word": " 12", "probability": 0.364501953125}, {"start": 2519.15, "end": 2522.47, "word": " اما", "probability": 0.6536865234375}, {"start": 2522.47, "end": 2522.63, "word": " هو", "probability": 0.857421875}, {"start": 2522.63, "end": 2522.77, "word": " انت", "probability": 0.875732421875}, {"start": 2522.77, "end": 2522.91, "word": " الان", "probability": 0.57159423828125}, {"start": 2522.91, "end": 2523.11, "word": " روحت", "probability": 0.760986328125}, {"start": 2523.11, "end": 2523.27, "word": " فانت", "probability": 0.57958984375}, {"start": 2523.27, "end": 2523.41, "word": " جيها", "probability": 0.6852213541666666}, {"start": 2523.41, "end": 2523.51, "word": " ال", "probability": 0.90966796875}, {"start": 2523.51, "end": 2524.09, "word": " disapprove", "probability": 0.62060546875}, {"start": 2524.09, "end": 2524.47, "word": " ال", "probability": 0.791015625}, {"start": 2524.47, "end": 2524.97, "word": " disapprove", "probability": 0.880126953125}, {"start": 2524.97, "end": 2525.41, "word": " بتقول", "probability": 0.9560546875}], "temperature": 1.0}, {"id": 92, "seek": 254723, "start": 2526.19, "end": 2547.23, "text": "هذا الكلام غير صحيح وهي counter example جذر التنين يساوي 2 والتنين is rational خلصنا في المسألة في التماعيش ماذا قاعد يقول؟ proof or disproof the product of non rational number يعني كل الإعداد المسبية معادل الصفر", "tokens": [3224, 15730, 2423, 28820, 10943, 32771, 13546, 20328, 5016, 1829, 5016, 37037, 1829, 5682, 1365, 10874, 8848, 2288, 16712, 1863, 9957, 7251, 3794, 995, 45865, 568, 16070, 2655, 1863, 9957, 307, 15090, 16490, 1211, 9381, 8315, 8978, 9673, 3794, 10721, 37977, 8978, 16712, 15042, 3615, 1829, 8592, 3714, 45636, 995, 12174, 995, 22488, 7251, 39648, 22807, 8177, 420, 717, 15690, 264, 1674, 295, 2107, 15090, 1230, 37495, 22653, 28242, 33688, 22488, 18513, 9673, 35457, 10632, 20449, 18513, 1211, 31767, 5172, 2288], "avg_logprob": -0.3729039637780771, 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0.482177734375}, {"start": 2531.95, "end": 2532.63, "word": " والتنين", "probability": 0.8134765625}, {"start": 2532.63, "end": 2532.79, "word": " is", "probability": 0.6220703125}, {"start": 2532.79, "end": 2533.11, "word": " rational", "probability": 0.91455078125}, {"start": 2533.11, "end": 2534.45, "word": " خلصنا", "probability": 0.7136077880859375}, {"start": 2534.45, "end": 2534.55, "word": " في", "probability": 0.7861328125}, {"start": 2534.55, "end": 2535.01, "word": " المسألة", "probability": 0.9639892578125}, {"start": 2535.01, "end": 2536.03, "word": " في", "probability": 0.380615234375}, {"start": 2536.03, "end": 2536.55, "word": " التماعيش", "probability": 0.58662109375}, {"start": 2536.55, "end": 2536.63, "word": " ماذا", "probability": 0.6895345052083334}, {"start": 2536.63, "end": 2536.81, "word": " قاعد", "probability": 0.4945475260416667}, {"start": 2536.81, "end": 2537.55, "word": " يقول؟", "probability": 0.6849772135416666}, {"start": 2537.55, "end": 2537.87, "word": " proof", "probability": 0.315673828125}, {"start": 2537.87, "end": 2538.09, "word": " or", "probability": 0.8916015625}, {"start": 2538.09, "end": 2538.73, "word": " disproof", "probability": 0.616455078125}, {"start": 2538.73, "end": 2539.83, "word": " the", "probability": 0.58984375}, {"start": 2539.83, "end": 2540.25, "word": " product", "probability": 0.9326171875}, {"start": 2540.25, "end": 2540.51, "word": " of", "probability": 0.9736328125}, {"start": 2540.51, "end": 2541.11, "word": " non", "probability": 0.83740234375}, {"start": 2541.11, "end": 2541.79, "word": " rational", "probability": 0.62939453125}, {"start": 2541.79, "end": 2543.89, "word": " number", "probability": 0.89453125}, {"start": 2543.89, "end": 2545.43, "word": " يعني", "probability": 0.65478515625}, {"start": 2545.43, "end": 2545.65, "word": " كل", "probability": 0.912109375}, {"start": 2545.65, "end": 2546.07, "word": " الإعداد", "probability": 0.9573567708333334}, {"start": 2546.07, "end": 2546.47, "word": " المسبية", "probability": 0.7274576822916666}, {"start": 2546.47, "end": 2546.81, "word": " معادل", "probability": 0.6376139322916666}, {"start": 2546.81, "end": 2547.23, "word": " الصفر", "probability": 0.8031412760416666}], "temperature": 1.0}, {"id": 93, "seek": 257003, "start": 2549.15, "end": 2570.03, "text": "لو أخدت عدد نسبي غير الصفر و ضربته في irrational بتديني irrational number هذه true و بدها إثبات تمام؟ هذه true و بدها إثبات ليش بدها إثبات؟ ليش true؟ لأن لو ضربت اتنين في جزر التنين، اتنين جزر التنين عدد غير نسبي", "tokens": [1211, 2407, 5551, 9778, 3215, 2655, 6225, 3215, 3215, 8717, 35457, 1829, 32771, 13546, 31767, 5172, 2288, 4032, 48812, 25513, 47395, 8978, 39914, 39894, 3215, 9957, 1829, 39914, 1230, 29538, 2074, 4032, 47525, 11296, 11933, 12984, 3555, 9307, 46811, 10943, 22807, 29538, 2074, 4032, 47525, 11296, 11933, 12984, 3555, 9307, 32239, 8592, 47525, 11296, 11933, 12984, 3555, 9307, 22807, 32239, 8592, 2074, 22807, 5296, 33456, 45164, 48812, 25513, 2655, 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هكذا لأن شرط المقام البسط و المقام يجب يكون يتملوا لمين؟ للأعداد الصحيحة .. و بالتالي هذه بدها إثبات .. إيش استخدام معاها؟ Contrapositive ولا Contradiction ولا Direct؟ فكر فيها زي ما بدك .. احنا أيها؟ اختح لناها هان .. في تسعة .. احنا جمعناهم هان ..", "tokens": [2304, 9381, 3555, 2407, 9566, 22807, 8717, 9381, 8978, 10874, 8848, 2288, 16712, 1863, 9957, 4386, 10874, 8848, 2288, 16712, 1863, 9957, 15844, 1975, 2655, 1863, 9957, 4724, 43042, 3224, 6225, 3215, 3215, 32771, 13546, 8717, 35457, 1829, 4032, 8032, 4117, 15730, 5296, 33456, 13412, 2288, 9566, 9673, 4587, 10943, 29739, 3794, 9566, 4032, 9673, 4587, 10943, 7251, 7435, 3555, 7251, 30544, 7251, 39237, 1211, 14407, 32767, 9957, 22807, 24976, 10721, 22488, 18513, 31767, 5016, 1829, 5016, 3660, 4386, 4032, 20666, 2655, 6027, 1829, 29538, 47525, 11296, 11933, 12984, 3555, 9307, 4386, 11933, 1829, 8592, 44713, 9778, 3215, 10943, 20449, 995, 11296, 22807, 4839, 4007, 329, 2187, 49429, 4839, 6206, 4105, 49429, 18308, 22807, 6156, 37983, 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هلخد هدول عامل مشترك التنين 2 في 2KH زائد K زائد H زائد واحد هذا odd Contrapositive ولو افترضت انت B and not Q في ال contradiction B is even", "tokens": [17, 42, 1975, 25513, 3615, 34854, 30767, 16373, 3215, 568, 42, 30767, 16373, 3215, 568, 39, 30767, 16373, 3215, 36764, 24401, 8032, 1211, 9778, 3215, 8032, 3215, 12610, 6225, 10943, 1211, 37893, 2655, 31747, 16712, 1863, 9957, 568, 8978, 568, 42, 39, 30767, 16373, 3215, 591, 30767, 16373, 3215, 389, 30767, 16373, 3215, 36764, 24401, 23758, 7401, 4839, 4007, 329, 2187, 4032, 1211, 2407, 1975, 5172, 2655, 43042, 2655, 16472, 2655, 363, 293, 406, 1249, 8978, 2423, 34937, 363, 307, 754], "avg_logprob": -0.3046874858257247, "compression_ratio": 1.5207100591715976, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2775.24, "end": 2775.92, "word": "2K", "probability": 0.5419921875}, {"start": 2775.92, "end": 2777.26, "word": " اربع", "probability": 0.4386393229166667}, {"start": 2777.26, "end": 2777.76, "word": " KH", 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2", "probability": 0.254150390625}, {"start": 2787.66, "end": 2787.92, "word": " في", "probability": 0.25927734375}, {"start": 2787.92, "end": 2788.88, "word": " 2KH", "probability": 0.78759765625}, {"start": 2788.88, "end": 2789.94, "word": " زائد", "probability": 0.9383138020833334}, {"start": 2789.94, "end": 2790.36, "word": " K", "probability": 0.9345703125}, {"start": 2790.36, "end": 2791.3, "word": " زائد", "probability": 0.96337890625}, {"start": 2791.3, "end": 2791.7, "word": " H", "probability": 0.99462890625}, {"start": 2791.7, "end": 2792.5, "word": " زائد", "probability": 0.9597981770833334}, {"start": 2792.5, "end": 2792.82, "word": " واحد", "probability": 0.761962890625}, {"start": 2792.82, "end": 2793.06, "word": " هذا", "probability": 0.68505859375}, {"start": 2793.06, "end": 2793.52, "word": " odd", "probability": 0.274658203125}, {"start": 2793.52, "end": 2795.28, "word": " Contrapositive", "probability": 0.694976806640625}, {"start": 2795.28, "end": 2796.12, "word": " ولو", "probability": 0.667236328125}, {"start": 2796.12, "end": 2796.64, "word": " افترضت", "probability": 0.95927734375}, {"start": 2796.64, "end": 2798.24, "word": " انت", "probability": 0.822998046875}, {"start": 2798.24, "end": 2798.72, "word": " B", "probability": 0.3681640625}, {"start": 2798.72, "end": 2798.96, "word": " and", "probability": 0.76416015625}, {"start": 2798.96, "end": 2799.2, "word": " not", "probability": 0.81787109375}, {"start": 2799.2, "end": 2799.48, "word": " Q", "probability": 0.93994140625}, {"start": 2799.48, "end": 2799.62, "word": " في", "probability": 0.84375}, {"start": 2799.62, "end": 2799.68, "word": " ال", "probability": 0.92138671875}, {"start": 2799.68, "end": 2800.24, "word": " contradiction", "probability": 0.59130859375}, {"start": 2800.24, "end": 2802.34, "word": " B", "probability": 0.54638671875}, {"start": 2802.34, "end": 2802.6, "word": " is", "probability": 0.93310546875}, {"start": 2802.6, "end": 2802.94, "word": " even", "probability": 0.90087890625}], "temperature": 1.0}, {"id": 102, "seek": 283215, "start": 2804.71, "end": 2832.15, "text": "و نقطة Q هيها مظبوط يعني هدولة odd هتحل نفس الحل هذا و في الآخر هتقول إنه هذا بتناقض أو contradiction لأ بس في الحالة هذه إحنا لما قولنا assume نقطة Q مفروض نقول هنا Contra positive ليش؟ اللي هي بين جسين نقطة ال B نقطة ال B نقطة Q وصلتني لنقطة ال B 17", "tokens": [2407, 8717, 47432, 3660, 1249, 39896, 11296, 3714, 19913, 3555, 2407, 9566, 37495, 22653, 8032, 3215, 12610, 3660, 7401, 8032, 2655, 5016, 1211, 8717, 36178, 21542, 1211, 23758, 4032, 8978, 6024, 95, 34740, 8032, 2655, 39648, 36145, 3224, 23758, 39894, 8315, 4587, 11242, 34051, 34937, 5296, 10721, 4724, 3794, 8978, 21542, 6027, 3660, 29538, 11933, 5016, 8315, 5296, 15042, 12174, 12610, 8315, 6552, 8717, 47432, 3660, 1249, 3714, 5172, 32887, 11242, 8717, 39648, 34105, 4839, 424, 3353, 32239, 8592, 22807, 13672, 1829, 39896, 49374, 10874, 3794, 9957, 8717, 47432, 3660, 2423, 363, 8717, 47432, 3660, 2423, 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لأ", "probability": 0.77490234375}, {"start": 2814.13, "end": 2815.39, "word": " بس", "probability": 0.9453125}, {"start": 2815.39, "end": 2815.49, "word": " في", "probability": 0.955078125}, {"start": 2815.49, "end": 2815.81, "word": " الحالة", "probability": 0.9573567708333334}, {"start": 2815.81, "end": 2816.05, "word": " هذه", "probability": 0.287353515625}, {"start": 2816.05, "end": 2816.21, "word": " إحنا", "probability": 0.7933756510416666}, {"start": 2816.21, "end": 2816.37, "word": " لما", "probability": 0.927734375}, {"start": 2816.37, "end": 2816.59, "word": " قولنا", "probability": 0.79150390625}, {"start": 2816.59, "end": 2817.23, "word": " assume", "probability": 0.81982421875}, {"start": 2817.23, "end": 2818.11, "word": " نقطة", "probability": 0.9814453125}, {"start": 2818.11, "end": 2818.43, "word": " Q", "probability": 0.9169921875}, {"start": 2818.43, "end": 2819.49, "word": " مفروض", "probability": 0.78564453125}, {"start": 2819.49, "end": 2819.63, "word": " نقول", "probability": 0.6171875}, {"start": 2819.63, "end": 2819.79, "word": " هنا", "probability": 0.309814453125}, {"start": 2819.79, "end": 2820.21, "word": " Contra", "probability": 0.464111328125}, {"start": 2820.21, "end": 2820.63, "word": " positive", "probability": 0.75}, {"start": 2820.63, "end": 2824.65, "word": " ليش؟", "probability": 0.83154296875}, {"start": 2824.65, "end": 2824.81, "word": " اللي", "probability": 0.947265625}, {"start": 2824.81, "end": 2824.91, "word": " هي", "probability": 0.81298828125}, {"start": 2824.91, "end": 2825.07, "word": " بين", "probability": 0.86669921875}, {"start": 2825.07, "end": 2825.39, "word": " جسين", "probability": 0.6471354166666666}, {"start": 2825.39, "end": 2826.45, "word": " نقطة", "probability": 0.9563802083333334}, {"start": 2826.45, "end": 2827.01, "word": " ال", "probability": 0.58837890625}, {"start": 2827.01, "end": 2827.21, "word": " B", "probability": 0.7275390625}, {"start": 2827.21, "end": 2827.87, "word": " نقطة", "probability": 0.9716796875}, {"start": 2827.87, "end": 2827.97, "word": " ال", "probability": 0.8740234375}, {"start": 2827.97, "end": 2828.09, "word": " B", "probability": 0.9775390625}, {"start": 2828.09, "end": 2828.47, "word": " نقطة", "probability": 0.8956705729166666}, {"start": 2828.47, "end": 2828.65, "word": " Q", "probability": 0.916015625}, {"start": 2828.65, "end": 2829.29, "word": " وصلتني", "probability": 0.921630859375}, {"start": 2829.29, "end": 2830.29, "word": " لنقطة", "probability": 0.94873046875}, {"start": 2830.29, "end": 2830.41, "word": " ال", "probability": 0.8916015625}, {"start": 2830.41, "end": 2830.57, "word": " B", "probability": 0.98388671875}, {"start": 2830.57, "end": 2832.15, "word": " 17", "probability": 0.365234375}], "temperature": 1.0}, {"id": 103, "seek": 286414, "start": 2834.66, "end": 2864.14, "text": "إذا الـ N هو إنتجار N is an integer بس بقولك الـ N is integer حتى الآن and ال N زائد خمسة is odd وكأنه بقولك if ال N تكعيب زائد الخمسة is odd then ال N is even جاهزة جاهزة يعني قاعد أبديكيها if N تكعيب زائد خمسة", "tokens": [28814, 15730, 2423, 39184, 426, 31439, 11933, 29399, 7435, 9640, 426, 307, 364, 24922, 4724, 3794, 4724, 39648, 4117, 2423, 39184, 426, 307, 24922, 11331, 49975, 6024, 48506, 293, 2423, 426, 30767, 16373, 3215, 16490, 2304, 3794, 3660, 307, 7401, 4032, 4117, 33456, 3224, 4724, 39648, 4117, 498, 2423, 426, 6055, 4117, 3615, 1829, 3555, 30767, 16373, 3215, 33962, 2304, 3794, 3660, 307, 7401, 550, 2423, 426, 307, 754, 10874, 40294, 11622, 3660, 10874, 40294, 11622, 3660, 37495, 22653, 12174, 995, 22488, 5551, 3555, 16254, 4117, 1829, 11296, 498, 426, 6055, 4117, 3615, 1829, 3555, 30767, 16373, 3215, 16490, 2304, 3794, 3660], "avg_logprob": -0.29581310853217413, "compression_ratio": 1.7391304347826086, "no_speech_prob": 0.0, "words": [{"start": 2834.66, "end": 2835.0, "word": "إذا", "probability": 0.559326171875}, {"start": 2835.0, "end": 2835.18, "word": " الـ", "probability": 0.3253173828125}, {"start": 2835.18, "end": 2835.42, "word": " N", "probability": 0.53564453125}, {"start": 2835.42, "end": 2836.8, "word": " هو", "probability": 0.24072265625}, {"start": 2836.8, "end": 2836.8, "word": " إنتجار", "probability": 0.5540924072265625}, {"start": 2836.8, "end": 2836.8, "word": " N", "probability": 0.40234375}, {"start": 2836.8, "end": 2836.8, "word": " is", "probability": 0.051055908203125}, {"start": 2836.8, "end": 2837.08, "word": " an", "probability": 0.350341796875}, {"start": 2837.08, "end": 2837.68, "word": " integer", "probability": 0.904296875}, {"start": 2837.68, "end": 2838.7, "word": " بس", "probability": 0.56500244140625}, {"start": 2838.7, "end": 2838.96, "word": " بقولك", "probability": 0.8606770833333334}, {"start": 2838.96, "end": 2839.08, "word": " الـ", "probability": 0.670654296875}, {"start": 2839.08, "end": 2839.18, "word": " N", "probability": 0.9150390625}, {"start": 2839.18, "end": 2839.36, "word": " is", "probability": 0.82470703125}, {"start": 2839.36, "end": 2839.8, "word": " integer", "probability": 0.75048828125}, {"start": 2839.8, "end": 2840.32, "word": " حتى", "probability": 0.897216796875}, {"start": 2840.32, "end": 2840.66, "word": " الآن", "probability": 0.75390625}, {"start": 2840.66, "end": 2842.18, "word": " and", "probability": 0.5869140625}, {"start": 2842.18, "end": 2845.32, "word": " ال", "probability": 0.80615234375}, {"start": 2845.32, "end": 2845.52, "word": " N", "probability": 0.5986328125}, {"start": 2845.52, "end": 2845.84, "word": " زائد", "probability": 0.8121744791666666}, {"start": 2845.84, "end": 2846.54, "word": " خمسة", "probability": 0.93994140625}, {"start": 2846.54, "end": 2847.56, "word": " is", "probability": 0.87451171875}, {"start": 2847.56, "end": 2847.86, "word": " odd", "probability": 0.8759765625}, {"start": 2847.86, "end": 2848.46, "word": " وكأنه", "probability": 0.841552734375}, {"start": 2848.46, "end": 2848.88, "word": " بقولك", "probability": 0.8779296875}, {"start": 2848.88, "end": 2849.16, "word": " if", "probability": 0.456298828125}, {"start": 2849.16, "end": 2849.46, "word": " ال", "probability": 0.8310546875}, {"start": 2849.46, "end": 2849.72, "word": " N", "probability": 0.927734375}, {"start": 2849.72, "end": 2850.44, "word": " تكعيب", "probability": 0.9888671875}, {"start": 2850.44, "end": 2850.78, "word": " زائد", "probability": 0.94970703125}, {"start": 2850.78, "end": 2851.28, "word": " الخمسة", "probability": 0.97998046875}, {"start": 2851.28, "end": 2851.44, "word": " is", "probability": 0.955078125}, {"start": 2851.44, "end": 2851.88, "word": " odd", "probability": 0.9326171875}, {"start": 2851.88, "end": 2852.84, "word": " then", "probability": 0.7939453125}, {"start": 2852.84, "end": 2853.66, "word": " ال", "probability": 0.91357421875}, {"start": 2853.66, "end": 2853.98, "word": " N", "probability": 0.927734375}, {"start": 2853.98, "end": 2854.96, "word": " is", "probability": 0.95654296875}, {"start": 2854.96, "end": 2855.48, "word": " even", 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اما بتثبتها بال contrapositive او بالcontradiction ايوة انا بدي اختار انا اختار الواحدة عشان احلها بواحدة و التانية عليك خلاص مابديهاش كلام يعني contradiction or contraposition position positive مش فارقة كتير دي لبالك في المصطلح يعني اه شباب", "tokens": [271, 7401, 813, 293, 307, 754, 4032, 4724, 1829, 39648, 4117, 1975, 15042, 39894, 12984, 3555, 2655, 11296, 20666, 660, 4007, 329, 2187, 1975, 2407, 20666, 9000, 6206, 4105, 1975, 1829, 2407, 3660, 1975, 8315, 4724, 16254, 1975, 46456, 9640, 1975, 8315, 1975, 46456, 9640, 2423, 14407, 24401, 3660, 6225, 8592, 7649, 1975, 5016, 1211, 11296, 4724, 14407, 24401, 3660, 4032, 16712, 7649, 10632, 25894, 4117, 16490, 1211, 33546, 3714, 16758, 16254, 3224, 33599, 28242, 10943, 37495, 22653, 660, 6206, 4105, 420, 660, 4007, 5830, 2535, 3353, 37893, 6156, 9640, 28671, 9122, 2655, 13546, 11778, 1829, 5296, 3555, 6027, 4117, 8978, 9673, 9381, 9566, 1211, 5016, 37495, 22653, 1975, 3224, 13412, 3555, 16758], "avg_logprob": -0.2839912210117307, 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/pKrZGwbVnlc_raw.srt b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/pKrZGwbVnlc_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..8b50f8b6f1dfeeaddecce8b9ba68bb9092ffb081
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/pKrZGwbVnlc_raw.srt
@@ -0,0 +1,2244 @@
+1
+00:00:21,040 --> 00:00:22,880
+بسم الله و الحمد لله و الصلاة والسلام علي رسول
+
+2
+00:00:22,880 --> 00:00:26,900
+الله اليوم ان شاء الله شباب هنكمل في ال
+
+3
+00:00:26,900 --> 00:00:32,960
+mathematical proving بالإثبات الرياضي لكن محاضرتنا
+
+4
+00:00:32,960 --> 00:00:35,520
+مش هتكون فيها .. يعني هتكلم عن موضوع واحد جديد
+
+5
+00:00:35,520 --> 00:00:39,240
+اللي هو الإثبات بالتناقض و من ثم نحاول نحل مجموعة
+
+6
+00:00:39,240 --> 00:00:43,840
+من الأمثل عشان نثبت موضوع الإثباتات السابقة طبعا
+
+7
+00:00:43,840 --> 00:00:47,240
+كنا احنا الأسبوع الماضي بدأنا بالإثبات الرياضي و
+
+8
+00:00:47,240 --> 00:00:51,190
+قلنا كتالةلأن معظم المسائل أو معظم النظريات اللى
+
+9
+00:00:51,190 --> 00:00:54,630
+بيطلب مننا نثبتها هتلاقيها موجودة على صورة if
+
+10
+00:00:54,630 --> 00:01:00,110
+implied او if them او P implies Q وأول نوع من
+
+11
+00:01:00,110 --> 00:01:03,930
+اثبات الرياضي قولنا هروح انا افترض فيه ال Q is
+
+12
+00:01:03,930 --> 00:01:10,050
+true و جينا قولنا كتالي احنا الأساس .. الأساس انB
+
+13
+00:01:10,050 --> 00:01:13,950
+implies Q لو تحققت ال hypothesis معناته ال
+
+14
+00:01:13,950 --> 00:01:18,690
+conclusion هتكون عندي true دايما true تقول ال true
+
+15
+00:01:18,690 --> 00:01:24,970
+فبالمجمل هتكون عندي العملية كلها true الأول طريقة
+
+16
+00:01:24,970 --> 00:01:29,930
+مقرره الإثبات كانت ال direct إثبات المباشر و منها
+
+17
+00:01:29,930 --> 00:01:36,220
+انا بعتمد على او بفترض ان بي isTrue لما بفترض ان P
+
+18
+00:01:36,220 --> 00:01:40,280
+is true هتوصلني ان الـ Q تتحقق عندى و بالتالي انا
+
+19
+00:01:40,280 --> 00:01:44,900
+بكون وصلت للمطلوب اللى موجود عندى بمعنى اخر انه في
+
+20
+00:01:44,900 --> 00:01:46,960
+النظرية اللى هتكون موجودة عندى او المطلوب من
+
+21
+00:01:46,960 --> 00:01:51,790
+اثباتها مطلوب اذا ماكنتش مكتوبة بشكل مباشر Fthen
+
+22
+00:01:51,790 --> 00:01:54,710
+معناته انا بدى اكتبها if then هذا خطوة رقم واحد
+
+23
+00:01:54,710 --> 00:02:00,650
+واروح افترض ان ال B is true وبناء على ال B احاول
+
+24
+00:02:00,650 --> 00:02:05,830
+اصل لمين ل ال Q وطبعا كلنا بنعرف نضرب ونجمع ونقول
+
+25
+00:02:05,830 --> 00:02:09,550
+العدد علي اليمين ويمين ويسار اشارة ليه ساوي وها
+
+26
+00:02:09,550 --> 00:02:14,190
+كذا وطبعا كان بالمثال اللي عندنا الأسهل هي if ال M
+
+27
+00:02:14,190 --> 00:02:17,810
+is odd then and ترميه is odd بس من باب التذكير
+
+28
+00:02:17,810 --> 00:02:26,620
+الآن هي ال Bو هذه ال Q ال N شو يعني ال N is odd؟ و
+
+29
+00:02:26,620 --> 00:02:31,920
+انا اخوك واحد عن واحد هقول Assume ال
+
+30
+00:02:31,920 --> 00:02:37,160
+B خلاص لو كنت بتديش كمان is it true انا بفترض ان
+
+31
+00:02:37,160 --> 00:02:42,700
+انت جاي بتشتغل صح Assume ال B is true يعني ال N is
+
+32
+00:02:42,700 --> 00:02:50,450
+odd مفهومها ال N isالخطوة التالية اللي هي الكلام
+
+33
+00:02:50,450 --> 00:02:55,690
+تجيب صورة الان كعدد فردي اللي هي صورة اتنين K زائد
+
+34
+00:02:55,690 --> 00:03:00,770
+واحد for some K تنتمي الى Z الخطوة رقم تلاتة بعد
+
+35
+00:03:00,770 --> 00:03:04,810
+هيك هو بيقولك ان الان تربيع معناته انك تربع الان
+
+36
+00:03:04,810 --> 00:03:12,490
+اللي عندك وتمشي الخطوة التالية تربع الان تصير
+
+37
+00:03:12,490 --> 00:03:17,640
+اتنين او ان تربيعبدا تساوي اتنين كي زائد واحد لكل
+
+38
+00:03:17,640 --> 00:03:23,060
+تربيع بدا تساوي اربع كي تربيع زائد اربع كي زائد
+
+39
+00:03:23,060 --> 00:03:27,560
+واحد لان باخد عامل تاني عامل مشترك من هنا اتنين في
+
+40
+00:03:27,560 --> 00:03:33,180
+اتنين كي تربيع زائد اربع كي لكل زائد واحد وهذه
+
+41
+00:03:33,180 --> 00:03:39,800
+الصورة الاتنين كي عفوا وهذه الصورة صورة العدد
+
+42
+00:03:39,800 --> 00:03:48,660
+الفردي odd integerوبالتالي انت وصلت لمين؟ للحل
+
+43
+00:03:48,660 --> 00:03:55,340
+اللي وصلت ل Q هذا بنسميه Direct Proof بعض
+
+44
+00:03:55,340 --> 00:03:59,180
+المسائل .. بعض المسائل هتحس ان ال Direct Proof مش
+
+45
+00:03:59,180 --> 00:04:04,180
+هينشي معاها خطوة فيها مش هتقدر تمصل لنتيجة طب ايش
+
+46
+00:04:04,180 --> 00:04:06,800
+بيكون الحل؟ بيكون الحل ان انا اعتمد على ال
+
+47
+00:04:06,800 --> 00:04:09,740
+Contrapositive تبعتها ايش ال Contrapositive؟ احنا
+
+48
+00:04:09,740 --> 00:04:18,000
+بنعرف ان ال B implies Q تكافئنقطة Q تعني نقطة B
+
+49
+00:04:18,000 --> 00:04:26,160
+وبالتالي إذا تحققت هذه المعروفة صحيحة في هذه
+
+50
+00:04:26,160 --> 00:04:29,980
+المعروفة سأفترض الـ Negation تابعة الـ Q سأقول
+
+51
+00:04:29,980 --> 00:04:34,260
+Assume نقطة Q ونفس الخطوات التي اتبعتها في ال
+
+52
+00:04:34,260 --> 00:04:38,260
+Direct Proof بس الفرق أن بدل ما انا افترض الـ B
+
+53
+00:04:38,260 --> 00:04:43,580
+افترضت أو اعتمدت على نقطة Q في الحلو من الأمثلة
+
+54
+00:04:43,580 --> 00:04:51,420
+اللي ممكن نشوفها بالشكل هذا لما قال لي تلاتة N
+
+55
+00:04:51,420 --> 00:04:56,500
+زائد اتنين is odd if ال N .. if ال N if التلاتة N
+
+56
+00:04:56,500 --> 00:05:03,900
+زائد اتنين is odd هي ال B معناته ال N is odd هي ال
+
+57
+00:05:03,900 --> 00:05:07,580
+Q الآن لو أنا فكرت أبدأ في ال B في ال direct proof
+
+58
+00:05:07,580 --> 00:05:11,560
+هذا مش هتوصلني لنتيجة مش هتوصلني لنتيجة لأنها
+
+59
+00:05:11,560 --> 00:05:17,790
+complexبالتالي انا بدى احاول اشوف الاسهل لو انا
+
+60
+00:05:17,790 --> 00:05:23,850
+بدى احولها بال contrapositive ماذا هقول if ال N is
+
+61
+00:05:23,850 --> 00:05:27,610
+even نقطة
+
+62
+00:05:27,610 --> 00:05:32,830
+Q ثم تلاتة N زائد اتنين is even
+
+63
+00:05:38,070 --> 00:05:42,450
+هذه النظرية هيك بيتصير و بروح بقوله assume not ..
+
+64
+00:05:42,450 --> 00:05:48,510
+هذي إيش بتمثل؟ هذي نفي ال Q Assume not Q حصل لمين؟
+
+65
+00:05:48,510 --> 00:05:51,970
+حصل ل not B وبالتالي حصلت على Contra positive
+
+66
+00:05:51,970 --> 00:05:56,870
+وبالتالي المعادلة اللي عند الأولى هتكون صحيحة في
+
+67
+00:05:56,870 --> 00:06:02,050
+الحالة هذه هروح أقوله assume not
+
+68
+00:06:02,050 --> 00:06:03,070
+Q is true
+
+69
+00:06:07,500 --> 00:06:14,220
+ماذا يعني نقطة Q is true؟ معناته N is not odd بين
+
+70
+00:06:14,220 --> 00:06:20,820
+جو سين هيكون even فبصورة ال even ال N بيبقى تساوي
+
+71
+00:06:20,820 --> 00:06:28,420
+اتنين في K وK تنتمي لزد في قرصان K الخطوة بعد هيك
+
+72
+00:06:28,420 --> 00:06:34,040
+تلاتة N زائد اتنين تساوي
+
+73
+00:06:34,040 --> 00:06:42,070
+تلاتة في اتنين Kزائد اتنين تساوي ستة K زائد اتنين
+
+74
+00:06:42,070 --> 00:06:47,610
+تساوي خد التنين عامل مشترك تلاتة K زائد واحد هذه
+
+75
+00:06:47,610 --> 00:06:51,990
+integer وهذه العدد عبارة عن is even integer
+
+76
+00:06:51,990 --> 00:06:55,510
+contrapositive
+
+77
+00:06:55,510 --> 00:07:03,150
+إلى اخرها تمام؟ ابدأ مع مين؟ مع ال direct ولا مع
+
+78
+00:07:03,150 --> 00:07:09,590
+ال contrapositive؟الاصل انك بدك تجرب وتتطلع في
+
+79
+00:07:09,590 --> 00:07:15,230
+المسألة بشكل كويس اول خطوة او اول جهد لازم تبذله
+
+80
+00:07:15,230 --> 00:07:22,030
+انك تحدد من ال B و من ال Q في المسألة عشان تمشي لل
+
+81
+00:07:22,030 --> 00:07:25,390
+next step الآن بقى اذا اتحددت B و Q انت صاحب
+
+82
+00:07:25,390 --> 00:07:31,750
+القراروالتجربة هي اكتر نجاعة ستمشي معاك مباشرة
+
+83
+00:07:31,750 --> 00:07:36,210
+تمسك بيك وحالتك ستتأدي وغالبا كل ما تلاقي بيك
+
+84
+00:07:36,210 --> 00:07:41,310
+كومبليكس ستلاقي كومبليكس كونترا بوزيتيف وهو الحل
+
+85
+00:07:41,310 --> 00:07:45,250
+كل ما تلاقي بيك كومبليكس ستكون كونترا بوزيتيف انت
+
+86
+00:07:45,250 --> 00:07:50,470
+قارن مين أسهل بيك و لا كيو؟ كيو أسهل يعني تقوم
+
+87
+00:07:50,470 --> 00:07:55,030
+باستخدام نقطة كيو لن تبقى بسهولة بمكان اللي موجود
+
+88
+00:07:55,030 --> 00:08:00,110
+عندكوبالتالي انت لازم .. يعني بدك تحاول و تجرب مرة
+
+89
+00:08:00,110 --> 00:08:03,490
+و اتنين و تلاتة لحد ما تصير انت عايش صرف عندك خبرة
+
+90
+00:08:03,490 --> 00:08:08,470
+في بناء او في .. بأي اتجاه انا بدي اروحه طيب النوع
+
+91
+00:08:08,470 --> 00:08:15,390
+التالت من الاثبات في ال .. بي implies q أحيانا مش
+
+92
+00:08:15,390 --> 00:08:18,430
+هيكون في اللي بنسميه احنا بالتناقض يعني لا جاية
+
+93
+00:08:18,430 --> 00:08:23,310
+معايابالـ Direct Proof ولا جاية معايا بالـ
+
+94
+00:08:23,310 --> 00:08:26,890
+Contrapositive في عندك طريقة تالتة او طريقة تالتة
+
+95
+00:08:26,890 --> 00:08:31,410
+هم يسميها الـ Contradiction اثبات بالتناقض الاثبات
+
+96
+00:08:31,410 --> 00:08:38,230
+بالتناقض احنا كلنا بنعرف ان ال B implies Q
+
+97
+00:08:38,230 --> 00:08:45,290
+equivalent to B or not Q يعني لو تحققت واحدة من
+
+98
+00:08:45,290 --> 00:08:49,370
+التنتين هدول بتكون العملية إيش ال trueجالك الإثبات
+
+99
+00:08:49,370 --> 00:08:54,550
+للتناقض كالتالي إذا أنا روحت كالتالي أخدت الموضوع
+
+100
+00:08:54,550 --> 00:08:59,790
+P و أخدت Q و مش قادر أصل لواحدة منهم بالاتجاهين
+
+101
+00:08:59,790 --> 00:09:03,350
+سواء كانت بال direct أو بال contrapositive معناته
+
+102
+00:09:03,350 --> 00:09:08,910
+ممكن أنا أجرب أروح أفرض أن ال P صحيحة و ال Q ..
+
+103
+00:09:08,910 --> 00:09:11,430
+not ال Q صحيحة يعني ال Q .. ال Q false يعني بدي
+
+104
+00:09:11,430 --> 00:09:15,870
+أقول أن النظرية دي مش صحيحةوأجرب أشتغل مع ال band
+
+105
+00:09:15,870 --> 00:09:20,690
+الأسهل منهم إذا حصلت على أي تناقض معناته النظرية
+
+106
+00:09:20,690 --> 00:09:25,630
+الأصلية هيش هتكون صحيحة كمان مرة انت ايش عاملك
+
+107
+00:09:25,630 --> 00:09:29,810
+بتفترض ان ال B is true و ال conclusion المحصلة
+
+108
+00:09:29,810 --> 00:09:34,470
+تبعت النظرية ال Q is true مصبوط فانت روحت و قلتله
+
+109
+00:09:34,470 --> 00:09:38,790
+false قلتله انك بتفترض ان ال B is true و ال Q is
+
+110
+00:09:38,790 --> 00:09:44,860
+falseو أثناء الحل وصلت إن ال false اللي أنت فرضتها
+
+111
+00:09:44,860 --> 00:09:52,940
+is false نفي نفي يعني false false وكأنك تنفي إنك
+
+112
+00:09:52,940 --> 00:09:57,460
+ننفي تمام؟ وبالتالي بتكون حصلت على شغل إيه اسمها؟
+
+113
+00:09:57,460 --> 00:10:01,720
+طلاق بين الفرضيات طبعا بدون ما تتطلع في .. إسميلك
+
+114
+00:10:01,720 --> 00:10:07,200
+يا غزال يا سويسي خلّيك معايا هنا عشان تفهم إيش
+
+115
+00:10:07,200 --> 00:10:07,880
+المقصود بيه
+
+116
+00:10:14,580 --> 00:10:22,660
+لو كان تربيع العدد فردي فمعناته العدد لن يكون عندي
+
+117
+00:10:22,660 --> 00:10:38,210
+إيش فردي if ال n تربيع is odd then ال n isأضعف
+
+118
+00:10:38,210 --> 00:10:42,930
+غزال أدم يثبتها بإيش Contra
+
+119
+00:10:42,930 --> 00:10:48,310
+positive تجه 100% معانا بروح بقوله assume not q
+
+120
+00:10:48,310 --> 00:10:51,910
+يعني الأن is even الحاجة قبل شويه أثبتناها مصبوط
+
+121
+00:10:51,910 --> 00:10:56,170
+ولا لأ أو أثبتنا مثلها قريب منها even وربع ال even
+
+122
+00:10:56,170 --> 00:11:00,310
+في الآخر تصل لكن أنا بدأ أستخدم معاها الإثبات
+
+123
+00:11:00,310 --> 00:11:01,790
+بالتناقض
+
+124
+00:11:04,060 --> 00:11:07,340
+كمان مرة عشان الناس صحابنا ميتهوش ايش يعني ب
+
+125
+00:11:07,340 --> 00:11:13,780
+Contrapositive بتجربة Contrapositive proof by
+
+126
+00:11:13,780 --> 00:11:17,840
+contrapositive للمسألة
+
+127
+00:11:17,840 --> 00:11:23,320
+هذه هروح أقول له assume not
+
+128
+00:11:23,320 --> 00:11:29,720
+q is true ايش يعني not q is true ان ال N is not
+
+129
+00:11:29,720 --> 00:11:31,380
+odd
+
+130
+00:11:32,870 --> 00:11:36,610
+even هي المصدر اللي حللناه قبل شوية اتوا ال N
+
+131
+00:11:36,610 --> 00:11:42,410
+equal 2K و ال K تنتبي الى Z و قاعد بدوا من ال N
+
+132
+00:11:42,410 --> 00:11:47,170
+تربيع N تربيع بدها تساوي 2K كل تربيع و بدها تساوي
+
+133
+00:11:47,170 --> 00:11:54,310
+4K تربيع و بدها تساوي هاتين في 2K تربيع even
+
+134
+00:11:54,310 --> 00:11:58,170
+integer contrapositive
+
+135
+00:12:01,440 --> 00:12:07,580
+مظبوط؟ اللي هي دي بتمثل ات نط ال B خلص البرهان هدف
+
+136
+00:12:07,580 --> 00:12:10,900
+ال contrapositive هدف ال contrapositive صحيح مية
+
+137
+00:12:10,900 --> 00:12:14,940
+في المية مافيش عليه مشكلة لأن ب contradiction ايش
+
+138
+00:12:14,940 --> 00:12:21,500
+بدك تفترض انت؟ بدك تقول لل B is it true؟و and ..
+
+139
+00:12:21,500 --> 00:12:25,080
+نه .. بالضبط و ال Q غلط .. false إيش .. إذا .. لما
+
+140
+00:12:25,080 --> 00:12:29,320
+تكون n is odd false يعني ال n is .. even .. even
+
+141
+00:12:29,320 --> 00:12:31,860
+.. فيه .. فيش حاجة غير هيك و لا لأ .. بقيت هروح
+
+142
+00:12:31,860 --> 00:12:40,820
+أقوله أنا أسيوم .. افترض ال P and .. نقطة Q .. مين
+
+143
+00:12:40,820 --> 00:12:47,040
+ال P هيها؟ و مين ال Q؟ هيها .. أصبت؟
+
+144
+00:12:50,200 --> 00:12:59,800
+معناته ال B أو ال N تربيع is odd and ال N is not
+
+145
+00:12:59,800 --> 00:13:04,080
+odd اللي هي بين جثين even إن شاءت يا شباب ما
+
+146
+00:13:04,080 --> 00:13:06,460
+تكتبليش is not odd ماعنديش مشكلة أنا في الموضوع
+
+147
+00:13:06,460 --> 00:13:11,800
+كتبلي مباشرة even مافيش مشكلةيعني صار انا فيه عندى
+
+148
+00:13:11,800 --> 00:13:15,780
+الان وكأنه موقعيات اتنين بين ايديا اعتمد على مين
+
+149
+00:13:15,780 --> 00:13:19,860
+فيهم في الشغل الان تربيع اقول الان تربيع بيده
+
+150
+00:13:19,860 --> 00:13:23,280
+تساوي اتنين كساوية واحد واخد الجذر ولا اعتمد على
+
+151
+00:13:23,280 --> 00:13:27,660
+الأسهل اللى هى الان اكوال اتنين اك واربعها لأ و
+
+152
+00:13:27,660 --> 00:13:30,660
+الله بيربعها بعدها هروح لخبرة تالية هقول الان بيده
+
+153
+00:13:30,660 --> 00:13:37,340
+تساوي اتنين ك مصبوط ليش هي is not odd is not odd
+
+154
+00:13:37,340 --> 00:13:42,510
+even يعني2K لان equal 2K أن تربيع الخطوة اللي
+
+155
+00:13:42,510 --> 00:13:48,530
+بعدها أن تربيع بدها تساوي 4K تربيع ونتساوي 2 في 2K
+
+156
+00:13:48,530 --> 00:13:58,470
+تربيع صح even وها دي even integer not
+
+157
+00:13:58,470 --> 00:14:00,990
+odd contradiction
+
+158
+00:14:07,020 --> 00:14:14,960
+with ترقض معميل مع الفرضية and تربيع is odd خلصنا
+
+159
+00:14:14,960 --> 00:14:19,400
+البرهان إيش يعني؟ يعني لما بتكون ال and تربيع is
+
+160
+00:14:19,400 --> 00:14:27,140
+odd ال and is odd وهذا هو الإثبات بالترقض إنك أنت
+
+161
+00:14:27,140 --> 00:14:30,760
+بتفرض حالتين و بتشتغل مع أي واحدة فيهم مش مشكلة
+
+162
+00:14:30,760 --> 00:14:34,700
+عندك معميل بلام أنك حققتهم في الفرضيات يعني بتقدر
+
+163
+00:14:34,700 --> 00:14:39,000
+تعتمد عليهم زي ما بدكوبتمشي للاتجاه التالي لحد ما
+
+164
+00:14:39,000 --> 00:14:43,260
+تصل لأي طلاقط عشان هيك كتبنا لك هان assume P and
+
+165
+00:14:43,260 --> 00:14:48,460
+not Q then deduce any contradiction وحاول ابحث او
+
+166
+00:14:48,460 --> 00:15:01,220
+اوجد عن اي طلاقط موجود في المسألة اللي عندها تمام
+
+167
+00:15:01,220 --> 00:15:01,780
+مثال؟
+
+168
+00:15:14,740 --> 00:15:21,720
+وقول لي لو كانت ال M زائد ال N أقل من 89 هذي مثلت
+
+169
+00:15:21,720 --> 00:15:35,820
+مين؟ ال B ثم M أقل من 45 او ال N أقل من 45 ل Q و
+
+170
+00:15:35,820 --> 00:15:39,240
+بدنا نثبتها بال contradiction نثبتها بالتراقد تثبت
+
+171
+00:15:39,240 --> 00:15:41,100
+بالتراقد يعني assume
+
+172
+00:15:55,040 --> 00:16:06,260
+ممتاز ايش ال B ال M زائد ال M اكبر اصغر من 89 and
+
+173
+00:16:06,260 --> 00:16:09,860
+ال
+
+174
+00:16:09,860 --> 00:16:14,470
+and بدك تنفي تنساه بدك تنفي كل Q ال Mال M أكبر أو
+
+175
+00:16:14,470 --> 00:16:19,190
+تساوي خمسة و أربعين ال or بتصير and و ال M أكبر أو
+
+176
+00:16:19,190 --> 00:16:24,050
+تساوي خمسة و أربعين مظبوط؟ و بالتالي هقوله الآن ال
+
+177
+00:16:24,050 --> 00:16:33,230
+M أكبر أو تساوي خمسة و أربعين and ال M أكبر أو
+
+178
+00:16:33,230 --> 00:16:39,070
+تساوي خمسة و أربعين لاحظ
+
+179
+00:16:39,070 --> 00:16:43,740
+الفرضية تبعتك كم عنصر فيها موجودة الآنواحدة تنتين
+
+180
+00:16:43,740 --> 00:16:49,380
+تلاتة تستخدمين فيهم الأسهل لك اللي ممكن ياش تمشي
+
+181
+00:16:49,380 --> 00:16:51,860
+معاك في الحل لأن الأن دول الفرقويات التلاتة
+
+182
+00:16:51,860 --> 00:16:55,400
+الموجودة وانت مطلوب منك توجد اي تناقض مطلوب منك
+
+183
+00:16:55,400 --> 00:17:00,080
+توجد اي تناقض الان لو مسكت الأولى هذي مش حصل الحل
+
+184
+00:17:00,080 --> 00:17:04,380
+انا ولا لا؟ بدأ ادور علاقة بدأ امسك هذه او التانية
+
+185
+00:17:04,380 --> 00:17:09,740
+هوحى باللهيك ال M أكبر او تساوي
+
+186
+00:17:17,980 --> 00:17:23,440
+معناته M زائد M هتكون أكبر أو تساوي خمسة و أربعين
+
+187
+00:17:23,440 --> 00:17:28,560
+زائد ال N تصبر
+
+188
+00:17:28,560 --> 00:17:31,800
+ان اضافنا ال N على ال برافين عشان النساء اللي
+
+189
+00:17:31,800 --> 00:17:37,580
+اتبعها صحيحةطب احنا أساسا عندنا ال N أكبر من 45،
+
+190
+00:17:37,580 --> 00:17:42,080
+مصبوط؟ معناته بما أن ال N هذه أكبر من 45، معناته
+
+191
+00:17:42,080 --> 00:17:49,760
+حصي الجمع هذا أكبر أو تساوي 45 زاد ال 45، صح؟ اللي
+
+192
+00:17:49,760 --> 00:17:57,230
+هي 90وبخصيتي التعدي إذا كانت ال M أكبر من M من 45
+
+193
+00:17:57,230 --> 00:18:02,670
+زائد ال M و أكبر من 90 فهي هتكون M زائد M أكبر من
+
+194
+00:18:02,670 --> 00:18:10,050
+90 وهذا هيقدر أن M زائد M أكبر أو تساوي 90 هذا
+
+195
+00:18:10,050 --> 00:18:15,290
+بتناقض معنى Contradiction أنا وصلت ل Contradiction
+
+196
+00:18:20,510 --> 00:18:25,510
+ماذا يعني؟ يعني لما تكون ال M زائد ال M أقل من 89،
+
+197
+00:18:25,510 --> 00:18:30,170
+معناته ال M هتكون أقل من 45، أو يعني واحدة منهم
+
+198
+00:18:30,170 --> 00:18:34,610
+هتكون أقل من 45، هاي الإثبات بالتناقض، هتحس إنه
+
+199
+00:18:34,610 --> 00:18:38,770
+فعلا أن الأمر صار سهل و ممكن أنا أجيب حل و أوجد
+
+200
+00:18:38,770 --> 00:18:40,530
+منه برهان بكل بساطة
+
+201
+00:18:43,490 --> 00:18:46,930
+قبل أن ألتقى للموضوع التالي اللي هو ال
+
+202
+00:18:46,930 --> 00:18:49,530
+mathematical induction لكن أنا بدي أتركه للمحاضرة
+
+203
+00:18:49,530 --> 00:18:53,130
+الجاية و بدي أشوف أسئلة الكتاب يعني قبل ما أجي على
+
+204
+00:18:53,130 --> 00:18:59,510
+المحاضرة أخدت snapshot من أول تمنتاشر سؤال تقريبا
+
+205
+00:18:59,510 --> 00:19:04,850
+بدنا نحلهم مش مش حلهم كلهمبنتحاول ناخد بعضهم و
+
+206
+00:19:04,850 --> 00:19:08,470
+نشوف كيف ممكن احنا نحل نعتمد على direct نعتمد على
+
+207
+00:19:08,470 --> 00:19:12,170
+contrapositive نستخدم ال contradiction اي واحد من
+
+208
+00:19:12,170 --> 00:19:16,810
+الاثباتات انا اتبعهم طبعا هتلاقي انك بعض الأحيان
+
+209
+00:19:16,810 --> 00:19:22,770
+من الكتاب بيقولك استخدم كده تمام؟ و غالبا .. غالبا
+
+210
+00:19:22,770 --> 00:19:25,550
+في الامتحان اذا انا .. يعني انا ممكن طريقة انحلب
+
+211
+00:19:25,550 --> 00:19:29,950
+اكتر من شغله ممكن اقولك انا استخدمهكذا اذا كان انا
+
+212
+00:19:29,950 --> 00:19:32,810
+بدي اياها او ممكن يسيبك اياها مفتوحة معناته بتقدر
+
+213
+00:19:32,810 --> 00:19:37,930
+تحل مثلا ال contrapositive او الcontradiction طيب
+
+214
+00:19:37,930 --> 00:19:43,670
+direct proof ده هتشوف السؤال الأول بيقول استخدم ال
+
+215
+00:19:43,670 --> 00:19:47,510
+direct proof عشان تثبت جمع او حاصل جمع two odd
+
+216
+00:19:47,510 --> 00:19:55,090
+integers is even فيها if و then يا شباب انت اللي
+
+217
+00:19:55,090 --> 00:19:59,680
+بكي تركب ال if و then الآنمين ال B و مين ال Q في
+
+218
+00:19:59,680 --> 00:20:03,280
+المسألة؟ جيل بيقول لك show that the sum of two odd
+
+219
+00:20:03,280 --> 00:20:08,760
+integers لأ لأ اللي قد تقول two odd integers هي
+
+220
+00:20:08,760 --> 00:20:16,260
+المعطاه حصل جمعهم even يعني هتقول هيك if ال M and
+
+221
+00:20:16,260 --> 00:20:27,760
+ال N are odd then M زائد ال M iseven؟ ولا شو رأيك؟
+
+222
+00:20:27,760 --> 00:20:31,060
+لأن هيك صحيحة المسألة عشان هيك عشان هيك انت لازم
+
+223
+00:20:31,060 --> 00:20:35,200
+تروح تطلع على أسئلة الكتاب وتجرب لأن مش كل المسائل
+
+224
+00:20:35,200 --> 00:20:38,720
+جاياكي مجشرة بيقولك اتفضل يعني أنت أحيانا بتكون
+
+225
+00:20:38,720 --> 00:20:42,340
+عند ضيف أو تكون ضيف عند ناس عفوا بيقعد بيجشرلك
+
+226
+00:20:42,340 --> 00:20:45,080
+الموزة و بيقدملك إيها بكل احترام أو بيقعد بيجشرلك
+
+227
+00:20:45,080 --> 00:20:49,810
+التفاحة و بيقولك اتفضل مصبوط؟ أيوةأحياناً بتكون
+
+228
+00:20:49,810 --> 00:20:54,290
+كتر ما شافك وزورتك تيل خلال الفصل يا راني جرف منك
+
+229
+00:20:54,290 --> 00:20:58,450
+بقولك احمل هاي ال بورتجانه و هاي السكينه لأ احمل
+
+230
+00:20:58,450 --> 00:21:03,210
+ال بورتجانه مش المادة تمام؟ وبالتالي المطموع ان
+
+231
+00:21:03,210 --> 00:21:09,490
+انت ايش تبدأ تشتغل تبدأ تشتغل والاصل انك تبدأ تعرف
+
+232
+00:21:09,490 --> 00:21:13,490
+لانه كمان مرة مفتاح الحل في المسائل يا شباب اذا
+
+233
+00:21:13,490 --> 00:21:20,110
+ماكنتش موجودة F و Thenانت بدك ايش تبحث او توجد ال
+
+234
+00:21:20,110 --> 00:21:24,550
+F within هذي اليك عشان تبدأ الحل بتهيألي بعد هيك
+
+235
+00:21:24,550 --> 00:21:31,330
+حلت المسألة ولا شو رايكوا في دا حلها دا يعني
+
+236
+00:21:31,330 --> 00:21:35,410
+اما بدها تساوي اتنين K زائد واحد ان بدها تساوي
+
+237
+00:21:35,410 --> 00:21:42,640
+اتنين Kأنا ماعرف ليش k زال واحد غلط لإنك انت خدت
+
+238
+00:21:42,640 --> 00:21:46,540
+نفس الايم انتوا جماعته لا نفسه خد اي رقم تاني غير
+
+239
+00:21:46,540 --> 00:21:51,560
+ال k لو .. لو قلت نقص واحد okay بمشي الحل بس في
+
+240
+00:21:51,560 --> 00:21:56,930
+الآخر خد different numberزائد H اتنين H زائد واحد
+
+241
+00:21:56,930 --> 00:22:00,590
+و إجمعهم و أحصل على نتيجة ستكون صح السؤال التاني
+
+242
+00:22:00,590 --> 00:22:03,370
+برضه استخدم ال direct proof to show the sum of
+
+243
+00:22:03,370 --> 00:22:08,750
+even عكسه كماما، مصبوط؟ مالاش تدخل فيه تلاتة show
+
+244
+00:22:08,750 --> 00:22:20,250
+that the square of even number is even number بدي
+
+245
+00:22:20,250 --> 00:22:30,140
+حد يصيغليها F withinأه سويسي قول اتديني اها if و
+
+246
+00:22:30,140 --> 00:22:35,520
+then ايوه
+
+247
+00:22:35,520 --> 00:22:41,720
+ممتاز على الرغم انه بدالك المسألة the square زي
+
+248
+00:22:41,720 --> 00:22:45,700
+المجلة كان the sum the square of an even number
+
+249
+00:22:45,700 --> 00:22:53,140
+يعني لو كانت ال n is even then if ال n is even
+
+250
+00:22:55,820 --> 00:23:01,320
+ذن الآن ترميع is even هذه صيغة المسألة اللي موجودة
+
+251
+00:23:01,320 --> 00:23:04,940
+عندك وبالتالي أول ما تفشوف مسألة زي هيك مش قادر
+
+252
+00:23:04,940 --> 00:23:09,160
+تمسك فيها if و then بدك تحاول توجد ال if و ال then
+
+253
+00:23:09,160 --> 00:23:15,340
+تباعتها المسألة هاي أربعة show that the additive
+
+254
+00:23:15,340 --> 00:23:19,920
+inverse المعكوس الجامعي additive inverse المعكوس
+
+255
+00:23:19,920 --> 00:23:26,200
+الجامعي أو حطوط قياب انبوسين ال negativeof an even
+
+256
+00:23:26,200 --> 00:23:30,840
+integer او even number is even number using the
+
+257
+00:23:30,840 --> 00:23:39,400
+direct proof كمان مرة بدنا واحد من السرحانين يحاول
+
+258
+00:23:39,400 --> 00:23:45,120
+يجيب اللي هي f و then the
+
+259
+00:23:45,120 --> 00:23:49,220
+additive inverse المعكوس الجمعى اللي هو بين جثين
+
+260
+00:23:49,220 --> 00:23:54,060
+حطولا كيان نيجاتيف لل even number is even number
+
+261
+00:23:58,310 --> 00:24:08,410
+إذا ال N هو نيجاتيف، إذا ال N هو نيجاتيف، إذا ال N
+
+262
+00:24:08,410 --> 00:24:14,110
+هو نيجاتيف، إذا ال N هو نيجاتيف، إذا ال N هو
+
+263
+00:24:14,110 --> 00:24:20,050
+نيجاتيف، إذا ال
+
+264
+00:24:20,050 --> 00:24:23,030
+N هو نيجاتيف، إذا ال N هو نيجاتيف، إذا ال N هو
+
+265
+00:24:23,030 --> 00:24:26,390
+نيجاتيف، إذا ال N هو نيجاتيف، إذا ال N هو نيجاتيف،
+
+266
+00:24:26,390 --> 00:24:26,390
+إذا ال N هو نيجاتيف، إذا ال N هو نيجاتيف، إذا ال N
+
+267
+00:24:26,390 --> 00:24:26,390
+هو نيجاتيف، إذا ال N هو نيجاتيف، إذا ال N هو
+
+268
+00:24:26,390 --> 00:24:26,390
+نيجاتيف، إذا ال N هو نيجاتيف، إذا ال N هو نيجاتيف،
+
+269
+00:24:26,390 --> 00:24:26,390
+إذا ال N هو نيجاتيف، إذا ال N هو نيجاتيف، إذا ال N
+
+270
+00:24:26,390 --> 00:24:26,430
+هو نيجاتيف، إذا ال N
+
+271
+00:24:33,060 --> 00:24:38,900
+لو كانت ال N even هيكون المعكوس الجامعي تبقتها
+
+272
+00:24:38,900 --> 00:24:47,020
+ناقص ن is even هي show that the additive inverse
+
+273
+00:24:47,020 --> 00:24:53,040
+of an even integer يعني المعكوس الجامعي للعدد
+
+274
+00:24:53,040 --> 00:25:02,040
+الزوجي عدد زوجياتنين و سالم اتنين بصبوط هاي ..
+
+275
+00:25:02,040 --> 00:25:07,960
+ماتبتها .. ماعكستش لأ انا حاولت استخلص منها اف و
+
+276
+00:25:07,960 --> 00:25:13,720
+دل هو ايش عمله قاعد يقول ليه تعالى نشوف بشكل عام
+
+277
+00:25:13,720 --> 00:25:20,140
+انا مطلوب مني في المسألة هي اقول له اف فراغ
+
+278
+00:25:21,920 --> 00:25:25,940
+ثم فرح اكتب على الشكل هذا افصلها ايش قاعد هو
+
+279
+00:25:25,940 --> 00:25:31,800
+بيقولها المعكوس الجامعى للعدد الزوجى يعني ايش
+
+280
+00:25:31,800 --> 00:25:36,380
+المعطى اليك عدد الزوجى المعطى اليك العدد الزوجى
+
+281
+00:25:36,380 --> 00:25:40,300
+وقاعد بيقولك انه اثبت ان المعكوس الجامعى للعدد
+
+282
+00:25:40,300 --> 00:25:46,600
+الزوجى هو عبارة عن عدد زوجى يعني هو back and is
+
+283
+00:25:46,600 --> 00:25:53,690
+evenو اثبت ان المعكوس الجمعى اللى هو سالب N is
+
+284
+00:25:53,690 --> 00:26:00,870
+even طبعا بضبط بس انت عارفش هتروح تقوله هتروح تقول
+
+285
+00:26:00,870 --> 00:26:11,370
+Assume B is true صح يعني N isEVEN هذا بيقدر ان
+
+286
+00:26:11,370 --> 00:26:15,870
+الان equal اتنين K و K تان تانى الى Z هذا لاحظ انه
+
+287
+00:26:15,870 --> 00:26:20,230
+بتحس انه اول سطرين بنكتبهم في البرهان و كأنهم نسخ
+
+288
+00:26:20,230 --> 00:26:23,650
+نحطه على مكان التصوير و بنضغط عليك تكتبهم حسب نوع
+
+289
+00:26:23,650 --> 00:26:27,930
+الاثبات اللى عندك اتنين K زائد واحد او اتنين K عفر
+
+290
+00:26:27,930 --> 00:26:34,830
+اش هو بده من ايه؟المعكوس الجمعي هذا يؤدى ان سالب N
+
+291
+00:26:34,830 --> 00:26:40,550
+تساوي سالب واحد او سالب واحد مضروبة في اتنين K
+
+292
+00:26:40,550 --> 00:26:47,110
+وتساوي سالب اتنين K صح؟ وتساوي اتنين في سالب K وهك
+
+293
+00:26:47,110 --> 00:26:53,430
+و تصير جوعانها even يا خالد اه الفكرة ان دايما
+
+294
+00:26:53,430 --> 00:26:57,630
+صورة عدد الزوج هي عبارة عن اتنين مضروبة في some
+
+295
+00:26:57,630 --> 00:27:02,260
+integerهي التنين وهي الـ sum integer لو انت من
+
+296
+00:27:02,260 --> 00:27:05,580
+اللحظة هذه قلتلي انا بصدقك و بقول مية لمية كلامك
+
+297
+00:27:05,580 --> 00:27:09,740
+صح بس الخطوة التالتة الأخيرة هذه عشان ما تتركش
+
+298
+00:27:09,740 --> 00:27:13,660
+مجال لأي حد قلتلي هى التنين اللي حار يا عم وهي ال
+
+299
+00:27:13,660 --> 00:27:21,640
+integer اللي هو السالب K ضربناها is even خلصنا خلص
+
+300
+00:27:21,640 --> 00:27:24,520
+البرهان معته سالب N is even
+
+301
+00:27:37,010 --> 00:27:45,690
+خمسة مضيك F within في خمسة show that F ال N زائد
+
+302
+00:27:45,690 --> 00:27:55,150
+ال M and N زائد ال B are even integers هذا
+
+303
+00:27:55,150 --> 00:28:00,480
+ال Bهذه ال B كلها تمام؟ where بقى بقولك ال M و ال
+
+304
+00:28:00,480 --> 00:28:02,940
+N are integers أعداد صحيحة يعني مش real number
+
+305
+00:28:02,940 --> 00:28:11,180
+then M زائد ال B وهذه Q M زائد ال N افضل M زائد ال
+
+306
+00:28:11,180 --> 00:28:19,440
+B is even اسكت يا أحمد تسمعني صوتك if ال M زائد ال
+
+307
+00:28:19,440 --> 00:28:25,200
+N and N زائد ال B are even
+
+308
+00:28:28,050 --> 00:28:36,550
+ثم M زائد N is even M زائد B عفوا هى المسألة اللى
+
+309
+00:28:36,550 --> 00:28:46,970
+بديك إياها هو N الان احنا هقوله assume B
+
+310
+00:28:46,970 --> 00:28:47,550
+is true
+
+311
+00:28:51,590 --> 00:28:55,450
+هل هو ضروري الدارك تكون صح؟ ماعرفش بدي أجرب وبناء
+
+312
+00:28:55,450 --> 00:29:01,330
+على تجربتي بعد خطوات اتنين بشوف كيف الوضع M زائد
+
+313
+00:29:01,330 --> 00:29:05,430
+ال N is even و
+
+314
+00:29:05,430 --> 00:29:13,330
+N زائد ال B is even هذا بيقدر ان M زائد ال N equal
+
+315
+00:29:13,330 --> 00:29:23,020
+2K و N زائد ال B equal 2Hfor some K تنتمي إلى Z و
+
+316
+00:29:23,020 --> 00:29:27,220
+for some H تنتمي إلى Z for some K و H integers
+
+317
+00:29:27,220 --> 00:29:31,800
+تمام؟ بس هو في الطرف التاني إيش مستخدم هنا يا
+
+318
+00:29:31,800 --> 00:29:38,200
+شباب؟م زائد ال B يعني ال N مش في الحسبة ال N مش في
+
+319
+00:29:38,200 --> 00:29:43,020
+الحسبة و كأنه بيقول خاصيتي التعدي هنا حروح أنا بدي
+
+320
+00:29:43,020 --> 00:29:46,260
+أخد ال M لحالها و ياخد ال B لحالها بناء على
+
+321
+00:29:46,260 --> 00:29:52,660
+المعادلة هذه ال M مش بده تساوي اتنين K نقص ال M و
+
+322
+00:29:52,660 --> 00:29:58,300
+ال B بده تساوي اتنين H نقطة في ال N مصبوط اجمعهم
+
+323
+00:29:58,300 --> 00:30:04,660
+الآن مع المعادلة الخطوة اللي بعدهام زائد ب هو
+
+324
+00:30:04,660 --> 00:30:15,720
+المطلوب يساوي اتنين H اتنين K ناقص M زائد اتنين H
+
+325
+00:30:15,720 --> 00:30:26,920
+ناقص M ناجس M ناجس N ناجس اتنين M ايش تشيل؟ اتنين
+
+326
+00:30:26,920 --> 00:30:32,220
+K زائد اتنين H ناقص اتنين M ويساوي اتنين عامل
+
+327
+00:30:32,220 --> 00:30:40,810
+مشتركK زائد H نقص M اتنين مضبوطة في some integer
+
+328
+00:30:40,810 --> 00:30:46,710
+even خلصت
+
+329
+00:30:46,710 --> 00:30:53,230
+المسألة direct نعم ال M لحالها odd صح؟ مين قال؟
+
+330
+00:30:53,230 --> 00:30:57,170
+مين قال؟ اتنين K نقص واحد .. اتنين K نقصان و ليه؟
+
+331
+00:30:57,170 --> 00:30:59,470
+و ليه؟ و ليش لإن افترضتها نقد؟ لأنها ممكن تكون
+
+332
+00:30:59,470 --> 00:31:02,610
+even اتنين زائد أربعة ستة
+
+333
+00:31:04,600 --> 00:31:09,700
+بس اصبر احنا مالاش في قيمة n هو الذاك فرضيه ايش هي
+
+334
+00:31:09,700 --> 00:31:15,980
+فرضيته ان ال M زائد ال N عبارة عن even صح؟ يعني
+
+335
+00:31:15,980 --> 00:31:21,060
+اما ال M .. حسب ما احنا بنقعد M زائد N even يعني
+
+336
+00:31:21,060 --> 00:31:25,560
+يا اما التنين odd يا اما التنين even وبتاني ليش
+
+337
+00:31:25,560 --> 00:31:28,480
+دخل في هاللخمة أنا هاي؟ هو كل اللي قاللي ايه ايه M
+
+338
+00:31:28,480 --> 00:31:32,920
+زائد N is even معناته is even معناته M زائد N يكتب
+
+339
+00:31:32,920 --> 00:31:37,690
+على صورةأتنين K خلصت و هو بده مني ال N لحالها
+
+340
+00:31:37,690 --> 00:31:44,510
+فباخد ال N على الطرف التاني و خلصت تطلع ال N odd
+
+341
+00:31:44,510 --> 00:31:48,570
+تطلع even انا مابعننيش انا كانت اللي بيعنيني N
+
+342
+00:31:48,570 --> 00:31:52,150
+زائد ال N اللي هي ال even و انا حققتله إياها عشان
+
+343
+00:31:52,150 --> 00:31:55,630
+ايه مافيش داعي دايما احاول التفكير اللي انت فكرت
+
+344
+00:31:55,630 --> 00:32:00,830
+فيه صح بس انت وجعت وين انت افترضت ان هذي odd اذا
+
+345
+00:32:00,830 --> 00:32:04,310
+هذي odd لازم تكون ال N is oddبس في الآخر مجموعهم
+
+346
+00:32:04,310 --> 00:32:09,310
+even و لو كانت هذه even ال uneven عشان يكون
+
+347
+00:32:09,310 --> 00:32:11,830
+مجموعهم even فبالتالي ماليش دخل في الموضوع انا
+
+348
+00:32:11,830 --> 00:32:15,430
+يعني فبالتالي نمشي بالبرغام حسب المسألة اللي
+
+349
+00:32:15,430 --> 00:32:19,850
+موجودة عندي بالتدريج تتوجه ال contrapositive او ال
+
+350
+00:32:19,850 --> 00:32:23,450
+contradiction ممكن نجيب حل ال contrapositive ممكن
+
+351
+00:32:23,450 --> 00:32:27,050
+نجيب حل متوقع
+
+352
+00:32:27,050 --> 00:32:32,840
+ان ال contrapositive توصلي لحل اثباتفاكر .. قبل ما
+
+353
+00:32:32,840 --> 00:32:38,780
+تجاوب فاكر .. اه
+
+354
+00:32:38,780 --> 00:32:46,460
+يا عمر .. لأ .. ليش .. مش عارف .. غيره .. سواركي
+
+355
+00:32:46,460 --> 00:32:50,960
+.. ممكن ال contrapositive يوصلني لحال .. انت
+
+356
+00:32:50,960 --> 00:32:56,080
+سواركي .. مايرزعيل فاك .. انا بوصحكوا تدوش الجنسية
+
+357
+00:32:56,080 --> 00:33:04,780
+.. اه .. ممكن ..طيب اقولكوا شغلة انت تعالى تطلع
+
+358
+00:33:04,780 --> 00:33:11,940
+فيها هنا بدوش عندي M و B أصبت؟ و الطرف التاني فيه
+
+359
+00:33:11,940 --> 00:33:15,960
+عندي N طب ال N اللي انا بدأ افرضها شو بدأ افرضها؟
+
+360
+00:33:15,960 --> 00:33:19,980
+بدأ افرضها عدد زوجي ولا بدأ افرضها عدد فردي؟ مش
+
+361
+00:33:19,980 --> 00:33:25,220
+عارف وبالتالي ال contrapositive مابتمشيش معايا لكن
+
+362
+00:33:25,220 --> 00:33:29,180
+ال contradiction ممكن تصبط يا حمد؟ ال
+
+363
+00:33:29,180 --> 00:33:34,720
+contradiction ممكن تصبط؟ليش لأ؟ في الcontradiction
+
+364
+00:33:34,720 --> 00:33:38,640
+أنا إيش بده أقوله؟ بده أقوله B and not the Q وهذه
+
+365
+00:33:38,640 --> 00:33:42,520
+صورة هو إيه؟ صورة هي إيش؟ Odd فلما تشتغل نفس الشغل
+
+366
+00:33:42,520 --> 00:33:51,360
+هذا بس مع فرضية .. مع الفرضية أنها and not the Q
+
+367
+00:33:51,360 --> 00:33:58,860
+اللي هي M زائد B is not even لبين جوسين Odd
+
+368
+00:33:59,390 --> 00:34:03,350
+Contradiction بالتناقض هتشتغل مع هدوء تكتب نفس
+
+369
+00:34:03,350 --> 00:34:07,850
+الخطوات السابقة هتوصل ان ال M زي ال B is even
+
+370
+00:34:07,850 --> 00:34:11,270
+Contradiction مع مين؟ مع الفرضية اللى موجودة عندى
+
+371
+00:34:11,270 --> 00:34:17,590
+السابقة كمان؟ وبالتالي هي بدالك تتبعه في انحلت و
+
+372
+00:34:17,590 --> 00:34:23,610
+بالcontradiction انحلت اي حل اعتمد فيهم اي واحد اي
+
+373
+00:34:23,610 --> 00:34:28,330
+واحد اللى انت تقدر تجيبه في الامتحانطبعا لو انا
+
+374
+00:34:28,330 --> 00:34:33,290
+كنت بتقول لك استخدم ال contradiction تمام؟ و روحت
+
+375
+00:34:33,290 --> 00:34:41,290
+تبتليها بال direct بتاخد ال big zero اه مابقالله
+
+376
+00:34:41,290 --> 00:34:45,110
+اتعب هذا شسمه عند المجاولين انا ماخدش المجاولة لأ
+
+377
+00:34:45,110 --> 00:34:51,670
+و بالتالي .. لأ الكلامتين هدول يا سوستفان بيعنوا
+
+378
+00:34:51,670 --> 00:34:55,270
+انك انت فاهم ايش الطريقة اللي بتفرج هدى عن هدى
+
+379
+00:34:56,600 --> 00:35:00,300
+كمان؟ الان في التاسع عاش بقول ليه؟ استخدم ال proof
+
+380
+00:35:00,300 --> 00:35:03,780
+by contradiction to prove that .. بيقول استخدم
+
+381
+00:35:03,780 --> 00:35:08,320
+الأثبات بالتناقض عشان تثبت أن حاصل جامع irrational
+
+382
+00:35:08,320 --> 00:35:17,760
+number and rational number is irrational بس
+
+383
+00:35:17,760 --> 00:35:19,180
+المهم إيش الأولة و إيش التانية
+
+384
+00:35:30,010 --> 00:35:35,910
+بقول لك اثبت بالتناقض use proof by contradiction
+
+385
+00:35:35,910 --> 00:35:40,230
+to prove that عشان تثبت the sum of an irrational
+
+386
+00:35:40,230 --> 00:35:45,470
+number and rational number is irrational سؤال تسعة
+
+387
+00:35:45,470 --> 00:35:48,830
+اللي هو انا حاولت اكتبه بالخطة اللي مافيش فوق هذا
+
+388
+00:35:48,830 --> 00:35:58,110
+تمام الان عشان تحله بدك تعمله if then بي و كيو if
+
+389
+00:35:58,110 --> 00:35:59,810
+then if b then q
+
+390
+00:36:05,350 --> 00:36:19,650
+ال M is rational and ال M is irrational then ال M
+
+391
+00:36:19,650 --> 00:36:25,790
+زائد ال N is irrational
+
+392
+00:36:25,790 --> 00:36:31,070
+لأ
+
+393
+00:36:31,070 --> 00:36:37,210
+هو جايب يقولك شوفها مرة تانيةthe sum of an
+
+394
+00:36:37,210 --> 00:36:41,370
+irrational number and a rational number يعني واحد
+
+395
+00:36:41,370 --> 00:36:45,850
+rational واحد irrational اثبت انه حاصل جمعه
+
+396
+00:36:45,850 --> 00:36:53,350
+irrational irrational number طبعا كونه محدد لك
+
+397
+00:36:53,350 --> 00:37:01,190
+فانت مش هتتعب بالفرضية طيب الآن assume
+
+398
+00:37:06,570 --> 00:37:18,570
+B and not Q ايش يعني B؟ B M is rational و
+
+399
+00:37:18,570 --> 00:37:25,830
+هذا بيقدّي ان ال M equal A على B مصبوط A و B تنتمي
+
+400
+00:37:25,830 --> 00:37:30,470
+الى Z and ال B لا تسوى صفر هي تعريف ال rational
+
+401
+00:37:30,470 --> 00:37:34,110
+number M is rational تمام
+
+402
+00:37:35,610 --> 00:37:41,550
+الـ M is irrational و
+
+403
+00:37:41,550 --> 00:37:49,330
+لا Q و M زائد الـ N is rational
+
+404
+00:37:49,330 --> 00:37:56,830
+ايش يعني؟ برضه يُكتب على الصورة الفرضية
+
+405
+00:37:56,830 --> 00:38:01,850
+تبعتاش في الـ contradiction لا Q فالـ M زائد الـ N
+
+406
+00:38:05,110 --> 00:38:15,010
+يساوي X على Y X و Y تنتمي إلى Z و Y لا تساوي صفر و
+
+407
+00:38:15,010 --> 00:38:19,450
+حتى لو احنا ما كتبناهاش تمام الاصل تيجي لأنه خلاص
+
+408
+00:38:19,450 --> 00:38:23,790
+من تعريف rational تمام الخطوة اللي بعد هيك شو
+
+409
+00:38:23,790 --> 00:38:32,430
+بنسوي يا شباب؟ بدي اجمع ال M زائد ال N M زائد ال N
+
+410
+00:38:32,430 --> 00:38:44,200
+يساويA على B زائد ال N صح؟ يساوي X
+
+411
+00:38:44,200 --> 00:38:57,240
+على Y صح؟ بظهر؟ كمان هذا يؤدي ان ال N تساوي X على
+
+412
+00:38:57,240 --> 00:39:00,280
+Y لاقص A على B
+
+413
+00:39:06,700 --> 00:39:19,060
+يساوي واحد المقامات Y في B هتساوي B في X ناقص
+
+414
+00:39:19,060 --> 00:39:28,860
+Y في A أنا بقول هذا is rational ولا لا يا شباب؟
+
+415
+00:39:28,860 --> 00:39:38,880
+ليش rational؟ ليش rational؟ لأنهBX Integer YA
+
+416
+00:39:38,880 --> 00:39:44,220
+Integer حاصل ضرحهم Integer YB Integer و لا يساوي
+
+417
+00:39:44,220 --> 00:39:47,820
+صفر لأن ال Y لا تساوي صفر و ال B لا تساوي صفر يعني
+
+418
+00:39:47,820 --> 00:39:56,180
+أن ال N is rational وهذا Contradiction تناقض
+
+419
+00:39:56,180 --> 00:40:01,480
+لماذا؟ لأن أنا أعرف أن ال N is irrational لأن أعرف
+
+420
+00:40:01,480 --> 00:40:07,280
+أن ال N is irrationalوخلصنا معناته بنقدر نقول حاصل
+
+421
+00:40:07,280 --> 00:40:12,820
+جمع عدد rational عدد نسبي مع عدد غير نسبي بالكون
+
+422
+00:40:12,820 --> 00:40:13,600
+غير نسبي
+
+423
+00:40:41,300 --> 00:40:46,760
+في الـ 11 بقول لك prove or disprove اثبت او جيب
+
+424
+00:40:46,760 --> 00:40:51,000
+مثال او انفي طبعا لما تنفي تجيب مثال بيقول ان
+
+425
+00:40:51,000 --> 00:40:54,140
+الكلام هذا غير صحيح بيقول ان الكلام هذا غير صالح
+
+426
+00:40:54,140 --> 00:40:59,380
+اللي هو بتسميه counter example prove or disprove
+
+427
+00:40:59,380 --> 00:41:03,540
+that the product of two irrational numbers is
+
+428
+00:41:03,540 --> 00:41:08,340
+irrational حاصل ضرب اي عدد اي عددين غير نسبيين
+
+429
+00:41:08,340 --> 00:41:10,540
+بتديني عدد غير نسبي
+
+430
+00:41:15,930 --> 00:41:19,210
+بال contrapositive يعني انت بتقول ان الاهل الكلام
+
+431
+00:41:19,210 --> 00:41:23,870
+صحيح و بده اثبات بتقول
+
+432
+00:41:23,870 --> 00:41:31,110
+ان الكلام هذا صحيح و بده اثبات حاصل ضرب اي عددين
+
+433
+00:41:31,110 --> 00:41:37,450
+غير نسبيين بديني عدد غير نسبي بتعرفوا العدد الغير
+
+434
+00:41:37,450 --> 00:41:42,610
+نسبية انتوا؟ بتعرف ال by؟ بتعرف جذر التنين؟ هذه
+
+435
+00:41:42,610 --> 00:41:48,650
+عدد غير نسبيةأيوة هذا الكلام غير صحيح لو جربنا جذر
+
+436
+00:41:48,650 --> 00:41:54,150
+التنين في جذر التنين عدد نسبي في عدد غير نسبي في
+
+437
+00:41:54,150 --> 00:41:58,650
+عدد غير نسبي بيطلع تنين و التنين عدد نسبي طيب في
+
+438
+00:41:58,650 --> 00:42:02,470
+12 اما
+
+439
+00:42:02,470 --> 00:42:04,470
+هو انت الان روحت فانت جيها ال disapprove ال
+
+440
+00:42:04,470 --> 00:42:08,090
+disapprove بتقولهذا الكلام غير صحيح وهي counter
+
+441
+00:42:08,090 --> 00:42:13,110
+example جذر التنين يساوي 2 والتنين is rational
+
+442
+00:42:13,110 --> 00:42:17,870
+خلصنا في المسألة في التماعيش ماذا قاعد يقول؟ proof
+
+443
+00:42:17,870 --> 00:42:23,890
+or disproof the product of non rational number
+
+444
+00:42:23,890 --> 00:42:32,430
+يعني كل الإعداد المسبية معادل الصفرلو أخدت عدد
+
+445
+00:42:32,430 --> 00:42:36,010
+نسبي غير الصفر و ضربته في irrational بتديني
+
+446
+00:42:36,010 --> 00:42:41,270
+irrational number هذه true و بدها إثبات تمام؟ هذه
+
+447
+00:42:41,270 --> 00:42:45,230
+true و بدها إثبات ليش بدها إثبات؟ ليش true؟ لأن لو
+
+448
+00:42:45,230 --> 00:42:49,650
+ضربت اتنين في جزر التنين، اتنين جزر التنين عدد غير
+
+449
+00:42:49,650 --> 00:42:54,550
+نسبيمصبوط؟ نص في جذر التنين .. جذر التنين على
+
+450
+00:42:54,550 --> 00:42:58,930
+اتنين برضه عدد غير نسبي و هكذا لأن شرط المقام
+
+451
+00:42:58,930 --> 00:43:01,590
+البسط و المقام يجب يكون يتملوا لمين؟ للأعداد
+
+452
+00:43:01,590 --> 00:43:05,810
+الصحيحة .. و بالتالي هذه بدها إثبات .. إيش استخدام
+
+453
+00:43:05,810 --> 00:43:09,710
+معاها؟ Contrapositive ولا Contradiction ولا
+
+454
+00:43:09,710 --> 00:43:13,170
+Direct؟ فكر فيها زي ما بدك .. احنا أيها؟ اختح
+
+455
+00:43:13,170 --> 00:43:19,140
+لناها هان .. في تسعة .. احنا جمعناهم هان ..بس في
+
+456
+00:43:19,140 --> 00:43:22,240
+السؤال ده عمالش بيقول إيه؟ the product حاصل ضربهم
+
+457
+00:43:22,240 --> 00:43:26,760
+و من هنا بتفهم إيش حطلّك non-zero عشان لما بيبقى
+
+458
+00:43:26,760 --> 00:43:38,520
+تروح تجلب ماطلعش المكان صفر معاك طيب في 16
+
+459
+00:43:38,520 --> 00:43:45,060
+prove that if M and N are integers و حاصل ضربهم is
+
+460
+00:43:45,060 --> 00:43:45,440
+even
+
+461
+00:43:48,430 --> 00:43:55,590
+معناته واحد منهم is even شو رأيك هو؟ انا بقولك لو
+
+462
+00:43:55,590 --> 00:44:01,410
+أخدنا اي عددين صحيحين وضربناهم في بعض وطلع الناتج
+
+463
+00:44:01,410 --> 00:44:07,150
+عدد زوجي فهذا يعني ان واحد منهم على الأقل هيكون
+
+464
+00:44:07,150 --> 00:44:12,510
+عدد زوجي true true يعني انك تثبتها يا باشا true
+
+465
+00:44:12,510 --> 00:44:17,700
+يعني انك تثبت تتجدم بثبات رياضيلأن انا بقولك both
+
+466
+00:44:17,700 --> 00:44:24,720
+الان كمان مرة اش و بقولك ستاش if ال M في N is even
+
+467
+00:44:24,720 --> 00:44:36,940
+then ال N ال M is even or ال N is even او لو كانوا
+
+468
+00:44:36,940 --> 00:44:43,880
+اتنين صح هاي ال F و ال then contradiction ولا
+
+469
+00:44:43,880 --> 00:44:45,520
+contrapositive ولا direct
+
+470
+00:44:48,500 --> 00:44:51,920
+الـ Direct والعمرها بتجيب معاك نتيجة
+
+471
+00:44:51,920 --> 00:44:55,680
+Contrapositive او Contradiction هدول اللي ممكن
+
+472
+00:44:55,680 --> 00:45:00,880
+يجيبوا معاك ليش يا شباب لأن هنا M و N is even يعني
+
+473
+00:45:00,880 --> 00:45:11,340
+كتيرك هتقول ليه M N equal 2K M بدها تساوي 2K على N
+
+474
+00:45:11,340 --> 00:45:18,950
+ولو قمتلي هيك ماحدش بضمن ان هذا ينتمي الى Zفي حد
+
+475
+00:45:18,950 --> 00:45:24,450
+يفتيلنا فيه هذا؟ لأ ممتاز integer على integer مش
+
+476
+00:45:24,450 --> 00:45:29,530
+ضروري يكون integer اتنين على اربعة تلاتة على اتنين
+
+477
+00:45:29,530 --> 00:45:33,030
+مش ضروري يكون integer وبالتالي اذا هذه مش هذه مش
+
+478
+00:45:33,030 --> 00:45:37,230
+مضمونة بالتالي ال direct proof لقد مسكرة
+
+479
+00:45:37,230 --> 00:45:46,130
+contrapositive بتصير و contradiction بتصير تمام؟
+
+480
+00:45:46,130 --> 00:45:54,220
+بتروح تقولها assumeنطق U يعني ال M is odd and ال M
+
+481
+00:45:54,220 --> 00:45:57,740
+is odd اتنين K زائد واحد اتنين H زائد واحد و
+
+482
+00:45:57,740 --> 00:46:06,560
+تضربهم في بعض هتقل معاك ايه .. خطأ هتقل معاك odd
+
+483
+00:46:06,560 --> 00:46:14,060
+الأصل اتنين K اتنين K زائد واحد في اتنين H زائد
+
+484
+00:46:14,060 --> 00:46:25,220
+واحد2K اربع KH زائد 2K زائد 2H زائد واحد هلخد هدول
+
+485
+00:46:25,220 --> 00:46:32,820
+عامل مشترك التنين 2 في 2KH زائد K زائد H زائد واحد
+
+486
+00:46:32,820 --> 00:46:39,480
+هذا odd Contrapositive ولو افترضت انت B and not Q
+
+487
+00:46:39,480 --> 00:46:47,050
+في ال contradiction B is evenو نقطة Q هيها مظبوط
+
+488
+00:46:47,050 --> 00:46:51,710
+يعني هدولة odd هتحل نفس الحل هذا و في الآخر هتقول
+
+489
+00:46:51,710 --> 00:46:55,810
+إنه هذا بتناقض أو contradiction لأ بس في الحالة
+
+490
+00:46:55,810 --> 00:46:59,790
+هذه إحنا لما قولنا assume نقطة Q مفروض نقول هنا
+
+491
+00:46:59,790 --> 00:47:04,650
+Contra positive ليش؟
+
+492
+00:47:04,650 --> 00:47:09,290
+اللي هي بين جسين نقطة ال B نقطة ال B نقطة Q وصلتني
+
+493
+00:47:09,290 --> 00:47:12,150
+لنقطة ال B 17
+
+494
+00:47:14,660 --> 00:47:19,180
+إذا الـ N هو إنتجار N is an integer بس بقولك الـ N
+
+495
+00:47:19,180 --> 00:47:25,320
+is integer حتى الآن and ال
+
+496
+00:47:25,320 --> 00:47:30,780
+N زائد خمسة is odd وكأنه بقولك if ال N تكعيب زائد
+
+497
+00:47:30,780 --> 00:47:39,020
+الخمسة is odd then ال N is even جاهزة جاهزة يعني
+
+498
+00:47:39,020 --> 00:47:48,540
+قاعد أبديكيها if N تكعيب زائد خمسةis odd than and
+
+499
+00:47:48,540 --> 00:47:54,760
+is even و بيقولك اما بتثبتها بال contrapositive او
+
+500
+00:47:54,760 --> 00:47:58,760
+بالcontradiction ايوة
+
+501
+00:47:58,760 --> 00:48:02,760
+انا بدي اختار انا اختار الواحدة عشان احلها بواحدة
+
+502
+00:48:02,760 --> 00:48:04,600
+و التانية عليك خلاص مابديهاش كلام يعني
+
+503
+00:48:04,600 --> 00:48:08,440
+contradiction or contraposition position positive
+
+504
+00:48:08,440 --> 00:48:13,370
+مش فارقة كتير دي لبالك في المصطلح يعني اه شبابأنا
+
+505
+00:48:13,370 --> 00:48:24,530
+هحل واحدة بس مش هحل التنتين والله
+
+506
+00:48:24,530 --> 00:48:27,550
+التنتين ميفرجوا معاك ولا حاجة في الآخر بس لإن في
+
+507
+00:48:27,550 --> 00:48:32,610
+كل الأحوال انت بدك تفرض B ونبت Q صح؟ بس هذي تصير
+
+508
+00:48:32,610 --> 00:48:40,510
+نبت Q بدون ال B وحتين مش هيتصل عكسها طيب assume B
+
+509
+00:48:40,510 --> 00:48:41,530
+and
+
+510
+00:48:50,640 --> 00:49:00,740
+not even is not
+
+511
+00:49:00,740 --> 00:49:04,960
+even
+
+512
+00:49:04,960 --> 00:49:05,560
+يعني odd
+
+513
+00:49:12,280 --> 00:49:16,640
+يعني بين جثين odd الخطوة اللي بعد هيك مناته n
+
+514
+00:49:16,640 --> 00:49:30,300
+تساوي 2k زائد 1 و ال k تنتمي إلى z طيب بدك
+
+515
+00:49:30,300 --> 00:49:34,500
+اتعود غير في المسألة اللي فوق هذا يؤدي ان ال n
+
+516
+00:49:34,500 --> 00:49:45,010
+تكعيب زائد 5 تساوي2K زائد واحد لكل تكييب زائد خمسة
+
+517
+00:49:45,010 --> 00:49:53,690
+وهذه تساوي 2K زائد واحد مضروبة فيه 4K تربيع زائد
+
+518
+00:49:53,690 --> 00:50:02,810
+4K زائد واحد صح؟ ليش عكس الإشارة؟ طب ما الإشارة
+
+519
+00:50:02,810 --> 00:50:07,990
+عندي موجة بفوق زائد صح؟
+
+520
+00:50:08,360 --> 00:50:12,540
+أنت في السالب تحكز الإشارة وبعدين أنا روحت معاك
+
+521
+00:50:12,540 --> 00:50:20,600
+على شغل أسهل حتى لو كانت 2k-1 تكعيب عشان ما
+
+522
+00:50:20,600 --> 00:50:25,320
+اتخرطتش في الإشارة أنا ايش افترضتها هي عبارة عن 2k
+
+523
+00:50:25,320 --> 00:50:31,800
+-1 في 2k-1 تربيع حالة المربع حدا لحاله تربيع الأول
+
+524
+00:50:31,800 --> 00:50:34,860
+الأول
+
+525
+00:50:34,860 --> 00:50:39,210
+في التربيع التانيواحد زي الأول في التاني في اتنين
+
+526
+00:50:39,210 --> 00:50:44,850
+ماقص اربع K زائد واحد وروحت بدربهم في بعض بالشكل
+
+527
+00:50:44,850 --> 00:50:49,390
+هذا فانا روحت لك على شغل أسهل ما أنا كنتاش لأنه
+
+528
+00:50:49,390 --> 00:50:53,570
+متوقع ومتأكد انه حصلوا فيه خربطة في الموضوع حل
+
+529
+00:50:53,570 --> 00:50:59,890
+التكعيب خصوصا لما تكون الإشارات زي بعضها تساوي
+
+530
+00:50:59,890 --> 00:51:07,350
+تمانية K التكعيب زائدزائد الخمسة أنا ماعش الحل بس
+
+531
+00:51:07,350 --> 00:51:13,150
+برا عملت الضرب زائد تمانية ك تربيع زائد اتنين ك
+
+532
+00:51:13,150 --> 00:51:19,850
+زائد اربعة ك تربيع زائد اربعة ك زائد واحد زائد
+
+533
+00:51:19,850 --> 00:51:30,890
+خمسة وهذه تساوي تمانية ك تكعيب زائد
+
+534
+00:51:30,890 --> 00:51:35,960
+تربيع هي تمانية وانا اربعة اتماشىمعشر ك تربيع زائد
+
+535
+00:51:35,960 --> 00:51:43,100
+ستة ك زائد ستة خد التانين على المشترك تصير اتنين
+
+536
+00:51:43,100 --> 00:51:48,560
+مضغوبة في اربعة ك تربيع تكعيب زائد ستة ك تربيع
+
+537
+00:51:48,560 --> 00:51:56,320
+زائد تلاتة ك زائد تلاتة اتنين في انتجار even
+
+538
+00:51:56,320 --> 00:52:02,080
+معناته احنا حصلنا على contradictionلأن المفروض هذي
+
+539
+00:52:02,080 --> 00:52:08,580
+تكون إيش؟ Odd طب في الـ Contrapositive هروح أنا
+
+540
+00:52:08,580 --> 00:52:13,340
+أقول له assume not Q هيا و همشي معاها هيك أصلا مين
+
+541
+00:52:13,340 --> 00:52:18,160
+أن هذي عبارة عن even و هي not ال B وبالتالي حصلت
+
+542
+00:52:18,160 --> 00:52:22,160
+على Contrapositive تمام الأمور يا شباب؟ اعتقد ..
+
+543
+00:52:22,160 --> 00:52:27,540
+اعتقد بعد هيك .. احنا بدلنا جهد كويس أنا وجد داعمك
+
+544
+00:52:27,540 --> 00:52:31,530
+في الأمثلة و مع الأسئلةالمفروض ان ترجع على الأسئلة
+
+545
+00:52:31,530 --> 00:52:35,530
+هذه سواء حلتها او ماحلتهاش و تبدأ تحلها عندك عليش
+
+546
+00:52:35,530 --> 00:52:39,390
+على ورقة لان هذه مفتاح حل اي سؤال لاحقا ان شاء
+
+547
+00:52:39,390 --> 00:52:42,010
+الله تبارك وتعالى ماشي الحال يا شباب؟ فى حد عنده
+
+548
+00:52:42,010 --> 00:52:44,390
+اي سؤال في محاضرتنا الجاية هنتكلم عن ال
+
+549
+00:52:44,390 --> 00:52:47,750
+mathematical induction هنشرح ال concept ونروح على
+
+550
+00:52:47,750 --> 00:52:50,470
+ال section ونشوف الأسئلة اللى موجودة عليه ونختارنا
+
+551
+00:52:50,470 --> 00:52:54,990
+كام سؤال زى كده ونحلهم ونكون خلصنا الجزئيةاللي
+
+552
+00:52:54,990 --> 00:52:57,430
+احنا حكيناها من البداية اللي هي البعض
+
+553
+00:52:57,430 --> 00:53:00,370
+الاستراتيجيات انك تحاول تجسم ال set اللي موجودة
+
+554
+00:53:00,370 --> 00:53:05,870
+عندك لما بيقولك أن تربيع أكبر من صفر أو أكبر من أن
+
+555
+00:53:05,870 --> 00:53:10,870
+لكل الأعداد الموجبة أو لكل الأعداد الصحيحة او لكل
+
+556
+00:53:10,870 --> 00:53:15,290
+الأعداد الموجبة او لكل الأعداد الصحيحة او لكل
+
+557
+00:53:15,290 --> 00:53:17,890
+الأعداد الصحيحة او لكل الأعداد الموجبة او لكل
+
+558
+00:53:17,890 --> 00:53:18,310
+الأعداد الصحيحة او لكل الأعداد الصحيحة او لكل
+
+559
+00:53:18,310 --> 00:53:18,390
+الأعداد الصحيحة او لكل الأعداد الصحيحة او لكل
+
+560
+00:53:18,390 --> 00:53:19,930
+الأعداد الصحيحة او لكل الأعداد الصحيحة او لكل
+
+561
+00:53:19,930 --> 00:53:20,690
+الأعداد الصحيحة او لكل الأعد
+
diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/rqvb-KVP0rg_postprocess.srt b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/rqvb-KVP0rg_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..d2205e88ca08e6fd2f3701ec06dbe53bb741322c
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/rqvb-KVP0rg_postprocess.srt
@@ -0,0 +1,2808 @@
+1
+00:00:21,190 --> 00:00:23,730
+طيب شباب بسم الله والحمد لله والصلاة والسلام على
+
+2
+00:00:23,730 --> 00:00:25,750
+رسول الله اليوم ان شاء الله هنبدأ بال chapter
+
+3
+00:00:25,750 --> 00:00:30,430
+الرابع اللي هو number theory and cryptography ليش
+
+4
+00:00:30,430 --> 00:00:35,170
+مهتم احنا بال number theory او نظرية الاعداد نظرية
+
+5
+00:00:35,170 --> 00:00:37,610
+الاعداد من ال .. او اللي هو العلم اللي بيهتم
+
+6
+00:00:37,610 --> 00:00:40,910
+بدراسة الاعداد او ال integers الاعداد الصحيحة
+
+7
+00:00:40,910 --> 00:00:48,190
+وخلاصها و اهمفكرة في موضوع نظرية الأعداد هي خاصية
+
+8
+00:00:48,190 --> 00:00:54,030
+القسمة أو عملية القسمة والأعداد الأولية ليش؟ هنشوف
+
+9
+00:00:54,030 --> 00:00:58,990
+كمان شوية تطبيقين .. تطبيقات من المستخدمات في علوم
+
+10
+00:00:58,990 --> 00:01:03,390
+الحسوب تمثيل اللي هنشوف كذلك لما نتكلم عن تمثيل
+
+11
+00:01:03,390 --> 00:01:05,870
+الأعداد احنا كلنا بنعرف ال binary من أين اتت فكرة
+
+12
+00:01:05,870 --> 00:01:09,010
+ال binary و ال octal و ال hexadecimal؟ من الأعداد
+
+13
+00:01:09,010 --> 00:01:12,350
+وبالتالي صار لنا نقدر نتكلم عن تمثيل ال integers
+
+14
+00:01:12,350 --> 00:01:13,530
+اللي موجودة عندها
+
+15
+00:01:16,360 --> 00:01:20,440
+الافكار اللى موجودة دائما فهو فعل نظرية الأعداد
+
+16
+00:01:20,440 --> 00:01:24,900
+تشغل الدماغ بشكل كويس لإنه فعليا أحيان بتحس أن
+
+17
+00:01:24,900 --> 00:01:29,460
+النظريات أو العيوم اللى موجودة شغلة و أنت بتفكر
+
+18
+00:01:29,460 --> 00:01:36,280
+فيها بتستمتع عشان هيك في ناس كتير بيقولك .. ناس
+
+19
+00:01:36,280 --> 00:01:39,960
+اللى بتنجذب لعلم الرياضيات أو لعلم نظرية الأعداد
+
+20
+00:01:39,960 --> 00:01:45,570
+بالدرجة الأولى بتجذبها أيش؟ جمال الأفكارفي الموضوع
+
+21
+00:01:45,570 --> 00:01:49,590
+هذا طبعا لو اتكلم مع جماعة الأفكار معناته الشيء
+
+22
+00:01:49,590 --> 00:01:54,790
+اللي بتحسه عن جد و انت بتدرس في الموضوع انه على
+
+23
+00:01:54,790 --> 00:01:57,330
+خلاف الرياضيات اللي احنا بنعرفها على رغم انه علمها
+
+24
+00:01:57,330 --> 00:01:59,730
+من ال pure mathematics يعني المفروض انه من العلوم
+
+25
+00:01:59,730 --> 00:02:05,230
+الصعبة اللي غير انه لأن تطبيقاته ملموسة تمام فبتحس
+
+26
+00:02:05,230 --> 00:02:09,880
+ان فيها فكرة كويسةنجيك ان القيامة للناس القديمة من
+
+27
+00:02:09,880 --> 00:02:13,920
+زمان كانوا بتعاملوا مع نظرية الاعداد الموجودة هل
+
+28
+00:02:13,920 --> 00:02:18,600
+ال sections الخمسة او الستة الموجودة خوص القسمة و
+
+29
+00:02:18,600 --> 00:02:22,080
+تمثيل الاعداد الـprimes و كيف ال congrance و
+
+30
+00:02:22,080 --> 00:02:24,380
+انحلهم ال application سبعتهم و ال cryptography
+
+31
+00:02:24,380 --> 00:02:28,320
+اللي هو اخر section هيكون موجود عندنا هنخلص غالبا
+
+32
+00:02:28,320 --> 00:02:31,240
+هنغطسه ال section واحد و اتنين اليوم ان شاء الله
+
+33
+00:02:31,240 --> 00:02:34,860
+تعالىقولها نظرية الأعداد هو العلم اللي باهتم
+
+34
+00:02:34,860 --> 00:02:40,420
+بدراسة الأرقام الأعداد الصحيحة وخواصها و أهم خاصية
+
+35
+00:02:40,420 --> 00:02:48,540
+خاصية القسمة لما باجي بقول الشباب A تقسم ال B
+
+36
+00:02:48,540 --> 00:02:53,280
+مباشرة بدي تبقى برا ذهنك ان ال D او ال A هي ال
+
+37
+00:02:53,280 --> 00:02:57,500
+divisor ايش
+
+38
+00:02:57,500 --> 00:03:03,720
+يعني؟القاسم القاسم كانوا يعلمونا زمان في عندي في
+
+39
+00:03:03,720 --> 00:03:09,160
+كل عملية قسمة في عندي مقسوم و مقسوم عليه اللي هو
+
+40
+00:03:09,160 --> 00:03:14,840
+ال divisor و معامل القسمة او ناتج القسمة و الباقي
+
+41
+00:03:14,840 --> 00:03:20,220
+remainder باقي القسمة يعني لو اتيت انا قلتلك جسم
+
+42
+00:03:20,220 --> 00:03:23,140
+17 على 3
+
+43
+00:03:29,180 --> 00:03:37,840
+17 على 3 تساوي 5 تمام؟ و 2 as
+
+44
+00:03:37,840 --> 00:03:41,120
+a remainder و بينجو سينم لك تبقى بصيغة بالشكل هذا
+
+45
+00:03:41,120 --> 00:03:52,680
+3 ضرب 5 زائد 2 هذا تساوي من 17 17 تساوي 3 في 5
+
+46
+00:03:52,680 --> 00:03:58,690
+زائد 2 3 هي القاسم او المقسوم عليهQuantity يعني
+
+47
+00:03:58,690 --> 00:04:01,750
+كمية
+
+48
+00:04:01,750 --> 00:04:08,070
+والباقي ال remainder اللى موجود عندها وبالتالي لما
+
+49
+00:04:08,070 --> 00:04:13,130
+باجب اقول a divides ال b او ال a تقسم ال b معناته
+
+50
+00:04:13,130 --> 00:04:22,340
+انا جاهز بقول ان ال b من مضاعفاتالـ A Divides يعني
+
+51
+00:04:22,340 --> 00:04:27,640
+تقسم أن الـ B من مضاعفات الـ A طبق القسمة صفر مش
+
+52
+00:04:27,640 --> 00:04:33,060
+موجود لما باجي بقول التلاتة تقسم التمنعش التلاتة
+
+53
+00:04:33,060 --> 00:04:37,750
+تقسم الواحد وعشرينالـ3 لا تقسم الـ17، لماذا لا
+
+54
+00:04:37,750 --> 00:04:41,590
+تقسم الـ17؟ لأن في عندي باقي قسمة، لأن في عندي
+
+55
+00:04:41,590 --> 00:04:45,930
+باقي قسمة، فالمفهوم الـdivides أنه أنا ماعنديش
+
+56
+00:04:45,930 --> 00:04:50,590
+باقي قسمة، ماعنديش باقي قسمة، ولمّا بقول A divides
+
+57
+00:04:50,590 --> 00:04:56,230
+الـB، A divides الـB، أول حاجة الـA ليه تسوى صفر؟
+
+58
+00:04:56,230 --> 00:05:02,280
+لأن القسمة على صفر عملية غير معرفةمعناته بلاقي
+
+59
+00:05:02,280 --> 00:05:05,640
+integer C بحيث ان الـ B تساوي A في C وهذا معناته
+
+60
+00:05:05,640 --> 00:05:18,900
+ان الـ B من المضاعفات الـ A لما
+
+61
+00:05:18,900 --> 00:05:24,420
+بلاقي A تقسم الـ B و الـ A تقسم الـ C معناته الـ A
+
+62
+00:05:24,420 --> 00:05:35,010
+بتقسم مجموحهم الآن اذا كانت الـ Aالتلاتة تقسم
+
+63
+00:05:35,010 --> 00:05:41,310
+التسعة بالظبط التلاتة تقسم الخمستاش مباشرة انا
+
+64
+00:05:41,310 --> 00:05:46,050
+بقول التلاتة تقسم الاربع عشرين الاربع عشرين عبارة
+
+65
+00:05:46,050 --> 00:05:53,170
+عن ايش؟ اللي هي تسعة زاد الخمستاش بالظبط فبالتالي
+
+66
+00:05:53,170 --> 00:05:58,510
+و لا بتلاقي ان ال a تقسم b يعني ال b من المضاعفات
+
+67
+00:05:59,740 --> 00:06:03,680
+الـ A والـ A تقسم الـ C .. C يعني المضاعفات الـ A
+
+68
+00:06:03,680 --> 00:06:09,640
+فحصل جمعهم هيكون من المضاعفات الـ A تعالي شوية بس
+
+69
+00:06:09,640 --> 00:06:14,460
+.. هيا عشان أقولك ليش هذا الكلام إيجي صح؟ قول لما
+
+70
+00:06:14,460 --> 00:06:17,920
+تكون A من المضاعفات أو الـ B من المضاعفات الـ C أو
+
+71
+00:06:17,920 --> 00:06:21,520
+الـ B من المضاعفات الـ A معناته بيبدأ تساوي افترض
+
+72
+00:06:21,520 --> 00:06:30,200
+A برب K واحد والـ K تمتمي للـ Z عدد صحيحوالـ C
+
+73
+00:06:30,200 --> 00:06:33,140
+كذلك الـ A تقسم الـ C يعني الـ C من مضاعفات الـ A
+
+74
+00:06:33,140 --> 00:06:41,760
+الـ C بتها تساوي A في K اتنين مصبوط اجمع اجمع الان
+
+75
+00:06:41,760 --> 00:06:50,080
+B وزائد C B زائد C ايش يساوي الشباب A K واحد زائد
+
+76
+00:06:50,080 --> 00:06:55,080
+A K اتنين وتساوي خد ال A عامل مشترك A في K واحد
+
+77
+00:06:55,080 --> 00:07:00,120
+زائد K اتنين هذا العدد ينتميللـ Z ده الأعداد
+
+78
+00:07:00,120 --> 00:07:05,180
+الصحيحة مظبوط وبالتالي أصبح العدد هذا من مضاعفات
+
+79
+00:07:05,180 --> 00:07:09,100
+ال A هيه من مضاعفات ال A عشان هيك بنقول إن ال A
+
+80
+00:07:09,100 --> 00:07:13,920
+تقسم ال B A تقسم ال C معناته ال A تقسم B زائد C
+
+81
+00:07:13,920 --> 00:07:20,820
+أنا مش هطلبك بأي أثبات رياضي لكن بدي دايما تستحضر
+
+82
+00:07:20,820 --> 00:07:24,800
+أو تحاول تسأل نفسك ليش؟ ليش الأعمالية هذه بتصير صح
+
+83
+00:07:24,800 --> 00:07:25,520
+أو غلط؟
+
+84
+00:07:30,610 --> 00:07:36,470
+الان if a تقسم ال b معناته
+
+85
+00:07:36,470 --> 00:07:43,130
+a تقسم ال b لأي integer c ايش يعني مفهومها ان ال b
+
+86
+00:07:43,130 --> 00:07:46,950
+هي قيمتها من المضاعفات اللي موجودة او ايش ما كانت
+
+87
+00:07:46,950 --> 00:07:48,770
+ال b هي ال c اللي هتطلع عندى
+
+88
+00:07:51,550 --> 00:07:55,630
+هل التلاتة تقسم الستة لحالها و بس؟ لأ تقسم الستة
+
+89
+00:07:55,630 --> 00:08:00,050
+تقسم التسعة عشر خمس عشر كمان عشر واحد و عشرين كل
+
+90
+00:08:00,050 --> 00:08:03,290
+مضاعفات التلاتة التلاتة بتبقى ثابتة و ميه اللي
+
+91
+00:08:03,290 --> 00:08:06,990
+بيختلف ال constant اللي أنا بضربه فيه في التلاتة
+
+92
+00:08:06,990 --> 00:08:09,610
+اللي بيمثل المضاعف عشان هيك بقول ان هذه بتكون
+
+93
+00:08:09,610 --> 00:08:15,150
+صحيحة لأي integer لأي integer C طيب لو كانت ال A
+
+94
+00:08:15,150 --> 00:08:21,190
+تقسم ال B و ال B تقسم ال C معناته ال A تقسم ال C
+
+95
+00:08:22,350 --> 00:08:28,590
+طيب التعدى ايه سمناها عندما تكلمنا عن ال
+
+96
+00:08:28,590 --> 00:08:34,530
+relations؟ حد بتذكر ايه سمنا خاصيتي التعدى؟
+
+97
+00:08:34,530 --> 00:08:39,570
+Transitive خاصيتي التعدى لو كانت ال a تقسم ال b
+
+98
+00:08:39,570 --> 00:08:47,190
+and ال b تقسم ال c معناه هذا يؤدي إلى ان ال a تقسم
+
+99
+00:08:47,190 --> 00:08:50,970
+ال c صح؟
+
+100
+00:08:51,760 --> 00:08:56,700
+طيب نحاول نثبتها على السريع بس المهاتب ال B بيضها
+
+101
+00:08:56,700 --> 00:09:05,180
+تساوي A في K تمام؟ و ال C بيضها تساوي B في K واحد
+
+102
+00:09:05,180 --> 00:09:17,300
+عوّب عن ال بيها A K لقيمة ال B في K واحد بتساوي A
+
+103
+00:09:17,300 --> 00:09:25,920
+في K في K واحدأصبحت ان الـ C هادي من المضاعفات الـ
+
+104
+00:09:25,920 --> 00:09:30,440
+A وبالتالي تقسم الـ A تقسم الـ C كمان مرة إذا الـ
+
+105
+00:09:30,440 --> 00:09:35,180
+A تقسم الـ B و الـ B تقسم الـ C معناته الـ A تقسم
+
+106
+00:09:35,180 --> 00:09:40,740
+الـ C كيف؟
+
+107
+00:09:40,740 --> 00:09:48,180
+عملنا رقم ماشي الحال الآن لو أنا اديت قلت التلاتة
+
+108
+00:09:48,180 --> 00:10:01,560
+تقسم التسعة andتسعة تقسم الواحد و تمانين تقسم
+
+109
+00:10:01,560 --> 00:10:04,320
+الواحد و تمانين تقسم الواحد و تمانين تقسم الواحد و
+
+110
+00:10:04,320 --> 00:10:04,400
+تمانين تقسم الواحد و تمانين تقسم الواحد و تمانين
+
+111
+00:10:04,400 --> 00:10:04,560
+الواحد و تمانين تقسم الواحد و تمانين تقسم الواحد و
+
+112
+00:10:04,560 --> 00:10:05,480
+تمانين تقسم الواحد و تمانين تقسم الواحد و تمانين
+
+113
+00:10:05,480 --> 00:10:05,500
+الواحد و تمانين تقسم الواحد و تمانين تقسم الواحد و
+
+114
+00:10:05,500 --> 00:10:08,440
+تمانين تقسم الواحد و تمانين تقسم الواحد و تمانين
+
+115
+00:10:08,440 --> 00:10:17,410
+تقسم الواحد و تمانين تقسم الواحد و تمانين تتقسم
+
+116
+00:10:17,410 --> 00:10:26,890
+التسعة تقسم التمنطعش التلاتة تقسم التمنطعش تقسم
+
+117
+00:10:26,890 --> 00:10:28,770
+التمنطعش تقسم التمنطعش تقسم التمنطعش تقسم التمنطعش
+
+118
+00:10:28,770 --> 00:10:28,930
+تقسم التمنطعش تقسم التمنطعش تقسم التمنطعش تقسم
+
+119
+00:10:28,930 --> 00:10:32,070
+التمنطعش تقسم التمنطعش تقسم التمنطعش تقسم التمنطعش
+
+120
+00:10:32,070 --> 00:10:34,170
+تقسم التمنطعش تقسم التمنطعش تقسم التمنطعش تقسم
+
+121
+00:10:34,170 --> 00:10:38,310
+التمنطعش تقسم التمنطعش تقسم التمنطعش تقسم التمنطعش
+
+122
+00:10:38,310 --> 00:10:43,070
+تقسم التمنطعش تقسم التمنطعش تقسم التمنطعش تقسم
+
+123
+00:10:43,070 --> 00:10:44,190
+التمنطعش تقسم التمنطعش تقسم التمنطعش تقسم التمنط
+
+124
+00:10:44,620 --> 00:10:53,580
+الان اذا ماكنش الرقم العدد
+
+125
+00:10:53,580 --> 00:10:59,420
+المقصوم لو ماكنش من مضاعفات ال divisor معناته حتما
+
+126
+00:10:59,420 --> 00:11:04,360
+هقدر اكتب على صورة معادلة كمية مضغوبة في ال
+
+127
+00:11:04,360 --> 00:11:10,950
+divisor زائد remainder يعني الآن 17ما هي علاجاتها
+
+128
+00:11:10,950 --> 00:11:14,930
+بالتلاتة؟ هل هي مباعثات التلاتة؟ لأ، لكن بقدر أقول
+
+129
+00:11:14,930 --> 00:11:18,730
+السبعة عشر تساوي التلاتة كـ divisor مضروبة في
+
+130
+00:11:18,730 --> 00:11:22,790
+خمسة، تمام؟ وهذه الخمسة بسميها الـ quotient أو
+
+131
+00:11:22,790 --> 00:11:27,810
+الكمية، تمام؟ أو ناتج القسمة، زائد اتنين، الـ
+
+132
+00:11:27,810 --> 00:11:33,770
+remainder، باقى القسمة، الأن تبقي معايا ال
+
+133
+00:11:33,770 --> 00:11:39,770
+divisor لازم يكون positive integerالـ divisor لازم
+
+134
+00:11:39,770 --> 00:11:48,130
+يكون positive integer طيب لو كانت الرقم سالب سالب
+
+135
+00:11:48,130 --> 00:11:56,490
+17 شوف انها تساوي او سالب 15 ثلاثة
+
+136
+00:11:56,490 --> 00:12:00,790
+في سالب خمسة الكمية ممكن تكون بالسالب الكمية اللي
+
+137
+00:12:00,790 --> 00:12:05,390
+عندي هذه او ال quotient ممكن تكون بالسالببس ال
+
+138
+00:12:05,390 --> 00:12:10,510
+remainder لأ ال remainder ميزته او خصائصه ان هو
+
+139
+00:12:10,510 --> 00:12:15,490
+اكبر او تساوي الصفر و اقل او تساوي ال D فإذا كانت
+
+140
+00:12:15,490 --> 00:12:19,330
+ال D positive ال divisor يعني ال R لازم تكون
+
+141
+00:12:19,330 --> 00:12:24,730
+positive لأنها اكبر او تساوي الصفر تمام لما باج
+
+142
+00:12:24,730 --> 00:12:32,470
+انا بقول كمان مرة هي المعادلة A تساوي D Q زائد ال
+
+143
+00:12:32,470 --> 00:12:38,040
+Rالـ R محصورة ما بين الصفر والـ D أكبر أو تساوي
+
+144
+00:12:38,040 --> 00:12:47,680
+الصفر أو أقل من الـ D A Divident المقسوم D Divisor
+
+145
+00:12:47,680 --> 00:12:54,220
+القاسم Q Quotient كمية أو ناتج القسمة والـ R
+
+146
+00:12:54,220 --> 00:12:59,500
+remainder أو بقى القسمة لما أنا بدي أجري أقول
+
+147
+00:12:59,500 --> 00:13:00,140
+كتالي
+
+148
+00:13:02,780 --> 00:13:07,720
+تلاتة و عشرين تساوي
+
+149
+00:13:07,720 --> 00:13:10,960
+لو انا اخترت التنين as divisor بيمشي الحلولة يا
+
+150
+00:13:10,960 --> 00:13:20,300
+شباب بيمشي مضوبة فيه اتنين في احداشر اتنين و عشرين
+
+151
+00:13:20,300 --> 00:13:31,280
+زائد واحد مباشرة الان divisor quantity a quotient
+
+152
+00:13:32,390 --> 00:13:37,750
+Reminder بقى قسمة لما يكون الرقم سالب يجب أن تحافظ
+
+153
+00:13:37,750 --> 00:13:41,830
+على نفس المعادلة لما يكون الرقم سالب يجب أن تحافظ
+
+154
+00:13:41,830 --> 00:13:44,870
+على نفس المعادلة ايش هنتحافظ على نفس المعادلات انه
+
+155
+00:13:44,870 --> 00:13:50,870
+دائما ال divisor positive و ال reminder positive
+
+156
+00:13:50,870 --> 00:13:59,670
+تعالج يقول سالب 23 مع ال divisor 2 تساوي
+
+157
+00:14:03,380 --> 00:14:09,280
+-11 ايه صارت؟ نقص 22 عشان تصير سالب 23 بدي اعمل
+
+158
+00:14:09,280 --> 00:14:13,540
+نقص 1 وهي ما صارت انا و جاعت في غلط لانه لازم ال
+
+159
+00:14:13,540 --> 00:14:20,080
+remainder يكون positive فايش الحل اضرب
+
+160
+00:14:20,080 --> 00:14:29,440
+في 12 صارت سالب 24 زائد ال 1 نفس
+
+161
+00:14:29,440 --> 00:14:32,200
+الكلام اللي انا بدي اعمله على خمسة على سبيل المثال
+
+162
+00:14:33,060 --> 00:14:38,180
+بدي استخدم divisor آخر اللي هو الخمسة تلاتة و
+
+163
+00:14:38,180 --> 00:14:51,720
+عشرين تساوي خمسة في أربعة زائد تلاتة حان خمسة
+
+164
+00:14:51,720 --> 00:14:58,860
+في خمسة خمسة و عشرين زائد اتنين ممتاز خمسة في سالب
+
+165
+00:14:58,860 --> 00:15:06,040
+خمسة سالب خمسة و عشرينزائد اتنين وطبعا
+
+166
+00:15:06,040 --> 00:15:10,300
+لو كنت انت ماخد برمجة وجربت تستخدم ال modulus او
+
+167
+00:15:10,300 --> 00:15:14,360
+باقى القسمة ايش ما كان الرقم دايما كانت بيطلع باقى
+
+168
+00:15:14,360 --> 00:15:19,820
+القسمة معاك positive والاصل تكون سألت نفسك ليش
+
+169
+00:15:19,820 --> 00:15:23,300
+بتديني positive مع الأرقام السالبة لأن بالصمم هادر
+
+170
+00:15:23,300 --> 00:15:27,020
+انه لازم دايما ال remainder يكون عدد محصور ما بين
+
+171
+00:15:27,020 --> 00:15:30,840
+أكبر أو تساوي صفر واقل من ال divisor اللى موجودة
+
+172
+00:15:30,840 --> 00:15:31,120
+انها
+
+173
+00:15:35,650 --> 00:15:41,050
+الـ 101 لو أنا بدأ أجسمها على الـ 11 كيف بدأ أكتب
+
+174
+00:15:41,050 --> 00:15:47,010
+المعادلة اللي عندي 101
+
+175
+00:15:47,010 --> 00:15:53,850
+تساوي
+
+176
+00:15:53,850 --> 00:15:58,750
+ال device هو 11 يعني إيش مطلوب مني أحدد ال
+
+177
+00:15:58,750 --> 00:16:02,750
+quantity ال quotient و ال remainder
+
+178
+00:16:07,360 --> 00:16:11,900
+بكل بساطة شباب عشان تقدر تحدد ال quotient صح بدك
+
+179
+00:16:11,900 --> 00:16:15,300
+تاخد رقم يقارب القيمة اللي عندها أسهل هيضرب في
+
+180
+00:16:15,300 --> 00:16:19,180
+عشرة و لاش رايك عشرة في أحد عاشر مية و عشرة كبيرة
+
+181
+00:16:19,180 --> 00:16:22,900
+مباشرة خد اللي أقل منه تسعة في أحد عاشر تسعة
+
+182
+00:16:22,900 --> 00:16:28,700
+وتسعين ماتت تسعة مناسبة جدا زائد اتنين هي القيمة
+
+183
+00:16:28,700 --> 00:16:33,360
+اللي موجودة عندها طيب لو انا يا جيل قلتلك
+
+184
+00:16:36,400 --> 00:16:45,140
+المية واحد هذه تجسمها على سبعة ال
+
+185
+00:16:45,140 --> 00:16:48,300
+divisor سبعة ال reminder بدي ال quotient و ال
+
+186
+00:16:48,300 --> 00:16:55,820
+reminder شو بقى تساوي سبعة فا اتناش سبعة
+
+187
+00:16:55,820 --> 00:17:01,180
+فا عشرة سبعينأربعة و تمانى لسه مازلنا بقعد بصبوط
+
+188
+00:17:01,180 --> 00:17:04,620
+بقيتوا انا بتكلم على سبعة في خمس تاش جديش تطلع
+
+189
+00:17:04,620 --> 00:17:07,300
+خمسة و تلاتيه مية و عشرة .. مية و خمس تاش تطلع
+
+190
+00:17:07,300 --> 00:17:11,300
+زيادة اربعة و طعاش بدون ما استخدم ال calculator
+
+191
+00:17:11,300 --> 00:17:16,220
+الأصل يتجرب تشغل لتروس اللي فوق لأن هيك هم كانوا
+
+192
+00:17:16,220 --> 00:17:19,300
+بيعلمونا بفعالية من و احنا في المدرسة ماحفظوناش
+
+193
+00:17:19,300 --> 00:17:22,660
+أرقام أو جداو للضرب عادة بحيث اننا نحاول نستفيد
+
+194
+00:17:22,660 --> 00:17:26,740
+منها قدر المستطاع الآن كمان مرة انا حاسب ticket
+
+195
+00:17:26,740 --> 00:17:32,180
+تانى7×12 هو 84 هذا كان السقف اللي احنا حفظناه في
+
+196
+00:17:32,180 --> 00:17:39,320
+الجداول بدي ارفع ل 15 انا بدور ب 15 5×3 هيك او 7×5
+
+197
+00:17:39,320 --> 00:17:46,120
+هو 35 و 70 تلت معايا 115 out 105 عفوا 105 out
+
+198
+00:17:46,120 --> 00:17:53,700
+وبالتالي لأ انا بدي اللي جابلها 5×14 زاد كده ايش؟
+
+199
+00:17:53,700 --> 00:17:56,720
+زاد ال remainder 3
+
+200
+00:17:59,790 --> 00:18:05,650
+7×4 هو 28 7×1
+
+201
+00:18:05,650 --> 00:18:22,370
+هو 7 9 هو 98 ثانية
+
+202
+00:18:22,370 --> 00:18:22,690
+ثانية ثانية ثانية ثانية ثانية ثانية ثانية ثانية
+
+203
+00:18:22,690 --> 00:18:22,850
+ثانية ثانية ثانية ثانية ثانية ثانية ثانية ثانية
+
+204
+00:18:22,850 --> 00:18:22,890
+ثانية ثانية ثانية ثانية ثانية ثانية ثانية ثانية
+
+205
+00:18:26,480 --> 00:18:30,460
+انه لازم يكون دائما ال remainder positive لازم
+
+206
+00:18:30,460 --> 00:18:34,340
+يكون ال remainder positive فممكن اذا صح و غلط اروح
+
+207
+00:18:34,340 --> 00:18:42,940
+اقولك سالب .. سالب 11 بسمتها
+
+208
+00:18:42,940 --> 00:18:48,060
+على 3 تساوي المعادلة هذه صح ولا غلط؟ مباشر غلط
+
+209
+00:18:48,950 --> 00:18:54,150
+مباشرة غلط كحسبة كحسبة انت حسبت صح ماحدش بيقولك لا
+
+210
+00:18:54,150 --> 00:19:01,250
+بس لما انا بتكلم على خاصية القسمة يعرفته انسان
+
+211
+00:19:01,250 --> 00:19:05,470
+الموضوع لأ لازم تكون دايما ال remainder positive
+
+212
+00:19:05,470 --> 00:19:10,330
+ماحبنقول احنا هذا غلط وبالتالي احنا لازم نمثله
+
+213
+00:19:10,330 --> 00:19:13,910
+بالشكل هذا طيب
+
+214
+00:19:15,120 --> 00:19:19,720
+الان بعد ما شوفنا القسمة و باقي القسمة في عندي
+
+215
+00:19:19,720 --> 00:19:24,960
+شغلة بسميها ال modular arithmetic ال modular باقي
+
+216
+00:19:24,960 --> 00:19:29,900
+القسمة من ال modulus الان في عندي نظرية بتقولك
+
+217
+00:19:29,900 --> 00:19:33,860
+التالي او definition لو كان في عندي two positive
+
+218
+00:19:33,860 --> 00:19:38,900
+integers a و b و عندي positive او عفوا a و b عبارة
+
+219
+00:19:38,900 --> 00:19:41,880
+عن integers و عندي positive integer ام اللي هو ال
+
+220
+00:19:41,880 --> 00:19:57,170
+divisorبقدر أقول A is congruent to B modulo M يعني
+
+221
+00:19:57,170 --> 00:20:02,770
+ال A متجانسة مع ال B من ناحية باقي القسمة على ال M
+
+222
+00:20:09,450 --> 00:20:12,690
+ماذا يعني؟ يعني أن الـA و الـB بكل بساطة لهم نفس
+
+223
+00:20:12,690 --> 00:20:18,570
+باقي القسمة لما يكون الـA و الـB لهم نفس باقي
+
+224
+00:20:18,570 --> 00:20:26,510
+القسمة معناته بقول أن الـM divides A لاقص الـB
+
+225
+00:20:26,510 --> 00:20:30,570
+بالمثال اللي موجود عندها بكل بساطة و بنعيده على
+
+226
+00:20:30,570 --> 00:20:31,230
+مثال آخر
+
+227
+00:20:33,930 --> 00:20:38,730
+والاربعة او السبعة is congruent اربعة مدل التلاتة
+
+228
+00:20:38,730 --> 00:20:43,850
+السبعة متجانسة مع الأربعة من حيث باق القسم على
+
+229
+00:20:43,850 --> 00:20:49,570
+تلاتة شو يعني؟ يعني السبعة باق قسم السبعة تلاتة
+
+230
+00:20:49,570 --> 00:20:53,770
+كام يا شباب؟ واحد باق قسم الأربعة على تلاتة كام؟
+
+231
+00:20:53,770 --> 00:20:59,550
+واحد النظرية هذه بتقول كالتالي هتلاقي ان التلاتة
+
+232
+00:20:59,550 --> 00:21:05,670
+هذهdivides تقسم السبعة نقص الأربعة سبعة نقص
+
+233
+00:21:05,670 --> 00:21:09,850
+الأربعة كام يا شباب؟ تلاتة التلاتة تقسم التلاتة؟
+
+234
+00:21:09,850 --> 00:21:15,010
+true فاش reminder فاش بقى قسمة واحد تعالى نشوف
+
+235
+00:21:15,010 --> 00:21:20,430
+مثال آخر بقولش
+
+236
+00:21:20,430 --> 00:21:27,450
+اتحصل السبعة تعاشر والخمسة مدر التلاتة congruent
+
+237
+00:21:27,450 --> 00:21:35,120
+ولا لأ؟مدل الستة عفواً 17 is congruent مدل الخمسة
+
+238
+00:21:35,120 --> 00:21:40,500
+مد الستة ولا لأ الآن مباشرة تقدر تقول true ولا
+
+239
+00:21:40,500 --> 00:21:49,160
+false بحيث انك تروح تقول 17 مد الستة وخمسة مد
+
+240
+00:21:49,160 --> 00:21:52,440
+الستة اذا الانتين هدولة طلعوا متساويات فال 17
+
+241
+00:21:52,440 --> 00:21:58,840
+congruent لمن للخمسةمدل الستة بقى قسم السبعبعاش
+
+242
+00:21:58,840 --> 00:22:06,440
+على ستة جداش الشباب ستة في اتنين زي خمسة ستة في
+
+243
+00:22:06,440 --> 00:22:12,140
+اتنين زي خمسة يعني باقوا القسمة خمسة خمسة مدل
+
+244
+00:22:12,140 --> 00:22:18,580
+الستة خمسة ليش اتنين؟ بشوي اقل يعني الآن الخمسة
+
+245
+00:22:18,580 --> 00:22:25,080
+تساوي ستة في quotient equal zero زاد الخمسة عشان
+
+246
+00:22:25,080 --> 00:22:29,940
+ليس واحد واحدالان ..واشي الحالة ده يمكن المثال
+
+247
+00:22:29,940 --> 00:22:33,600
+مابديش أكون الصبجته عيد تاني ..الان يا شباب لو أنا
+
+248
+00:22:33,600 --> 00:22:37,240
+اتيت دايما قولتلك لو كان العدد اللي عندك أقل من ال
+
+249
+00:22:37,240 --> 00:22:42,580
+divisor ايش ال quotient تبعته؟ صفر ..والعدد كله
+
+250
+00:22:42,580 --> 00:22:48,200
+بيكون remainder يعني لما باجي بقول انا التلاتة
+
+251
+00:22:48,200 --> 00:22:53,060
+مض الخمسة او تلاتة و خمسة ..divisor خمسة تساوي
+
+252
+00:22:53,060 --> 00:22:58,270
+اتنين ..مصبور؟تساوي اتنين او تلاتة؟ تلاتة التلاتة
+
+253
+00:22:58,270 --> 00:23:03,050
+هذه تساوي ال device وغير الخمسة مضروبة في صفر زائد
+
+254
+00:23:03,050 --> 00:23:07,350
+التلاتة as remainder وبالتالي ال quotient زي ما
+
+255
+00:23:07,350 --> 00:23:10,950
+كانت سالبة ممكن تكون صفر زي ما كانت سالبة ممكن
+
+256
+00:23:10,950 --> 00:23:13,850
+تكون صفر بس لازم ان ال remainder يكون positive
+
+257
+00:23:13,850 --> 00:23:18,710
+فالان الادية حسبت اتنين اللي هم نفس ال modulus نفس
+
+258
+00:23:18,710 --> 00:23:21,970
+بقع نفس ال remainder نفس بقع القسمة وبالتالي السبع
+
+259
+00:23:21,970 --> 00:23:27,670
+عشر is congruent toخمسة النظرية بتقول كتاري لو هذا
+
+260
+00:23:27,670 --> 00:23:34,310
+الكلام كان صحيح معناته .. معناته ان الستة بتقسم
+
+261
+00:23:34,310 --> 00:23:38,410
+الفرق ما بين الاتنين او بين جسين فرق ما بين اتنين
+
+262
+00:23:38,410 --> 00:23:46,490
+هيكون من مضاعفات الستة تعالى نشوف ستة تقسم سبعتاش
+
+263
+00:23:46,490 --> 00:23:53,780
+ناقص خمسة عشر true مية لميةتعالى نشوف المثال
+
+264
+00:23:53,780 --> 00:23:59,340
+التالي بيقول شوف ليه هى ال 24 وال 14 is congruent
+
+265
+00:23:59,340 --> 00:24:07,900
+to 4 او 6 or not فجدامك انت تاخد طريقتين ايه اسهل
+
+266
+00:24:07,900 --> 00:24:11,420
+بالنسبة لك عشان تاخد decision yes or no اللي
+
+267
+00:24:11,420 --> 00:24:23,510
+اريحلك بدي اقوله 24 مض 6 و 14 مض 6أربع عشر مد ..
+
+268
+00:24:23,510 --> 00:24:27,270
+أربع عشر مد الستة صفر لأن الستة مد .. الأربع عشر
+
+269
+00:24:27,270 --> 00:24:32,390
+مد المضاعفات الستة أربع عشر مد الستة تساوى اتنين
+
+270
+00:24:32,390 --> 00:24:39,430
+ال remainder مختلف معناه it is not congruent for
+
+271
+00:24:39,430 --> 00:24:44,090
+twenty four is not congruent to fourteen modulo
+
+272
+00:24:44,090 --> 00:24:53,100
+الستة بدك تتأكد أكثر أربع عشرين ناقص أربع عشربساوي
+
+273
+00:24:53,100 --> 00:25:00,540
+عشرة العشرة او الستة لا تقسم العشرة الستة لا تقسم
+
+274
+00:25:00,540 --> 00:25:04,500
+العشرة او بنجوسين العشرة مش من المضاعفات الستة
+
+275
+00:25:04,500 --> 00:25:09,280
+واضح الفكرة يا شباب؟
+
+276
+00:25:09,280 --> 00:25:18,000
+لغاية
+
+277
+00:25:18,000 --> 00:25:24,820
+تانية بقول كتاليلو كان عندي two integers a و b و
+
+278
+00:25:24,820 --> 00:25:28,960
+positive integer m اللي هو الـ divisor و لجيت أن
+
+279
+00:25:28,960 --> 00:25:35,120
+الـ a is congruent to b أو modulo ال m لجيت الأول
+
+280
+00:25:35,120 --> 00:25:37,900
+congruent للتاني أو العكس طبعا الأسر تبقى أنا
+
+281
+00:25:37,900 --> 00:25:40,320
+بتكلم عن التانين congruent لبعض لأن الفرق بيكون
+
+282
+00:25:40,320 --> 00:25:43,700
+سالب و السالب من ضمن الأقام اللي تنفع تجب تسمع
+
+283
+00:25:43,700 --> 00:25:48,720
+عليها من المضاعفات ولا لأ لأن الآن سالب تلاتة أو
+
+284
+00:25:48,720 --> 00:25:57,170
+سالب تسعةعالتلاتة ايه بعدين بقول انه التسابق تسعة
+
+285
+00:25:57,170 --> 00:26:03,530
+من المضاعفات التلاتة بقول لو لجيت رقمين congruent
+
+286
+00:26:03,530 --> 00:26:09,430
+a,b congruent modulo M معناته بتقدر تكتب الأول
+
+287
+00:26:09,430 --> 00:26:14,330
+الدلالة التاني بحيث ان ال a equal b زائد ال
+
+288
+00:26:14,330 --> 00:26:16,770
+divisor مضروب في some k
+
+289
+00:26:19,570 --> 00:26:24,330
+ما هو الكلام بكل بساطة اللي بيقوله هان كالتالي لو
+
+290
+00:26:24,330 --> 00:26:29,890
+احنا لجينا او جيبنا عددين a مجهولة على سبيل المثال
+
+291
+00:26:29,890 --> 00:26:33,970
+و ال b انا عرفتها و قلتلك x او ال a هذي is
+
+292
+00:26:33,970 --> 00:26:42,850
+congruent to خمسة modulo تلاتة ال a is congruent
+
+293
+00:26:42,850 --> 00:26:50,020
+to خمسة modulo تلاتةدعوني أعرف قيمة الـ A هذه ..
+
+294
+00:26:50,020 --> 00:26:53,780
+ماذا تريد أن تفعل؟ يعني .. يعني .. أنه .. أجهزك و
+
+295
+00:26:53,780 --> 00:26:59,460
+أقول لي أن الخمسة أو الـ A هذه تماثل الخمسة في
+
+296
+00:26:59,460 --> 00:27:02,140
+باقي قسمتها على التلاتة يعني كم هو كم في باقي
+
+297
+00:27:02,140 --> 00:27:06,100
+قسمتها؟ اتنين .. ايش العناصر اللي باقي قسمتها
+
+298
+00:27:06,100 --> 00:27:12,480
+اتنين؟ اتنين .. اتنين على التلاتة .. ده قسمته
+
+299
+00:27:12,480 --> 00:27:20,750
+اتنين .. ايش كمان؟خمسة موضلة بناشية اللي بعده سبعة
+
+300
+00:27:20,750 --> 00:27:25,610
+لأ بقى قسمتها واحد تمانية تمانية دايما اتشوف
+
+301
+00:27:25,610 --> 00:27:29,890
+مضاعفات التلاتة واضيف عليها ايش اتنين احداش
+
+302
+00:27:29,890 --> 00:27:36,830
+اربعاطعاش صح هو
+
+303
+00:27:36,830 --> 00:27:40,050
+ايش بقاعد بقولك بقولك ال a هاد عشان انت متورش فيها
+
+304
+00:27:40,050 --> 00:27:44,410
+كتير عشان ال a هاد متورش فيها كتير ابتخدني ال a
+
+305
+00:27:45,320 --> 00:27:51,200
+بتقول الـ A تساوي الـ B في المثال تبعناه كانت الـ
+
+306
+00:27:51,200 --> 00:27:55,660
+B خمسة زائد
+
+307
+00:27:55,660 --> 00:28:01,000
+الـ divisor اللي عندنا جديد الشباب كان تلاتة بقى
+
+308
+00:28:01,000 --> 00:28:05,680
+القسم التنين تمام؟ احنا قولنا modulo تلاتة مضروبة
+
+309
+00:28:05,680 --> 00:28:12,300
+في أي كي و الـ K عبارة عن integer تمام يعني بقدر
+
+310
+00:28:12,300 --> 00:28:13,600
+انا اجي اقولك التالي
+
+311
+00:28:16,750 --> 00:28:23,490
+تسعة تلاتة في تلاتة تسعة وخمسة اربع عشر بقدر اقول
+
+312
+00:28:23,490 --> 00:28:28,390
+الاربع عشر is modulo الخمسة is congruent خمسة
+
+313
+00:28:28,390 --> 00:28:33,330
+modulo التلاتة ممكن تكبر رقم هذه كلمة بزيادة عشرة
+
+314
+00:28:33,330 --> 00:28:36,630
+تلاتين
+
+315
+00:28:36,630 --> 00:28:40,390
+خمسة
+
+316
+00:28:40,390 --> 00:28:47,420
+و تلاتين is congruent to خمسة modulo التلاتةهذه هي
+
+317
+00:28:47,420 --> 00:28:55,340
+المعادلة اللي نتكلم عليها من أين أتيت؟ من الكلام
+
+318
+00:28:55,340 --> 00:29:01,400
+اللي قلناه قبل شوية أنه الآن هو
+
+319
+00:29:01,400 --> 00:29:06,480
+مالذي يقولني هنا؟ يقولني أرقم جروات لبعض مايعني
+
+320
+00:29:06,480 --> 00:29:13,480
+أرقم جروات لبعض؟ مانعته ال divisor ال M بيقسم A
+
+321
+00:29:13,480 --> 00:29:15,800
+مقص ال B من النظرية السابقة
+
+322
+00:29:19,310 --> 00:29:24,670
+بصبوط a congruent to b modulo m يعني ال m تقسم ال
+
+323
+00:29:24,670 --> 00:29:30,310
+a نقص ال b هيها
+
+324
+00:29:30,310 --> 00:29:36,450
+بصبوط فانا كتبت هيها هيها ايش يعني ال m تقسم هذا
+
+325
+00:29:36,450 --> 00:29:44,510
+معناه تقعد بقولنا ان ال a نقص ال b تساوي m مضروبة
+
+326
+00:29:44,510 --> 00:29:48,110
+في quantity في كمية يعني ان هذا من مضاعفات ال m
+
+327
+00:29:48,830 --> 00:29:51,870
+بظبط خيّر من المضاعفات الان مضروبة في K و K تنتمي
+
+328
+00:29:51,870 --> 00:29:55,470
+لانتجر A
+
+329
+00:29:55,470 --> 00:29:59,910
+ناطص معناته بقدر اقول ايه؟ بدها تساوي بقول B عن
+
+330
+00:29:59,910 --> 00:30:07,750
+ناحية التانية بضعين positive بي زائد N في K ال N
+
+331
+00:30:07,750 --> 00:30:12,530
+هي ال divisor و ال Q هي عبارة عن انتجر اللي عامله
+
+332
+00:30:12,530 --> 00:30:18,250
+اقترح عليها تمام مرة بالمثال لو انا اجل قلتلك
+
+333
+00:30:26,890 --> 00:30:36,110
+A is congruent to
+
+334
+00:30:36,110 --> 00:30:40,230
+تسعة
+
+335
+00:30:40,230 --> 00:30:45,390
+موديلو الأربعة
+
+336
+00:30:45,390 --> 00:30:49,390
+مد
+
+337
+00:30:49,390 --> 00:30:53,510
+الأربعة A
+
+338
+00:30:53,510 --> 00:31:00,140
+اللي هي العددis congruent to 9 مد الأربعة الديني
+
+339
+00:31:00,140 --> 00:31:07,840
+رقم يحقق المعادلة هذه الأصل
+
+340
+00:31:07,840 --> 00:31:11,220
+يتفكر فيها بورقتين مختلفتين والتنتين هيدوك لنفس
+
+341
+00:31:11,220 --> 00:31:20,900
+النتيجة الأولى تسعة مد الأربعة واحد تسعة مد
+
+342
+00:31:20,900 --> 00:31:26,550
+الأربعة واحد فلو انت جيبت اي قيمة لل aمد الأربعة
+
+343
+00:31:26,550 --> 00:31:36,350
+بتدي واحد فهي تكون صح زي إيش؟ خمسة سبعة غلط تسعة
+
+344
+00:31:36,350 --> 00:31:42,210
+هي already أنا بديكي إياها تلتاش سبعتاش كل الأرقام
+
+345
+00:31:42,210 --> 00:31:46,490
+اللي بتزيد عن المضاعفات الأربعة بواحد هذا ممكن
+
+346
+00:31:46,490 --> 00:31:51,930
+تفكر فيها أو تفكر كالتالي مباشرة تقول ال A بدها
+
+347
+00:31:51,930 --> 00:31:54,470
+تساوي تسعة
+
+348
+00:31:56,790 --> 00:32:02,450
+زائد اربعة مضروبة في اي كي في اتنين خلصنا اقصد رقم
+
+349
+00:32:02,450 --> 00:32:06,090
+تمانية
+
+350
+00:32:06,090 --> 00:32:14,350
+سبعة عشر ما هتقول ايه ممكن تكون سبعة عشر كيف؟ اه
+
+351
+00:32:14,350 --> 00:32:17,210
+لازم يكون عدد صحيح لان من اول ال chapter وانا
+
+352
+00:32:17,210 --> 00:32:21,350
+بتكلم يا شباب بتكلم على ال integers number theory
+
+353
+00:32:21,350 --> 00:32:24,790
+بتكلم على ال integers العدد الصحيحة وخصائصها
+
+354
+00:32:28,180 --> 00:32:35,740
+ممتاز ايش هاله نتيجة الهاتف اللي قلتلنا 17 17
+
+355
+00:32:35,740 --> 00:32:47,800
+مد الأربعة جديش واحد تسعة مد الأربعة جديش ميناته
+
+356
+00:32:47,800 --> 00:32:52,180
+ال 17 is congrant تسعة مد الأربعة انت ايش بتقول
+
+357
+00:32:52,180 --> 00:32:53,760
+الخمسة
+
+358
+00:33:01,410 --> 00:33:08,730
+سالب واحد بالظبط لأنه قاعد بيقول ال K هي عبارة عن
+
+359
+00:33:08,730 --> 00:33:13,610
+integer ما جليش positive او negative انتجر اي عدد
+
+360
+00:33:13,610 --> 00:33:18,350
+وبالتالي السؤال اللي بيطلح نفسه التسعة congruent
+
+361
+00:33:18,350 --> 00:33:25,930
+للتسعة تسعة congruent للتسعة جاوبني congruent
+
+362
+00:33:25,930 --> 00:33:29,130
+للتسعة congruent للتسعة مد للاربعة
+
+363
+00:33:31,130 --> 00:33:36,490
+حرام عليك true true ايش الشرط الأساسي يا شباب ان
+
+364
+00:33:36,490 --> 00:33:42,050
+اتنين كلهم باقي نص باقي القسمة بصبت او لما انا
+
+365
+00:33:42,050 --> 00:33:46,430
+اروح اطرحهم من بعض يقبل القسمة على ال divisor اللي
+
+366
+00:33:46,430 --> 00:33:52,650
+عندي طيب الان تسعة ناقص تسعة صفر يقبل قسمة على
+
+367
+00:33:52,650 --> 00:33:55,370
+اربعة اه يقبل قسمة على اربعة صفر و الباقي صفر
+
+368
+00:33:55,370 --> 00:33:59,550
+الصفر تساوي
+
+369
+00:34:01,190 --> 00:34:07,930
+الاربعة مضروبة في Zero والReminder Zero ايش يعني؟
+
+370
+00:34:07,930 --> 00:34:11,410
+يعني ال Quotient تبعتي Zero وبالتالي الصفر من
+
+371
+00:34:11,410 --> 00:34:15,950
+المضاعفات اي رقم الصفر من المضاعفات اي رقم عشان
+
+372
+00:34:15,950 --> 00:34:22,190
+هيك احنا بنقول الصفر على خمسة صفر بصبوط؟ بسبب
+
+373
+00:34:22,190 --> 00:34:26,970
+المعادلة هاي واضح
+
+374
+00:34:26,970 --> 00:34:32,680
+الامور يا شباب؟من أهم التطبيقات تبقى الخاصة القسمة
+
+375
+00:34:32,680 --> 00:34:37,280
+و ال modulus ال hash function ال hash function
+
+376
+00:34:37,280 --> 00:34:42,180
+هتشوفها
+
+377
+00:34:42,180 --> 00:34:49,340
+لاحقا يعني ايش يعني hash ايش
+
+378
+00:34:49,340 --> 00:34:51,780
+معنى hash tag على الفيسبوك او على ال media بشكل
+
+379
+00:34:51,780 --> 00:34:57,810
+عام على ال social media شو يعني hash tagهاش انك
+
+380
+00:34:57,810 --> 00:35:01,310
+بتعطي اشارة لحاجة تانية او اشارة أخرى انك بتحاول
+
+381
+00:35:01,310 --> 00:35:06,350
+تعطي قيمة مميزة للعناصر هذه عشان تصنفهم كلهم وين
+
+382
+00:35:06,350 --> 00:35:11,790
+تيجي عشان هي الكل كان في عندك هاش اسمها العودة
+
+383
+00:35:11,790 --> 00:35:19,110
+الكبرى، مصبوط؟ ليش؟ صار كل واحد .. كل واحد بروح ..
+
+384
+00:35:19,110 --> 00:35:25,340
+بضيفالـHash هذي أو الرقم هذا كلهم بييجي تحت نفس
+
+385
+00:35:25,340 --> 00:35:29,360
+التصنيف، مين كتب في العالم على الفيسبوك أو تويتر
+
+386
+00:35:31,060 --> 00:35:35,720
+تستخدم التسمية هذه تمام راح تقولها ال boss اتصنفت
+
+387
+00:35:35,720 --> 00:35:41,600
+او نعملها ادراج تحت مسمة واحد الهاش هي عبارة عن
+
+388
+00:35:41,600 --> 00:35:45,780
+ترقيم عبارة عن هاش عن ترقيم لما اتكلم هاشينج او
+
+389
+00:35:45,780 --> 00:35:49,960
+هاش فانشينج جاعت بتكلم على فانشينج ده اللي رياضية
+
+390
+00:35:49,960 --> 00:35:53,160
+بتديني قيمة ده اللي رياضية بتديني قيمة بناء على
+
+391
+00:35:53,160 --> 00:35:57,680
+ايش؟ بناء على ال value المحتوى الآن لاحظوا يا شباب
+
+392
+00:35:58,550 --> 00:36:00,990
+الان لو ايه كتبت العوجة الكبرى وماحققش ال
+
+393
+00:36:00,990 --> 00:36:06,890
+underscore هذي بتكلم جاهد على different ..
+
+394
+00:36:06,890 --> 00:36:11,390
+different value بصبت؟ و لو انا ساجد في الإملة و
+
+395
+00:36:11,390 --> 00:36:15,990
+روح اتحققت الكبريحطيته جطينها تحت الألف الليينة
+
+396
+00:36:15,990 --> 00:36:21,090
+برضه أخد .. لا بتطلعش 100% أخد different title
+
+397
+00:36:21,090 --> 00:36:25,110
+عنوان مختلف تماما لإيش؟ لأن المفروض ال hash
+
+398
+00:36:25,110 --> 00:36:30,630
+function ال value تبعتها تحسبها حسب القيمة
+
+399
+00:36:30,630 --> 00:36:38,090
+المُعطاة بعيدا عن ال facebook و ال social media بس
+
+400
+00:36:38,090 --> 00:36:42,430
+فكرتها رياضيات بالمناسبةبعيدا عن الـ social media
+
+401
+00:36:42,430 --> 00:36:44,890
+و الـ hash function و الـ hash تبعت الـ hashtag
+
+402
+00:36:44,890 --> 00:36:49,910
+الان يا سيد العزيزي ال hash function هي دالة دالة
+
+403
+00:36:49,910 --> 00:36:56,530
+بتحدد موقع البيانات او موقع ال record في الملف او
+
+404
+00:36:56,530 --> 00:37:01,570
+في ال memory تبعل ال value تبعتها الان اسمعتوا شغل
+
+405
+00:37:01,570 --> 00:37:05,150
+اسمها database لما درستوا مقدمة صح؟لأن الـ
+
+406
+00:37:05,150 --> 00:37:08,690
+database file ال data اللي بتتخزن على ال file
+
+407
+00:37:08,690 --> 00:37:13,390
+بتتخزن as binary بتتخزن ضمن ترتيب معين مين بيحدد
+
+408
+00:37:13,390 --> 00:37:17,310
+ال position تبع ال file هذا ال hash function بتاخد
+
+409
+00:37:17,310 --> 00:37:22,270
+القيمة تبع ال record بتعمل عليها حسبة بسيطة و بروح
+
+410
+00:37:22,270 --> 00:37:26,970
+بيحدد ال position تبعها وين بتتخزن اجيبك مثال بسيط
+
+411
+00:37:26,970 --> 00:37:30,950
+عشان اوضحك ال hash لو افترضنا و مش علاقة بال
+
+412
+00:37:30,950 --> 00:37:32,770
+modulus كمان لو افترضنا
+
+413
+00:37:37,160 --> 00:37:44,000
+إنه اجينا بدنا نصنف .. نصنف أسماء الطلاب الذكور
+
+414
+00:37:44,000 --> 00:37:51,320
+لمصنفات، بتجمحهم كلهم لفئات، هتصنفهم تبقى لإيش؟
+
+415
+00:37:51,320 --> 00:37:57,060
+عدد؟ هذا واحد، اسمي الكلب اخترق عدد الحرقاش
+
+416
+00:37:57,060 --> 00:38:02,090
+الترتيبأبجد يعني الحروف اللي بتبدأ بحرف ال A كلها
+
+417
+00:38:02,090 --> 00:38:05,490
+مع بعض الحروف اللي بتبدأ بحرف ال B مع بعض ازميلة
+
+418
+00:38:05,490 --> 00:38:09,730
+كانت ذاكرة مصطفى السوسي سوسي ولا سويسي سويسي جالك
+
+419
+00:38:09,730 --> 00:38:14,610
+التالي انا بدي اصنفهم على عدد الحروف يعني جال كل
+
+420
+00:38:14,610 --> 00:38:17,950
+الطلاب اللي أسميهم من أربع حروف اللي كله في فئة
+
+421
+00:38:17,950 --> 00:38:22,330
+واحدة مصبوب التاني التالت الرانع الخامس إلى آخرهم
+
+422
+00:38:22,330 --> 00:38:26,750
+طب لو أنا جالك و قلتلك يا مصطفى بس اللي عندك عشر
+
+423
+00:38:26,750 --> 00:38:31,320
+حروف جحد أقصىما زاد .. ده اكتشف على اسمه رباعي ..
+
+424
+00:38:31,320 --> 00:38:33,860
+ما زاد عن العشر حروف اللي كنت تدبره .. كده كنت
+
+425
+00:38:33,860 --> 00:38:38,520
+تدبره .. هتصير تعتمد على ال modulus .. باقى القسمة
+
+426
+00:38:38,520 --> 00:38:43,280
+.. حدش حد ساوي .. هتروح تقد الحروف .. هذا اتناش ..
+
+427
+00:38:43,280 --> 00:38:47,080
+طب أنا عندي عشر .. عشر فئات .. تحت أي فئة بدي احطه
+
+428
+00:38:47,080 --> 00:38:51,380
+.. بدي احطه تحت الفئة اتنين .. ليش؟ عشان باقى
+
+429
+00:38:51,380 --> 00:38:54,200
+القسمة بدي اعتمد على باقى القسمة اللي ساوة ..
+
+430
+00:38:54,200 --> 00:38:57,840
+اتنين .. يعني صارت تلين ولا اتناش ..في الواحد
+
+431
+00:38:57,840 --> 00:39:02,440
+العشرة وعشرين وتلاتين جايين في صفر بصبوط لأن بقى
+
+432
+00:39:02,440 --> 00:39:05,980
+قسمتهم صفر طيب تسعة وأتعاشر تسعة وعشرين تسعة
+
+433
+00:39:05,980 --> 00:39:09,100
+وتلاتين وتسعة كلهم دول في خانة واحدة اللي هم
+
+434
+00:39:09,100 --> 00:39:13,540
+الخانة التاسعة او الأخيرة اللي موجودة عندها وهذه
+
+435
+00:39:13,540 --> 00:39:18,080
+الشغل ال hash ان بتاخد منك ال value وبناء على ال
+
+436
+00:39:18,080 --> 00:39:20,900
+implementation اللي في داخلها بتديك قيمة ودائما
+
+437
+00:39:20,900 --> 00:39:24,020
+القيمة هذه غالبا تعتمد على ال modulus
+
+438
+00:39:34,280 --> 00:39:39,960
+لو انا افترضت اليك كالتالي انه انا بس يا مصطفى
+
+439
+00:39:39,960 --> 00:39:46,140
+اللي عندي تلت فئات و
+
+440
+00:39:46,140 --> 00:39:49,220
+بدك توزع كل أسماء الطلاب اللي في القاعة نفس الفكرة
+
+441
+00:39:49,220 --> 00:39:53,320
+اللي انت قلتها على التلاتة هدول شبك تساوي؟ هتصيرش
+
+442
+00:39:53,320 --> 00:40:00,950
+تعتمد؟ مد .. مد التلاتة سافر؟وهنا بنحط فيه كل
+
+443
+00:40:00,950 --> 00:40:07,130
+الأسماء اللي قولها مضاعفات التلاتة كل الأسماء في
+
+444
+00:40:07,130 --> 00:40:09,850
+الخانة التانية كل الأسماء اللي باقى قسمتها على
+
+445
+00:40:09,850 --> 00:40:16,370
+التلاتة واحد والباقي اللي بعديها اتنين اللي باقى
+
+446
+00:40:16,370 --> 00:40:19,250
+قسمتها على التلاتة اتنين يعني أنا من جنب العسابي
+
+447
+00:40:19,250 --> 00:40:26,430
+للمثال احمد كم حرف اربعة اربعة مدت تلاتة واحد احمد
+
+448
+00:40:26,430 --> 00:40:26,650
+هان
+
+449
+00:40:30,860 --> 00:40:38,960
+عالى صفر ماشت من تلاتة مدت تلاتة صفر لاحظ يا محمد
+
+450
+00:40:38,960 --> 00:40:42,480
+يا باز انا باتكلمش على الجرية لان عندي تصنيف مختلف
+
+451
+00:40:42,480 --> 00:40:49,060
+تمام الهاش فانشن هي اللي اخدت من الاسم ادت الحروف
+
+452
+00:40:49,060 --> 00:40:52,140
+ورجعتلي بالرقم المكان اللي انا بدي احط فيه مين
+
+453
+00:40:52,140 --> 00:40:53,260
+محمد
+
+454
+00:41:02,670 --> 00:41:09,790
+ثلاثة .. ستة .. تمانية طبعاً
+
+455
+00:41:09,790 --> 00:41:13,590
+هتفرق مقات لو انت كتبت محمد بأم واحدة اللهم صلي و
+
+456
+00:41:13,590 --> 00:41:16,350
+أسلم على صيد ده محمد، مظبوط؟ هتفرج، هتيجي في
+
+457
+00:41:16,350 --> 00:41:21,160
+الخارج أيه؟وهكذا تصبح كل الأسماء التي كنت تصنفها
+
+458
+00:41:21,160 --> 00:41:24,200
+تكون من تصنيف صحيح، ماهو مجلس تصنيفها يا دا وليها
+
+459
+00:41:24,200 --> 00:41:31,160
+شيء؟ عندما أريد أن أبحث عن عبدالعزيز، عبدالعزيز
+
+460
+00:41:31,160 --> 00:41:32,960
+تحت أي خانة الكون موجود يا شباب؟
+
+461
+00:41:43,900 --> 00:41:47,800
+بغض النظر، أنا لم أقدر أن أعطيك الاسم بس اعطيني
+
+462
+00:41:47,800 --> 00:41:54,560
+الاسم مثلما أعطيتني أول مرة هايو عبد أربعة ال سبعة
+
+463
+00:41:54,560 --> 00:42:00,400
+و تلاتة عشرة وين هي الكون؟ واحد هنا فلاحظ انك
+
+464
+00:42:00,400 --> 00:42:03,380
+مباشرة اتدور في المكان هذا اتدور في كل ال data
+
+465
+00:42:03,380 --> 00:42:07,120
+الموجودة وكل ما ازادت عندك ال locations اللي بتخزن
+
+466
+00:42:07,120 --> 00:42:13,490
+فيها تمام؟ معناته انك بتجلشأو تقارنة على عصر في ال
+
+467
+00:42:13,490 --> 00:42:17,810
+location اللي موجود عندها هذه الهاش فانكشن ان شاء
+
+468
+00:42:17,810 --> 00:42:20,350
+الله تبارك وتعالى بكرا لما تدرس database او اللي
+
+469
+00:42:20,350 --> 00:42:23,830
+درس database بيعرف شو يعني هاش و شو يعني index و
+
+470
+00:42:23,830 --> 00:42:29,030
+هنشوفها لاحقا من الشغلات التانية الشغلات التانية
+
+471
+00:42:29,030 --> 00:42:32,430
+اللي بتستخدم فيها ال number و ال modulus و باقى
+
+472
+00:42:32,430 --> 00:42:35,570
+القسمة اللي هي ال random number او اللي احنا
+
+473
+00:42:35,570 --> 00:42:37,670
+بسميها في ال computer science ال procedural random
+
+474
+00:42:37,670 --> 00:42:45,530
+number الرقم العشوائيلو انا جيت سألت اي واحد فيكوا
+
+475
+00:42:45,530 --> 00:42:53,410
+اعطينا رقم عشوائي 13 تمام هو قرر انه يختار فيها
+
+476
+00:42:53,410 --> 00:43:03,450
+صغيرة و اعطينا رقم عشوائي 13 تمام
+
+477
+00:43:03,450 --> 00:43:08,310
+ايه لو واحد قرر يروح بالالاف 1999
+
+478
+00:43:10,970 --> 00:43:15,230
+في مشكلة؟ برضه random طب بينما انا محتاج .. محتاج
+
+479
+00:43:15,230 --> 00:43:20,830
+الرقم اللى بده يطلع عندى يكون محصور ما بين الصفر و
+
+480
+00:43:20,830 --> 00:43:25,530
+الخمسة او اقل من خمسة شو بيك تساوي؟ الرقم ايش ما
+
+481
+00:43:25,530 --> 00:43:29,910
+يطلع الرغم اللى مد الخمسة ايش بتساوي؟ لأن كمان مرة
+
+482
+00:43:29,910 --> 00:43:37,190
+شوف انا الآن تخيل بدي رقم عشوائي من صفر لاربعةمن
+
+483
+00:43:37,190 --> 00:43:42,170
+صفر لاربعة الان انت ايش ممكن تطلعلي بأي رقم ممشي
+
+484
+00:43:42,170 --> 00:43:46,610
+الحال بس في الآخر انا بدي الرقم يكون هان و بديش
+
+485
+00:43:46,610 --> 00:43:50,830
+أسهل حاجة عشان مابلكاش رقم غلط لأ لأ بديش يحصل
+
+486
+00:43:50,830 --> 00:43:53,590
+ليها هاتلي random number تفضلي random number خد
+
+487
+00:43:53,590 --> 00:43:57,750
+الرقم و اعمله modulus لما انا باجي بقوله تلاتنعاش
+
+488
+00:43:57,750 --> 00:44:05,460
+مضي لاربعة واحد من هوا randomوالـ 1999 مد الأربعة
+
+489
+00:44:05,460 --> 00:44:10,500
+لازم .. مد الخمسة عفوا بصبوط مد الخمسة لازم يطلع
+
+490
+00:44:10,500 --> 00:44:14,360
+عيش يا شباب من صفر لأربعة ضمن ال range هدا بير
+
+491
+00:44:14,360 --> 00:44:17,580
+المضاعفات اللي خمسة بطلع عندك عيش أربعة هي ال
+
+492
+00:44:17,580 --> 00:44:20,200
+range اللي عندك واحد يقول طب مافي تكرار كتير يا
+
+493
+00:44:20,200 --> 00:44:24,740
+أستاذ لأن المدة تبعك قليل من صفر لأربعة زيد المدة
+
+494
+00:44:24,740 --> 00:44:28,850
+لعشرةبتصير تعمل مو بلس لعشرة بتصير الرقام من صفر
+
+495
+00:44:28,850 --> 00:44:35,690
+لتسعة بدك random 800 واسه ل 100 فبتصير من صفر ل 99
+
+496
+00:44:35,690 --> 00:44:41,950
+هي مفهوم ال random لأن ال computer عادة لما تقوله
+
+497
+00:44:41,950 --> 00:44:46,650
+random integer ال random ان هو افتوح ممكن الرقم
+
+498
+00:44:46,650 --> 00:44:51,590
+يكون في اي rangeانتجر الان لو انا اكتب لك واحد او
+
+499
+00:44:51,590 --> 00:44:58,370
+بلاش سبعة صفر تسعة واحد تمانية سبعة ستة خمسة اتنين
+
+500
+00:44:58,370 --> 00:45:03,910
+تلاتة اربعة صفر صفر واحد انتجر و لاك بس انا بديش
+
+501
+00:45:03,910 --> 00:45:06,910
+random بالشكل هذا بدي random عجبدي من واحد لعشرة
+
+502
+00:45:06,910 --> 00:45:11,310
+اشي بروح مساوي بعمل مدرس و بريح راسي وهذا من اهم
+
+503
+00:45:11,310 --> 00:45:17,700
+ال implementation اللي موجود عندك الان حتمالعبته
+
+504
+00:45:17,700 --> 00:45:21,680
+سيلوتير او شد على الكمبيوتر صح؟ كيف بتتم توزيع
+
+505
+00:45:21,680 --> 00:45:25,580
+الأوراق ومعاملتها وسحبها وكذا؟ Random بس ال random
+
+506
+00:45:25,580 --> 00:45:30,560
+ضمن جداش من واحد ل .. او من صفر لاطناش من واحد
+
+507
+00:45:30,560 --> 00:45:34,220
+لثلاثاش او تلاتاشر كارت اللي بيكونوا موجودات عندك
+
+508
+00:45:34,220 --> 00:45:37,580
+واحد يقول أستاذ ما حاببتي؟ لا يا صاحبي أنا بتكلم
+
+509
+00:45:37,580 --> 00:45:40,500
+ضمن إحصائي احتمالات و random number و هذا الكلام
+
+510
+00:45:40,500 --> 00:45:47,790
+موجود طيب خلصنا ال section الأول ساعة كام؟في
+
+511
+00:45:47,790 --> 00:45:51,830
+المطعة اللى موجودة قالوا عليها سابقا طيب الجزئية
+
+512
+00:45:51,830 --> 00:45:54,230
+التانية اللى هنتكلم عليها شباب ال section التانى
+
+513
+00:45:54,230 --> 00:46:01,950
+كلام مر عليك سابقا في المقدمة او حتى في
+
+514
+00:46:01,950 --> 00:46:05,550
+التكنولوجيا لما درست في الثانوية سواء كانت في أولى
+
+515
+00:46:05,550 --> 00:46:10,550
+ثانوي او في تانية ثانوي بغض النظر نتكلم على تمثيل
+
+516
+00:46:10,550 --> 00:46:16,500
+الأرقام وال algorithm بدأ بعيد عنها شوية اناماليش
+
+517
+00:46:16,500 --> 00:46:24,180
+دخل فيها تمام عشانها سهلة بالضبط عشانها سهلة الآن
+
+518
+00:46:24,180 --> 00:46:28,680
+في العصر الحديث أو عصر الحالي بنتعامل مع أرقام
+
+519
+00:46:28,680 --> 00:46:33,320
+بالنظام ال 10 ال decimal اللي هو ال base تبعته
+
+520
+00:46:33,320 --> 00:46:38,540
+جديش ال base تبعته النظام العشر جديش عشرة خليك
+
+521
+00:46:38,540 --> 00:46:42,840
+معايا يعني تكتب؟ كويس الله يزيدك الخير أنا بحسبك
+
+522
+00:46:42,840 --> 00:46:47,490
+صراحة مع الجوالالان وبالتالي اللي بيوجدش بيقولك
+
+523
+00:46:47,490 --> 00:46:53,190
+تسعمية خمسة و ستين الخمسة
+
+524
+00:46:53,190 --> 00:47:01,430
+كانوا بعلمونا أحد مصبوط ست عشرات مئات يعني خمسة في
+
+525
+00:47:01,430 --> 00:47:08,230
+عشر أقص صفر زائد ستة في عشر أقص واحد زائد تسعة في
+
+526
+00:47:08,230 --> 00:47:14,230
+عشر أقص اتنينخطف المقاطمة و خطف الفول ثانيا و اول
+
+527
+00:47:14,230 --> 00:47:19,930
+مدرس تتكلم عن تكنولوجيا مش قضية الان لاحظ ان
+
+528
+00:47:19,930 --> 00:47:23,290
+الأرقام هذه او العشر هذه مثلة الأساس لنظام العدل
+
+529
+00:47:23,290 --> 00:47:27,990
+اللي موجود و من هيك صار في عندي أرقام تبع ال base
+
+530
+00:47:27,990 --> 00:47:32,750
+اللي بدك هي نقرأ في حين ال binary ال base تبعتها
+
+531
+00:47:32,750 --> 00:47:41,330
+اتنين ال octal16 اكسا ديسمل ثلاثي بينفع بثلاثي اه
+
+532
+00:47:41,330 --> 00:47:46,970
+بينفع من صفر لتنين صفر واحد اتنين تلت ارقام لاحظ
+
+533
+00:47:46,970 --> 00:47:52,910
+ان الأرقام اللي موجودة دائما مد ال base يعني هي
+
+534
+00:47:52,910 --> 00:47:56,210
+بتمثل ال remainder اللي هو انجسمت على ال base من
+
+535
+00:47:56,210 --> 00:48:03,220
+صفر لحد اقل من ال base بتعرفوا شعب المياه؟برضه ايه
+
+536
+00:48:03,220 --> 00:48:08,100
+يا حميدالله؟ وين بيعيشوا كانوا؟ امريكا
+
+537
+00:48:08,100 --> 00:48:12,760
+اللاتينية انا بعرفهمش تعرفوا البابليون؟ وين كانوا
+
+538
+00:48:12,760 --> 00:48:17,280
+بيعيشوا؟ في العراق لأن شعب الميه كان بيعتمد على
+
+539
+00:48:17,280 --> 00:48:23,800
+نظام عد بيعتمد على ال base عشرين يعني من صفر لتسعة
+
+540
+00:48:23,800 --> 00:48:29,720
+عشر البابليين كان عندهم نظام العد من ستين digit
+
+541
+00:48:31,410 --> 00:48:37,250
+من صفر لتسعة وخمسين من صفر لتسعة وخمسين الفرعنة من
+
+542
+00:48:37,250 --> 00:48:41,990
+اتناش هى و الله في التاريخ انا بعرفش و الله اه
+
+543
+00:48:41,990 --> 00:48:45,090
+طبعا اسملكم بأكد انه الفرعنة كانت بتتوضع على نظام
+
+544
+00:48:45,090 --> 00:48:50,990
+عد من اتناش و المعلومة مرت عليه طبعا الفكرة وين ان
+
+545
+00:48:50,990 --> 00:48:56,650
+انت ممكن توجد نظام العد اللى بدكياه حسب ال system
+
+546
+00:48:56,650 --> 00:49:00,450
+او الحالة اللى انت بدكياها يعني لو انا اجل قلتلك
+
+547
+00:49:00,450 --> 00:49:01,010
+كالتانى
+
+548
+00:49:03,540 --> 00:49:11,580
+واحد .. سبعة .. خمسة .. صفر .. تلاتة .. كم قيمة
+
+549
+00:49:11,580 --> 00:49:16,400
+الرقم هذا؟ سبعتاشر ألف و خمسمية و تلاتة لو كنت أنا
+
+550
+00:49:16,400 --> 00:49:20,720
+بتكلم decimal بس غلط مش decimal كم قيمته؟ بنوه
+
+551
+00:49:20,720 --> 00:49:26,340
+نظام .. أيوة بنوه نظام .. إيش ال base تلاته؟ لاحظ
+
+552
+00:49:26,340 --> 00:49:29,920
+لما أنا كتبت الرقم بالشكل هذا و سبته .. تمام؟
+
+553
+00:49:29,920 --> 00:49:35,970
+معناته أنا فتحت ..مجهول على الرقم هذا لأنه بينفع
+
+554
+00:49:35,970 --> 00:49:41,290
+ال base تبقى تتكون من تمانية واطلع بينفع يكون نظام
+
+555
+00:49:41,290 --> 00:49:44,990
+ثماني تساعي
+
+556
+00:49:44,990 --> 00:49:50,030
+وعشري اللي قرناه .. قرناه بال 17000 و 11 و 12 و 13
+
+557
+00:49:50,030 --> 00:49:56,430
+و 60 و 75 و 100 لو حد بتألف فاش مشكلة وممكن تكون
+
+558
+00:49:56,430 --> 00:50:01,640
+تاخد الرقم نفسه و هو ال baseبس فعليا دائما هروح
+
+559
+00:50:01,640 --> 00:50:06,480
+على value مختلفة تماما في كل نظام يعني بين جثين لو
+
+560
+00:50:06,480 --> 00:50:13,060
+أنت تبعت لواحد رقم معين ممكن تبعته بصورة غير صورته
+
+561
+00:50:13,060 --> 00:50:19,320
+و اللي نشوفه يفهم معنى التشفير ايوة و من هنا اندر
+
+562
+00:50:19,320 --> 00:50:23,580
+بالك كانت بداية ايش التشفير هم الاشق دائما .. اللي
+
+563
+00:50:23,580 --> 00:50:27,520
+هو في العصر الحديث أخد وجه طويلفي فهم الحضرات
+
+564
+00:50:27,520 --> 00:50:31,860
+السابقة كانت كل كتب العلوم اللي موجودة فيها أرقام
+
+565
+00:50:31,860 --> 00:50:35,060
+فيها رموز هم مش عارفين أيش مهيئة الرمز اللي موجود
+
+566
+00:50:35,060 --> 00:50:40,540
+هذا و لو وصلولها بشكل سريع فانت ايش اتصل يعني الآن
+
+567
+00:50:40,540 --> 00:50:48,040
+لو مثلا واحد بده يغش الزميله في الامتحان صح ولا
+
+568
+00:50:48,040 --> 00:50:52,780
+غلط او في الخيارات بده يقول واحد اتنين تلاتة طب ما
+
+569
+00:50:52,780 --> 00:50:56,990
+هي مكشوفة ولا لا؟صارت استخدم حاجة جديدة فيه تموّر
+
+570
+00:50:56,990 --> 00:51:00,810
+على ان المراجعين بدأوا يفتحوا عليكوا حكّوا انتل
+
+571
+00:51:00,810 --> 00:51:05,150
+تلاتة و بيعدّلك اه؟ الله يكبّع شركه الفكرة وين؟ ان
+
+572
+00:51:05,150 --> 00:51:09,110
+ممكن انا استخدم هذه التقنيات و فعليا احمي ال data
+
+573
+00:51:09,110 --> 00:51:14,410
+اللي موجودة عندى بحيث لو اي واحد في المنتصف قرأ
+
+574
+00:51:14,410 --> 00:51:17,670
+البيانات اللي موجودة هذهش مايفهمش أيش القيمة اللي
+
+575
+00:51:17,670 --> 00:51:21,450
+موجودة او بين جثين افتح عليه باب من المجهول و من
+
+576
+00:51:21,450 --> 00:51:26,740
+احتمالات القيم اللي موجودة عندهمطيب احنا الآن لما
+
+577
+00:51:26,740 --> 00:51:33,140
+بنتكلم على نظام هد دائما ال digits اقل من قيمة ال
+
+578
+00:51:33,140 --> 00:51:36,740
+base يعني دائما هيك ال digits موجودة اكبر او تساوي
+
+579
+00:51:36,740 --> 00:51:42,460
+الصفر وال digits هذي بدأت تكون اقل من ال base عشرة
+
+580
+00:51:42,460 --> 00:51:47,840
+يعني من صفر لتسعة تمانية من صفر لسبعة خمسة من صفر
+
+581
+00:51:47,840 --> 00:51:51,600
+لاربعة اتنين من صفر لاحد بظبط هى ال range اللى
+
+582
+00:51:51,600 --> 00:51:57,500
+موجود عندى هنا ستة عشرمن صفر لخمستاشر في الستاشر
+
+583
+00:51:57,500 --> 00:52:01,700
+كمان مرة احنا ماعناش مشكلة هي من صفر لحد التسعة
+
+584
+00:52:01,700 --> 00:52:08,060
+لكن عندي عشرة احداشر اتناشر تلاتاشر اربعتاشر
+
+585
+00:52:08,060 --> 00:52:15,460
+خمستاشر هذا الأصل هيك لكن لما روحت انا اكتب الرقم
+
+586
+00:52:15,460 --> 00:52:19,760
+بتعامل مع الرقم only one digit يعني لما انا بدي
+
+587
+00:52:19,760 --> 00:52:28,820
+اكتب عشان اقولك كتاري الرقم هذااحد صفر واحد خمسة
+
+588
+00:52:28,820 --> 00:52:38,140
+hexadecimal او بالست عشر الاصل الاصل ان انا بتعامل
+
+589
+00:52:38,140 --> 00:52:41,580
+digit by digit لان احنا كل واحد اللي ونزلته زي ما
+
+590
+00:52:41,580 --> 00:52:46,440
+شوفنا قبل شوية مصبوط يعني هذا المفروض خمسة ضرب16
+
+591
+00:52:46,440 --> 00:52:50,900
+أز صفر واحد ضرب 16 أز واحد صفر ضرب 16 أز اتنين
+
+592
+00:52:50,900 --> 00:52:56,000
+واحد ضرب 16 أز تلاتة لان انا عامل 16 طب كيف بدي
+
+593
+00:52:56,000 --> 00:52:59,420
+امثل الأرقام هذه انا لو انا في اندي 15 هذه طب هي
+
+594
+00:52:59,420 --> 00:53:04,460
+ال 15 هي نفس هيك لان هتختلف تخيل هذه لو انا بتعامل
+
+595
+00:53:04,460 --> 00:53:11,410
+معاك 15درب 16 أصفر أو هتكون خمسة ضرب ستة عشر أصفر
+
+596
+00:53:11,410 --> 00:53:15,670
+زائد واحد ضرب ستة عشر أصفر واحد خمسة زاد ستة عشر
+
+597
+00:53:15,670 --> 00:53:20,370
+واحد وعشرين واحد وعشرين غير على خمسة عشر فليه
+
+598
+00:53:20,370 --> 00:53:23,530
+يقولوا إنه يستخدموا لما اتكلموا عن الأرقام من two
+
+599
+00:53:23,530 --> 00:53:27,570
+digits يستبدلوها برمز ليش؟ عشان أقدر أعرف القيمة
+
+600
+00:53:27,570 --> 00:53:30,430
+تبع الرمز هذا جديش أنا مابقدرش أعتمد على two
+
+601
+00:53:30,430 --> 00:53:35,450
+digits فصار هذا الرقم بيفرج تماما عن ال AF
+
+602
+00:53:38,470 --> 00:53:43,470
+هذا رقم من خانتين وهذا رقم من اربع خانات يعني اعلى
+
+603
+00:53:43,470 --> 00:53:48,890
+قص عندك هان هيكون عندك ستة عشر قص تلاتة
+
+604
+00:53:51,090 --> 00:53:55,230
+هذه المعلومات كلها احنا بيعرفها ضمن أي base بدك
+
+605
+00:53:55,230 --> 00:54:00,330
+إياها ضمن أي base بدك إياها زي ما قلنا سابقا بتحدد
+
+606
+00:54:00,330 --> 00:54:04,410
+ال base بتحدد ال digits اللي هو المفروض يكون أكبر
+
+607
+00:54:04,410 --> 00:54:08,010
+أو تساوي صفر وأقل من ال base ولو كان عندك من ال
+
+608
+00:54:08,010 --> 00:54:12,520
+digits هذه رقم من two digits بدك تستبدله برمزعشان
+
+609
+00:54:12,520 --> 00:54:16,980
+هيك كانت البابليون ستين يعني انا ممكن استوعب من
+
+610
+00:54:16,980 --> 00:54:20,280
+صفر لتسعة بعد الستين بدوا يستخدموا letters في
+
+611
+00:54:20,280 --> 00:54:23,660
+العمليات الحسابية تبعتهم لحد ما وصلوا لل system أو
+
+612
+00:54:23,660 --> 00:54:26,500
+لنظام العدل اللي موجود بدنا نفهم المعادلات اللي
+
+613
+00:54:26,500 --> 00:54:30,420
+موجودة وبشكل عام اي رقم بال decimal هياخد الشكل
+
+614
+00:54:30,420 --> 00:54:34,040
+هذا ايه
+
+615
+00:54:34,040 --> 00:54:39,430
+الصفر؟اللي هو ال digit الأول ضرب ال base أُس صفر
+
+616
+00:54:39,430 --> 00:54:44,730
+زائد ال digit التانية في ال base أُس واحد زائد ال
+
+617
+00:54:44,730 --> 00:54:50,290
+digit التالتة في ال base أُس اتنين زائد .. زائد ال
+
+618
+00:54:50,290 --> 00:54:55,830
+digit اللي في المنزلة K مضروب في ال base أُس K
+
+619
+00:54:55,830 --> 00:55:01,010
+الأن هاريش منزلته الشباب أنا بدي أسألك هذا الأن ال
+
+620
+00:55:01,010 --> 00:55:04,150
+K number هو ال K نقص واحد
+
+621
+00:55:09,050 --> 00:55:13,410
+والا ك زائد واحد؟
+
+622
+00:55:13,410 --> 00:55:17,010
+يعني
+
+623
+00:55:17,010 --> 00:55:23,690
+من صفر ل ك من صفر ل ك جداش من صفر ل ك جداش عدد ال
+
+624
+00:55:23,690 --> 00:55:29,790
+digit اللي موجودين ك زائد واحد من صفر ل ك ك زائد
+
+625
+00:55:29,790 --> 00:55:34,310
+واحد العددهم تمام؟ اه وبالتالي هذا ال ك زائد واحد
+
+626
+00:55:34,310 --> 00:55:37,290
+ال digit اللي موجود عندها تمام
+
+627
+00:55:38,950 --> 00:55:42,810
+أحنا بنعرف ال binary و بنعرف التحويل، مظبوط؟ لأن
+
+628
+00:55:42,810 --> 00:55:46,970
+هاي الرقم ال binary اه بيتحول هاي العدد ال binary
+
+629
+00:55:46,970 --> 00:55:52,830
+ال least significant digit اللي هو أكتر عنصر في ..
+
+630
+00:55:52,830 --> 00:55:57,930
+أول عنصر في اليمين، أقل منزلة، ابدا من عنده و أطلع
+
+631
+00:55:57,930 --> 00:56:03,330
+نيرو الصفر في واحد واحد ضرب اتنين أس واحد، واحد
+
+632
+00:56:03,330 --> 00:56:05,470
+ضرب اتنين أس اتنين، واحد ضرب اتنين أس ثلاثة أس
+
+633
+00:56:05,470 --> 00:56:11,480
+أربع أس خمسة ستة سبعة تمانية و هكذاطيب لو انا بدي
+
+634
+00:56:11,480 --> 00:56:16,680
+اعمل العكس شباب بدي احول من decimal يعني تخيل
+
+635
+00:56:16,680 --> 00:56:25,220
+بتبقى بيقولك هال بدي ال 27 بيجسم على ال base 27
+
+636
+00:56:25,220 --> 00:56:30,720
+بال decimal بدي احوله ل binary شو بدي اساوي؟
+
+637
+00:56:30,720 --> 00:56:34,460
+بالضبط بدي اجسم على 2 واحدة فقط بباقى القسمة لإن
+
+638
+00:56:34,460 --> 00:56:38,100
+باقى القسمة صفر او واحد اللي هم بتمثل ال digits
+
+639
+00:56:38,100 --> 00:56:45,370
+تبع ال binary27 على 2 13 و باقى القسم واحد هذا
+
+640
+00:56:45,370 --> 00:56:50,430
+الرقم بمثل ال least significant digit ايش عن ال
+
+641
+00:56:50,430 --> 00:56:55,250
+least significant digit؟ اول واحد في اليمين 13 على
+
+642
+00:56:55,250 --> 00:57:03,630
+2 6 و ببقى الواحد 6 على 2 3 و ببقى الصفر 3 على 2 1
+
+643
+00:57:03,630 --> 00:57:09,280
+و ببقى الواحدواحد على اتنين صفر و بقى قسم خلصنا و
+
+644
+00:57:09,280 --> 00:57:12,780
+هذا هو ال most significant digit يعني الرقم ..
+
+645
+00:57:12,780 --> 00:57:18,280
+برضه مال الأرقام عندي تطلع؟ واحد واحد صفر واحد
+
+646
+00:57:18,280 --> 00:57:26,540
+واحد binary هذا هو هذا least least least أقل منزلة
+
+647
+00:57:26,540 --> 00:57:33,060
+طيب في التماني نفس الكلامبتكلم على من صفر ل سبعة
+
+648
+00:57:33,060 --> 00:57:36,400
+digits و ال base تمانية وهي الرقم اللى بقناه بدي
+
+649
+00:57:36,400 --> 00:57:45,600
+احول من ثمانى او من ثمانى ل decimal و
+
+650
+00:57:45,600 --> 00:57:48,500
+بدي اجسم على تمانية لو بدي اعمل التحويل العكسى بدي
+
+651
+00:57:48,500 --> 00:57:51,980
+اجسم على تمانية لو بدي اعمل التحويل العكسى
+
+652
+00:57:51,980 --> 00:57:57,660
+hexadecimal كل ستناشر digits من صفر لتسعة بالاضافة
+
+653
+00:57:57,660 --> 00:58:01,860
+واحد اتنين تلاتة اربعةلحد ال F من A لحد ال F اللي
+
+654
+00:58:01,860 --> 00:58:07,380
+هو عشر احد اتناش تلتاشر اربعاش خمستاشر والتحويل هي
+
+655
+00:58:07,380 --> 00:58:13,180
+نعرفها انا بتجسم اتجسم على ستناشر
+
+656
+00:58:13,180 --> 00:58:17,680
+فيما يتعلق في
+
+657
+00:58:17,680 --> 00:58:21,020
+التحويل من binary ل octal او hexadecimal لو انا
+
+658
+00:58:21,020 --> 00:58:28,240
+اجير و قلتلك بال octal اكبر رقم جديش الشباب سبعة
+
+659
+00:58:28,240 --> 00:58:29,460
+حوله ل binary
+
+660
+00:58:34,370 --> 00:58:37,330
+يساوي سبعة بالديسميل يساوي واحد واحد واحد بال
+
+661
+00:58:37,330 --> 00:58:44,910
+binary الآن ال F أكبر element بال 8 بال 16 يساوي
+
+662
+00:58:44,910 --> 00:58:51,390
+خمستاشر بال decimal يساوي واحد واحد واحد binary
+
+663
+00:58:51,390 --> 00:58:55,170
+الآن
+
+664
+00:58:55,170 --> 00:58:58,450
+حلقة الوصول ما بين النظم هذا ال decimal لو احنا
+
+665
+00:58:58,450 --> 00:59:04,090
+أجينا أقولك التالي هذه الرقم عندي هذا واحد واحد
+
+666
+00:59:04,490 --> 00:59:09,850
+واحد صفر واحد
+
+667
+00:59:09,850 --> 00:59:15,390
+صفر واحد صفر واحد صفر واحد صفر واحد صفر واحد صفر
+
+668
+00:59:15,390 --> 00:59:18,670
+واحد صفر واحد صفر واحد صفر واحد صفر واحد صفر واحد
+
+669
+00:59:18,670 --> 00:59:18,710
+واحد صفر واحد صفر واحد صفر واحد صفر واحد صفر واحد
+
+670
+00:59:18,710 --> 00:59:19,010
+صفر واحد صفر واحد صفر واحد صفر واحد صفر واحد صفر
+
+671
+00:59:19,010 --> 00:59:21,910
+واحد صفر واحد صفر واحد صفر واحد صفر واحد صفر واحد
+
+672
+00:59:21,910 --> 00:59:32,350
+صفر واحد صفر واحد صفر واحد صفر واحد صفر واحد صفر
+
+673
+00:59:32,350 --> 00:59:33,900
+واحد صفر واحد صفر واحد صفر واحد صفر واحد صفالنقص
+
+674
+00:59:33,900 --> 00:59:42,640
+اللي هو الأول عنصر في اليمين هي تلت خرات الان
+
+675
+00:59:42,640 --> 00:59:47,600
+قدرا ربنا يقدر ان هذا العدد مجسم ع كمتات لو خاصة
+
+676
+00:59:47,600 --> 00:59:51,740
+عندك كمان واحد مباشرة الأصفار اللي على اليسار
+
+677
+00:59:51,740 --> 00:59:56,560
+مالهاش معنى ولا لا فبضيف أصفار زي ما بدك والان
+
+678
+00:59:56,560 --> 01:00:07,400
+مباشرة يحول كل رقم سبعة لبعدهتنين اللي بعده خمسة
+
+679
+01:00:07,400 --> 01:00:13,220
+واحد واربع خمسة خمسة واحد وبالتالي الرقم هذا يساوي
+
+680
+01:00:13,220 --> 01:00:20,460
+واحد خمسة خمسة اتنين سبعة بال اكتل لاحظ التحويل
+
+681
+01:00:20,460 --> 01:00:25,660
+كانت أسهل مايمكن لو بيتحول لست معاش خد اربع خلات
+
+682
+01:00:25,660 --> 01:00:30,340
+اربع خلات وجدت
+
+683
+01:00:30,340 --> 01:00:31,520
+ما بدنا الجلم من الخضراء
+
+684
+01:00:38,910 --> 01:00:47,210
+و هيضفنا تلت أصفار الان هذا الرقم سبعة خمسة
+
+685
+01:00:47,210 --> 01:00:54,710
+أيوة تمانية و تلاتة احداشر بي و هذا واحد و صار هذا
+
+686
+01:00:54,710 --> 01:01:02,460
+الرقم واحد بخمسة سبعةبالـ 16 لاحظت التحويلة هذه
+
+687
+01:01:02,460 --> 01:01:07,680
+كانت هي الأسهل بالنسبالنا وضملة ان اتعامل مع ال
+
+688
+01:01:07,680 --> 01:01:11,020
+binary و ال decimal و ال hexadecimal بشكل سريع
+
+689
+01:01:11,020 --> 01:01:17,100
+عشان هيك تم التركيز على اكتل و ال hexadecimal في
+
+690
+01:01:17,100 --> 01:01:21,320
+ال .. في الكمبيوتر بينما ما استخدموش أنظمة العدد
+
+691
+01:01:21,320 --> 01:01:25,500
+تانية زي السادس او السابع ليش؟ لأن الأرقام اللي
+
+692
+01:01:25,500 --> 01:01:30,800
+موجودةمش هتظل بنفس الكيفية اللي احنا بنشتغل فيها
+
+693
+01:01:30,800 --> 01:01:35,160
+هان، هلا أربع خنات صفر أربع خنات مباشرة، بينما لو
+
+694
+01:01:35,160 --> 01:01:38,160
+بدنا نغير نظام العد مش ضروري، يعني بيصير مثلا تخيل
+
+695
+01:01:38,160 --> 01:01:41,360
+اتكلم على نظام العد الخباسي، برضه بدي أربع خنات
+
+696
+01:01:41,360 --> 01:01:44,880
+ولا لا؟ بدي أربع خنات، لكن ولا مرة هيكون في عندي
+
+697
+01:01:44,880 --> 01:01:48,540
+مسكر زي ما كانت عندي هان السابعة أو كانت عندي إيش؟
+
+698
+01:01:48,540 --> 01:01:52,110
+الخمستاشر اللي موجودة عندي هانهيه خلصنا من ال
+
+699
+01:01:52,110 --> 01:01:54,650
+section التاني، بدنا نتكلم المحاضرة اللي جاء إن
+
+700
+01:01:54,650 --> 01:01:57,690
+شاء الله على الأعداد الأولية والعامل المشترك أو
+
+701
+01:01:57,690 --> 01:02:02,390
+قاسم المشترك الأكبر، في أي سؤال يا شباب؟ الله
+
+702
+01:02:02,390 --> 01:02:03,010
+يعطيكوا العافية
+
diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/rqvb-KVP0rg_raw.json b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/rqvb-KVP0rg_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..bc62c08e7312aa4b7b36eb5b4d199614d8396ddb
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/rqvb-KVP0rg_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4377, "start": 21.19, "end": 43.77, "text": "طيب شباب بسم الله والحمد لله والصلاة والسلام على رسول الله اليوم ان شاء الله هنبدأ بال chapter الرابع اللي هو number theory and cryptography ليش مهتم احنا بال number theory او نظرية الاعداد نظرية الاعداد من ال .. او اللي هو العلم اللي بيهتم بدراسة الاعداد او ال integers الاعداد الصحيحة وخلاصها و اهم", "tokens": [9566, 1829, 3555, 13412, 3555, 16758, 4724, 38251, 21984, 16070, 35571, 3215, 24976, 3224, 16070, 9381, 15040, 3660, 16070, 3794, 37440, 15844, 12602, 3794, 12610, 21984, 45595, 20498, 16472, 13412, 16606, 21984, 8032, 1863, 44510, 10721, 20666, 7187, 34892, 16758, 3615, 13672, 1829, 31439, 1230, 5261, 293, 9844, 5820, 32239, 8592, 3714, 3224, 39237, 1975, 5016, 8315, 20666, 1230, 5261, 1975, 2407, 8717, 19913, 2288, 10632, 42963, 22488, 18513, 8717, 19913, 2288, 10632, 42963, 22488, 18513, 9154, 2423, 4386, 1975, 2407, 13672, 1829, 31439, 18863, 19528, 13672, 1829, 4724, 1829, 3224, 39237, 47525, 23557, 3794, 3660, 42963, 22488, 18513, 1975, 2407, 2423, 41674, 42963, 22488, 18513, 31767, 5016, 1829, 5016, 3660, 4032, 9778, 1211, 33546, 11296, 4032, 1975, 16095], "avg_logprob": -0.16184896069268387, "compression_ratio": 1.9678714859437751, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 21.19, "end": 21.55, "word": "طيب", "probability": 0.7670084635416666}, {"start": 21.55, "end": 21.91, "word": " شباب", "probability": 0.7737630208333334}, {"start": 21.91, "end": 22.37, "word": " بسم", "probability": 0.802490234375}, {"start": 22.37, "end": 22.51, "word": " الله", "probability": 0.96533203125}, {"start": 22.51, "end": 22.79, "word": " والحمد", "probability": 0.790283203125}, {"start": 22.79, "end": 22.91, "word": " لله", "probability": 0.92919921875}, {"start": 22.91, "end": 23.23, "word": " والصلاة", "probability": 0.916015625}, {"start": 23.23, "end": 23.57, "word": " والسلام", "probability": 0.9638671875}, {"start": 23.57, "end": 23.73, "word": " على", "probability": 0.446044921875}, {"start": 23.73, "end": 23.99, "word": " رسول", "probability": 0.97412109375}, {"start": 23.99, "end": 24.21, "word": " الله", "probability": 0.91650390625}, {"start": 24.21, "end": 24.87, "word": " اليوم", "probability": 0.962646484375}, {"start": 24.87, "end": 24.97, "word": " ان", "probability": 0.595703125}, {"start": 24.97, "end": 25.11, "word": " شاء", "probability": 0.97412109375}, {"start": 25.11, "end": 25.11, "word": " الله", "probability": 0.92431640625}, {"start": 25.11, "end": 25.45, "word": " هنبدأ", "probability": 0.886474609375}, {"start": 25.45, "end": 25.55, "word": " بال", "probability": 0.8701171875}, {"start": 25.55, "end": 25.75, "word": " chapter", "probability": 0.7177734375}, {"start": 25.75, "end": 26.27, "word": " الرابع", "probability": 0.9453125}, {"start": 26.27, "end": 27.07, "word": " اللي", "probability": 0.73046875}, {"start": 27.07, "end": 27.37, "word": " هو", "probability": 0.98291015625}, {"start": 27.37, "end": 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binary من أين اتت فكرة ال binary و ال octal و ال hexadecimal؟ من الأعداد وبالتالي صار لنا نقدر نتكلم عن تمثيل ال integers اللي موجودة عندها", "tokens": [5172, 4117, 25720, 8978, 3714, 2407, 11242, 45367, 8717, 19913, 2288, 10632, 16247, 22488, 18513, 39896, 16490, 33546, 10632, 25062, 38251, 3660, 34051, 6225, 42213, 10632, 25062, 38251, 3660, 16070, 10721, 22488, 18513, 16247, 12610, 10632, 32239, 8592, 22807, 8032, 1863, 8592, 38688, 9122, 2304, 7649, 13412, 2407, 10632, 6055, 9566, 21292, 4587, 9957, 4386, 6055, 9566, 21292, 4587, 9307, 9154, 9673, 14851, 9778, 40448, 9307, 8978, 11203, 20498, 21542, 3794, 37746, 46811, 12984, 26895, 13672, 1829, 8032, 1863, 8592, 38688, 9122, 8848, 23275, 5296, 15042, 8717, 2655, 4117, 19528, 18871, 46811, 12984, 26895, 16247, 22488, 18513, 1975, 5016, 8315, 28242, 8315, 44945, 3615, 28480, 2423, 17434, 9154, 5551, 9957, 1975, 2655, 2655, 6156, 4117, 25720, 2423, 17434, 4032, 2423, 13350, 304, 4032, 2423, 23291, 762, 66, 10650, 22807, 9154, 16247, 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hash", "probability": 0.5498046875}, {"start": 2207.39, "end": 2207.87, "word": " function", "probability": 0.939453125}, {"start": 2207.87, "end": 2208.51, "word": " هي", "probability": 0.87255859375}, {"start": 2208.51, "end": 2208.99, "word": " دالة", "probability": 0.6005045572916666}, {"start": 2208.99, "end": 2209.91, "word": " دالة", "probability": 0.9332682291666666}, {"start": 2209.91, "end": 2211.57, "word": " بتحدد", "probability": 0.9534505208333334}, {"start": 2211.57, "end": 2212.27, "word": " موقع", "probability": 0.99609375}, {"start": 2212.27, "end": 2213.03, "word": " البيانات", "probability": 0.9017333984375}, {"start": 2213.03, "end": 2213.47, "word": " او", "probability": 0.760498046875}, {"start": 2213.47, "end": 2213.89, "word": " موقع", "probability": 0.982421875}, {"start": 2213.89, "end": 2214.03, "word": " ال", "probability": 0.96533203125}, {"start": 2214.03, "end": 2214.49, "word": " record", "probability": 0.97900390625}, {"start": 2214.49, "end": 2215.79, 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بيعدّلك اه؟ الله يكبّع شركه الفكرة وين؟ ان ممكن انا استخدم هذه التقنيات و فعليا احمي ال data اللي موجودة عندى بحيث لو اي واحد في المنتصف قرأ البيانات اللي موجودة هذهش مايفهمش أيش القيمة اللي موجودة او بين جثين افتح عليه باب من المجهول و من احتمالات القيم اللي موجودة عندهم", "tokens": [9381, 9640, 2655, 44713, 9778, 40448, 11331, 26108, 3660, 10874, 16254, 41891, 8978, 3224, 46811, 2407, 11703, 2288, 15844, 16472, 9673, 23557, 7435, 3615, 9957, 47525, 10721, 14407, 7251, 5172, 2655, 5016, 14407, 25894, 4117, 14407, 11331, 4117, 11703, 14407, 16472, 2655, 1211, 6055, 1211, 9307, 3660, 4032, 4724, 1829, 22488, 11703, 23275, 1975, 3224, 22807, 21984, 7251, 4117, 3555, 11703, 3615, 13412, 31747, 3224, 27188, 4117, 25720, 4032, 9957, 22807, 16472, 3714, 43020, 1975, 8315, 44713, 9778, 40448, 29538, 16712, 4587, 22653, 9307, 4032, 6156, 3615, 20292, 995, 1975, 35571, 1829, 2423, 1412, 13672, 1829, 3714, 29245, 23328, 3660, 43242, 7578, 4724, 5016, 1829, 12984, 45164, 1975, 1829, 36764, 24401, 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وأقل من ال base ولو كان عندك من ال digits هذه رقم من two digits بدك تستبدله برمز", "tokens": [3224, 24192, 9673, 30241, 20498, 9307, 28242, 11296, 1975, 5016, 8315, 4724, 40228, 28480, 11296, 48812, 27842, 36632, 3096, 47525, 4117, 11933, 25528, 11296, 48812, 27842, 36632, 3096, 47525, 4117, 11933, 25528, 11296, 30767, 1829, 19446, 12174, 1211, 8315, 8608, 16758, 4587, 995, 39894, 24401, 3215, 2423, 3096, 39894, 24401, 3215, 2423, 27011, 13672, 1829, 31439, 9673, 5172, 32887, 11242, 7251, 30544, 5551, 4117, 26890, 34051, 6055, 3794, 995, 45865, 20328, 5172, 2288, 36725, 4587, 1211, 9154, 2423, 3096, 4032, 1211, 2407, 25961, 43242, 4117, 9154, 2423, 27011, 29538, 12602, 4587, 2304, 9154, 732, 27011, 47525, 4117, 6055, 14851, 44510, 43761, 4724, 2288, 2304, 11622], "avg_logprob": -0.18307782850175533, "compression_ratio": 1.9271844660194175, "no_speech_prob": 0.0, "words": [{"start": 3231.09, "end": 3231.31, "word": "هذه", "probability": 0.881591796875}, {"start": 3231.31, "end": 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هياخد", "probability": 0.8994140625}, {"start": 3270.1, "end": 3270.42, "word": " الشكل", "probability": 0.97607421875}, {"start": 3270.42, "end": 3270.74, "word": " هذا", "probability": 0.767578125}, {"start": 3270.74, "end": 3274.04, "word": " ايه", "probability": 0.5863444010416666}, {"start": 3274.04, "end": 3274.84, "word": " الصفر؟", "probability": 0.8809814453125}], "temperature": 1.0}, {"id": 119, "seek": 330415, "start": 3275.91, "end": 3304.15, "text": "اللي هو ال digit الأول ضرب ال base أُس صفر زائد ال digit التانية في ال base أُس واحد زائد ال digit التالتة في ال base أُس اتنين زائد .. زائد ال digit اللي في المنزلة K مضروب في ال base أُس K الأن هاريش منزلته الشباب أنا بدي أسألك هذا الأن ال K number هو ال K نقص واحد", "tokens": [6027, 20292, 31439, 2423, 14293, 16247, 12610, 48812, 25513, 2423, 3096, 5551, 10859, 3794, 20328, 5172, 2288, 30767, 16373, 3215, 2423, 14293, 16712, 7649, 10632, 8978, 2423, 3096, 5551, 10859, 3794, 36764, 24401, 30767, 16373, 3215, 2423, 14293, 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"probability": 0.91259765625}, {"start": 3293.57, "end": 3295.63, "word": " أُس", "probability": 0.9313151041666666}, {"start": 3295.63, "end": 3295.83, "word": " K", "probability": 0.6162109375}, {"start": 3295.83, "end": 3296.77, "word": " الأن", "probability": 0.60125732421875}, {"start": 3296.77, "end": 3297.21, "word": " هاريش", "probability": 0.589324951171875}, {"start": 3297.21, "end": 3297.63, "word": " منزلته", "probability": 0.95654296875}, {"start": 3297.63, "end": 3298.05, "word": " الشباب", "probability": 0.9886067708333334}, {"start": 3298.05, "end": 3299.53, "word": " أنا", "probability": 0.1806640625}, {"start": 3299.53, "end": 3299.73, "word": " بدي", "probability": 0.7093505859375}, {"start": 3299.73, "end": 3300.03, "word": " أسألك", "probability": 0.9373779296875}, {"start": 3300.03, "end": 3300.27, "word": " هذا", "probability": 0.357177734375}, {"start": 3300.27, "end": 3300.69, "word": " الأن", "probability": 0.6904296875}, {"start": 3300.69, "end": 3301.01, 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least least least أقل منزلة طيب في التماني نفس الكلام", "tokens": [14407, 24401, 15844, 1975, 2655, 1863, 9957, 20328, 5172, 2288, 4032, 4724, 4587, 7578, 12174, 38251, 16490, 1211, 9381, 8315, 4032, 23758, 31439, 2423, 881, 4776, 14293, 37495, 22653, 34892, 4587, 2304, 4386, 4724, 43042, 3224, 3714, 6027, 16247, 2288, 4587, 10943, 18871, 16254, 6055, 9566, 1211, 3615, 22807, 36764, 24401, 36764, 24401, 20328, 5172, 2288, 36764, 24401, 36764, 24401, 17434, 23758, 31439, 23758, 1935, 1935, 1935, 5551, 4587, 1211, 9154, 11622, 37977, 23032, 1829, 3555, 8978, 16712, 2304, 7649, 1829, 8717, 36178, 2423, 28820, 10943], "avg_logprob": -0.3020833374439985, "compression_ratio": 1.6176470588235294, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 3425.2, "end": 3425.66, "word": "واحد", "probability": 0.5679931640625}, {"start": 3425.66, "end": 3425.86, "word": " على", "probability": 0.4599609375}, {"start": 3425.86, "end": 3426.3, "word": " اتنين", "probability": 0.935546875}, 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"probability": 0.83837890625}, {"start": 3608.6, "end": 3609.12, "word": " خمسة", "probability": 0.9586181640625}, {"start": 3609.12, "end": 3610.56, "word": " خمسة", "probability": 0.94677734375}, {"start": 3610.56, "end": 3611.4, "word": " واحد", "probability": 0.9384765625}, {"start": 3611.4, "end": 3612.12, "word": " وبالتالي", "probability": 0.91240234375}, {"start": 3612.12, "end": 3612.48, "word": " الرقم", "probability": 0.986328125}, {"start": 3612.48, "end": 3612.68, "word": " هذا", "probability": 0.489990234375}, {"start": 3612.68, "end": 3613.22, "word": " يساوي", "probability": 0.9591064453125}, {"start": 3613.22, "end": 3613.84, "word": " واحد", "probability": 0.865234375}, {"start": 3613.84, "end": 3614.32, "word": " خمسة", "probability": 0.9791259765625}, {"start": 3614.32, "end": 3614.78, "word": " خمسة", "probability": 0.9305419921875}, {"start": 3614.78, "end": 3615.18, "word": " اتنين", "probability": 0.9111328125}, {"start": 3615.18, "end": 3616.4, "word": " سبعة", 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"end": 3718.41, "word": " المشترك", "probability": 0.9930419921875}, {"start": 3718.41, "end": 3719.53, "word": " الأكبر،", "probability": 0.84552001953125}, {"start": 3719.53, "end": 3720.31, "word": " في", "probability": 0.78076171875}, {"start": 3720.31, "end": 3720.41, "word": " أي", "probability": 0.5126953125}, {"start": 3720.41, "end": 3720.63, "word": " سؤال", "probability": 0.99072265625}, {"start": 3720.63, "end": 3720.73, "word": " يا", "probability": 0.81884765625}, {"start": 3720.73, "end": 3721.27, "word": " شباب؟", "probability": 0.95947265625}, {"start": 3721.27, "end": 3722.39, "word": " الله", "probability": 0.7705078125}, {"start": 3722.39, "end": 3722.65, "word": " يعطيكوا", "probability": 0.837109375}, {"start": 3722.65, "end": 3723.01, "word": " العافية", "probability": 0.7263997395833334}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3723.0875625, "duration_after_vad": 3513.7706249999846}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/rqvb-KVP0rg_raw.srt b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/rqvb-KVP0rg_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..dc448208dbe05cacd76efb6f0e1c4e385e4ce8fa
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/rqvb-KVP0rg_raw.srt
@@ -0,0 +1,2828 @@
+1
+00:00:21,190 --> 00:00:23,730
+طيب شباب بسم الله والحمد لله والصلاة والسلام على
+
+2
+00:00:23,730 --> 00:00:25,750
+رسول الله اليوم ان شاء الله هنبدأ بال chapter
+
+3
+00:00:25,750 --> 00:00:30,430
+الرابع اللي هو number theory and cryptography ليش
+
+4
+00:00:30,430 --> 00:00:35,170
+مهتم احنا بال number theory او نظرية الاعداد نظرية
+
+5
+00:00:35,170 --> 00:00:37,610
+الاعداد من ال .. او اللي هو العلم اللي بيهتم
+
+6
+00:00:37,610 --> 00:00:40,910
+بدراسة الاعداد او ال integers الاعداد الصحيحة
+
+7
+00:00:40,910 --> 00:00:48,190
+وخلاصها و اهمفكرة في موضوع نظرية الأعداد هي خاصية
+
+8
+00:00:48,190 --> 00:00:54,030
+القسمة أو عملية القسمة والأعداد الأولية ليش؟ هنشوف
+
+9
+00:00:54,030 --> 00:00:58,990
+كمان شوية تطبيقين .. تطبيقات من المستخدمات في علوم
+
+10
+00:00:58,990 --> 00:01:03,390
+الحسوب تمثيل اللي هنشوف كذلك لما نتكلم عن تمثيل
+
+11
+00:01:03,390 --> 00:01:05,870
+الأعداد احنا كلنا بنعرف ال binary من أين اتت فكرة
+
+12
+00:01:05,870 --> 00:01:09,010
+ال binary و ال octal و ال hexadecimal؟ من الأعداد
+
+13
+00:01:09,010 --> 00:01:12,350
+وبالتالي صار لنا نقدر نتكلم عن تمثيل ال integers
+
+14
+00:01:12,350 --> 00:01:13,530
+اللي موجودة عندها
+
+15
+00:01:16,360 --> 00:01:20,440
+الافكار اللى موجودة دائما فهو فعل نظرية الأعداد
+
+16
+00:01:20,440 --> 00:01:24,900
+تشغل الدماغ بشكل كويس لإنه فعليا أحيان بتحس أن
+
+17
+00:01:24,900 --> 00:01:29,460
+النظريات أو العيوم اللى موجودة شغلة و أنت بتفكر
+
+18
+00:01:29,460 --> 00:01:36,280
+فيها بتستمتع عشان هيك في ناس كتير بيقولك .. ناس
+
+19
+00:01:36,280 --> 00:01:39,960
+اللى بتنجذب لعلم الرياضيات أو لعلم نظرية الأعداد
+
+20
+00:01:39,960 --> 00:01:45,570
+بالدرجة الأولى بتجذبها أيش؟ جمال الأفكارفي الموضوع
+
+21
+00:01:45,570 --> 00:01:49,590
+هذا طبعا لو اتكلم مع جماعة الأفكار معناته الشيء
+
+22
+00:01:49,590 --> 00:01:54,790
+اللي بتحسه عن جد و انت بتدرس في الموضوع انه على
+
+23
+00:01:54,790 --> 00:01:57,330
+خلاف الرياضيات اللي احنا بنعرفها على رغم انه علمها
+
+24
+00:01:57,330 --> 00:01:59,730
+من ال pure mathematics يعني المفروض انه من العلوم
+
+25
+00:01:59,730 --> 00:02:05,230
+الصعبة اللي غير انه لأن تطبيقاته ملموسة تمام فبتحس
+
+26
+00:02:05,230 --> 00:02:09,880
+ان فيها فكرة كويسةنجيك ان القيامة للناس القديمة من
+
+27
+00:02:09,880 --> 00:02:13,920
+زمان كانوا بتعاملوا مع نظرية الاعداد الموجودة هل
+
+28
+00:02:13,920 --> 00:02:18,600
+ال sections الخمسة او الستة الموجودة خوص القسمة و
+
+29
+00:02:18,600 --> 00:02:22,080
+تمثيل الاعداد الـprimes و كيف ال congrance و
+
+30
+00:02:22,080 --> 00:02:24,380
+انحلهم ال application سبعتهم و ال cryptography
+
+31
+00:02:24,380 --> 00:02:28,320
+اللي هو اخر section هيكون موجود عندنا هنخلص غالبا
+
+32
+00:02:28,320 --> 00:02:31,240
+هنغطسه ال section واحد و اتنين اليوم ان شاء الله
+
+33
+00:02:31,240 --> 00:02:34,860
+تعالىقولها نظرية الأعداد هو العلم اللي باهتم
+
+34
+00:02:34,860 --> 00:02:40,420
+بدراسة الأرقام الأعداد الصحيحة وخواصها و أهم خاصية
+
+35
+00:02:40,420 --> 00:02:48,540
+خاصية القسمة لما باجي بقول الشباب A تقسم ال B
+
+36
+00:02:48,540 --> 00:02:53,280
+مباشرة بدي تبقى برا ذهنك ان ال D او ال A هي ال
+
+37
+00:02:53,280 --> 00:02:57,500
+divisor ايش
+
+38
+00:02:57,500 --> 00:03:03,720
+يعني؟القاسم القاسم كانوا يعلمونا زمان في عندي في
+
+39
+00:03:03,720 --> 00:03:09,160
+كل عملية قسمة في عندي مقسوم و مقسوم عليه اللي هو
+
+40
+00:03:09,160 --> 00:03:14,840
+ال divisor و معامل القسمة او ناتج القسمة و الباقي
+
+41
+00:03:14,840 --> 00:03:20,220
+remainder باقي القسمة يعني لو اتيت انا قلتلك جسم
+
+42
+00:03:20,220 --> 00:03:23,140
+17 على 3
+
+43
+00:03:29,180 --> 00:03:37,840
+17 على 3 تساوي 5 تمام؟ و 2 as
+
+44
+00:03:37,840 --> 00:03:41,120
+a remainder و بينجو سينم لك تبقى بصيغة بالشكل هذا
+
+45
+00:03:41,120 --> 00:03:52,680
+3 ضرب 5 زائد 2 هذا تساوي من 17 17 تساوي 3 في 5
+
+46
+00:03:52,680 --> 00:03:58,690
+زائد 2 3 هي القاسم او المقسوم عليهQuantity يعني
+
+47
+00:03:58,690 --> 00:04:01,750
+كمية
+
+48
+00:04:01,750 --> 00:04:08,070
+والباقي ال remainder اللى موجود عندها وبالتالي لما
+
+49
+00:04:08,070 --> 00:04:13,130
+باجب اقول a divides ال b او ال a تقسم ال b معناته
+
+50
+00:04:13,130 --> 00:04:22,340
+انا جاهز بقول ان ال b من مضاعفاتالـ A Divides يعني
+
+51
+00:04:22,340 --> 00:04:27,640
+تقسم أن الـ B من مضاعفات الـ A طبق القسمة صفر مش
+
+52
+00:04:27,640 --> 00:04:33,060
+موجود لما باجي بقول التلاتة تقسم التمنعش التلاتة
+
+53
+00:04:33,060 --> 00:04:37,750
+تقسم الواحد وعشرينالـ3 لا تقسم الـ17، لماذا لا
+
+54
+00:04:37,750 --> 00:04:41,590
+تقسم الـ17؟ لأن في عندي باقي قسمة، لأن في عندي
+
+55
+00:04:41,590 --> 00:04:45,930
+باقي قسمة، فالمفهوم الـdivides أنه أنا ماعنديش
+
+56
+00:04:45,930 --> 00:04:50,590
+باقي قسمة، ماعنديش باقي قسمة، ولمّا بقول A divides
+
+57
+00:04:50,590 --> 00:04:56,230
+الـB، A divides الـB، أول حاجة الـA ليه تسوى صفر؟
+
+58
+00:04:56,230 --> 00:05:02,280
+لأن القسمة على صفر عملية غير معرفةمعناته بلاقي
+
+59
+00:05:02,280 --> 00:05:05,640
+integer C بحيث ان الـ B تساوي A في C وهذا معناته
+
+60
+00:05:05,640 --> 00:05:18,900
+ان الـ B من المضاعفات الـ A لما
+
+61
+00:05:18,900 --> 00:05:24,420
+بلاقي A تقسم الـ B و الـ A تقسم الـ C معناته الـ A
+
+62
+00:05:24,420 --> 00:05:35,010
+بتقسم مجموحهم الآن اذا كانت الـ Aالتلاتة تقسم
+
+63
+00:05:35,010 --> 00:05:41,310
+التسعة بالظبط التلاتة تقسم الخمستاش مباشرة انا
+
+64
+00:05:41,310 --> 00:05:46,050
+بقول التلاتة تقسم الاربع عشرين الاربع عشرين عبارة
+
+65
+00:05:46,050 --> 00:05:53,170
+عن ايش؟ اللي هي تسعة زاد الخمستاش بالظبط فبالتالي
+
+66
+00:05:53,170 --> 00:05:58,510
+و لا بتلاقي ان ال a تقسم b يعني ال b من المضاعفات
+
+67
+00:05:59,740 --> 00:06:03,680
+الـ A والـ A تقسم الـ C .. C يعني المضاعفات الـ A
+
+68
+00:06:03,680 --> 00:06:09,640
+فحصل جمعهم هيكون من المضاعفات الـ A تعالي شوية بس
+
+69
+00:06:09,640 --> 00:06:14,460
+.. هيا عشان أقولك ليش هذا الكلام إيجي صح؟ قول لما
+
+70
+00:06:14,460 --> 00:06:17,920
+تكون A من المضاعفات أو الـ B من المضاعفات الـ C أو
+
+71
+00:06:17,920 --> 00:06:21,520
+الـ B من المضاعفات الـ A معناته بيبدأ تساوي افترض
+
+72
+00:06:21,520 --> 00:06:30,200
+A برب K واحد والـ K تمتمي للـ Z عدد صحيحوالـ C
+
+73
+00:06:30,200 --> 00:06:33,140
+كذلك الـ A تقسم الـ C يعني الـ C من مضاعفات الـ A
+
+74
+00:06:33,140 --> 00:06:41,760
+الـ C بتها تساوي A في K اتنين مصبوط اجمع اجمع الان
+
+75
+00:06:41,760 --> 00:06:50,080
+B وزائد C B زائد C ايش يساوي الشباب A K واحد زائد
+
+76
+00:06:50,080 --> 00:06:55,080
+A K اتنين وتساوي خد ال A عامل مشترك A في K واحد
+
+77
+00:06:55,080 --> 00:07:00,120
+زائد K اتنين هذا العدد ينتميللـ Z ده الأعداد
+
+78
+00:07:00,120 --> 00:07:05,180
+الصحيحة مظبوط وبالتالي أصبح العدد هذا من مضاعفات
+
+79
+00:07:05,180 --> 00:07:09,100
+ال A هيه من مضاعفات ال A عشان هيك بنقول إن ال A
+
+80
+00:07:09,100 --> 00:07:13,920
+تقسم ال B A تقسم ال C معناته ال A تقسم B زائد C
+
+81
+00:07:13,920 --> 00:07:20,820
+أنا مش هطلبك بأي أثبات رياضي لكن بدي دايما تستحضر
+
+82
+00:07:20,820 --> 00:07:24,800
+أو تحاول تسأل نفسك ليش؟ ليش الأعمالية هذه بتصير صح
+
+83
+00:07:24,800 --> 00:07:25,520
+أو غلط؟
+
+84
+00:07:30,610 --> 00:07:36,470
+الان if a تقسم ال b معناته
+
+85
+00:07:36,470 --> 00:07:43,130
+a تقسم ال b لأي integer c ايش يعني مفهومها ان ال b
+
+86
+00:07:43,130 --> 00:07:46,950
+هي قيمتها من المضاعفات اللي موجودة او ايش ما كانت
+
+87
+00:07:46,950 --> 00:07:48,770
+ال b هي ال c اللي هتطلع عندى
+
+88
+00:07:51,550 --> 00:07:55,630
+هل التلاتة تقسم الستة لحالها و بس؟ لأ تقسم الستة
+
+89
+00:07:55,630 --> 00:08:00,050
+تقسم التسعة عشر خمس عشر كمان عشر واحد و عشرين كل
+
+90
+00:08:00,050 --> 00:08:03,290
+مضاعفات التلاتة التلاتة بتبقى ثابتة و ميه اللي
+
+91
+00:08:03,290 --> 00:08:06,990
+بيختلف ال constant اللي أنا بضربه فيه في التلاتة
+
+92
+00:08:06,990 --> 00:08:09,610
+اللي بيمثل المضاعف عشان هيك بقول ان هذه بتكون
+
+93
+00:08:09,610 --> 00:08:15,150
+صحيحة لأي integer لأي integer C طيب لو كانت ال A
+
+94
+00:08:15,150 --> 00:08:21,190
+تقسم ال B و ال B تقسم ال C معناته ال A تقسم ال C
+
+95
+00:08:22,350 --> 00:08:28,590
+طيب التعدى ايه سمناها عندما تكلمنا عن ال
+
+96
+00:08:28,590 --> 00:08:34,530
+relations؟ حد بتذكر ايه سمنا خاصيتي التعدى؟
+
+97
+00:08:34,530 --> 00:08:39,570
+Transitive خاصيتي التعدى لو كانت ال a تقسم ال b
+
+98
+00:08:39,570 --> 00:08:47,190
+and ال b تقسم ال c معناه هذا يؤدي إلى ان ال a تقسم
+
+99
+00:08:47,190 --> 00:08:50,970
+ال c صح؟
+
+100
+00:08:51,760 --> 00:08:56,700
+طيب نحاول نثبتها على السريع بس المهاتب ال B بيضها
+
+101
+00:08:56,700 --> 00:09:05,180
+تساوي A في K تمام؟ و ال C بيضها تساوي B في K واحد
+
+102
+00:09:05,180 --> 00:09:17,300
+عوّب عن ال بيها A K لقيمة ال B في K واحد بتساوي A
+
+103
+00:09:17,300 --> 00:09:25,920
+في K في K واحدأصبحت ان الـ C هادي من المضاعفات الـ
+
+104
+00:09:25,920 --> 00:09:30,440
+A وبالتالي تقسم الـ A تقسم الـ C كمان مرة إذا الـ
+
+105
+00:09:30,440 --> 00:09:35,180
+A تقسم الـ B و الـ B تقسم الـ C معناته الـ A تقسم
+
+106
+00:09:35,180 --> 00:09:40,740
+الـ C كيف؟
+
+107
+00:09:40,740 --> 00:09:48,180
+عملنا رقم ماشي الحال الآن لو أنا اديت قلت التلاتة
+
+108
+00:09:48,180 --> 00:10:01,560
+تقسم التسعة andتسعة تقسم الواحد و تمانين تقسم
+
+109
+00:10:01,560 --> 00:10:04,320
+الواحد و تمانين تقسم الواحد و تمانين تقسم الواحد و
+
+110
+00:10:04,320 --> 00:10:04,400
+تمانين تقسم الواحد و تمانين تقسم الواحد و تمانين
+
+111
+00:10:04,400 --> 00:10:04,400
+تقسم الواحد و تمانين تقسم الواحد و تمانين تقسم
+
+112
+00:10:04,400 --> 00:10:04,560
+الواحد و تمانين تقسم الواحد و تمانين تقسم الواحد و
+
+113
+00:10:04,560 --> 00:10:05,480
+تمانين تقسم الواحد و تمانين تقسم الواحد و تمانين
+
+114
+00:10:05,480 --> 00:10:05,480
+تقسم الواحد و تمانين تقسم الواحد و تمانين تقسم
+
+115
+00:10:05,480 --> 00:10:05,500
+الواحد و تمانين تقسم الواحد و تمانين تقسم الواحد و
+
+116
+00:10:05,500 --> 00:10:08,440
+تمانين تقسم الواحد و تمانين تقسم الواحد و تمانين
+
+117
+00:10:08,440 --> 00:10:17,410
+تقسم الواحد و تمانين تقسم الواحد و تمانين تتقسم
+
+118
+00:10:17,410 --> 00:10:26,890
+التسعة تقسم التمنطعش التلاتة تقسم التمنطعش تقسم
+
+119
+00:10:26,890 --> 00:10:28,770
+التمنطعش تقسم التمنطعش تقسم التمنطعش تقسم التمنطعش
+
+120
+00:10:28,770 --> 00:10:28,930
+تقسم التمنطعش تقسم التمنطعش تقسم التمنطعش تقسم
+
+121
+00:10:28,930 --> 00:10:32,070
+التمنطعش تقسم التمنطعش تقسم التمنطعش تقسم التمنطعش
+
+122
+00:10:32,070 --> 00:10:34,170
+تقسم التمنطعش تقسم التمنطعش تقسم التمنطعش تقسم
+
+123
+00:10:34,170 --> 00:10:38,310
+التمنطعش تقسم التمنطعش تقسم التمنطعش تقسم التمنطعش
+
+124
+00:10:38,310 --> 00:10:43,070
+تقسم التمنطعش تقسم التمنطعش تقسم التمنطعش تقسم
+
+125
+00:10:43,070 --> 00:10:44,190
+التمنطعش تقسم التمنطعش تقسم التمنطعش تقسم التمنط
+
+126
+00:10:44,620 --> 00:10:53,580
+الان اذا ماكنش الرقم العدد
+
+127
+00:10:53,580 --> 00:10:59,420
+المقصوم لو ماكنش من مضاعفات ال divisor معناته حتما
+
+128
+00:10:59,420 --> 00:11:04,360
+هقدر اكتب على صورة معادلة كمية مضغوبة في ال
+
+129
+00:11:04,360 --> 00:11:10,950
+divisor زائد remainder يعني الآن 17ما هي علاجاتها
+
+130
+00:11:10,950 --> 00:11:14,930
+بالتلاتة؟ هل هي مباعثات التلاتة؟ لأ، لكن بقدر أقول
+
+131
+00:11:14,930 --> 00:11:18,730
+السبعة عشر تساوي التلاتة كـ divisor مضروبة في
+
+132
+00:11:18,730 --> 00:11:22,790
+خمسة، تمام؟ وهذه الخمسة بسميها الـ quotient أو
+
+133
+00:11:22,790 --> 00:11:27,810
+الكمية، تمام؟ أو ناتج القسمة، زائد اتنين، الـ
+
+134
+00:11:27,810 --> 00:11:33,770
+remainder، باقى القسمة، الأن تبقي معايا ال
+
+135
+00:11:33,770 --> 00:11:39,770
+divisor لازم يكون positive integerالـ divisor لازم
+
+136
+00:11:39,770 --> 00:11:48,130
+يكون positive integer طيب لو كانت الرقم سالب سالب
+
+137
+00:11:48,130 --> 00:11:56,490
+17 شوف انها تساوي او سالب 15 ثلاثة
+
+138
+00:11:56,490 --> 00:12:00,790
+في سالب خمسة الكمية ممكن تكون بالسالب الكمية اللي
+
+139
+00:12:00,790 --> 00:12:05,390
+عندي هذه او ال quotient ممكن تكون بالسالببس ال
+
+140
+00:12:05,390 --> 00:12:10,510
+remainder لأ ال remainder ميزته او خصائصه ان هو
+
+141
+00:12:10,510 --> 00:12:15,490
+اكبر او تساوي الصفر و اقل او تساوي ال D فإذا كانت
+
+142
+00:12:15,490 --> 00:12:19,330
+ال D positive ال divisor يعني ال R لازم تكون
+
+143
+00:12:19,330 --> 00:12:24,730
+positive لأنها اكبر او تساوي الصفر تمام لما باج
+
+144
+00:12:24,730 --> 00:12:32,470
+انا بقول كمان مرة هي المعادلة A تساوي D Q زائد ال
+
+145
+00:12:32,470 --> 00:12:38,040
+Rالـ R محصورة ما بين الصفر والـ D أكبر أو تساوي
+
+146
+00:12:38,040 --> 00:12:47,680
+الصفر أو أقل من الـ D A Divident المقسوم D Divisor
+
+147
+00:12:47,680 --> 00:12:54,220
+القاسم Q Quotient كمية أو ناتج القسمة والـ R
+
+148
+00:12:54,220 --> 00:12:59,500
+remainder أو بقى القسمة لما أنا بدي أجري أقول
+
+149
+00:12:59,500 --> 00:13:00,140
+كتالي
+
+150
+00:13:02,780 --> 00:13:07,720
+تلاتة و عشرين تساوي
+
+151
+00:13:07,720 --> 00:13:10,960
+لو انا اخترت التنين as divisor بيمشي الحلولة يا
+
+152
+00:13:10,960 --> 00:13:20,300
+شباب بيمشي مضوبة فيه اتنين في احداشر اتنين و عشرين
+
+153
+00:13:20,300 --> 00:13:31,280
+زائد واحد مباشرة الان divisor quantity a quotient
+
+154
+00:13:32,390 --> 00:13:37,750
+Reminder بقى قسمة لما يكون الرقم سالب يجب أن تحافظ
+
+155
+00:13:37,750 --> 00:13:41,830
+على نفس المعادلة لما يكون الرقم سالب يجب أن تحافظ
+
+156
+00:13:41,830 --> 00:13:44,870
+على نفس المعادلة ايش هنتحافظ على نفس المعادلات انه
+
+157
+00:13:44,870 --> 00:13:50,870
+دائما ال divisor positive و ال reminder positive
+
+158
+00:13:50,870 --> 00:13:59,670
+تعالج يقول سالب 23 مع ال divisor 2 تساوي
+
+159
+00:14:03,380 --> 00:14:09,280
+-11 ايه صارت؟ نقص 22 عشان تصير سالب 23 بدي اعمل
+
+160
+00:14:09,280 --> 00:14:13,540
+نقص 1 وهي ما صارت انا و جاعت في غلط لانه لازم ال
+
+161
+00:14:13,540 --> 00:14:20,080
+remainder يكون positive فايش الحل اضرب
+
+162
+00:14:20,080 --> 00:14:29,440
+في 12 صارت سالب 24 زائد ال 1 نفس
+
+163
+00:14:29,440 --> 00:14:32,200
+الكلام اللي انا بدي اعمله على خمسة على سبيل المثال
+
+164
+00:14:33,060 --> 00:14:38,180
+بدي استخدم divisor آخر اللي هو الخمسة تلاتة و
+
+165
+00:14:38,180 --> 00:14:51,720
+عشرين تساوي خمسة في أربعة زائد تلاتة حان خمسة
+
+166
+00:14:51,720 --> 00:14:58,860
+في خمسة خمسة و عشرين زائد اتنين ممتاز خمسة في سالب
+
+167
+00:14:58,860 --> 00:15:06,040
+خمسة سالب خمسة و عشرينزائد اتنين وطبعا
+
+168
+00:15:06,040 --> 00:15:10,300
+لو كنت انت ماخد برمجة وجربت تستخدم ال modulus او
+
+169
+00:15:10,300 --> 00:15:14,360
+باقى القسمة ايش ما كان الرقم دايما كانت بيطلع باقى
+
+170
+00:15:14,360 --> 00:15:19,820
+القسمة معاك positive والاصل تكون سألت نفسك ليش
+
+171
+00:15:19,820 --> 00:15:23,300
+بتديني positive مع الأرقام السالبة لأن بالصمم هادر
+
+172
+00:15:23,300 --> 00:15:27,020
+انه لازم دايما ال remainder يكون عدد محصور ما بين
+
+173
+00:15:27,020 --> 00:15:30,840
+أكبر أو تساوي صفر واقل من ال divisor اللى موجودة
+
+174
+00:15:30,840 --> 00:15:31,120
+انها
+
+175
+00:15:35,650 --> 00:15:41,050
+الـ 101 لو أنا بدأ أجسمها على الـ 11 كيف بدأ أكتب
+
+176
+00:15:41,050 --> 00:15:47,010
+المعادلة اللي عندي 101
+
+177
+00:15:47,010 --> 00:15:53,850
+تساوي
+
+178
+00:15:53,850 --> 00:15:58,750
+ال device هو 11 يعني إيش مطلوب مني أحدد ال
+
+179
+00:15:58,750 --> 00:16:02,750
+quantity ال quotient و ال remainder
+
+180
+00:16:07,360 --> 00:16:11,900
+بكل بساطة شباب عشان تقدر تحدد ال quotient صح بدك
+
+181
+00:16:11,900 --> 00:16:15,300
+تاخد رقم يقارب القيمة اللي عندها أسهل هيضرب في
+
+182
+00:16:15,300 --> 00:16:19,180
+عشرة و لاش رايك عشرة في أحد عاشر مية و عشرة كبيرة
+
+183
+00:16:19,180 --> 00:16:22,900
+مباشرة خد اللي أقل منه تسعة في أحد عاشر تسعة
+
+184
+00:16:22,900 --> 00:16:28,700
+وتسعين ماتت تسعة مناسبة جدا زائد اتنين هي القيمة
+
+185
+00:16:28,700 --> 00:16:33,360
+اللي موجودة عندها طيب لو انا يا جيل قلتلك
+
+186
+00:16:36,400 --> 00:16:45,140
+المية واحد هذه تجسمها على سبعة ال
+
+187
+00:16:45,140 --> 00:16:48,300
+divisor سبعة ال reminder بدي ال quotient و ال
+
+188
+00:16:48,300 --> 00:16:55,820
+reminder شو بقى تساوي سبعة فا اتناش سبعة
+
+189
+00:16:55,820 --> 00:17:01,180
+فا عشرة سبعينأربعة و تمانى لسه مازلنا بقعد بصبوط
+
+190
+00:17:01,180 --> 00:17:04,620
+بقيتوا انا بتكلم على سبعة في خمس تاش جديش تطلع
+
+191
+00:17:04,620 --> 00:17:07,300
+خمسة و تلاتيه مية و عشرة .. مية و خمس تاش تطلع
+
+192
+00:17:07,300 --> 00:17:11,300
+زيادة اربعة و طعاش بدون ما استخدم ال calculator
+
+193
+00:17:11,300 --> 00:17:16,220
+الأصل يتجرب تشغل لتروس اللي فوق لأن هيك هم كانوا
+
+194
+00:17:16,220 --> 00:17:19,300
+بيعلمونا بفعالية من و احنا في المدرسة ماحفظوناش
+
+195
+00:17:19,300 --> 00:17:22,660
+أرقام أو جداو للضرب عادة بحيث اننا نحاول نستفيد
+
+196
+00:17:22,660 --> 00:17:26,740
+منها قدر المستطاع الآن كمان مرة انا حاسب ticket
+
+197
+00:17:26,740 --> 00:17:32,180
+تانى7×12 هو 84 هذا كان السقف اللي احنا حفظناه في
+
+198
+00:17:32,180 --> 00:17:39,320
+الجداول بدي ارفع ل 15 انا بدور ب 15 5×3 هيك او 7×5
+
+199
+00:17:39,320 --> 00:17:46,120
+هو 35 و 70 تلت معايا 115 out 105 عفوا 105 out
+
+200
+00:17:46,120 --> 00:17:53,700
+وبالتالي لأ انا بدي اللي جابلها 5×14 زاد كده ايش؟
+
+201
+00:17:53,700 --> 00:17:56,720
+زاد ال remainder 3
+
+202
+00:17:59,790 --> 00:18:05,650
+7×4 هو 28 7×1
+
+203
+00:18:05,650 --> 00:18:22,370
+هو 7 9 هو 98 ثانية
+
+204
+00:18:22,370 --> 00:18:22,690
+ثانية ثانية ثانية ثانية ثانية ثانية ثانية ثانية
+
+205
+00:18:22,690 --> 00:18:22,850
+ثانية ثانية ثانية ثانية ثانية ثانية ثانية ثانية
+
+206
+00:18:22,850 --> 00:18:22,890
+ثانية ثانية ثانية ثانية ثانية ثانية ثانية ثانية
+
+207
+00:18:22,890 --> 00:18:22,890
+ثانية ثانية ثانية ثانية ثانية ثانية ثانية ثانية
+
+208
+00:18:22,890 --> 00:18:22,890
+ثانية ثانية ثانية ثانية
+
+209
+00:18:26,480 --> 00:18:30,460
+انه لازم يكون دائما ال remainder positive لازم
+
+210
+00:18:30,460 --> 00:18:34,340
+يكون ال remainder positive فممكن اذا صح و غلط اروح
+
+211
+00:18:34,340 --> 00:18:42,940
+اقولك سالب .. سالب 11 بسمتها
+
+212
+00:18:42,940 --> 00:18:48,060
+على 3 تساوي المعادلة هذه صح ولا غلط؟ مباشر غلط
+
+213
+00:18:48,950 --> 00:18:54,150
+مباشرة غلط كحسبة كحسبة انت حسبت صح ماحدش بيقولك لا
+
+214
+00:18:54,150 --> 00:19:01,250
+بس لما انا بتكلم على خاصية القسمة يعرفته انسان
+
+215
+00:19:01,250 --> 00:19:05,470
+الموضوع لأ لازم تكون دايما ال remainder positive
+
+216
+00:19:05,470 --> 00:19:10,330
+ماحبنقول احنا هذا غلط وبالتالي احنا لازم نمثله
+
+217
+00:19:10,330 --> 00:19:13,910
+بالشكل هذا طيب
+
+218
+00:19:15,120 --> 00:19:19,720
+الان بعد ما شوفنا القسمة و باقي القسمة في عندي
+
+219
+00:19:19,720 --> 00:19:24,960
+شغلة بسميها ال modular arithmetic ال modular باقي
+
+220
+00:19:24,960 --> 00:19:29,900
+القسمة من ال modulus الان في عندي نظرية بتقولك
+
+221
+00:19:29,900 --> 00:19:33,860
+التالي او definition لو كان في عندي two positive
+
+222
+00:19:33,860 --> 00:19:38,900
+integers a و b و عندي positive او عفوا a و b عبارة
+
+223
+00:19:38,900 --> 00:19:41,880
+عن integers و عندي positive integer ام اللي هو ال
+
+224
+00:19:41,880 --> 00:19:57,170
+divisorبقدر أقول A is congruent to B modulo M يعني
+
+225
+00:19:57,170 --> 00:20:02,770
+ال A متجانسة مع ال B من ناحية باقي القسمة على ال M
+
+226
+00:20:09,450 --> 00:20:12,690
+ماذا يعني؟ يعني أن الـA و الـB بكل بساطة لهم نفس
+
+227
+00:20:12,690 --> 00:20:18,570
+باقي القسمة لما يكون الـA و الـB لهم نفس باقي
+
+228
+00:20:18,570 --> 00:20:26,510
+القسمة معناته بقول أن الـM divides A لاقص الـB
+
+229
+00:20:26,510 --> 00:20:30,570
+بالمثال اللي موجود عندها بكل بساطة و بنعيده على
+
+230
+00:20:30,570 --> 00:20:31,230
+مثال آخر
+
+231
+00:20:33,930 --> 00:20:38,730
+والاربعة او السبعة is congruent اربعة مدل التلاتة
+
+232
+00:20:38,730 --> 00:20:43,850
+السبعة متجانسة مع الأربعة من حيث باق القسم على
+
+233
+00:20:43,850 --> 00:20:49,570
+تلاتة شو يعني؟ يعني السبعة باق قسم السبعة تلاتة
+
+234
+00:20:49,570 --> 00:20:53,770
+كام يا شباب؟ واحد باق قسم الأربعة على تلاتة كام؟
+
+235
+00:20:53,770 --> 00:20:59,550
+واحد النظرية هذه بتقول كالتالي هتلاقي ان التلاتة
+
+236
+00:20:59,550 --> 00:21:05,670
+هذهdivides تقسم السبعة نقص الأربعة سبعة نقص
+
+237
+00:21:05,670 --> 00:21:09,850
+الأربعة كام يا شباب؟ تلاتة التلاتة تقسم التلاتة؟
+
+238
+00:21:09,850 --> 00:21:15,010
+true فاش reminder فاش بقى قسمة واحد تعالى نشوف
+
+239
+00:21:15,010 --> 00:21:20,430
+مثال آخر بقولش
+
+240
+00:21:20,430 --> 00:21:27,450
+اتحصل السبعة تعاشر والخمسة مدر التلاتة congruent
+
+241
+00:21:27,450 --> 00:21:35,120
+ولا لأ؟مدل الستة عفواً 17 is congruent مدل الخمسة
+
+242
+00:21:35,120 --> 00:21:40,500
+مد الستة ولا لأ الآن مباشرة تقدر تقول true ولا
+
+243
+00:21:40,500 --> 00:21:49,160
+false بحيث انك تروح تقول 17 مد الستة وخمسة مد
+
+244
+00:21:49,160 --> 00:21:52,440
+الستة اذا الانتين هدولة طلعوا متساويات فال 17
+
+245
+00:21:52,440 --> 00:21:58,840
+congruent لمن للخمسةمدل الستة بقى قسم السبعبعاش
+
+246
+00:21:58,840 --> 00:22:06,440
+على ستة جداش الشباب ستة في اتنين زي خمسة ستة في
+
+247
+00:22:06,440 --> 00:22:12,140
+اتنين زي خمسة يعني باقوا القسمة خمسة خمسة مدل
+
+248
+00:22:12,140 --> 00:22:18,580
+الستة خمسة ليش اتنين؟ بشوي اقل يعني الآن الخمسة
+
+249
+00:22:18,580 --> 00:22:25,080
+تساوي ستة في quotient equal zero زاد الخمسة عشان
+
+250
+00:22:25,080 --> 00:22:29,940
+ليس واحد واحدالان ..واشي الحالة ده يمكن المثال
+
+251
+00:22:29,940 --> 00:22:33,600
+مابديش أكون الصبجته عيد تاني ..الان يا شباب لو أنا
+
+252
+00:22:33,600 --> 00:22:37,240
+اتيت دايما قولتلك لو كان العدد اللي عندك أقل من ال
+
+253
+00:22:37,240 --> 00:22:42,580
+divisor ايش ال quotient تبعته؟ صفر ..والعدد كله
+
+254
+00:22:42,580 --> 00:22:48,200
+بيكون remainder يعني لما باجي بقول انا التلاتة
+
+255
+00:22:48,200 --> 00:22:53,060
+مض الخمسة او تلاتة و خمسة ..divisor خمسة تساوي
+
+256
+00:22:53,060 --> 00:22:58,270
+اتنين ..مصبور؟تساوي اتنين او تلاتة؟ تلاتة التلاتة
+
+257
+00:22:58,270 --> 00:23:03,050
+هذه تساوي ال device وغير الخمسة مضروبة في صفر زائد
+
+258
+00:23:03,050 --> 00:23:07,350
+التلاتة as remainder وبالتالي ال quotient زي ما
+
+259
+00:23:07,350 --> 00:23:10,950
+كانت سالبة ممكن تكون صفر زي ما كانت سالبة ممكن
+
+260
+00:23:10,950 --> 00:23:13,850
+تكون صفر بس لازم ان ال remainder يكون positive
+
+261
+00:23:13,850 --> 00:23:18,710
+فالان الادية حسبت اتنين اللي هم نفس ال modulus نفس
+
+262
+00:23:18,710 --> 00:23:21,970
+بقع نفس ال remainder نفس بقع القسمة وبالتالي السبع
+
+263
+00:23:21,970 --> 00:23:27,670
+عشر is congruent toخمسة النظرية بتقول كتاري لو هذا
+
+264
+00:23:27,670 --> 00:23:34,310
+الكلام كان صحيح معناته .. معناته ان الستة بتقسم
+
+265
+00:23:34,310 --> 00:23:38,410
+الفرق ما بين الاتنين او بين جسين فرق ما بين اتنين
+
+266
+00:23:38,410 --> 00:23:46,490
+هيكون من مضاعفات الستة تعالى نشوف ستة تقسم سبعتاش
+
+267
+00:23:46,490 --> 00:23:53,780
+ناقص خمسة عشر true مية لميةتعالى نشوف المثال
+
+268
+00:23:53,780 --> 00:23:59,340
+التالي بيقول شوف ليه هى ال 24 وال 14 is congruent
+
+269
+00:23:59,340 --> 00:24:07,900
+to 4 او 6 or not فجدامك انت تاخد طريقتين ايه اسهل
+
+270
+00:24:07,900 --> 00:24:11,420
+بالنسبة لك عشان تاخد decision yes or no اللي
+
+271
+00:24:11,420 --> 00:24:23,510
+اريحلك بدي اقوله 24 مض 6 و 14 مض 6أربع عشر مد ..
+
+272
+00:24:23,510 --> 00:24:27,270
+أربع عشر مد الستة صفر لأن الستة مد .. الأربع عشر
+
+273
+00:24:27,270 --> 00:24:32,390
+مد المضاعفات الستة أربع عشر مد الستة تساوى اتنين
+
+274
+00:24:32,390 --> 00:24:39,430
+ال remainder مختلف معناه it is not congruent for
+
+275
+00:24:39,430 --> 00:24:44,090
+twenty four is not congruent to fourteen modulo
+
+276
+00:24:44,090 --> 00:24:53,100
+الستة بدك تتأكد أكثر أربع عشرين ناقص أربع عشربساوي
+
+277
+00:24:53,100 --> 00:25:00,540
+عشرة العشرة او الستة لا تقسم العشرة الستة لا تقسم
+
+278
+00:25:00,540 --> 00:25:04,500
+العشرة او بنجوسين العشرة مش من المضاعفات الستة
+
+279
+00:25:04,500 --> 00:25:09,280
+واضح الفكرة يا شباب؟
+
+280
+00:25:09,280 --> 00:25:18,000
+لغاية
+
+281
+00:25:18,000 --> 00:25:24,820
+تانية بقول كتاليلو كان عندي two integers a و b و
+
+282
+00:25:24,820 --> 00:25:28,960
+positive integer m اللي هو الـ divisor و لجيت أن
+
+283
+00:25:28,960 --> 00:25:35,120
+الـ a is congruent to b أو modulo ال m لجيت الأول
+
+284
+00:25:35,120 --> 00:25:37,900
+congruent للتاني أو العكس طبعا الأسر تبقى أنا
+
+285
+00:25:37,900 --> 00:25:40,320
+بتكلم عن التانين congruent لبعض لأن الفرق بيكون
+
+286
+00:25:40,320 --> 00:25:43,700
+سالب و السالب من ضمن الأقام اللي تنفع تجب تسمع
+
+287
+00:25:43,700 --> 00:25:48,720
+عليها من المضاعفات ولا لأ لأن الآن سالب تلاتة أو
+
+288
+00:25:48,720 --> 00:25:57,170
+سالب تسعةعالتلاتة ايه بعدين بقول انه التسابق تسعة
+
+289
+00:25:57,170 --> 00:26:03,530
+من المضاعفات التلاتة بقول لو لجيت رقمين congruent
+
+290
+00:26:03,530 --> 00:26:09,430
+a,b congruent modulo M معناته بتقدر تكتب الأول
+
+291
+00:26:09,430 --> 00:26:14,330
+الدلالة التاني بحيث ان ال a equal b زائد ال
+
+292
+00:26:14,330 --> 00:26:16,770
+divisor مضروب في some k
+
+293
+00:26:19,570 --> 00:26:24,330
+ما هو الكلام بكل بساطة اللي بيقوله هان كالتالي لو
+
+294
+00:26:24,330 --> 00:26:29,890
+احنا لجينا او جيبنا عددين a مجهولة على سبيل المثال
+
+295
+00:26:29,890 --> 00:26:33,970
+و ال b انا عرفتها و قلتلك x او ال a هذي is
+
+296
+00:26:33,970 --> 00:26:42,850
+congruent to خمسة modulo تلاتة ال a is congruent
+
+297
+00:26:42,850 --> 00:26:50,020
+to خمسة modulo تلاتةدعوني أعرف قيمة الـ A هذه ..
+
+298
+00:26:50,020 --> 00:26:53,780
+ماذا تريد أن تفعل؟ يعني .. يعني .. أنه .. أجهزك و
+
+299
+00:26:53,780 --> 00:26:59,460
+أقول لي أن الخمسة أو الـ A هذه تماثل الخمسة في
+
+300
+00:26:59,460 --> 00:27:02,140
+باقي قسمتها على التلاتة يعني كم هو كم في باقي
+
+301
+00:27:02,140 --> 00:27:06,100
+قسمتها؟ اتنين .. ايش العناصر اللي باقي قسمتها
+
+302
+00:27:06,100 --> 00:27:12,480
+اتنين؟ اتنين .. اتنين على التلاتة .. ده قسمته
+
+303
+00:27:12,480 --> 00:27:20,750
+اتنين .. ايش كمان؟خمسة موضلة بناشية اللي بعده سبعة
+
+304
+00:27:20,750 --> 00:27:25,610
+لأ بقى قسمتها واحد تمانية تمانية دايما اتشوف
+
+305
+00:27:25,610 --> 00:27:29,890
+مضاعفات التلاتة واضيف عليها ايش اتنين احداش
+
+306
+00:27:29,890 --> 00:27:36,830
+اربعاطعاش صح هو
+
+307
+00:27:36,830 --> 00:27:40,050
+ايش بقاعد بقولك بقولك ال a هاد عشان انت متورش فيها
+
+308
+00:27:40,050 --> 00:27:44,410
+كتير عشان ال a هاد متورش فيها كتير ابتخدني ال a
+
+309
+00:27:45,320 --> 00:27:51,200
+بتقول الـ A تساوي الـ B في المثال تبعناه كانت الـ
+
+310
+00:27:51,200 --> 00:27:55,660
+B خمسة زائد
+
+311
+00:27:55,660 --> 00:28:01,000
+الـ divisor اللي عندنا جديد الشباب كان تلاتة بقى
+
+312
+00:28:01,000 --> 00:28:05,680
+القسم التنين تمام؟ احنا قولنا modulo تلاتة مضروبة
+
+313
+00:28:05,680 --> 00:28:12,300
+في أي كي و الـ K عبارة عن integer تمام يعني بقدر
+
+314
+00:28:12,300 --> 00:28:13,600
+انا اجي اقولك التالي
+
+315
+00:28:16,750 --> 00:28:23,490
+تسعة تلاتة في تلاتة تسعة وخمسة اربع عشر بقدر اقول
+
+316
+00:28:23,490 --> 00:28:28,390
+الاربع عشر is modulo الخمسة is congruent خمسة
+
+317
+00:28:28,390 --> 00:28:33,330
+modulo التلاتة ممكن تكبر رقم هذه كلمة بزيادة عشرة
+
+318
+00:28:33,330 --> 00:28:36,630
+تلاتين
+
+319
+00:28:36,630 --> 00:28:40,390
+خمسة
+
+320
+00:28:40,390 --> 00:28:47,420
+و تلاتين is congruent to خمسة modulo التلاتةهذه هي
+
+321
+00:28:47,420 --> 00:28:55,340
+المعادلة اللي نتكلم عليها من أين أتيت؟ من الكلام
+
+322
+00:28:55,340 --> 00:29:01,400
+اللي قلناه قبل شوية أنه الآن هو
+
+323
+00:29:01,400 --> 00:29:06,480
+مالذي يقولني هنا؟ يقولني أرقم جروات لبعض مايعني
+
+324
+00:29:06,480 --> 00:29:13,480
+أرقم جروات لبعض؟ مانعته ال divisor ال M بيقسم A
+
+325
+00:29:13,480 --> 00:29:15,800
+مقص ال B من النظرية السابقة
+
+326
+00:29:19,310 --> 00:29:24,670
+بصبوط a congruent to b modulo m يعني ال m تقسم ال
+
+327
+00:29:24,670 --> 00:29:30,310
+a نقص ال b هيها
+
+328
+00:29:30,310 --> 00:29:36,450
+بصبوط فانا كتبت هيها هيها ايش يعني ال m تقسم هذا
+
+329
+00:29:36,450 --> 00:29:44,510
+معناه تقعد بقولنا ان ال a نقص ال b تساوي m مضروبة
+
+330
+00:29:44,510 --> 00:29:48,110
+في quantity في كمية يعني ان هذا من مضاعفات ال m
+
+331
+00:29:48,830 --> 00:29:51,870
+بظبط خيّر من المضاعفات الان مضروبة في K و K تنتمي
+
+332
+00:29:51,870 --> 00:29:55,470
+لانتجر A
+
+333
+00:29:55,470 --> 00:29:59,910
+ناطص معناته بقدر اقول ايه؟ بدها تساوي بقول B عن
+
+334
+00:29:59,910 --> 00:30:07,750
+ناحية التانية بضعين positive بي زائد N في K ال N
+
+335
+00:30:07,750 --> 00:30:12,530
+هي ال divisor و ال Q هي عبارة عن انتجر اللي عامله
+
+336
+00:30:12,530 --> 00:30:18,250
+اقترح عليها تمام مرة بالمثال لو انا اجل قلتلك
+
+337
+00:30:26,890 --> 00:30:36,110
+A is congruent to
+
+338
+00:30:36,110 --> 00:30:40,230
+تسعة
+
+339
+00:30:40,230 --> 00:30:45,390
+موديلو الأربعة
+
+340
+00:30:45,390 --> 00:30:49,390
+مد
+
+341
+00:30:49,390 --> 00:30:53,510
+الأربعة A
+
+342
+00:30:53,510 --> 00:31:00,140
+اللي هي العددis congruent to 9 مد الأربعة الديني
+
+343
+00:31:00,140 --> 00:31:07,840
+رقم يحقق المعادلة هذه الأصل
+
+344
+00:31:07,840 --> 00:31:11,220
+يتفكر فيها بورقتين مختلفتين والتنتين هيدوك لنفس
+
+345
+00:31:11,220 --> 00:31:20,900
+النتيجة الأولى تسعة مد الأربعة واحد تسعة مد
+
+346
+00:31:20,900 --> 00:31:26,550
+الأربعة واحد فلو انت جيبت اي قيمة لل aمد الأربعة
+
+347
+00:31:26,550 --> 00:31:36,350
+بتدي واحد فهي تكون صح زي إيش؟ خمسة سبعة غلط تسعة
+
+348
+00:31:36,350 --> 00:31:42,210
+هي already أنا بديكي إياها تلتاش سبعتاش كل الأرقام
+
+349
+00:31:42,210 --> 00:31:46,490
+اللي بتزيد عن المضاعفات الأربعة بواحد هذا ممكن
+
+350
+00:31:46,490 --> 00:31:51,930
+تفكر فيها أو تفكر كالتالي مباشرة تقول ال A بدها
+
+351
+00:31:51,930 --> 00:31:54,470
+تساوي تسعة
+
+352
+00:31:56,790 --> 00:32:02,450
+زائد اربعة مضروبة في اي كي في اتنين خلصنا اقصد رقم
+
+353
+00:32:02,450 --> 00:32:06,090
+تمانية
+
+354
+00:32:06,090 --> 00:32:14,350
+سبعة عشر ما هتقول ايه ممكن تكون سبعة عشر كيف؟ اه
+
+355
+00:32:14,350 --> 00:32:17,210
+لازم يكون عدد صحيح لان من اول ال chapter وانا
+
+356
+00:32:17,210 --> 00:32:21,350
+بتكلم يا شباب بتكلم على ال integers number theory
+
+357
+00:32:21,350 --> 00:32:24,790
+بتكلم على ال integers العدد الصحيحة وخصائصها
+
+358
+00:32:28,180 --> 00:32:35,740
+ممتاز ايش هاله نتيجة الهاتف اللي قلتلنا 17 17
+
+359
+00:32:35,740 --> 00:32:47,800
+مد الأربعة جديش واحد تسعة مد الأربعة جديش ميناته
+
+360
+00:32:47,800 --> 00:32:52,180
+ال 17 is congrant تسعة مد الأربعة انت ايش بتقول
+
+361
+00:32:52,180 --> 00:32:53,760
+الخمسة
+
+362
+00:33:01,410 --> 00:33:08,730
+سالب واحد بالظبط لأنه قاعد بيقول ال K هي عبارة عن
+
+363
+00:33:08,730 --> 00:33:13,610
+integer ما جليش positive او negative انتجر اي عدد
+
+364
+00:33:13,610 --> 00:33:18,350
+وبالتالي السؤال اللي بيطلح نفسه التسعة congruent
+
+365
+00:33:18,350 --> 00:33:25,930
+للتسعة تسعة congruent للتسعة جاوبني congruent
+
+366
+00:33:25,930 --> 00:33:29,130
+للتسعة congruent للتسعة مد للاربعة
+
+367
+00:33:31,130 --> 00:33:36,490
+حرام عليك true true ايش الشرط الأساسي يا شباب ان
+
+368
+00:33:36,490 --> 00:33:42,050
+اتنين كلهم باقي نص باقي القسمة بصبت او لما انا
+
+369
+00:33:42,050 --> 00:33:46,430
+اروح اطرحهم من بعض يقبل القسمة على ال divisor اللي
+
+370
+00:33:46,430 --> 00:33:52,650
+عندي طيب الان تسعة ناقص تسعة صفر يقبل قسمة على
+
+371
+00:33:52,650 --> 00:33:55,370
+اربعة اه يقبل قسمة على اربعة صفر و الباقي صفر
+
+372
+00:33:55,370 --> 00:33:59,550
+الصفر تساوي
+
+373
+00:34:01,190 --> 00:34:07,930
+الاربعة مضروبة في Zero والReminder Zero ايش يعني؟
+
+374
+00:34:07,930 --> 00:34:11,410
+يعني ال Quotient تبعتي Zero وبالتالي الصفر من
+
+375
+00:34:11,410 --> 00:34:15,950
+المضاعفات اي رقم الصفر من المضاعفات اي رقم عشان
+
+376
+00:34:15,950 --> 00:34:22,190
+هيك احنا بنقول الصفر على خمسة صفر بصبوط؟ بسبب
+
+377
+00:34:22,190 --> 00:34:26,970
+المعادلة هاي واضح
+
+378
+00:34:26,970 --> 00:34:32,680
+الامور يا شباب؟من أهم التطبيقات تبقى الخاصة القسمة
+
+379
+00:34:32,680 --> 00:34:37,280
+و ال modulus ال hash function ال hash function
+
+380
+00:34:37,280 --> 00:34:42,180
+هتشوفها
+
+381
+00:34:42,180 --> 00:34:49,340
+لاحقا يعني ايش يعني hash ايش
+
+382
+00:34:49,340 --> 00:34:51,780
+معنى hash tag على الفيسبوك او على ال media بشكل
+
+383
+00:34:51,780 --> 00:34:57,810
+عام على ال social media شو يعني hash tagهاش انك
+
+384
+00:34:57,810 --> 00:35:01,310
+بتعطي اشارة لحاجة تانية او اشارة أخرى انك بتحاول
+
+385
+00:35:01,310 --> 00:35:06,350
+تعطي قيمة مميزة للعناصر هذه عشان تصنفهم كلهم وين
+
+386
+00:35:06,350 --> 00:35:11,790
+تيجي عشان هي الكل كان في عندك هاش اسمها العودة
+
+387
+00:35:11,790 --> 00:35:19,110
+الكبرى، مصبوط؟ ليش؟ صار كل واحد .. كل واحد بروح ..
+
+388
+00:35:19,110 --> 00:35:25,340
+بضيفالـHash هذي أو الرقم هذا كلهم بييجي تحت نفس
+
+389
+00:35:25,340 --> 00:35:29,360
+التصنيف، مين كتب في العالم على الفيسبوك أو تويتر
+
+390
+00:35:31,060 --> 00:35:35,720
+تستخدم التسمية هذه تمام راح تقولها ال boss اتصنفت
+
+391
+00:35:35,720 --> 00:35:41,600
+او نعملها ادراج تحت مسمة واحد الهاش هي عبارة عن
+
+392
+00:35:41,600 --> 00:35:45,780
+ترقيم عبارة عن هاش عن ترقيم لما اتكلم هاشينج او
+
+393
+00:35:45,780 --> 00:35:49,960
+هاش فانشينج جاعت بتكلم على فانشينج ده اللي رياضية
+
+394
+00:35:49,960 --> 00:35:53,160
+بتديني قيمة ده اللي رياضية بتديني قيمة بناء على
+
+395
+00:35:53,160 --> 00:35:57,680
+ايش؟ بناء على ال value المحتوى الآن لاحظوا يا شباب
+
+396
+00:35:58,550 --> 00:36:00,990
+الان لو ايه كتبت العوجة الكبرى وماحققش ال
+
+397
+00:36:00,990 --> 00:36:06,890
+underscore هذي بتكلم جاهد على different ..
+
+398
+00:36:06,890 --> 00:36:11,390
+different value بصبت؟ و لو انا ساجد في الإملة و
+
+399
+00:36:11,390 --> 00:36:15,990
+روح اتحققت الكبريحطيته جطينها تحت الألف الليينة
+
+400
+00:36:15,990 --> 00:36:21,090
+برضه أخد .. لا بتطلعش 100% أخد different title
+
+401
+00:36:21,090 --> 00:36:25,110
+عنوان مختلف تماما لإيش؟ لأن المفروض ال hash
+
+402
+00:36:25,110 --> 00:36:30,630
+function ال value تبعتها تحسبها حسب القيمة
+
+403
+00:36:30,630 --> 00:36:38,090
+المُعطاة بعيدا عن ال facebook و ال social media بس
+
+404
+00:36:38,090 --> 00:36:42,430
+فكرتها رياضيات بالمناسبةبعيدا عن الـ social media
+
+405
+00:36:42,430 --> 00:36:44,890
+و الـ hash function و الـ hash تبعت الـ hashtag
+
+406
+00:36:44,890 --> 00:36:49,910
+الان يا سيد العزيزي ال hash function هي دالة دالة
+
+407
+00:36:49,910 --> 00:36:56,530
+بتحدد موقع البيانات او موقع ال record في الملف او
+
+408
+00:36:56,530 --> 00:37:01,570
+في ال memory تبعل ال value تبعتها الان اسمعتوا شغل
+
+409
+00:37:01,570 --> 00:37:05,150
+اسمها database لما درستوا مقدمة صح؟لأن الـ
+
+410
+00:37:05,150 --> 00:37:08,690
+database file ال data اللي بتتخزن على ال file
+
+411
+00:37:08,690 --> 00:37:13,390
+بتتخزن as binary بتتخزن ضمن ترتيب معين مين بيحدد
+
+412
+00:37:13,390 --> 00:37:17,310
+ال position تبع ال file هذا ال hash function بتاخد
+
+413
+00:37:17,310 --> 00:37:22,270
+القيمة تبع ال record بتعمل عليها حسبة بسيطة و بروح
+
+414
+00:37:22,270 --> 00:37:26,970
+بيحدد ال position تبعها وين بتتخزن اجيبك مثال بسيط
+
+415
+00:37:26,970 --> 00:37:30,950
+عشان اوضحك ال hash لو افترضنا و مش علاقة بال
+
+416
+00:37:30,950 --> 00:37:32,770
+modulus كمان لو افترضنا
+
+417
+00:37:37,160 --> 00:37:44,000
+إنه اجينا بدنا نصنف .. نصنف أسماء الطلاب الذكور
+
+418
+00:37:44,000 --> 00:37:51,320
+لمصنفات، بتجمحهم كلهم لفئات، هتصنفهم تبقى لإيش؟
+
+419
+00:37:51,320 --> 00:37:57,060
+عدد؟ هذا واحد، اسمي الكلب اخترق عدد الحرقاش
+
+420
+00:37:57,060 --> 00:38:02,090
+الترتيبأبجد يعني الحروف اللي بتبدأ بحرف ال A كلها
+
+421
+00:38:02,090 --> 00:38:05,490
+مع بعض الحروف اللي بتبدأ بحرف ال B مع بعض ازميلة
+
+422
+00:38:05,490 --> 00:38:09,730
+كانت ذاكرة مصطفى السوسي سوسي ولا سويسي سويسي جالك
+
+423
+00:38:09,730 --> 00:38:14,610
+التالي انا بدي اصنفهم على عدد الحروف يعني جال كل
+
+424
+00:38:14,610 --> 00:38:17,950
+الطلاب اللي أسميهم من أربع حروف اللي كله في فئة
+
+425
+00:38:17,950 --> 00:38:22,330
+واحدة مصبوب التاني التالت الرانع الخامس إلى آخرهم
+
+426
+00:38:22,330 --> 00:38:26,750
+طب لو أنا جالك و قلتلك يا مصطفى بس اللي عندك عشر
+
+427
+00:38:26,750 --> 00:38:31,320
+حروف جحد أقصىما زاد .. ده اكتشف على اسمه رباعي ..
+
+428
+00:38:31,320 --> 00:38:33,860
+ما زاد عن العشر حروف اللي كنت تدبره .. كده كنت
+
+429
+00:38:33,860 --> 00:38:38,520
+تدبره .. هتصير تعتمد على ال modulus .. باقى القسمة
+
+430
+00:38:38,520 --> 00:38:43,280
+.. حدش حد ساوي .. هتروح تقد الحروف .. هذا اتناش ..
+
+431
+00:38:43,280 --> 00:38:47,080
+طب أنا عندي عشر .. عشر فئات .. تحت أي فئة بدي احطه
+
+432
+00:38:47,080 --> 00:38:51,380
+.. بدي احطه تحت الفئة اتنين .. ليش؟ عشان باقى
+
+433
+00:38:51,380 --> 00:38:54,200
+القسمة بدي اعتمد على باقى القسمة اللي ساوة ..
+
+434
+00:38:54,200 --> 00:38:57,840
+اتنين .. يعني صارت تلين ولا اتناش ..في الواحد
+
+435
+00:38:57,840 --> 00:39:02,440
+العشرة وعشرين وتلاتين جايين في صفر بصبوط لأن بقى
+
+436
+00:39:02,440 --> 00:39:05,980
+قسمتهم صفر طيب تسعة وأتعاشر تسعة وعشرين تسعة
+
+437
+00:39:05,980 --> 00:39:09,100
+وتلاتين وتسعة كلهم دول في خانة واحدة اللي هم
+
+438
+00:39:09,100 --> 00:39:13,540
+الخانة التاسعة او الأخيرة اللي موجودة عندها وهذه
+
+439
+00:39:13,540 --> 00:39:18,080
+الشغل ال hash ان بتاخد منك ال value وبناء على ال
+
+440
+00:39:18,080 --> 00:39:20,900
+implementation اللي في داخلها بتديك قيمة ودائما
+
+441
+00:39:20,900 --> 00:39:24,020
+القيمة هذه غالبا تعتمد على ال modulus
+
+442
+00:39:34,280 --> 00:39:39,960
+لو انا افترضت اليك كالتالي انه انا بس يا مصطفى
+
+443
+00:39:39,960 --> 00:39:46,140
+اللي عندي تلت فئات و
+
+444
+00:39:46,140 --> 00:39:49,220
+بدك توزع كل أسماء الطلاب اللي في القاعة نفس الفكرة
+
+445
+00:39:49,220 --> 00:39:53,320
+اللي انت قلتها على التلاتة هدول شبك تساوي؟ هتصيرش
+
+446
+00:39:53,320 --> 00:40:00,950
+تعتمد؟ مد .. مد التلاتة سافر؟وهنا بنحط فيه كل
+
+447
+00:40:00,950 --> 00:40:07,130
+الأسماء اللي قولها مضاعفات التلاتة كل الأسماء في
+
+448
+00:40:07,130 --> 00:40:09,850
+الخانة التانية كل الأسماء اللي باقى قسمتها على
+
+449
+00:40:09,850 --> 00:40:16,370
+التلاتة واحد والباقي اللي بعديها اتنين اللي باقى
+
+450
+00:40:16,370 --> 00:40:19,250
+قسمتها على التلاتة اتنين يعني أنا من جنب العسابي
+
+451
+00:40:19,250 --> 00:40:26,430
+للمثال احمد كم حرف اربعة اربعة مدت تلاتة واحد احمد
+
+452
+00:40:26,430 --> 00:40:26,650
+هان
+
+453
+00:40:30,860 --> 00:40:38,960
+عالى صفر ماشت من تلاتة مدت تلاتة صفر لاحظ يا محمد
+
+454
+00:40:38,960 --> 00:40:42,480
+يا باز انا باتكلمش على الجرية لان عندي تصنيف مختلف
+
+455
+00:40:42,480 --> 00:40:49,060
+تمام الهاش فانشن هي اللي اخدت من الاسم ادت الحروف
+
+456
+00:40:49,060 --> 00:40:52,140
+ورجعتلي بالرقم المكان اللي انا بدي احط فيه مين
+
+457
+00:40:52,140 --> 00:40:53,260
+محمد
+
+458
+00:41:02,670 --> 00:41:09,790
+ثلاثة .. ستة .. تمانية طبعاً
+
+459
+00:41:09,790 --> 00:41:13,590
+هتفرق مقات لو انت كتبت محمد بأم واحدة اللهم صلي و
+
+460
+00:41:13,590 --> 00:41:16,350
+أسلم على صيد ده محمد، مظبوط؟ هتفرج، هتيجي في
+
+461
+00:41:16,350 --> 00:41:21,160
+الخارج أيه؟وهكذا تصبح كل الأسماء التي كنت تصنفها
+
+462
+00:41:21,160 --> 00:41:24,200
+تكون من تصنيف صحيح، ماهو مجلس تصنيفها يا دا وليها
+
+463
+00:41:24,200 --> 00:41:31,160
+شيء؟ عندما أريد أن أبحث عن عبدالعزيز، عبدالعزيز
+
+464
+00:41:31,160 --> 00:41:32,960
+تحت أي خانة الكون موجود يا شباب؟
+
+465
+00:41:43,900 --> 00:41:47,800
+بغض النظر، أنا لم أقدر أن أعطيك الاسم بس اعطيني
+
+466
+00:41:47,800 --> 00:41:54,560
+الاسم مثلما أعطيتني أول مرة هايو عبد أربعة ال سبعة
+
+467
+00:41:54,560 --> 00:42:00,400
+و تلاتة عشرة وين هي الكون؟ واحد هنا فلاحظ انك
+
+468
+00:42:00,400 --> 00:42:03,380
+مباشرة اتدور في المكان هذا اتدور في كل ال data
+
+469
+00:42:03,380 --> 00:42:07,120
+الموجودة وكل ما ازادت عندك ال locations اللي بتخزن
+
+470
+00:42:07,120 --> 00:42:13,490
+فيها تمام؟ معناته انك بتجلشأو تقارنة على عصر في ال
+
+471
+00:42:13,490 --> 00:42:17,810
+location اللي موجود عندها هذه الهاش فانكشن ان شاء
+
+472
+00:42:17,810 --> 00:42:20,350
+الله تبارك وتعالى بكرا لما تدرس database او اللي
+
+473
+00:42:20,350 --> 00:42:23,830
+درس database بيعرف شو يعني هاش و شو يعني index و
+
+474
+00:42:23,830 --> 00:42:29,030
+هنشوفها لاحقا من الشغلات التانية الشغلات التانية
+
+475
+00:42:29,030 --> 00:42:32,430
+اللي بتستخدم فيها ال number و ال modulus و باقى
+
+476
+00:42:32,430 --> 00:42:35,570
+القسمة اللي هي ال random number او اللي احنا
+
+477
+00:42:35,570 --> 00:42:37,670
+بسميها في ال computer science ال procedural random
+
+478
+00:42:37,670 --> 00:42:45,530
+number الرقم العشوائيلو انا جيت سألت اي واحد فيكوا
+
+479
+00:42:45,530 --> 00:42:53,410
+اعطينا رقم عشوائي 13 تمام هو قرر انه يختار فيها
+
+480
+00:42:53,410 --> 00:43:03,450
+صغيرة و اعطينا رقم عشوائي 13 تمام
+
+481
+00:43:03,450 --> 00:43:08,310
+ايه لو واحد قرر يروح بالالاف 1999
+
+482
+00:43:10,970 --> 00:43:15,230
+في مشكلة؟ برضه random طب بينما انا محتاج .. محتاج
+
+483
+00:43:15,230 --> 00:43:20,830
+الرقم اللى بده يطلع عندى يكون محصور ما بين الصفر و
+
+484
+00:43:20,830 --> 00:43:25,530
+الخمسة او اقل من خمسة شو بيك تساوي؟ الرقم ايش ما
+
+485
+00:43:25,530 --> 00:43:29,910
+يطلع الرغم اللى مد الخمسة ايش بتساوي؟ لأن كمان مرة
+
+486
+00:43:29,910 --> 00:43:37,190
+شوف انا الآن تخيل بدي رقم عشوائي من صفر لاربعةمن
+
+487
+00:43:37,190 --> 00:43:42,170
+صفر لاربعة الان انت ايش ممكن تطلعلي بأي رقم ممشي
+
+488
+00:43:42,170 --> 00:43:46,610
+الحال بس في الآخر انا بدي الرقم يكون هان و بديش
+
+489
+00:43:46,610 --> 00:43:50,830
+أسهل حاجة عشان مابلكاش رقم غلط لأ لأ بديش يحصل
+
+490
+00:43:50,830 --> 00:43:53,590
+ليها هاتلي random number تفضلي random number خد
+
+491
+00:43:53,590 --> 00:43:57,750
+الرقم و اعمله modulus لما انا باجي بقوله تلاتنعاش
+
+492
+00:43:57,750 --> 00:44:05,460
+مضي لاربعة واحد من هوا randomوالـ 1999 مد الأربعة
+
+493
+00:44:05,460 --> 00:44:10,500
+لازم .. مد الخمسة عفوا بصبوط مد الخمسة لازم يطلع
+
+494
+00:44:10,500 --> 00:44:14,360
+عيش يا شباب من صفر لأربعة ضمن ال range هدا بير
+
+495
+00:44:14,360 --> 00:44:17,580
+المضاعفات اللي خمسة بطلع عندك عيش أربعة هي ال
+
+496
+00:44:17,580 --> 00:44:20,200
+range اللي عندك واحد يقول طب مافي تكرار كتير يا
+
+497
+00:44:20,200 --> 00:44:24,740
+أستاذ لأن المدة تبعك قليل من صفر لأربعة زيد المدة
+
+498
+00:44:24,740 --> 00:44:28,850
+لعشرةبتصير تعمل مو بلس لعشرة بتصير الرقام من صفر
+
+499
+00:44:28,850 --> 00:44:35,690
+لتسعة بدك random 800 واسه ل 100 فبتصير من صفر ل 99
+
+500
+00:44:35,690 --> 00:44:41,950
+هي مفهوم ال random لأن ال computer عادة لما تقوله
+
+501
+00:44:41,950 --> 00:44:46,650
+random integer ال random ان هو افتوح ممكن الرقم
+
+502
+00:44:46,650 --> 00:44:51,590
+يكون في اي rangeانتجر الان لو انا اكتب لك واحد او
+
+503
+00:44:51,590 --> 00:44:58,370
+بلاش سبعة صفر تسعة واحد تمانية سبعة ستة خمسة اتنين
+
+504
+00:44:58,370 --> 00:45:03,910
+تلاتة اربعة صفر صفر واحد انتجر و لاك بس انا بديش
+
+505
+00:45:03,910 --> 00:45:06,910
+random بالشكل هذا بدي random عجبدي من واحد لعشرة
+
+506
+00:45:06,910 --> 00:45:11,310
+اشي بروح مساوي بعمل مدرس و بريح راسي وهذا من اهم
+
+507
+00:45:11,310 --> 00:45:17,700
+ال implementation اللي موجود عندك الان حتمالعبته
+
+508
+00:45:17,700 --> 00:45:21,680
+سيلوتير او شد على الكمبيوتر صح؟ كيف بتتم توزيع
+
+509
+00:45:21,680 --> 00:45:25,580
+الأوراق ومعاملتها وسحبها وكذا؟ Random بس ال random
+
+510
+00:45:25,580 --> 00:45:30,560
+ضمن جداش من واحد ل .. او من صفر لاطناش من واحد
+
+511
+00:45:30,560 --> 00:45:34,220
+لثلاثاش او تلاتاشر كارت اللي بيكونوا موجودات عندك
+
+512
+00:45:34,220 --> 00:45:37,580
+واحد يقول أستاذ ما حاببتي؟ لا يا صاحبي أنا بتكلم
+
+513
+00:45:37,580 --> 00:45:40,500
+ضمن إحصائي احتمالات و random number و هذا الكلام
+
+514
+00:45:40,500 --> 00:45:47,790
+موجود طيب خلصنا ال section الأول ساعة كام؟في
+
+515
+00:45:47,790 --> 00:45:51,830
+المطعة اللى موجودة قالوا عليها سابقا طيب الجزئية
+
+516
+00:45:51,830 --> 00:45:54,230
+التانية اللى هنتكلم عليها شباب ال section التانى
+
+517
+00:45:54,230 --> 00:46:01,950
+كلام مر عليك سابقا في المقدمة او حتى في
+
+518
+00:46:01,950 --> 00:46:05,550
+التكنولوجيا لما درست في الثانوية سواء كانت في أولى
+
+519
+00:46:05,550 --> 00:46:10,550
+ثانوي او في تانية ثانوي بغض النظر نتكلم على تمثيل
+
+520
+00:46:10,550 --> 00:46:16,500
+الأرقام وال algorithm بدأ بعيد عنها شوية اناماليش
+
+521
+00:46:16,500 --> 00:46:24,180
+دخل فيها تمام عشانها سهلة بالضبط عشانها سهلة الآن
+
+522
+00:46:24,180 --> 00:46:28,680
+في العصر الحديث أو عصر الحالي بنتعامل مع أرقام
+
+523
+00:46:28,680 --> 00:46:33,320
+بالنظام ال 10 ال decimal اللي هو ال base تبعته
+
+524
+00:46:33,320 --> 00:46:38,540
+جديش ال base تبعته النظام العشر جديش عشرة خليك
+
+525
+00:46:38,540 --> 00:46:42,840
+معايا يعني تكتب؟ كويس الله يزيدك الخير أنا بحسبك
+
+526
+00:46:42,840 --> 00:46:47,490
+صراحة مع الجوالالان وبالتالي اللي بيوجدش بيقولك
+
+527
+00:46:47,490 --> 00:46:53,190
+تسعمية خمسة و ستين الخمسة
+
+528
+00:46:53,190 --> 00:47:01,430
+كانوا بعلمونا أحد مصبوط ست عشرات مئات يعني خمسة في
+
+529
+00:47:01,430 --> 00:47:08,230
+عشر أقص صفر زائد ستة في عشر أقص واحد زائد تسعة في
+
+530
+00:47:08,230 --> 00:47:14,230
+عشر أقص اتنينخطف المقاطمة و خطف الفول ثانيا و اول
+
+531
+00:47:14,230 --> 00:47:19,930
+مدرس تتكلم عن تكنولوجيا مش قضية الان لاحظ ان
+
+532
+00:47:19,930 --> 00:47:23,290
+الأرقام هذه او العشر هذه مثلة الأساس لنظام العدل
+
+533
+00:47:23,290 --> 00:47:27,990
+اللي موجود و من هيك صار في عندي أرقام تبع ال base
+
+534
+00:47:27,990 --> 00:47:32,750
+اللي بدك هي نقرأ في حين ال binary ال base تبعتها
+
+535
+00:47:32,750 --> 00:47:41,330
+اتنين ال octal16 اكسا ديسمل ثلاثي بينفع بثلاثي اه
+
+536
+00:47:41,330 --> 00:47:46,970
+بينفع من صفر لتنين صفر واحد اتنين تلت ارقام لاحظ
+
+537
+00:47:46,970 --> 00:47:52,910
+ان الأرقام اللي موجودة دائما مد ال base يعني هي
+
+538
+00:47:52,910 --> 00:47:56,210
+بتمثل ال remainder اللي هو انجسمت على ال base من
+
+539
+00:47:56,210 --> 00:48:03,220
+صفر لحد اقل من ال base بتعرفوا شعب المياه؟برضه ايه
+
+540
+00:48:03,220 --> 00:48:08,100
+يا حميدالله؟ وين بيعيشوا كانوا؟ امريكا
+
+541
+00:48:08,100 --> 00:48:12,760
+اللاتينية انا بعرفهمش تعرفوا البابليون؟ وين كانوا
+
+542
+00:48:12,760 --> 00:48:17,280
+بيعيشوا؟ في العراق لأن شعب الميه كان بيعتمد على
+
+543
+00:48:17,280 --> 00:48:23,800
+نظام عد بيعتمد على ال base عشرين يعني من صفر لتسعة
+
+544
+00:48:23,800 --> 00:48:29,720
+عشر البابليين كان عندهم نظام العد من ستين digit
+
+545
+00:48:31,410 --> 00:48:37,250
+من صفر لتسعة وخمسين من صفر لتسعة وخمسين الفرعنة من
+
+546
+00:48:37,250 --> 00:48:41,990
+اتناش هى و الله في التاريخ انا بعرفش و الله اه
+
+547
+00:48:41,990 --> 00:48:45,090
+طبعا اسملكم بأكد انه الفرعنة كانت بتتوضع على نظام
+
+548
+00:48:45,090 --> 00:48:50,990
+عد من اتناش و المعلومة مرت عليه طبعا الفكرة وين ان
+
+549
+00:48:50,990 --> 00:48:56,650
+انت ممكن توجد نظام العد اللى بدكياه حسب ال system
+
+550
+00:48:56,650 --> 00:49:00,450
+او الحالة اللى انت بدكياها يعني لو انا اجل قلتلك
+
+551
+00:49:00,450 --> 00:49:01,010
+كالتانى
+
+552
+00:49:03,540 --> 00:49:11,580
+واحد .. سبعة .. خمسة .. صفر .. تلاتة .. كم قيمة
+
+553
+00:49:11,580 --> 00:49:16,400
+الرقم هذا؟ سبعتاشر ألف و خمسمية و تلاتة لو كنت أنا
+
+554
+00:49:16,400 --> 00:49:20,720
+بتكلم decimal بس غلط مش decimal كم قيمته؟ بنوه
+
+555
+00:49:20,720 --> 00:49:26,340
+نظام .. أيوة بنوه نظام .. إيش ال base تلاته؟ لاحظ
+
+556
+00:49:26,340 --> 00:49:29,920
+لما أنا كتبت الرقم بالشكل هذا و سبته .. تمام؟
+
+557
+00:49:29,920 --> 00:49:35,970
+معناته أنا فتحت ..مجهول على الرقم هذا لأنه بينفع
+
+558
+00:49:35,970 --> 00:49:41,290
+ال base تبقى تتكون من تمانية واطلع بينفع يكون نظام
+
+559
+00:49:41,290 --> 00:49:44,990
+ثماني تساعي
+
+560
+00:49:44,990 --> 00:49:50,030
+وعشري اللي قرناه .. قرناه بال 17000 و 11 و 12 و 13
+
+561
+00:49:50,030 --> 00:49:56,430
+و 60 و 75 و 100 لو حد بتألف فاش مشكلة وممكن تكون
+
+562
+00:49:56,430 --> 00:50:01,640
+تاخد الرقم نفسه و هو ال baseبس فعليا دائما هروح
+
+563
+00:50:01,640 --> 00:50:06,480
+على value مختلفة تماما في كل نظام يعني بين جثين لو
+
+564
+00:50:06,480 --> 00:50:13,060
+أنت تبعت لواحد رقم معين ممكن تبعته بصورة غير صورته
+
+565
+00:50:13,060 --> 00:50:19,320
+و اللي نشوفه يفهم معنى التشفير ايوة و من هنا اندر
+
+566
+00:50:19,320 --> 00:50:23,580
+بالك كانت بداية ايش التشفير هم الاشق دائما .. اللي
+
+567
+00:50:23,580 --> 00:50:27,520
+هو في العصر الحديث أخد وجه طويلفي فهم الحضرات
+
+568
+00:50:27,520 --> 00:50:31,860
+السابقة كانت كل كتب العلوم اللي موجودة فيها أرقام
+
+569
+00:50:31,860 --> 00:50:35,060
+فيها رموز هم مش عارفين أيش مهيئة الرمز اللي موجود
+
+570
+00:50:35,060 --> 00:50:40,540
+هذا و لو وصلولها بشكل سريع فانت ايش اتصل يعني الآن
+
+571
+00:50:40,540 --> 00:50:48,040
+لو مثلا واحد بده يغش الزميله في الامتحان صح ولا
+
+572
+00:50:48,040 --> 00:50:52,780
+غلط او في الخيارات بده يقول واحد اتنين تلاتة طب ما
+
+573
+00:50:52,780 --> 00:50:56,990
+هي مكشوفة ولا لا؟صارت استخدم حاجة جديدة فيه تموّر
+
+574
+00:50:56,990 --> 00:51:00,810
+على ان المراجعين بدأوا يفتحوا عليكوا حكّوا انتل
+
+575
+00:51:00,810 --> 00:51:05,150
+تلاتة و بيعدّلك اه؟ الله يكبّع شركه الفكرة وين؟ ان
+
+576
+00:51:05,150 --> 00:51:09,110
+ممكن انا استخدم هذه التقنيات و فعليا احمي ال data
+
+577
+00:51:09,110 --> 00:51:14,410
+اللي موجودة عندى بحيث لو اي واحد في المنتصف قرأ
+
+578
+00:51:14,410 --> 00:51:17,670
+البيانات اللي موجودة هذهش مايفهمش أيش القيمة اللي
+
+579
+00:51:17,670 --> 00:51:21,450
+موجودة او بين جثين افتح عليه باب من المجهول و من
+
+580
+00:51:21,450 --> 00:51:26,740
+احتمالات القيم اللي موجودة عندهمطيب احنا الآن لما
+
+581
+00:51:26,740 --> 00:51:33,140
+بنتكلم على نظام هد دائما ال digits اقل من قيمة ال
+
+582
+00:51:33,140 --> 00:51:36,740
+base يعني دائما هيك ال digits موجودة اكبر او تساوي
+
+583
+00:51:36,740 --> 00:51:42,460
+الصفر وال digits هذي بدأت تكون اقل من ال base عشرة
+
+584
+00:51:42,460 --> 00:51:47,840
+يعني من صفر لتسعة تمانية من صفر لسبعة خمسة من صفر
+
+585
+00:51:47,840 --> 00:51:51,600
+لاربعة اتنين من صفر لاحد بظبط هى ال range اللى
+
+586
+00:51:51,600 --> 00:51:57,500
+موجود عندى هنا ستة عشرمن صفر لخمستاشر في الستاشر
+
+587
+00:51:57,500 --> 00:52:01,700
+كمان مرة احنا ماعناش مشكلة هي من صفر لحد التسعة
+
+588
+00:52:01,700 --> 00:52:08,060
+لكن عندي عشرة احداشر اتناشر تلاتاشر اربعتاشر
+
+589
+00:52:08,060 --> 00:52:15,460
+خمستاشر هذا الأصل هيك لكن لما روحت انا اكتب الرقم
+
+590
+00:52:15,460 --> 00:52:19,760
+بتعامل مع الرقم only one digit يعني لما انا بدي
+
+591
+00:52:19,760 --> 00:52:28,820
+اكتب عشان اقولك كتاري الرقم هذااحد صفر واحد خمسة
+
+592
+00:52:28,820 --> 00:52:38,140
+hexadecimal او بالست عشر الاصل الاصل ان انا بتعامل
+
+593
+00:52:38,140 --> 00:52:41,580
+digit by digit لان احنا كل واحد اللي ونزلته زي ما
+
+594
+00:52:41,580 --> 00:52:46,440
+شوفنا قبل شوية مصبوط يعني هذا المفروض خمسة ضرب16
+
+595
+00:52:46,440 --> 00:52:50,900
+أز صفر واحد ضرب 16 أز واحد صفر ضرب 16 أز اتنين
+
+596
+00:52:50,900 --> 00:52:56,000
+واحد ضرب 16 أز تلاتة لان انا عامل 16 طب كيف بدي
+
+597
+00:52:56,000 --> 00:52:59,420
+امثل الأرقام هذه انا لو انا في اندي 15 هذه طب هي
+
+598
+00:52:59,420 --> 00:53:04,460
+ال 15 هي نفس هيك لان هتختلف تخيل هذه لو انا بتعامل
+
+599
+00:53:04,460 --> 00:53:11,410
+معاك 15درب 16 أصفر أو هتكون خمسة ضرب ستة عشر أصفر
+
+600
+00:53:11,410 --> 00:53:15,670
+زائد واحد ضرب ستة عشر أصفر واحد خمسة زاد ستة عشر
+
+601
+00:53:15,670 --> 00:53:20,370
+واحد وعشرين واحد وعشرين غير على خمسة عشر فليه
+
+602
+00:53:20,370 --> 00:53:23,530
+يقولوا إنه يستخدموا لما اتكلموا عن الأرقام من two
+
+603
+00:53:23,530 --> 00:53:27,570
+digits يستبدلوها برمز ليش؟ عشان أقدر أعرف القيمة
+
+604
+00:53:27,570 --> 00:53:30,430
+تبع الرمز هذا جديش أنا مابقدرش أعتمد على two
+
+605
+00:53:30,430 --> 00:53:35,450
+digits فصار هذا الرقم بيفرج تماما عن ال AF
+
+606
+00:53:38,470 --> 00:53:43,470
+هذا رقم من خانتين وهذا رقم من اربع خانات يعني اعلى
+
+607
+00:53:43,470 --> 00:53:48,890
+قص عندك هان هيكون عندك ستة عشر قص تلاتة
+
+608
+00:53:51,090 --> 00:53:55,230
+هذه المعلومات كلها احنا بيعرفها ضمن أي base بدك
+
+609
+00:53:55,230 --> 00:54:00,330
+إياها ضمن أي base بدك إياها زي ما قلنا سابقا بتحدد
+
+610
+00:54:00,330 --> 00:54:04,410
+ال base بتحدد ال digits اللي هو المفروض يكون أكبر
+
+611
+00:54:04,410 --> 00:54:08,010
+أو تساوي صفر وأقل من ال base ولو كان عندك من ال
+
+612
+00:54:08,010 --> 00:54:12,520
+digits هذه رقم من two digits بدك تستبدله برمزعشان
+
+613
+00:54:12,520 --> 00:54:16,980
+هيك كانت البابليون ستين يعني انا ممكن استوعب من
+
+614
+00:54:16,980 --> 00:54:20,280
+صفر لتسعة بعد الستين بدوا يستخدموا letters في
+
+615
+00:54:20,280 --> 00:54:23,660
+العمليات الحسابية تبعتهم لحد ما وصلوا لل system أو
+
+616
+00:54:23,660 --> 00:54:26,500
+لنظام العدل اللي موجود بدنا نفهم المعادلات اللي
+
+617
+00:54:26,500 --> 00:54:30,420
+موجودة وبشكل عام اي رقم بال decimal هياخد الشكل
+
+618
+00:54:30,420 --> 00:54:34,040
+هذا ايه
+
+619
+00:54:34,040 --> 00:54:39,430
+الصفر؟اللي هو ال digit الأول ضرب ال base أُس صفر
+
+620
+00:54:39,430 --> 00:54:44,730
+زائد ال digit التانية في ال base أُس واحد زائد ال
+
+621
+00:54:44,730 --> 00:54:50,290
+digit التالتة في ال base أُس اتنين زائد .. زائد ال
+
+622
+00:54:50,290 --> 00:54:55,830
+digit اللي في المنزلة K مضروب في ال base أُس K
+
+623
+00:54:55,830 --> 00:55:01,010
+الأن هاريش منزلته الشباب أنا بدي أسألك هذا الأن ال
+
+624
+00:55:01,010 --> 00:55:04,150
+K number هو ال K نقص واحد
+
+625
+00:55:09,050 --> 00:55:13,410
+والا ك زائد واحد؟
+
+626
+00:55:13,410 --> 00:55:17,010
+يعني
+
+627
+00:55:17,010 --> 00:55:23,690
+من صفر ل ك من صفر ل ك جداش من صفر ل ك جداش عدد ال
+
+628
+00:55:23,690 --> 00:55:29,790
+digit اللي موجودين ك زائد واحد من صفر ل ك ك زائد
+
+629
+00:55:29,790 --> 00:55:34,310
+واحد العددهم تمام؟ اه وبالتالي هذا ال ك زائد واحد
+
+630
+00:55:34,310 --> 00:55:37,290
+ال digit اللي موجود عندها تمام
+
+631
+00:55:38,950 --> 00:55:42,810
+أحنا بنعرف ال binary و بنعرف التحويل، مظبوط؟ لأن
+
+632
+00:55:42,810 --> 00:55:46,970
+هاي الرقم ال binary اه بيتحول هاي العدد ال binary
+
+633
+00:55:46,970 --> 00:55:52,830
+ال least significant digit اللي هو أكتر عنصر في ..
+
+634
+00:55:52,830 --> 00:55:57,930
+أول عنصر في اليمين، أقل منزلة، ابدا من عنده و أطلع
+
+635
+00:55:57,930 --> 00:56:03,330
+نيرو الصفر في واحد واحد ضرب اتنين أس واحد، واحد
+
+636
+00:56:03,330 --> 00:56:05,470
+ضرب اتنين أس اتنين، واحد ضرب اتنين أس ثلاثة أس
+
+637
+00:56:05,470 --> 00:56:11,480
+أربع أس خمسة ستة سبعة تمانية و هكذاطيب لو انا بدي
+
+638
+00:56:11,480 --> 00:56:16,680
+اعمل العكس شباب بدي احول من decimal يعني تخيل
+
+639
+00:56:16,680 --> 00:56:25,220
+بتبقى بيقولك هال بدي ال 27 بيجسم على ال base 27
+
+640
+00:56:25,220 --> 00:56:30,720
+بال decimal بدي احوله ل binary شو بدي اساوي؟
+
+641
+00:56:30,720 --> 00:56:34,460
+بالضبط بدي اجسم على 2 واحدة فقط بباقى القسمة لإن
+
+642
+00:56:34,460 --> 00:56:38,100
+باقى القسمة صفر او واحد اللي هم بتمثل ال digits
+
+643
+00:56:38,100 --> 00:56:45,370
+تبع ال binary27 على 2 13 و باقى القسم واحد هذا
+
+644
+00:56:45,370 --> 00:56:50,430
+الرقم بمثل ال least significant digit ايش عن ال
+
+645
+00:56:50,430 --> 00:56:55,250
+least significant digit؟ اول واحد في اليمين 13 على
+
+646
+00:56:55,250 --> 00:57:03,630
+2 6 و ببقى الواحد 6 على 2 3 و ببقى الصفر 3 على 2 1
+
+647
+00:57:03,630 --> 00:57:09,280
+و ببقى الواحدواحد على اتنين صفر و بقى قسم خلصنا و
+
+648
+00:57:09,280 --> 00:57:12,780
+هذا هو ال most significant digit يعني الرقم ..
+
+649
+00:57:12,780 --> 00:57:18,280
+برضه مال الأرقام عندي تطلع؟ واحد واحد صفر واحد
+
+650
+00:57:18,280 --> 00:57:26,540
+واحد binary هذا هو هذا least least least أقل منزلة
+
+651
+00:57:26,540 --> 00:57:33,060
+طيب في التماني نفس الكلامبتكلم على من صفر ل سبعة
+
+652
+00:57:33,060 --> 00:57:36,400
+digits و ال base تمانية وهي الرقم اللى بقناه بدي
+
+653
+00:57:36,400 --> 00:57:45,600
+احول من ثمانى او من ثمانى ل decimal و
+
+654
+00:57:45,600 --> 00:57:48,500
+بدي اجسم على تمانية لو بدي اعمل التحويل العكسى بدي
+
+655
+00:57:48,500 --> 00:57:51,980
+اجسم على تمانية لو بدي اعمل التحويل العكسى
+
+656
+00:57:51,980 --> 00:57:57,660
+hexadecimal كل ستناشر digits من صفر لتسعة بالاضافة
+
+657
+00:57:57,660 --> 00:58:01,860
+واحد اتنين تلاتة اربعةلحد ال F من A لحد ال F اللي
+
+658
+00:58:01,860 --> 00:58:07,380
+هو عشر احد اتناش تلتاشر اربعاش خمستاشر والتحويل هي
+
+659
+00:58:07,380 --> 00:58:13,180
+نعرفها انا بتجسم اتجسم على ستناشر
+
+660
+00:58:13,180 --> 00:58:17,680
+فيما يتعلق في
+
+661
+00:58:17,680 --> 00:58:21,020
+التحويل من binary ل octal او hexadecimal لو انا
+
+662
+00:58:21,020 --> 00:58:28,240
+اجير و قلتلك بال octal اكبر رقم جديش الشباب سبعة
+
+663
+00:58:28,240 --> 00:58:29,460
+حوله ل binary
+
+664
+00:58:34,370 --> 00:58:37,330
+يساوي سبعة بالديسميل يساوي واحد واحد واحد بال
+
+665
+00:58:37,330 --> 00:58:44,910
+binary الآن ال F أكبر element بال 8 بال 16 يساوي
+
+666
+00:58:44,910 --> 00:58:51,390
+خمستاشر بال decimal يساوي واحد واحد واحد binary
+
+667
+00:58:51,390 --> 00:58:55,170
+الآن
+
+668
+00:58:55,170 --> 00:58:58,450
+حلقة الوصول ما بين النظم هذا ال decimal لو احنا
+
+669
+00:58:58,450 --> 00:59:04,090
+أجينا أقولك التالي هذه الرقم عندي هذا واحد واحد
+
+670
+00:59:04,490 --> 00:59:09,850
+واحد صفر واحد
+
+671
+00:59:09,850 --> 00:59:15,390
+صفر واحد صفر واحد صفر واحد صفر واحد صفر واحد صفر
+
+672
+00:59:15,390 --> 00:59:18,670
+واحد صفر واحد صفر واحد صفر واحد صفر واحد صفر واحد
+
+673
+00:59:18,670 --> 00:59:18,670
+صفر واحد صفر واحد صفر واحد صفر واحد صفر واحد صفر
+
+674
+00:59:18,670 --> 00:59:18,710
+واحد صفر واحد صفر واحد صفر واحد صفر واحد صفر واحد
+
+675
+00:59:18,710 --> 00:59:19,010
+صفر واحد صفر واحد صفر واحد صفر واحد صفر واحد صفر
+
+676
+00:59:19,010 --> 00:59:21,910
+واحد صفر واحد صفر واحد صفر واحد صفر واحد صفر واحد
+
+677
+00:59:21,910 --> 00:59:32,350
+صفر واحد صفر واحد صفر واحد صفر واحد صفر واحد صفر
+
+678
+00:59:32,350 --> 00:59:33,900
+واحد صفر واحد صفر واحد صفر واحد صفر واحد صفالنقص
+
+679
+00:59:33,900 --> 00:59:42,640
+اللي هو الأول عنصر في اليمين هي تلت خرات الان
+
+680
+00:59:42,640 --> 00:59:47,600
+قدرا ربنا يقدر ان هذا العدد مجسم ع كمتات لو خاصة
+
+681
+00:59:47,600 --> 00:59:51,740
+عندك كمان واحد مباشرة الأصفار اللي على اليسار
+
+682
+00:59:51,740 --> 00:59:56,560
+مالهاش معنى ولا لا فبضيف أصفار زي ما بدك والان
+
+683
+00:59:56,560 --> 01:00:07,400
+مباشرة يحول كل رقم سبعة لبعدهتنين اللي بعده خمسة
+
+684
+01:00:07,400 --> 01:00:13,220
+واحد واربع خمسة خمسة واحد وبالتالي الرقم هذا يساوي
+
+685
+01:00:13,220 --> 01:00:20,460
+واحد خمسة خمسة اتنين سبعة بال اكتل لاحظ التحويل
+
+686
+01:00:20,460 --> 01:00:25,660
+كانت أسهل مايمكن لو بيتحول لست معاش خد اربع خلات
+
+687
+01:00:25,660 --> 01:00:30,340
+اربع خلات وجدت
+
+688
+01:00:30,340 --> 01:00:31,520
+ما بدنا الجلم من الخضراء
+
+689
+01:00:38,910 --> 01:00:47,210
+و هيضفنا تلت أصفار الان هذا الرقم سبعة خمسة
+
+690
+01:00:47,210 --> 01:00:54,710
+أيوة تمانية و تلاتة احداشر بي و هذا واحد و صار هذا
+
+691
+01:00:54,710 --> 01:01:02,460
+الرقم واحد بخمسة سبعةبالـ 16 لاحظت التحويلة هذه
+
+692
+01:01:02,460 --> 01:01:07,680
+كانت هي الأسهل بالنسبالنا وضملة ان اتعامل مع ال
+
+693
+01:01:07,680 --> 01:01:11,020
+binary و ال decimal و ال hexadecimal بشكل سريع
+
+694
+01:01:11,020 --> 01:01:17,100
+عشان هيك تم التركيز على اكتل و ال hexadecimal في
+
+695
+01:01:17,100 --> 01:01:21,320
+ال .. في الكمبيوتر بينما ما استخدموش أنظمة العدد
+
+696
+01:01:21,320 --> 01:01:25,500
+تانية زي السادس او السابع ليش؟ لأن الأرقام اللي
+
+697
+01:01:25,500 --> 01:01:30,800
+موجودةمش هتظل بنفس الكيفية اللي احنا بنشتغل فيها
+
+698
+01:01:30,800 --> 01:01:35,160
+هان، هلا أربع خنات صفر أربع خنات مباشرة، بينما لو
+
+699
+01:01:35,160 --> 01:01:38,160
+بدنا نغير نظام العد مش ضروري، يعني بيصير مثلا تخيل
+
+700
+01:01:38,160 --> 01:01:41,360
+اتكلم على نظام العد الخباسي، برضه بدي أربع خنات
+
+701
+01:01:41,360 --> 01:01:44,880
+ولا لا؟ بدي أربع خنات، لكن ولا مرة هيكون في عندي
+
+702
+01:01:44,880 --> 01:01:48,540
+مسكر زي ما كانت عندي هان السابعة أو كانت عندي إيش؟
+
+703
+01:01:48,540 --> 01:01:52,110
+الخمستاشر اللي موجودة عندي هانهيه خلصنا من ال
+
+704
+01:01:52,110 --> 01:01:54,650
+section التاني، بدنا نتكلم المحاضرة اللي جاء إن
+
+705
+01:01:54,650 --> 01:01:57,690
+شاء الله على الأعداد الأولية والعامل المشترك أو
+
+706
+01:01:57,690 --> 01:02:02,390
+قاسم المشترك الأكبر، في أي سؤال يا شباب؟ الله
+
+707
+01:02:02,390 --> 01:02:03,010
+يعطيكوا العافية
+
diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/tnT14Wninao.srt b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/tnT14Wninao.srt
new file mode 100644
index 0000000000000000000000000000000000000000..a17f0581a3925f81644c9da3c82446581d2c6296
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/tnT14Wninao.srt
@@ -0,0 +1,2065 @@
+1
+00:00:20,910 --> 00:00:23,050
+بسم الله و الحمد لله و الصلاة والسلام على رسول الله
+
+2
+00:00:23,050 --> 00:00:25,570
+الله اليوم إن شاء الله هنكمل في موضوع ال
+
+3
+00:00:25,570 --> 00:00:30,670
+algorithms لكن موضوع أنا شوية اليوم بده مخ مفتح
+
+4
+00:00:30,670 --> 00:00:34,370
+فبدي أنا أتصحصح معايا و ما تنعسش و إن شاء الله
+
+5
+00:00:34,370 --> 00:00:38,150
+ما تكونش المحاضرة طويلة كنا بدنا نتكلم عن ال
+
+6
+00:00:38,150 --> 00:00:41,790
+algorithms المحاضرة الماضية و قلنا ال algorithm هي
+
+7
+00:00:41,790 --> 00:00:42,910
+عبارة عن finite
+
+8
+00:00:46,470 --> 00:00:50,550
+set of precise instructions مجموعة منتهية من
+
+9
+00:00:50,550 --> 00:00:55,250
+الأوامر الواضحة أو التعليمات الواضحة لإيش؟ عشان
+
+10
+00:00:55,250 --> 00:00:58,270
+تسوي computation for performing computation or
+
+11
+00:00:58,270 --> 00:01:03,170
+solving a problem وقولنا في عندي ال algorithm فيه
+
+12
+00:01:03,170 --> 00:01:07,250
+مجموعة من الخصائص ال input و ال output و
+
+13
+00:01:07,250 --> 00:01:11,150
+التعريفات الخطوات اللي لازم يكون معرفة بشكل واضح
+
+14
+00:01:11,150 --> 00:01:15,880
+يكون ال output صحيح بناء على ال input الموجودة وال
+
+15
+00:01:15,880 --> 00:01:21,700
+fitness أن يكون أنه بعد finite steps بحصل على ال
+
+16
+00:01:21,700 --> 00:01:24,340
+output بناء على ال input اللي موجود و لازم يكون
+
+17
+00:01:24,340 --> 00:01:28,400
+فيه تناسب ما بين عدد الخطوات و حجم ال input لازم
+
+18
+00:01:28,400 --> 00:01:34,420
+يكون effective معنى أنه يجب أن يكون بعد فترة زمنية
+
+19
+00:01:34,420 --> 00:01:38,460
+مقبولة يرد و ال general أن ال application تبقى
+
+20
+00:01:38,460 --> 00:01:42,220
+قادرة أن أعممه على العناصر اللي موجودة وشوفنا ال
+
+21
+00:01:42,220 --> 00:01:46,220
+linear search كيف أنا أدور بشكل sequential على
+
+22
+00:01:46,220 --> 00:01:50,740
+العناصر وشوفنا ال binary search وشوفنا الفرق ما
+
+23
+00:01:50,740 --> 00:01:54,260
+بينهم و بعد هيك شوفنا مثال ال sorting كيف لو أنا
+
+24
+00:01:54,260 --> 00:01:59,420
+بده أرتب البيانات ترتيب تصاعدي وقلنا في عندنا واحد
+
+25
+00:01:59,420 --> 00:02:03,960
+من الأمثلة اللي هو ال bubble sort وشوفناه واتكلمنا
+
+26
+00:02:03,960 --> 00:02:08,080
+عليه وكنا وصلنا لحد شغلة اسمها ال greedy
+
+27
+00:02:08,080 --> 00:02:12,500
+algorithms ال greedy algorithms هي عبارة عن نوع من
+
+28
+00:02:12,500 --> 00:02:16,340
+أنواع ال algorithms وتستخدم في ال optimization
+
+29
+00:02:16,340 --> 00:02:20,620
+problem في المسائل اللي بنحصل فيها على أفضل
+
+30
+00:02:20,620 --> 00:02:25,470
+solution بأقل تكلفة، أكبر إنتاج، شغلات زي هيك بيسميها
+
+31
+00:02:25,470 --> 00:02:29,650
+optimization لكن في مفهوم ال greedy algorithms
+
+32
+00:02:29,650 --> 00:02:34,770
+أن هذه ال algorithms غالبا ما بتنظر للحل حسب
+
+33
+00:02:34,770 --> 00:02:38,910
+المرحلة القادمة، هو هتجيبلك مثال عشان نوضح شو يعني
+
+34
+00:02:38,910 --> 00:02:44,090
+مفهوم greedy، greedy قمع بالترجمة الحرفية لو أنا
+
+35
+00:02:44,090 --> 00:02:51,050
+أجيت قلت لك في ال tree هذه بتجيب لي بتجيب لي الـ
+
+36
+00:02:51,050 --> 00:02:54,970
+Largest Path، إيش ال Largest Path؟ هو المسار اللي
+
+37
+00:02:54,970 --> 00:02:59,190
+بتجمع من خلاله أكبر نقاط. وين ال Largest Path
+
+38
+00:02:59,190 --> 00:03:04,990
+هيكون عندك؟ سبعة، ثلاثة، تسعة وتسعون. هذا ليش؟
+
+39
+00:03:04,990 --> 00:03:09,450
+لأنك أنت فعليا شايف كل tree قدام عينك. لكن لو أنا
+
+40
+00:03:09,450 --> 00:03:13,590
+خبأت قدامك، خبأت أن ال layer هادي اللي تحت،
+
+41
+00:03:13,590 --> 00:03:18,370
+قلت لك أن ال layer هادي مش موجودة. إيش بتعمل؟
+
+42
+00:03:19,610 --> 00:03:23,730
+هتبدأ تفكر أن أنا اروح أدور على الأكبر بما هو بده
+
+43
+00:03:23,730 --> 00:03:28,730
+ال largest، أنا عندي السابعة وعندي ثلاثة وأطمعش
+
+44
+00:03:28,730 --> 00:03:33,890
+المنغش، بقول، بقول اروح باتجاه الأطمعش، وعند الأطمعش
+
+45
+00:03:33,890 --> 00:03:36,770
+بشوف إيش ال output اللي بعدين وبناء على نفس الكلام
+
+46
+00:03:36,770 --> 00:03:39,590
+بعد الأطمعش بروح باتجاه الستة ولا السابعة، الخامسة؟
+
+47
+00:03:39,590 --> 00:03:44,310
+بروحي باتجاه الستة لأن أنا فعليا بدي ال largest هذا
+
+48
+00:03:44,310 --> 00:03:50,180
+الحل، أو هذه الحركة اللي صارت، على الرغم أنها صحيحة
+
+49
+00:03:50,180 --> 00:03:56,620
+بنسميها احنا حركة طماعة، ليش؟ فعليا بس نظر وين؟ على ال
+
+50
+00:03:56,620 --> 00:04:00,120
+current situation تحت رجليك، ما كانش عنده بعد
+
+51
+00:04:00,120 --> 00:04:04,000
+نظر في أنه يحسب المسافة اللي موجودة كم، أما في
+
+52
+00:04:04,000 --> 00:04:06,740
+المثال هذا زي المثال اللي احنا شفناه المرة
+
+53
+00:04:06,740 --> 00:04:15,100
+الماضية، بقول لك لو كان أنا في هاي في، عندي مثلث A
+
+54
+00:04:15,100 --> 00:04:17,600
+B C
+
+55
+00:04:22,030 --> 00:04:33,570
+وعندي الطريق هذه وبدي أصل من ال A أصل لل D الآن
+
+56
+00:04:33,570 --> 00:04:40,070
+المفروض أقصر الطرق يكون عبر ال water هذا أقصر
+
+57
+00:04:40,070 --> 00:04:45,970
+الطرق، shortest path، أقصر الطرق، لكن ال greedy إيش
+
+58
+00:04:45,970 --> 00:04:50,690
+بيروح بيساوي، بفترض أنه موجود عند ال A، بدي يتحرك، مين
+
+59
+00:04:50,690 --> 00:04:56,230
+النقطة الأقرب؟ عشان أصل ال algorithm وأصل للشباب
+
+60
+00:04:56,230 --> 00:05:09,030
+ماشي، بروح بيساوي، بروح بكتب A B D، A B C D، A C B D، A C
+
+61
+00:05:09,030 --> 00:05:15,450
+D، هاي كل ال possible roots ولا لأ؟ الآن، الآن إيش
+
+62
+00:05:15,450 --> 00:05:19,230
+بيروح بيساوي في ال greedy؟ بقول لك أنا عشان أسلك بدي أخد
+
+63
+00:05:21,180 --> 00:05:25,060
+أقصر طريق في اللي موجودين هدول؟ مين أقصر طريق؟ من
+
+64
+00:05:25,060 --> 00:05:29,400
+الـA للـC ولا من الـA للـB؟ من الـA للـC، معناته
+
+65
+00:05:29,400 --> 00:05:33,880
+هو خلاص حسن أموره، راح باتجاه الـC، صار عنده هدول،
+
+66
+00:05:33,880 --> 00:05:37,620
+مين الأقصر الآن؟ من الـC للـD ولا من الـC للـB؟
+
+67
+00:05:37,620 --> 00:05:41,460
+على الرغم أن الـC للـB direct، هتصل بشكل مباشر،
+
+68
+00:05:41,460 --> 00:05:45,540
+هروح باتجاه مين؟ الـB، ومن بعد الـB، هروح باتجاه
+
+69
+00:05:45,540 --> 00:05:47,440
+الـD، وبالتالي
+
+70
+00:05:49,750 --> 00:05:53,390
+الـ position، لاحظ أن هو سلك أطول الطرق.. أطول
+
+71
+00:05:53,390 --> 00:05:56,650
+الطرق من أجل الوصول لهدف اللي موجود عندها، على
+
+72
+00:05:56,650 --> 00:06:03,010
+الرغم أنه كان بإمكانه يصل بشكل أسرع من خلال A, B, D
+
+73
+00:06:05,040 --> 00:06:08,460
+الآن هذا هو المفهوم أو مبدأ ال greedy algorithms
+
+74
+00:06:08,460 --> 00:06:11,960
+وأنا ما بديش منك أكثر من هيك، تفهم أن ال greedy
+
+75
+00:06:11,960 --> 00:06:14,920
+algorithms هو عبارة عن algorithms تستخدم في مسائل
+
+76
+00:06:14,920 --> 00:06:18,820
+ال optimization لما أنا بهمني أحصل على أقصر طريق،
+
+77
+00:06:18,820 --> 00:06:23,080
+أفضل إنتاج، أعلى رقم، أعلى، ما بعرف إيش الشغلات دي
+
+78
+00:06:23,080 --> 00:06:26,660
+كلها تهاشت، بتسميها أو بتخضع لمبدأ ال greedy
+
+79
+00:06:26,660 --> 00:06:30,080
+algorithms، كل solution، solution، و acceptable
+
+80
+00:06:30,080 --> 00:06:36,730
+solution، حل مقبول لكنه، فيه أفضل منه، فيه أفضل منه
+
+81
+00:06:36,730 --> 00:06:42,390
+تمام، بدنا
+
+82
+00:06:42,390 --> 00:06:46,030
+ننتقل معكم يا شباب، خلال المحاضرة أو خلال
+
+83
+00:06:46,030 --> 00:06:49,430
+الجزئية اللي باقية، هقبل فيها two sections، تمام بس
+
+84
+00:06:49,430 --> 00:06:55,770
+مش هركز على المفهوم النظري كتير، تمام، بقدر ما بدي إياك
+
+85
+00:06:57,100 --> 00:06:59,940
+تكون تشغل مخك كويس وتفهم ال concept، لأن ال
+
+86
+00:06:59,940 --> 00:07:04,180
+concept بسيط جدا، خصوصا أن معظمكم مش هياخد مادة اسمها
+
+87
+00:07:04,180 --> 00:07:08,560
+data structure، تمام؟ مش هياخد مادة تركيب بيانات، و
+
+88
+00:07:08,560 --> 00:07:12,880
+بيقيم ال algorithms، لو أنا أجيت سألتك، أنا في عندي
+
+89
+00:07:12,880 --> 00:07:21,160
+two algorithms، a1 و a2، والاثنين بيستخدموا لحل نفس
+
+90
+00:07:21,160 --> 00:07:28,320
+المشكلة، والاثنين بيدوني نفس النتيجة، في أفضلية بينهم؟
+
+91
+00:07:28,320 --> 00:07:34,480
+في أفضلية بينهم حسب السرعة، حسب جودته، إيش معيار
+
+92
+00:07:34,480 --> 00:07:38,990
+الجودة؟ الخصائص اللي شفناها قبل كده، ال input و
+
+93
+00:07:38,990 --> 00:07:41,370
+output، هما الأساس، نفس ال input ونفس ال
+
+94
+00:07:41,370 --> 00:07:44,830
+output، خلصنا، معناته الاثنين من ناحية الصحة، صحيحين
+
+95
+00:07:44,830 --> 00:07:50,090
+في شغلات ثانية ببدأ أدور، هل هو من ناحية ال
+
+96
+00:07:50,090 --> 00:07:55,630
+definition صحيح، صحيح، effective، correctness، تمام؟
+
+97
+00:07:55,630 --> 00:08:00,910
+وبالتالي، ببدأ أدور على شغلات ثانية، تمام؟ الآن
+
+98
+00:08:00,910 --> 00:08:06,610
+من الشغلات هذه اللي أنا بهمني، في شغلة اسمها الـ
+
+99
+00:08:06,610 --> 00:08:09,750
+Growth Functions، ماشي، يعني Growth Functions؟ وشو
+
+100
+00:08:09,750 --> 00:08:13,990
+دخل الـ Algorithm بالـ Functions؟ الآن لما أنا
+
+101
+00:08:13,990 --> 00:08:17,070
+اتكلمنا على الـ Effectiveness، قلت أن الـ
+
+102
+00:08:17,070 --> 00:08:24,310
+Algorithm بيعطيني الـ Output من فترة زمنية
+
+103
+00:08:24,310 --> 00:08:29,330
+محدودة، يعني وكأني بتكلم على سرعة الـ Algorithm
+
+104
+00:08:29,330 --> 00:08:35,540
+يكون متناسب مع حجم ال input اللي موجود عندي، ولما
+
+105
+00:08:35,540 --> 00:08:39,680
+أنا بتكلم على growth of functions، أن بدي أمثل ال
+
+106
+00:08:39,680 --> 00:08:44,240
+algorithm تبعي.. أمثل ال algorithm تبعي بدالة..
+
+107
+00:08:44,240 --> 00:08:48,500
+function، والدالة هادي بدها تزيد بزيادة مين؟
+
+108
+00:08:48,500 --> 00:08:53,660
+بزيادة ال input، لأن نرجع لمثال ال sort، أو بلاش
+
+109
+00:08:53,660 --> 00:08:59,340
+مثال ال search، كان في عندي linear search، صحيح؟
+
+110
+00:08:59,340 --> 00:09:01,980
+وكان في عندي binary search
+
+111
+00:09:10,020 --> 00:09:19,460
+الآن لما كان في عندي من a1، a2 لحد an، من a1، a2
+
+112
+00:09:19,460 --> 00:09:28,600
+لحد an، من ال element أو من العناصر، قديش كان
+
+113
+00:09:28,600 --> 00:09:33,360
+عملية مقارنة كانت بتلزمني عشان أقول أن ال element
+
+114
+00:09:33,360 --> 00:09:39,000
+هذا مش موجود، n من المرات، يعني بقدر أقول
+
+115
+00:09:39,000 --> 00:09:47,220
+له f of n تساوي n، n من المرات، طب وهذا؟
+
+116
+00:09:47,220 --> 00:09:51,860
+أنت شوف ال element مش موجود، أنا روحت على ال worst
+
+117
+00:09:51,860 --> 00:10:00,360
+case، أن ال element مش موجود، لاحظ هو عبارة عن n
+
+118
+00:10:00,360 --> 00:10:08,640
+على 2، صح؟ زائد n على 4، زائد n على 8، زائد n على 16
+
+119
+00:10:08,640 --> 00:10:17,020
+زائد n على 32، زائد n على 64، زائد زائد لحد ما وصل ل 1
+
+120
+00:10:17,020 --> 00:10:20,760
+احنا شفنا المثال على 1024، كان قال، وهذه ال series
+
+121
+00:10:20,760 --> 00:10:29,380
+series هاي كمان متسلسلة، sequence، مجموعها يساوي
+
+122
+00:10:33,270 --> 00:10:37,490
+لغاية ال الأساس اثنين، وعادة بالرياضيات يعني ال F of
+
+123
+00:10:37,490 --> 00:10:41,610
+n تبع ال algorithm الثاني هذا، تساوي لغاية n
+
+124
+00:10:41,610 --> 00:10:48,910
+للأساس اثنين، لاحظ الآن لما قدرت أحولهم أو أجيبهم
+
+125
+00:10:48,910 --> 00:10:52,390
+وهنا صارت أهمية ال sequence، صار أنا مش بدي فيه
+
+126
+00:10:52,390 --> 00:10:58,230
+جمع المتسلسلات، ممكن تظهر يعني بعضكم بيقول نفسه ليش
+
+127
+00:10:58,230 --> 00:11:01,710
+أنا محتاج أجمع متسلسلة؟ أنت محتاجش أجمع متسلسلة
+
+128
+00:11:01,710 --> 00:11:07,760
+عشان هيك، الآن بدك تفهم ال sequence اللي عندك عشان
+
+129
+00:11:07,760 --> 00:11:12,480
+تقدر تجيب ال function تبعتها، و ال function هذه
+
+130
+00:11:12,480 --> 00:11:15,380
+بناء عليها بده يصير decision، مين أفضل في ال
+
+131
+00:11:15,380 --> 00:11:19,900
+algorithm، مين أداؤه أفضل، ال linear search ولا ال
+
+132
+00:11:19,900 --> 00:11:23,900
+binary search، حسب ال function اللي موجودة عندك، حسب
+
+133
+00:11:23,900 --> 00:11:27,900
+ال function اللي موجودة عندك، لما بأجي بقارن في ال
+
+134
+00:11:27,900 --> 00:11:32,120
+worst case، في عندي n من ال elements، هذا كان بيحتاج
+
+135
+00:11:33,590 --> 00:11:36,890
+n من المرات عشان يقول لي أن ال element does not
+
+136
+00:11:36,890 --> 00:11:42,290
+exist، لكن هذا بيستخدم log n، log n على
+
+137
+00:11:42,290 --> 00:11:47,890
+أساس اثنين، عشان يقول لي، تعال، لما اتكلم على n
+
+138
+00:11:47,890 --> 00:11:53,970
+بدها تساوي ثمانية، هذه ثمانية، ثمان خطوات، يعني عدد
+
+139
+00:11:53,970 --> 00:12:00,270
+ال elements، ثمان عناصر، وال n تساوي ثمانية، هنا log
+
+140
+00:12:01,250 --> 00:12:05,250
+ثمانية، اثنين أس ثلاثة، ثمانية، ثمانية، ثمانية، ثمانية
+
+141
+00:12:05,250 --> 00:12:11,530
+ثمانية، ثمانية، ثمانية، ثمانية، ثمانية، ثمانية، ثمانية
+
+142
+00:12:11,530 --> 00:12:13,390
+ثمانية، ثمانية، ثمانية، ثمانية، ثمانية، ثمانية، ثمانية
+
+143
+00:12:13,390 --> 00:12:13,450
+ثمانية، ثمانية، ثمانية، ثمانية، ثمانية، ثمانية، ثمانية
+
+144
+00:12:13,450 --> 00:12:13,990
+ثمانية، ثمانية، ثمانية، ثمانية، ثمانية، ثمانية، ثمانية
+
+145
+00:12:13,990 --> 00:12:14,530
+ثمانية، ثمانية، ثمانية، ثمانية، ثمانية، ثمانية، ثمانية
+
+146
+00:12:14,530 --> 00:12:15,450
+ثمانية، ثمانية، ثمانية، ثمانية، ثمانية، ثمانية، ثمانية
+
+147
+00:12:15,450 --> 00:12:15,490
+ثمانية، ثمانية، ثمانية، ثمانية، ثمانية، ثمانية، ثمانية
+
+148
+00:12:15,490 --> 00:12:22,790
+ثمانية، ثمانية، ثمانية، ثمانية، ثمانية، ثمانية، ثمانية
+
+149
+00:12:22,790 --> 00:12:29,290
+ثمانية
+
+150
+00:12:29,290 --> 00:12:36,510
+و أربعة وعشرين، وهذه log اثنين، لعشرة للأساس
+
+151
+00:12:36,510 --> 00:12:43,150
+اثنين، عشرة، صارت الشغلة مشددة، ولاحظ لما زادت ال
+
+152
+00:12:43,150 --> 00:12:51,650
+input، ال function تبعتها كيف بتكبر، growth، فكلمة
+
+153
+00:12:51,650 --> 00:12:56,490
+ال growth هذه، مفهومها زيادة أو حجم ال function
+
+154
+00:12:56,490 --> 00:13:02,030
+مقارنة أو تبع لمين؟ لل input، حجم ال function تبع
+
+155
+00:13:02,030 --> 00:13:07,030
+ال input، تمام؟ يعني الآن أنا بتكلم على ال graph
+
+156
+00:13:07,030 --> 00:13:10,670
+function، معناته أنا بدي أحاول أعمل quantifying، بدي
+
+157
+00:13:10,670 --> 00:13:17,030
+أقيم الدوال، مقارنة مع بعضها، وأجي أقول أن ال F
+
+158
+00:13:17,030 --> 00:13:23,730
+تبعتي، أو ال function G، بتتزيد، إيش بتتزيد؟ يعني بكبر
+
+159
+00:13:23,730 --> 00:13:31,670
+حجمها، تنمو، تبع ال input، at least as the
+
+160
+00:13:31,670 --> 00:13:36,730
+function، as fast as the function f، يعني بتزيد
+
+161
+00:13:36,730 --> 00:13:42,710
+مثلها مثل ال f، طيب لو أنا أجيت وقلت لك أن ال f of n
+
+162
+00:13:42,710 --> 00:13:52,010
+تبعتي بدها تساوي 4n زائد 2، إيش المعادلة هذه؟ معادلة
+
+163
+00:13:52,010 --> 00:13:58,570
+خطية، صح؟ طيب، هل بنقدر نقارنها، بنقول زيادة هذه مثل
+
+164
+00:13:58,570 --> 00:14:04,350
+الـG of n دي تساوي n؟
+
+165
+00:14:04,350 --> 00:14:09,130
+إيش الفرق بين المعادلة هاي والمعادلة هاي؟ هذه
+
+166
+00:14:09,130 --> 00:14:15,250
+الكتابة الآن؟ طيب، لو أنا ببدأ أرسم الاثنتين على نفس
+
+167
+00:14:15,250 --> 00:14:19,910
+المخطط، كيف تتوقعوا الفرق بينهم؟
+
+168
+00:14:31,750 --> 00:14:40,210
+الثانية 4n زائد 2، في
+
+169
+00:14:40,210 --> 00:14:46,090
+الأخرى
+
+170
+00:14:46,090 --> 00:14:51,810
+هتحصل على خط موازي للخط اللي موجود عنه بس معمول له
+
+171
+00:14:51,810 --> 00:14:56,030
+إزاحة ومرفوع لفوق بمقدار، يعني الآن، انضربت في
+
+172
+00:14:56,030 --> 00:15:02,770
+أربعة، ونعمل لها scaling وبعدين shifting أو
+
+173
+00:15:02,770 --> 00:15:08,730
+translation، إزاحة، الآن هذه الدالة، بالتالي بقدر أنا
+
+174
+00:15:08,730 --> 00:15:12,450
+أقارن الدالة هذه مع الدالة هذه، من حيث نمو
+
+175
+00:15:1
+
+223
+00:19:18,970 --> 00:19:22,990
+كمان فيها اتنين يعني اتنين في اتنين في .. بتصير
+
+224
+00:19:22,990 --> 00:19:28,670
+اتنين في اتنين M لإن كل اتنين هذه كل مرة من اللي
+
+225
+00:19:28,670 --> 00:19:32,270
+فوق الجيوبة تتكرر لإن العلاقة بينهم ضرب
+
+226
+00:19:32,270 --> 00:19:36,410
+بصبوت وبالتالي بقدر أقول الدالة الزمنية تبع ال
+
+227
+00:19:36,410 --> 00:19:40,890
+algorithm هذه اللي عندي F of M بدها تساوي اتنين في
+
+228
+00:19:40,890 --> 00:19:46,720
+اتنين M أربعة N زائد واحد وانشئت تقولي والله كمان
+
+229
+00:19:46,720 --> 00:19:49,560
+ال output بتحسبها كمان عملية انا ماعنديش مشكلة في
+
+230
+00:19:49,560 --> 00:19:55,140
+الموضوع بس في الآخر هي الدالة الزمنية تبعتي هي ال
+
+231
+00:19:55,140 --> 00:19:58,700
+function اللي مثلت ال algorithm هي ال function
+
+232
+00:19:58,700 --> 00:20:03,900
+اللي مثلت ال algorithm الآن وبالتالي انا بقدر اقول
+
+233
+00:20:03,900 --> 00:20:07,380
+هي ال function ال growth تبعها لما انا بدي اقارنه
+
+234
+00:20:08,060 --> 00:20:11,880
+عشان اتكلم على ال quality تبعت ال algorithm كل ال
+
+235
+00:20:11,880 --> 00:20:15,660
+constant هذا الأصل انهاء الشباب مابتعنيش معايا ولا
+
+236
+00:20:15,660 --> 00:20:19,460
+حاجة شو يعني process؟ وشو يعني أربع process؟ أو
+
+237
+00:20:19,460 --> 00:20:22,700
+حتى لدربت العدد ال process كمان في أربع مرات مش
+
+238
+00:20:22,700 --> 00:20:26,940
+خضية كتير بالنسبة لنا المهم الأن لأن هي كمان مرة
+
+239
+00:20:26,940 --> 00:20:31,940
+زيادتها بتعني زيادة ال algorithm او زيادة الوقت
+
+240
+00:20:31,940 --> 00:20:34,840
+اللي بيستحقوا ال algorithm في الحل هي المفروض ان
+
+241
+00:20:34,840 --> 00:20:38,770
+انا اتعامل مع كل ال algorithm و اوجد مين ال DALLA
+
+242
+00:20:38,770 --> 00:20:41,610
+أو ال function الزمنية تبعتنا بنرجع مرة تانية
+
+243
+00:20:41,610 --> 00:20:46,490
+للحسبة اللي نشوفها طيب تمام وبالتالي أنا بدي أجيب
+
+244
+00:20:46,490 --> 00:20:51,190
+الدالة الزمنية من خلال ال algorithm اللي موجود
+
+245
+00:20:51,190 --> 00:20:57,550
+عندي طيب وإن
+
+246
+00:20:57,550 --> 00:21:01,070
+كان في بعض الرموز مخفية مش عارف ليش لكن في الآخر
+
+247
+00:21:01,070 --> 00:21:10,080
+there exist بدي أروح هايه أقل من الان هذه أقل أو
+
+248
+00:21:10,080 --> 00:21:18,120
+تساوي فيه عندش مصطلح اسمه ال big O ال
+
+249
+00:21:18,120 --> 00:21:23,700
+big O هذا مصطلح بنستخدمه عشان نقول ان الدالة تبعت
+
+250
+00:21:23,700 --> 00:21:29,400
+ال function او تبعت ال algorithm تبعي بتزيد تبعا
+
+251
+00:21:29,400 --> 00:21:33,560
+او في ال worst case في أسوأ الحالات بتزيد بزيادة
+
+252
+00:21:33,560 --> 00:21:41,320
+كده هذا يجب أن يكون لديه 2 functions F of N من أين
+
+253
+00:21:41,320 --> 00:21:44,680
+أريد أن أحصلها؟ من ال Algorithm، يجب أن تحسبها
+
+254
+00:21:44,680 --> 00:21:51,020
+ويجب أن تحصل على G of N واحدة من الدوالي المشهورة
+
+255
+00:21:51,020 --> 00:21:56,860
+constant يعني big O of واحد linear big O او F of G
+
+256
+00:21:56,860 --> 00:22:07,170
+F of N G of واحد equal واحد G of N equal N G of N
+
+257
+00:22:07,170 --> 00:22:17,450
+equal N تربيع G of N equal N أُس X مثلا G of N
+
+258
+00:22:17,450 --> 00:22:25,170
+بتساوي log N G of N هذه الدوال اللي ألاحظ مجرد
+
+259
+00:22:25,170 --> 00:22:29,630
+تماما من كل ال constant ليش؟ لأنه دائما بتهمني ال
+
+260
+00:22:29,630 --> 00:22:32,490
+basic function وحاليا هنتكلم عليهم و أعرضك
+
+261
+00:22:32,490 --> 00:22:37,290
+إياهم عن خلال ال slides الفكرة وين؟ إنه دائما بدي
+
+262
+00:22:37,290 --> 00:22:44,350
+أحاول أوجد constant C بحيث إنه لو ضربت في ال G of
+
+263
+00:22:44,350 --> 00:22:50,150
+N هذه اطلعلي ال F of N أقل من أو تساوي ال function
+
+264
+00:22:50,150 --> 00:22:53,190
+اللي موجودة عندها تعالي ناخد المثال البسيط اللي
+
+265
+00:22:53,190 --> 00:22:58,760
+عندها أربعة قبل شوية حسبت ال F of N بالمثال أربعة N
+
+266
+00:22:58,760 --> 00:23:04,940
+زائد واحد عشان تكون الأربعة N زائد واحد هذه أقل أو
+
+267
+00:23:04,940 --> 00:23:11,360
+تساوي أربعة N زائد واحد أقل أو تساوي أول حاجة
+
+268
+00:23:11,360 --> 00:23:15,180
+هيبدأك تدور على أعلى أُس للمتغير N مين أعلى أُس
+
+269
+00:23:15,180 --> 00:23:19,440
+للمتغير N اللي عندك؟ واحد معناته بدك تكتب N كما هي
+
+270
+00:23:19,440 --> 00:23:26,440
+مجرد هيك N يعني ال G of N تبعتها هي الآن ال
+
+271
+00:23:26,440 --> 00:23:31,060
+constant بدي أجيب C إيش ال C اللي بتحقق المعادلة
+
+272
+00:23:31,060 --> 00:23:38,640
+هذه؟ أربعة؟ أربعة N ما بتثبتش يعني لإنه أربعة N
+
+273
+00:23:38,640 --> 00:23:43,200
+زائد واحد أكبر من N من أربعة N يعني هيك أنا الآن
+
+274
+00:23:43,200 --> 00:23:48,620
+بدي أحط هنا C لو حطيت هنا أربعة أربعة N زائد واحد
+
+275
+00:23:48,620 --> 00:23:54,340
+أقل أو تساوي أربعة N غلط لكن لو أنا مباشر روحت
+
+276
+00:23:54,340 --> 00:24:01,400
+حطيت خمسة N هتكون المعادلة تبعتي صحيحة فباجي بقول
+
+277
+00:24:01,400 --> 00:24:11,560
+ان ال function تبعتي f of n is big O of ال N سيبنا
+
+278
+00:24:11,560 --> 00:24:14,940
+من ال constant من الدالة هذه اللي موجودة عندها
+
+279
+00:24:14,940 --> 00:24:19,820
+يعني هيك بقول ان الدالة الزمنية تبعتي ال algorithm
+
+280
+00:24:19,820 --> 00:24:22,000
+تبعي تزداد
+
+281
+00:24:24,340 --> 00:24:30,980
+بسرعة مكافئة لزيادة ال N يعني بين جثين الكلام
+
+282
+00:24:30,980 --> 00:24:35,300
+أبسط من هكذا انه لما هذا ال increment تبعتها او ال
+
+283
+00:24:35,300 --> 00:24:38,380
+growth تبعتها اللي بتتحكم فيها ال N مش ال Interval
+
+284
+00:24:38,380 --> 00:24:44,960
+طيب تعالى نشوف algorithm تاني و نحل نفس الكلام في
+
+285
+00:24:44,960 --> 00:24:49,460
+موضوع ال sort في موضوع ال sort انا هسكر ال slide
+
+286
+00:24:49,460 --> 00:24:52,380
+slide كمان مرة و اكتب ال algorithm هنا على اللوحة
+
+287
+00:24:54,550 --> 00:25:00,930
+في ال sort في ال bubble sort ال
+
+288
+00:25:00,930 --> 00:25:05,150
+procedure وروحت
+
+289
+00:25:05,150 --> 00:25:12,930
+ال data اك a1 a2 لحد a n integer من ال input تمام؟
+
+290
+00:25:12,930 --> 00:25:18,170
+ايش راح تسوينا في ال algorithm احنا؟
+
+291
+00:25:18,170 --> 00:25:22,170
+فحصت كل أنصر ما قال اكبر منه طالما هو اكبر اشكت
+
+292
+00:25:22,170 --> 00:25:29,990
+بساوي بعمل swap بظل بعمل swap تمام هاي four ال I
+
+293
+00:25:29,990 --> 00:25:39,790
+equal واحد to N نقص واحد four ال J equal I زائد
+
+294
+00:25:39,790 --> 00:25:51,070
+واحد to N if ال AI أكبر من ال A من ال J كنت بعمل
+
+295
+00:25:51,070 --> 00:25:56,960
+swap تصعدي تصعدي تصعدي تصعدي تصعدي تصعدي تصعدي
+
+296
+00:25:56,960 --> 00:25:57,240
+تصعدي تصعدي تصعدي تصعدي تصعدي تصعدي تصعدي تصعدي
+
+297
+00:25:57,240 --> 00:26:02,580
+تصعدي تصعدي تصعدي تصعدي تصعدي تصعدي تصعدي تصعدي
+
+298
+00:26:02,580 --> 00:26:03,920
+تصعدي تصعدي تصعدي تصعدي تصعدي تصعدي تصعدي تصعدي
+
+299
+00:26:03,920 --> 00:26:10,420
+تصعدي تصعدي تصعدي تصعدي تصعدي تصعدي تصعدي تصعدي
+
+300
+00:26:10,420 --> 00:26:15,240
+تصعدي تصعدي تصعدي تصعدي تصعدي تصعدي تصعدي تصعدي
+
+301
+00:26:15,240 --> 00:26:20,520
+تصعدي تصعدي تصعدي تصعدي تصعدي تصعدي تصعدي تصعدي
+
+302
+00:26:20,520 --> 00:26:28,650
+تصعالان أبسط .. هدولة أربعة وليش رايك؟ واحد اتنين
+
+303
+00:26:28,650 --> 00:26:33,110
+تلاتة أربعة بس أصبر شوية هدولة بيتكرروا مع اللوب
+
+304
+00:26:33,110 --> 00:26:37,930
+هادي يعني أربعة في عدة مرات اللوب مرات اللوب
+
+305
+00:26:37,930 --> 00:26:43,110
+قديش؟ N من المرات أو N نقص واحد بشكل أدق سابق نقول
+
+306
+00:26:43,110 --> 00:26:49,330
+لإن بدت من ال N واحد مصبوط من اتنين لحد ال N بس في
+
+307
+00:26:49,330 --> 00:26:53,310
+فعليا كمان الشباب مش بس من التنين المرة اللي جاية
+
+308
+00:26:53,310 --> 00:26:56,510
+هتبدأ من تلاتة و اللي بعديها هتبدأ من أربعة كل مرة
+
+309
+00:26:56,510 --> 00:27:00,030
+بتنقص واحد لكن بتتكلم عن ال worst case ال worst
+
+310
+00:27:00,030 --> 00:27:04,350
+case أنا بدي أقول هذه N نقص واحد N نقص واحد من
+
+311
+00:27:04,350 --> 00:27:11,580
+المرات وهذه اللي فوق بما هذه كلها هتتكرر N نقص واحد
+
+312
+00:27:11,580 --> 00:27:17,440
+من المرات مع أن الدالة الزمنية تبعتي F of N بدها
+
+313
+00:27:17,440 --> 00:27:25,740
+تساوي N نقص واحد مضروبة في N نقص واحد مضروب في
+
+314
+00:27:25,740 --> 00:27:29,020
+أربعة هي الدالة الزمنية اللي موجودة عندها تعالي
+
+315
+00:27:29,020 --> 00:27:33,560
+نظبطها كويس نضيها شكل ألطف N تربيع
+
+316
+00:27:35,330 --> 00:27:41,150
+N ماقص N زائد واحد مضروبي اربع الكل مضروبي اربعة
+
+317
+00:27:41,150 --> 00:27:55,050
+مظبوط تساوي أربعة N تربيع ناقص ثمانية N زائد أربعة
+
+318
+00:27:55,050 --> 00:28:00,210
+زائد أربعة هاي دي الدالة الزمنية تبعتي F of N شوف
+
+319
+00:28:00,210 --> 00:28:06,000
+كيف انحسبت اجيت ان اللي جوا ال loop عديتهم أربعة
+
+320
+00:28:06,000 --> 00:28:10,060
+process ال loop كان مرة بتتكرر N من المرات أو N
+
+321
+00:28:10,060 --> 00:28:13,980
+نقص واحد فوحد ضربتها و هذا كله جا جوا loop تانية
+
+322
+00:28:13,980 --> 00:28:17,960
+فضربته في كل مرة .. هيك الفكرة وين؟ مع كل مرة من
+
+323
+00:28:17,960 --> 00:28:22,360
+ال loop بتتكرر كل اللي جوا، تمام؟ يعني هذا كله
+
+324
+00:28:22,360 --> 00:28:26,160
+بتتكرر N نقص واحد بالمرات، طب هاد ال iteration،
+
+325
+00:28:26,160 --> 00:28:30,740
+loop مع كل واحد ماتوا فيه تكرار جديد صارت العلاقة
+
+326
+00:28:30,740 --> 00:28:34,420
+بينهم ضرب وهذه فيه أربعة هاي الدالة الزمنية الدالة
+
+327
+00:28:34,420 --> 00:28:38,640
+الزمنية تبعتها دي تقارن بإيش ال growth function
+
+328
+00:28:38,640 --> 00:28:48,980
+تبعتها زي إيش تجي تطلع عليها بشكل سريع جدا أقل أو
+
+329
+00:28:48,980 --> 00:28:52,740
+أو
+
+330
+00:28:52,740 --> 00:28:59,330
+تساوي N تربيع أنا بروح اضربها في تسعة N أو خمسة
+
+331
+00:28:59,330 --> 00:29:03,210
+N أو عشرة N الشرط الوحيد لل constant اللي عندك
+
+332
+00:29:03,210 --> 00:29:09,570
+كان انه ما يوصلش N ليش؟ لأن اذا وصل N معناته انت
+
+333
+00:29:09,570 --> 00:29:13,830
+نقلت المسألة لمستوى أعلى منها وانا ما بديش يا
+
+334
+00:29:13,830 --> 00:29:17,510
+الكلام هذا صح هتبقى صحيحة يعني تتخيل دورت في N
+
+335
+00:29:17,510 --> 00:29:23,120
+هتصير انت كئيبهتبقى المسألة صح .. هتبقى المسألة صح
+
+336
+00:29:23,120 --> 00:29:26,640
+لكن المقارنة مش fair مش عادلة عشان المقارنة تكون
+
+337
+00:29:26,640 --> 00:29:31,600
+عادلة لازم تحافظ على أنه تشغل على نفس الأساس فانت
+
+338
+00:29:31,600 --> 00:29:36,280
+معاك تختار أي N بدك إياها طيب لو أنا أجيت قلت
+
+339
+00:29:36,280 --> 00:29:44,400
+خمسة N okay خمسة N كويس هتبقى الأكبر نقص ..
+
+340
+00:29:44,400 --> 00:29:48,460
+والله أنا خايف ممكن تزيدي شوية هذي كمان هيكيا سيدة
+
+341
+00:29:48,460 --> 00:29:51,080
+خلّيها عشر .. لأ ما تسيبهاش زي ما هي خد عشر N
+
+342
+00:29:51,080 --> 00:29:54,360
+ماعناش مشكلة في الموضوع المهم ال constant هذا
+
+343
+00:29:54,360 --> 00:30:01,940
+ما يزيدش عن N وفي نفس الوقت ما يقلش عن مين عن
+
+344
+00:30:01,940 --> 00:30:05,260
+الأربعة وما يساويش الأربعة لازم يكون أكبر من
+
+345
+00:30:05,260 --> 00:30:09,740
+الأربعة و أقل من ال N لازم يكون أكبر من الأربعة و
+
+346
+00:30:09,740 --> 00:30:13,020
+أقل من ال N لأن لو ساوي الأربعة يا شباب خلاص بطلت
+
+347
+00:30:13,020 --> 00:30:16,610
+المسألة مستوي وليش رأيك؟ فانت بدك تقمن دايماً ان
+
+348
+00:30:16,610 --> 00:30:21,110
+هذي صحيحة و بدك تزيد في ال constant معناته الافتة
+
+349
+00:30:21,110 --> 00:30:26,410
+باعتناها دي is big O of لل N تربيع، big O من ال N
+
+350
+00:30:26,410 --> 00:30:33,230
+تربيع نعم؟
+
+351
+00:30:33,230 --> 00:30:38,150
+ايش قلت دي؟ قلت ال N مجهولة، و لو انها معروفة،
+
+352
+00:30:38,150 --> 00:30:39,290
+كانت حلت المشكلة
+
+353
+00:30:41,900 --> 00:30:46,640
+قيمة ال M مجهولة لو كانت معروفة فخلصت يعني لو قلت
+
+354
+00:30:46,640 --> 00:30:51,940
+لك انا اجمع خمس أعداد هتجمعهم باستمرار و ايش ميكون
+
+355
+00:30:51,940 --> 00:30:55,700
+ال algorithm مش لازم يزيد على الخمس خطوات بس احنا
+
+356
+00:30:55,700 --> 00:31:00,020
+بندور على algorithm يكون general ايش يعني general
+
+357
+00:31:00,020 --> 00:31:05,440
+لما اغير حجم ال input يظل صحيح يديه output صحيح حد
+
+358
+00:31:05,440 --> 00:31:05,620
+من
+
+359
+00:31:08,780 --> 00:31:17,400
+عشان هيك دائما
+
+360
+00:31:17,400 --> 00:31:21,540
+هتلاقي ده عندنا نتكلم انه complexity ال algorithm
+
+361
+00:31:21,540 --> 00:31:26,620
+complexity ما يقصدش جدش هو معجد قدر ما انا بتكلم على
+
+362
+00:31:26,620 --> 00:31:31,820
+انه ال time cost التكلفة الزمنية للألجوريثم ليش
+
+363
+00:31:31,820 --> 00:31:36,600
+تكلفة زمنية يا شباب لأنه أنا بركز على عدد ال
+
+364
+00:31:36,600 --> 00:31:41,340
+process و ال process بالنسبة لل CPU زمن كل one
+
+365
+00:31:41,340 --> 00:31:45,240
+cycle كل one process one cycle one nanosecond و
+
+366
+00:31:45,240 --> 00:31:52,720
+هكذا طيب في ال properties مش هخوض فيها كتير الفكرة
+
+367
+00:31:52,720 --> 00:31:53,800
+فيها كتالة
+
+368
+00:31:56,600 --> 00:32:06,600
+ال F is big O of G و ال G is big O of F معناته
+
+369
+00:32:06,600 --> 00:32:12,600
+الاثنين متساوية الاثنين يعني هيك تخيل أنت قلت F
+
+370
+00:32:12,600 --> 00:32:20,100
+أقل أو تساوي C في G و G أقل أو تساوي K في F
+
+371
+00:32:21,180 --> 00:32:24,520
+Constant تاني معناه تنسى الموضوع
+
+372
+00:32:24,520 --> 00:32:27,600
+بغض النظر إيش كان ال constant اللي موجود عندك كان
+
+373
+00:32:27,600 --> 00:32:34,560
+كذلك لو أنا أجيب قلت لك ال F is big O of C of G
+
+374
+00:32:34,560 --> 00:32:43,540
+أروح ضربت ال C هادي في اتنين هتظل المعادلة صح وليش
+
+375
+00:32:43,540 --> 00:32:46,880
+رأيك؟ بدون أي مشاكل هدف مجموعة ال Probability
+
+376
+00:32:46,880 --> 00:32:50,820
+كمان مرة أنا اللي بهمني مش كل الكلام النظري هذا
+
+377
+00:32:50,820 --> 00:32:55,660
+بهمني ال concept اللي احنا عمالا بنحاول نوصله رقم
+
+378
+00:32:55,660 --> 00:32:59,960
+واحد مطلوب مني احسب الدالة أو اكتب الدالة الزمنية
+
+379
+00:32:59,960 --> 00:33:05,300
+اللي بتعبر عن ال algorithm و اجيب ال big O تبعتها
+
+380
+00:33:05,300 --> 00:33:10,920
+و غالبا ال big O تبعتها الشماماللي هي أكبر أُس
+
+381
+00:33:10,920 --> 00:33:20,360
+أكبر أُس الأكبر أُس ل N اللي موجودة عندك الآن
+
+382
+00:33:20,360 --> 00:33:28,100
+لو كان في عندي F1 هدول القوانين .. القوانين
+
+383
+00:33:28,100 --> 00:33:33,820
+الثانية مهمات جداً لو كانت F is big O of G1 و F2
+
+384
+00:33:33,820 --> 00:33:45,000
+is big O of G2 ايش يعني F1 أقل أو تساوي C1 في G1 و
+
+385
+00:33:45,000 --> 00:33:55,600
+F2 أقل أو تساوي C2 في G2 بينفع نضرب دول مع بعض يا
+
+386
+00:33:55,600 --> 00:34:02,230
+شباب بينفع نضرب two functions في بعض F of X F of
+
+387
+00:34:02,230 --> 00:34:06,950
+واحد of X بيبقى تساوي اتنين X و F اتنين of X تساوي
+
+388
+00:34:06,950 --> 00:34:15,190
+X تربيع F واحد ضرب F اتنين of X تساوي اتنين X ضرب
+
+389
+00:34:15,190 --> 00:34:20,970
+X تربيع و تساوي اتنين X تكعيب آخذ نفسي لما اتكلم
+
+390
+00:34:20,970 --> 00:34:25,330
+عن ال functions وبينفع اجمع الاثنين مع بعض اه
+
+391
+00:34:25,330 --> 00:34:35,250
+بينفع F1 زائد F2 of X بده تساوي 2X زائد X تربيع
+
+392
+00:34:35,250 --> 00:34:40,330
+خدناهم الآن لما بتكون الدالة زي ما قلنا قبل شوية
+
+393
+00:34:40,330 --> 00:34:49,690
+عند الضرب معناته F1 ضرب F2 is big O of G1 ضرب G2
+
+394
+00:34:
+
+445
+00:39:49,670 --> 00:39:53,510
+comparison لما أنا بدي أجري قريب من two algorithms
+
+446
+00:39:53,510 --> 00:39:57,290
+بحسب الدالة الزمنية تبع الـ algorithm وبجي بقول
+
+447
+00:39:57,290 --> 00:40:02,240
+هذه Big O لواحدة من الدوال اللي عندنا الآن في الـ
+
+448
+00:40:02,240 --> 00:40:05,820
+linear أو في الـ binary search لما إحنا كتبناه، إيش
+
+449
+00:40:05,820 --> 00:40:08,540
+الـ binary search كان بيقول إيه؟ كان بيقول أول مرة
+
+450
+00:40:08,540 --> 00:40:17,680
+n على 2 زائد n على 4 زائد n على 8 زائد زائد ...للموصل
+
+451
+00:40:17,680 --> 00:40:24,000
+لـ 1 وهذا كان تساوي log الـ n الأساسي 2، هذه الـ series
+
+452
+00:40:24,000 --> 00:40:29,360
+أو sequence، هي الـ value تبعها، وبالتالي الـ growth
+
+453
+00:40:29,360 --> 00:40:35,160
+function تبعها، الـ F of N للـ binary search
+
+454
+00:40:35,160 --> 00:40:44,300
+algorithm is O of log N، زيادته لما بزيد الـ output
+
+455
+00:40:44,300 --> 00:40:48,660
+الـ process بتزيد بمقدار الـ log اللي موجود عندها،
+
+456
+00:40:48,660 --> 00:40:54,960
+واللي هي فعلياً أقل من الـ n، عشان هيك
+
+457
+00:40:54,960 --> 00:41:01,660
+دائماً بدنا نحاول لما نشتغل، بدنا نوجد أو نقارن الـ
+
+458
+00:41:01,660 --> 00:41:05,120
+function أو الـ time function تبع الـ algorithm تبعي
+
+459
+00:41:05,120 --> 00:41:10,580
+بواحدة من الدوال هذول، لاحظ لو كان عندي log n هي
+
+460
+00:41:10,580 --> 00:41:14,680
+صح أن أقارنها بـ log n، مش غلط لأن أنا بقدر أتأكد
+
+461
+00:41:14,680 --> 00:41:17,720
+عندي أقل من log n،
+
+462
+00:41:21,840 --> 00:41:27,360
+مظبوط؟ بس إيش إحنا قلنا؟ قلنا دائماً اختار أقل من
+
+463
+00:41:27,360 --> 00:41:30,600
+قيمة الـ n، ما توصلهاش للـ n عشان ما ترفعهاش للـ next
+
+464
+00:41:30,600 --> 00:41:33,580
+level، وفعلياً الـ next level هي اللي جايه، ما أنا
+
+465
+00:41:33,580 --> 00:41:38,800
+بدّي أروح، بنتقل للمستوى اللي بعده في عمليات المقارنة،
+
+466
+00:41:38,800 --> 00:41:43,120
+تمام، تعالَ
+
+467
+00:41:43,120 --> 00:41:46,780
+أشوف الـ algorithm اللي موجود عندها، مديني دالة
+
+468
+00:41:46,780 --> 00:41:50,700
+زمنية، بس التنسيق تبعها ما عرف ليش فكرتها، هكتبها
+
+469
+00:41:50,700 --> 00:41:58,260
+مرة ثانية: N في N factorial زائد ثلاثة N زائد اثنين،
+
+470
+00:41:58,260 --> 00:42:08,480
+زائد ثلاثة N، أسمّي الكل هذا مضروب في N أس N زائد
+
+471
+00:42:08,480 --> 00:42:14,000
+N أس اثنين N وهتلاقي
+
+472
+00:42:14,000 --> 00:42:19,360
+الـ Big O تبعها، هيخدمك في الموضوع هذا، شكل كبير
+
+473
+00:42:19,360 --> 00:42:25,960
+تبقى أنك تعتبر كل واحدة فيهم دالة لحالها، وتطبق
+
+474
+00:42:25,960 --> 00:42:29,360
+قانون الجمع وقانون الضرب اللي إحنا شفناهم قبل
+
+475
+00:42:29,360 --> 00:42:38,160
+شوية، هذول كيفك تساوي؟ هتيجي هذول معادلتين، مين
+
+476
+00:42:38,160 --> 00:42:43,540
+الأكبر؟ لما تكون الاثنتين مضروبات في بعض؟ معناته N في
+
+477
+00:42:43,540 --> 00:42:51,380
+N factorial لا تساوي، لا تساوي N تربيع factorial،
+
+478
+00:42:51,380 --> 00:42:59,340
+هذه n مضروبة في n factorial، يعني n مضروبة في n في
+
+479
+00:42:59,340 --> 00:43:06,800
+n ناقص واحد في n ناقص اثنين في اثنين في واحد، لما
+
+480
+00:43:06,800 --> 00:43:10,460
+بدخل الـ n، بدخلها مرة واحدة، بدخلها على كل الجملة لكن
+
+481
+00:43:10,460 --> 00:43:14,800
+لما بأجي بقول n تربيع factorial اختلفت تماماً،
+
+482
+00:43:14,800 --> 00:43:20,410
+مظبوط؟ عشان هيك هذه N في N factorial، المعنى طول
+
+483
+00:43:20,410 --> 00:43:29,230
+الوقت باخد، برشح مين؟ الـ N factorial زائد ham N، ham
+
+484
+00:43:29,230 --> 00:43:42,330
+constant، ham N، أسمّي N، أسمّيها ham، الاثنين جمع،
+
+485
+00:43:42,330 --> 00:43:49,410
+بأخذ بينهم الـ maximum، N أس اثنين N، طيب، لأن هذا
+
+486
+00:43:49,410 --> 00:43:53,270
+الجُزء بتاخد فيه الـ maximum، الـ maximum حسب المثال،
+
+487
+00:43:53,270 --> 00:43:58,870
+هذا أو حسب ... بقول الفكتوريال أكبر، أكبر شيء حتى
+
+488
+00:43:58,870 --> 00:44:07,790
+أكبر من n أس j، الـ n أس mية، وبالتالي n factorial في
+
+489
+00:44:07,790 --> 00:44:14,240
+n أس 2، هذا حُصّ ... لأ لأ، الـ maximum بين الجمع ... لما
+
+490
+00:44:14,240 --> 00:44:17,660
+أكون جمع، بأخذ الـ maximum ... لما بكون ضرب ...
+
+491
+00:44:17,660 --> 00:44:20,380
+بضرب الـ two terms في بعضهم ... هي الدالة الزمنية
+
+492
+00:44:20,380 --> 00:44:28,280
+اللي عندي ... يعني هان ... وبالتالي ... لما
+
+493
+00:44:28,280 --> 00:44:30,980
+راح إحنا نحسب ... اه حتى شوف ...
+
+494
+00:44:33,980 --> 00:44:40,180
+أنا فاكر ثلاثة أس n مظبوط، وهذه ثلاثة أس n زائد
+
+495
+00:44:40,180 --> 00:44:44,560
+اثنين، اه، ثلاثة أس n زائد اثنين، في التنسيق بس فيه
+
+496
+00:44:44,560 --> 00:44:48,260
+مشكلة في الآخر، هذه هي هي الـ Big O، من أين حصلت
+
+497
+00:44:48,260 --> 00:44:51,320
+عليها؟ أو كيف حصلت عليها؟ شباب، بنفس الخطوات اللي
+
+498
+00:44:51,320 --> 00:44:54,960
+إحنا اشتغلنا عليها سابقاً، عند الضرب، أخدت الاثنتين
+
+499
+00:44:54,960 --> 00:44:58,300
+عند
+
+500
+00:44:58,300 --> 00:45:00,200
+الضرب، هان
+
+501
+00:45:03,590 --> 00:45:06,690
+أخذت الـ N factorial، ولو دمجتها مع الـ N لأنها
+
+502
+00:45:06,690 --> 00:45:10,490
+function ما فيش مشكلة عندي في الموضوع، الـ N، وهذه
+
+503
+00:45:10,490 --> 00:45:16,650
+أخذت الـ maximum في الآخر، هحصل على دالة، هذه هي الـ N
+
+504
+00:45:16,650 --> 00:45:23,690
+أس N، في الـ term اللي موجود عندي الآن، تعالَ نشوف
+
+505
+00:45:23,690 --> 00:45:27,630
+الـ algorithm الثاني، هذا، أو في عندي two algorithms
+
+506
+00:45:27,630 --> 00:45:33,100
+بدي أقارن ما بينهم، عندي two algorithms، بقول هاي الـ
+
+507
+00:45:33,100 --> 00:45:39,800
+time complexity تبعتهم، هاي الـ time function، f1
+
+508
+00:45:39,800 --> 00:45:49,620
+of n بده تساوي n تربيع ناقص n زائد واحد، f2 of n بده
+
+509
+00:45:49,620 --> 00:45:55,340
+تساوي n تربيع على اثنين زائد ثلاثة n زائد اثنين،
+
+510
+00:45:55,340 --> 00:46:07,060
+الآن، هادي Big O من إيه الشباب؟ أنت ربيع، وهذه وهذه
+
+511
+00:46:07,060 --> 00:46:15,520
+أنت ربيع، هذا الكلام صحيح 100%، بس لأن الاثنتين أنت
+
+512
+00:46:15,520 --> 00:46:19,600
+ربيع، لازم
+
+513
+00:46:19,600 --> 00:46:23,980
+أسوي، أدوّر علشان المفاصلة بينهم، هل بقدر أفصل بينهم
+
+514
+00:46:23,980 --> 00:46:30,420
+ولا بقدرش؟ ادخل معايا، مين؟ تعالَ نجي للدالة هيك،
+
+515
+00:46:31,260 --> 00:46:38,060
+معناته هذه عبارة عن N تربيع، وراها
+
+516
+00:46:38,060 --> 00:46:46,720
+Big O للـ N، صح؟ طب واللي قبلها؟ نصف الـ N تربيع،
+
+517
+00:46:46,720 --> 00:46:52,920
+وراها Big O للـ N، يعني هذه وهذه متساويات، صار
+
+518
+00:46:52,920 --> 00:46:57,040
+الفيصل مين في اللعبة؟ عندها الـ N تربيع، طب الـ N
+
+519
+00:46:57,040 --> 00:47:02,540
+تربيع ولا نصف الـ N تربيع؟ لأ، من أوفر من وقت ... من
+
+520
+00:47:02,540 --> 00:47:06,600
+زمنه، أو باختصار زمن أقل، الـ n تربيع ولا نصفها؟
+
+521
+00:47:06,600 --> 00:47:10,980
+فصرت أنا هان، ممكن التزم بمين؟ لاحظوا أنا من البداية
+
+522
+00:47:10,980 --> 00:47:15,620
+أخذت الـ أسّين، لَجِئتهم متساويات، ما ودّونيش للمقارنة
+
+523
+00:47:15,620 --> 00:47:21,100
+فعلياً، فحاولت أنزل لِبعدهم، لَجِئتهم نفس الـ algorithm،
+
+524
+00:47:21,100 --> 00:47:23,900
+بالتالي أنا الآن بدي أقول أن والله الـ complexity
+
+525
+00:47:23,900 --> 00:47:28,640
+اللي تبعها، هي واحد n تربيع، زاد الـ Big O للـ n،
+
+526
+00:47:31,200 --> 00:47:35,940
+والثاني نصف n تربيع، زاد الـ Big O للـ n، الأفضلية
+
+527
+00:47:35,940 --> 00:47:40,040
+الآن لمين؟ للـ algorithm الثاني، لأن نصف n تربيع
+
+528
+00:47:40,040 --> 00:47:47,640
+أوفر، نصف الزمن، الـ
+
+529
+00:47:47,640 --> 00:47:50,140
+complexity، هو الكلام اللي إحنا قلناه لفترة، وبنحسب
+
+530
+00:47:50,140 --> 00:47:58,170
+الـ algorithm، أنا مخلّص الـ section من قبل ما أبدأ، طيب،
+
+531
+00:47:58,170 --> 00:48:02,110
+الـ Time Complexity ... الـ Time Complexity معناته
+
+532
+00:48:02,110 --> 00:48:08,370
+أنا بأجي بتكلم، بأحدد approximate number of
+
+533
+00:48:08,370 --> 00:48:12,010
+operations اللي هو أنا كنت بحاول أسويه، عشان أقول لك
+
+534
+00:48:12,010 --> 00:48:15,450
+هذه ... هذه فيها أربع خطوات، هذه جوا الـ loop، أربع خطوات،
+
+535
+00:48:15,450 --> 00:48:19,790
+وهذه أربع خطوات، لاقصى واحد، وروحت approximate، ما حدش
+
+536
+00:48:19,790 --> 00:48:24,660
+مقدر يديك exact value، تقريباً، وعشان هي approximate،
+
+537
+00:48:24,660 --> 00:48:27,780
+روح نقولها، بدنا نغيّر كل الـ constant، يعني، وليه
+
+538
+00:48:27,780 --> 00:48:32,580
+كثير؟ ولا لأ؟ بتبقى المعادلة صحيحة، هدف الـ time
+
+539
+00:48:32,580 --> 00:48:36,480
+complexity كذلك، لو تساوت الـ algorithms من ناحية الـ
+
+540
+00:48:36,480 --> 00:48:42,080
+time، بروح للجهة لبراميتر الثاني، الـ space، قداش بده
+
+541
+00:48:42,080 --> 00:48:47,140
+space هذا عشان يغيّر، عشان ينفذ الـ task تبعته، قداش
+
+542
+00:48:47,140 --> 00:48:51,000
+بده space عشان ينفذ الـ task تبعته، طبعاً أنا بتكلم
+
+543
+00:48:51,000 --> 00:48:56,440
+لـ space، حجم الـ memory، قداش في عندي حجم مطلوب، في
+
+544
+00:48:56,440 --> 00:48:59,920
+الـ Time Complexity، إحنا دائماً بنستخدم مين؟ الـ
+
+545
+00:48:59,920 --> 00:49:03,960
+Big O Notation، وبدّيها لكل الدوال الثانية، والـ
+
+546
+00:49:03,960 --> 00:49:08,680
+constant الثانية، وعادة بقعد فقط الـ expensive
+
+547
+00:49:08,680 --> 00:49:15,420
+operations، العمليات الأساسية، زي إيش؟ المقارنة في الـ
+
+548
+00:49:15,420 --> 00:49:19,560
+search algorithm، كم عملية مقارنة أنت بتعمل؟ يعني
+
+549
+00:49:19,560 --> 00:49:24,880
+إحنا قبل شوية كتبنا أربعة n زائد واحد، الـ algorithm
+
+550
+00:49:24,880 --> 00:49:27,620
+تبقى تعدّها، أنا عندي عملية جمع واحدة، الـ
+
+551
+00:49:27,620 --> 00:49:31,840
+assignment، اليساوي، واليساوي هذه بنبطل نعدّها، بدوّر
+
+552
+00:49:31,840 --> 00:49:34,600
+على الـ operations الأساسية، الـ core في الـ algorithm،
+
+553
+00:49:34,600 --> 00:49:37,280
+في الـ algorithm اللي كتبته في الأول، كنت أنا بأجمع،
+
+554
+00:49:37,280 --> 00:49:42,240
+فكم عملية جمع بدأت تتنفذ n من المرات، لأنه جوا الـ
+
+555
+00:49:42,240 --> 00:49:46,260
+loop، في المقارنات في الـ search، كم عملية مقارنة في
+
+556
+00:49:46,260 --> 00:49:51,280
+الـ binary search؟ عندي n من المقارنات، في الـ binary
+
+557
+00:49:52,050 --> 00:49:56,070
+log n من المقارنات، والأربعة، والخمسة، والاثنين هذول
+
+558
+00:49:56,070 --> 00:50:00,190
+كلها ما بنعدّها، بيبقى قبلها حساب عادي زي ما قلنا سابقاً،
+
+559
+00:50:00,190 --> 00:50:07,110
+ودائماً ... دائماً في عادي، بتكلم على الـ worst case،
+
+560
+00:50:07,110 --> 00:50:12,950
+والـ best case أو الـ average case، أفضل حالة أو
+
+561
+00:50:12,950 --> 00:50:18,130
+المتوسط، وأسوأ حالة، أنا بهمّني الـ algorithm يشتغل
+
+562
+00:50:18,130 --> 00:50:23,320
+دائماً في الـ best case، طبعاً أنا بهمّني دائماً الـ output
+
+563
+00:50:23,320 --> 00:50:28,100
+تبعه فين؟ في الـ worst case، يعني لو على سبيل المثال
+
+564
+00:50:28,100 --> 00:50:34,580
+أنا أجهد الـ data series، قلت لك خمسة، سبعة، ثلاثة،
+
+565
+00:50:34,580 --> 00:50:43,040
+اثنين، ثمانية، ستة، في نفس الوجهة، التي قلت لك اثنين،
+
+566
+00:50:43,040 --> 00:50:52,410
+ثلاثة، خمسة، خمسة، ستة ... سبعة ... ثمانية، Two different
+
+567
+00:50:52,410 --> 00:50:57,810
+series، صح؟ أجيب، قلت لك ما بيجيلي عليهم linear search،
+
+568
+00:50:57,810 --> 00:51:06,270
+عشان أصل للخمسة، الـ best case من أول مرة، خلاص،
+
+569
+00:51:06,270 --> 00:51:11,950
+ما أكملش، الـ worst case، الـ worst case أن الخمسة مش
+
+570
+00:51:11,950 --> 00:51:12,650
+موجودة،
+
+571
+00:51:15,650 --> 00:51:22,890
+الخطر هو أن الخمسة لن تكون موجودة في الـ binary
+
+572
+00:51:22,890 --> 00:51:28,490
+search، في
+
+573
+00:51:28,490 --> 00:51:32,230
+الـ case، أفضل، مباشرة من أول الحكاية، سأجلب الخمسة،
+
+574
+00:51:32,230 --> 00:51:35,470
+لماذا ثلاثة؟ نحن نريد أن نجسّمها من النص، ونضع الـ
+
+575
+00:51:35,470 --> 00:51:41,520
+pointer على النص، اه، ما بتمدّ على الـ floor، فراح جابِ
+
+576
+00:51:41,520 --> 00:51:45,620
+الخمسة مباشرةً، أين اللي جيتها الثانية؟ تساوي n في الـ
+
+577
+00:51:45,620 --> 00:51:49,620
+best case، تخيّل أن أنا بدوّر مثلاً على التسعة في
+
+578
+00:51:49,620 --> 00:51:54,680
+الحالتين، التسعة فوق مش موجودة، والتسعة تحت مش
+
+579
+00:51:54,680 --> 00:52:00,240
+موجودة، اللي فوق هيحتاج ست خطوات، ست عمليات مقارنة،
+
+580
+00:52:00,240 --> 00:52:04,560
+بينما هذا هيحتاج عمليتين أو ثلاثة، اللي هي log، لأن
+
+581
+00:52:05,330 --> 00:52:09,410
+لجِئنا الآن، مظبوط؟ وبالتالي ... بالتالي هذه الحكاية
+
+582
+00:52:09,410 --> 00:52:12,690
+اللي بتدّعي ... عشان إيه؟ دائماً إحنا بنجيب الـ worst
+
+583
+00:52:12,690 --> 00:52:15,810
+case، في أسوأ الأحوال، إيش أنا بعنيني؟ بعنيني الـ
+
+584
+00:52:15,810 --> 00:52:19,870
+algorithm أو الـ behavior، وإحنا فعلياً لما بتدور
+
+585
+00:52:19,870 --> 00:52:24,630
+على حد أو صديق أو حد بتعتمد عليه، بدك يَهاجِد الفرح
+
+586
+00:52:24,630 --> 00:52:28,830
+والرخّة؟ لأ، مش بيقول لك الصديق وقت الضيق، في الـ
+
+587
+00:52:28,830 --> 00:52:31,250
+worst case، في أسوأ الظروف، أنا بدي صديقي يكون موجود
+
+588
+00:52:31,250 --> 00:52:34,530
+حوليا، ما بدّيش يقول: ما أنا غني ومعايا فلوس وبصحة و
+
+589
+00:52:34,530 --> 00:52:38,510
+تمام، وما عنديش مشاكل، إيه هو مُلزَم فيا، مظبوط ولا لأ؟
+
+590
+00:52:38,510 --> 00:52:43,790
+فإحنا دائماً دائماً بندوّر على العنصر اللي بيخدمنا في
+
+591
+00:52:43,790 --> 00:52:46,710
+الـ worst case أكثر من اللي بيخدمنا في الـ best case
+
+592
+00:52:46,710 --> 00:52:55,270
+اللي موجودة، طيب، هذه الـ algorithm، بقول
+
+593
+00:52:55,270 --> 00:53:03,590
+بدي أضرب مصفوفة بـ scalar، عنصر ثابت C، بدي أضرب
+
+594
+00:53:03,590 --> 00:53:12,650
+المصفوفة، والمصفوفة هي square matrix، الـ
+
+595
+00:53:12,650 --> 00:53:18,090
+function تبعها مباشرةً
+
+596
+00:53:18,090 --> 00:53:25,210
+هي العملية الواحدة، هي C ضرب الـ value اللي موجودة، بس
+
+597
+00:53:25,210 --> 00:53:28,390
+الـ C دي موجودة في الـ loop، مقدارها N، واللي بعدها
+
+598
+00:53:28,390 --> 00:53:34,230
+N، معناته F of N مباشرة بتساوي N في N في واحد، N
+
+599
+00:53:34,230 --> 00:53:42,470
+تربيع، N في N في واحد، N تربيع، خلصتها، هي Big O من الـ
+
+600
+00:53:42,470 --> 00:53:48,190
+N تربيع، Quadratic Complexity، تعالَ نشوف هذه
+
+601
+00:53:52,840 --> 00:53:57,760
+الآن، لاحظ، تقريباً نفس الكلام، بس أشبه بقول لي بدي
+
+602
+00:53:57,760 --> 00:54:04,140
+أجمع الـ upper triangle في الـ matrix، الآن المصفوفة
+
+603
+00:54:04,140 --> 00:54:08,260
+المربعة، خليني أفترض أن في عندي مصفوفة أربعة في
+
+604
+00:54:08,260 --> 00:54:15,440
+أربعة، واحد، اثنين، ثلاثة، أربعة، خمسة، ستة، سبعة، ثمانية،
+
+605
+00:54:15,440 --> 00:54:21,130
+تسعة، واحد، اثنين، ثلاثة، أربعة، خمسة، ستة، سبعة، الآن
+
+606
+00:54:21,130 --> 00:54:26,070
+المصفوفة المربعة، فيها قطر ولا لأ؟ الـ upper triangle
+
+607
+00:54:26,070 --> 00:54:33,970
+هو المثلث العلوي، من
+
+608
+00:54:33,970 --> 00:54:41,590
+أين يبدأ المثلث العلوي؟ اهي اثنين، وسبعة، إذا بدك
+
+609
+00:54:41,590 --> 00:54:44,550
+تحط كمان القطر الرئيسي، كمان ما فيش مشكلة في الموضوع،
+
+610
+00:54:44,550 --> 00:54:49,870
+هنقول: ن
+
+667
+00:59:38,820 --> 00:59:42,660
+عدد القصّ مفروغة، وشغلة أجرب أحسب على الكلام هذا
+
+668
+00:59:42,660 --> 00:59:46,360
+هحاول خلال اليومين الجاية، هنزل لك كام مثال، تمام
+
+669
+00:59:46,360 --> 00:59:53,460
+تحاول تحسب الـ big O تبعتهم في أي سؤال يا شباب؟ الله
+
+670
+00:59:53,460 --> 00:59:54,000
+يعطيكم العافية
diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/tnT14Wninao_postprocess.srt b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/tnT14Wninao_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..30ef3f5bf1a62878f6f771411e4566c42fff8faa
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/tnT14Wninao_postprocess.srt
@@ -0,0 +1,2680 @@
+1
+00:00:20,910 --> 00:00:23,050
+بسم الله و الحمد لله و الصلاة والسلام على رسول
+
+2
+00:00:23,050 --> 00:00:25,570
+الله اليوم ان شاء الله هنكمل في موضوع ال
+
+3
+00:00:25,570 --> 00:00:30,670
+algorithms لكن موضوع انا شوية اليوم بده مخ مفتح
+
+4
+00:00:30,670 --> 00:00:34,370
+فبدي انا اتصحصح معايا و ماتنعسش و ان شاء الله
+
+5
+00:00:34,370 --> 00:00:38,150
+ماتكونش المحاضرة طويلة كنا بدنا نتكلم عن ال
+
+6
+00:00:38,150 --> 00:00:41,790
+algorithms المحاضرة الماضية و قلنا ال algorithm هي
+
+7
+00:00:41,790 --> 00:00:42,910
+عبارة عن finite
+
+8
+00:00:46,470 --> 00:00:50,550
+set of precise instructions مجموعة منتهية من
+
+9
+00:00:50,550 --> 00:00:55,250
+الأوامر الواضحة أو التعليمات الواضحة لإيش؟ عشان
+
+10
+00:00:55,250 --> 00:00:58,270
+تسوي computation for performing computation or
+
+11
+00:00:58,270 --> 00:01:03,170
+solving a problem وقولنا في عندي ال algorithm فيه
+
+12
+00:01:03,170 --> 00:01:07,250
+مجموعة من الخصائص ال input و ال output و
+
+13
+00:01:07,250 --> 00:01:11,150
+بالتعريفات الخطوات اللي لازم يكون معرفة بشكل واضح
+
+14
+00:01:11,150 --> 00:01:15,880
+يكون ال output صحيح بناء على ال input الموجودةوال
+
+15
+00:01:15,880 --> 00:01:21,700
+fitness ان يكون انه بعد finite steps بحصل على ال
+
+16
+00:01:21,700 --> 00:01:24,340
+output بناء على ال input اللي موجود و لازم يكون
+
+17
+00:01:24,340 --> 00:01:28,400
+فيه تناسب ما بين عدد الخطوات و حجم ال input لازم
+
+18
+00:01:28,400 --> 00:01:34,420
+يكون effectiveمعنى أنه يجب أن يكون بعد فترة زمنية
+
+19
+00:01:34,420 --> 00:01:38,460
+مقبولة يرد و ال general أن ال application تبقى
+
+20
+00:01:38,460 --> 00:01:42,220
+قادر أن أعممه على العناصر اللي موجودة وشوفنا ال
+
+21
+00:01:42,220 --> 00:01:46,220
+linear search كيف انا أدور بشكل sequential على
+
+22
+00:01:46,220 --> 00:01:50,740
+العناصر وشوفنا ال binary search وشوفنا الفرق ما
+
+23
+00:01:50,740 --> 00:01:54,260
+بينهم و بعد هيك شوفنا مثال ال sortingكيف لو انا
+
+24
+00:01:54,260 --> 00:01:59,420
+بده ارتب البيانات ترتيب تصعدي وقلنا في عندنا واحد
+
+25
+00:01:59,420 --> 00:02:03,960
+من الأمثلة اللي هو ال bubble sort وشوفناه واتكلمنا
+
+26
+00:02:03,960 --> 00:02:08,080
+عليه وكنا وصلنا لحد شغلة اسمها ال greedy
+
+27
+00:02:08,080 --> 00:02:12,500
+algorithms ال greedy algorithms هي عبارة عن نوع من
+
+28
+00:02:12,500 --> 00:02:16,340
+أنواع ال algorithms وتستخدم في ال optimization
+
+29
+00:02:16,340 --> 00:02:20,620
+problem في المسائل اللي بنحصل فيها على أفضل
+
+30
+00:02:20,620 --> 00:02:25,470
+solution بأقل تكلفةأكبر إنتاج شغلات زي هيك بيسميها
+
+31
+00:02:25,470 --> 00:02:29,650
+optimization لكن في المفهوم ال greedy algorithms
+
+32
+00:02:29,650 --> 00:02:34,770
+ان هذه ال algorithms غالبا ما بتنظر للحل حسب
+
+33
+00:02:34,770 --> 00:02:38,910
+المرحلة القانية هو هتجيبلك مثال عشان نوضح شو يعني
+
+34
+00:02:38,910 --> 00:02:44,090
+مفهوم greedy greedy قمع بالترجمة الحرفية لو انا
+
+35
+00:02:44,090 --> 00:02:51,050
+اجل قلتلك في ال tree هذه بتجيبلي بتجيبليالـ
+
+36
+00:02:51,050 --> 00:02:54,970
+Largest Path ايش ال Largest Path؟ هو المسار اللي
+
+37
+00:02:54,970 --> 00:02:59,190
+بتجمع من خلاله أكبر نقاط. وين ال Largest Path
+
+38
+00:02:59,190 --> 00:03:04,990
+هينكون عندك؟ سبعة، تلاتة، تسعة وتسعين. هذا ليش؟
+
+39
+00:03:04,990 --> 00:03:09,450
+لأنك انت فعليا شايف كل tree قدام عينك. لكن لو أنا
+
+40
+00:03:09,450 --> 00:03:13,590
+خافيت قدامك، خافيت انك ال layer هادي اللي تحت،
+
+41
+00:03:13,590 --> 00:03:18,370
+قلتلك ان ال layer هادي مش موجودة. ايش بك تساوي؟
+
+42
+00:03:19,610 --> 00:03:23,730
+هتبدأ تفكر ان انا اروح ادور على الأكبر بما هو بده
+
+43
+00:03:23,730 --> 00:03:28,730
+ال largest انا عندى السابعة وعندي تلاتة واطمعاش
+
+44
+00:03:28,730 --> 00:03:33,890
+المنغش بقول بقول اروح باتجاه الاطمعش وعند الاطمعش
+
+45
+00:03:33,890 --> 00:03:36,770
+بشوف ايش ال output اللى بعدين وبناء على نفس الكلام
+
+46
+00:03:36,770 --> 00:03:39,590
+بعد الاطمعش بروح باتجاه الستة و لا السابعة الخامسة
+
+47
+00:03:39,590 --> 00:03:44,310
+بروح باتجاه الستة لان انا فعليا بدي ال largest هذا
+
+48
+00:03:44,310 --> 00:03:50,180
+الحل او هذه الحركة اللى صارتعلى الرغم انها صحيحة
+
+49
+00:03:50,180 --> 00:03:56,620
+بنسميها احنا حركة طماع ليش فعليا بس نظر وين على ال
+
+50
+00:03:56,620 --> 00:04:00,120
+current situation تحت رجليك مطلع ماكانش عنده بعد
+
+51
+00:04:00,120 --> 00:04:04,000
+نظر في انه يحسب المسافة اللي موجودة كماما في
+
+52
+00:04:04,000 --> 00:04:06,740
+المثال هذا زي المثال اللي احنا شوفناه المرة
+
+53
+00:04:06,740 --> 00:04:15,100
+الماضية بقولت لو كان انا في هاي فيي عندى مثلث A
+
+54
+00:04:15,100 --> 00:04:17,600
+B C
+
+55
+00:04:22,030 --> 00:04:33,570
+وعند الطريق هذه وبدى أصل من ال A أصل لل D الآن
+
+56
+00:04:33,570 --> 00:04:40,070
+المفروض أقصر الطرق يكون عبر ال water هذا أقصر
+
+57
+00:04:40,070 --> 00:04:45,970
+الطرق shortest path أقصر الطرق لكن ال grade ايش
+
+58
+00:04:45,970 --> 00:04:50,690
+بروح بساوي بفترض أنه موجود عند ال A بدى يتحركمين
+
+59
+00:04:50,690 --> 00:04:56,230
+النقطة الأقرب؟ عشان أصل ال algorithm و أصل الشباب
+
+60
+00:04:56,230 --> 00:05:09,030
+ماشي روح يساوي بروح بكتب a b d a b c d a c b d a c
+
+61
+00:05:09,030 --> 00:05:15,450
+d هاي كل ال possible roots ولا لأ؟ الان الان إيش
+
+62
+00:05:15,450 --> 00:05:19,230
+بروح يساوي في الجريدي؟ بقولك أنا عشان أسلك بدي أخد
+
+63
+00:05:21,180 --> 00:05:25,060
+أقصر طريق في اللي موجودين هدول؟ مين أقصر طريق؟ من
+
+64
+00:05:25,060 --> 00:05:29,400
+الـA للـC و لا من الـA للـB؟ من الـA للـC، معناته
+
+65
+00:05:29,400 --> 00:05:33,880
+هو خلاص حسن أمره، راح باتجاه الـC، صار عنده هدول،
+
+66
+00:05:33,880 --> 00:05:37,620
+مين الأقصر الآن؟ من الـC للـD و لا من الـC للـB؟
+
+67
+00:05:37,620 --> 00:05:41,460
+على الرغم أن الـC للـB direct هتصل بشكل مباشر،
+
+68
+00:05:41,460 --> 00:05:45,540
+هروح باتجاه مين؟ الـB، و من بعد الـB، هروح باتجاه
+
+69
+00:05:45,540 --> 00:05:47,440
+الـD، وبالتالي
+
+70
+00:05:49,750 --> 00:05:53,390
+الـ Position لاحظ ان هو سلك أطول الطرق .. أطول
+
+71
+00:05:53,390 --> 00:05:56,650
+الطرق من أجل الوصول لهدف اللي موجود عندها على
+
+72
+00:05:56,650 --> 00:06:03,010
+الرغم انه كان بإمكانه يصل بشكل أسرع من قلال A,B,D
+
+73
+00:06:05,040 --> 00:06:08,460
+الان هذا هو المفهوم او مبدأ لـ greedy algorithms
+
+74
+00:06:08,460 --> 00:06:11,960
+وانا بديش منك اكتر من هيك تفهم ان ال greedy
+
+75
+00:06:11,960 --> 00:06:14,920
+algorithms هو عبارة عن algorithms تستخدم في مسائل
+
+76
+00:06:14,920 --> 00:06:18,820
+ال optimization لما انا بهمني احصل على اقصر طريق
+
+77
+00:06:18,820 --> 00:06:23,080
+افضل إنتاج اعلى رقم اعلى مش عارف ايش الشغلات دي
+
+78
+00:06:23,080 --> 00:06:26,660
+كلها تهاشت بتسميها او بتخضع على مبدأ لـ greedy
+
+79
+00:06:26,660 --> 00:06:30,080
+algorithms كل solution solution و acceptable
+
+80
+00:06:30,080 --> 00:06:36,730
+solution حل مقمول لكنه فيهأفضل منه في أفضل منه
+
+81
+00:06:36,730 --> 00:06:42,390
+تمام بدنا
+
+82
+00:06:42,390 --> 00:06:46,030
+ننتقل معاكم يا شام شباب خلال المحاضرة أو خلال
+
+83
+00:06:46,030 --> 00:06:49,430
+الجزئية اللي بقايلة هقبل فيها two sections تمام بس
+
+84
+00:06:49,430 --> 00:06:55,770
+مش هركز على المفهوم النظري كتير تمام بقدر ما بدياك
+
+85
+00:06:57,100 --> 00:06:59,940
+تكون تشغّل مخك كويس و تفهم ال concept لأن ال
+
+86
+00:06:59,940 --> 00:07:04,180
+concept بسيط جدا خصوصا ان معظمكم مش هياخد مادة اسم
+
+87
+00:07:04,180 --> 00:07:08,560
+data structure تمام؟ مش هياخد مادة تركيب بيانات و
+
+88
+00:07:08,560 --> 00:07:12,880
+يقيم ال algorithms لو انا اجيت سألتك انا في عندى
+
+89
+00:07:12,880 --> 00:07:21,160
+two algorithms a1 و a2 والتانى يستخدموا لحل نفس
+
+90
+00:07:21,160 --> 00:07:28,320
+المشكلة والتانى بدوني نفس النتيجةفى أفضلية بينهم؟
+
+91
+00:07:28,320 --> 00:07:34,480
+فى أفضلية بينهم حسب السرعة، حسب جودته، إيش معيّر
+
+92
+00:07:34,480 --> 00:07:38,990
+الجودة؟ الست عراسة اللى شوفناهم قبلالان input و
+
+93
+00:07:38,990 --> 00:07:41,370
+output هم السلم و نفس ال input و الدون نفس ال
+
+94
+00:07:41,370 --> 00:07:44,830
+output خلصنا معناته التانية من ناحية الصحة صحيحات
+
+95
+00:07:44,830 --> 00:07:50,090
+في شغلات تانية بدأ أبدأ أدور هل هو من ناحية ال
+
+96
+00:07:50,090 --> 00:07:55,630
+definition صحيح صحيح effective correctness تمام؟
+
+97
+00:07:55,630 --> 00:08:00,910
+وبالتالي بدأ أبدأ أدور على شغلات تانية تمام؟ الآن
+
+98
+00:08:00,910 --> 00:08:06,610
+من الشغلات هذه اللي أنا بتهمنيفى شغل اسمها الـ
+
+99
+00:08:06,610 --> 00:08:09,750
+Growth Functions ماش يعني Growth Functions؟ وشو
+
+100
+00:08:09,750 --> 00:08:13,990
+دخل الـ Algorithm بالـ Functions؟ الآن لما انا
+
+101
+00:08:13,990 --> 00:08:17,070
+اتكلمنا على الـ Effectiveness قولت ان الـ
+
+102
+00:08:17,070 --> 00:08:24,310
+Algorithm يعطيني الـ Output من فترة زمنية
+
+103
+00:08:24,310 --> 00:08:29,330
+محدودة يعني وكأنى بتكلم على سرعة الـ Algorithm
+
+104
+00:08:29,330 --> 00:08:35,540
+يكون متناسب مع الحجم ال input اللى موجود عندىولمّا
+
+105
+00:08:35,540 --> 00:08:39,680
+انا بتكلم على growth of functions ان بدي امثل ال
+
+106
+00:08:39,680 --> 00:08:44,240
+algorithm تبعي .. امثل ال algorithm تبعي بدالة ..
+
+107
+00:08:44,240 --> 00:08:48,500
+function و الدالة هادي بدها تزيد بزيادة مين؟
+
+108
+00:08:48,500 --> 00:08:53,660
+بزيادة ال input لان نرجع لمثال ال sort او بلاش
+
+109
+00:08:53,660 --> 00:08:59,340
+مثال ال search كان في عندي linear search مصبوط
+
+110
+00:08:59,340 --> 00:09:01,980
+وكان في عندي binary search
+
+111
+00:09:10,020 --> 00:09:19,460
+الان لما كان في الان دي من a1 a2 لحد an من a1 a2
+
+112
+00:09:19,460 --> 00:09:28,600
+لحد an ان من ال element او ان من العناصر جديش كان
+
+113
+00:09:28,600 --> 00:09:33,360
+عملية مقارنة كانت بتلزمني عشان اقول ان ال element
+
+114
+00:09:33,360 --> 00:09:39,000
+هذا مش موجود ان من القرار من المراتيعني بقدر أقول
+
+115
+00:09:39,000 --> 00:09:47,220
+له f of n تساوي n، نصبوت n من المرات، طب و هذا؟
+
+116
+00:09:47,220 --> 00:09:51,860
+انت شوف ال element مش موجود، أنا روحت على ال worst
+
+117
+00:09:51,860 --> 00:10:00,360
+case ان ال element مش موجود، لاحظ هو عبارة عن نصN
+
+118
+00:10:00,360 --> 00:10:08,640
+على 2 صح؟ زائد N على زائد N على 8 زائد N على 16
+
+119
+00:10:08,640 --> 00:10:17,020
+زائد N على 32 زائد N على 64 زائد زائد لحد وصل ل 1
+
+120
+00:10:17,020 --> 00:10:20,760
+احنا شوفنا المثال على 1024 كان قال وهذه ال series
+
+121
+00:10:20,760 --> 00:10:29,380
+series هاي كمان متسلسلة sequence مجموعة يساوي
+
+122
+00:10:33,270 --> 00:10:37,490
+لغّي الأن للأساس اتنين وعادة للرياضية يعني ال F of
+
+123
+00:10:37,490 --> 00:10:41,610
+N تبع ال algorithm التاني هذا تساوي لغي الأن
+
+124
+00:10:41,610 --> 00:10:48,910
+للأساس اتنين لاحظ الآن لما قدرت أحولهم أو أجيبهم
+
+125
+00:10:48,910 --> 00:10:52,390
+وهنا صارت أهمية ال sequence صافغة أنا مش بده في
+
+126
+00:10:52,390 --> 00:10:58,230
+جمع المتسلسلات ممكن تظهر يعني بعضكم ساعة نفسه ليش
+
+127
+00:10:58,230 --> 00:11:01,710
+أنا محتاج أجمع متسلسلة أنت محتاجش أجمع متسلسلة
+
+128
+00:11:01,710 --> 00:11:07,760
+عشان هيكالان بدك تفهم الـ sequence اللي عندك عشان
+
+129
+00:11:07,760 --> 00:11:12,480
+تقدر تجيب ال function تبعتها و ال function هذه
+
+130
+00:11:12,480 --> 00:11:15,380
+بناء عليها بده يصير decision مين أفضل في ال
+
+131
+00:11:15,380 --> 00:11:19,900
+algorithm مين قضاه أفضل ال linear search ولا ال
+
+132
+00:11:19,900 --> 00:11:23,900
+binary search حسب ال function اللي موجودة عندك حسب
+
+133
+00:11:23,900 --> 00:11:27,900
+ال function اللي موجودة عندك لما باجي بقارن في ال
+
+134
+00:11:27,900 --> 00:11:32,120
+worst case في عندي N من ال elements هذا كان بيحتاج
+
+135
+00:11:33,590 --> 00:11:36,890
+ان من المرات عشان يقول لي ان ال element does not
+
+136
+00:11:36,890 --> 00:11:42,290
+exist بل لكن هذا بيستخدم log الان log الان على
+
+137
+00:11:42,290 --> 00:11:47,890
+أساس اتنين عشان يقول لي تعالي لما اتكلم على الان
+
+138
+00:11:47,890 --> 00:11:53,970
+بدها تساوي تمانية هذه تمانية تمان خطوات يعني عدد
+
+139
+00:11:53,970 --> 00:12:00,270
+ال element تمان عناصر والان تساوي تمانية هنا log
+
+140
+00:12:01,250 --> 00:12:05,250
+تمنية اثنين أس تلاتة تمنية تمنية تمنية تمنية تمنية
+
+141
+00:12:05,250 --> 00:12:11,530
+تمنية تمنية تمنية تمنية تمنية تمنية تمنية تمنية
+
+142
+00:12:11,530 --> 00:12:13,390
+تمنية تمنية تمنية تمنية تمنية تمنية تمنية تمنية
+
+143
+00:12:13,390 --> 00:12:13,450
+تمنية تمنية تمنية تمنية تمنية تمنية تمنية تمنية
+
+144
+00:12:13,450 --> 00:12:13,990
+تمنية تمنية تمنية تمنية تمنية تمنية تمنية تمنية
+
+145
+00:12:13,990 --> 00:12:14,530
+تمنية تمنية تمنية تمنية تمنية تمنية تمنية تمنية
+
+146
+00:12:14,530 --> 00:12:15,450
+تمنية تمنية تمنية تمنية تمنية تمنية تمنية تمنية
+
+147
+00:12:15,450 --> 00:12:15,490
+تمنية تمنية تمنية تمنية تمنية تمنية تمنية تمنية
+
+148
+00:12:15,490 --> 00:12:22,790
+تمنية تمنية تمنية تمنية تمنية تمنية تمنية تمنية
+
+149
+00:12:22,790 --> 00:12:29,290
+تمنية
+
+150
+00:12:29,290 --> 00:12:36,510
+تالف و أربعة و عشرين وهذه log اتنين اص عشرة للأساس
+
+151
+00:12:36,510 --> 00:12:43,150
+اتنين عشرة صارت الشغل مشدية و لاحظ لما زادت ال
+
+152
+00:12:43,150 --> 00:12:51,650
+input ال function تبعت ايه كيف بتكبر growth فكلمة
+
+153
+00:12:51,650 --> 00:12:56,490
+ال growth هذه مفهومها زيادة او حجم ال function
+
+154
+00:12:56,490 --> 00:13:02,030
+مقارنة او تبع لمين لل inputحجم الـ function تبعد
+
+155
+00:13:02,030 --> 00:13:07,030
+لل input تمام يعني الآن انا بتكلم على ال graph
+
+156
+00:13:07,030 --> 00:13:10,670
+function معناته انا بدي احاول اعمل quantifying بدي
+
+157
+00:13:10,670 --> 00:13:17,030
+اقيم الدوال مقارنة مع بعضها و اجي اقول ان ال F
+
+158
+00:13:17,030 --> 00:13:23,730
+تبعتي او ال function G بتتزيد ايش بتتزيد يعني بكبر
+
+159
+00:13:23,730 --> 00:13:31,670
+حجمهاتنمو تبقى على ال input at least as the
+
+160
+00:13:31,670 --> 00:13:36,730
+function as fast as the function f يعني بتزيد
+
+161
+00:13:36,730 --> 00:13:42,710
+مثلها مثل ال f طيب لو انا جيت وقلتلك ان ال f of n
+
+162
+00:13:42,710 --> 00:13:52,010
+تبعتي بدها تساوي 4n زائد 2 ايش المعادلة هذه معادلة
+
+163
+00:13:52,010 --> 00:13:58,570
+خطية صح؟طيب، هل بنقدر نقارنها بنقول زيادة هذه مثل
+
+164
+00:13:58,570 --> 00:14:04,350
+الـG of N دي تساوي N؟
+
+165
+00:14:04,350 --> 00:14:09,130
+إيش الفرق بين المعادلة هاي والمعادلة هاي؟ هذي
+
+166
+00:14:09,130 --> 00:14:15,250
+كتابة الآن؟ طيب، لو أنا بدأ أرسم التنتين على نفس
+
+167
+00:14:15,250 --> 00:14:19,910
+المخطط كيف تتوقعوا الفرق بينهم؟
+
+168
+00:14:31,750 --> 00:14:40,210
+الثانية اربعة N زائد اتنين في
+
+169
+00:14:40,210 --> 00:14:46,090
+الاخر
+
+170
+00:14:46,090 --> 00:14:51,810
+هتحصل على خطموازي للخط اللي موجود عنه بس معمله
+
+171
+00:14:51,810 --> 00:14:56,030
+إزاحة و مرفوقة لفوق بمقدار يعني الان انضربت في
+
+172
+00:14:56,030 --> 00:15:02,770
+أربعة و نعملها scaling و بعدين shifting أو
+
+173
+00:15:02,770 --> 00:15:08,730
+translation إزاحة الآن هذه الدالة بالتالي مقدر أنا
+
+174
+00:15:08,730 --> 00:15:12,450
+أقارن الدالة هذه مع الدالة هذه بين قصين نمو
+
+175
+00:15:12,450 --> 00:15:18,750
+الدالتينمتوازي متقارب وبالتالي بقدر اقد مقارنة ما
+
+176
+00:15:18,750 --> 00:15:22,730
+بين الدالة هذه بيجي اقول والله ان ال F of N هذه
+
+177
+00:15:22,730 --> 00:15:28,550
+ابتنموا بنفس سرعة نمو ال N ال G N ليش هذا الكلام
+
+178
+00:15:28,550 --> 00:15:34,370
+بعنيني؟ لأنه في الآخرالتنين هذه يا شباب ايش بتمثل؟
+
+179
+00:15:34,370 --> 00:15:37,510
+بتمثل عدد العمليات يعني كانت ال algorithm تبعي
+
+180
+00:15:37,510 --> 00:15:40,250
+زائد 2 الحاجز بقولك كيف حسبناها والاربعة هذي
+
+181
+00:15:40,250 --> 00:15:45,210
+constant بس فعليا ال value او ال growth الأكبر كان
+
+182
+00:15:45,210 --> 00:15:49,090
+وين من وين جاي من ال N كل ما تزيد عدد ال N زي ما
+
+183
+00:15:49,090 --> 00:15:53,290
+شاء الله تهو في المثال بتبين جديش مقدار الزيادة في
+
+184
+00:15:53,290 --> 00:15:57,150
+ال algorithm يعني كل ما كانت ال N صغيرة اربعة في
+
+185
+00:15:57,150 --> 00:16:00,750
+اتنين تفرض ان انا انا اتنين اربعة في اتنينتمانية و
+
+186
+00:16:00,750 --> 00:16:05,510
+اتنين عشرة هال اتنين الفرق بينهم مش كبير حتى و
+
+187
+00:16:05,510 --> 00:16:09,270
+نيجي نقولك يعني من الآخر شو يعني فرق تمان خطوات
+
+188
+00:16:09,270 --> 00:16:12,810
+بين ال algorithm هذا و ال algorithm هذا على تمان
+
+189
+00:16:12,810 --> 00:16:17,670
+خطوات او ال eight cycles في ال CPU ولا شيء يعني
+
+190
+00:16:17,670 --> 00:16:22,610
+تمانية nano second خلصت جاب البنت تفكر ترمش بكون
+
+191
+00:16:22,610 --> 00:16:26,710
+خلص ال system compensation لها مصدوق ولا لأ لكن
+
+192
+00:16:26,710 --> 00:16:31,750
+الزيادة فعليا من العامل المؤثم اكتر فيهالما أجيب
+
+193
+00:16:31,750 --> 00:16:37,190
+أتكلم ألف و أربعة و عشرين هتصير فيه أمدي هاني
+
+194
+00:16:37,190 --> 00:16:43,830
+أربعة تلاف و تمانية و خمسين، مظبوط؟ ألف و أربعة و
+
+195
+00:16:43,830 --> 00:16:48,750
+عشرين في أربعة .. ألف و أربعة و عشرين في أربعة ستة
+
+196
+00:16:49,580 --> 00:16:54,580
+الـ 16 اه تمام تسعة اربع تلاف و ستة وتسعين اربع
+
+197
+00:16:54,580 --> 00:16:59,480
+تلاف و ستة وتسعين الان زاد اتنين مظبوط اربع تلاف
+
+198
+00:16:59,480 --> 00:17:03,260
+تمانية وتسعين في الآخر فعليا الزيادة يعني هيك
+
+199
+00:17:03,260 --> 00:17:06,860
+الاتحاكم او العنصر الرئيسي في ال growth كانت الان
+
+200
+00:17:06,860 --> 00:17:11,340
+عشان هيك انا بتهمني مين بهمني الان بتهمني الان
+
+201
+00:17:11,340 --> 00:17:16,850
+تمام يعني لما انا بتكلم الانالـ Growth Function
+
+202
+00:17:16,850 --> 00:17:20,490
+تبعتي الـ Algorithm معناته بيكتفها مباشرة أن الـ
+
+203
+00:17:20,490 --> 00:17:25,230
+Algorithm هذا بيتحول لمعادلة زمانية معادلة زمانية
+
+204
+00:17:25,230 --> 00:17:29,730
+بدلالة الآن وأبدأ أقارنها بدالة من الدوال المعروفة
+
+205
+00:17:29,730 --> 00:17:33,830
+بدالة من الدوال المعروفة دعونا نشوف مثال الـ
+
+206
+00:17:33,830 --> 00:17:37,290
+Algorithm البسيط اللي موجود عندنا هنا لو أنا جيت
+
+207
+00:17:37,290 --> 00:17:42,230
+جولت في مثال الجامع فقط بدي أتكلم على مثال الجامع
+
+208
+00:17:42,230 --> 00:17:53,730
+اجيت جولت 4أو الـ Procedure Sum فتحت
+
+209
+00:17:53,730 --> 00:17:59,590
+جوس و اديتك N من ال input A1, A2 لحد An Integers
+
+210
+00:17:59,590 --> 00:18:03,870
+هتروح
+
+211
+00:18:03,870 --> 00:18:08,990
+تقول ال S بدها تساوي صفر بعد ذلك بتعملي four ال I
+
+212
+00:18:08,990 --> 00:18:19,700
+equal one to Nالـ S بدها تساوي S زائد AI بصبوت و
+
+213
+00:18:19,700 --> 00:18:26,340
+هتقول لي output الـ S و I end خلص ال algorithm
+
+214
+00:18:26,340 --> 00:18:33,780
+جمعت فيه كل العناصر ال sequence اللي موجودة ال
+
+215
+00:18:33,780 --> 00:18:39,480
+algorithm هذا جديش تكلفته إيش ال function دلالة N
+
+216
+00:18:39,480 --> 00:18:45,450
+إيش ال function تبعتهماذا تفعل؟ تحتب الفكرة التي
+
+217
+00:18:45,450 --> 00:18:51,250
+كانت تالية كل يساوي assignment process كل جنع ب
+
+218
+00:18:51,250 --> 00:18:57,950
+process تمام؟ و تبدأ تعد أي واحد يعني هيك حاجة
+
+219
+00:18:57,950 --> 00:19:03,650
+تقول أي واحد طب و هذا؟ واحد اتنين لأن في
+
+220
+00:19:03,650 --> 00:19:07,850
+assignment و في increment مصبور اتنين كم مرة هذه
+
+221
+00:19:07,850 --> 00:19:13,750
+الاتنين بتتكرر؟ تمانية N من المرات من واحد ل N2M
+
+222
+00:19:13,750 --> 00:19:18,970
+وفي داخلها وفي داخلها في عندي واحد اتنين يعني هذه
+
+223
+00:19:18,970 --> 00:19:22,990
+كمان فيها اتنين يعني اتنين في اتنين في .. بتصير
+
+224
+00:19:22,990 --> 00:19:28,670
+اتنين في اتنين M لإن كل اتنين هذه كل مرة من اللي
+
+225
+00:19:28,670 --> 00:19:32,270
+فوق الجيوبة تتكرر لإن العلاقة ماعيش بينهم ضرب
+
+226
+00:19:32,270 --> 00:19:36,410
+بصبوت وبالتالي بقدر أقول الدالة الزمنية تبع ال
+
+227
+00:19:36,410 --> 00:19:40,890
+algorithm هذه اللي عندي F of M بدها تساوي اتنين في
+
+228
+00:19:40,890 --> 00:19:46,720
+اتنين Mأربعة N زائد واحد وانشئت تقولي والله كمان
+
+229
+00:19:46,720 --> 00:19:49,560
+ال output بتحسبها كمان عملية انا ماعنديش مشكلة في
+
+230
+00:19:49,560 --> 00:19:55,140
+الموضوع بس في الآخر هي الدالة الزمنية تبعتي هي ال
+
+231
+00:19:55,140 --> 00:19:58,700
+function اللي مثلت ال algorithm هي ال function
+
+232
+00:19:58,700 --> 00:20:03,900
+اللي مثلت ال algorithm الآن وبالتالي انا بقدر اقول
+
+233
+00:20:03,900 --> 00:20:07,380
+هي ال function ال growth تبعها لما انا بدي اقارنه
+
+234
+00:20:08,060 --> 00:20:11,880
+عشان اتكلم على الـ quality تبعت ال algorithm كل ال
+
+235
+00:20:11,880 --> 00:20:15,660
+constant هذا الأصل انهاء الشباب مابتعنيش معايا ولا
+
+236
+00:20:15,660 --> 00:20:19,460
+حاجة شو يعني process؟ وشو يعني أربع process؟ أو
+
+237
+00:20:19,460 --> 00:20:22,700
+حتى لدربت العدد ال process كمان في أربع مرات مش
+
+238
+00:20:22,700 --> 00:20:26,940
+خضية كتير بالنسبة لنا المهم الأن لأن هي كمان مرة
+
+239
+00:20:26,940 --> 00:20:31,940
+زيادتها بتعني زيادة ال algorithm او زيادة الوقت
+
+240
+00:20:31,940 --> 00:20:34,840
+اللي بيستحقوا ال algorithm في الحل هي المفروض ان
+
+241
+00:20:34,840 --> 00:20:38,770
+انا اتعامل مع كل ال algorithm و اوجد مينالـ DALLA
+
+242
+00:20:38,770 --> 00:20:41,610
+أو الـ function الزمنية تبعتنا بنرجع مرة تانية
+
+243
+00:20:41,610 --> 00:20:46,490
+للحسبة اللي نشوفها طيب تمام وبالتالي أنا بدي أجيب
+
+244
+00:20:46,490 --> 00:20:51,190
+الدالة الزمنية من خلال ال algorithm اللي موجود
+
+245
+00:20:51,190 --> 00:20:57,550
+عندي طيب وإن
+
+246
+00:20:57,550 --> 00:21:01,070
+كان في بعض الرموز مخفية مش عارف ليش لكن في الآخر
+
+247
+00:21:01,070 --> 00:21:10,080
+there exist بدي أروح هايه أقل من الانوهذه اقل او
+
+248
+00:21:10,080 --> 00:21:18,120
+تساوي فيه عندش مصطلح اسمه ال big O ال
+
+249
+00:21:18,120 --> 00:21:23,700
+big O هذا مصطلح بنستخدمه عشان نقول ان الدالة تبعت
+
+250
+00:21:23,700 --> 00:21:29,400
+ال function او تبعت ال algorithm تبعي بتزيد تبعا
+
+251
+00:21:29,400 --> 00:21:33,560
+او في ال worst case في أسوأ الحالات بتزيد بزيادة
+
+252
+00:21:33,560 --> 00:21:41,320
+كدههذا يجب أن يكون لديه 2 functions F of N من أين
+
+253
+00:21:41,320 --> 00:21:44,680
+أريد أن أحصلها؟ من الـ Algorithm، يجب أن تحسبها
+
+254
+00:21:44,680 --> 00:21:51,020
+ويجب أن تحصل على G of N واحدة من الدوالي المشهورة
+
+255
+00:21:51,020 --> 00:21:56,860
+constant يعني big O of واحد linear big O او F of G
+
+256
+00:21:56,860 --> 00:22:07,170
+F of N G of واحد equal واحد G of N equal NG of N
+
+257
+00:22:07,170 --> 00:22:17,450
+equal N تربيع G of N equal N أُس X مثلا G of N
+
+258
+00:22:17,450 --> 00:22:25,170
+بتساوي log N G of N هذه الدواء اللي ألاحظ مجرد
+
+259
+00:22:25,170 --> 00:22:29,630
+تماما من كل ال constantليش؟ لأنه دائما بتهمني ال
+
+260
+00:22:29,630 --> 00:22:32,490
+basic function وحاليا هتحنا نتكلم عليهم و أعرضك
+
+261
+00:22:32,490 --> 00:22:37,290
+إياهم عن خلال ال slides الفكرة وين؟ إنه دائما بدي
+
+262
+00:22:37,290 --> 00:22:44,350
+أحاول أوجد constant C بحيث إنه لو ضربت في ال G of
+
+263
+00:22:44,350 --> 00:22:50,150
+N هذه اطلعلي ال F of N أقل من أو تساوي ال function
+
+264
+00:22:50,150 --> 00:22:53,190
+اللي موجودة عندها تعالي ناخد المثال البسيط اللي
+
+265
+00:22:53,190 --> 00:22:58,760
+عندها أربعة قبل شوية حسبت ال F of N بالمثالأربعة N
+
+266
+00:22:58,760 --> 00:23:04,940
+زائد واحد عشان تكون الأربعة N زائد واحد هذه أقل أو
+
+267
+00:23:04,940 --> 00:23:11,360
+تساوي أربعة N زائد واحد أقل أو تساوي أول حاجة
+
+268
+00:23:11,360 --> 00:23:15,180
+هيبدأك تدور على أعلى أُص للمتغير N مين أعلى أُص
+
+269
+00:23:15,180 --> 00:23:19,440
+للمتغير N اللي عندك؟ واحد معناته بدك تكتب N كما هي
+
+270
+00:23:19,440 --> 00:23:26,440
+مجرد هيك N يعني الـG of N تبعتها هيالان ال
+
+271
+00:23:26,440 --> 00:23:31,060
+constant بدي أجيب C إيش ال C اللي بتحقق المعادلة
+
+272
+00:23:31,060 --> 00:23:38,640
+هذه؟ أربعة؟ أربعة N ما بتثبتش يعني لإنه أربعة N
+
+273
+00:23:38,640 --> 00:23:43,200
+زائد واحد أكبر من N من أربعة N يعني هيك أنا الآن
+
+274
+00:23:43,200 --> 00:23:48,620
+بدي أحط هنا C لو حطيت هنا أربعة أربعة N زائد واحد
+
+275
+00:23:48,620 --> 00:23:54,340
+أقل أو تساوي أربعة N غلط لكن لو أنا مباشر روحت
+
+276
+00:23:54,340 --> 00:24:01,400
+حطيت خمسة Nهتكون المعادلة تبعتي صحيحة فباجي بقول
+
+277
+00:24:01,400 --> 00:24:11,560
+ان ال function تبعتي f of n is big O of ال N سيبنا
+
+278
+00:24:11,560 --> 00:24:14,940
+من ال constant من الدالة هذه اللي موجودة عندها
+
+279
+00:24:14,940 --> 00:24:19,820
+يعني هيك بقول ان الدالة الزمنية تبعتي ال algorithm
+
+280
+00:24:19,820 --> 00:24:22,000
+تبعي تزداد
+
+281
+00:24:24,340 --> 00:24:30,980
+بسرعة مكافئة لزيادة الـ N يعني بين جثين الكلام
+
+282
+00:24:30,980 --> 00:24:35,300
+أبسط من هكذا انه لما هذا ال increment تبعتها او ال
+
+283
+00:24:35,300 --> 00:24:38,380
+growth تبعتها اللي بتتحكم فيها ال N مش ال Interval
+
+284
+00:24:38,380 --> 00:24:44,960
+طيب تعالى نشوف algorithm تاني و نحل نفس الكلام في
+
+285
+00:24:44,960 --> 00:24:49,460
+موضوع ال sort في موضوع ال sort انا هسكر ال slide
+
+286
+00:24:49,460 --> 00:24:52,380
+slide كمان مرة و اكتب ال algorithm هنا على اللوحة
+
+287
+00:24:54,550 --> 00:25:00,930
+في الـ sort في ال bubble sort ال
+
+288
+00:25:00,930 --> 00:25:05,150
+procedure وروحت
+
+289
+00:25:05,150 --> 00:25:12,930
+ال data اك a1 a2 لحد a n integer من ال input تمام؟
+
+290
+00:25:12,930 --> 00:25:18,170
+ايش راح تسوينا في ال algorithm احنا؟
+
+291
+00:25:18,170 --> 00:25:22,170
+فحصت كل أنصر ما قال اكبر منه طالما هو اكبر اشكت
+
+292
+00:25:22,170 --> 00:25:29,990
+بساويبعمل swap بظل بعمل swap تمام هاي four ال I
+
+293
+00:25:29,990 --> 00:25:39,790
+equal واحد to N نقص واحد four ال J equal I زائد
+
+294
+00:25:39,790 --> 00:25:51,070
+واحد to N if ال AI أكبر من ال A من ال J كنت بعمل
+
+295
+00:25:51,070 --> 00:25:56,960
+swapT تصعدي تصعدي تصعدي تصعدي تصعدي تصعدي تصعدي
+
+296
+00:25:56,960 --> 00:25:57,240
+تصعدي تصعدي تصعدي تصعدي تصعدي تصعدي تصعدي تصعدي
+
+297
+00:25:57,240 --> 00:26:02,580
+تصعدي تصعدي تصعدي تصعدي تصعدي تصعدي تصعدي تصعدي
+
+298
+00:26:02,580 --> 00:26:03,920
+تصعدي تصعدي تصعدي تصعدي تصعدي تصعدي تصعدي تصعدي
+
+299
+00:26:03,920 --> 00:26:10,420
+تصعدي تصعدي تصعدي تصعدي تصعدي تصعدي تصعدي تصعدي
+
+300
+00:26:10,420 --> 00:26:15,240
+تصعدي تصعدي تصعدي تصعدي تصعدي تصعدي تصعدي تصعدي
+
+301
+00:26:15,240 --> 00:26:20,520
+تصعدي تصعدي تصعدي تصعدي تصعدي تصعدي تصعدي تصعدي
+
+302
+00:26:20,520 --> 00:26:28,650
+تصعالان أبسط .. هدولة أربعة وليش رايك؟ واحد اتنين
+
+303
+00:26:28,650 --> 00:26:33,110
+تلاتة أربعة بس أصبر شوية هدولة بيتكرروا مع اللوب
+
+304
+00:26:33,110 --> 00:26:37,930
+هادي يعني أربعة في فعدة مرات اللوب مرات اللوب
+
+305
+00:26:37,930 --> 00:26:43,110
+قديش؟ن من المرات أو ن نقص واحد بشكل أدق سابق نقول
+
+306
+00:26:43,110 --> 00:26:49,330
+لإن بدت من الان واحد مصبوط من اتنين لحد الآن بس في
+
+307
+00:26:49,330 --> 00:26:53,310
+فعليا كمان الشباب مش بس من التنين المرة اللي جاية
+
+308
+00:26:53,310 --> 00:26:56,510
+هتبدأ من تلاتة و اللي بعديها هتبدأ من أربعة كل مرة
+
+309
+00:26:56,510 --> 00:27:00,030
+بتنقص واحد لكن بتتكلم عن ال worst case ال worst
+
+310
+00:27:00,030 --> 00:27:04,350
+case أنا بدي أقول هذه ن نقص واحد ن نقص واحد من
+
+311
+00:27:04,350 --> 00:27:11,580
+المرات وهذه اللي فوق بما هذه كلها هتتكررن نقص واحد
+
+312
+00:27:11,580 --> 00:27:17,440
+من المرات مع أن الدالة الزمنية تبعتي F of N بدها
+
+313
+00:27:17,440 --> 00:27:25,740
+تساوي N نقص واحد مضروبة في N نقص واحد مضروب في
+
+314
+00:27:25,740 --> 00:27:29,020
+أربعة هي الدالة الزمنية اللي موجودة عندها تعالي
+
+315
+00:27:29,020 --> 00:27:33,560
+نظبطها كويس نضيها شكل ألطف N تربيع
+
+316
+00:27:35,330 --> 00:27:41,150
+ن ماقص N زائد واحد مضروفي اربع الكل مضروفي اربعة
+
+317
+00:27:41,150 --> 00:27:55,050
+مظبوط تساوي اربعة N تربيع ماقص تمانية N زائد اربعة
+
+318
+00:27:55,050 --> 00:28:00,210
+زائد اربعة هاي دي الدلة الزمنية تبعتي F of N شوف
+
+319
+00:28:00,210 --> 00:28:06,000
+كيف انحسبت اجيت اناللي جوا ال loop عديتهم أربعة
+
+320
+00:28:06,000 --> 00:28:10,060
+process ال loop كان مرة بتتكرر N من المرات أو N
+
+321
+00:28:10,060 --> 00:28:13,980
+نقص واحد فوحد ضربتها و هذا كله جا جوا loop تانية
+
+322
+00:28:13,980 --> 00:28:17,960
+فضربته في كل مرة .. هيك الفكرة وين؟ مع كل مرة من
+
+323
+00:28:17,960 --> 00:28:22,360
+ال loop بتتكرر كل اللي جوا، تمام؟ يعني هذا كله
+
+324
+00:28:22,360 --> 00:28:26,160
+بتتكرر N من نقص واحد بالمرات، طب هاد ال iteration،
+
+325
+00:28:26,160 --> 00:28:30,740
+loopمع كل واحد ماتوا فيه تكرار جديد صارت العلاقة
+
+326
+00:28:30,740 --> 00:28:34,420
+بينهم ضرب وهذه فيه أربعة هاي الدالة الزمنية الدالة
+
+327
+00:28:34,420 --> 00:28:38,640
+الزمنية تبعتها دي تقارن بإيش ال growth function
+
+328
+00:28:38,640 --> 00:28:48,980
+تبعتها زي إيش تجي تطلع عليها بشكل سريع جدا اقل اقل
+
+329
+00:28:48,980 --> 00:28:52,740
+او
+
+330
+00:28:52,740 --> 00:28:59,330
+تساويان تربيع انا بتروح اضربها في تسعة ان او خمسة
+
+331
+00:28:59,330 --> 00:29:03,210
+ان او عشرة ان الشرط الوحيد لل constant اللي عندك
+
+332
+00:29:03,210 --> 00:29:09,570
+كان انه مايوصلش ان ليش لأن اذا وصل ان معناته انت
+
+333
+00:29:09,570 --> 00:29:13,830
+نقلت المسألة لمستوى اعلى منها وانا مابديش يا
+
+334
+00:29:13,830 --> 00:29:17,510
+الكلام هذا صح هتبقى صحيحة يعني تتخيل دورت في ان
+
+335
+00:29:17,510 --> 00:29:23,120
+هتصير انت كئيبهتبقى المسألة صح .. هتبقى المسألة صح
+
+336
+00:29:23,120 --> 00:29:26,640
+لكن المقارنة مش fair مش عادلة عشان المقارنة تكون
+
+337
+00:29:26,640 --> 00:29:31,600
+عادلة لازم تحافظ على أنه تشغل على نفس الأساس فانت
+
+338
+00:29:31,600 --> 00:29:36,280
+معاك تختار أي أن بدك إياها طيب لو أنا أجيت قلت
+
+339
+00:29:36,280 --> 00:29:44,400
+خمسة أن okay خمسة أن كويس هتبقى الأكبر نقص ..
+
+340
+00:29:44,400 --> 00:29:48,460
+والله أنا خايف ممكن تزيدي شوية هذي كمان هيكيا سيدة
+
+341
+00:29:48,460 --> 00:29:51,080
+خلّيها عشر .. لأ ما تسيبهاش زي ما هي خد عشر ان
+
+342
+00:29:51,080 --> 00:29:54,360
+ماعناش مشكلة في الموضوع المهم ال constant هذا
+
+343
+00:29:54,360 --> 00:30:01,940
+مايزيدش عن n وفي نفس الوجود مايقلش عن مين عن
+
+344
+00:30:01,940 --> 00:30:05,260
+الأربعة ومامساويش الأربعة لازم يكون أكبر من
+
+345
+00:30:05,260 --> 00:30:09,740
+الأربعة و أقل من ال n لازم يكون أكبر من الأربعة و
+
+346
+00:30:09,740 --> 00:30:13,020
+أقل من ال n لأن لو ساوي الأربعة يا شباب خلاص بطلت
+
+347
+00:30:13,020 --> 00:30:16,610
+المسألة مستوي وليش رأيك؟فانت بدك تقمن دايماً ان
+
+348
+00:30:16,610 --> 00:30:21,110
+هذي صحيحة و بدك تزيد في الـ constant معناته الافتة
+
+349
+00:30:21,110 --> 00:30:26,410
+باعتناها دي is big O of للان تربيع، big O من الان
+
+350
+00:30:26,410 --> 00:30:33,230
+تربيع نعم؟
+
+351
+00:30:33,230 --> 00:30:38,150
+ايش قلت دي؟ قلت الان مجهولة، و لو انها معروفة،
+
+352
+00:30:38,150 --> 00:30:39,290
+كانت حلت المشكلة
+
+353
+00:30:41,900 --> 00:30:46,640
+قيمة الـ M مجهولة لو كانت معروفة فخلصت يعني لو قلت
+
+354
+00:30:46,640 --> 00:30:51,940
+لك انا اجمع خمس اعداد هتجمعهم باستمرار و ايش ميكون
+
+355
+00:30:51,940 --> 00:30:55,700
+ال algorithm مش لازم يزيد على الخلاص خطوات بس احنا
+
+356
+00:30:55,700 --> 00:31:00,020
+بندور على algorithm يكون general ايش يعني general
+
+357
+00:31:00,020 --> 00:31:05,440
+لما اغير حجم ال input يظل صحيح يديه output صحيح حد
+
+358
+00:31:05,440 --> 00:31:05,620
+من
+
+359
+00:31:08,780 --> 00:31:17,400
+عشان هيك دائما
+
+360
+00:31:17,400 --> 00:31:21,540
+هتلاقي ده عندنا نتكلم انه complexity ال algorithm
+
+361
+00:31:21,540 --> 00:31:26,620
+complexity مقتصدش جدش هو معجد قدر ما انا بتكلم على
+
+362
+00:31:26,620 --> 00:31:31,820
+انه ال timeCost التكلفة الزمنية للألجوريثم ليش
+
+363
+00:31:31,820 --> 00:31:36,600
+تكلفة زمنية يا شباب لأنه أنا بركز على عدد ال
+
+364
+00:31:36,600 --> 00:31:41,340
+process و ال process بالنسبة لل CPU زمن كل one
+
+365
+00:31:41,340 --> 00:31:45,240
+cycle كل one process one cycle one nanosecond و
+
+366
+00:31:45,240 --> 00:31:52,720
+هكذا طيب في ال properties مش هخوض فيها كتير الفكرة
+
+367
+00:31:52,720 --> 00:31:53,800
+فيها كتالة
+
+368
+00:31:56,600 --> 00:32:06,600
+الـ F is big O of G و الـ G is big O of F معناته
+
+369
+00:32:06,600 --> 00:32:12,600
+التنتين متساوية التنتين يعني هيك تخيل أنت قلت F
+
+370
+00:32:12,600 --> 00:32:20,100
+أقل أو تساوي C في G و G أقل أو تساوي K في F
+
+371
+00:32:21,180 --> 00:32:24,520
+Constant تاني معناه تدلت المتساويات تنسى الموضوع
+
+372
+00:32:24,520 --> 00:32:27,600
+بغض النظر إيش كان ال constant اللي موجود عندك كان
+
+373
+00:32:27,600 --> 00:32:34,560
+كذلك لو أنا أجيب قلتلك ال F is big O of C of G
+
+374
+00:32:34,560 --> 00:32:43,540
+أروح اضربت ال C هادي في اتنينهتظل المعادلة صح وليش
+
+375
+00:32:43,540 --> 00:32:46,880
+رأيك؟ بدون أي مشاكل هدف مجموعة الـ Probability
+
+376
+00:32:46,880 --> 00:32:50,820
+كمان مرة أنا اللي بهمني مش كل الكلام النظري هذا
+
+377
+00:32:50,820 --> 00:32:55,660
+بهمني ال concept اللي احنا عمالا بنحاول نوصله رقم
+
+378
+00:32:55,660 --> 00:32:59,960
+واحد مطلوب مني احسب الدالة او اكتب الدالة الزمنية
+
+379
+00:32:59,960 --> 00:33:05,300
+اللي بتعبر عن ال algorithm و اجيب ال big O تبعتها
+
+380
+00:33:05,300 --> 00:33:10,920
+و غالبا ال big O تبعتها الشماماللي هي أكبر أُس
+
+381
+00:33:10,920 --> 00:33:20,360
+أكبر أُس الأكبر أُس لـ N اللي موجودة عندك الآن
+
+382
+00:33:20,360 --> 00:33:28,100
+لو كان في عندي F1 هدول القوانين .. القوانين
+
+383
+00:33:28,100 --> 00:33:33,820
+التانية مهمات جداً لو كانت F is big O of G1 و F2
+
+384
+00:33:33,820 --> 00:33:45,000
+is big O ofG2 ايش يعني F1 اقل او تساوي C1 في G1 و
+
+385
+00:33:45,000 --> 00:33:55,600
+F2 اقل او تساوي C2 في G2 بينفع نضرب دول مع بعض يا
+
+386
+00:33:55,600 --> 00:34:02,230
+شباببينفع نضرب two functions في بعض F of X F of
+
+387
+00:34:02,230 --> 00:34:06,950
+واحد of X بيبقى تساوي اتنين X و F اتنين of X تساوي
+
+388
+00:34:06,950 --> 00:34:15,190
+X تربيع F واحد ضرب F اتنين of X تساوي اتنين X ضرب
+
+389
+00:34:15,190 --> 00:34:20,970
+X تربيع و تساوي اتنين X تكعيب اخد نفسي لما اتكلملي
+
+390
+00:34:20,970 --> 00:34:25,330
+عن ال functions وبينفع اجمع التنتين مع بعض اه
+
+391
+00:34:25,330 --> 00:34:35,250
+بينفعF1 زائد F2 of X بده تساوي X2 X زائد X تربيع
+
+392
+00:34:35,250 --> 00:34:40,330
+خدناهم الآن لما بتكون الدالة زي ما قلنا قبل شوية
+
+393
+00:34:40,330 --> 00:34:49,690
+عند الضرب معناته F1 ضرب F2 is big O of G1 ضرب G2
+
+394
+00:34:49,690 --> 00:34:57,400
+وعند الجامع big O من ال maximum تبعتهم big O منالـ
+
+395
+00:34:57,400 --> 00:35:03,840
+maximum تبعتهم.طيب، إيش يعني؟ نجي للمثال كتابناه
+
+396
+00:35:03,840 --> 00:35:09,720
+قبل شوية.الأن F of N بديها تساوي أربعة N زائد واحد
+
+397
+00:35:09,720 --> 00:35:20,160
+.هذه F واحد، F اتنين of N بديها تساوي N تربيع احنا
+
+398
+00:35:20,160 --> 00:35:23,720
+ما كانت أربعة N زائد واحد، وهذه كانت أربعة N
+
+399
+00:35:23,720 --> 00:35:31,850
+تربيع، ناقص تمانية Nزائد أربعة الان احنا اتفقنا ان
+
+400
+00:35:31,850 --> 00:35:38,770
+هادي big O من خمسة N وهادي big O من عشرة او خمسة
+
+401
+00:35:38,770 --> 00:35:44,730
+او ستن اللي بدك إياها N تربين مش قضية كتير الان
+
+402
+00:35:44,730 --> 00:35:52,460
+اجمع التنتين او اضرب التنتين في بعض ماتوا FM هيكأف
+
+403
+00:35:52,460 --> 00:35:57,820
+واحد ضرب أف اتنين أقصى كم يصبح شباب يطلع لثلاثة
+
+404
+00:35:57,820 --> 00:36:04,440
+يعني أف واحد ضرب أف اتنين of n أقل أو تساوي
+
+405
+00:36:04,440 --> 00:36:12,900
+constant اضربهم في بعض هدول خمسين
+
+406
+00:36:12,900 --> 00:36:20,290
+أن أقصى ثلاثةوانا اختارت constant وضربته في بعض بس
+
+407
+00:36:20,290 --> 00:36:24,390
+اعمل حسابك ان ال constant هذا كون كون اقل من قيمة
+
+408
+00:36:24,390 --> 00:36:31,890
+ال N نسميه C عند الجامع لما بتكلم على جامعهم مين
+
+409
+00:36:31,890 --> 00:36:36,650
+قال اصدر اللي عندي لما انا روحت جماعتهم مع بعض F1
+
+410
+00:36:36,650 --> 00:36:44,180
+زائد F2أربعة .. عفوا .. أربعة N تربيع ناقص تمانية
+
+411
+00:36:44,180 --> 00:36:52,440
+N زائد أربعة زائد أربعة N زائد واحد وهذه
+
+412
+00:36:52,440 --> 00:36:56,760
+صارت أربعة مقالة تساوي أربعة N تربيع ناقص أربعة N
+
+413
+00:36:56,760 --> 00:37:03,080
+زائد خمسة تمام؟ ضالت من عندي ال maximum أقل أو
+
+414
+00:37:03,080 --> 00:37:09,000
+تساوي C في N تربيع وبالتالي أنا روحت باتجاهالـ
+
+415
+00:37:09,000 --> 00:37:16,340
+Maximum اللي بينهم الـ Maximum لـ G1 أو لـ G2 هذا
+
+416
+00:37:16,340 --> 00:37:23,740
+الإثبات من ناحية رياضيات مابيعننش طيب، الان من
+
+417
+00:37:23,740 --> 00:37:26,540
+الدوال اللي دائما أنا بدور عليها عشان أقارن معاها
+
+418
+00:37:26,540 --> 00:37:31,340
+طبعا في عندها كمان خطأ هن المفروض تكون أكبر من 2
+
+419
+00:37:31,340 --> 00:37:37,000
+أكبر من 2 طيب
+
+420
+00:37:38,240 --> 00:37:43,900
+Big O of 1 Constant Function One Process Log N
+
+421
+00:37:43,900 --> 00:37:51,220
+الأساس يتنين مقصود بال log هنا يا شباب ال N إشارة
+
+422
+00:37:51,220 --> 00:37:55,420
+ال subset معناتها إن الدالة اللي جابليها already
+
+423
+00:37:55,420 --> 00:37:59,920
+موجودة تضمن يعني بتقدر تقارنها مع حدي بس مش منطق
+
+424
+00:37:59,920 --> 00:38:07,900
+أجي أقارن log N مع ال factorialلأن الفرق بينهم
+
+425
+00:38:07,900 --> 00:38:11,980
+شاسة شاسة و شاسة جدا كمان وبالتالي لأ انت بتدور
+
+426
+00:38:11,980 --> 00:38:19,200
+على اقرب function تمثل الدالة اللي عندك طبعا الان
+
+427
+00:38:19,200 --> 00:38:24,460
+الان و ال unlock الان مين اكبر الان ولا ال unlock
+
+428
+00:38:24,460 --> 00:38:31,240
+الان يا شباب مين اكبر الان ولا
+
+429
+00:38:31,240 --> 00:38:36,140
+ال unlock الان خبي هايان تساوي ان و راح اتضرب
+
+430
+00:38:36,140 --> 00:38:39,880
+تهادي في value بدون ما تضرب هادي ايش بتصير في ال
+
+431
+00:38:39,880 --> 00:38:45,180
+value اللي عندك هان عارفين
+
+432
+00:38:45,180 --> 00:38:52,660
+بس مش خايفين نتكلم نعم مين
+
+433
+00:38:52,660 --> 00:38:57,520
+قال؟ مين قال؟ مين قال؟ لو كان كسر okay بس الان
+
+434
+00:38:57,520 --> 00:39:01,720
+احنا بتكلم قاعدين اول حاجة ان الان اللي عندي بتكلم
+
+435
+00:39:01,720 --> 00:39:08,530
+على integerبنتكلم على انتجار ونتكلم على عدد بخم
+
+436
+00:39:08,530 --> 00:39:11,870
+بنتكلم مش على واحد واتنين وتلاتة ولا لا لان مش هي
+
+437
+00:39:11,870 --> 00:39:14,610
+كان شرطنا بنتكلم جانا ع ال growth function بنتكلم
+
+438
+00:39:14,610 --> 00:39:17,730
+مش على انصرين و تلاتة اخرين مع بعض انا بتكلم لما
+
+439
+00:39:17,730 --> 00:39:22,450
+كد ده اللي بكون عندي الان بتطير وبالتالي انت تخيل
+
+440
+00:39:22,450 --> 00:39:28,170
+الان هذا قيمته ألف واربع وعشرين يا سيدي معناته ان
+
+441
+00:39:28,170 --> 00:39:33,410
+ألف واربع وعشرينوهنا ألف و أربع و عشرين ضرب عشرة
+
+442
+00:39:33,410 --> 00:39:37,430
+أصبت؟
+
+443
+00:39:37,430 --> 00:39:45,510
+طيب هذه الدوال هي الدوال الرئيسية اللي غالبا
+
+444
+00:39:45,510 --> 00:39:49,670
+بتلاقي ال algorithm تبعتها أو استخداماتها في ال
+
+445
+00:39:49,670 --> 00:39:53,510
+comparison لما أنا بدي أجري قريب من two algorithm
+
+446
+00:39:53,510 --> 00:39:57,290
+بحسب الدالة الزمنية تبعت ال algorithm وبجي بقول
+
+447
+00:39:57,290 --> 00:40:02,240
+هذه big O لواحدة منالدوالي اللي عندنا الان في ال
+
+448
+00:40:02,240 --> 00:40:05,820
+linear او في ال binary search لما احنا كتبناه ايش
+
+449
+00:40:05,820 --> 00:40:08,540
+ال binary search كان بيقول ايه؟ كان بيقول اول مرة
+
+450
+00:40:08,540 --> 00:40:17,680
+n على 2 زائد n على 4 زائد n على 8 زائد زائد لموصل
+
+451
+00:40:17,680 --> 00:40:24,000
+1 وهذا كان تساوي log ال n الأساسي 2 هذه ال series
+
+452
+00:40:24,000 --> 00:40:29,360
+او sequenceهي ال value تبعتها وبالتالي ال growth
+
+453
+00:40:29,360 --> 00:40:35,160
+function تبعتها ال F of N لل binary search
+
+454
+00:40:35,160 --> 00:40:44,300
+algorithm is O of log N زيادته لما بزيد ال output
+
+455
+00:40:44,300 --> 00:40:48,660
+ال process بتزيد بمقدار ال log اللي موجود عندها
+
+456
+00:40:48,660 --> 00:40:54,960
+واللي هي فعليا أقل منالان اقل من الان عشان هيك
+
+457
+00:40:54,960 --> 00:41:01,660
+دائما بدنا نحاول لما نشتغل بدنا نوجد او نقارن ال
+
+458
+00:41:01,660 --> 00:41:05,120
+function او ال time function تبع ال algorithm تبعي
+
+459
+00:41:05,120 --> 00:41:10,580
+بواحدة من الدول هدول لاحظ لو كان عندي log الان هيه
+
+460
+00:41:10,580 --> 00:41:14,680
+صح ان اقارنها ب log الان مش غلط لان انا بقدر اتحقق
+
+461
+00:41:14,680 --> 00:41:17,720
+عندي اقل من log الان
+
+462
+00:41:21,840 --> 00:41:27,360
+مصبوح؟ بس ايش احنا قلنا؟ قلنا دائما اختار اقل من
+
+463
+00:41:27,360 --> 00:41:30,600
+قيمة الان ماتوصلهاش للان عشان ماترفعهاش لل next
+
+464
+00:41:30,600 --> 00:41:33,580
+level وفعلا ال next level هي اللي جاية ما انا
+
+465
+00:41:33,580 --> 00:41:38,800
+بدربها بنتقل للمستوى اللي بعده في عمليات المقارنة
+
+466
+00:41:38,800 --> 00:41:43,120
+تمام تعالى
+
+467
+00:41:43,120 --> 00:41:46,780
+أشوف ال algorithm اللي موجود عندها مديني دالة
+
+468
+00:41:46,780 --> 00:41:50,700
+زمانية بس التنسيق تبعها ماعرفش ليش فكرته هكتبها
+
+469
+00:41:50,700 --> 00:41:58,260
+مرة تانيةN في N factorial زائد تلاتة N زائد اتنين
+
+470
+00:41:58,260 --> 00:42:08,480
+زائد تلاتة N أُسمية الكل هذا مضروب في N أُس N زائد
+
+471
+00:42:08,480 --> 00:42:14,000
+N أُس اتنين N وهتلي
+
+472
+00:42:14,000 --> 00:42:19,360
+ال big O تبعتها هيخدمك في الموضوع هذا شكل كبير
+
+473
+00:42:19,360 --> 00:42:25,960
+تبقىانك تعتبر كل واحدة فيهم دالة لحالها واتطبق
+
+474
+00:42:25,960 --> 00:42:29,360
+قانون الجمع وقانون الضرب اللي احنا شوفناهم قبل
+
+475
+00:42:29,360 --> 00:42:38,160
+شوية هدول كيفك تساوي؟ هتيجي هدولة معادلتين مين
+
+476
+00:42:38,160 --> 00:42:43,540
+الأكبر لما تكون التنتين مضربات في بعض؟ معناته N في
+
+477
+00:42:43,540 --> 00:42:51,380
+N factorial لا تساوي لا تساويالان تربية factorial
+
+478
+00:42:51,380 --> 00:42:59,340
+هذه n مضروبة في n factorial يعني n مضروبة في n في
+
+479
+00:42:59,340 --> 00:43:06,800
+n ناقص واحد في n ناقص اتنين في اتنين في واحد لما
+
+480
+00:43:06,800 --> 00:43:10,460
+بدخل الان بدخلها مرة واحدة بدخلاش على كل الجثة لكن
+
+481
+00:43:10,460 --> 00:43:14,800
+لما باشي بقول الان تربية factorial اختلفت تماما،
+
+482
+00:43:14,800 --> 00:43:20,410
+مصبوط؟ عشان هيك هذهN في N factorial المعنى طول
+
+483
+00:43:20,410 --> 00:43:29,230
+الوقت باخد برشح مين ال N factorial زائد ham N ham
+
+484
+00:43:29,230 --> 00:43:42,330
+constant ham N أسمية N أسمية ابو ham تنتين جمع
+
+485
+00:43:42,330 --> 00:43:49,410
+باخد بينهم ال maximum N أس اتنين Nطيب لان هذا
+
+486
+00:43:49,410 --> 00:43:53,270
+الجوز بتاخد فيه ال maximum ال maximum حسب المثال
+
+487
+00:43:53,270 --> 00:43:58,870
+هذا او حسب .. بقول الفكتوريال اكبر اكبر اشي حتى
+
+488
+00:43:58,870 --> 00:44:07,790
+اكبر من n اص j ال n أص مية وبالتالي n factorial في
+
+489
+00:44:07,790 --> 00:44:14,240
+n اص 2هذا حص .. لأ لأ ال maximum بين الجامع .. لما
+
+490
+00:44:14,240 --> 00:44:17,660
+أكون الجامع باخده ال maximum .. لما بكون ضارب ..
+
+491
+00:44:17,660 --> 00:44:20,380
+بضرب ال two terms في بعضهم .. هي الدالة الزمانية
+
+492
+00:44:20,380 --> 00:44:28,280
+اللي عندى .. يعني هان .. وبالتالي .. لما
+
+493
+00:44:28,280 --> 00:44:30,980
+راحنا أحسب .. اه حتى شوف ..
+
+494
+00:44:33,980 --> 00:44:40,180
+أنا فاجأت تلاتة أس أن مظبوط وهذه تلاتة أس أن زائد
+
+495
+00:44:40,180 --> 00:44:44,560
+اتنين اه تلاتة أس أن زائد اتنين في التنسيق بس فيه
+
+496
+00:44:44,560 --> 00:44:48,260
+مشكلة في الآخر هذا هي هي ال big O من أين حصلت
+
+497
+00:44:48,260 --> 00:44:51,320
+عليها او كيف حصلت عليها شباب بنفس الخطوات اللي
+
+498
+00:44:51,320 --> 00:44:54,960
+احنا اشتغلنا عليها سابقا عند الضرب أخدت التنتين
+
+499
+00:44:54,960 --> 00:44:58,300
+عند
+
+500
+00:44:58,300 --> 00:45:00,200
+الضرب هان
+
+501
+00:45:03,590 --> 00:45:06,690
+أخذت الـ N factorial و لو دلتها مع ال N لأنها
+
+502
+00:45:06,690 --> 00:45:10,490
+function مافيش مشكلة عندي في الموضوع ال N و هذه
+
+503
+00:45:10,490 --> 00:45:16,650
+أخذت ال maximum في الآخر هحصل على دالة هذا هي ال N
+
+504
+00:45:16,650 --> 00:45:23,690
+أُس N في ال term اللي موجود عندي الآن تعالى نشوف
+
+505
+00:45:23,690 --> 00:45:27,630
+ال algorithm التاني هذا او في عندي two algorithms
+
+506
+00:45:27,630 --> 00:45:33,100
+بدي أقارن ما بينهمعندي two algorithms بقول هاي ال
+
+507
+00:45:33,100 --> 00:45:39,800
+time complexity تبعتهم هاي ال time function f1
+
+508
+00:45:39,800 --> 00:45:49,620
+of n بده تساوي n تربيع نقص n زائد واحد f2 of n بده
+
+509
+00:45:49,620 --> 00:45:55,340
+تساوي n تربيع على اتنين زائد تلاتة n زائد اتنين
+
+510
+00:45:55,340 --> 00:46:07,060
+الان هادي big O من ايه الشباب؟أنت ربيع وهذه وهذه
+
+511
+00:46:07,060 --> 00:46:15,520
+أنت ربيع هذا الكلام صحيح 100% بس لأن تنتين أنت
+
+512
+00:46:15,520 --> 00:46:19,600
+ربيع لازم
+
+513
+00:46:19,600 --> 00:46:23,980
+أسوي أدور علشان المفاصلة بينهم هل بقدر أفصل بينهم
+
+514
+00:46:23,980 --> 00:46:30,420
+و لا بقدرش تدخل معايا مين تعالي نجي للدالة هيك
+
+515
+00:46:31,260 --> 00:46:38,060
+معناته هذه عبارة عن N تربيع وراها
+
+516
+00:46:38,060 --> 00:46:46,720
+big O ل ال N صح؟ طب و اللي قبلها نص ال N تربيع
+
+517
+00:46:46,720 --> 00:46:52,920
+وراها big O ل ال N يعني هذه و هذه متساعدة صار
+
+518
+00:46:52,920 --> 00:46:57,040
+الفيصل مين في اللعبة عندها ال N تربيع طب ال N
+
+519
+00:46:57,040 --> 00:47:02,540
+تربيع ولا نص ال N تربيع؟لأ من اوفر من وقت .. من
+
+520
+00:47:02,540 --> 00:47:06,600
+زمنه او باستخلافني زمن اقل الان تربيع ولا نصها
+
+521
+00:47:06,600 --> 00:47:10,980
+فصرت انا هان ممكن التزم بمين لاحظوا انا من البداية
+
+522
+00:47:10,980 --> 00:47:15,620
+اخدت على أسين لاجيتهم متساويات ماودونيش لمقارنة
+
+523
+00:47:15,620 --> 00:47:21,100
+فعليا فحاولت انزل لبعدهم لاجيتهم نفس ال algorithm
+
+524
+00:47:21,100 --> 00:47:23,900
+بالتالي انا الان بدي اقول ان والله ال complexity
+
+525
+00:47:23,900 --> 00:47:28,640
+اللي تبعت هي واحد الان تربيع زاد ال big O ل ال M
+
+526
+00:47:31,200 --> 00:47:35,940
+والثاني نص الان تربيه زاد ال big O للان الأفضلية
+
+527
+00:47:35,940 --> 00:47:40,040
+الأن لمن؟ لل algorithm التاني لأن نص الان تربيه
+
+528
+00:47:40,040 --> 00:47:47,640
+اوفن نص الزمن ال
+
+529
+00:47:47,640 --> 00:47:50,140
+complexة هو الكلام اللي احنا قلناه لفترة و بنحسب
+
+530
+00:47:50,140 --> 00:47:58,170
+ال algorithm انا مخلص ال section من قبل ما ابداطيب
+
+531
+00:47:58,170 --> 00:48:02,110
+الـ Time Complexity .. الـ Time Complexity معناته
+
+532
+00:48:02,110 --> 00:48:08,370
+أنا جاعت بتكلم أحدد approximate number of
+
+533
+00:48:08,370 --> 00:48:12,010
+operations اللي هو أنا كنت بحاول أسويه عشان أقولك
+
+534
+00:48:12,010 --> 00:48:15,450
+هذه .. هذه فيها أربع خطوات هذه جوا اللوب أربع فئان
+
+535
+00:48:15,450 --> 00:48:19,790
+وهذه أربع فئان لاقص واحد وروحت approximate ماحدش
+
+536
+00:48:19,790 --> 00:48:24,660
+مقدر يديك exact valueتقريبا وعشان هي approximate
+
+537
+00:48:24,660 --> 00:48:27,780
+روح نقولها بدنا نقيّر كل ال constant يعني و ليش
+
+538
+00:48:27,780 --> 00:48:32,580
+كتيرولا لأ بتبقى المعادلة صحيحة هدف الـtime
+
+539
+00:48:32,580 --> 00:48:36,480
+complexity كذلك لو تساوت ال algorithm من ناحية ال
+
+540
+00:48:36,480 --> 00:48:42,080
+time بروح بالجهة لبراميتر التاني ال space جداش بده
+
+541
+00:48:42,080 --> 00:48:47,140
+space هذا عشان يغيب عشان ينفذ ال task تبعته جداش
+
+542
+00:48:47,140 --> 00:48:51,000
+بده space عشان ينفذ ال task تبعته طبعا أنا بتكلمها
+
+543
+00:48:51,000 --> 00:48:56,440
+لأ ال space حجم ال memory جداش في عندي حجم مطلوبفي
+
+544
+00:48:56,440 --> 00:48:59,920
+الـ Time Complexity احنا دائما بنستخدم مين؟ الـ
+
+545
+00:48:59,920 --> 00:49:03,960
+Big O Notation وبديها لكل الدوالة التانية و ال
+
+546
+00:49:03,960 --> 00:49:08,680
+constant تانية و عادة بقعد فقط ال expensive
+
+547
+00:49:08,680 --> 00:49:15,420
+operation العمليات الأساسية زي ايش؟ المقارنة في ال
+
+548
+00:49:15,420 --> 00:49:19,560
+search algorithm كم عملية مقارنة انت بتعمل؟ يعني
+
+549
+00:49:19,560 --> 00:49:24,880
+احنا قبل شوية كتبنا أربعة N زائد واحدالألغوريثم
+
+550
+00:49:24,880 --> 00:49:27,620
+تبقى عدب عنانيش أنا عند عملية جامعة واحدة ال
+
+551
+00:49:27,620 --> 00:49:31,840
+assignment اليساوي و اليساوي هذه بنبطل انعدها بدور
+
+552
+00:49:31,840 --> 00:49:34,600
+على ال operation الأساسية ال core في ال algorithm
+
+553
+00:49:34,600 --> 00:49:37,280
+في ال algorithm اللي كتبته في الأول كنت أنا باجمع
+
+554
+00:49:37,280 --> 00:49:42,240
+فكم عملية جامعة بدأت تتنفذ N من المرات لأنه جوا ال
+
+555
+00:49:42,240 --> 00:49:46,260
+loop في المقارنات في ال search كم عملية مقارنة في
+
+556
+00:49:46,260 --> 00:49:51,280
+ال binary search عندي N من المقارنات في ال binary
+
+557
+00:49:52,050 --> 00:49:56,070
+Log N من المقارنات والاربعة والخمسة والاتنين هدولة
+
+558
+00:49:56,070 --> 00:50:00,190
+كلها تمنعش بيبقى قبلهم حساب عمدي زي ما قلنا سابقا
+
+559
+00:50:00,190 --> 00:50:07,110
+ودائما .. دائما في عمدي بتكلم على ال worst case
+
+560
+00:50:07,110 --> 00:50:12,950
+وال best case او ال average case افضل حالة او
+
+561
+00:50:12,950 --> 00:50:18,130
+المتوسط واسوأ حالة انا بهمنيش ال algorithm يشتغل
+
+562
+00:50:18,130 --> 00:50:23,320
+دائما في ال best caseطبعا انا بهم دائما ال output
+
+563
+00:50:23,320 --> 00:50:28,100
+تبع وين في ال worst case يعني لو على سبيل المثال
+
+564
+00:50:28,100 --> 00:50:34,580
+انا اجهد ال data series قلتلك خمسة سبعة تلاتة
+
+565
+00:50:34,580 --> 00:50:43,040
+اتنين تمانية ستة في نفس الوجه التي قلتلك اتنين
+
+566
+00:50:43,040 --> 00:50:52,410
+تلاتة خمسة خمسةستة .. سبعة .. تمانية Two different
+
+567
+00:50:52,410 --> 00:50:57,810
+series صح؟ أجيب قلتلك مابيجلي عليهم linear search
+
+568
+00:50:57,810 --> 00:51:06,270
+عشان أصل للخمسة ال best case من أول مرة خلاص
+
+569
+00:51:06,270 --> 00:51:11,950
+ماكملش ال worst case ال worst case أن الخمسة مش
+
+570
+00:51:11,950 --> 00:51:12,650
+موجودة
+
+571
+00:51:15,650 --> 00:51:22,890
+الخطر هو أن الخمسة لن تكون موجودة في الـ binary
+
+572
+00:51:22,890 --> 00:51:28,490
+search في
+
+573
+00:51:28,490 --> 00:51:32,230
+ال case أفضل مباشرة من أول الهواية سأجلب الخمسة
+
+574
+00:51:32,230 --> 00:51:35,470
+لماذا تلاتة؟ نحن نريد أن نجسمها من النص و نضع ال
+
+575
+00:51:35,470 --> 00:51:41,520
+pointer على النصأه ماتمد على ال floor فراح جابي
+
+576
+00:51:41,520 --> 00:51:45,620
+الخمسة مباشرة اين اللي جيتها التانية تساوين في ال
+
+577
+00:51:45,620 --> 00:51:49,620
+best case تخيل ان انا بدور مثلا على التسعة في
+
+578
+00:51:49,620 --> 00:51:54,680
+الحالتين التسعة فوق مش موجودة والتسعة تحت مش
+
+579
+00:51:54,680 --> 00:52:00,240
+موجودة اللي فوق هيحتاج ست خطوات ست عمليات مقارنة
+
+580
+00:52:00,240 --> 00:52:04,560
+بينما هذا هيحتاج عمليتين او تلاتة اللي هي log لان
+
+581
+00:52:05,330 --> 00:52:09,410
+لجي الآن، مظبوط؟ وبالتالي .. بالتالي هذه الفيهانة
+
+582
+00:52:09,410 --> 00:52:12,690
+اللي بتدعي .. عشان ايه دائما احنا بقدم ال worst
+
+583
+00:52:12,690 --> 00:52:15,810
+case في أسوأ الأحوال، إيش أنا بعنيني؟ بعنيني ال
+
+584
+00:52:15,810 --> 00:52:19,870
+algorithm أو ال behavior واحنا فعليا تلما بتدور
+
+585
+00:52:19,870 --> 00:52:24,630
+على حد أو صديق أو حد بتعتمد عليه، بدك يهاجد الفرح
+
+586
+00:52:24,630 --> 00:52:28,830
+و الرخة؟ لأ، مش بيقولك الصديق وقت الضيقفي الـ
+
+587
+00:52:28,830 --> 00:52:31,250
+worst case في أسوأ الظروف انا بدي صديقي يكون موجود
+
+588
+00:52:31,250 --> 00:52:34,530
+حوليا مانديش يقول ما انا غني و معايا فلوس و بصحة و
+
+589
+00:52:34,530 --> 00:52:38,510
+تمام و ماعنديش مشاكل ايه هو ملزج فيا مظبوط ولا لأ
+
+590
+00:52:38,510 --> 00:52:43,790
+فاحنا دائما دائما بندور على العنصر اللي بيخدمني في
+
+591
+00:52:43,790 --> 00:52:46,710
+ال worst case اكتر من اللي بيخدمني في ال best case
+
+592
+00:52:46,710 --> 00:52:55,270
+اللي موجودة طيب هذه ال algorithm بقول
+
+593
+00:52:55,270 --> 00:53:03,590
+بدي أضرب مصفوفةبـ Scalar عنصر ثابت C بدي أضرب
+
+594
+00:53:03,590 --> 00:53:12,650
+المصوفة والمصوفة هي square matrix الـ
+
+595
+00:53:12,650 --> 00:53:18,090
+function تبعتي مباشرة
+
+596
+00:53:18,090 --> 00:53:25,210
+هي العملية واحد هي C ضرب ال value اللي موجودةبس
+
+597
+00:53:25,210 --> 00:53:28,390
+الـ C دي موجودة في ال loop مقدارها N و اللي بعدها
+
+598
+00:53:28,390 --> 00:53:34,230
+N ميناته F of N مباشرة بتساوي N في N في واحد N
+
+599
+00:53:34,230 --> 00:53:42,470
+تربيع N في N في واحد N تربيع خلصتها هي Big O من ال
+
+600
+00:53:42,470 --> 00:53:48,190
+N تربيع Quadratic Complexity تعالى نشوف هذه
+
+601
+00:53:52,840 --> 00:53:57,760
+الان لاحظ تقريبا نفس الكلام بس اشبه بقوللي بدي
+
+602
+00:53:57,760 --> 00:54:04,140
+اجمع ال upper triangle في ال matrix الان المصفوفة
+
+603
+00:54:04,140 --> 00:54:08,260
+المربعة خليني افترض ان في عندى مصفوفة اربعة في
+
+604
+00:54:08,260 --> 00:54:15,440
+اربعة واحد اتنين تلاتة اربعة خمسة ستة سبعة تمانية
+
+605
+00:54:15,440 --> 00:54:21,130
+تسعة واحد اتنين تلاتة اربعة خمسة ستة سبعةالان
+
+606
+00:54:21,130 --> 00:54:26,070
+المصفوفة المربعة فيها قطر ولا لأ ال upper triangle
+
+607
+00:54:26,070 --> 00:54:33,970
+هو المثلث العلوي من
+
+608
+00:54:33,970 --> 00:54:41,590
+أين يبدأ المثلث العلوي؟ اهي اتنين وسبعة اذا بدك
+
+609
+00:54:41,590 --> 00:54:44,550
+تحط كمان القطر الرئيسي كمان مافيش مشكلة في الموضوع
+
+610
+00:54:44,550 --> 00:54:49,870
+هنقول ناخد النصف العلوي للمصفوفة بما فيه القطرلما
+
+611
+00:54:49,870 --> 00:54:54,450
+تكون الـ I بيتساوى ال J بتبديش تجمع ولا لا؟ فيك
+
+612
+00:54:54,450 --> 00:55:02,030
+تعمل اللوب هيك four ال I equal واحد to N four ال J
+
+613
+00:55:02,030 --> 00:55:09,910
+equal واحد to N if ال I equal J تمام؟ اه مهم من
+
+614
+00:55:09,910 --> 00:55:17,200
+بعدها ايسيري بقى if ال I او if ال Jالـ J أكبر أو
+
+615
+00:55:17,200 --> 00:55:21,360
+تساوي الـ I ابدأ اجبع العناصر اللي بدأك اياها هي
+
+616
+00:55:21,360 --> 00:55:26,560
+الـ S equals 0 الـ S equals S زائد A I J اجبع
+
+617
+00:55:26,560 --> 00:55:30,360
+العناصر المصفوفة هيو بس الآن ال algorithm هذا دخل
+
+618
+00:55:30,360 --> 00:55:36,800
+عندي N في N في 1 مظبوط وهيو كمان عملية مقارنة
+
+619
+00:55:36,800 --> 00:55:41,780
+انتين يعني اتنين N كربين مظبوط طيب فعليا انا قاعد
+
+620
+00:55:41,780 --> 00:55:49,960
+بأشطل هيوكل مرة مش من الواحد الاصل من ال I لأن ال
+
+621
+00:55:49,960 --> 00:55:55,520
+element لما أنتقل على الصف التاني هيه لما أنتقل
+
+622
+00:55:55,520 --> 00:55:58,940
+على الصف التالت الرابع الخامس ال N دائما كل مرة
+
+623
+00:55:58,940 --> 00:56:03,380
+بنتقل على عمود نفسه فممكن أن أبدأ من ال I لاحظ
+
+624
+00:56:03,380 --> 00:56:10,600
+اللي فوق N نعم بس اللي تحت بس اللي تحت N ناقص I
+
+625
+00:56:10,600 --> 00:56:18,670
+يعني المرة هيك Nنقص واحد زائد N نقص اتنين هيك
+
+626
+00:56:18,670 --> 00:56:22,990
+بتتعامل معاها، مظبوط ولا لأ؟ تلاتة؟ طيب، اضربها في
+
+627
+00:56:22,990 --> 00:56:27,030
+إيش هذه؟ بدي أروح أجيب ال sequence تبعتها و أروح
+
+628
+00:56:27,030 --> 00:56:30,190
+أضربها فيها لكن لو إحنا جينا تكلمنا على ال worst
+
+629
+00:56:30,190 --> 00:56:36,350
+case أطول لعب هذه جديش N نقص واحد معناته بقدر أنا
+
+630
+00:56:36,350 --> 00:56:39,690
+أقول N في N نقص واحد و الله بالسر عليهم F of N
+
+631
+00:56:39,690 --> 00:56:46,340
+تبعتنا هنا F of N بدها تساويN في N ناقص واحد وليه
+
+632
+00:56:46,340 --> 00:56:55,700
+تساوي N تربيع ناقص N ال maximum بينهم N تربيع
+
+633
+00:56:55,700 --> 00:57:03,860
+فحصلت على complexity time اللي موجودة عندي رجعنا
+
+634
+00:57:03,860 --> 00:57:08,090
+لنفس الكلام السابقطيب هو الان تربية والسابق ان
+
+635
+00:57:08,090 --> 00:57:11,250
+تربية بعد ما احنا فيه ان نص قلنا قبل شوية ممكناش
+
+636
+00:57:11,250 --> 00:57:15,470
+تفرج فعليا انا هيك في المرة التانية لما كنت
+
+637
+00:57:15,470 --> 00:57:24,270
+باجمعكم باجمع العناصر هي وهذا يمثل ان تربية على ان
+
+638
+00:57:24,270 --> 00:57:27,230
+تربية نقص ان على اتنين ال series زاد الكل زاد ان
+
+639
+00:57:27,230 --> 00:57:32,670
+لأن هذه ال sequence اللي موجودة عندىن تربع على
+
+640
+00:57:32,670 --> 00:57:37,750
+اتنين زائد big O من ال N لأنه صارت فعليا هذه ال
+
+641
+00:57:37,750 --> 00:57:42,570
+algorithm و اللي جابله اتنين بيشتغلوا او حصلتوا
+
+642
+00:57:42,570 --> 00:57:45,990
+لهم ان ال big O نفس ال value لكن واحد كان له
+
+643
+00:57:45,990 --> 00:57:52,490
+بالتانية for ال I او ال J بتبدأ من واحد والتانية
+
+644
+00:57:52,490 --> 00:57:57,980
+for ال J equal من ال Iوبالتالي الحالة التانية هذه
+
+645
+00:57:57,980 --> 00:58:02,920
+كانت بالتامة reduction لعدد المرات بتقلل طب اروح
+
+646
+00:58:02,920 --> 00:58:07,040
+enter بيها او enter بيها unfair فانا جايت لمين
+
+647
+00:58:07,040 --> 00:58:10,480
+اروح لل details ال deep details ودخلت النص في
+
+648
+00:58:10,480 --> 00:58:18,920
+الموضوع ال bubble sort algorithm هي الحالة الأولى
+
+649
+00:58:18,920 --> 00:58:26,680
+الناقص واحد طب الحالة التانية من واحدالى I جدّيش
+
+650
+00:58:26,680 --> 00:58:31,600
+عددهم اول مرة من واحد لواحد من واحد اعد بدت من N
+
+651
+00:58:31,600 --> 00:58:36,530
+ناقص واحدمن 1 إلى N نقص 1 وهكذا الـ sequence كمان
+
+652
+00:58:36,530 --> 00:58:39,470
+مرة في حالة زي هذه الشباب انت بحاجة انك تكتب او
+
+653
+00:58:39,470 --> 00:58:42,810
+تحاول تكتب ال sequence بشكل كامل وتجيب القانون
+
+654
+00:58:42,810 --> 00:58:46,430
+تبعها عشان تقدر تضرب وتحصل على النتيجة بشكل صحيح
+
+655
+00:58:46,430 --> 00:58:51,250
+في الآخر حصلنا على ان N نقص 1 زائد N نقص 2 زائد
+
+656
+00:58:51,250 --> 00:58:54,930
+زائد زائد حسب ال rule اللي موجود عندي هان اللي
+
+657
+00:58:54,930 --> 00:58:59,350
+احنا شوفناها قبل شوية هايوم enter D ناقص كده فهذا
+
+658
+00:58:59,350 --> 00:59:04,110
+ال algorithm اللي عندي في الآخر تطلع big O منالان
+
+659
+00:59:04,110 --> 00:59:08,870
+تربيع هذا
+
+660
+00:59:08,870 --> 00:59:11,830
+اللي انا بديه منك ايش المفروض ان تتساوي الان بتحل
+
+661
+00:59:11,830 --> 00:59:15,430
+الأسئلة بدك المفروض تحل الأسئلة من وين تجيب أسئلة
+
+662
+00:59:15,430 --> 00:59:20,650
+سيبقى من أسئلة الكتاب وانت خدت برمجة صح؟ الان
+
+663
+00:59:20,650 --> 00:59:25,010
+الأمثلة اللي فيها ال loops دور على الأمثلة اللي
+
+664
+00:59:25,010 --> 00:59:30,290
+فيها ال loops وابدأ يحسب ال complexity تبعتها ال
+
+665
+00:59:30,290 --> 00:59:34,480
+process تبعتهاكل ما كانت في عندك two loops مانعته
+
+666
+00:59:34,480 --> 00:59:38,820
+انت بتتكلم على أنت ربيع كل ما زادت عدد ال loop زيد
+
+667
+00:59:38,820 --> 00:59:42,660
+عدد القص مفروغة وشغلة اجرب احسب على الكلام هذا
+
+668
+00:59:42,660 --> 00:59:46,360
+هحاول خلال اليومين الجاية هنزلك كام مثال تمام
+
+669
+00:59:46,360 --> 00:59:53,460
+تحاول تحسب ال big O تبعتهم في اي سؤال يا شباب الله
+
+670
+00:59:53,460 --> 00:59:54,000
+يعطيكوا العافية
+
diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/tnT14Wninao_raw.json b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/tnT14Wninao_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..51829c117288276b3ea049fd126022a145b2b01a
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/tnT14Wninao_raw.json
@@ -0,0 +1 @@
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مع", "probability": 0.9912109375}, {"start": 2278.3, "end": 2278.62, "word": " حدي", "probability": 0.439208984375}, {"start": 2278.62, "end": 2279.2, "word": " بس", "probability": 0.90625}, {"start": 2279.2, "end": 2279.38, "word": " مش", "probability": 0.98388671875}, {"start": 2279.38, "end": 2279.92, "word": " منطق", "probability": 0.9261067708333334}, {"start": 2279.92, "end": 2280.8, "word": " أجي", "probability": 0.7224934895833334}, {"start": 2280.8, "end": 2281.48, "word": " أقارن", "probability": 0.9822998046875}, {"start": 2281.48, "end": 2282.08, "word": " log", "probability": 0.47021484375}, {"start": 2282.08, "end": 2282.56, "word": " N", "probability": 0.7724609375}, {"start": 2282.56, "end": 2285.28, "word": " مع", "probability": 0.96630859375}, {"start": 2285.28, "end": 2285.42, "word": " ال", "probability": 0.533203125}, {"start": 2285.42, "end": 2285.86, "word": " factorial", "probability": 0.91162109375}], "temperature": 1.0}, {"id": 85, "seek": 231328, "start": 2286.76, "end": 2313.28, "text": "لأن الفرق بينهم شاسة شاسة و شاسة جدا كمان وبالتالي لأ انت بتدور على اقرب function تمثل الدالة اللي عندك طبعا الان الان و ال unlock الان مين اكبر الان ولا ال unlock الان يا شباب مين اكبر الان ولا ال unlock الان خبي هاي", "tokens": [1211, 33456, 27188, 2288, 4587, 49374, 16095, 13412, 32277, 3660, 13412, 32277, 3660, 4032, 13412, 32277, 3660, 10874, 28259, 9122, 2304, 7649, 46599, 6027, 2655, 6027, 1829, 5296, 10721, 16472, 2655, 39894, 3215, 13063, 15844, 1975, 4587, 25513, 2445, 6055, 2304, 12984, 1211, 32748, 6027, 3660, 13672, 1829, 43242, 4117, 23032, 3555, 3615, 995, 2423, 7649, 2423, 7649, 4032, 2423, 11634, 2423, 7649, 3714, 9957, 1975, 4117, 26890, 2423, 7649, 49429, 2423, 11634, 2423, 7649, 35186, 13412, 3555, 16758, 3714, 9957, 1975, 4117, 26890, 2423, 7649, 49429, 2423, 11634, 2423, 7649, 16490, 21292, 8032, 47302], "avg_logprob": -0.26188150824358064, "compression_ratio": 1.9782608695652173, "no_speech_prob": 5.960464477539063e-08, "words": 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تبعتها أو استخداماتها في ال comparison لما أنا بدي أجري قريب من two algorithm بحسب الدالة الزمنية تبعت ال algorithm وبجي بقول هذه big O لواحدة من", "tokens": [2407, 3224, 8315, 5551, 46538, 4032, 5551, 25513, 3615, 4032, 6225, 46309, 9957, 48812, 25513, 6225, 8592, 25720, 5551, 9381, 3555, 2655, 22807, 23032, 1829, 3555, 29538, 32748, 2407, 6027, 39896, 32748, 2407, 6027, 34892, 19986, 1829, 3794, 10632, 13672, 1829, 32771, 6027, 3555, 995, 39894, 15040, 38436, 2423, 9284, 6055, 3555, 34268, 11296, 34051, 44713, 9778, 3215, 10943, 9307, 11296, 8978, 2423, 9660, 5296, 15042, 41850, 4724, 16254, 5551, 7435, 16572, 12174, 16572, 3555, 9154, 732, 9284, 4724, 5016, 35457, 32748, 6027, 3660, 6024, 110, 27842, 10632, 6055, 3555, 34268, 2423, 9284, 46599, 7435, 1829, 4724, 39648, 29538, 955, 422, 5296, 14407, 24401, 3660, 9154], "avg_logprob": -0.23306074237155022, "compression_ratio": 1.7142857142857142, "no_speech_prob": 0.0, "words": [{"start": 2370.55, "end": 2371.11, "word": "وهنا", 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"الدوالي اللي عندنا الان في ال linear او في ال binary search لما احنا كتبناه ايش ال binary search كان بيقول ايه؟ كان بيقول اول مرة n على 2 زائد n على 4 زائد n على 8 زائد زائد لموصل 1 وهذا كان تساوي log ال n الأساسي 2 هذه ال series او sequence", "tokens": [6027, 3215, 2407, 6027, 1829, 13672, 1829, 43242, 8315, 2423, 7649, 8978, 2423, 8213, 1975, 2407, 8978, 2423, 17434, 3164, 5296, 15042, 1975, 5016, 8315, 9122, 2655, 3555, 8315, 3224, 1975, 1829, 8592, 2423, 17434, 3164, 25961, 4724, 1829, 39648, 1975, 1829, 3224, 22807, 25961, 4724, 1829, 39648, 1975, 12610, 3714, 25720, 297, 15844, 568, 30767, 16373, 3215, 297, 15844, 1017, 30767, 16373, 3215, 297, 15844, 1649, 30767, 16373, 3215, 30767, 16373, 3215, 32767, 2407, 36520, 502, 37037, 15730, 25961, 6055, 3794, 995, 45865, 3565, 2423, 297, 16247, 3794, 32277, 1829, 568, 29538, 2423, 2638, 1975, 2407, 8310], "avg_logprob": -0.2239583261085279, "compression_ratio": 1.8374384236453203, "no_speech_prob": 5.960464477539063e-08, "words": 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algorithm من ناحية ال time بروح بالجهة لبراميتر التاني ال space جداش بده space هذا عشان يغيب عشان ينفذ ال task تبعته جداش بده space عشان ينفذ ال task تبعته طبعا أنا بتكلمها لأ ال space حجم ال memory جداش في عندي حجم مطلوب", "tokens": [12610, 995, 5296, 10721, 39894, 3555, 4587, 7578, 9673, 3615, 18513, 37977, 20328, 5016, 1829, 5016, 3660, 8032, 3215, 5172, 2423, 39184, 3766, 14024, 9122, 8848, 23275, 45164, 6055, 3794, 995, 35473, 2423, 9284, 9154, 8717, 39319, 10632, 2423, 565, 4724, 32887, 5016, 20666, 7435, 3224, 3660, 5296, 26890, 10943, 36081, 2288, 16712, 7649, 1829, 2423, 1901, 10874, 3215, 33599, 47525, 3224, 1901, 23758, 6225, 8592, 7649, 7251, 17082, 1829, 3555, 6225, 8592, 7649, 7251, 1863, 5172, 8848, 2423, 5633, 6055, 3555, 34268, 3224, 10874, 3215, 33599, 47525, 3224, 1901, 6225, 8592, 7649, 7251, 1863, 5172, 8848, 2423, 5633, 6055, 3555, 34268, 3224, 23032, 3555, 3615, 995, 41850, 39894, 4117, 19528, 11296, 5296, 10721, 2423, 1901, 11331, 7435, 2304, 2423, 4675, 10874, 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Complexity احنا دائما بنستخدم مين؟ الـ Big O Notation وبديها لكل الدوالة التانية و ال constant تانية و عادة بقعد فقط ال expensive operation العمليات الأساسية زي ايش؟ المقارنة في ال search algorithm كم عملية مقارنة انت بتعمل؟ يعني احنا قبل شوية كتبنا أربعة N زائد واحد", "tokens": [41185, 2423, 39184, 6161, 41184, 507, 1975, 5016, 8315, 11778, 16373, 15042, 44945, 14851, 9778, 40448, 3714, 9957, 22807, 2423, 39184, 5429, 422, 1726, 399, 46599, 16254, 11296, 5296, 28820, 32748, 2407, 6027, 3660, 16712, 7649, 10632, 4032, 2423, 5754, 6055, 7649, 10632, 4032, 6225, 18513, 3660, 4724, 4587, 22488, 6156, 47432, 2423, 5124, 6916, 18863, 2304, 20292, 9307, 16247, 3794, 32277, 10632, 30767, 1829, 1975, 1829, 8592, 22807, 9673, 4587, 9640, 1863, 3660, 8978, 2423, 3164, 9284, 9122, 2304, 6225, 42213, 10632, 3714, 4587, 9640, 1863, 3660, 16472, 2655, 39894, 25957, 1211, 22807, 37495, 22653, 1975, 5016, 8315, 12174, 36150, 13412, 2407, 10632, 9122, 2655, 3555, 8315, 5551, 25513, 27884, 426, 30767, 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بتدعي .. عشان ايه دائما احنا بقدم ال worst case في أسوأ الأحوال، إيش أنا بعنيني؟ بعنيني ال algorithm أو ال behavior واحنا فعليا تلما بتدور على حد أو صديق أو حد بتعتمد عليه، بدك يهاجد الفرح و الرخة؟ لأ، مش بيقولك الصديق وقت الضيق", "tokens": [1211, 7435, 1829, 6024, 48506, 12399, 3714, 19913, 3555, 2407, 9566, 22807, 46599, 6027, 2655, 6027, 1829, 4386, 4724, 6027, 2655, 6027, 1829, 29538, 27188, 1829, 3224, 7649, 3660, 13672, 1829, 39894, 3215, 3615, 1829, 4386, 6225, 8592, 7649, 1975, 1829, 3224, 11778, 16373, 15042, 1975, 5016, 8315, 4724, 28543, 2304, 2423, 5855, 1389, 8978, 5551, 3794, 2407, 10721, 16247, 5016, 2407, 6027, 12399, 11933, 1829, 8592, 41850, 45030, 1863, 9957, 1829, 22807, 45030, 1863, 9957, 1829, 2423, 9284, 34051, 2423, 5223, 4032, 39319, 8315, 6156, 3615, 20292, 995, 6055, 1211, 15042, 39894, 3215, 13063, 15844, 11331, 3215, 34051, 20328, 16254, 4587, 34051, 11331, 3215, 39894, 34268, 2304, 3215, 47356, 12399, 47525, 4117, 7251, 3224, 26108, 3215, 27188, 2288, 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الأسئلة من وين تجيب أسئلة سيبقى من أسئلة الكتاب وانت خدت برمجة صح؟ الان الأمثلة اللي فيها ال loops دور على الأمثلة اللي فيها ال loops وابدأ يحسب ال complexity تبعتها ال process تبعتها", "tokens": [6027, 7649, 6055, 2288, 21292, 3615, 23758, 13672, 1829, 1975, 8315, 4724, 16254, 3224, 9154, 4117, 1975, 1829, 8592, 9673, 5172, 32887, 11242, 16472, 6055, 2655, 3794, 995, 45865, 2423, 7649, 39894, 5016, 1211, 16247, 3794, 19986, 37977, 47525, 4117, 9673, 5172, 32887, 11242, 6055, 5016, 1211, 16247, 3794, 19986, 37977, 9154, 4032, 9957, 6055, 7435, 1829, 3555, 5551, 3794, 19986, 37977, 8608, 1829, 3555, 4587, 7578, 9154, 5551, 3794, 19986, 37977, 33251, 2655, 16758, 4032, 7649, 2655, 16490, 3215, 2655, 4724, 2288, 2304, 7435, 3660, 20328, 5016, 22807, 2423, 7649, 16247, 2304, 12984, 37977, 13672, 1829, 8978, 11296, 2423, 16121, 11778, 13063, 15844, 16247, 2304, 12984, 37977, 13672, 1829, 8978, 11296, 2423, 16121, 4032, 16758, 3215, 10721, 7251, 5016, 35457, 2423, 14024, 6055, 3555, 34268, 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3550.39, "end": 3550.79, "word": " تتساوي", "probability": 0.90126953125}, {"start": 3550.79, "end": 3551.13, "word": " الان", "probability": 0.676513671875}, {"start": 3551.13, "end": 3551.83, "word": " بتحل", "probability": 0.6988525390625}, {"start": 3551.83, "end": 3552.25, "word": " الأسئلة", "probability": 0.82275390625}, {"start": 3552.25, "end": 3552.93, "word": " بدك", "probability": 0.637451171875}, {"start": 3552.93, "end": 3553.35, "word": " المفروض", "probability": 0.992431640625}, {"start": 3553.35, "end": 3553.65, "word": " تحل", "probability": 0.88330078125}, {"start": 3553.65, "end": 3554.11, "word": " الأسئلة", "probability": 0.91748046875}, {"start": 3554.11, "end": 3554.71, "word": " من", "probability": 0.8681640625}, {"start": 3554.71, "end": 3554.89, "word": " وين", "probability": 0.857666015625}, {"start": 3554.89, "end": 3555.15, "word": " تجيب", "probability": 0.86785888671875}, {"start": 3555.15, "end": 3555.43, "word": " أسئلة", "probability": 0.9842529296875}, {"start": 3555.43, "end": 3555.69, "word": " سيبقى", "probability": 0.7125}, {"start": 3555.69, "end": 3555.83, "word": " من", "probability": 0.9541015625}, {"start": 3555.83, "end": 3556.49, "word": " أسئلة", "probability": 0.974609375}, {"start": 3556.49, "end": 3557.01, "word": " الكتاب", "probability": 0.9728190104166666}, {"start": 3557.01, "end": 3558.73, "word": " وانت", "probability": 0.72900390625}, {"start": 3558.73, "end": 3558.97, "word": " خدت", "probability": 0.9768880208333334}, {"start": 3558.97, "end": 3559.63, "word": " برمجة", "probability": 0.9916015625}, {"start": 3559.63, "end": 3560.43, "word": " صح؟", "probability": 0.79150390625}, {"start": 3560.43, "end": 3560.65, "word": " الان", "probability": 0.6585693359375}, {"start": 3560.65, "end": 3561.79, "word": " الأمثلة", "probability": 0.9622802734375}, {"start": 3561.79, "end": 3561.95, "word": " اللي", "probability": 0.91748046875}, {"start": 3561.95, "end": 3562.17, "word": " فيها", "probability": 0.986572265625}, {"start": 3562.17, "end": 3562.31, "word": " ال", "probability": 0.90478515625}, {"start": 3562.31, "end": 3562.65, "word": " loops", "probability": 0.87890625}, {"start": 3562.65, "end": 3564.25, "word": " دور", "probability": 0.921142578125}, {"start": 3564.25, "end": 3564.43, "word": " على", "probability": 0.78564453125}, {"start": 3564.43, "end": 3564.85, "word": " الأمثلة", "probability": 0.9837646484375}, {"start": 3564.85, "end": 3565.01, "word": " اللي", "probability": 0.984619140625}, {"start": 3565.01, "end": 3565.41, "word": " فيها", "probability": 0.991943359375}, {"start": 3565.41, "end": 3566.07, "word": " ال", "probability": 0.95654296875}, {"start": 3566.07, "end": 3566.41, "word": " loops", "probability": 0.9638671875}, {"start": 3566.41, "end": 3567.31, "word": " وابدأ", "probability": 0.760986328125}, {"start": 3567.31, "end": 3567.81, "word": " يحسب", "probability": 0.8543294270833334}, {"start": 3567.81, "end": 3568.47, "word": " ال", "probability": 0.98291015625}, {"start": 3568.47, "end": 3569.03, "word": " complexity", "probability": 0.92236328125}, {"start": 3569.03, "end": 3569.75, "word": " تبعتها", "probability": 0.925537109375}, {"start": 3569.75, "end": 3570.29, "word": " ال", "probability": 0.90185546875}, {"start": 3570.29, "end": 3570.59, "word": " process", "probability": 0.97998046875}, {"start": 3570.59, "end": 3571.15, "word": " تبعتها", "probability": 0.9879150390625}], "temperature": 1.0}, {"id": 133, "seek": 359400, "start": 3571.76, "end": 3594.0, "text": "كل ما كانت في عندك two loops مانعته انت بتتكلم على أنت ربيع كل ما زادت عدد ال loop زيد عدد القص مفروغة وشغلة اجرب احسب على الكلام هذا هحاول خلال اليومين الجاية هنزلك كام مثال تمام تحاول تحسب ال big O تبعتهم في اي سؤال يا شباب الله يعطيكوا العافية", "tokens": [28820, 19446, 25961, 2655, 8978, 43242, 4117, 732, 16121, 3714, 7649, 34268, 3224, 16472, 2655, 39894, 2655, 4117, 19528, 15844, 14739, 2655, 12602, 21292, 3615, 28242, 19446, 30767, 18513, 2655, 6225, 3215, 3215, 2423, 6367, 30767, 1829, 3215, 6225, 3215, 3215, 25062, 9381, 3714, 5172, 32887, 17082, 3660, 4032, 8592, 17082, 37977, 1975, 7435, 25513, 1975, 5016, 35457, 15844, 2423, 28820, 10943, 23758, 8032, 5016, 995, 12610, 16490, 1211, 6027, 45595, 20498, 9957, 25724, 995, 10632, 8032, 1863, 11622, 1211, 4117, 9122, 10943, 50113, 6027, 46811, 10943, 6055, 5016, 995, 12610, 6055, 5016, 35457, 2423, 955, 422, 6055, 3555, 34268, 16095, 8978, 1975, 1829, 8608, 33604, 6027, 35186, 13412, 3555, 16758, 21984, 37495, 9566, 1829, 4117, 14407, 18863, 31845, 10632], "avg_logprob": -0.2361828532100709, "compression_ratio": 1.7530864197530864, "no_speech_prob": 7.152557373046875e-07, "words": [{"start": 3571.76, "end": 3572.1, "word": "كل", "probability": 0.662109375}, {"start": 3572.1, "end": 3572.3, "word": " ما", "probability": 0.7724609375}, {"start": 3572.3, "end": 3572.68, "word": " كانت", "probability": 0.928955078125}, {"start": 3572.68, "end": 3572.84, "word": " في", "probability": 0.6787109375}, {"start": 3572.84, "end": 3573.2, "word": " عندك", "probability": 0.7232666015625}, {"start": 3573.2, "end": 3573.4, "word": " two", "probability": 0.43994140625}, {"start": 3573.4, "end": 3573.82, "word": " loops", "probability": 0.95361328125}, {"start": 3573.82, "end": 3574.48, "word": " مانعته", "probability": 0.5318603515625}, {"start": 3574.48, "end": 3574.6, "word": " انت", "probability": 0.69287109375}, {"start": 3574.6, "end": 3574.96, "word": " بتتكلم", "probability": 0.9373779296875}, {"start": 3574.96, "end": 3575.38, "word": " على", "probability": 0.55078125}, {"start": 3575.38, "end": 3576.42, "word": " أنت", "probability": 0.5689697265625}, {"start": 3576.42, "end": 3576.82, "word": " ربيع", "probability": 0.7942708333333334}, {"start": 3576.82, "end": 3577.58, "word": " كل", "probability": 0.43408203125}, {"start": 3577.58, "end": 3577.76, "word": " ما", "probability": 0.7158203125}, {"start": 3577.76, "end": 3578.06, "word": " زادت", "probability": 0.8883463541666666}, {"start": 3578.06, "end": 3578.28, "word": " عدد", "probability": 0.9816080729166666}, {"start": 3578.28, "end": 3578.4, "word": " ال", "probability": 0.8037109375}, {"start": 3578.4, "end": 3578.56, "word": " loop", "probability": 0.90673828125}, {"start": 3578.56, "end": 3578.82, "word": " زيد", "probability": 0.6217447916666666}, {"start": 3578.82, "end": 3579.02, "word": " عدد", "probability": 0.990234375}, {"start": 3579.02, "end": 3579.38, "word": " القص", "probability": 0.6300048828125}, {"start": 3579.38, "end": 3580.56, "word": " مفروغة", "probability": 0.780859375}, {"start": 3580.56, "end": 3580.96, "word": " وشغلة", "probability": 0.728515625}, {"start": 3580.96, "end": 3581.5, "word": " اجرب", "probability": 0.76513671875}, {"start": 3581.5, "end": 3581.78, "word": " احسب", "probability": 0.88525390625}, {"start": 3581.78, "end": 3581.94, "word": " على", "probability": 0.7255859375}, {"start": 3581.94, "end": 3582.32, "word": " الكلام", "probability": 0.9508463541666666}, {"start": 3582.32, "end": 3582.66, "word": " هذا", "probability": 0.82470703125}, {"start": 3582.66, "end": 3583.32, "word": " هحاول", "probability": 0.8873291015625}, {"start": 3583.32, "end": 3583.62, "word": " خلال", "probability": 0.9930013020833334}, {"start": 3583.62, "end": 3583.96, "word": " اليومين", "probability": 0.98681640625}, {"start": 3583.96, "end": 3584.32, "word": " الجاية", "probability": 0.5999348958333334}, {"start": 3584.32, "end": 3584.78, "word": " هنزلك", "probability": 0.778955078125}, {"start": 3584.78, "end": 3584.96, "word": " كام", "probability": 0.828857421875}, {"start": 3584.96, "end": 3585.42, "word": " مثال", "probability": 0.986328125}, {"start": 3585.42, "end": 3586.36, "word": " تمام", "probability": 0.858642578125}, {"start": 3586.36, "end": 3587.08, "word": " تحاول", "probability": 0.852783203125}, {"start": 3587.08, "end": 3587.52, "word": " تحسب", "probability": 0.9627278645833334}, {"start": 3587.52, "end": 3588.0, "word": " ال", "probability": 0.9541015625}, {"start": 3588.0, "end": 3588.22, "word": " big", "probability": 0.8359375}, {"start": 3588.22, "end": 3588.42, "word": " O", "probability": 0.72998046875}, {"start": 3588.42, "end": 3588.92, "word": " تبعتهم", "probability": 0.912841796875}, {"start": 3588.92, "end": 3590.34, "word": " في", "probability": 0.71923828125}, {"start": 3590.34, "end": 3590.54, "word": " اي", "probability": 0.754638671875}, {"start": 3590.54, "end": 3590.8, "word": " سؤال", "probability": 0.99267578125}, {"start": 3590.8, "end": 3590.92, "word": " يا", "probability": 0.900390625}, {"start": 3590.92, "end": 3591.26, "word": " شباب", "probability": 0.9876302083333334}, {"start": 3591.26, "end": 3593.46, "word": " الله", "probability": 0.791015625}, {"start": 3593.46, "end": 3593.7, "word": " يعطيكوا", "probability": 0.7576171875}, {"start": 3593.7, "end": 3594.0, "word": " العافية", "probability": 0.8308919270833334}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3594.26325, "duration_after_vad": 3428.2337499999826}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/xQty_gvEjms_postprocess.srt b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/xQty_gvEjms_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..c8df25554e74394254ebee8aaf51ec428c468e7a
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/xQty_gvEjms_postprocess.srt
@@ -0,0 +1,1876 @@
+1
+00:00:20,770 --> 00:00:22,590
+بسم الله والحمد لله والصلاة والسلام علي الرسول
+
+2
+00:00:22,590 --> 00:00:25,450
+الله اليوم ان شاء الله شباب هنكمل في chapter لل
+
+3
+00:00:25,450 --> 00:00:30,150
+graphs او graph theory خلينا نراجع بشكل سريع
+
+4
+00:00:30,150 --> 00:00:34,780
+نخططنا المحاضرة الماضية خصوصا انه قلنا أسبوعبعيد
+
+5
+00:00:34,780 --> 00:00:39,360
+عن المادة اتفقنا ان ال graph هو عبارة عن زوج مرتب
+
+6
+00:00:39,360 --> 00:00:44,500
+من مجموعتين المجموعة الأولى بتمثل مجموعة النقاط ال
+
+7
+00:00:44,500 --> 00:00:48,160
+vertices والمجموعة التانية بتمثل مجموعة الجسور
+
+8
+00:00:48,160 --> 00:00:54,220
+اللي موجودة بين النقاط هاي وقلنا أهم ما يميز ال
+
+9
+00:00:54,220 --> 00:01:01,560
+vertices انها نم MT فعلى الأقل ال graph يساوي زوج
+
+10
+00:01:01,560 --> 00:01:10,050
+مرتبمن vertex one او من one vertex و five هذا أبسط
+
+11
+00:01:10,050 --> 00:01:14,570
+graph ممكن يكون هنا هذا أبسط graph ممكن يكون موجود
+
+12
+00:01:14,570 --> 00:01:20,370
+هنا و لما اتينا نمثل بالرسم حطينا النقطة و كتبنا
+
+13
+00:01:20,370 --> 00:01:27,450
+اسم ال vertex v1 وهذا أبسط graph ممكن يكون موجود
+
+14
+00:01:27,450 --> 00:01:35,880
+معنا وانتقلنا بعد هيكوقلنا ان الجسور هي عبارة عن
+
+15
+00:01:35,880 --> 00:01:42,660
+مجموعة من نقطتين يعني لما انا باجب ارسم او لو انا
+
+16
+00:01:42,660 --> 00:01:51,020
+افترض ان في عندي ال graph هذا يمثل المثلث a,b,c
+
+17
+00:01:51,020 --> 00:01:59,900
+لما بدأت مجموعة ال vertices معروفة a,b,c ومجموعة
+
+18
+00:01:59,900 --> 00:02:13,270
+الجسوربكتبها AB BC و AC كمجموعة تانية وهنا دلالة
+
+19
+00:02:13,270 --> 00:02:16,910
+على ان مافيش عندي اتجاه مابحتمش للاتجاه انا سواء
+
+20
+00:02:16,910 --> 00:02:23,090
+كانت AB هي نفسها ب A وهنا بتكلم على اليسار وقولنا
+
+21
+00:02:23,090 --> 00:02:29,440
+هنا يا شباب انه انا بتكلم على اليسار ABمجاور للجسر
+
+22
+00:02:29,440 --> 00:02:35,120
+AC لأنهم مشتركوا في نفس النقطة وقولت كذلك A وC
+
+23
+00:02:35,120 --> 00:02:43,320
+كنقات متجاورات لأنه في بينهم جسر وبعد
+
+24
+00:02:43,320 --> 00:02:50,440
+ذلك انتقلنا لشيء سمناها الدرجة رتبة النقطة ال
+
+25
+00:02:50,440 --> 00:02:55,730
+degree للنقطة ايش ال degree؟الـ degree للنقطة هي
+
+26
+00:02:55,730 --> 00:03:01,810
+عبارة عن عدد الجسور الواصلة للنقطة هذه عدد الجسور
+
+27
+00:03:01,810 --> 00:03:05,390
+الواصلة للنقطة اللي موجودة عندنا هنا يعني ال
+
+28
+00:03:05,390 --> 00:03:10,430
+degree لل a اتنين و ال degree لل c اتنين و ال
+
+29
+00:03:10,430 --> 00:03:14,030
+degree لل b اتنين و قلنا في عنا شغل اسمها ال
+
+30
+00:03:14,030 --> 00:03:17,450
+pseudocode او اعفر ان ال pseudograph لما بكون انا
+
+31
+00:03:17,450 --> 00:03:24,600
+في عندي loopوقلنا اللوب نحسبها تنقل وبتصير الرطبة
+
+32
+00:03:24,600 --> 00:03:29,220
+لل CND أربعة
+
+33
+00:03:29,220 --> 00:03:32,960
+طيب
+
+34
+00:03:32,960 --> 00:03:37,180
+وإذا كان في عندي vertex زي V تلاتها وقلنا عنه
+
+35
+00:03:37,180 --> 00:03:41,620
+isolated vertex أو isolated point نقمة معزولة ال
+
+36
+00:03:41,620 --> 00:03:45,040
+degree تبعتها جد الشباب صفر عنها مش مقتصر ولا
+
+37
+00:03:45,040 --> 00:03:46,140
+إبجسر
+
+38
+00:03:48,220 --> 00:03:51,660
+وانتقل بعد ذلك لموضوع ال sub graph وقلنا في ال sub
+
+39
+00:03:51,660 --> 00:03:57,300
+graph بهمني جدا ان انا اكون فاهم ان لو كان في عندي
+
+40
+00:03:57,300 --> 00:04:07,340
+ال G تمثل الزوج المرتب V1 و V2 و V3 ومجموعة الجسور
+
+41
+00:04:07,340 --> 00:04:16,940
+V1 V2 V2V3 V1 V3 اللي هي نفس الرسمة المثلثة اللي
+
+42
+00:04:16,940 --> 00:04:23,360
+كنت رسمها سابقا بس بدل AB V1 و V2 الآن بقدر أقول
+
+43
+00:04:23,360 --> 00:04:33,860
+أنا G1 تساوي V1 و V3 V1
+
+44
+00:04:33,860 --> 00:04:41,470
+V3 كجسور الآن هل G1 صبصت من G2عشان اقول ان جي واحد
+
+45
+00:04:41,470 --> 00:04:46,210
+subset من جي اتنين بيلزم افحص هل مجموعة النقاط
+
+46
+00:04:46,210 --> 00:04:52,190
+مجموعة جزئية من النقاط الرئيسية هل V1 subset من V؟
+
+47
+00:04:52,190 --> 00:04:58,090
+subset هل ال E1 subset من ال E؟ subset إذا كانت ال
+
+48
+00:04:58,090 --> 00:05:01,370
+V subset من V و ال E subset من E معناته جي واحد
+
+49
+00:05:01,370 --> 00:05:08,480
+subset من G وهنا الجي واحد subset من الجيولا
+
+50
+00:05:08,480 --> 00:05:13,360
+تتجاهل الرسمة ولا حجمها ولا أي حاجة يعني هذا
+
+51
+00:05:13,360 --> 00:05:21,020
+الرسمة شايفين احنا V2 V5 مظبوط؟ لو انا رسمت هيك V2
+
+52
+00:05:21,020 --> 00:05:30,480
+V5 هي نفسها subset ولا اشي تغير لو رسمت هيك V2
+
+53
+00:05:30,480 --> 00:05:35,150
+V5هذه خمسة لأن الطول ليس معيارا لدي ولا direction
+
+54
+00:05:35,150 --> 00:05:41,430
+وبالتالي كل اللي بهمه هي مجموعة الجسور ومجموعة
+
+55
+00:05:41,430 --> 00:05:48,510
+النقاط ومجموعة الجسور وانتقلنا بعدها لشيء سمناه ال
+
+56
+00:05:48,510 --> 00:05:53,550
+complete graph قلنا ان ال complete graph هو عبارة
+
+57
+00:05:53,550 --> 00:05:59,490
+عن ال graphكل نقطة فيه كل vertex فيه متصلة مع كل
+
+58
+00:05:59,490 --> 00:06:04,490
+النقاط الأخرى الموجودة في ال graph وكل هذا
+
+59
+00:06:04,490 --> 00:06:12,970
+complete graph تلاتة رمزنا
+
+60
+00:06:12,970 --> 00:06:18,450
+له K تلاتة تلاتة على كناية عن عدد النقاط و K
+
+61
+00:06:18,450 --> 00:06:22,410
+اختصارا complete الآن
+
+62
+00:06:24,280 --> 00:06:29,280
+كل جسر كل نقطة موجودة فيها متصلة مع كل المقابل
+
+63
+00:06:29,280 --> 00:06:38,240
+التالية، وإذا كنت تتكلم عن K4، فهي كذلك، كمان كمان
+
+64
+00:06:38,240 --> 00:06:40,620
+كمان كمان كمان كمان كمان كمان كمان كمان كمان كمان
+
+65
+00:06:40,620 --> 00:06:40,900
+كمان كمان كمان كمان كمان كمان كمان كمان كمان كمان
+
+66
+00:06:40,900 --> 00:06:42,280
+كمان كمان كمان كمان كمان كمان كمان كمان كمان كمان
+
+67
+00:06:42,280 --> 00:06:42,300
+كمان كمان كمان كمان كمان كمان كمان كمان كمان كمان
+
+68
+00:06:42,300 --> 00:06:48,440
+كمان كمان كمان كمان كمان كمان كمان
+
+69
+00:06:49,370 --> 00:06:53,790
+عدد النقاط نقص واحد لإيش؟ لأنه فعلا هو كل نقطة
+
+70
+00:06:53,790 --> 00:06:57,510
+متصلة مع كل النقاط المقابلة أي باقية عندك في ال
+
+71
+00:06:57,510 --> 00:07:01,410
+graph و هو أربعة و متصل مع الباقية كلهم معاكم مع
+
+72
+00:07:01,410 --> 00:07:05,230
+تلاتة إذا هو تلاتة متصل مع اتنين و لو كان اتنين
+
+73
+00:07:05,230 --> 00:07:13,570
+واحد و هكذا و قلنا أبسط complete graph نقطة واحد
+
+74
+00:07:13,570 --> 00:07:19,250
+isolated point oneوانتقل بعدها لشيء صميناه الـ
+
+75
+00:07:19,250 --> 00:07:23,310
+Bipartite Graph وقلنا الـ Bipartite Graph هو عبارة
+
+76
+00:07:23,310 --> 00:07:30,670
+هانيغراف انا بروح بأجسم النقاط اللي فيه لمجموعتين
+
+77
+00:07:30,670 --> 00:07:36,890
+مختلفتين الان لو انا اخترت هذا ال graph سميناه A B
+
+78
+00:07:36,890 --> 00:07:40,830
+C D E الان V
+
+79
+00:07:43,690 --> 00:07:49,670
+A,B,C,D,E هاي الخمس نقاط اللي موجودة عندي هان بقول
+
+80
+00:07:49,670 --> 00:07:54,130
+عن هذا الـ Bipartite Graph لو أقدرت أسوي التاني
+
+81
+00:07:54,130 --> 00:07:59,430
+أجسم الـ V هذه لمجموعتين disjoint التقنعة بينهم
+
+82
+00:07:59,430 --> 00:08:04,770
+five بحيث إنه ال connection أو اليسور فقط بتكون
+
+83
+00:08:04,770 --> 00:08:08,330
+بين عناصر المجموعتين يعني عناصر المجموعة الواحدة
+
+84
+00:08:08,330 --> 00:08:11,710
+مافيش بينهم connection معناته أنا بقدر قاعدي أقول
+
+85
+00:08:11,710 --> 00:08:25,410
+هذه V واحدتساوي هذه واحدة وهذه الثانية D او B وD و
+
+86
+00:08:25,410 --> 00:08:34,840
+V2 تساوي A C وE التقابل بينهم فاية ولا لا؟وفي نفس
+
+87
+00:08:34,840 --> 00:08:40,480
+الوقت مافيش جسر بين B وD ومافيش جسور بين A وC وR
+
+88
+00:08:40,480 --> 00:08:44,540
+وE وC وE، مافيش، يعني على أسر المجموعة الواحدة
+
+89
+00:08:44,540 --> 00:08:48,660
+مافيش بينهم جسور، بس الجسور ممتدة بين المجموعتين،
+
+90
+00:08:48,660 --> 00:08:53,080
+الجسور ممتدة بين المجموعتين، هذا ال graph بسميه
+
+91
+00:08:53,080 --> 00:08:57,860
+bipartate graph، bipartate graph يعني graph مجسوم
+
+92
+00:08:58,580 --> 00:09:02,900
+لجسمين لجزئين و باية يا شباب اختصار ل binary ثنائي
+
+93
+00:09:02,900 --> 00:09:07,380
+باي بارتت و بارتت بارتشن زي ما قلنا سابقا و
+
+94
+00:09:07,380 --> 00:09:13,300
+بالتالي هذا بسميه باي بارتت اجراف هذا باي بارتت
+
+95
+00:09:13,300 --> 00:09:16,320
+اجراف المجموعة الأولى اللى فوق المجموعة التانية
+
+96
+00:09:16,320 --> 00:09:20,120
+المجموعة الأولى المجموعة التانية و هكذا الان ال
+
+97
+00:09:20,120 --> 00:09:24,020
+باي بارتت اجراف ده ممكن انا اسميه completeBy
+
+98
+00:09:24,020 --> 00:09:29,500
+Partity Graph لو كان كل أنصر في المجموعة الأولى
+
+99
+00:09:29,500 --> 00:09:34,240
+متقفل مع كل عناصر المجموعة التانية والعكس صحيح هذا
+
+100
+00:09:34,240 --> 00:09:36,920
+ال graph اللي أنا رسمته ممكن يصير By Partity Graph
+
+101
+00:09:36,920 --> 00:09:43,120
+لو إجيت هنا و حطيت كمان connection هيك كمان هنا
+
+102
+00:09:43,120 --> 00:09:49,900
+connection هيك الان Complete By Partity Graph
+
+103
+00:09:49,900 --> 00:09:54,820
+المرموز له Kلكمplete المجموعة الأولى جداش عنصر
+
+104
+00:09:54,820 --> 00:10:01,880
+فيها اتنين كمه تلاته يعني المجموع تاني كمليت بي
+
+105
+00:10:01,880 --> 00:10:06,280
+budget graph من مجموع تاني اتنين و تلاته الآن لو
+
+106
+00:10:06,280 --> 00:10:10,400
+طلعت لبطبة العراسر في المجموعة الأولى بدها تساوي
+
+107
+00:10:10,400 --> 00:10:17,260
+عدد عناصر المجموعة التانيةيعني روتب الـ B تلاتة
+
+108
+00:10:17,260 --> 00:10:21,840
+بعدد العناصر ليش؟ لأن هو فعليا متصي مع كل عناصر
+
+109
+00:10:21,840 --> 00:10:25,840
+المجموعة التانية و لو أتيت لأي عنصر فيه المجموعة
+
+110
+00:10:25,840 --> 00:10:30,700
+التانية V2 ال degree تبعتها هتكون اتنين اللي هي
+
+111
+00:10:30,700 --> 00:10:34,120
+عدد عناصر المجموعة الأولى المقابلة أو التالتة
+
+112
+00:10:34,120 --> 00:10:36,960
+سامية زي ما بدك مش مشكلة كتير الفكرة وين؟ أنه فيها
+
+113
+00:10:36,960 --> 00:10:39,580
+عنصرين وهذا لازم يكون مرتبط مع كل العناصر في
+
+114
+00:10:39,580 --> 00:10:47,710
+المجموعة التانية تمام وانتقلنا بعدهالشغل صمناها
+
+115
+00:10:47,710 --> 00:10:55,350
+مجموع الـ degrees مجموع الرتب في أي graph مجموع
+
+116
+00:10:55,350 --> 00:11:00,510
+الرتب يساوي summation
+
+117
+00:11:00,510 --> 00:11:08,350
+لل degree لكل
+
+118
+00:11:08,350 --> 00:11:14,730
+ال vertices يساوي ضعف عدد الجسور ضعف عددالجسور
+
+119
+00:11:14,730 --> 00:11:20,090
+فالرسم اللي احنا رسميه لها الان جداش الرطب لل D لل
+
+120
+00:11:20,090 --> 00:11:28,930
+B ثلاثة رطب ال D ثلاثة رطب ال A اتنين C اتنين و ال
+
+121
+00:11:28,930 --> 00:11:34,510
+E اتنين لو جمعنا كل الرطب مع بعض هدول ستة و ستة
+
+122
+00:11:34,510 --> 00:11:42,340
+ماشي مظبوط ماشي هذا تساوم لضعف حدد الجسورو ايه
+
+123
+00:11:42,340 --> 00:11:45,520
+الجسور اللى موجودة عندى؟ هيهم واحد اتنين تلاتة
+
+124
+00:11:45,520 --> 00:11:50,140
+اربعة خمسة ستة ست جسور وبالتالي هذا القانون يطبق
+
+125
+00:11:50,140 --> 00:11:55,780
+على اي graph هذا القانون يطبق على اي graph وسألنا
+
+126
+00:11:55,780 --> 00:12:05,640
+سؤال كنا صادقا كي اربعة كي اربعة جداش عدد الجسور
+
+127
+00:12:05,640 --> 00:12:06,720
+اللى موجودة فيه؟
+
+128
+00:12:13,130 --> 00:12:18,610
+جدّيش هذا الجسور اللي موجودة فيه؟ ايوة .. ايوة
+
+129
+00:12:18,610 --> 00:12:24,490
+اسمع عنكم؟ عريب .. ايش يعني كده الأربعة؟ Complete
+
+130
+00:12:24,490 --> 00:12:30,850
+Graph من أربع نقاط .. أصبت؟ الموضع Complete Graph
+
+131
+00:12:30,850 --> 00:12:35,670
+من أربع نقاط طيب .. شو يعني Complete Graph؟ ان كل
+
+132
+00:12:35,670 --> 00:12:40,270
+نقطة متصلة معك مع جميع النقاط التالية .. أصبت؟
+
+133
+00:12:40,270 --> 00:12:48,210
+يعني رتبة كل واحدة فيهموهما أربعة يعني أن عدد
+
+134
+00:12:48,210 --> 00:12:53,730
+الجثور أو عدد مجموع الرتب للـ vertices يساوي تلاتة
+
+135
+00:12:53,730 --> 00:12:59,910
+أو أربع نقاط كل واحدة فيهم رتبتها تلاتة يساوي
+
+136
+00:12:59,910 --> 00:13:07,010
+اتناشر وهذا يساوي ضعف عدد الجثور يعني أننا نتكلم
+
+137
+00:13:07,010 --> 00:13:13,090
+عن ست جثور موجودة في الرسمة وين هما؟عشان يصيركم
+
+138
+00:13:13,090 --> 00:13:19,310
+جيتي graph يجب أن أضع القطنين بتاعت المربع 6
+
+139
+00:13:19,310 --> 00:13:24,570
+ولا لا؟ وهذا الكلام يتطبق على أي graph .. وشوفنا
+
+140
+00:13:24,570 --> 00:13:29,950
+الأمثلة بشكل .. وهذا تقريبا كان مدخس أو مجمل اللي
+
+141
+00:13:29,950 --> 00:13:33,910
+أخدناه في المحاضرة الماضية يعني هي رجعنا محاضرة
+
+142
+00:13:33,910 --> 00:13:40,800
+بالكامل خلال نص ساعة طيب بعد هيكأتكلمني على شغل أو
+
+143
+00:13:40,800 --> 00:13:48,520
+الـ degree أو الـ isomorphism التقابل
+
+144
+00:13:48,520 --> 00:13:51,320
+بين two graphs الآن لو أنا كان في عندي two graphs
+
+145
+00:13:51,320 --> 00:13:57,280
+هل بقدر أقول عنهم متشابهين و تقابلين أو لأ؟ الآن
+
+146
+00:13:57,280 --> 00:14:05,840
+عشان انا أقول ان G1مطابق للجي اتنين لازم اوجد شغل
+
+147
+00:14:05,840 --> 00:14:10,600
+بيجيكتف function اوجد بيجيكتف function شو يعني
+
+148
+00:14:10,600 --> 00:14:15,860
+بيجيكتف function يا شباب؟ one to one و one to one
+
+149
+00:14:15,860 --> 00:14:18,400
+و one to one و one to one و one to one ال domain
+
+150
+00:14:18,400 --> 00:14:22,760
+تبعت ال function هذي بدها تكون ال vertices تبعت
+
+151
+00:14:22,760 --> 00:14:29,120
+الجراف الأول و ال target set ال verticesتابعك للـ
+
+152
+00:14:29,120 --> 00:14:32,220
+Target أو الـ Graph التاني اللي موجود عندي هو
+
+153
+00:14:32,220 --> 00:14:35,920
+بنموذلها Phi أو Lambda زي ما بدك مافيش مشكلة كتير
+
+154
+00:14:35,920 --> 00:14:38,500
+عندي تعالى نشوف ال Graph البسيط اللي موجود عندنا
+
+155
+00:14:38,500 --> 00:14:47,200
+هل ال Graph هذا G1 يقابق G2 ولا لأ؟ عشان كمان مرة
+
+156
+00:14:47,200 --> 00:14:51,520
+نقول يقابق او لا يقابق بيلزمني اعرف او اوجد
+
+157
+00:14:51,520 --> 00:14:57,050
+Byjective function ال domain تبعتهاG1 يعني انا بدي
+
+158
+00:14:57,050 --> 00:15:12,370
+اقول Phi of النقاب اللي هنا U و W V و X هاي عناصر
+
+159
+00:15:12,370 --> 00:15:17,990
+الدمية شو بيدها تساوي ال function هذه ال
+
+160
+00:15:17,990 --> 00:15:22,960
+Aالمفروض .. المفروض ان الـ vertex هتكون تقاعد و
+
+161
+00:15:22,960 --> 00:15:28,160
+vertex تانية قلنا كمان مرة ال domain تبعتها V1 و
+
+162
+00:15:28,160 --> 00:15:31,480
+ال target set تبعتها V2 تحت الجرافة التانية اللي
+
+163
+00:15:31,480 --> 00:15:35,440
+هم هدول يعني الـ Phi اللي انا بده اعرفها يا شباب
+
+164
+00:15:35,440 --> 00:15:45,280
+بدها تكون من V1 إلى V2 اللي هي X Y .. اه مافيش ..
+
+165
+00:15:45,280 --> 00:15:55,770
+U و Wو V و X الى A,B,C,D
+
+166
+00:15:59,800 --> 00:16:02,740
+كيف بدي اوجد ال value تبعتها عشان اوجد التقابق هذا
+
+167
+00:16:02,740 --> 00:16:06,820
+اولا؟ هل الرسم هذه نفس الرسم هذه؟ طبعا انت تتذكر
+
+168
+00:16:06,820 --> 00:16:09,520
+الكلام اللي قلناه من البداية، فموضوع ال graphs يا
+
+169
+00:16:09,520 --> 00:16:14,260
+شباب ماتدجوش على الشكل يكون كيف شكله، لا بهم نقول
+
+170
+00:16:14,260 --> 00:16:17,480
+ولا direction، لا بهم نقول ال graph ولا شكله ولا
+
+171
+00:16:17,480 --> 00:16:22,490
+ال direction، بهم دائما دائماأبحث عن أشياء أساسية
+
+172
+00:16:22,490 --> 00:16:25,650
+في الرسم هل ال graph هي نفس .. لأ .. العدد النقاط
+
+173
+00:16:25,650 --> 00:16:29,530
+نفس عدد النقاط الجسور نفس عدد الجسور إذا كان هذا
+
+174
+00:16:29,530 --> 00:16:33,390
+الكلام متوفر معناته احتمال كبير جدا أن هذا ال
+
+175
+00:16:33,390 --> 00:16:37,910
+graph يكون مطابق الآن تبقى عليش أشتغل شغل بسيط
+
+176
+00:16:37,910 --> 00:16:44,950
+الآن هذا ال graph تخيل لو أنا جبت ال W هنا إيش
+
+177
+00:16:44,950 --> 00:16:53,510
+يعني أجيب ال W هنا؟ يعني هتصير الرسم هيك100% بيصير
+
+178
+00:16:53,510 --> 00:16:58,990
+واسمة هادي هادي بيصير عندي متوازي أطلع بصير ولا لأ
+
+179
+00:16:58,990 --> 00:17:02,370
+ببصر في التطابق بالمتوازي الأطلع والمربع اللي عندي
+
+180
+00:17:02,370 --> 00:17:09,170
+ببلاش بدي أزده كمان شويه ل هيك عشان أعدله بيصير في
+
+181
+00:17:09,170 --> 00:17:15,410
+تطابق الآن التطابق مفاده أن ال W أصبح تقابلها مين
+
+182
+00:17:15,410 --> 00:17:27,760
+ال A ال V تقابلها Bالـ X تقابلها C و الـ U تقابلها
+
+183
+00:17:28,610 --> 00:17:33,090
+أيه دي؟ هيك أنت أعرفت ال function تبعتك بيجيبتب
+
+184
+00:17:33,090 --> 00:17:38,290
+one-to-one و one-to اعرفت ال function بيجيبتب one
+
+185
+00:17:38,290 --> 00:17:42,750
+-to-one و one-to لكن هل ال function هذه صحيحة أو
+
+186
+00:17:42,750 --> 00:17:47,490
+غير صحيحة بتحكم عليها من خلال فحصك للجسور اللي
+
+187
+00:17:47,490 --> 00:17:51,130
+موجودة في مين في ال graph يعني مين الجسور اللي
+
+188
+00:17:51,130 --> 00:17:57,450
+موجودة عندي هنا شباب تيجي تقولي five of w u
+
+189
+00:18:13,320 --> 00:18:14,720
+وووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووو
+
+190
+00:18:27,020 --> 00:18:32,740
+ما هو الـ W في مكانها؟ الـ A و الـ U؟ الـ D هل الـ
+
+191
+00:18:32,740 --> 00:18:38,760
+A و الـ D جسر موجود في الرسم الجديد؟ موجود تنتقل
+
+192
+00:18:38,760 --> 00:18:43,440
+خطوة للأعلى؟ one step forward باتجاه الجسر التاني؟
+
+193
+00:18:43,440 --> 00:18:47,600
+الـ W هو A و الـ W هو V و الـ V مكانها بيه هل الـ
+
+194
+00:18:47,600 --> 00:18:55,360
+A و الـ B موجود؟ موجود V X الـ R V X الـ V بولا
+
+195
+00:18:55,360 --> 00:19:03,690
+بيه؟والـ XC DC موجود؟ اه موجود الجسم الأخير UX DC
+
+196
+00:19:03,690 --> 00:19:10,050
+و ال DC موجودإذا الآن الـ Function تبعتي تم
+
+197
+00:19:10,050 --> 00:19:14,190
+تعريفها بشكل صحيح بـ Adjective Function وعملت
+
+198
+00:19:14,190 --> 00:19:18,050
+Mapping حتى ما بين الجثور اللي موجودة قبل في الـ
+
+199
+00:19:18,050 --> 00:19:22,990
+Graph، يعني قد تتمثل كل جثر، توصله للجثر المقابل،
+
+200
+00:19:22,990 --> 00:19:29,950
+معناته أنا بقى هنا بقول إن G1 is isomorphic to G2،
+
+201
+00:19:29,950 --> 00:19:35,120
+G1 تقابقالرسم جي اتنين جي واحد تقارب جي اتنين نعم
+
+202
+00:19:35,120 --> 00:19:39,040
+ايوة
+
+203
+00:19:39,040 --> 00:19:42,120
+طبعا كل ما تكبر ال graph هتزداد العملية تعقيد أكيد
+
+204
+00:19:42,120 --> 00:19:48,000
+بس هذه هي الخطوات العملية من أجل إثبات التطابق لكن
+
+205
+00:19:48,000 --> 00:19:51,280
+احنا جولا فيه كلام أساسي صادق الآن لو كان ال two
+
+206
+00:19:51,280 --> 00:19:55,960
+and two graphs كبار واحد في عشر نقاط والتاني في
+
+207
+00:19:55,960 --> 00:20:01,590
+احداش ولا عمره بيصير فيه تطابقفلو كانت الآن عشر
+
+208
+00:20:01,590 --> 00:20:06,490
+نقاط، عشر نقاط، لكن التاني فيه خمس ديصور، والأول
+
+209
+00:20:06,490 --> 00:20:10,190
+فيه سبعة، ولا عمرو بيخوفيه تقارب، بتنسى الموضوع،
+
+210
+00:20:10,190 --> 00:20:13,410
+طبعا، تفضل يعني ال graph بلقى فيه زي ما بديه،
+
+211
+00:20:13,410 --> 00:20:18,900
+أكيد، يعني مش طواله متوازنأنت لو خلّيته أعمل وازي
+
+212
+00:20:18,900 --> 00:20:22,440
+أطلع حيك مافيش مشكلة، شوف هذا الرسم اللي أنا رسمته
+
+213
+00:20:22,440 --> 00:20:28,400
+عشان أحاول أصل بسهولة، تمام؟ لمين؟ للـfunction،
+
+214
+00:20:28,400 --> 00:20:31,160
+أصل للـfunction بشكل سهل، اما بإمكاني مارفعوش
+
+215
+00:20:31,160 --> 00:20:34,460
+مطلقا، إذا بتقدر تشغل في مخيلتك، مافيش مشكلة،
+
+216
+00:20:34,460 --> 00:20:35,780
+تعالي شوف المثال اللي بعده
+
+217
+00:20:46,710 --> 00:20:52,970
+تعالى نشوف الإجابة هذه G1 و G2 هل في بينهم تقابق؟
+
+218
+00:20:52,970 --> 00:20:56,310
+مباشرة قبل ما تفكر بالـ function طلع على عدد
+
+219
+00:20:56,310 --> 00:21:01,090
+النقاط و عدد الجسور 4
+
+220
+00:21:01,090 --> 00:21:07,590
+نقاط و 4 جسور خمس جسور مش أربعة أربعة أربعة للنقاط
+
+221
+00:21:07,590 --> 00:21:12,900
+و خمسة خمسة للجسور معناه تحتمال التقابقموجود يكون
+
+222
+00:21:12,900 --> 00:21:16,120
+عالي جدا اقول لك شغلة تتذكر شغلة يمكن احنا فشجناها
+
+223
+00:21:16,120 --> 00:21:20,020
+في ال review اليوم اللي سمناها sequence of degrees
+
+224
+00:21:20,020 --> 00:21:23,280
+ترتيب الدجريز مش كما احنا قولنا في ال graph اشرح
+
+225
+00:21:23,280 --> 00:21:28,500
+ساوي بنرتب الرتب تبعته جدش رتبة ايه؟ تقولنا تلاتة
+
+226
+00:21:28,500 --> 00:21:36,720
+دي اتنين تلاتة اتنين تلاتة اتنين تلاتة اتنين تلاتة
+
+227
+00:21:36,720 --> 00:21:39,600
+اتنين تلاتة اتنين تلاتة اتنين sequence of degrees
+
+228
+00:21:42,820 --> 00:21:49,180
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+229
+00:21:49,180 --> 00:21:50,200
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+230
+00:21:50,200 --> 00:21:53,340
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+231
+00:21:53,340 --> 00:21:53,360
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+232
+00:21:53,360 --> 00:21:53,780
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+233
+00:21:53,780 --> 00:22:11,000
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+234
+00:22:12,110 --> 00:22:15,050
+جراف ممكن يكون فيه تطابق عالي ايش انا هساوي الان؟
+
+235
+00:22:15,050 --> 00:22:21,590
+كيف ممكن اعمل ماب؟ الان لو انت تفكر تاخد ال a w او
+
+236
+00:22:21,590 --> 00:22:27,550
+اخد ال a u غلط ليش؟ لإن رتبة ال a تلاتة و المفروض
+
+237
+00:22:27,550 --> 00:22:31,290
+ال vertex اللي بيكون مقابل إلها لازم يكون نفس ال
+
+238
+00:22:31,290 --> 00:22:36,970
+رتبة وبالتالي انت الان بتشتغل كتالة تقول في of a
+
+239
+00:22:36,970 --> 00:22:43,450
+في of b في of c5 of D هاي الأربع نقاط اللي موجودة
+
+240
+00:22:43,450 --> 00:22:49,910
+عندى في غيرهم لو ماعنديش بدي أشوف إيش مقابلهم الآن
+
+241
+00:22:49,910 --> 00:22:53,350
+في موضوع الرسم الرسم بسهل عليك كتير في فهمك لل
+
+242
+00:22:53,350 --> 00:22:57,670
+isomorphism تعال معايا هيك و أنا بدي أجيب ال X هان
+
+243
+00:22:57,670 --> 00:23:04,130
+بتحط ال X هان هيك
+
+244
+00:23:04,130 --> 00:23:12,210
+و انسانياها من هان هيك شوية الآنصار في شبه تطابق،
+
+245
+00:23:12,210 --> 00:23:16,870
+بصبوط، بس دلني أعمل كمان خطوة، أعمل rotation
+
+246
+00:23:16,870 --> 00:23:21,670
+باتجاه اليسار، ألف ال graph عشان القطر يطابق مع
+
+247
+00:23:21,670 --> 00:23:24,370
+القطر، شوف هذا الرسم اللي أنا قاعد بسويه مش إلزاني
+
+248
+00:23:25,060 --> 00:23:28,580
+مش إذاني لكنه بالنسبة لي .. بالنسبة لي أنا كواحد
+
+249
+00:23:28,580 --> 00:23:33,380
+بدي أحل بخلّيني أجيب ال graph function تبعتي 100%
+
+250
+00:23:33,380 --> 00:23:36,760
+صح خلّيني أجيب ال graph function تبعتي 100% صح بعد
+
+251
+00:23:36,760 --> 00:23:40,800
+ما أنا عملت rotation معناته شكل ال graph تبعي صحيك
+
+252
+00:23:40,800 --> 00:23:44,960
+الآن
+
+253
+00:23:44,960 --> 00:23:57,050
+هذه U وهذه W وهنا X وهذه بلّة مين ال Vمصبوط او لا؟
+
+254
+00:23:57,050 --> 00:23:59,050
+بعد الـ rotation هاي إذا أنا عملت ال rotation
+
+255
+00:23:59,050 --> 00:24:07,870
+بتاعة المثل خلصنا ال a صارت ال w ال b ال u ال c I
+
+256
+00:24:07,870 --> 00:24:11,870
+can't see الآن بعد ما عملنا .. قولنا rotation بعد
+
+257
+00:24:11,870 --> 00:24:22,210
+ما هي الرسمة عملنا لها rotation الآن a w b u c v و
+
+258
+00:24:22,210 --> 00:24:28,170
+ال d x طبعا هذه ال functionبقى انا ممكن اكتبها
+
+259
+00:24:28,170 --> 00:24:35,710
+بصورة تانية اقول الفايف يتساوي او ال labda AW على
+
+260
+00:24:35,710 --> 00:24:40,290
+نفسي المرتبة فهي ماب برضه بي يو بأي شكل انت بتكتبه
+
+261
+00:24:40,290 --> 00:24:49,790
+أنا ماعنديش مشكلة في الموضوع C وV وDو X الآن تتحقق
+
+262
+00:24:49,790 --> 00:24:53,970
+أن الـ function هذه صحيحة تعطيك كل الدسور اللي
+
+263
+00:24:53,970 --> 00:24:58,150
+موجودة طبعا ماضحة صحيحة لإن انت ما بقترصر بالكامل
+
+264
+00:24:58,150 --> 00:25:06,270
+Phi of AD
+
+265
+00:25:06,270 --> 00:25:18,760
+Phi of AB Phi of AC هاي تلات دسورالان فاي اف بي سي
+
+266
+00:25:18,760 --> 00:25:25,900
+و فاي اف بي سي مظبوط؟ هذه الخمس جسور اللي موجودة
+
+267
+00:25:25,900 --> 00:25:37,520
+عندها سنة ا دي دابليو اكس موجود ا بي دابليو يو
+
+268
+00:25:37,520 --> 00:25:52,700
+موجود ا سي دابليو في موجودالان DC X V X V موجود؟
+
+269
+00:25:52,700 --> 00:26:03,660
+موجود اخر جسم U بل هي B و CV وبالتالي موجود بحيث
+
+270
+00:26:03,660 --> 00:26:07,680
+ان انا بقول جي واحد is isomorphic مقابل دائمة
+
+271
+00:26:15,310 --> 00:26:20,230
+الأمر السهل أنك تشغّل في دماغك رصيد كثير عشان
+
+272
+00:26:20,230 --> 00:26:23,950
+تتحلل الرسمين و تتبقوا مع بعض
+
+273
+00:26:37,520 --> 00:26:41,020
+بقول إن لما يكون هناك isomorphism بين الـ two
+
+274
+00:26:41,020 --> 00:26:46,580
+graphs، معناته لازم يكون نفس عدد النقاء، نفس عدد
+
+275
+00:26:46,580 --> 00:26:53,740
+الجسور، و نفس ال degree sequence، عكسها يعني if G1
+
+276
+00:26:53,740 --> 00:26:56,520
+isomorphic to G2، then هدول
+
+277
+00:26:59,980 --> 00:27:04,340
+لو اتبعتها اذا كانت هدولة غير متوفرات او واحدة
+
+278
+00:27:04,340 --> 00:27:07,980
+منهم فالس معاكم مافيش isomorphism اللي هو انا قلت
+
+279
+00:27:07,980 --> 00:27:12,040
+الكلام قبل ما .. عشان هيك انتبه للرسم كويس انه بكل
+
+280
+00:27:12,040 --> 00:27:15,840
+بساطة هو ممكن تجيك السؤال هل في طابق بين الرسم ال
+
+281
+00:27:15,840 --> 00:27:20,900
+graph a و graph 2؟ if yes اديني ال function give
+
+282
+00:27:20,900 --> 00:27:25,360
+me the objective function عشان هيك بلاك تنتبه
+
+283
+00:27:25,360 --> 00:27:30,520
+وتقول نعم او لا و ليشالان فينا مجموعة من التعريفات
+
+284
+00:27:30,520 --> 00:27:34,640
+البسيطة والجميلة كذلك في موضوع ال graphs .. في
+
+285
+00:27:34,640 --> 00:27:38,740
+موضوع ال graphs دي جاي عن رمضان اه؟ كل عام تبخير
+
+286
+00:27:38,740 --> 00:27:45,820
+هيفنوس رمضان طيب الان في عند التلات مصطلحات لو انا
+
+287
+00:27:45,820 --> 00:27:50,680
+بدأ ترجمهم ترجمة حرفية كلهم هتيجي نفس المعنى walk
+
+288
+00:27:50,680 --> 00:27:56,180
+و trail و path walk و trail و path اللي هي بمعنى
+
+289
+00:27:56,180 --> 00:28:00,480
+ممر او مسارأنا مابديش أترجمهم بالعربي لإن حاجز
+
+290
+00:28:00,480 --> 00:28:03,980
+اترجمهم بالعربي هنحتفظ بقاشي بالترجم بالمصطلح
+
+291
+00:28:03,980 --> 00:28:09,470
+الانجليزي لإنه فيه فرق بين كل واحد والتانيالـ Walk
+
+292
+00:28:09,470 --> 00:28:14,070
+الـ Walk هو عبارة عن Alternating Sequence of
+
+293
+00:28:14,070 --> 00:28:21,330
+Vertices and Edges هي عبارة عن Sequence من النقاط
+
+294
+00:28:21,330 --> 00:28:26,550
+والمثول شو يعني؟ يعني كل نقطة مع النقطة اللي
+
+295
+00:28:26,550 --> 00:28:31,830
+بعديها في بينهم إياش جسر باجي على الرسمة هذه بقول
+
+296
+00:28:31,830 --> 00:28:43,540
+A D B C A DB C هذا walk مسار الآن هو عبارة عن
+
+297
+00:28:43,540 --> 00:28:48,820
+مجموعة من اللقاءات تمام وبين كل قطين فيه ايش؟ فيه
+
+298
+00:28:48,820 --> 00:28:55,140
+جسر هذا walk is a walk لكن
+
+299
+00:28:55,140 --> 00:29:01,660
+تخيل A C E F is not a walk
+
+300
+00:29:05,400 --> 00:29:08,380
+على الرغم من أن النقاط الموجودة موجودة على الـ
+
+301
+00:29:08,380 --> 00:29:12,360
+Graph اللي يبقى بين الـ A والـ C مافيش جسر
+
+302
+00:29:12,360 --> 00:29:19,240
+وبالتالي هذا مش مسار يعني الآن لما بيتفتح خريطة
+
+303
+00:29:19,240 --> 00:29:27,280
+جوجل ماب أو أي خريطة بينفعش يحطلك خطعشان اقولك
+
+304
+00:29:27,280 --> 00:29:31,740
+تنتقل من A ل B او من A ل X لازم تمر مجموعة من
+
+305
+00:29:31,740 --> 00:29:35,480
+النقاط النقاط هذه لازم تكون متصلة مصبوط او لا؟ هذا
+
+306
+00:29:35,480 --> 00:29:38,920
+اللي احنا بنسميه ال walk هذا بنسميه بالمصطلح
+
+307
+00:29:38,920 --> 00:29:44,480
+البسيط ال walk يعني
+
+308
+00:29:44,480 --> 00:29:50,780
+بين جثين في ال walk اي نقطتين لازم يكون متجاورات
+
+309
+00:29:50,780 --> 00:29:55,010
+ايش يعني مفهوم التجاور انه في بينهم جسرفي بينهم
+
+310
+00:29:55,010 --> 00:29:58,950
+جسر مش جانب بعض انه في بينهم جسر والجسرين
+
+311
+00:29:58,950 --> 00:30:06,170
+المتجاورين بينهم نقطة يعني هيك اللي احنا كتبنا A D
+
+312
+00:30:06,170 --> 00:30:14,800
+Bمصبوط و بعدين C الان AD adjacent vertices لأن في
+
+313
+00:30:14,800 --> 00:30:20,560
+بينهم جسر مصبوط و DB adjacent vertices الان
+
+314
+00:30:20,560 --> 00:30:27,620
+الجسرين AD و BB adjacent X بالكتير يفلقها D تمام
+
+315
+00:30:27,620 --> 00:30:33,760
+مية ميةخلّصنا من ال walk و ننتقل للمصطلح اللي بعده
+
+316
+00:30:33,760 --> 00:30:38,620
+الآن ال walk له مسار و المسار يقاس بعدد الجسور
+
+317
+00:30:38,620 --> 00:30:44,080
+اللي موجودة في ال walk هذا ال walk هذا اللي live
+
+318
+00:30:44,080 --> 00:30:51,100
+اللي طول و طول يقاس بعدد الجسور اللي موجودة ايه دي
+
+319
+00:30:51,100 --> 00:30:59,840
+بي سي مصبوط walkهنجسر فيه واحد اتنين تلاتة دائما
+
+320
+00:30:59,840 --> 00:31:05,440
+عدد ال vertices نقص واحد عدد ال vertices نقص واحد
+
+321
+00:31:05,440 --> 00:31:15,100
+طيب بد الطول تبقى a c d b جدش قوله ايوة هو احتجاز
+
+322
+00:31:15,100 --> 00:31:18,480
+في المطبخ هذا is not a walk مش walk معناته مقدرش
+
+323
+00:31:18,480 --> 00:31:19,460
+اتكلم على قوله
+
+324
+00:31:25,170 --> 00:31:29,570
+الـ Walk دا ممكن يكون Closed ايش يعني Closed؟ مغلق
+
+325
+00:31:29,570 --> 00:31:40,310
+يعني نقطة البداية هي نفسها نقطة النهاية A B C D A
+
+326
+00:31:40,310 --> 00:31:45,830
+Closed Walk Closed Walk لما اصطلح ليه Closed انه
+
+327
+00:31:45,830 --> 00:31:50,550
+نقطة البداية هي نفسها نقطة النهاية بس بقت حافظ ان
+
+328
+00:31:50,550 --> 00:31:54,770
+يبقى الـ Walk يعني بينفعش اروح اقفزيعني هيك مافيه
+
+329
+00:31:54,770 --> 00:32:01,830
+عروح اقفز اقوله a b c a هي a b c a is a closed
+
+330
+00:32:01,830 --> 00:32:07,230
+walk خالص غلط لإنه مش walk أساسا عشان نتكلم عن انه
+
+331
+00:32:07,230 --> 00:32:14,130
+closed طبعا
+
+332
+00:32:14,130 --> 00:32:17,690
+لما بيكونش closed بيكون open تمام المصطلح فيش في
+
+333
+00:32:17,690 --> 00:32:23,580
+الجديد لأن انتبهانتبه، في عنده مصطلح جديد بنفس
+
+334
+00:32:23,580 --> 00:32:30,200
+معنى كلمة walk بالحرف طب هو ال trail ممر مشاء أو
+
+335
+00:32:30,200 --> 00:32:35,940
+مسار برضه ال trail هو عبارة عن walk لكن كل الجسور
+
+336
+00:32:35,940 --> 00:32:43,760
+اللي فيه جسور مختلفة ولا مرة بتمشي على الجسر مرتين
+
+337
+00:32:43,760 --> 00:32:49,260
+يعني أوريك شغلة بريق واحد okay لأ تعالى شوف أوريك
+
+338
+00:32:49,260 --> 00:32:53,730
+الشغلةالان لو انا جيت كتبت .. ماعرف ماكتبها تكتب
+
+339
+00:32:53,730 --> 00:33:03,650
+تاني ليش؟ الان a b c d a walk مظبوط؟ لإن في جثور
+
+340
+00:33:03,650 --> 00:33:06,790
+ما بين كل ال vertices اللي عندي هنا closed walk
+
+341
+00:33:06,790 --> 00:33:16,970
+مية لميةTrail لماذا؟ لأن A,B لا تتكرر أبداً B,C لا
+
+342
+00:33:16,970 --> 00:33:20,290
+تتكرر أبداً C,D لا تتكرر أبداً D,A لا تتكرر أبداً،
+
+343
+00:33:20,290 --> 00:33:24,930
+لا يوجد جسر يتكرر أبداً فهذا بيرتقى لمرتبة Trail
+
+344
+00:33:24,930 --> 00:33:31,270
+فكل Trail هو عبارة عن و لكن الجسور اللي فيه مختلفة
+
+345
+00:33:31,270 --> 00:33:37,590
+تعالى نشوف هذا A,B,C,D,A,D
+
+346
+00:33:40,930 --> 00:33:49,650
+في تكرار هذا walk لكن هو not a trail، أصبت؟ ليش؟
+
+347
+00:33:49,650 --> 00:33:53,470
+الآن لو انت فحصت كل النقاط اللي موجودة متجاورة و
+
+348
+00:33:53,470 --> 00:33:59,650
+كل الجسور اللي موجودة متجاورة لكن التكرار ال a دي
+
+349
+00:33:59,650 --> 00:34:02,150
+بيبقى هناك و لا فيه ندياش؟ مشكلة
+
+350
+00:34:06,230 --> 00:34:20,250
+الان a b b c a b c e f c b لاحظ بي سي هي نفسها، بي
+
+351
+00:34:20,250 --> 00:34:22,310
+سي هي نفسها، بي سي هي نفسها، بي سي هي نفسها، بي سي
+
+352
+00:34:22,310 --> 00:34:22,330
+هي نفسها، بي سي هي نفسها، بي سي هي نفسها، بي سي هي
+
+353
+00:34:22,330 --> 00:34:22,390
+نفسها، بي سي هي نفسها، بي سي هي نفسها، بي سي هي
+
+354
+00:34:22,390 --> 00:34:22,890
+نفسها، بي سي هي نفسها، بي سي هي نفسها، بي سي هي
+
+355
+00:34:22,890 --> 00:34:23,450
+نفسها، بي سي هي نفسها، بي سي هي نفسها، بي سي هي
+
+356
+00:34:23,450 --> 00:34:23,870
+نفسها، بي سي هي نفسها، بي سي هي نفسها، بي سي هي
+
+357
+00:34:23,870 --> 00:34:29,950
+نفسها، بي سي هي نفسها، بي سي هي نفسها،
+
+358
+00:34:29,950 --> 00:34:35,020
+بي سي هي نفسها، بلأن صار في عندي walk و trail لأن
+
+359
+00:34:35,020 --> 00:34:39,880
+صار في عندي مصطلح جديد اسمه path ال path هو عبارة
+
+360
+00:34:39,880 --> 00:34:46,440
+عن walk كل النقاط اللي فيه مختلفة هو عبارة عن walk
+
+361
+00:34:46,440 --> 00:34:51,660
+كل النقاط اللي فيه مختلفة بينما ال trail كان كل
+
+362
+00:34:51,660 --> 00:34:55,220
+الجسور اللي فيه مختلفة تعالى نشوف المسارات اللي
+
+363
+00:34:55,220 --> 00:34:59,080
+عندي هنا ABCD
+
+364
+00:35:01,560 --> 00:35:08,000
+walk و trail و path تطبق عليه تلت مصطلحات تلت
+
+365
+00:35:08,000 --> 00:35:17,780
+تعريفات الان c b d e walk و trail و path a d c e f
+
+366
+00:35:17,780 --> 00:35:24,200
+c it's not path صار
+
+367
+00:35:24,200 --> 00:35:27,660
+في عندى نقطة مريت عليها انا عايش مرتين
+
+368
+00:35:30,350 --> 00:35:35,270
+walk صح لكنها مش path is not a path الأخيرة ال ..
+
+369
+00:35:35,270 --> 00:35:44,670
+ال .. ال .. ال ..
+
+370
+00:35:44,670 --> 00:35:46,970
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+371
+00:35:46,970 --> 00:35:49,330
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+372
+00:35:49,330 --> 00:35:50,790
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+373
+00:35:50,790 --> 00:35:51,790
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+374
+00:35:51,790 --> 00:35:53,110
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+375
+00:35:57,200 --> 00:36:01,680
+لأنه لازم يبقى ال connection موجود كويسة إنه في
+
+376
+00:36:01,680 --> 00:36:08,940
+ناس مصحصها، فهذه ميزة الحمد لله القال الأخير A B A
+
+377
+00:36:08,940 --> 00:36:20,800
+B C E F C B كمان مرة، لاحظوا؟ ال B و ال C معناته
+
+378
+00:36:20,800 --> 00:36:25,420
+لا هو trail ولا هو path لأنه تكرر الجسر و تكررت ال
+
+379
+00:36:25,420 --> 00:36:26,540
+نقاط اللي موجودة
+
+380
+00:36:30,660 --> 00:36:35,140
+للـ trail بسميه circuit لو كان مغلق الـ trail إيش
+
+381
+00:36:35,140 --> 00:36:40,380
+يعني مغلق؟ بينفي بنفس النقطة بسميه إيش؟ circuit
+
+382
+00:36:40,380 --> 00:36:45,180
+بسميه circuit دكتور بيه و إيه؟ فيه بين الجثر؟ لأ،
+
+383
+00:36:45,180 --> 00:36:47,840
+صح؟ يعني لما قلنا هاي خلمة أنت ساعدت ابنك قبل
+
+384
+00:36:47,840 --> 00:36:52,960
+شويهان مباشر لأ لازم يمر بـC مجهدنا ينبهن عليها
+
+385
+00:36:52,960 --> 00:36:57,300
+زميلك و جوهاش اسمه و عدلناها هو قلنا لازم أشطبها
+
+386
+00:36:57,300 --> 00:37:02,950
+خليني أشطبها من الـA عشان أنا إيشماانساهاش كمان ال
+
+387
+00:37:02,950 --> 00:37:10,990
+slide اللى جابل D
+
+388
+00:37:10,990 --> 00:37:19,910
+بديش ارجع باتجاه ال C A حط ال A مش مشكلة I shift
+
+389
+00:37:19,910 --> 00:37:29,770
+الخمسة كلام الآن بنقول المسار هذاالـ Trail ممكن
+
+390
+00:37:29,770 --> 00:37:34,810
+يسميه circuit لو كانه closed walk لو كان closed ال
+
+391
+00:37:34,810 --> 00:37:38,710
+trail بقول عنه إيش؟ circuit إيش عن closed؟ نقطة
+
+392
+00:37:38,710 --> 00:37:42,230
+البداية هي نفس نقطة النهاية و ال trail إنه مقع
+
+393
+00:37:42,230 --> 00:37:46,610
+الجسور الجوية و مافيها تكرار في عندي مصطلح تاني
+
+394
+00:37:46,610 --> 00:37:52,530
+بسميه cycle وهذا حالة خاصة .. حالة خاصة مع مين؟ مع
+
+395
+00:37:52,530 --> 00:37:56,510
+المسار ال pathلأن الباق ايش تعريفه شباب ان هو
+
+396
+00:37:56,510 --> 00:38:02,430
+عبارة عن و كل النقاط اللي فيه مختلفة طب لو كانت
+
+397
+00:38:02,430 --> 00:38:10,170
+النقطة البداية هي نفسها نقطة النهاية يعني A B C D
+
+398
+00:38:10,170 --> 00:38:18,390
+A لو انا تجاهلت النقطة الأخيرة هو عبارة عن باث
+
+399
+00:38:18,390 --> 00:38:23,210
+مصدر ولا لأ و بما أن نقطة البداية هي نقطة النهاية
+
+400
+00:38:25,140 --> 00:38:30,380
+فهو closed walk صح؟ الان لو closed walk هذا او بين
+
+401
+00:38:30,380 --> 00:38:35,780
+جثين خلاص خلنا نسميه لو كان في عندى path ونقطة
+
+402
+00:38:35,780 --> 00:38:41,300
+النهاية هي نفس نقطة البداية بالضبط هو هيكون closed
+
+403
+00:38:41,300 --> 00:38:47,040
+tree حتما هذا بدي اسميه cycle ليش؟ لأنه فعليا
+
+404
+00:38:47,040 --> 00:38:51,960
+المسار هدا ماخد صفة ال path مع ده النقطة الأخيرة
+
+405
+00:38:51,960 --> 00:38:58,410
+فسمونها ايش؟ساموليه Cycle تعالى نشوف على السريع
+
+406
+00:38:58,410 --> 00:39:03,290
+بدي اخد هذا مثال المفروض تكمله انت لوحدك كله بس
+
+407
+00:39:03,290 --> 00:39:09,190
+بدي اخد منه على سبيل المثال الرسمي هاي ايش مقولي F
+
+408
+00:39:09,190 --> 00:39:27,180
+G C B A E F G C B A Eهل هو closed؟ لأ طبعا walk
+
+409
+00:39:27,180 --> 00:39:32,220
+مصبوط لأنه كان ماشي على الجسور كل هاتها موجودة هل
+
+410
+00:39:32,220 --> 00:39:39,320
+هو closed؟ لأ trail كل الجسور اللي فيه مختلفة فهو
+
+411
+00:39:39,320 --> 00:39:47,980
+trail هل هو bad؟ النقاط اللي فيه كلها مختلفة فهو
+
+412
+00:39:47,980 --> 00:39:53,620
+badهل هو circuit؟ لأ لأنه مش closed وبالتالي مش
+
+413
+00:39:53,620 --> 00:39:59,380
+cycle لأنه open، مظبوط ولا لا؟ عليك بيبدأك تشتغل
+
+414
+00:39:59,380 --> 00:40:05,340
+الان في المفهوم الان cycle هو المفروض اللي بيتكلم
+
+415
+00:40:05,340 --> 00:40:10,840
+على عدد مرات الدوران اللي موجودة عندها، الآن في ال
+
+416
+00:40:10,840 --> 00:40:16,600
+graph one أي واحد فيهم بيحقق تمام؟
+
+417
+00:40:18,910 --> 00:40:27,190
+Euler circuit Euler circuit يعني
+
+418
+00:40:27,190 --> 00:40:32,870
+لازم يكون مغلق و امر في كل النقاط اللي موجودة او
+
+419
+00:40:32,870 --> 00:40:42,850
+كل الجثور اللي موجودة عندي G1 A C
+
+420
+00:40:42,850 --> 00:40:45,810
+D من ال E يبدو حضر
+
+421
+00:41:11,170 --> 00:41:12,570
+EEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCED
+
+422
+00:41:21,030 --> 00:41:30,290
+مظبوط؟ circuit او
+
+423
+00:41:30,290 --> 00:41:35,670
+لا ال circuit اللي بعده a
+
+424
+00:41:35,670 --> 00:41:44,990
+,b,c مش مجال طالما انك سوف تروح ادخل على منطقة
+
+425
+00:41:44,990 --> 00:41:52,030
+تانية ايوة مش زرقالفكرة كمان مرة يا شباب ال
+
+426
+00:41:52,030 --> 00:41:55,850
+circuit closed ال trail مش لازم ترجع على الجسر مرة
+
+427
+00:41:55,850 --> 00:41:59,790
+تانية ممكن تمر بر مخضع مافي مشكلة عندك طيب مرة
+
+428
+00:41:59,790 --> 00:42:08,150
+تانية A D C D الآن اذا انا بدي ارجع هلال A صارت
+
+429
+00:42:08,150 --> 00:42:12,270
+closed trail صارت circle لكنها مش Euler فانا
+
+430
+00:42:12,270 --> 00:42:17,250
+ماتجمعكش من ال up اللي موجودة عندي هان طيب تعالى
+
+431
+00:42:17,250 --> 00:42:24,450
+نفكر فيها زي ما فكرنا بهك هل في مجالA,B
+
+432
+00:42:24,450 --> 00:42:35,590
+,A,E,C,D وبدى ارجع تانى هناك لأ و الأخيرة بقى
+
+433
+00:42:35,590 --> 00:42:37,270
+تهيألك Her
+
+434
+00:42:47,880 --> 00:42:51,080
+الان طالما ان في عندك وطر هتحسه في الرسم المرسوم
+
+435
+00:42:51,080 --> 00:42:54,980
+غالبا انت مش هتقدر تاش اللي هتمره على جسر من
+
+436
+00:42:54,980 --> 00:42:58,180
+الجسرين او من الجسرها دي مرتين عشان تحقق خاصية
+
+437
+00:42:58,180 --> 00:43:02,260
+take closed تعالى نشوف هيك اقولك تخيل ان الوطر هذا
+
+438
+00:43:02,260 --> 00:43:06,180
+مش موجود تخيل
+
+439
+00:43:06,180 --> 00:43:13,740
+ان الوطر هذا مش موجود كيف انت حلت ايوة دي
+
+440
+00:43:17,380 --> 00:43:33,740
+C,A,B,C,A,B,C,A,B,C,A,B,C,A,B,C,A,B,C,A,B,C,A,B,C
+
+441
+00:43:33,740 --> 00:43:41,360
+,A,B,C,A,B,C,A,B,C,A,B,C,A,B,C,A,B,C,A,B,C,A,B,C,A
+
+442
+00:43:41,360 --> 00:43:44,940
+,B,C,A,B,C,A,B,C,A,B,C,A,B,C,A,B,C,A,B,C,A,B,C,A,B
+
+443
+00:43:44,940 --> 00:43:49,280
+,A,B,C,A,B,C,A,B,C,A,B,C,طبعا بيحتوي على مسار
+
+444
+00:43:49,280 --> 00:43:55,040
+بيجمع كل النقاط، مسار بيجمع كل النقاط من غير تكرار
+
+445
+00:43:55,040 --> 00:43:58,560
+للنقاط أكيد لأنه في الآخر بدك تحققك على ال public
+
+446
+00:43:58,560 --> 00:44:04,980
+على الاسم ال path طيب تعالى أقبلها فيك كتبلي مسار
+
+447
+00:44:04,980 --> 00:44:07,260
+بدون أنك تكرر فيه النقطة
+
+448
+00:44:16,630 --> 00:44:27,470
+الأول نقدر مرة نجيب مصار بيجمع كل المقاط A B E C D
+
+449
+00:44:27,470 --> 00:44:34,930
+اخر مرة A B E C D او A B E احفظ A B E C D او A B E
+
+450
+00:44:34,930 --> 00:44:40,090
+احفظ A B E C D
+
+451
+00:44:40,090 --> 00:44:44,390
+او A B E A B E احفظ A B E C D او A B E A B E A B E
+
+452
+00:44:44,390 --> 00:44:44,430
+B E A B E A B E A B E A B E A B E A B E A B E A B
+
+453
+00:44:44,430 --> 00:44:49,270
+E A B E Aهيو باذ او الفكرة وين ان مسار بيحتوي على
+
+454
+00:44:49,270 --> 00:44:54,170
+كل النقاط اللي في الرسمة بيحتوي على كل النقاط اللي
+
+455
+00:44:54,170 --> 00:45:00,030
+في الرسمة عشان يحافظ على باذ هيو باذ كل النقاط في
+
+456
+00:45:00,030 --> 00:45:04,090
+بينها جسور ونقاط مختلفة منها تهدأ أولا باذ تعالى
+
+457
+00:45:04,090 --> 00:45:08,370
+نشوفه التانية G2ABC
+
+458
+00:45:13,230 --> 00:45:19,110
+لأنه واصل مقاهة ما اتكلمش على الجسور الاخير نفس
+
+459
+00:45:19,110 --> 00:45:26,590
+الحاجة LAC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC
+
+460
+00:45:26,590 --> 00:45:26,970
+ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC
+
+461
+00:45:26,970 --> 00:45:27,990
+ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC
+
+462
+00:45:27,990 --> 00:45:28,430
+ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC
+
+463
+00:45:28,430 --> 00:45:28,470
+ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC
+
+464
+00:45:28,470 --> 00:45:28,490
+ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC
+
+465
+00:45:28,490 --> 00:45:30,790
+ABC BC ABC ABC ABC BC ABC BC ABC ABC ABC ABC ABC
+
+466
+00:45:30,790 --> 00:45:31,310
+ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC
+
+467
+00:45:31,310 --> 00:45:36,810
+ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC
+
+468
+00:45:44,180 --> 00:45:47,640
+خلاص بناقش هكلا هكلا يوم محاضرة هادى و بنكمل ان
+
+469
+00:45:47,640 --> 00:45:49,120
+شاء الله المحاضرة الجاية
+
diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/xQty_gvEjms_raw.json b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/xQty_gvEjms_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..8d2da9be4e5bc4269190274cdf5f08dfb23a32c3
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/xQty_gvEjms_raw.json
@@ -0,0 +1 @@
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"text": "G1 يعني انا بدي اقول Phi of النقاب اللي هنا U و W V و X هاي عناصر الدمية شو بيدها تساوي ال function هذه ال A", "tokens": [38, 16, 37495, 22653, 1975, 8315, 4724, 16254, 1975, 39648, 41435, 295, 28239, 4587, 16758, 13672, 1829, 34105, 624, 4032, 343, 691, 4032, 1783, 8032, 47302, 18871, 33546, 2288, 32748, 2304, 10632, 13412, 2407, 4724, 25708, 11296, 6055, 3794, 995, 45865, 2423, 2445, 29538, 2423, 316], "avg_logprob": -0.4381648948852052, "compression_ratio": 1.2686567164179106, "no_speech_prob": 0.0, "words": [{"start": 895.77, "end": 896.43, "word": "G1", "probability": 0.38427734375}, {"start": 896.43, "end": 896.67, "word": " يعني", "probability": 0.765625}, {"start": 896.67, "end": 896.83, "word": " انا", "probability": 0.73828125}, {"start": 896.83, "end": 897.05, "word": " بدي", "probability": 0.4796142578125}, {"start": 897.05, "end": 897.37, "word": " اقول", "probability": 0.8974609375}, {"start": 897.37, "end": 898.25, "word": " Phi", "probability": 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اللي هي X Y .. اه مافيش .. 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و CV وبالتالي موجود بحيث ان انا بقول جي واحد is isomorphic مقابل دائمة", "tokens": [6027, 7649, 9114, 1783, 691, 1783, 691, 3714, 29245, 23328, 22807, 3714, 29245, 23328, 1975, 34740, 10874, 38251, 624, 4724, 1211, 39896, 363, 4032, 22995, 46599, 6027, 2655, 6027, 1829, 3714, 29245, 23328, 4724, 5016, 1829, 12984, 16472, 1975, 8315, 4724, 39648, 10874, 1829, 36764, 24401, 307, 307, 32702, 299, 3714, 4587, 16758, 1211, 11778, 16373, 46007], "avg_logprob": -0.3615301698446274, "compression_ratio": 1.3805970149253732, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1546.32, "end": 1546.78, "word": "الان", "probability": 0.6414794921875}, {"start": 1546.78, "end": 1547.4, "word": " DC", "probability": 0.60107421875}, {"start": 1547.4, "end": 1550.04, "word": " X", "probability": 0.343994140625}, {"start": 1550.04, "end": 1551.12, "word": " V", "probability": 0.62353515625}, {"start": 1551.12, "end": 1551.52, "word": " X", "probability": 0.3427734375}, {"start": 1551.52, "end": 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كثير عشان تتحلل الرسمين و تتبقوا مع بعض", "tokens": [6027, 10721, 29973, 21136, 3224, 1211, 14739, 4117, 6055, 8592, 17082, 11703, 1211, 8978, 11778, 2304, 5718, 118, 4117, 12602, 9381, 25708, 9122, 12984, 13546, 6225, 8592, 7649, 6055, 2655, 5016, 1211, 1211, 34892, 38251, 9957, 4032, 6055, 2655, 3555, 4587, 14407, 20449, 45030, 11242], "avg_logprob": -0.5203804438528807, "compression_ratio": 1.3203883495145632, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1575.3100000000002, "end": 1576.39, "word": "الأمر", "probability": 0.40704345703125}, {"start": 1576.39, "end": 1577.47, "word": " السهل", "probability": 0.9168294270833334}, {"start": 1577.47, "end": 1578.11, "word": " أنك", "probability": 0.32080078125}, {"start": 1578.11, "end": 1578.87, "word": " تشغّل", "probability": 0.766796875}, {"start": 1578.87, "end": 1578.95, "word": " في", "probability": 0.095947265625}, {"start": 1578.95, "end": 1579.45, "word": " دماغك", "probability": 0.92578125}, {"start": 1579.45, 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1.4395604395604396, "no_speech_prob": 2.384185791015625e-07, "words": [{"start": 2744.1800000000003, "end": 2744.9, "word": "خلاص", "probability": 0.812744140625}, {"start": 2744.9, "end": 2745.16, "word": " بناقش", "probability": 0.384857177734375}, {"start": 2745.16, "end": 2745.52, "word": " هكلا", "probability": 0.3024088541666667}, {"start": 2745.52, "end": 2745.78, "word": " هكلا", "probability": 0.89404296875}, {"start": 2745.78, "end": 2745.94, "word": " يوم", "probability": 0.6209716796875}, {"start": 2745.94, "end": 2746.3, "word": " محاضرة", "probability": 0.928955078125}, {"start": 2746.3, "end": 2746.72, "word": " هادى", "probability": 0.655517578125}, {"start": 2746.72, "end": 2747.14, "word": " و", "probability": 0.72265625}, {"start": 2747.14, "end": 2747.54, "word": " بنكمل", "probability": 0.814697265625}, {"start": 2747.54, "end": 2747.64, "word": " ان", "probability": 0.63623046875}, {"start": 2747.64, "end": 2747.82, "word": " شاء", "probability": 0.9814453125}, 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/xQty_gvEjms_raw.srt b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/xQty_gvEjms_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..f8149564ea95c83f0718abf9fdaf2b258f9b1555
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/xQty_gvEjms_raw.srt
@@ -0,0 +1,1952 @@
+1
+00:00:20,770 --> 00:00:22,590
+بسم الله والحمد لله والصلاة والسلام علي الرسول
+
+2
+00:00:22,590 --> 00:00:25,450
+الله اليوم ان شاء الله شباب هنكمل في chapter لل
+
+3
+00:00:25,450 --> 00:00:30,150
+graphs او graph theory خلينا نراجع بشكل سريع
+
+4
+00:00:30,150 --> 00:00:34,780
+نخططنا المحاضرة الماضية خصوصا انه قلنا أسبوعبعيد
+
+5
+00:00:34,780 --> 00:00:39,360
+عن المادة اتفقنا ان ال graph هو عبارة عن زوج مرتب
+
+6
+00:00:39,360 --> 00:00:44,500
+من مجموعتين المجموعة الأولى بتمثل مجموعة النقاط ال
+
+7
+00:00:44,500 --> 00:00:48,160
+vertices والمجموعة التانية بتمثل مجموعة الجسور
+
+8
+00:00:48,160 --> 00:00:54,220
+اللي موجودة بين النقاط هاي وقلنا أهم ما يميز ال
+
+9
+00:00:54,220 --> 00:01:01,560
+vertices انها نم MT فعلى الأقل ال graph يساوي زوج
+
+10
+00:01:01,560 --> 00:01:10,050
+مرتبمن vertex one او من one vertex و five هذا أبسط
+
+11
+00:01:10,050 --> 00:01:14,570
+graph ممكن يكون هنا هذا أبسط graph ممكن يكون موجود
+
+12
+00:01:14,570 --> 00:01:20,370
+هنا و لما اتينا نمثل بالرسم حطينا النقطة و كتبنا
+
+13
+00:01:20,370 --> 00:01:27,450
+اسم ال vertex v1 وهذا أبسط graph ممكن يكون موجود
+
+14
+00:01:27,450 --> 00:01:35,880
+معنا وانتقلنا بعد هيكوقلنا ان الجسور هي عبارة عن
+
+15
+00:01:35,880 --> 00:01:42,660
+مجموعة من نقطتين يعني لما انا باجب ارسم او لو انا
+
+16
+00:01:42,660 --> 00:01:51,020
+افترض ان في عندي ال graph هذا يمثل المثلث a,b,c
+
+17
+00:01:51,020 --> 00:01:59,900
+لما بدأت مجموعة ال vertices معروفة a,b,c ومجموعة
+
+18
+00:01:59,900 --> 00:02:13,270
+الجسوربكتبها AB BC و AC كمجموعة تانية وهنا دلالة
+
+19
+00:02:13,270 --> 00:02:16,910
+على ان مافيش عندي اتجاه مابحتمش للاتجاه انا سواء
+
+20
+00:02:16,910 --> 00:02:23,090
+كانت AB هي نفسها ب A وهنا بتكلم على اليسار وقولنا
+
+21
+00:02:23,090 --> 00:02:29,440
+هنا يا شباب انه انا بتكلم على اليسار ABمجاور للجسر
+
+22
+00:02:29,440 --> 00:02:35,120
+AC لأنهم مشتركوا في نفس النقطة وقولت كذلك A وC
+
+23
+00:02:35,120 --> 00:02:43,320
+كنقات متجاورات لأنه في بينهم جسر وبعد
+
+24
+00:02:43,320 --> 00:02:50,440
+ذلك انتقلنا لشيء سمناها الدرجة رتبة النقطة ال
+
+25
+00:02:50,440 --> 00:02:55,730
+degree للنقطة ايش ال degree؟الـ degree للنقطة هي
+
+26
+00:02:55,730 --> 00:03:01,810
+عبارة عن عدد الجسور الواصلة للنقطة هذه عدد الجسور
+
+27
+00:03:01,810 --> 00:03:05,390
+الواصلة للنقطة اللي موجودة عندنا هنا يعني ال
+
+28
+00:03:05,390 --> 00:03:10,430
+degree لل a اتنين و ال degree لل c اتنين و ال
+
+29
+00:03:10,430 --> 00:03:14,030
+degree لل b اتنين و قلنا في عنا شغل اسمها ال
+
+30
+00:03:14,030 --> 00:03:17,450
+pseudocode او اعفر ان ال pseudograph لما بكون انا
+
+31
+00:03:17,450 --> 00:03:24,600
+في عندي loopوقلنا اللوب نحسبها تنقل وبتصير الرطبة
+
+32
+00:03:24,600 --> 00:03:29,220
+لل CND أربعة
+
+33
+00:03:29,220 --> 00:03:32,960
+طيب
+
+34
+00:03:32,960 --> 00:03:37,180
+وإذا كان في عندي vertex زي V تلاتها وقلنا عنه
+
+35
+00:03:37,180 --> 00:03:41,620
+isolated vertex أو isolated point نقمة معزولة ال
+
+36
+00:03:41,620 --> 00:03:45,040
+degree تبعتها جد الشباب صفر عنها مش مقتصر ولا
+
+37
+00:03:45,040 --> 00:03:46,140
+إبجسر
+
+38
+00:03:48,220 --> 00:03:51,660
+وانتقل بعد ذلك لموضوع ال sub graph وقلنا في ال sub
+
+39
+00:03:51,660 --> 00:03:57,300
+graph بهمني جدا ان انا اكون فاهم ان لو كان في عندي
+
+40
+00:03:57,300 --> 00:04:07,340
+ال G تمثل الزوج المرتب V1 و V2 و V3 ومجموعة الجسور
+
+41
+00:04:07,340 --> 00:04:16,940
+V1 V2 V2V3 V1 V3 اللي هي نفس الرسمة المثلثة اللي
+
+42
+00:04:16,940 --> 00:04:23,360
+كنت رسمها سابقا بس بدل AB V1 و V2 الآن بقدر أقول
+
+43
+00:04:23,360 --> 00:04:33,860
+أنا G1 تساوي V1 و V3 V1
+
+44
+00:04:33,860 --> 00:04:41,470
+V3 كجسور الآن هل G1 صبصت من G2عشان اقول ان جي واحد
+
+45
+00:04:41,470 --> 00:04:46,210
+subset من جي اتنين بيلزم افحص هل مجموعة النقاط
+
+46
+00:04:46,210 --> 00:04:52,190
+مجموعة جزئية من النقاط الرئيسية هل V1 subset من V؟
+
+47
+00:04:52,190 --> 00:04:58,090
+subset هل ال E1 subset من ال E؟ subset إذا كانت ال
+
+48
+00:04:58,090 --> 00:05:01,370
+V subset من V و ال E subset من E معناته جي واحد
+
+49
+00:05:01,370 --> 00:05:08,480
+subset من G وهنا الجي واحد subset من الجيولا
+
+50
+00:05:08,480 --> 00:05:13,360
+تتجاهل الرسمة ولا حجمها ولا أي حاجة يعني هذا
+
+51
+00:05:13,360 --> 00:05:21,020
+الرسمة شايفين احنا V2 V5 مظبوط؟ لو انا رسمت هيك V2
+
+52
+00:05:21,020 --> 00:05:30,480
+V5 هي نفسها subset ولا اشي تغير لو رسمت هيك V2
+
+53
+00:05:30,480 --> 00:05:35,150
+V5هذه خمسة لأن الطول ليس معيارا لدي ولا direction
+
+54
+00:05:35,150 --> 00:05:41,430
+وبالتالي كل اللي بهمه هي مجموعة الجسور ومجموعة
+
+55
+00:05:41,430 --> 00:05:48,510
+النقاط ومجموعة الجسور وانتقلنا بعدها لشيء سمناه ال
+
+56
+00:05:48,510 --> 00:05:53,550
+complete graph قلنا ان ال complete graph هو عبارة
+
+57
+00:05:53,550 --> 00:05:59,490
+عن ال graphكل نقطة فيه كل vertex فيه متصلة مع كل
+
+58
+00:05:59,490 --> 00:06:04,490
+النقاط الأخرى الموجودة في ال graph وكل هذا
+
+59
+00:06:04,490 --> 00:06:12,970
+complete graph تلاتة رمزنا
+
+60
+00:06:12,970 --> 00:06:18,450
+له K تلاتة تلاتة على كناية عن عدد النقاط و K
+
+61
+00:06:18,450 --> 00:06:22,410
+اختصارا complete الآن
+
+62
+00:06:24,280 --> 00:06:29,280
+كل جسر كل نقطة موجودة فيها متصلة مع كل المقابل
+
+63
+00:06:29,280 --> 00:06:38,240
+التالية، وإذا كنت تتكلم عن K4، فهي كذلك، كمان كمان
+
+64
+00:06:38,240 --> 00:06:40,620
+كمان كمان كمان كمان كمان كمان كمان كمان كمان كمان
+
+65
+00:06:40,620 --> 00:06:40,620
+كمان كمان كمان كمان كمان كمان كمان كمان كمان كمان
+
+66
+00:06:40,620 --> 00:06:40,900
+كمان كمان كمان كمان كمان كمان كمان كمان كمان كمان
+
+67
+00:06:40,900 --> 00:06:42,280
+كمان كمان كمان كمان كمان كمان كمان كمان كمان كمان
+
+68
+00:06:42,280 --> 00:06:42,300
+كمان كمان كمان كمان كمان كمان كمان كمان كمان كمان
+
+69
+00:06:42,300 --> 00:06:48,440
+كمان كمان كمان كمان كمان كمان كمان
+
+70
+00:06:49,370 --> 00:06:53,790
+عدد النقاط نقص واحد لإيش؟ لأنه فعلا هو كل نقطة
+
+71
+00:06:53,790 --> 00:06:57,510
+متصلة مع كل النقاط المقابلة أي باقية عندك في ال
+
+72
+00:06:57,510 --> 00:07:01,410
+graph و هو أربعة و متصل مع الباقية كلهم معاكم مع
+
+73
+00:07:01,410 --> 00:07:05,230
+تلاتة إذا هو تلاتة متصل مع اتنين و لو كان اتنين
+
+74
+00:07:05,230 --> 00:07:13,570
+واحد و هكذا و قلنا أبسط complete graph نقطة واحد
+
+75
+00:07:13,570 --> 00:07:19,250
+isolated point oneوانتقل بعدها لشيء صميناه الـ
+
+76
+00:07:19,250 --> 00:07:23,310
+Bipartite Graph وقلنا الـ Bipartite Graph هو عبارة
+
+77
+00:07:23,310 --> 00:07:30,670
+هانيغراف انا بروح بأجسم النقاط اللي فيه لمجموعتين
+
+78
+00:07:30,670 --> 00:07:36,890
+مختلفتين الان لو انا اخترت هذا ال graph سميناه A B
+
+79
+00:07:36,890 --> 00:07:40,830
+C D E الان V
+
+80
+00:07:43,690 --> 00:07:49,670
+A,B,C,D,E هاي الخمس نقاط اللي موجودة عندي هان بقول
+
+81
+00:07:49,670 --> 00:07:54,130
+عن هذا الـ Bipartite Graph لو أقدرت أسوي التاني
+
+82
+00:07:54,130 --> 00:07:59,430
+أجسم الـ V هذه لمجموعتين disjoint التقنعة بينهم
+
+83
+00:07:59,430 --> 00:08:04,770
+five بحيث إنه ال connection أو اليسور فقط بتكون
+
+84
+00:08:04,770 --> 00:08:08,330
+بين عناصر المجموعتين يعني عناصر المجموعة الواحدة
+
+85
+00:08:08,330 --> 00:08:11,710
+مافيش بينهم connection معناته أنا بقدر قاعدي أقول
+
+86
+00:08:11,710 --> 00:08:25,410
+هذه V واحدتساوي هذه واحدة وهذه الثانية D او B وD و
+
+87
+00:08:25,410 --> 00:08:34,840
+V2 تساوي A C وE التقابل بينهم فاية ولا لا؟وفي نفس
+
+88
+00:08:34,840 --> 00:08:40,480
+الوقت مافيش جسر بين B وD ومافيش جسور بين A وC وR
+
+89
+00:08:40,480 --> 00:08:44,540
+وE وC وE، مافيش، يعني على أسر المجموعة الواحدة
+
+90
+00:08:44,540 --> 00:08:48,660
+مافيش بينهم جسور، بس الجسور ممتدة بين المجموعتين،
+
+91
+00:08:48,660 --> 00:08:53,080
+الجسور ممتدة بين المجموعتين، هذا ال graph بسميه
+
+92
+00:08:53,080 --> 00:08:57,860
+bipartate graph، bipartate graph يعني graph مجسوم
+
+93
+00:08:58,580 --> 00:09:02,900
+لجسمين لجزئين و باية يا شباب اختصار ل binary ثنائي
+
+94
+00:09:02,900 --> 00:09:07,380
+باي بارتت و بارتت بارتشن زي ما قلنا سابقا و
+
+95
+00:09:07,380 --> 00:09:13,300
+بالتالي هذا بسميه باي بارتت اجراف هذا باي بارتت
+
+96
+00:09:13,300 --> 00:09:16,320
+اجراف المجموعة الأولى اللى فوق المجموعة التانية
+
+97
+00:09:16,320 --> 00:09:20,120
+المجموعة الأولى المجموعة التانية و هكذا الان ال
+
+98
+00:09:20,120 --> 00:09:24,020
+باي بارتت اجراف ده ممكن انا اسميه completeBy
+
+99
+00:09:24,020 --> 00:09:29,500
+Partity Graph لو كان كل أنصر في المجموعة الأولى
+
+100
+00:09:29,500 --> 00:09:34,240
+متقفل مع كل عناصر المجموعة التانية والعكس صحيح هذا
+
+101
+00:09:34,240 --> 00:09:36,920
+ال graph اللي أنا رسمته ممكن يصير By Partity Graph
+
+102
+00:09:36,920 --> 00:09:43,120
+لو إجيت هنا و حطيت كمان connection هيك كمان هنا
+
+103
+00:09:43,120 --> 00:09:49,900
+connection هيك الان Complete By Partity Graph
+
+104
+00:09:49,900 --> 00:09:54,820
+المرموز له Kلكمplete المجموعة الأولى جداش عنصر
+
+105
+00:09:54,820 --> 00:10:01,880
+فيها اتنين كمه تلاته يعني المجموع تاني كمليت بي
+
+106
+00:10:01,880 --> 00:10:06,280
+budget graph من مجموع تاني اتنين و تلاته الآن لو
+
+107
+00:10:06,280 --> 00:10:10,400
+طلعت لبطبة العراسر في المجموعة الأولى بدها تساوي
+
+108
+00:10:10,400 --> 00:10:17,260
+عدد عناصر المجموعة التانيةيعني روتب الـ B تلاتة
+
+109
+00:10:17,260 --> 00:10:21,840
+بعدد العناصر ليش؟ لأن هو فعليا متصي مع كل عناصر
+
+110
+00:10:21,840 --> 00:10:25,840
+المجموعة التانية و لو أتيت لأي عنصر فيه المجموعة
+
+111
+00:10:25,840 --> 00:10:30,700
+التانية V2 ال degree تبعتها هتكون اتنين اللي هي
+
+112
+00:10:30,700 --> 00:10:34,120
+عدد عناصر المجموعة الأولى المقابلة أو التالتة
+
+113
+00:10:34,120 --> 00:10:36,960
+سامية زي ما بدك مش مشكلة كتير الفكرة وين؟ أنه فيها
+
+114
+00:10:36,960 --> 00:10:39,580
+عنصرين وهذا لازم يكون مرتبط مع كل العناصر في
+
+115
+00:10:39,580 --> 00:10:47,710
+المجموعة التانية تمام وانتقلنا بعدهالشغل صمناها
+
+116
+00:10:47,710 --> 00:10:55,350
+مجموع الـ degrees مجموع الرتب في أي graph مجموع
+
+117
+00:10:55,350 --> 00:11:00,510
+الرتب يساوي summation
+
+118
+00:11:00,510 --> 00:11:08,350
+لل degree لكل
+
+119
+00:11:08,350 --> 00:11:14,730
+ال vertices يساوي ضعف عدد الجسور ضعف عددالجسور
+
+120
+00:11:14,730 --> 00:11:20,090
+فالرسم اللي احنا رسميه لها الان جداش الرطب لل D لل
+
+121
+00:11:20,090 --> 00:11:28,930
+B ثلاثة رطب ال D ثلاثة رطب ال A اتنين C اتنين و ال
+
+122
+00:11:28,930 --> 00:11:34,510
+E اتنين لو جمعنا كل الرطب مع بعض هدول ستة و ستة
+
+123
+00:11:34,510 --> 00:11:42,340
+ماشي مظبوط ماشي هذا تساوم لضعف حدد الجسورو ايه
+
+124
+00:11:42,340 --> 00:11:45,520
+الجسور اللى موجودة عندى؟ هيهم واحد اتنين تلاتة
+
+125
+00:11:45,520 --> 00:11:50,140
+اربعة خمسة ستة ست جسور وبالتالي هذا القانون يطبق
+
+126
+00:11:50,140 --> 00:11:55,780
+على اي graph هذا القانون يطبق على اي graph وسألنا
+
+127
+00:11:55,780 --> 00:12:05,640
+سؤال كنا صادقا كي اربعة كي اربعة جداش عدد الجسور
+
+128
+00:12:05,640 --> 00:12:06,720
+اللى موجودة فيه؟
+
+129
+00:12:13,130 --> 00:12:18,610
+جدّيش هذا الجسور اللي موجودة فيه؟ ايوة .. ايوة
+
+130
+00:12:18,610 --> 00:12:24,490
+اسمع عنكم؟ عريب .. ايش يعني كده الأربعة؟ Complete
+
+131
+00:12:24,490 --> 00:12:30,850
+Graph من أربع نقاط .. أصبت؟ الموضع Complete Graph
+
+132
+00:12:30,850 --> 00:12:35,670
+من أربع نقاط طيب .. شو يعني Complete Graph؟ ان كل
+
+133
+00:12:35,670 --> 00:12:40,270
+نقطة متصلة معك مع جميع النقاط التالية .. أصبت؟
+
+134
+00:12:40,270 --> 00:12:48,210
+يعني رتبة كل واحدة فيهموهما أربعة يعني أن عدد
+
+135
+00:12:48,210 --> 00:12:53,730
+الجثور أو عدد مجموع الرتب للـ vertices يساوي تلاتة
+
+136
+00:12:53,730 --> 00:12:59,910
+أو أربع نقاط كل واحدة فيهم رتبتها تلاتة يساوي
+
+137
+00:12:59,910 --> 00:13:07,010
+اتناشر وهذا يساوي ضعف عدد الجثور يعني أننا نتكلم
+
+138
+00:13:07,010 --> 00:13:13,090
+عن ست جثور موجودة في الرسمة وين هما؟عشان يصيركم
+
+139
+00:13:13,090 --> 00:13:19,310
+جيتي graph يجب أن أضع القطنين بتاعت المربع 6
+
+140
+00:13:19,310 --> 00:13:24,570
+ولا لا؟ وهذا الكلام يتطبق على أي graph .. وشوفنا
+
+141
+00:13:24,570 --> 00:13:29,950
+الأمثلة بشكل .. وهذا تقريبا كان مدخس أو مجمل اللي
+
+142
+00:13:29,950 --> 00:13:33,910
+أخدناه في المحاضرة الماضية يعني هي رجعنا محاضرة
+
+143
+00:13:33,910 --> 00:13:40,800
+بالكامل خلال نص ساعة طيب بعد هيكأتكلمني على شغل أو
+
+144
+00:13:40,800 --> 00:13:48,520
+الـ degree أو الـ isomorphism التقابل
+
+145
+00:13:48,520 --> 00:13:51,320
+بين two graphs الآن لو أنا كان في عندي two graphs
+
+146
+00:13:51,320 --> 00:13:57,280
+هل بقدر أقول عنهم متشابهين و تقابلين أو لأ؟ الآن
+
+147
+00:13:57,280 --> 00:14:05,840
+عشان انا أقول ان G1مطابق للجي اتنين لازم اوجد شغل
+
+148
+00:14:05,840 --> 00:14:10,600
+بيجيكتف function اوجد بيجيكتف function شو يعني
+
+149
+00:14:10,600 --> 00:14:15,860
+بيجيكتف function يا شباب؟ one to one و one to one
+
+150
+00:14:15,860 --> 00:14:18,400
+و one to one و one to one و one to one ال domain
+
+151
+00:14:18,400 --> 00:14:22,760
+تبعت ال function هذي بدها تكون ال vertices تبعت
+
+152
+00:14:22,760 --> 00:14:29,120
+الجراف الأول و ال target set ال verticesتابعك للـ
+
+153
+00:14:29,120 --> 00:14:32,220
+Target أو الـ Graph التاني اللي موجود عندي هو
+
+154
+00:14:32,220 --> 00:14:35,920
+بنموذلها Phi أو Lambda زي ما بدك مافيش مشكلة كتير
+
+155
+00:14:35,920 --> 00:14:38,500
+عندي تعالى نشوف ال Graph البسيط اللي موجود عندنا
+
+156
+00:14:38,500 --> 00:14:47,200
+هل ال Graph هذا G1 يقابق G2 ولا لأ؟ عشان كمان مرة
+
+157
+00:14:47,200 --> 00:14:51,520
+نقول يقابق او لا يقابق بيلزمني اعرف او اوجد
+
+158
+00:14:51,520 --> 00:14:57,050
+Byjective function ال domain تبعتهاG1 يعني انا بدي
+
+159
+00:14:57,050 --> 00:15:12,370
+اقول Phi of النقاب اللي هنا U و W V و X هاي عناصر
+
+160
+00:15:12,370 --> 00:15:17,990
+الدمية شو بيدها تساوي ال function هذه ال
+
+161
+00:15:17,990 --> 00:15:22,960
+Aالمفروض .. المفروض ان الـ vertex هتكون تقاعد و
+
+162
+00:15:22,960 --> 00:15:28,160
+vertex تانية قلنا كمان مرة ال domain تبعتها V1 و
+
+163
+00:15:28,160 --> 00:15:31,480
+ال target set تبعتها V2 تحت الجرافة التانية اللي
+
+164
+00:15:31,480 --> 00:15:35,440
+هم هدول يعني الـ Phi اللي انا بده اعرفها يا شباب
+
+165
+00:15:35,440 --> 00:15:45,280
+بدها تكون من V1 إلى V2 اللي هي X Y .. اه مافيش ..
+
+166
+00:15:45,280 --> 00:15:55,770
+U و Wو V و X الى A,B,C,D
+
+167
+00:15:59,800 --> 00:16:02,740
+كيف بدي اوجد ال value تبعتها عشان اوجد التقابق هذا
+
+168
+00:16:02,740 --> 00:16:06,820
+اولا؟ هل الرسم هذه نفس الرسم هذه؟ طبعا انت تتذكر
+
+169
+00:16:06,820 --> 00:16:09,520
+الكلام اللي قلناه من البداية، فموضوع ال graphs يا
+
+170
+00:16:09,520 --> 00:16:14,260
+شباب ماتدجوش على الشكل يكون كيف شكله، لا بهم نقول
+
+171
+00:16:14,260 --> 00:16:17,480
+ولا direction، لا بهم نقول ال graph ولا شكله ولا
+
+172
+00:16:17,480 --> 00:16:22,490
+ال direction، بهم دائما دائماأبحث عن أشياء أساسية
+
+173
+00:16:22,490 --> 00:16:25,650
+في الرسم هل ال graph هي نفس .. لأ .. العدد النقاط
+
+174
+00:16:25,650 --> 00:16:29,530
+نفس عدد النقاط الجسور نفس عدد الجسور إذا كان هذا
+
+175
+00:16:29,530 --> 00:16:33,390
+الكلام متوفر معناته احتمال كبير جدا أن هذا ال
+
+176
+00:16:33,390 --> 00:16:37,910
+graph يكون مطابق الآن تبقى عليش أشتغل شغل بسيط
+
+177
+00:16:37,910 --> 00:16:44,950
+الآن هذا ال graph تخيل لو أنا جبت ال W هنا إيش
+
+178
+00:16:44,950 --> 00:16:53,510
+يعني أجيب ال W هنا؟ يعني هتصير الرسم هيك100% بيصير
+
+179
+00:16:53,510 --> 00:16:58,990
+واسمة هادي هادي بيصير عندي متوازي أطلع بصير ولا لأ
+
+180
+00:16:58,990 --> 00:17:02,370
+ببصر في التطابق بالمتوازي الأطلع والمربع اللي عندي
+
+181
+00:17:02,370 --> 00:17:09,170
+ببلاش بدي أزده كمان شويه ل هيك عشان أعدله بيصير في
+
+182
+00:17:09,170 --> 00:17:15,410
+تطابق الآن التطابق مفاده أن ال W أصبح تقابلها مين
+
+183
+00:17:15,410 --> 00:17:27,760
+ال A ال V تقابلها Bالـ X تقابلها C و الـ U تقابلها
+
+184
+00:17:28,610 --> 00:17:33,090
+أيه دي؟ هيك أنت أعرفت ال function تبعتك بيجيبتب
+
+185
+00:17:33,090 --> 00:17:38,290
+one-to-one و one-to اعرفت ال function بيجيبتب one
+
+186
+00:17:38,290 --> 00:17:42,750
+-to-one و one-to لكن هل ال function هذه صحيحة أو
+
+187
+00:17:42,750 --> 00:17:47,490
+غير صحيحة بتحكم عليها من خلال فحصك للجسور اللي
+
+188
+00:17:47,490 --> 00:17:51,130
+موجودة في مين في ال graph يعني مين الجسور اللي
+
+189
+00:17:51,130 --> 00:17:57,450
+موجودة عندي هنا شباب تيجي تقولي five of w u
+
+190
+00:18:13,320 --> 00:18:14,720
+وووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووووو
+
+191
+00:18:27,020 --> 00:18:32,740
+ما هو الـ W في مكانها؟ الـ A و الـ U؟ الـ D هل الـ
+
+192
+00:18:32,740 --> 00:18:38,760
+A و الـ D جسر موجود في الرسم الجديد؟ موجود تنتقل
+
+193
+00:18:38,760 --> 00:18:43,440
+خطوة للأعلى؟ one step forward باتجاه الجسر التاني؟
+
+194
+00:18:43,440 --> 00:18:47,600
+الـ W هو A و الـ W هو V و الـ V مكانها بيه هل الـ
+
+195
+00:18:47,600 --> 00:18:55,360
+A و الـ B موجود؟ موجود V X الـ R V X الـ V بولا
+
+196
+00:18:55,360 --> 00:19:03,690
+بيه؟والـ XC DC موجود؟ اه موجود الجسم الأخير UX DC
+
+197
+00:19:03,690 --> 00:19:10,050
+و ال DC موجودإذا الآن الـ Function تبعتي تم
+
+198
+00:19:10,050 --> 00:19:14,190
+تعريفها بشكل صحيح بـ Adjective Function وعملت
+
+199
+00:19:14,190 --> 00:19:18,050
+Mapping حتى ما بين الجثور اللي موجودة قبل في الـ
+
+200
+00:19:18,050 --> 00:19:22,990
+Graph، يعني قد تتمثل كل جثر، توصله للجثر المقابل،
+
+201
+00:19:22,990 --> 00:19:29,950
+معناته أنا بقى هنا بقول إن G1 is isomorphic to G2،
+
+202
+00:19:29,950 --> 00:19:35,120
+G1 تقابقالرسم جي اتنين جي واحد تقارب جي اتنين نعم
+
+203
+00:19:35,120 --> 00:19:39,040
+ايوة
+
+204
+00:19:39,040 --> 00:19:42,120
+طبعا كل ما تكبر ال graph هتزداد العملية تعقيد أكيد
+
+205
+00:19:42,120 --> 00:19:48,000
+بس هذه هي الخطوات العملية من أجل إثبات التطابق لكن
+
+206
+00:19:48,000 --> 00:19:51,280
+احنا جولا فيه كلام أساسي صادق الآن لو كان ال two
+
+207
+00:19:51,280 --> 00:19:55,960
+and two graphs كبار واحد في عشر نقاط والتاني في
+
+208
+00:19:55,960 --> 00:20:01,590
+احداش ولا عمره بيصير فيه تطابقفلو كانت الآن عشر
+
+209
+00:20:01,590 --> 00:20:06,490
+نقاط، عشر نقاط، لكن التاني فيه خمس ديصور، والأول
+
+210
+00:20:06,490 --> 00:20:10,190
+فيه سبعة، ولا عمرو بيخوفيه تقارب، بتنسى الموضوع،
+
+211
+00:20:10,190 --> 00:20:13,410
+طبعا، تفضل يعني ال graph بلقى فيه زي ما بديه،
+
+212
+00:20:13,410 --> 00:20:18,900
+أكيد، يعني مش طواله متوازنأنت لو خلّيته أعمل وازي
+
+213
+00:20:18,900 --> 00:20:22,440
+أطلع حيك مافيش مشكلة، شوف هذا الرسم اللي أنا رسمته
+
+214
+00:20:22,440 --> 00:20:28,400
+عشان أحاول أصل بسهولة، تمام؟ لمين؟ للـfunction،
+
+215
+00:20:28,400 --> 00:20:31,160
+أصل للـfunction بشكل سهل، اما بإمكاني مارفعوش
+
+216
+00:20:31,160 --> 00:20:34,460
+مطلقا، إذا بتقدر تشغل في مخيلتك، مافيش مشكلة،
+
+217
+00:20:34,460 --> 00:20:35,780
+تعالي شوف المثال اللي بعده
+
+218
+00:20:46,710 --> 00:20:52,970
+تعالى نشوف الإجابة هذه G1 و G2 هل في بينهم تقابق؟
+
+219
+00:20:52,970 --> 00:20:56,310
+مباشرة قبل ما تفكر بالـ function طلع على عدد
+
+220
+00:20:56,310 --> 00:21:01,090
+النقاط و عدد الجسور 4
+
+221
+00:21:01,090 --> 00:21:07,590
+نقاط و 4 جسور خمس جسور مش أربعة أربعة أربعة للنقاط
+
+222
+00:21:07,590 --> 00:21:12,900
+و خمسة خمسة للجسور معناه تحتمال التقابقموجود يكون
+
+223
+00:21:12,900 --> 00:21:16,120
+عالي جدا اقول لك شغلة تتذكر شغلة يمكن احنا فشجناها
+
+224
+00:21:16,120 --> 00:21:20,020
+في ال review اليوم اللي سمناها sequence of degrees
+
+225
+00:21:20,020 --> 00:21:23,280
+ترتيب الدجريز مش كما احنا قولنا في ال graph اشرح
+
+226
+00:21:23,280 --> 00:21:28,500
+ساوي بنرتب الرتب تبعته جدش رتبة ايه؟ تقولنا تلاتة
+
+227
+00:21:28,500 --> 00:21:36,720
+دي اتنين تلاتة اتنين تلاتة اتنين تلاتة اتنين تلاتة
+
+228
+00:21:36,720 --> 00:21:39,600
+اتنين تلاتة اتنين تلاتة اتنين sequence of degrees
+
+229
+00:21:42,820 --> 00:21:49,180
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+230
+00:21:49,180 --> 00:21:49,180
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+231
+00:21:49,180 --> 00:21:50,200
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+232
+00:21:50,200 --> 00:21:53,340
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+233
+00:21:53,340 --> 00:21:53,360
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+234
+00:21:53,360 --> 00:21:53,780
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+235
+00:21:53,780 --> 00:22:11,000
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+236
+00:22:12,110 --> 00:22:15,050
+جراف ممكن يكون فيه تطابق عالي ايش انا هساوي الان؟
+
+237
+00:22:15,050 --> 00:22:21,590
+كيف ممكن اعمل ماب؟ الان لو انت تفكر تاخد ال a w او
+
+238
+00:22:21,590 --> 00:22:27,550
+اخد ال a u غلط ليش؟ لإن رتبة ال a تلاتة و المفروض
+
+239
+00:22:27,550 --> 00:22:31,290
+ال vertex اللي بيكون مقابل إلها لازم يكون نفس ال
+
+240
+00:22:31,290 --> 00:22:36,970
+رتبة وبالتالي انت الان بتشتغل كتالة تقول في of a
+
+241
+00:22:36,970 --> 00:22:43,450
+في of b في of c5 of D هاي الأربع نقاط اللي موجودة
+
+242
+00:22:43,450 --> 00:22:49,910
+عندى في غيرهم لو ماعنديش بدي أشوف إيش مقابلهم الآن
+
+243
+00:22:49,910 --> 00:22:53,350
+في موضوع الرسم الرسم بسهل عليك كتير في فهمك لل
+
+244
+00:22:53,350 --> 00:22:57,670
+isomorphism تعال معايا هيك و أنا بدي أجيب ال X هان
+
+245
+00:22:57,670 --> 00:23:04,130
+بتحط ال X هان هيك
+
+246
+00:23:04,130 --> 00:23:12,210
+و انسانياها من هان هيك شوية الآنصار في شبه تطابق،
+
+247
+00:23:12,210 --> 00:23:16,870
+بصبوط، بس دلني أعمل كمان خطوة، أعمل rotation
+
+248
+00:23:16,870 --> 00:23:21,670
+باتجاه اليسار، ألف ال graph عشان القطر يطابق مع
+
+249
+00:23:21,670 --> 00:23:24,370
+القطر، شوف هذا الرسم اللي أنا قاعد بسويه مش إلزاني
+
+250
+00:23:25,060 --> 00:23:28,580
+مش إذاني لكنه بالنسبة لي .. بالنسبة لي أنا كواحد
+
+251
+00:23:28,580 --> 00:23:33,380
+بدي أحل بخلّيني أجيب ال graph function تبعتي 100%
+
+252
+00:23:33,380 --> 00:23:36,760
+صح خلّيني أجيب ال graph function تبعتي 100% صح بعد
+
+253
+00:23:36,760 --> 00:23:40,800
+ما أنا عملت rotation معناته شكل ال graph تبعي صحيك
+
+254
+00:23:40,800 --> 00:23:44,960
+الآن
+
+255
+00:23:44,960 --> 00:23:57,050
+هذه U وهذه W وهنا X وهذه بلّة مين ال Vمصبوط او لا؟
+
+256
+00:23:57,050 --> 00:23:59,050
+بعد الـ rotation هاي إذا أنا عملت ال rotation
+
+257
+00:23:59,050 --> 00:24:07,870
+بتاعة المثل خلصنا ال a صارت ال w ال b ال u ال c I
+
+258
+00:24:07,870 --> 00:24:11,870
+can't see الآن بعد ما عملنا .. قولنا rotation بعد
+
+259
+00:24:11,870 --> 00:24:22,210
+ما هي الرسمة عملنا لها rotation الآن a w b u c v و
+
+260
+00:24:22,210 --> 00:24:28,170
+ال d x طبعا هذه ال functionبقى انا ممكن اكتبها
+
+261
+00:24:28,170 --> 00:24:35,710
+بصورة تانية اقول الفايف يتساوي او ال labda AW على
+
+262
+00:24:35,710 --> 00:24:40,290
+نفسي المرتبة فهي ماب برضه بي يو بأي شكل انت بتكتبه
+
+263
+00:24:40,290 --> 00:24:49,790
+أنا ماعنديش مشكلة في الموضوع C وV وDو X الآن تتحقق
+
+264
+00:24:49,790 --> 00:24:53,970
+أن الـ function هذه صحيحة تعطيك كل الدسور اللي
+
+265
+00:24:53,970 --> 00:24:58,150
+موجودة طبعا ماضحة صحيحة لإن انت ما بقترصر بالكامل
+
+266
+00:24:58,150 --> 00:25:06,270
+Phi of AD
+
+267
+00:25:06,270 --> 00:25:18,760
+Phi of AB Phi of AC هاي تلات دسورالان فاي اف بي سي
+
+268
+00:25:18,760 --> 00:25:25,900
+و فاي اف بي سي مظبوط؟ هذه الخمس جسور اللي موجودة
+
+269
+00:25:25,900 --> 00:25:37,520
+عندها سنة ا دي دابليو اكس موجود ا بي دابليو يو
+
+270
+00:25:37,520 --> 00:25:52,700
+موجود ا سي دابليو في موجودالان DC X V X V موجود؟
+
+271
+00:25:52,700 --> 00:26:03,660
+موجود اخر جسم U بل هي B و CV وبالتالي موجود بحيث
+
+272
+00:26:03,660 --> 00:26:07,680
+ان انا بقول جي واحد is isomorphic مقابل دائمة
+
+273
+00:26:15,310 --> 00:26:20,230
+الأمر السهل أنك تشغّل في دماغك رصيد كثير عشان
+
+274
+00:26:20,230 --> 00:26:23,950
+تتحلل الرسمين و تتبقوا مع بعض
+
+275
+00:26:37,520 --> 00:26:41,020
+بقول إن لما يكون هناك isomorphism بين الـ two
+
+276
+00:26:41,020 --> 00:26:46,580
+graphs، معناته لازم يكون نفس عدد النقاء، نفس عدد
+
+277
+00:26:46,580 --> 00:26:53,740
+الجسور، و نفس ال degree sequence، عكسها يعني if G1
+
+278
+00:26:53,740 --> 00:26:56,520
+isomorphic to G2، then هدول
+
+279
+00:26:59,980 --> 00:27:04,340
+لو اتبعتها اذا كانت هدولة غير متوفرات او واحدة
+
+280
+00:27:04,340 --> 00:27:07,980
+منهم فالس معاكم مافيش isomorphism اللي هو انا قلت
+
+281
+00:27:07,980 --> 00:27:12,040
+الكلام قبل ما .. عشان هيك انتبه للرسم كويس انه بكل
+
+282
+00:27:12,040 --> 00:27:15,840
+بساطة هو ممكن تجيك السؤال هل في طابق بين الرسم ال
+
+283
+00:27:15,840 --> 00:27:20,900
+graph a و graph 2؟ if yes اديني ال function give
+
+284
+00:27:20,900 --> 00:27:25,360
+me the objective function عشان هيك بلاك تنتبه
+
+285
+00:27:25,360 --> 00:27:30,520
+وتقول نعم او لا و ليشالان فينا مجموعة من التعريفات
+
+286
+00:27:30,520 --> 00:27:34,640
+البسيطة والجميلة كذلك في موضوع ال graphs .. في
+
+287
+00:27:34,640 --> 00:27:38,740
+موضوع ال graphs دي جاي عن رمضان اه؟ كل عام تبخير
+
+288
+00:27:38,740 --> 00:27:45,820
+هيفنوس رمضان طيب الان في عند التلات مصطلحات لو انا
+
+289
+00:27:45,820 --> 00:27:50,680
+بدأ ترجمهم ترجمة حرفية كلهم هتيجي نفس المعنى walk
+
+290
+00:27:50,680 --> 00:27:56,180
+و trail و path walk و trail و path اللي هي بمعنى
+
+291
+00:27:56,180 --> 00:28:00,480
+ممر او مسارأنا مابديش أترجمهم بالعربي لإن حاجز
+
+292
+00:28:00,480 --> 00:28:03,980
+اترجمهم بالعربي هنحتفظ بقاشي بالترجم بالمصطلح
+
+293
+00:28:03,980 --> 00:28:09,470
+الانجليزي لإنه فيه فرق بين كل واحد والتانيالـ Walk
+
+294
+00:28:09,470 --> 00:28:14,070
+الـ Walk هو عبارة عن Alternating Sequence of
+
+295
+00:28:14,070 --> 00:28:21,330
+Vertices and Edges هي عبارة عن Sequence من النقاط
+
+296
+00:28:21,330 --> 00:28:26,550
+والمثول شو يعني؟ يعني كل نقطة مع النقطة اللي
+
+297
+00:28:26,550 --> 00:28:31,830
+بعديها في بينهم إياش جسر باجي على الرسمة هذه بقول
+
+298
+00:28:31,830 --> 00:28:43,540
+A D B C A DB C هذا walk مسار الآن هو عبارة عن
+
+299
+00:28:43,540 --> 00:28:48,820
+مجموعة من اللقاءات تمام وبين كل قطين فيه ايش؟ فيه
+
+300
+00:28:48,820 --> 00:28:55,140
+جسر هذا walk is a walk لكن
+
+301
+00:28:55,140 --> 00:29:01,660
+تخيل A C E F is not a walk
+
+302
+00:29:05,400 --> 00:29:08,380
+على الرغم من أن النقاط الموجودة موجودة على الـ
+
+303
+00:29:08,380 --> 00:29:12,360
+Graph اللي يبقى بين الـ A والـ C مافيش جسر
+
+304
+00:29:12,360 --> 00:29:19,240
+وبالتالي هذا مش مسار يعني الآن لما بيتفتح خريطة
+
+305
+00:29:19,240 --> 00:29:27,280
+جوجل ماب أو أي خريطة بينفعش يحطلك خطعشان اقولك
+
+306
+00:29:27,280 --> 00:29:31,740
+تنتقل من A ل B او من A ل X لازم تمر مجموعة من
+
+307
+00:29:31,740 --> 00:29:35,480
+النقاط النقاط هذه لازم تكون متصلة مصبوط او لا؟ هذا
+
+308
+00:29:35,480 --> 00:29:38,920
+اللي احنا بنسميه ال walk هذا بنسميه بالمصطلح
+
+309
+00:29:38,920 --> 00:29:44,480
+البسيط ال walk يعني
+
+310
+00:29:44,480 --> 00:29:50,780
+بين جثين في ال walk اي نقطتين لازم يكون متجاورات
+
+311
+00:29:50,780 --> 00:29:55,010
+ايش يعني مفهوم التجاور انه في بينهم جسرفي بينهم
+
+312
+00:29:55,010 --> 00:29:58,950
+جسر مش جانب بعض انه في بينهم جسر والجسرين
+
+313
+00:29:58,950 --> 00:30:06,170
+المتجاورين بينهم نقطة يعني هيك اللي احنا كتبنا A D
+
+314
+00:30:06,170 --> 00:30:14,800
+Bمصبوط و بعدين C الان AD adjacent vertices لأن في
+
+315
+00:30:14,800 --> 00:30:20,560
+بينهم جسر مصبوط و DB adjacent vertices الان
+
+316
+00:30:20,560 --> 00:30:27,620
+الجسرين AD و BB adjacent X بالكتير يفلقها D تمام
+
+317
+00:30:27,620 --> 00:30:33,760
+مية ميةخلّصنا من ال walk و ننتقل للمصطلح اللي بعده
+
+318
+00:30:33,760 --> 00:30:38,620
+الآن ال walk له مسار و المسار يقاس بعدد الجسور
+
+319
+00:30:38,620 --> 00:30:44,080
+اللي موجودة في ال walk هذا ال walk هذا اللي live
+
+320
+00:30:44,080 --> 00:30:51,100
+اللي طول و طول يقاس بعدد الجسور اللي موجودة ايه دي
+
+321
+00:30:51,100 --> 00:30:59,840
+بي سي مصبوط walkهنجسر فيه واحد اتنين تلاتة دائما
+
+322
+00:30:59,840 --> 00:31:05,440
+عدد ال vertices نقص واحد عدد ال vertices نقص واحد
+
+323
+00:31:05,440 --> 00:31:15,100
+طيب بد الطول تبقى a c d b جدش قوله ايوة هو احتجاز
+
+324
+00:31:15,100 --> 00:31:18,480
+في المطبخ هذا is not a walk مش walk معناته مقدرش
+
+325
+00:31:18,480 --> 00:31:19,460
+اتكلم على قوله
+
+326
+00:31:25,170 --> 00:31:29,570
+الـ Walk دا ممكن يكون Closed ايش يعني Closed؟ مغلق
+
+327
+00:31:29,570 --> 00:31:40,310
+يعني نقطة البداية هي نفسها نقطة النهاية A B C D A
+
+328
+00:31:40,310 --> 00:31:45,830
+Closed Walk Closed Walk لما اصطلح ليه Closed انه
+
+329
+00:31:45,830 --> 00:31:50,550
+نقطة البداية هي نفسها نقطة النهاية بس بقت حافظ ان
+
+330
+00:31:50,550 --> 00:31:54,770
+يبقى الـ Walk يعني بينفعش اروح اقفزيعني هيك مافيه
+
+331
+00:31:54,770 --> 00:32:01,830
+عروح اقفز اقوله a b c a هي a b c a is a closed
+
+332
+00:32:01,830 --> 00:32:07,230
+walk خالص غلط لإنه مش walk أساسا عشان نتكلم عن انه
+
+333
+00:32:07,230 --> 00:32:14,130
+closed طبعا
+
+334
+00:32:14,130 --> 00:32:17,690
+لما بيكونش closed بيكون open تمام المصطلح فيش في
+
+335
+00:32:17,690 --> 00:32:23,580
+الجديد لأن انتبهانتبه، في عنده مصطلح جديد بنفس
+
+336
+00:32:23,580 --> 00:32:30,200
+معنى كلمة walk بالحرف طب هو ال trail ممر مشاء أو
+
+337
+00:32:30,200 --> 00:32:35,940
+مسار برضه ال trail هو عبارة عن walk لكن كل الجسور
+
+338
+00:32:35,940 --> 00:32:43,760
+اللي فيه جسور مختلفة ولا مرة بتمشي على الجسر مرتين
+
+339
+00:32:43,760 --> 00:32:49,260
+يعني أوريك شغلة بريق واحد okay لأ تعالى شوف أوريك
+
+340
+00:32:49,260 --> 00:32:53,730
+الشغلةالان لو انا جيت كتبت .. ماعرف ماكتبها تكتب
+
+341
+00:32:53,730 --> 00:33:03,650
+تاني ليش؟ الان a b c d a walk مظبوط؟ لإن في جثور
+
+342
+00:33:03,650 --> 00:33:06,790
+ما بين كل ال vertices اللي عندي هنا closed walk
+
+343
+00:33:06,790 --> 00:33:16,970
+مية لميةTrail لماذا؟ لأن A,B لا تتكرر أبداً B,C لا
+
+344
+00:33:16,970 --> 00:33:20,290
+تتكرر أبداً C,D لا تتكرر أبداً D,A لا تتكرر أبداً،
+
+345
+00:33:20,290 --> 00:33:24,930
+لا يوجد جسر يتكرر أبداً فهذا بيرتقى لمرتبة Trail
+
+346
+00:33:24,930 --> 00:33:31,270
+فكل Trail هو عبارة عن و لكن الجسور اللي فيه مختلفة
+
+347
+00:33:31,270 --> 00:33:37,590
+تعالى نشوف هذا A,B,C,D,A,D
+
+348
+00:33:40,930 --> 00:33:49,650
+في تكرار هذا walk لكن هو not a trail، أصبت؟ ليش؟
+
+349
+00:33:49,650 --> 00:33:53,470
+الآن لو انت فحصت كل النقاط اللي موجودة متجاورة و
+
+350
+00:33:53,470 --> 00:33:59,650
+كل الجسور اللي موجودة متجاورة لكن التكرار ال a دي
+
+351
+00:33:59,650 --> 00:34:02,150
+بيبقى هناك و لا فيه ندياش؟ مشكلة
+
+352
+00:34:06,230 --> 00:34:20,250
+الان a b b c a b c e f c b لاحظ بي سي هي نفسها، بي
+
+353
+00:34:20,250 --> 00:34:22,310
+سي هي نفسها، بي سي هي نفسها، بي سي هي نفسها، بي سي
+
+354
+00:34:22,310 --> 00:34:22,330
+هي نفسها، بي سي هي نفسها، بي سي هي نفسها، بي سي هي
+
+355
+00:34:22,330 --> 00:34:22,390
+نفسها، بي سي هي نفسها، بي سي هي نفسها، بي سي هي
+
+356
+00:34:22,390 --> 00:34:22,890
+نفسها، بي سي هي نفسها، بي سي هي نفسها، بي سي هي
+
+357
+00:34:22,890 --> 00:34:23,450
+نفسها، بي سي هي نفسها، بي سي هي نفسها، بي سي هي
+
+358
+00:34:23,450 --> 00:34:23,870
+نفسها، بي سي هي نفسها، بي سي هي نفسها، بي سي هي
+
+359
+00:34:23,870 --> 00:34:29,950
+نفسها، بي سي هي نفسها، بي سي هي نفسها،
+
+360
+00:34:29,950 --> 00:34:35,020
+بي سي هي نفسها، بلأن صار في عندي walk و trail لأن
+
+361
+00:34:35,020 --> 00:34:39,880
+صار في عندي مصطلح جديد اسمه path ال path هو عبارة
+
+362
+00:34:39,880 --> 00:34:46,440
+عن walk كل النقاط اللي فيه مختلفة هو عبارة عن walk
+
+363
+00:34:46,440 --> 00:34:51,660
+كل النقاط اللي فيه مختلفة بينما ال trail كان كل
+
+364
+00:34:51,660 --> 00:34:55,220
+الجسور اللي فيه مختلفة تعالى نشوف المسارات اللي
+
+365
+00:34:55,220 --> 00:34:59,080
+عندي هنا ABCD
+
+366
+00:35:01,560 --> 00:35:08,000
+walk و trail و path تطبق عليه تلت مصطلحات تلت
+
+367
+00:35:08,000 --> 00:35:17,780
+تعريفات الان c b d e walk و trail و path a d c e f
+
+368
+00:35:17,780 --> 00:35:24,200
+c it's not path صار
+
+369
+00:35:24,200 --> 00:35:27,660
+في عندى نقطة مريت عليها انا عايش مرتين
+
+370
+00:35:30,350 --> 00:35:35,270
+walk صح لكنها مش path is not a path الأخيرة ال ..
+
+371
+00:35:35,270 --> 00:35:44,670
+ال .. ال .. ال ..
+
+372
+00:35:44,670 --> 00:35:46,970
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+373
+00:35:46,970 --> 00:35:49,330
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+374
+00:35:49,330 --> 00:35:49,330
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+375
+00:35:49,330 --> 00:35:49,330
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+376
+00:35:49,330 --> 00:35:50,790
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+377
+00:35:50,790 --> 00:35:51,790
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+378
+00:35:51,790 --> 00:35:51,790
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+379
+00:35:51,790 --> 00:35:51,790
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+380
+00:35:51,790 --> 00:35:51,790
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+381
+00:35:51,790 --> 00:35:51,790
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+382
+00:35:51,790 --> 00:35:51,790
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+383
+00:35:51,790 --> 00:35:53,110
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+384
+00:35:57,200 --> 00:36:01,680
+لأنه لازم يبقى ال connection موجود كويسة إنه في
+
+385
+00:36:01,680 --> 00:36:08,940
+ناس مصحصها، فهذه ميزة الحمد لله القال الأخير A B A
+
+386
+00:36:08,940 --> 00:36:20,800
+B C E F C B كمان مرة، لاحظوا؟ ال B و ال C معناته
+
+387
+00:36:20,800 --> 00:36:25,420
+لا هو trail ولا هو path لأنه تكرر الجسر و تكررت ال
+
+388
+00:36:25,420 --> 00:36:26,540
+نقاط اللي موجودة
+
+389
+00:36:30,660 --> 00:36:35,140
+للـ trail بسميه circuit لو كان مغلق الـ trail إيش
+
+390
+00:36:35,140 --> 00:36:40,380
+يعني مغلق؟ بينفي بنفس النقطة بسميه إيش؟ circuit
+
+391
+00:36:40,380 --> 00:36:45,180
+بسميه circuit دكتور بيه و إيه؟ فيه بين الجثر؟ لأ،
+
+392
+00:36:45,180 --> 00:36:47,840
+صح؟ يعني لما قلنا هاي خلمة أنت ساعدت ابنك قبل
+
+393
+00:36:47,840 --> 00:36:52,960
+شويهان مباشر لأ لازم يمر بـC مجهدنا ينبهن عليها
+
+394
+00:36:52,960 --> 00:36:57,300
+زميلك و جوهاش اسمه و عدلناها هو قلنا لازم أشطبها
+
+395
+00:36:57,300 --> 00:37:02,950
+خليني أشطبها من الـA عشان أنا إيشماانساهاش كمان ال
+
+396
+00:37:02,950 --> 00:37:10,990
+slide اللى جابل D
+
+397
+00:37:10,990 --> 00:37:19,910
+بديش ارجع باتجاه ال C A حط ال A مش مشكلة I shift
+
+398
+00:37:19,910 --> 00:37:29,770
+الخمسة كلام الآن بنقول المسار هذاالـ Trail ممكن
+
+399
+00:37:29,770 --> 00:37:34,810
+يسميه circuit لو كانه closed walk لو كان closed ال
+
+400
+00:37:34,810 --> 00:37:38,710
+trail بقول عنه إيش؟ circuit إيش عن closed؟ نقطة
+
+401
+00:37:38,710 --> 00:37:42,230
+البداية هي نفس نقطة النهاية و ال trail إنه مقع
+
+402
+00:37:42,230 --> 00:37:46,610
+الجسور الجوية و مافيها تكرار في عندي مصطلح تاني
+
+403
+00:37:46,610 --> 00:37:52,530
+بسميه cycle وهذا حالة خاصة .. حالة خاصة مع مين؟ مع
+
+404
+00:37:52,530 --> 00:37:56,510
+المسار ال pathلأن الباق ايش تعريفه شباب ان هو
+
+405
+00:37:56,510 --> 00:38:02,430
+عبارة عن و كل النقاط اللي فيه مختلفة طب لو كانت
+
+406
+00:38:02,430 --> 00:38:10,170
+النقطة البداية هي نفسها نقطة النهاية يعني A B C D
+
+407
+00:38:10,170 --> 00:38:18,390
+A لو انا تجاهلت النقطة الأخيرة هو عبارة عن باث
+
+408
+00:38:18,390 --> 00:38:23,210
+مصدر ولا لأ و بما أن نقطة البداية هي نقطة النهاية
+
+409
+00:38:25,140 --> 00:38:30,380
+فهو closed walk صح؟ الان لو closed walk هذا او بين
+
+410
+00:38:30,380 --> 00:38:35,780
+جثين خلاص خلنا نسميه لو كان في عندى path ونقطة
+
+411
+00:38:35,780 --> 00:38:41,300
+النهاية هي نفس نقطة البداية بالضبط هو هيكون closed
+
+412
+00:38:41,300 --> 00:38:47,040
+tree حتما هذا بدي اسميه cycle ليش؟ لأنه فعليا
+
+413
+00:38:47,040 --> 00:38:51,960
+المسار هدا ماخد صفة ال path مع ده النقطة الأخيرة
+
+414
+00:38:51,960 --> 00:38:58,410
+فسمونها ايش؟ساموليه Cycle تعالى نشوف على السريع
+
+415
+00:38:58,410 --> 00:39:03,290
+بدي اخد هذا مثال المفروض تكمله انت لوحدك كله بس
+
+416
+00:39:03,290 --> 00:39:09,190
+بدي اخد منه على سبيل المثال الرسمي هاي ايش مقولي F
+
+417
+00:39:09,190 --> 00:39:27,180
+G C B A E F G C B A Eهل هو closed؟ لأ طبعا walk
+
+418
+00:39:27,180 --> 00:39:32,220
+مصبوط لأنه كان ماشي على الجسور كل هاتها موجودة هل
+
+419
+00:39:32,220 --> 00:39:39,320
+هو closed؟ لأ trail كل الجسور اللي فيه مختلفة فهو
+
+420
+00:39:39,320 --> 00:39:47,980
+trail هل هو bad؟ النقاط اللي فيه كلها مختلفة فهو
+
+421
+00:39:47,980 --> 00:39:53,620
+badهل هو circuit؟ لأ لأنه مش closed وبالتالي مش
+
+422
+00:39:53,620 --> 00:39:59,380
+cycle لأنه open، مظبوط ولا لا؟ عليك بيبدأك تشتغل
+
+423
+00:39:59,380 --> 00:40:05,340
+الان في المفهوم الان cycle هو المفروض اللي بيتكلم
+
+424
+00:40:05,340 --> 00:40:10,840
+على عدد مرات الدوران اللي موجودة عندها، الآن في ال
+
+425
+00:40:10,840 --> 00:40:16,600
+graph one أي واحد فيهم بيحقق تمام؟
+
+426
+00:40:18,910 --> 00:40:27,190
+Euler circuit Euler circuit يعني
+
+427
+00:40:27,190 --> 00:40:32,870
+لازم يكون مغلق و امر في كل النقاط اللي موجودة او
+
+428
+00:40:32,870 --> 00:40:42,850
+كل الجثور اللي موجودة عندي G1 A C
+
+429
+00:40:42,850 --> 00:40:45,810
+D من ال E يبدو حضر
+
+430
+00:41:11,170 --> 00:41:12,570
+EEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCEDCED
+
+431
+00:41:21,030 --> 00:41:30,290
+مظبوط؟ circuit او
+
+432
+00:41:30,290 --> 00:41:35,670
+لا ال circuit اللي بعده a
+
+433
+00:41:35,670 --> 00:41:44,990
+,b,c مش مجال طالما انك سوف تروح ادخل على منطقة
+
+434
+00:41:44,990 --> 00:41:52,030
+تانية ايوة مش زرقالفكرة كمان مرة يا شباب ال
+
+435
+00:41:52,030 --> 00:41:55,850
+circuit closed ال trail مش لازم ترجع على الجسر مرة
+
+436
+00:41:55,850 --> 00:41:59,790
+تانية ممكن تمر بر مخضع مافي مشكلة عندك طيب مرة
+
+437
+00:41:59,790 --> 00:42:08,150
+تانية A D C D الآن اذا انا بدي ارجع هلال A صارت
+
+438
+00:42:08,150 --> 00:42:12,270
+closed trail صارت circle لكنها مش Euler فانا
+
+439
+00:42:12,270 --> 00:42:17,250
+ماتجمعكش من ال up اللي موجودة عندي هان طيب تعالى
+
+440
+00:42:17,250 --> 00:42:24,450
+نفكر فيها زي ما فكرنا بهك هل في مجالA,B
+
+441
+00:42:24,450 --> 00:42:35,590
+,A,E,C,D وبدى ارجع تانى هناك لأ و الأخيرة بقى
+
+442
+00:42:35,590 --> 00:42:37,270
+تهيألك Her
+
+443
+00:42:47,880 --> 00:42:51,080
+الان طالما ان في عندك وطر هتحسه في الرسم المرسوم
+
+444
+00:42:51,080 --> 00:42:54,980
+غالبا انت مش هتقدر تاش اللي هتمره على جسر من
+
+445
+00:42:54,980 --> 00:42:58,180
+الجسرين او من الجسرها دي مرتين عشان تحقق خاصية
+
+446
+00:42:58,180 --> 00:43:02,260
+take closed تعالى نشوف هيك اقولك تخيل ان الوطر هذا
+
+447
+00:43:02,260 --> 00:43:06,180
+مش موجود تخيل
+
+448
+00:43:06,180 --> 00:43:13,740
+ان الوطر هذا مش موجود كيف انت حلت ايوة دي
+
+449
+00:43:17,380 --> 00:43:33,740
+C,A,B,C,A,B,C,A,B,C,A,B,C,A,B,C,A,B,C,A,B,C,A,B,C
+
+450
+00:43:33,740 --> 00:43:41,360
+,A,B,C,A,B,C,A,B,C,A,B,C,A,B,C,A,B,C,A,B,C,A,B,C,A
+
+451
+00:43:41,360 --> 00:43:44,940
+,B,C,A,B,C,A,B,C,A,B,C,A,B,C,A,B,C,A,B,C,A,B,C,A,B
+
+452
+00:43:44,940 --> 00:43:44,940
+,C,A,B,C,A,B,C,A,B,C,A,B,C,A,B,C,A,B,C,A,B,C,A,B,C
+
+453
+00:43:44,940 --> 00:43:49,280
+,A,B,C,A,B,C,A,B,C,A,B,C,طبعا بيحتوي على مسار
+
+454
+00:43:49,280 --> 00:43:55,040
+بيجمع كل النقاط، مسار بيجمع كل النقاط من غير تكرار
+
+455
+00:43:55,040 --> 00:43:58,560
+للنقاط أكيد لأنه في الآخر بدك تحققك على ال public
+
+456
+00:43:58,560 --> 00:44:04,980
+على الاسم ال path طيب تعالى أقبلها فيك كتبلي مسار
+
+457
+00:44:04,980 --> 00:44:07,260
+بدون أنك تكرر فيه النقطة
+
+458
+00:44:16,630 --> 00:44:27,470
+الأول نقدر مرة نجيب مصار بيجمع كل المقاط A B E C D
+
+459
+00:44:27,470 --> 00:44:34,930
+اخر مرة A B E C D او A B E احفظ A B E C D او A B E
+
+460
+00:44:34,930 --> 00:44:40,090
+احفظ A B E C D
+
+461
+00:44:40,090 --> 00:44:44,390
+او A B E A B E احفظ A B E C D او A B E A B E A B E
+
+462
+00:44:44,390 --> 00:44:44,390
+A B E A B E A B E A B E A B E A B E A B E A B E A
+
+463
+00:44:44,390 --> 00:44:44,430
+B E A B E A B E A B E A B E A B E A B E A B E A B
+
+464
+00:44:44,430 --> 00:44:44,430
+E A B E A B E A B E A B E A B E A B E A B E A B E
+
+465
+00:44:44,430 --> 00:44:44,430
+A B E A B E A B E A B E A B E A B E A B E A B E A
+
+466
+00:44:44,430 --> 00:44:44,430
+B E A B E A B E A B E A B E A B E A B E A B E A B
+
+467
+00:44:44,430 --> 00:44:49,270
+E A B E Aهيو باذ او الفكرة وين ان مسار بيحتوي على
+
+468
+00:44:49,270 --> 00:44:54,170
+كل النقاط اللي في الرسمة بيحتوي على كل النقاط اللي
+
+469
+00:44:54,170 --> 00:45:00,030
+في الرسمة عشان يحافظ على باذ هيو باذ كل النقاط في
+
+470
+00:45:00,030 --> 00:45:04,090
+بينها جسور ونقاط مختلفة منها تهدأ أولا باذ تعالى
+
+471
+00:45:04,090 --> 00:45:08,370
+نشوفه التانية G2ABC
+
+472
+00:45:13,230 --> 00:45:19,110
+لأنه واصل مقاهة ما اتكلمش على الجسور الاخير نفس
+
+473
+00:45:19,110 --> 00:45:26,590
+الحاجة LAC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC
+
+474
+00:45:26,590 --> 00:45:26,970
+ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC
+
+475
+00:45:26,970 --> 00:45:27,990
+ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC
+
+476
+00:45:27,990 --> 00:45:28,430
+ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC
+
+477
+00:45:28,430 --> 00:45:28,430
+ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC
+
+478
+00:45:28,430 --> 00:45:28,470
+ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC
+
+479
+00:45:28,470 --> 00:45:28,490
+ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC
+
+480
+00:45:28,490 --> 00:45:28,490
+ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC
+
+481
+00:45:28,490 --> 00:45:28,490
+ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC
+
+482
+00:45:28,490 --> 00:45:28,490
+ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC
+
+483
+00:45:28,490 --> 00:45:28,490
+ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC
+
+484
+00:45:28,490 --> 00:45:30,790
+ABC BC ABC ABC ABC BC ABC BC ABC ABC ABC ABC ABC
+
+485
+00:45:30,790 --> 00:45:31,310
+ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC
+
+486
+00:45:31,310 --> 00:45:36,810
+ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC ABC
+
+487
+00:45:44,180 --> 00:45:47,640
+خلاص بناقش هكلا هكلا يوم محاضرة هادى و بنكمل ان
+
+488
+00:45:47,640 --> 00:45:49,120
+شاء الله المحاضرة الجاية
+
diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/xXZat9maenA.srt b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/xXZat9maenA.srt
new file mode 100644
index 0000000000000000000000000000000000000000..8ceda01ccca08f35f8dd61e3c6907498b21d85e2
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/xXZat9maenA.srt
@@ -0,0 +1,2314 @@
+
+1
+00:00:21,010 --> 00:00:22,650
+بسم الله والحمد لله والصلاة والسلام على الرسول
+
+2
+00:00:22,650 --> 00:00:24,330
+إن شاء الله اليوم يا شباب، هنبدأ بـ chapter
+
+3
+00:00:24,330 --> 00:00:27,890
+ثلاثة، لو chapter  الـ algorithms، الـ chapter هيكون
+
+4
+00:00:27,890 --> 00:00:32,770
+نوعًا ما مريح بالنسبة لي لأن معظمكم أخذ برمجة واحد
+
+5
+00:00:32,770 --> 00:00:37,850
+وآخذ برمجة اثنين، وآخذ مقدمة، تمام؟ وفي ناس أخذت اختيارية في
+
+6
+00:00:37,850 --> 00:00:42,570
+المنطقة، وبالتالي، أيش وضعهم؟ تمام، فاليوم احنا نتكلم
+
+7
+00:00:42,570 --> 00:00:46,950
+على الـ algorithms، الخوارزميات.
+
+8
+00:00:49,310 --> 00:00:53,650
+عندما أتحدث عن الخوارزميات، سنغطي ثلاثة قطع في هذا
+
+9
+00:00:53,650 --> 00:00:58,190
+الفيديو فقط: ماهي الخوارزمية؟ وما هي الـ growth
+
+10
+00:00:58,190 --> 00:01:04,870
+functions؟ زيادة أو نمو الدالة، و الـ complexity، أو ما
+
+11
+00:01:04,870 --> 00:01:08,230
+يُدعى  الـ measurement الأساسية للـ algorithm.
+
+12
+00:01:08,230 --> 00:01:13,450
+جدًا، الـ algorithm بروح بيكبر أو بيكلفني وقت و space.
+
+13
+00:01:13,450 --> 00:01:16,530
+لما أتحدث عن complexity، أتحدث، مش عن تعقيده
+
+14
+00:01:16,530 --> 00:01:21,690
+كمشكلة كمًّا أو كطريقة حل، بقدر ما أتحدث عن التكلفة
+
+15
+00:01:21,690 --> 00:01:27,750
+الزمنية، تمام؟ و الـ space، تبع الذاكرة للجهاز اللي
+
+16
+00:01:27,750 --> 00:01:34,120
+موجود عندي. طيب، لما أتحدث عن الخوارزمية أو
+
+17
+00:01:34,120 --> 00:01:41,460
+الخوارزميات، ضروري نذكر الخوارزمي، اللي هو محمد بن
+
+18
+00:01:41,460 --> 00:01:46,440
+موسى الخوارزمي، أبو جعفر، أحد علماء المسلمين في عصره.
+
+19
+00:01:46,440 --> 00:01:53,700
+طبعًا، يمكنك تخيّل كم الحسنات اللي بتصب في صحيفة
+
+20
+00:01:53,700 --> 00:01:57,660
+الرجل هذا! ليش؟ طبعًا، لما نتحدث عن الـ algorithms،
+
+21
+00:01:57,660 --> 00:02:02,840
+نتحدث عن، زي ما قلنا، أبو جعفر محمد بن موسى
+
+22
+00:02:02,840 --> 00:02:08,260
+الخوارزمي، كان أحد علماء المسلمين، وكان مهتمًا أو بارعًا
+
+23
+00:02:08,260 --> 00:02:15,110
+في علمين: علم الفلك (astronomer)، والرياضيات، وطبعًا
+
+24
+00:02:15,110 --> 00:02:18,650
+بنتحدث عن علم الفلك وعلم الرياضيات، معناته بنتحدث
+
+25
+00:02:18,650 --> 00:02:22,570
+عن علوم الفضاء، وعن الرياضيات، والمكوك والفضاء
+
+26
+00:02:22,570 --> 00:02:26,290
+ومش عارف إيش، فالرجل هذا هو صاحب الأساس، طبعًا كان من
+
+27
+00:02:26,290 --> 00:02:30,350
+أبرز علماء المسلمين في بغداد، لما كانت بغداد مقصد
+
+28
+00:02:30,350 --> 00:02:33,090
+العلم في كل العالم، الموجود هناك، وكان موجود هناك
+
+29
+00:02:33,090 --> 00:02:36,870
+دار يسمونها بيت الحكمة أو دار الحكمة، تمام؟ نسأل الله
+
+30
+00:02:36,870 --> 00:02:40,210
+أن يرزقنا وإياكم وجميع المسلمين الحكمة. لكن لما أنا
+
+31
+00:02:40,210 --> 00:02:44,990
+أتحدث عن الـ algorithm، معناته أنا أتحدث عن حل
+
+32
+00:02:44,990 --> 00:02:50,370
+مشاكل، أتحدث عن حل لمشكلة معينة، والمشكلة دائمًا
+
+33
+00:02:50,370 --> 00:02:55,570
+نحاول نعكسها على مبدأ رياضيات، مثل لو أنا أعطيتك
+
+34
+00:02:55,570 --> 00:02:58,550
+sequence من الـ integers، مرة نسميها كلمة sequence،
+
+35
+00:02:58,550 --> 00:03:02,790
+مرة نسميها sequence، أو أجب الـ largest one، أجب لي
+
+36
+00:03:02,790 --> 00:03:06,490
+أكبر element في الـ sequence هذه، أو أعطيك مجموعة
+
+37
+00:03:06,490 --> 00:03:13,140
+set، وأروح أقول لك: هات لي كل subset منها، اللي احنا
+
+38
+00:03:13,140 --> 00:03:21,240
+سميناها الـ power set، مضبوط؟ أو بديك مجموعة من الـ
+
+39
+00:03:21,240 --> 00:03:26,600
+integers، و تروح ترتب لي إياها ترتيب تصاعدي أو تنازلي، أو
+
+40
+00:03:26,600 --> 00:03:31,180
+بديك شبكة... مجموعة من النقاط، وأقول لك: اديني أقصر
+
+41
+00:03:31,180 --> 00:03:36,200
+طريق ما بين نقطتين... أقصر طريق ما بين نقطتين... هذه
+
+42
+00:03:36,200 --> 00:03:41,100
+هي المسائل اللي... اللي سنتحدث عنها في الفصل أو
+
+43
+00:03:41,100 --> 00:03:46,040
+الـ chapter هذا. لما أتحدث عن الـ algorithm، معناته
+
+44
+00:03:46,040 --> 00:03:49,760
+أنا أتحدث عن طريقة للحل، methodology، ولما أتحدث
+
+45
+00:03:49,760 --> 00:03:54,830
+عن الـ methodology، معناته أنا أتحدث، لازم يكون model
+
+46
+00:03:54,830 --> 00:04:05,450
+model model model model model model model model
+
+47
+00:04:05,450 --> 00:04:10,070
+model model model نموذج نموذج نموذج نموذج
+
+48
+00:04:10,070 --> 00:04:13,550
+نموذج نموذج نموذج نموذج نموذج نموذج نموذج نموذج
+
+49
+00:04:13,550 --> 00:04:19,830
+نموذج نموذج نموذج نموذج نموذج نموذج نموذج نموذج
+
+50
+00:04:19,830 --> 00:04:20,710
+نموذج نموذج نموذج نموذج
+
+51
+00:04:23,230 --> 00:04:27,350
+لـ Mathematical Context، لنص رياضي، ليش نص رياضي أو
+
+52
+00:04:27,350 --> 00:04:31,990
+رياضيات يا شباب؟ لأن احنا شفنا سابقًا... شفنا سابقًا
+
+53
+00:04:31,990 --> 00:04:36,490
+أنه لما كنت أتحدث في مواصفات الـ systems، أنه ممكن
+
+54
+00:04:36,490 --> 00:04:39,410
+الـ system يحتمل تأويل النص اللي بالعربية أو
+
+55
+00:04:39,410 --> 00:04:42,650
+بالانجليزية، اللي بيتداول بين الناس، ممكن نختلف في
+
+56
+00:04:42,650 --> 00:04:45,950
+معناه، لأ، كان قصدك كذا، لأ، القصد كان كذا. لكن لما
+
+57
+00:04:45,950 --> 00:04:51,610
+تتحول أو أُبنيها برياضيات، زي ما شفنا بالـ
+
+58
+00:04:51,610 --> 00:04:54,510
+quantifiers والـ predicates، صارت ما فيش مجال يا
+
+59
+00:04:54,510 --> 00:04:57,430
+true يا false، ما فيش اثنين بيختلفوا على الـ values
+
+60
+00:04:57,430 --> 00:05:01,850
+تبعها، وبالتالي لما أنا أحول أو أحاول أُبني من خلال
+
+61
+00:05:01,850 --> 00:05:06,430
+الـ algorithm اللي عندي نموذج رياضي للمشكلة، عشان
+
+62
+00:05:06,430 --> 00:05:11,190
+أقدر أحلها، إذا قدرت أحول المشكلة أو أُحوِّر المشكلة
+
+63
+00:05:11,190 --> 00:05:15,290
+لموضوع رياضيات، بتنحل. وبالمناسبة، معظم بحوث الـ
+
+64
+00:05:15,290 --> 00:05:19,270
+computer science أو الـ IT اليوم، الغالبية العظمى
+
+65
+00:05:19,270 --> 00:05:23,060
+بتتركز وين؟ في موضوع الرياضيات. سيبني من الناس اللي
+
+66
+00:05:23,060 --> 00:05:27,040
+بتشتغل تطبيقات، على رغم أن أهميتها اللي غير... مش هي
+
+67
+00:05:27,040 --> 00:05:31,000
+الأساس في التطور... مش هي الأساس في التطور، لكن
+
+68
+00:05:31,000 --> 00:05:36,740
+الرياضيات هي الأهم، بعد ما تبني الـ model، تمام؟ بدك
+
+69
+00:05:36,740 --> 00:05:41,860
+تروح تبني طريقة أو تحدد خطوات عشان تحل الـ General
+
+70
+00:05:41,860 --> 00:05:45,860
+Problem، باعتمادك على الـ model الموجود هذا، باعتمادك
+
+71
+00:05:45,860 --> 00:05:48,820
+على الـ model اللي موجود. طبعًا هذا الكلام... خلّنا
+
+72
+00:05:48,820 --> 00:05:51,880
+نقول كلام إنشائي، مش هركز عليه كثير ولا هسألك يعني
+
+73
+00:05:51,880 --> 00:05:54,500
+في اللحظة من اللحظات: اكتب لي مواصفات الـ methodology،
+
+74
+00:05:54,500 --> 00:05:57,860
+وايش هو الـ model؟ والأخير، لأ، لأن المادة هي مادة
+
+75
+00:05:57,860 --> 00:06:03,900
+رياضيات، وبدنا نروح عليها بشكل أساسي وبسيط. معناته
+
+76
+00:06:03,900 --> 00:06:10,290
+أنت بحاجة لإجراء أو لخطوات تتبعها، تمام؟ نسميها
+
+77
+00:06:10,290 --> 00:06:17,430
+procedure that follows a sequence of steps، خطوات
+
+78
+00:06:17,430 --> 00:06:21,530
+متتالية، أو متتالية من الـ steps أو الخطوات، عشان
+
+79
+00:06:21,530 --> 00:06:28,270
+تحصل وتؤدي إلى حل المشكلة الموجودة. طبعًا، أحد يبدأ معك
+
+80
+00:06:28,270 --> 00:06:35,380
+بمثال طريف، تمام؟ والهدف أنه فعليًا أنا ممكن أحل
+
+81
+00:06:35,380 --> 00:06:41,140
+المشكلة اللي أنا بدي إياها بأكثر من طريقة، لكن في
+
+82
+00:06:41,140 --> 00:06:46,280
+شغلات سنتفق عليها، لازم تكون موجودة. المثال بكل
+
+83
+00:06:46,280 --> 00:06:52,460
+بساطة، لو أنت فكرت تعمل فنجان قهوة، تمام؟ أيش
+
+84
+00:06:52,460 --> 00:06:58,830
+الخطوات؟ الخطوات اللي أنت تعملها، تمام؟ أو تتبعها
+
+85
+00:06:58,830 --> 00:07:03,230
+عشان تنتج في الآخر أو تحصل على فنجان قهوة. المشكلة
+
+86
+00:07:03,230 --> 00:07:08,610
+... المشكلة الآن أن أنت مزاجك مش تمام، بيدفعك لفنجان
+
+87
+00:07:08,610 --> 00:07:13,430
+قهوة. الآن... بدنا نعمل فنجان قهوة... في أحد يقدر
+
+88
+00:07:13,430 --> 00:07:17,990
+يقول لي أيش الخطوات؟ آه... بعد الخيار اللي بيقول لك: أشوف
+
+89
+00:07:17,990 --> 00:07:22,280
+إذا في قهوة في الأول! هذه ليست خطوة، الجهاز لكي أعمل
+
+90
+00:07:22,280 --> 00:07:27,160
+في فنجان قهوة، لازم يكون فيه جهاز، لازم يكون فيه
+
+91
+00:07:27,160 --> 00:07:30,500
+غلاية، لازم يكون فيه نار، لازم يكون فيه ماء وغلاية.
+
+92
+00:07:30,500 --> 00:07:37,740
+كل الأشياء هذه، احنا بنسميها input، هذه المعطيات،
+
+93
+00:07:37,740 --> 00:07:42,800
+تمامًا، تمامًا مثل ما أنا أجي أقول لك: هي في عندك مثلث
+
+94
+00:07:42,800 --> 00:07:47,280
+و
+
+95
+00:07:47,280 --> 00:07:48,320
+بدي أقول لك قوله C.
+
+96
+00:07:53,340 --> 00:07:58,260
+بتقدر تجيب طوله بلا C ولا أمرك، بس أيش بتحتاج؟ لو
+
+97
+00:07:58,260 --> 00:08:02,660
+أنت... بدك بقية البيانات عشان تقدر تبني حسابك عليها، لو
+
+98
+00:08:02,660 --> 00:08:06,980
+أنا بديتك الـ A والـ C، أو A و B،  عفوًا، كأضلاع، أطوال
+
+99
+00:08:06,980 --> 00:08:10,780
+بتجيبها. بالإضافة، إذا قلت لك أن المثلث قائم الزاوية،
+
+100
+00:08:10,780 --> 00:08:16,400
+لو ما فيش زاوية قائمة، ممكن أديك إياها، وفي الآخر
+
+101
+00:08:16,400 --> 00:08:21,190
+تحصل عليها، لكن بدون الـ input ما تقدر تبني Algorithm.
+
+102
+00:08:21,190 --> 00:08:24,010
+فحكاية أن أنا بدي قهوة، وبدي ماء، وبدي كذا، هذه
+
+103
+00:08:24,010 --> 00:08:27,290
+كلها ننساها، هذه كلها متوفرة عندك الآن. أنا بدي
+
+104
+00:08:27,290 --> 00:08:35,050
+خطوات، sequence of steps، مجموعة من الخطوات توديني
+
+105
+00:08:35,050 --> 00:08:37,650
+أو توصلني أن أنا فعليًا أنشئ أو أعمل فنجان القهوة
+
+106
+00:08:37,650 --> 00:08:42,270
+اللي أنا بدي إياه. عشان أحل مشكلتي الآن، خطوات. سيبني من
+
+107
+00:08:42,270 --> 00:08:46,510
+الـ ingredients، المكونات، كلها متوفرة عندك، فضل خطوات.
+
+108
+00:08:48,830 --> 00:08:53,550
+أولًا: أغلي الماء، في خطوة قبلها، بدي أضيف الماء في
+
+109
+00:08:53,550 --> 00:08:59,210
+الغلاية، اتفضل. رجعنا نشتري القهوة! صحّ النوم يا
+
+110
+00:08:59,210 --> 00:09:03,350
+أستاذي! احنا قلنا كل المكونات الحين حاطيتها قدامك
+
+111
+00:09:03,350 --> 00:09:11,130
+على الطاولة، بحط البُن، بسكر، ما في سكر، تمام، حاطينها.
+
+112
+00:09:11,130 --> 00:09:15,530
+الماء في الغلاية، وقولناها. طيب، أحط القهوة على الماء
+
+113
+00:09:15,530 --> 00:09:22,290
+بعد ما غليت، أحركها شوية، جهزت، مضبوط؟ وصلنا لفنجان
+
+114
+00:09:22,290 --> 00:09:27,970
+القهوة، ممتاز! في أحد عنده خطوات ثانية؟
+
+115
+00:09:27,970 --> 00:09:36,950
+شايفين أنتم الظرف، جدّيش؟ طيب، الآن... الآن ممكن
+
+116
+00:09:36,950 --> 00:09:41,750
+أنا أعيد الخطوات ثانية بشكل مختلف: أحط القهوة، أدير
+
+117
+00:09:41,750 --> 00:09:44,570
+عليها الماء البارد، بعدين أحطها على نار، تغلي مع بعض.
+
+118
+00:09:46,100 --> 00:09:51,520
+لاحظ أن أنا أتحدث عن اختلاف الخطوات، المحصلة في
+
+119
+00:09:51,520 --> 00:09:57,180
+الأخير فنجان قهوة، بنفس المكونات اللي اعتمدت عليها
+
+120
+00:09:57,180 --> 00:10:01,480
+في الخطوات السابقة، أنا بدي أعتمد عليها... لكن كلنا
+
+121
+00:10:01,480 --> 00:10:07,040
+نتفق أن مستحيل أحصل أنا على فنجان القهوة بدون ما
+
+122
+00:10:07,040 --> 00:10:11,330
+أغلي الماء... لأ... شوف شباب، احنا اتفقنا أن
+
+123
+00:10:11,330 --> 00:10:14,910
+المكونات: الماء والقهوة والنار وكذا، كلها دي موجودة
+
+124
+00:10:14,910 --> 00:10:19,350
+وأساسية، عشان أنا أقدر أعمل، لأن مستحيل كمان مرة أجي
+
+125
+00:10:19,350 --> 00:10:21,430
+أقول: بدي أعمل قهوة وأنا ما عنديش قهوة، أو بدي أعمل
+
+126
+00:10:21,430 --> 00:10:23,750
+قهوة وأنا ما عنديش ماء، أو بدي أعمل قهوة وأنا
+
+127
+00:10:23,750 --> 00:10:27,740
+ما عنديش نار. هذه الـ input كلها لازم تتوفر، فأنا
+
+128
+00:10:27,740 --> 00:10:31,860
+أتحدث عن خطوات، الـ steps، اللي أنا بدي أحصل فيها
+
+129
+00:10:31,860 --> 00:10:35,440
+على الـ output تبعي، بناءً على الـ input اللي عندي،
+
+130
+00:10:35,440 --> 00:10:42,440
+المعطيات اللي عندي الآن. لو أنت عندك كل المعطيات، لو
+
+131
+00:10:42,440 --> 00:10:47,320
+أنت عندك كل المعطيات وما بتعرفش قانون فيثاغورس، ما بتقدر
+
+132
+00:10:47,320 --> 00:10:52,650
+تجيب طول الضلع. لو أنت ما بتعرفش حساب مثلثات وعندك كل
+
+133
+00:10:52,650 --> 00:10:56,730
+الزوايا معروفة أو الأضلاع معروفة، مع هذا الـ C،
+
+134
+00:10:56,730 --> 00:11:03,150
+ما تقدرش تجيبه، مضبوط؟ فالـ input الأساسي، احنا مش
+
+135
+00:11:03,150 --> 00:11:06,690
+مختلفين عليه، أنا أتحدث عن الخطوات اللي أنت
+
+136
+00:11:06,690 --> 00:11:11,960
+بتنفذها، وبالتالي اختلاف الخطوات، تمام؟ ممكن يكون
+
+137
+00:11:11,960 --> 00:11:15,880
+صحيح... ممكن يكون صحيح ويؤدي لنفس النتيجة، لكن ولا
+
+138
+00:11:15,880 --> 00:11:20,380
+واحد فينا هيجي يقول: والله أنا بدي أحط القهوة في
+
+139
+00:11:20,380 --> 00:11:25,600
+الغلاية بدون الماء... تمام؟ وأخليها تغلي، وبعدين
+
+140
+00:11:25,600 --> 00:11:30,380
+أضيف لها الماء... إيه صارت الخطوة هذه؟ غير منطقية...
+
+141
+00:11:30,380 --> 00:11:33,910
+الخطوة هذه غير منطقية، القهوة ما بتغليش، مضبوط؟ لأن
+
+142
+00:11:33,910 --> 00:11:37,310
+عشان تغلي لازم يكون في عندك الماء موجودة، وبالتالي
+
+143
+00:11:37,310 --> 00:11:40,330
+أنت اختلفت: إما تحط الماء في الأول، وتخليها تغلي لحالها،
+
+144
+00:11:40,330 --> 00:11:43,150
+أو تخلي القهوة والماء، وتخليهم يغلو مع بعض.
+
+145
+00:11:43,150 --> 00:11:47,450
+بالمحصلة... إعادة ترتيب للخطوات ضمن الـ logic أو
+
+146
+00:11:47,450 --> 00:11:50,950
+ضمن المنطق سليم، من أجل الوصول للـ output اللي عندك
+
+147
+00:11:50,950 --> 00:11:54,810
+إياه، وبالتالي دائمًا المفروض أنا أتحدث عن
+
+148
+00:11:54,810 --> 00:11:59,310
+procedure، مجموعة من الخطوات توديني
+
+149
+00:12:01,690 --> 00:12:05,150
+إلى من؟ للحل اللي أنا بدي إياه، لنتيجة الـ output اللي
+
+150
+00:12:05,150 --> 00:12:16,450
+أنا... آه، لازم تديني الحل، هو الهدف، الـ
+
+151
+00:12:16,450 --> 00:12:18,390
+algorithm.
+
+152
+00:12:20,860 --> 00:12:25,100
+تعريفه: هو عبارة عن finite sets of precise
+
+153
+00:12:25,100 --> 00:12:30,520
+instructions أو steps، مجموعة منتهية من الخطوات
+
+154
+00:12:30,520 --> 00:12:37,420
+الواضحة أو التعليمات الواضحة، ليش؟ for performing
+
+155
+00:12:37,420 --> 00:12:44,330
+computation، من أجل تنفيذ أو لتنفيذ عمليات حسابية، or
+
+156
+00:12:44,330 --> 00:12:49,230
+for solving a problem. الآن يا شباب، ما تفهمليش
+
+157
+00:12:49,230 --> 00:12:53,270
+دائمًا كلمة مشكلة، عن أنها trouble، تمام؟ أنه أنا في
+
+158
+00:12:53,270 --> 00:12:57,430
+عندي شغلة بدي أوصلها لنتيجة، يعني مش ضروري دائمًا
+
+159
+00:12:57,430 --> 00:13:02,310
+مصطلح مشكلة دائمًا سلبي، تمام؟ ممكن تُعبر عن حاجة
+
+160
+00:13:02,310 --> 00:13:08,210
+تمام؟ بتقول عنها حلّ، ونحن مشكلة. طيب، الآن، معناته الـ
+
+161
+00:13:08,210 --> 00:13:15,140
+algorithm هذا هو عبارة عن finite، مجموعة منتهية من
+
+162
+00:13:15,140 --> 00:13:19,420
+الخطوات الواضحة، أو من التعليمات الواضحة، من أجل
+
+163
+00:13:19,420 --> 00:13:28,960
+تنفيذ عملية حسابية أو حل مشكلة معينة، مثل لو أنا
+
+164
+00:13:28,960 --> 00:13:32,800
+بدي algorithm يجيب لي أكبر قيمة موجودة في الـ
+
+165
+00:13:32,800 --> 00:13:36,820
+sequence، أكبر قيمة موجودة في الـ sequence، والـ
+
+166
+00:13:36,820 --> 00:13:42,840
+sequence هذه finite، مثل لو إجينا قلنا: سبعة...
+
+167
+00:13:42,840 --> 00:13:50,700
+ثلاثة... خمسة... اثنان... ثمانية... واحد... عشرة، و
+
+168
+00:13:50,700 --> 00:13:55,880
+دي سألتك: أيش أكبر قيمة؟ عشرة... كلكم هتقولوا
+
+169
+00:13:55,880 --> 00:14:02,200
+عشرة. طيب، اذكر لي
+
+223
+00:17:55,920 --> 00:18:02,380
+temporary maximum قارنتها مع السبعة هل مصبوط؟ if
+
+224
+00:18:02,380 --> 00:18:07,720
+the larger لو كان الرقم أكبر مهراته بدل خلي ال
+
+225
+00:18:07,720 --> 00:18:13,480
+maximum تساوي كذا و هكذا و بتكرر الـ Previous Step
+
+226
+00:18:13,480 --> 00:18:17,040
+مع الـ Next Integer لحد ما تصل لنهاية الـ Sequence
+
+227
+00:18:17,040 --> 00:18:23,700
+في الأخير انت هتوقف إذا كان مافيش  No Integer مرة
+
+228
+00:18:23,700 --> 00:18:26,440
+يعني خلصت الـ Sequence تبعتك انت هتقف أو تكون حصيت
+
+229
+00:18:26,440 --> 00:18:30,380
+على ال .. عفوا الـ maximum أو الـ temporary maximum
+
+230
+00:18:30,380 --> 00:18:33,820
+number هو الـ max integer اللي هيكون عندك هاي الـ
+
+231
+00:18:33,820 --> 00:18:37,300
+Precise Steps ممكن انت تروح تصيغها بصورة أبسط من
+
+232
+00:18:37,300 --> 00:18:41,320
+هيك كمان كل ما كانت مقدرتك على كتابتها أو صيغتها
+
+233
+00:18:41,320 --> 00:18:45,900
+بشكل أبسط بكون الـ algorithm تبعك أفضل و إذا قدرت
+
+234
+00:18:45,900 --> 00:18:51,620
+تكتبوا رياضيات بكون أفضل و أفضل لإيش؟ لأنه أنا
+
+235
+00:18:51,620 --> 00:18:55,360
+مابديش ييجي لي حد يقولي إيش يعني الـ next integer
+
+236
+00:18:55,360 --> 00:19:00,640
+يعني بس إيه اتنين من الـ sequence طيب لما أنا
+
+237
+00:19:00,640 --> 00:19:03,180
+روحانة و رجحتني يقولي repeat with the previous
+
+238
+00:19:03,180 --> 00:19:06,510
+step طب انت ماقلتي ليه شهر أنه تحرك الـ pointer اللي
+
+239
+00:19:06,510 --> 00:19:10,250
+أمام خطوة؟ فأنت بتدخل في حالة من أنه ممكن ال
+
+240
+00:19:10,250 --> 00:19:14,030
+ambiguity أو عدم الوضوح في الـ steps إذا أنا بعتمد
+
+241
+00:19:14,030 --> 00:19:17,670
+على الـ natural language لغة الإنسان فبالتالي الآن
+
+242
+00:19:17,670 --> 00:19:22,730
+بحاول أصيغها بشكل رياضي عشان إيهاش تصير confirmed
+
+243
+00:19:22,730 --> 00:19:25,990
+واضحة 100% مابختلفوش عليها اتنين
+
+244
+00:19:28,660 --> 00:19:32,420
+من ضمن الصياغات البسيطة اللي عندي هان أن أنا أكتب
+
+245
+00:19:32,420 --> 00:19:35,560
+الـ algorithm ضمن special format بيسميه بينا بيسيدو
+
+246
+00:19:35,560 --> 00:19:42,640
+كود لغة .. لغة أعلى من لغة .. أو عفوا أقل من لغة
+
+247
+00:19:42,640 --> 00:19:47,520
+البشر و أعلى من لغة الكمبيوتر إيش لغة الكمبيوتر؟
+
+248
+00:19:47,520 --> 00:19:51,060
+لغة البرمجة تمام؟ يعني تكتب الـ pseudo code في مرحلة
+
+249
+00:19:51,060 --> 00:19:55,960
+منتصف ما بين لغتك اللغة الرائعة اللي هي human
+
+250
+00:19:55,960 --> 00:20:01,760
+languages و لغة الآلة مثل إيش؟ بروح بعرف بقوله أنا
+
+251
+00:20:01,760 --> 00:20:11,140
+بده أكتب الـ procedure أو الـ algorithm اسمه
+
+252
+00:20:11,140 --> 00:20:17,320
+و بعطيله الـ input اللي موجودين عندي finite
+
+253
+00:20:17,320 --> 00:20:22,240
+sequence يعني من a1 لحد am، بظبط؟ مش غير هيك هي
+
+254
+00:20:22,240 --> 00:20:25,200
+عشان تكون finite، ما بنفعش أحط بالقبل ellipses و أسكت
+
+255
+00:20:25,200 --> 00:20:28,710
+معاه تهتد، بتقول إلى ما لا نهاية الخطوة الثانية
+
+256
+00:20:28,710 --> 00:20:34,810
+كانت حط الـ max بشكل مؤقت يساوي الـ first element
+
+257
+00:20:34,810 --> 00:20:38,570
+اللي هي a واحد اللي عندي هنا بعد هيك اعمل for
+
+258
+00:20:38,570 --> 00:20:43,170
+جملة تكرار loop عشان هيك قلتلك لغة وسط ال
+
+259
+00:20:43,170 --> 00:20:47,890
+pseudocode هي عبارة عن لغة وسط ما بين لغة الآلة و
+
+260
+00:20:47,890 --> 00:20:53,120
+لغة الإنسان for الـ I بتساوي اتنين الـ next integer
+
+261
+00:20:53,120 --> 00:20:57,380
+الـ next position لو وجد واحد يتسأل وين الـ I و
+
+262
+00:20:57,380 --> 00:21:03,400
+هي البيانات هيها؟ شايف وينها؟ عند الـ AI إيش AI؟
+
+263
+00:21:03,400 --> 00:21:06,040
+هي الـ A1 و A2 و A3 و A4 و A5 و A6 و A7 و A8 و A9
+
+264
+00:21:06,040 --> 00:21:07,300
+و A10 و A11 و A12 و A13 و A14 و A15 و A16 و A16 و
+
+265
+00:21:07,300 --> 00:21:13,020
+A17 و A18 و A19 و A20 و A21 و A22 و A22 و A22 و
+
+266
+00:21:13,020 --> 00:21:14,380
+A23 و A22 و A23 و A21 و A21 و A21 و A22 و A21 و
+
+267
+00:21:14,380 --> 00:21:14,660
+A21 و A21 و A21 و A21 و A21 و A21 و A21 و A21 و
+
+268
+00:21:14,660 --> 00:21:17,820
+A21 و A21 و A21 و A21 و A21 و A21 و A21 و A21 و
+
+269
+00:21:17,820 --> 00:21:18,160
+A21 و A21 و A21 و A21 و A21 و
+
+270
+00:21:21,330 --> 00:21:26,090
+المقارنة مش هي F statement لو كانت الـ maximum أقل
+
+271
+00:21:26,090 --> 00:21:31,310
+من الـ AI AI أول مرة كانت تساوي A2 مظبوط ثم الـ
+
+272
+00:21:31,310 --> 00:21:38,010
+maximum يساوي AI وكرر العملية هذه لحد ما تنتهي من
+
+273
+00:21:38,010 --> 00:21:42,050
+الـ sequence كلها يعني هيك كل ما تنفذ هذا
+
+274
+00:21:42,050 --> 00:21:46,910
+الشرط أو تنفذ هذه ارجع مرة ثانية لحد ما توصل قيمة
+
+275
+00:21:46,910 --> 00:21:52,080
+الـ I تساوي الـ N بعد الـ N اوقف، لا تكمل الشغل لأن
+
+276
+00:21:52,080 --> 00:21:57,400
+سيكون الـ sequence خلصت وبهيك أنت تكون فعليا الـ max
+
+277
+00:21:57,400 --> 00:22:03,700
+بتحتوي على أكبر element موجود في الـ sequence ولو
+
+278
+00:22:03,700 --> 00:22:07,160
+طلعت الخطوات هذه كمان مرة هي نفس الخطوات اللي أنت
+
+279
+00:22:07,160 --> 00:22:12,840
+سويتها أثناء كتابتي للـ sequence ولو أنا .. لو
+
+280
+00:22:12,840 --> 00:22:17,420
+أظهرتلك الـ sequence الآن بشكل مفاجئ تمام؟ وقلتلك
+
+281
+00:22:17,420 --> 00:22:21,970
+هاتلي أكبر element فيها هتلقد المقارنات هذه بنفس
+
+282
+00:22:21,970 --> 00:22:26,790
+الترتيب بس طبعا صعب أنك تدرك السرعة اللي الله وهبك
+
+283
+00:22:26,790 --> 00:22:30,650
+إياها تمام في التحديد بمجرد أن عينيك بمر على
+
+284
+00:22:30,650 --> 00:22:35,950
+الأرقام دماغك كان بيقارن و بيحصل على الـ output أو
+
+285
+00:22:35,950 --> 00:22:39,130
+بيقرر من الـ max لحد ما تصل لأكبر element الموجود و
+
+286
+00:22:39,130 --> 00:22:43,910
+طبعا كل ما كانت الـ sequence أطول هتحس أن النتيجة
+
+287
+00:22:43,910 --> 00:22:49,150
+تتأخر في الوصول لمين لأن مدى الرؤية تبعك .. مدى
+
+288
+00:22:49,150 --> 00:22:53,270
+الرؤية تبعك .. تمام؟ محدود .. يعني أعتقد أن في
+
+289
+00:22:53,270 --> 00:22:56,830
+إشكالية بميز من تمانية لتسعة أو من سبعة
+
+290
+00:22:56,830 --> 00:23:00,990
+لتسعة أرقام كل مرة .. كل مرة الـ system .. ستة
+
+291
+00:23:00,990 --> 00:23:10,910
+لتمانية .. أكيد؟ في الآخر في عندك قدرتك محدودة لكن
+
+292
+00:23:10,910 --> 00:23:14,170
+الـ computer .. الـ computer ما بيقدر يعمل المقارنة هذه
+
+293
+00:23:14,170 --> 00:23:21,670
+مرة واحدة .. بيشتغل؟ اتنين اتنين طيب
+
+294
+00:23:21,670 --> 00:23:25,710
+و إذا نتذكر .. نتذكر في عامل .. لما قلنا زمان أو
+
+295
+00:23:25,710 --> 00:23:28,730
+كانوا يعلمونا الحساب لما قلنا واحد زائد تلاتة
+
+296
+00:23:28,730 --> 00:23:34,350
+زائد خمسة زائد سبعة زائد تسعة و بدي الـ output إيش
+
+297
+00:23:34,350 --> 00:23:40,070
+كنت بتساوي لما كانوا بدا يعلمونا و ما زلنا لليوم؟
+
+298
+00:23:40,070 --> 00:23:48,100
+هان أربعة زائد خمسة تسعة زائد السبعة ستة عشر زائد
+
+299
+00:23:48,100 --> 00:23:56,240
+التسعة خمسة وعشرين هذه المحصلة ما تقدرش تنفذ العملية
+
+300
+00:23:56,240 --> 00:24:03,100
+كلها مرة واحدة وبالتالي أنت بتشتغل sequence الـ
+
+301
+00:24:03,100 --> 00:24:08,320
+algorithm له مجموعة من الخصائص مجموعة من الخصائص
+
+302
+00:24:08,320 --> 00:24:14,230
+الخاصية الأولى الـ input ما بتقدرش تبني algorithm بدون
+
+303
+00:24:14,230 --> 00:24:18,530
+معطيات ما تقدرش تحل المشكلة بدون ما يكون في عندك
+
+304
+00:24:18,530 --> 00:24:22,850
+input معطياتك الأساسية من المعطيات لما قلنا بدنا
+
+305
+00:24:22,850 --> 00:24:25,830
+نجيب قطر المستطيل أو عفوا قطر المثلث القائم
+
+306
+00:24:25,830 --> 00:24:30,290
+الزاوية هنا قاعد بقولك مثلث قائم الزاوية هذا طول
+
+307
+00:24:30,290 --> 00:24:35,350
+طول الضلع كذا والزاوية كذا مع أن في عندك ضلع
+
+308
+00:24:35,350 --> 00:24:39,570
+وزاوية بتقدر تجيبه بناء على معرفتك القانون أو
+
+309
+00:24:39,570 --> 00:24:43,870
+المثلث حساب المثلثات اللي موجود عندك دائما
+
+310
+00:24:43,870 --> 00:24:49,830
+الـ algorithm زي ما قلنا له input values حسب إيش الـ
+
+311
+00:24:49,830 --> 00:24:54,190
+algorithm بده في المثال السابق لما قلنا جيب أكبر
+
+312
+00:24:54,190 --> 00:24:58,210
+element في الـ list أكبر element في الـ list إيش الـ
+
+313
+00:24:58,210 --> 00:25:03,650
+input؟ الـ list فقط تمام؟ هذا حد يختلف تماما للـ
+
+314
+00:25:03,650 --> 00:25:07,850
+input لو أنا جيت قلتلك بدي تدورلي على element في
+
+315
+00:25:07,850 --> 00:25:12,430
+list بدي تشوف الـ X موجودة ولا مش موجودة بصير الـ
+
+316
+00:25:12,430 --> 00:25:20,070
+input عندك شغلتين الـ list والـ X اتنين الـ output الـ
+
+317
+00:25:20,070 --> 00:25:23,830
+output الشباب هو المفروض إيش يمثل؟ يمثل الـ
+
+318
+00:25:23,830 --> 00:25:26,830
+solution المفروض الـ output يمثل الـ solution
+
+319
+00:25:26,830 --> 00:25:31,390
+النتيجة اللي أنا بدي إياها algorithm بدون نتيجة
+
+320
+00:25:31,390 --> 00:25:37,070
+ما بلزمش algorithm بدون نتيجة ما بلزمش لأنه فعليا لا
+
+321
+00:25:37,070 --> 00:25:41,170
+يشكل حل للمشكلة تبعتي لذا لازم أشوف منه output
+
+322
+00:25:47,850 --> 00:25:51,470
+definiteness تعريفه لازم يكون واضح تعريفه إيش احنا
+
+323
+00:25:51,470 --> 00:25:54,510
+قبل شوية لما عرفنا الـ algorithm بشكل عام قلنا هو
+
+324
+00:25:54,510 --> 00:25:59,750
+عبارة عن مجموعة finite set
+
+325
+00:25:59,750 --> 00:26:05,830
+of precise set أو steps عفوا كمان مرة عرفناه على
+
+326
+00:26:05,830 --> 00:26:11,990
+أنه finite set of precise steps أو instructions
+
+327
+00:26:11,990 --> 00:26:19,650
+مجموعة من الخطوات المتتالية و لا لأ وبالتالي لازم
+
+328
+00:26:19,650 --> 00:26:22,490
+يكون الـ algorithm تبعتك الخطوات تبعتك تكون معرفة
+
+329
+00:26:22,490 --> 00:26:27,390
+بشكل واضح لازم تكون معرفة بشكل واضح لا يحتمل
+
+330
+00:26:27,390 --> 00:26:31,810
+التأويل correctness correctness صحة الـ algorithm
+
+331
+00:26:31,810 --> 00:26:37,360
+لازم الـ algorithm يعطيني نتيجة صحيحة ما بنفعش بأي حال
+
+332
+00:26:37,360 --> 00:26:43,020
+من الأحوال أجي أقولك أنا بدي الـ maximum number و
+
+333
+00:26:43,020 --> 00:26:48,340
+تروح تقولي مجموع الأرقام 25 مش منطق فلازم يكون
+
+334
+00:26:48,340 --> 00:26:53,280
+الـ algorithm بدي output صحيح correctness بعد هيك
+
+335
+00:26:53,280 --> 00:26:58,320
+finiteness الخطوات شو صفتها يا شباب؟ finite لازم
+
+336
+00:26:58,320 --> 00:27:02,400
+تكون محدودة ما أقدرش أقول ماشي إلى ما لا نهاية أضعها
+
+337
+00:27:02,400 --> 00:27:04,120
+فوق؟ أكيد
+
+338
+00:27:06,820 --> 00:27:09,920
+ممكن أقولك اعددلي تلاتة اعددلي أربعة اعرفلي إيش
+
+339
+00:27:09,920 --> 00:27:18,760
+كده؟ اه رياضيات Effectiveness فعّالة مؤثرة إيش يعني
+
+340
+00:27:18,760 --> 00:27:23,100
+فعّالة مؤثرة؟ أنه فعليا بتديني النتيجة ضمن فترة
+
+341
+00:27:23,100 --> 00:27:28,240
+زمانية مقبولة فترة زمانية finite كمان مرة يا شباب إذا
+
+342
+00:27:28,240 --> 00:27:33,780
+فيه بده يجيني حل المشكلة تمام؟ أو بعض المشاكل بدي
+
+343
+00:27:33,780 --> 00:27:39,260
+أحلها الآن لو إجاني الحل بكرا بيلزمنيش؟ ولا لأ؟ زي
+
+344
+00:27:39,260 --> 00:27:41,640
+ما أنت بتكون عاصف مثال في الـ quiz زي يا أحمد
+
+345
+00:27:41,640 --> 00:27:45,940
+بيقولك أنا بستمر أي حد يحط إجابات الـ quiz على الـ
+
+346
+00:27:45,940 --> 00:27:50,560
+model أو على الـ facebook قبل ما فترة الـ quiz تخلص
+
+347
+00:27:50,560 --> 00:27:53,620
+أنت جيت يا خالد حطيت إجابتها بعد ما خلصنا؟ وإيش بده في
+
+348
+00:27:53,620 --> 00:27:57,480
+حلك أنا؟ ما بصيرش .. وبالتالي أحيانا بعض الـ
+
+349
+00:27:57,480 --> 00:28:01,560
+solutions لازم تكون ضمن فترة زمانية محددة
+
+350
+00:28:01,560 --> 00:28:08,520
+generality التعميم هل بقدر أعمم الـ algorithm تبعي؟
+
+351
+00:28:08,520 --> 00:28:12,780
+generality لازم يكون الـ algorithm .. لازم يكون الـ
+
+352
+00:28:12,780 --> 00:28:17,180
+algorithm general عام يعني بقدر أعممه على مشكلة
+
+353
+00:28:17,180 --> 00:28:20,760
+مشابهة احنا الآن كانت المشكلة السابقة في الـ
+
+354
+00:28:20,760 --> 00:28:26,060
+algorithm هذا أنه أنا أجيب أكبر element بين integer
+
+355
+00:28:26,060 --> 00:28:31,140
+في الـ sequence هذه لو قدّلت الـ sequence لمجموعة من
+
+356
+00:28:31,140 --> 00:28:36,220
+الـ strings مجموعة من الرسائل هل الـ algorithm بيشتغل
+
+357
+00:28:36,220 --> 00:28:45,420
+بالفعل؟ ليش لأ؟ ليش لأ؟ هاي الـ generality أنه بقدر
+
+358
+00:28:45,420 --> 00:28:49,040
+أعمل على مشكلة أكبر منه بنفس الـ concept اه بقدر
+
+359
+00:28:49,040 --> 00:28:57,190
+الآن لو أنا سألتك علي و راني أحط إشارة أكبر منه
+
+360
+00:28:57,190 --> 00:29:04,230
+وأصغر منه هذا
+
+361
+00:29:04,230 --> 00:29:10,010
+السؤال اللي بيطرح نفسه أنا بسألك بقدر أعممه أصلا
+
+362
+00:29:10,010 --> 00:29:13,930
+أنت بتقولي اه أي شغلتين بتقارنهم مع بعض اه بينفع
+
+363
+00:29:13,930 --> 00:29:16,970
+إيش بعد هي شرط المقارنة في الأكبر و الأصغر من شغلك
+
+364
+00:29:16,970 --> 00:29:20,810
+أنا بقدر أقولك أنا بقدر أقارن بناء على الـ value
+
+365
+00:29:20,810 --> 00:29:28,400
+لكل character بتطلع Rani أكبر لأن الـ R أكبر من الـ A
+
+366
+00:29:28,400 --> 00:29:33,560
+الـ ASCII value تبع الـ R أكبر من الـ A وبالتالي باخد
+
+367
+00:29:33,560 --> 00:29:42,080
+decision لكن لو جينا على علي و أحمد على
+
+368
+00:29:42,080 --> 00:29:48,040
+نفس الـ concept السابق بتطلع علي .. علي أكبر من
+
+369
+00:29:48,040 --> 00:29:53,820
+أحمد لأن الـ L أكبر من الـ H هذا الـ algorithm و هذا
+
+370
+00:29:53,820 --> 00:29:57,200
+التفاصيل أنت مش بالضرورة تعرفها بس الآن لما أنا
+
+371
+00:29:57,200 --> 00:30:02,180
+باجي أقولك هل الـ algorithm هذا قابل الـ generality
+
+372
+00:30:02,180 --> 00:30:06,100
+قابل أن أعمله أصلا أنت الوحيد اللي بيقدر يقولي اه
+
+373
+00:30:06,100 --> 00:30:09,640
+أي شغلتين بتقارنهم مع بعض و بقدر أحدد الـ maximum و
+
+374
+00:30:09,640 --> 00:30:13,240
+الـ minimum الـ algorithm بتبقى بتطبق ما بينهم يعني
+
+375
+00:30:13,240 --> 00:30:18,520
+لو أنا اجيتك و قلتلك في هنا عشر سيارات أحجامهم
+
+376
+00:30:18,520 --> 00:30:23,460
+مختلفة الـ Algorithm تبعك بتطبق عليهم؟ اه بتطبق
+
+377
+00:30:23,460 --> 00:30:26,760
+عليهم .. إذا أنت بتبقى الأكبر حسب الحجم اه بقدر
+
+378
+00:30:26,760 --> 00:30:30,140
+أحدد أي سيارة أكبر بنفس الخطوات بأعتمد السيارة
+
+379
+00:30:30,140 --> 00:30:33,740
+الأولى هي الأكبر و بعدها بصير أقارن حجم السيارة مع
+
+380
+00:30:33,740 --> 00:30:38,960
+اللي بعدها و كل ما ألاقي أكبر بقول الأكبر صار الـ
+
+381
+00:30:38,960 --> 00:30:42,820
+max و هكذا لحد ما بصل لنتيجة و هذا احنا بنسميه الـ
+
+382
+00:30:42,820 --> 00:30:49,830
+generality أنه قابلة للتوسيع أو التعميم يعني أنت في
+
+383
+00:30:49,830 --> 00:30:53,910
+عندك مجموعة من الخطوات input و output تعريف واضح
+
+384
+00:30:53,910 --> 00:30:58,410
+نتيجة واضحة أو صحيحة finite steps و لازم response
+
+385
+00:30:58,410 --> 00:31:01,570
+في زمن مقبول effectiveness و الـ generality أنه
+
+386
+00:31:01,570 --> 00:31:09,750
+جاهز يكون أعمم الـ algorithm اللي موجود عندي و
+
+387
+00:31:09,750 --> 00:31:13,990
+احنا ليش بنعمل قاعدين algorithm؟ احنا ليش بنعمل
+
+388
+00:31:13,990 --> 00:31:17,950
+algorithm؟ يعني المشكلة already موجودة، بس أنا
+
+389
+00:31:17,950 --> 00:31:21,550
+الآن بتكلم مش في مواصفات المشكلة، بتكلم في مواصفات
+
+390
+00:31:21,550 --> 00:31:26,590
+الحل اللي عندك، بدك مشاكل؟ فضل، رتبلي مصفوفة،
+
+391
+00:31:26,590 --> 00:31:30,970
+رتبلي مجموعة أرقام في المصفوفة،
+
+392
+00:31:30,970 --> 00:31:34,670
+ممتاز، ترتيب تصاعدي،
+
+393
+00:31:40,
+
+445
+00:36:00,340 --> 00:36:05,740
+لأ، اتنين تساوى اتنين، لأ، نعم، توقف، توقف، توقف،
+
+446
+00:36:05,740 --> 00:36:06,960
+توقف، توقف، توقف، توقف، توقف، توقف، توقف، توقف،
+
+447
+00:36:06,960 --> 00:36:09,760
+توقف، توقف، توقف، توقف، توقف، توقف، توقف، توقف،
+
+448
+00:36:09,760 --> 00:36:11,660
+توقف، توقف، توقف، توقف، توقف، توقف، توقف، توقف،
+
+449
+00:36:11,660 --> 00:36:13,780
+توقف، توقف، توقف، توقف، توقف،
+
+450
+00:36:15,570 --> 00:36:18,910
+تلاتة .. خمسة .. اتنين .. واحد .. عشرة .. تمانية
+
+451
+00:36:18,910 --> 00:36:22,750
+.. خلصت الـ list وانت ما وجدتهوش، معناته الـ element
+
+452
+00:36:22,750 --> 00:36:31,030
+موجود على الـ قائمة اللي موجودة، إذا
+
+453
+00:36:31,030 --> 00:36:37,190
+انت موجود، و في الـ position الموقع تبقى بناء على الـ
+
+454
+00:36:37,190 --> 00:36:40,170
+index .. واحد .. اتنين .. تلاتة .. أربعة .. خمسة
+
+455
+00:36:40,170 --> 00:36:43,650
+.. ستة .. سبعة ..  بصفة عامة الـ index بتيجي تقول هو
+
+456
+00:36:43,650 --> 00:36:44,730
+عبارة عن الـ location
+
+457
+00:36:48,180 --> 00:36:51,880
+في لحظات البرمجة، أنا ما أتكلمش برمجة، قاعد تمام؟
+
+458
+00:36:51,880 --> 00:36:55,120
+وشوفنا مع الـ sequence، وشوفنا مع الـ sequence الـ
+
+459
+00:36:55,120 --> 00:36:57,740
+index، تبقى يمكن يبدأ من واحد ويبدأ من صفر، ومافيش
+
+460
+00:36:57,740 --> 00:37:02,000
+عندي مشكلة في الموضوع، تمام؟ والآن الـ sequence
+
+461
+00:37:02,000 --> 00:37:10,360
+المعرفة عندك هيها من a1 لـ a n، كم element؟ n من الـ
+
+462
+00:37:10,360 --> 00:37:14,400
+.. من العناصر، n من العناصر، الـ index من وين يبدأ؟ من
+
+463
+00:37:14,400 --> 00:37:17,700
+واحد، هي الـ algorithm
+
+464
+00:37:27,070 --> 00:37:39,570
+هي A1, A2, A3, A4, A5, A6, A7، السيكوانس اللي عندي
+
+465
+00:37:39,570 --> 00:37:44,910
+من سبعة عناصر، وتخيل
+
+466
+00:37:44,910 --> 00:37:50,750
+أنا بدور على الخمسة، X بتساوي خمسة، من الـ input للـ
+
+467
+00:37:50,750 --> 00:37:55,720
+algorithm، الآن الـ Sequence والـ X اللي أنا بدأت
+
+468
+00:37:55,720 --> 00:37:59,020
+أدور عليها، الـ Sequence والـ X اللي أنا بدأت أدور
+
+469
+00:37:59,020 --> 00:38:06,940
+عليها، قلت له: هاي الـ X، وهي الـ Sequence، بعد اسم
+
+470
+00:38:06,940 --> 00:38:14,860
+الـ procedure: I equal 1، I اللي هي 1 و 2 و 3 و 4 و
+
+471
+00:38:14,860 --> 00:38:17,760
+5 و 6 و 7، اللي هي العداد اللي بده يمشي خطوة خطوة
+
+472
+00:38:17,760 --> 00:38:25,390
+مع الـ elements اللي عندي، طالما الـ بروسيجر هي لغة
+
+473
+00:38:25,390 --> 00:38:30,430
+متوسطة بين الـ human language أو الـ natural
+
+474
+00:38:30,430 --> 00:38:34,570
+language والكمبيوتر language، الـ I أقل أو تساوي الـ
+
+475
+00:38:34,570 --> 00:38:34,830
+N
+
+476
+00:38:39,080 --> 00:38:42,340
+آخر index في الـ sequence، آخر index في الـ
+
+477
+00:38:42,340 --> 00:38:46,540
+sequence، والـ I أو الواحد، أول index في الـ
+
+478
+00:38:46,540 --> 00:38:50,440
+sequence، طالما أن الـ I أقل من الـ N، بوبينجو
+
+479
+00:38:50,440 --> 00:38:54,400
+سين، طالما أنه الـ sequence، أو ما وصلتش لنهاية الـ
+
+480
+00:38:54,400 --> 00:39:00,220
+sequence، and الـ X لا تساوي الـ AI، الـ current
+
+481
+00:39:00,220 --> 00:39:03,600
+element  اللي أنا موجود عليه، أروح أزيد لـ I
+
+482
+00:39:03,600 --> 00:39:08,970
+حتضلك ماشي، اللي هو بعد ما تتحقق واحد من اتنين، في
+
+483
+00:39:08,970 --> 00:39:12,850
+حالة من اتنين، إما خلصت الـ loop، هذا الـ condition
+
+484
+00:39:12,850 --> 00:39:23,870
+الأول، تمام؟ أو لاقت الـ X الموجود، نعم، ليش الـ R؟ ممتاز
+
+485
+00:39:23,870 --> 00:39:29,790
+R، إيش يعني R؟ إذا واحد منهم الـ true، بقى لك تنفذ الـ
+
+486
+00:39:29,790 --> 00:39:33,610
+loop، أنا بقول: جاهز، متى بده يطلع من الـ loop؟ لما
+
+487
+00:39:33,610 --> 00:39:38,200
+واحد منهم يصير false، الـ loop دي ما بتكفّ، هتبقى
+
+488
+00:39:38,200 --> 00:39:42,280
+المستمرة، لما الشرطين هدول .. لما إنت ما لاقيتش الـ
+
+489
+00:39:42,280 --> 00:39:45,620
+element، ولسّه .. لسه فيها عناصر .. لما اتحققت
+
+490
+00:39:45,620 --> 00:39:50,780
+الشرطين ..
+
+491
+00:39:50,780 --> 00:39:54,500
+طيب .. if الـ I أقل من الـ N، خلصت الـ loop .. إنت
+
+492
+00:39:54,500 --> 00:39:59,300
+انتقلت من الـ loop هذه الآن .. طب ليش طلعت؟ طلعت
+
+493
+00:39:59,300 --> 00:40:05,580
+لواحد من السببين: إما خلصت الـ list، تمام؟ أو لاقت الـ
+
+494
+00:40:05,580 --> 00:40:09,240
+X، أنت في الآخر طلعت من الـ loop، بدك تسأل: ليش أنا
+
+495
+00:40:09,240 --> 00:40:15,240
+طلعت؟ إذا كانت الـ I أقل أو تساوي الـ N، معناته هذا
+
+496
+00:40:15,240 --> 00:40:18,540
+الـ condition هو اللي صار false، يعني أنت فعلياً لاقت
+
+497
+00:40:18,540 --> 00:40:21,260
+الـ X اللي بدك إياها، وبالتالي الـ location تبعنا
+
+498
+00:40:21,260 --> 00:40:26,640
+تساوي I، otherwise الـ location equal 0، دلالة على أن
+
+499
+00:40:26,640 --> 00:40:30,140
+الـ element ما لهوش وجود، ممكن تحقق بدل I ناقص واحد
+
+500
+00:40:30,140 --> 00:40:35,400
+عشان الناس اللي بتبدأ بالـ index من صفر، نعم، نعم
+
+501
+00:40:35,400 --> 00:40:41,340
+مضطر تكتب مع الـ pseudocode ده، وبالتالي هاي الـ
+
+502
+00:40:41,340 --> 00:40:45,840
+algorithm، هذا الـ algorithm، تمام؟ بنسميه linear
+
+503
+00:40:45,840 --> 00:40:50,500
+search، ليش linear؟ لأنه فعلياً بيمشي مع كل element خطوة
+
+504
+00:40:50,500 --> 00:40:52,040
+خطوة خطوة
+
+505
+00:40:56,390 --> 00:41:00,310
+في عندي منهجية تانية في البحث، اسمها الـ binary
+
+506
+00:41:00,310 --> 00:41:04,570
+search، اسمها الـ binary search، بس الـ binary search
+
+507
+00:41:04,570 --> 00:41:09,830
+إيش بفترض؟ بقول لي: أنا بشتغل فقط لما تكون الـ list
+
+508
+00:41:09,830 --> 00:41:15,310
+عندي مرتبة، ترتيب تصاعدي أو تنازلي، إيش يعني مرتبة؟
+
+509
+00:41:15,310 --> 00:41:22,990
+يعني واحد، اتنين، تلاتة، خمسة، سبعة، تمانية، عشرة
+
+510
+00:41:27,190 --> 00:41:31,210
+كيف بيشتغل؟ خلصنا من اللي فوق، الآن الـ binary
+
+511
+00:41:31,210 --> 00:41:36,510
+search، منهجية تانية في البحث، بيقول: أنا بأشتغل في
+
+512
+00:41:36,510 --> 00:41:40,310
+حالة، ده كانت الـ sequence مرتبة، والـ concept
+
+513
+00:41:40,310 --> 00:41:44,370
+تبعها بكل بساطة هيجي كالتالي: الـ sequence كم
+
+514
+00:41:44,370 --> 00:41:49,550
+element فيها؟ واحد، اتنين، تلاتة، أربعة، خمسة، ستة، سبعة
+
+515
+00:41:49,550 --> 00:41:56,780
+هييجي يمسك الـ sequence من النص، هيجي ياخد الـ
+
+516
+00:41:56,780 --> 00:42:00,500
+element اللي في المنتصف، هل تساوي القيمة اللي بتدور
+
+517
+00:42:00,500 --> 00:42:07,840
+عليها؟ لأ، إذا ساواتها خلصت، أنت جبتها من أول مرة، لو
+
+518
+00:42:07,840 --> 00:42:12,600
+ما ساواتهاش، معناته بدك تكمل في البحث، بس تكملتك في
+
+519
+00:42:12,600 --> 00:42:16,620
+البحث الآن، هتاخد نص المصفوفة، أو نص الـ list
+
+520
+00:42:16,620 --> 00:42:21,060
+اللي قدامك، ليش؟ لأن هي مرتبة ترتيب تصاعدي، وبناء
+
+521
+00:42:21,060 --> 00:42:24,300
+عليها، تخيل أني أنا على سبيل المثال بدي أدور على
+
+522
+00:42:24,300 --> 00:42:31,320
+الأربعة، بدي أدور على أربعة، الآن باجي بقارن: الأربعة
+
+523
+00:42:31,320 --> 00:42:34,980
+تساوي خمسة؟ لأ، طب .. خمسة .. وبالتالي يمين ولا
+
+524
+00:42:34,980 --> 00:42:39,060
+يسار؟ بدي أروح أدور في الجزء اليسار، بدي آخد نص
+
+525
+00:42:39,060 --> 00:42:44,080
+المصفوفة اللي كانت هي إيش
+
+526
+00:42:44,080 --> 00:42:47,520
+ممكن تسوي فيها؟ كمان مرة، بدي أجي أُمسك الـ list من النص
+
+527
+00:42:47,520 --> 00:42:54,100
+عند مين؟ عند الاتنين، وأقارن: الأربعة تساوي اتنين؟
+
+528
+00:42:54,100 --> 00:43:00,880
+لأ، تمام؟ تمام .. الأربعة أكبر ولا أصغر؟ أكبر ..
+
+529
+00:43:00,880 --> 00:43:06,400
+أكبر .. أكبر
+
+530
+00:43:06,400 --> 00:43:09,500
+.. أكبر
+
+531
+00:43:09,500 --> 00:43:09,680
+.. أكبر .. أكبر .. أكبر .. أكبر .. أكبر .. أكبر ..
+
+532
+00:43:09,680 --> 00:43:09,840
+أكبر .. أكبر .. أكبر .. أكبر .. أكبر .. أكبر ..
+
+533
+00:43:09,840 --> 00:43:10,060
+أكبر .. أكبر .. أكبر .. أكبر .. أكبر .. أكبر ..
+
+534
+00:43:10,060 --> 00:43:19,980
+أكبر .. أكبر .. أكبر
+
+535
+00:43:19,980 --> 00:43:28,440
+.. أكبر .. أكبر ..  أكتّر خطوات، استني بس، الآن لو
+
+536
+00:43:28,440 --> 00:43:32,620
+قلت لك في الـ linear search كم خطوة عشان توصل؟ تقول
+
+537
+00:43:32,620 --> 00:43:39,220
+الأربعة مش موجودة، سبع خطوات، مضبوط؟ طيب، تعال نجرب
+
+538
+00:43:39,220 --> 00:43:45,840
+على element موجود، محمد، البيع زي إيش كنت بدك؟ ممكن
+
+539
+00:43:45,840 --> 00:43:48,900
+يعني الأربعة، ممكن مجلد، وتاني الأربعة يكون بعيد
+
+540
+00:43:48,900 --> 00:43:52,240
+ماشي، إحنا عمال نقول يا صاحبي، قول للـ binary search
+
+541
+00:43:52,240 --> 00:43:54,300
+شرط إن تكون الـ list مرتبة
+
+542
+00:43:57,190 --> 00:44:01,210
+مش بيرتب القرية، ما لهاش علاقة بترتيب القرية، الشرط هو
+
+543
+00:44:01,210 --> 00:44:06,610
+binary search، بقول: أنا بأصلح، بنفع أشتغل مع list
+
+544
+00:44:06,610 --> 00:44:12,710
+مرتبة، بس الآن في الـ linear search، حتى لو أديتك الـ
+
+545
+00:44:12,710 --> 00:44:17,970
+list مرتبة، هيها، وقلت لك ابحث linear search عليها
+
+546
+00:44:17,970 --> 00:44:22,710
+إيش هتسوي؟ هتمشي السبع خطوات عشان تجيب الأربعة، مش
+
+547
+00:44:22,710 --> 00:44:28,990
+موجودة، لكن مع ضمان إن الـ list هات مرتبة، الـ binary
+
+548
+00:44:28,990 --> 00:44:32,910
+search، بقول لك ما بتكفّش حلقة، هنورّجيك شغل، فايدة إنّه
+
+549
+00:44:32,910 --> 00:44:39,770
+كويسة، تعال ندور على التمانية، نص الـ list، خمسة
+
+550
+00:44:39,770 --> 00:44:48,430
+تمانية أكبر، معناته النص هيجي ينزل، ماشي، الآن بروح على
+
+551
+00:44:48,430 --> 00:44:52,740
+القائمة هذه، وبمسكها من المنتصف،  بجيب التمانية
+
+552
+00:44:52,740 --> 00:44:56,720
+خطوتين، طب تخيل أنا بدي أدور على السبعة أو على
+
+553
+00:44:56,720 --> 00:45:01,800
+التلاتة .. السبعة أو التلاتة أو العشرة، تلت خطوات
+
+554
+00:45:01,800 --> 00:45:07,160
+طيب، تعال بس نتكلم على شغل أكبر، تخيل إن لو كانت
+
+555
+00:45:07,160 --> 00:45:11,220
+عندك في القائمة ألف وأربعة وعشرين element، وهلأ
+
+556
+00:45:11,220 --> 00:45:14,640
+بتبقى أقول لك ليش ألف وأربعة وعشرين بالتحديد؟ ألف و
+
+557
+00:45:14,640 --> 00:45:19,480
+أربعة وعشرين element، عشان آخد decision فوق على
+
+558
+00:45:19,480 --> 00:45:23,540
+الـ linear search، معناته بدك تشتغل ألف وأربعة و
+
+559
+00:45:23,540 --> 00:45:29,200
+عشرين عملية مقارنة، مظبوط؟ طيب، بينما على
+
+560
+00:45:29,200 --> 00:45:32,840
+الـ binary search، لما تكون البيانات مرتبة، إنت بس
+
+561
+00:45:32,840 --> 00:45:37,140
+بحاجة تشتغل عشر مرات تفحص، عشان إما تلاقي الـ element
+
+562
+00:45:37,140 --> 00:45:43,450
+أو تقول مش موجود، عشر خطوات كحد أقصى، كيف هذا الكلام
+
+563
+00:45:43,450 --> 00:45:46,850
+اللي أنا بقوله؟ تعال نحسبها بكل بساطة، أول مرة
+
+564
+00:45:46,850 --> 00:45:51,830
+وَفّرت عليه خمسين في المئة من الـ list، صح ولا لأ؟ في
+
+565
+00:45:51,830 --> 00:45:56,410
+المرة اللي بعديها طيّرت
+
+566
+00:45:56,410 --> 00:46:02,150
+كمان ربع، يعني نص النص، ربع، مضبوط؟ وبعدين طيّرت تمن
+
+567
+00:46:02,150 --> 00:46:06,290
+وبعدين طيّرت واحد على ستة عشر، واحد على اثنين و
+
+568
+00:46:06,290 --> 00:46:12,780
+ثلاثين، واحد على أربعة و ستين، واحد على مئة و ثمانية
+
+569
+00:46:12,780 --> 00:46:17,440
+وعشرين، واحد على متين وستة وخمسين، واحد على خمسماية
+
+570
+00:46:17,440 --> 00:46:23,900
+وإثنين، واحد على ألف وأربعة وعشرين، هذه عشر خطوات، كل
+
+571
+00:46:23,900 --> 00:46:28,120
+مرة كنت بقى أخلص من النص اللي باقي، وهذه الـ
+
+572
+00:46:28,120 --> 00:46:31,640
+sequence بدها تساوي log
+
+573
+00:46:34,230 --> 00:46:40,170
+الـ 1024 للأساس اتنين، لأنه عملية binary ثنائي، كل
+
+574
+00:46:40,170 --> 00:46:46,790
+مرة بخلص من النص، اتنين، مضبوط؟ الـ 1024 هذه تساوي
+
+575
+00:46:46,790 --> 00:46:52,670
+اتنين أس عشرة، وهذه
+
+576
+00:46:52,670 --> 00:47:02,470
+المحصلة تساوي عشرة، هتلاحظ إن كل ما زاد الرقم، كل
+
+577
+00:47:02,470 --> 00:47:07,690
+ما يقلّ خطوات الحل، يعني لو كان عندي من 512 element
+
+578
+00:47:07,690 --> 00:47:15,270
+عشان تجيب النتيجة كحد أقصى بدك تسع خطوات، ألف وأربعة
+
+579
+00:47:15,270 --> 00:47:20,770
+وعشرين، ضعفها، زادت خطوة واحدة بس في البحث، الآن
+
+580
+00:47:20,770 --> 00:47:26,270
+ضعفها كمان مرة، خطوة واحدة اللي هتزيد، مش أكتر، بس في
+
+581
+00:47:26,270 --> 00:47:32,450
+عين الرقم هذا بيكون ضعف، مضبوط؟ بتصير ألفين و ثمانية
+
+582
+00:47:32,450 --> 00:47:36,990
+واربعين، وضل زي ذلك، وبالتالي أصبح الـ binary search
+
+583
+00:47:36,990 --> 00:47:43,290
+ممكن يشكل فرق، لو أنا تأكدت المصفوفة تبعتي مرتبة،
+
+584
+00:47:43,290 --> 00:47:46,790
+طب لو ما كانتش مرتبة، بقدر أطبّق الـ binary search؟ لأ
+
+585
+00:47:46,790 --> 00:47:51,450
+طب أروح أرتبها، وأقف شوية تروح ترتبها، معناته هتدخل
+
+586
+00:47:51,450 --> 00:47:55,030
+تكلفة تانية، عملية ترتيب المصفوفة بحد ذاتها
+
+587
+00:47:55,030 --> 00:47:59,440
+algorithm بحد ذاتها مشكلة بدها حل، وبالتالي إحنا
+
+588
+00:47:59,440 --> 00:48:03,160
+قاعد أنا بتكلم، أنا زودتك بمصفوفة وبدي تعمل الـ
+
+589
+00:48:03,160 --> 00:48:07,280
+search، في مجال public binary، وفي مجال public
+
+590
+00:48:07,280 --> 00:48:13,300
+linear، إيش تستخدم؟ حسب وضع القضية، إذا والله هي
+
+591
+00:48:13,300 --> 00:48:17,240
+مرتبة، ترتيب تصاعدي أو تنازلي، بروح باتجاه الـ binary
+
+592
+00:48:17,240 --> 00:48:23,240
+search، شوف
+
+593
+00:48:23,240 --> 00:48:26,620
+إنت مقارنة عشر خطوات عشان تأخذ decision
+
+594
+00:48:30,950 --> 00:48:45,550
+هذه الخطوات، كل
+
+595
+00:48:45,550 --> 00:48:50,110
+مرة بتمسك الـ sequence لجزئينه وبتقرر أين تذهب، وكل
+
+596
+00:48:50,110 --> 00:48:52,930
+مرة بتنصّف الـ sequence اللي موجود عندك، لحد ما توصل
+
+597
+00:48:52,930 --> 00:48:58,000
+للحل، الـ algorithm، Procedure binary search، بدي الـ X
+
+598
+00:48:58,000 --> 00:49:00,920
+وبدي الـ list، نفس الـ procedure السابق، linear كـ
+
+599
+00:49:00,920 --> 00:49:06,640
+input، وافترضت إن الـ I equal 1، تمام؟ والـ J equal
+
+600
+00:49:06,640 --> 00:49:12,900
+الـ N، ليش؟ عشان بدي أحصر دائماً الفترة تبعها بين I و
+
+601
+00:49:12,900 --> 00:49:18,200
+J، I و J، أول مرة كانت فترة واحدة، مضبوط؟ لأن بعد ما
+
+602
+00:49:18,200 --> 00:49:21,160
+أنصفها، بدي أقرر بدي أروح ليمين ولا شمال، فيّا إما
+
+603
+00:49:21,160 --> 00:49:24,920
+بدي أحرك الـ I للمنتصف، أو بدي أجيب الـ J للمنتصف، عشان
+
+604
+00:49:24,920 --> 00:49:29,780
+أحافظ على الفترة اللي موجودة، يعني تخيل، هاي،
+
+605
+00:49:29,780 --> 00:49:37,540
+اتنين، سبعة، خمسة، ثمانية، تسعة، عشرة، إثني عشر،
+
+606
+00:49:37,540 --> 00:49:41,720
+أربعة، إثني عشر، واحد، اتنين، تلاتة، أربعة، خمسة،
+
+607
+00:49:41,720 --> 00:49:48,100
+ستة، سبعة، هذا I، وهنا الـ J اللي هي السبعة، لأن لما
+
+608
+00:49:48,100 --> 00:49:52,600
+أنا بدي أجيب هاي المنتصف، اجيت عند التسعة، لأن الـ
+
+609
+00:49:52,600 --> 00:49:56,520
+element اللي أنا بدور عليه، الأربعة، إيش هو المفروض
+
+610
+00:49:56,520 --> 00:49:59,900
+اساوي؟ بدي أروح باتجاه الـ I، يعني بدي أحرك مين؟
+
+611
+00:49:5
+
+667
+00:55:26,230 --> 00:55:31,830
+ثمانية زي ما هي، طيب كمان مرة، لأن ايش بيتصرف أول
+
+668
+00:55:31,830 --> 00:55:37,450
+عنصر وآخر عنصر؟ هل حصل له نتيجة بالتبديل هذا؟ مش
+
+669
+00:55:37,450 --> 00:55:40,730
+شايف الحل، أنو وصل لنتيجة بالشكل هذا بدون ما ايش
+
+670
+00:55:42,530 --> 00:55:44,890
+وبالتالي... هاي... لو أنا بدي أرجع أبدل... هل
+
+671
+00:55:44,890 --> 00:55:48,650
+مافيش تغيير؟ هل مافيش تغيير؟ هل مافيش تغيير؟ بدي
+
+672
+00:55:48,650 --> 00:55:56,650
+أبدأ على مين؟ على الـ Next Element 2 و 7... 2 و 7
+
+673
+00:55:56,650 --> 00:56:01,410
+... وأنا 1 و 3... يعني 5... 2... 7... 1... 3... هي
+
+674
+00:56:01,410 --> 00:56:08,800
+8... الآن... في... في تبديل... بس أصبر شوية، بين من
+
+675
+00:56:08,800 --> 00:56:12,960
+ومين؟ بين السبعة والاثنين؟ خلاص، هلاّ السبعة و الواحد
+
+676
+00:56:12,960 --> 00:56:17,040
+والخمسة
+
+677
+00:56:17,040 --> 00:56:21,020
+والاثنين. فأنتَ فعليًا ممكن، بس في الآخر بدك تكتب عدد
+
+678
+00:56:21,020 --> 00:56:25,380
+خطوات، أو بدك تبدأ تفكر بخطوات. ما أمكنكَش تكتبها بشكل
+
+679
+00:56:25,380 --> 00:56:28,880
+precise واضح، يعني زي ما قلت قبل شوية، ما نفعش أنا
+
+680
+00:56:28,880 --> 00:56:33,000
+أظل أشتغل إلّا ما اللي هي لازم تكون خطواتي واضحة.
+
+681
+00:56:33,000 --> 00:56:36,120
+لازم الفكرة تكون واضحة، والناس ممكن تبقى تعتمد عليها.
+
+682
+00:56:36,120 --> 00:56:41,740
+في حل من أشهر أنواع الـ sort اللي شغال اسمها الـ bubble
+
+683
+00:56:41,740 --> 00:56:50,760
+sort اللي احنا اشتغلناه قبل شوية مع العناصر اللي
+
+684
+00:56:50,760 --> 00:56:58,080
+موجودة عندنا. طبعًا نموذج ثالث للحل ممكن أفكر أنا هي
+
+685
+00:56:58,080 --> 00:57:03,170
+المصفوفة عندي، أعتمد دائماً أجيب الـ minimum، جبت الـ
+
+686
+00:57:03,170 --> 00:57:08,050
+minimum وشطبته وحطيته في list جديدة. مظبوط، أدور مرة
+
+687
+00:57:08,050 --> 00:57:10,770
+ثانية، أجيب الـ minimum. لاحظ كل مرة الـ list ايش
+
+688
+00:57:10,770 --> 00:57:17,230
+بتصغر، بتجي واحد وأحطه في الـ list. هذا برضه حل، بس
+
+689
+00:57:17,230 --> 00:57:19,710
+في الآخر لما تكون قادر على كتابته، في الـ bubble
+
+690
+00:57:19,710 --> 00:57:24,650
+sort اللي احنا كتبناه في الأول، بقارن كل element مع
+
+691
+00:57:24,650 --> 00:57:27,930
+اللي بعده، ولما بكون فيه swap ببدل. الـ iteration
+
+692
+00:57:27,930 --> 00:57:31,250
+الأولى، الثانية، الثالثة، الرابعة، ما أكون أوصل
+
+693
+00:57:31,250 --> 00:57:36,070
+نلاقي الحل اللي موجود عندي. هاي الـ bubble sort بكل
+
+694
+00:57:36,070 --> 00:57:40,750
+بساطة، مريت على عناصر من اللي عندي فقط، عند الـ list
+
+695
+00:57:40,750 --> 00:57:46,030
+والـ output هيكون list اللي هي مرتبة. مريت على كل
+
+696
+00:57:46,030 --> 00:57:51,890
+عناصر المصفوفة من الأول للآخر، للآخر، و
+
+697
+00:57:51,890 --> 00:57:57,160
+جرت، وكمان لو كمان مرة من واحد للآخر اللي هو
+
+698
+00:57:57,160 --> 00:58:03,260
+نقصد I، وكل ما بلاقي أنّه I<sub>G</sub> أكبر من A<sub>IG</sub> زائد واحد
+
+699
+00:58:03,260 --> 00:58:08,700
+بروْح ببدل العناصر اللي موجودة عندي لحد ما بوصل للـ
+
+700
+00:58:08,700 --> 00:58:12,720
+list أو العناصر الـ list اللي موجودة. بعض الـ
+
+701
+00:58:12,720 --> 00:58:16,820
+algorithm بنسميها greedy algorithm. هنا مش
+
+702
+00:58:16,820 --> 00:58:20,780
+هنكمل، نسميها greedy algorithms اللي هي ما نسميها
+
+703
+00:58:20,780 --> 00:58:24,620
+أو الخوارزمية الطماعة. ايش الخوارزمية الطماعة؟
+
+704
+00:58:24,620 --> 00:58:29,080
+الفكرة فيها بكل بساطة أنّه أنا بجيب حل، لكن الحل هذا
+
+705
+00:58:29,080 --> 00:58:34,600
+مش أفضل حل. بناءً على ايش؟ بناءً على أنّه أنا دائماً
+
+706
+00:58:34,600 --> 00:58:38,940
+بأَنظُر لأبسط أو أفضل حل في اللحظة الآنية، ببقى اللي
+
+707
+00:58:38,940 --> 00:58:42,900
+بستشرفش المستقبل. المثال البسيط جدًا اللي ممكن
+
+708
+00:58:42,900 --> 00:58:51,340
+أقدر أحكي لكم إياه، تخيل أن في عندي مثلث بالشكل هذا: A
+
+709
+00:58:51,340 --> 00:59:01,700
+B C، وعندي كمان نقطة D، وهي الرسمة هيك، وأنتَ
+
+710
+00:59:01,700 --> 00:59:11,380
+واقف هنا عند الـ A وبدك تروح لـ D، ايش أقصر طريق؟ C
+
+711
+00:59:11,380 --> 00:59:15,680
+D أقصر طريق، بناءً على أنك الآن واقف عند الـ A، و
+
+712
+00:59:15,680 --> 00:59:22,400
+حسبت أن الـ A للـ D، والـ A للـ C، كمان اللي هي الـ
+
+713
+00:59:22,400 --> 00:59:26,060
+وتر، وهذا مثلث قائم الزاوية، فالوتر هيكون
+
+714
+00:59:26,060 --> 00:59:29,360
+أقرب element، أروح الطريق في الـ greedy algorithm
+
+715
+00:59:29,360 --> 00:59:32,800
+بتطلعش للحسبة اللي بعيدة، ايش بياخذ الـ decision
+
+716
+00:59:32,800 --> 00:59:36,460
+بناءً على ايش؟ بناءً على أنّه أنا الآن من أقصر طريق ليه
+
+717
+00:59:36,460 --> 00:59:42,170
+أروح على B ولا أروح على C؟ مباشرة هيروح على الـ B، لأن
+
+718
+00:59:42,170 --> 00:59:46,850
+هو فعليًا الآن شايفها أقصر طريق، وبناءً عليها هو أخد
+
+719
+00:59:46,850 --> 00:59:51,750
+الـ decision وراح عليها. الآن قدامه بدو يروح على الـ
+
+720
+00:59:51,750 --> 00:59:56,930
+D، يروح على الـ C ولا يروح على الـ D؟ هيروح على الـ C
+
+721
+00:59:56,930 --> 01:00:04,190
+لأن الـ C أقصر من الـ D.  أصلاً، وبعدين ما فيش قدامه غير
+
+722
+01:00:04,190 --> 01:00:11,520
+يروح على الـ D. فعليًا هو سلك أطول طريق ممكن، ليش؟ لأنه
+
+723
+01:00:11,520 --> 01:00:15,400
+كان ياخد الـ decision بناءً على الـ current situation
+
+724
+01:00:15,400 --> 01:00:19,620
+هو
+
+725
+01:00:19,620 --> 01:00:22,640
+دائمًا بياخد decision بمقارنة بين اثنين، الآن مين
+
+726
+01:00:22,640 --> 01:00:26,960
+أحسن إليه؟ أروح يمين ولا أروح شمال؟ طيب أنا الآن
+
+727
+01:00:26,960 --> 01:00:35,040
+قاعد بالجامعة وبدي أروح غزة، إيش أقصر الطرق اللي
+
+728
+01:00:35,040 --> 01:00:35,620
+بالنسبة لي؟
+
+729
+01:00:44,510 --> 01:00:48,490
+المنطقي بيقول أن أنا أروح لأقرب موقف بالنسبة لي.
+
+730
+01:00:48,490 --> 01:00:51,870
+مين أقرب موقف؟ أروح على الأزهر أو على الشجاعية؟
+
+731
+01:00:51,870 --> 01:00:57,670
+على الأزهر. طيب، تخيل أن السيارة اللي في الأزهر أو
+
+732
+01:00:57,670 --> 01:01:02,370
+على موقف الأزهر بدها تروح أولاً على الشجاعية
+
+733
+01:01:02,370 --> 01:01:07,250
+وبعدين بترجع تاني، معينة وصارت، فهذه الطريق؟ بقولش
+
+734
+01:01:07,250 --> 01:01:10,510
+اللي هو هذا الطمع، لكن فعليًا كانت decision مبني على
+
+735
+01:01:10,510 --> 01:01:16,380
+مين أقصر الطرق الموجودة عندي. هنا احنا بنسميه كمان
+
+736
+01:01:16,380 --> 01:01:21,060
+مرة هو algorithm بتعطيني حل، مش ما بيدلّيش، بوصلّي لـ
+
+737
+01:01:21,060 --> 01:01:25,940
+output المطلوب، لكن هذا الحل هل هو أفضل حل؟ لأ، في
+
+738
+01:01:25,940 --> 01:01:28,240
+أحسن منه. والله يعطيكم العافية.
diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/xXZat9maenA_postprocess.srt b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/xXZat9maenA_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..4cf4dec656d4555cb86786fb76380d5392119977
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/xXZat9maenA_postprocess.srt
@@ -0,0 +1,2952 @@
+1
+00:00:21,010 --> 00:00:22,650
+بسم الله والحمد لله والصلاة والسلام علي الرسول
+
+2
+00:00:22,650 --> 00:00:24,330
+الله اليوم ان شاء الله يا شباب هنبدأ ب chapter
+
+3
+00:00:24,330 --> 00:00:27,890
+تلاتة لو chapter ال algorithm ال chapter هيكون
+
+4
+00:00:27,890 --> 00:00:32,770
+نوعا ما مريح بالنسبالي لأن مؤدام كو أخد برمجة واحد
+
+5
+00:00:32,770 --> 00:00:37,850
+واخد برمجة اتنين واخد مقدمة تمام وفي ناس ختيرية في
+
+6
+00:00:37,850 --> 00:00:42,570
+المنطقة وبالتالي ايش وضعهم تمام فاليوم احنا نتكلم
+
+7
+00:00:42,570 --> 00:00:46,950
+على ال algorithms الخوارزميات
+
+8
+00:00:49,310 --> 00:00:53,650
+عندما أتكلم عن الخوارزميات سنغطي ثلاثة قطع في هذا
+
+9
+00:00:53,650 --> 00:00:58,190
+الفيديو فقط ماهي الخوارزمية وماهي الـ growth
+
+10
+00:00:58,190 --> 00:01:04,870
+functions زيادة أو نمو الدالة و ال complexityأو ما
+
+11
+00:01:04,870 --> 00:01:08,230
+ده خلاني أقول الـmeasurement الأساسية لل algorithm
+
+12
+00:01:08,230 --> 00:01:13,450
+جداش ال algorithm بروح بيكبر أو بكلفني وقت و space
+
+13
+00:01:13,450 --> 00:01:16,530
+لما بتكلم على complexity بتكلم مش على تعقيده
+
+14
+00:01:16,530 --> 00:01:21,690
+كمشكلة كمام أو كطريقة حل بقدر ما بتكلم على التكلفة
+
+15
+00:01:21,690 --> 00:01:27,750
+الزمنية تمام؟ و ال space تبع الداكرة للجهاز اللي
+
+16
+00:01:27,750 --> 00:01:34,120
+موجود عندى طيب لما بتكلم علىالخوارزمية او
+
+17
+00:01:34,120 --> 00:01:41,460
+الخوارزميات ضرورى نذكر الخوارزمى اللى هو محمد ابن
+
+18
+00:01:41,460 --> 00:01:46,440
+موسى الخوارزمى ابو جعفر احد علماء المسلمين في عصره
+
+19
+00:01:46,440 --> 00:01:53,700
+طبعا فيك تتخيل كام الحسنات اللى بتصب في صحيفة
+
+20
+00:01:53,700 --> 00:01:57,660
+الراجل هذا ليش؟ طبعا لما نتكلم على ال algorithms
+
+21
+00:01:57,660 --> 00:02:02,840
+نتكلم علىزي ما قلنا أبو جعفر محمد المنصور ابن موسى
+
+22
+00:02:02,840 --> 00:02:08,260
+الخوارزمى كان أحد علماء المسلمين وكان مهتم أو بارع
+
+23
+00:02:08,260 --> 00:02:15,110
+في علمين علم الفلكأسترونومر والرياضيات وطبعا
+
+24
+00:02:15,110 --> 00:02:18,650
+بنتكلم على علم الفلك و علم الرياضيات معناته بنتكلم
+
+25
+00:02:18,650 --> 00:02:22,570
+على العلوم الفضاء وعلى الرياضيات والمكوك و الفضاء
+
+26
+00:02:22,570 --> 00:02:26,290
+ومش عارفش فالراجل هذا هو صاحب الأساس طبعا كان من
+
+27
+00:02:26,290 --> 00:02:30,350
+أبرز علماء المسلمين في بغداد لما كانت بغداد مقصد
+
+28
+00:02:30,350 --> 00:02:33,090
+العلم في كل العالم الموجود هناك وكان موجود هناك
+
+29
+00:02:33,090 --> 00:02:36,870
+دار بسموها بيت الحكمة أو دار الحكمة تمام نسأل الله
+
+30
+00:02:36,870 --> 00:02:40,210
+أن يرزقنا وإياك وجميع المسلمين الحكمةلكن لما انا
+
+31
+00:02:40,210 --> 00:02:44,990
+بتكلم على ال algorithm معناته انا بتكلم على حل
+
+32
+00:02:44,990 --> 00:02:50,370
+مشاكل بتكلم على حل لمشكلة معينة والمشكلة دائما
+
+33
+00:02:50,370 --> 00:02:55,570
+بنحاول نعكسها على مبدأ رياضيات مثل لو انا اعطيتك
+
+34
+00:02:55,570 --> 00:02:58,550
+sequence من ال integers مرة تعلينا كلمة sequence
+
+35
+00:02:58,550 --> 00:03:02,790
+مرة تعلينا sequence او اجيب ال largest one اجيبلي
+
+36
+00:03:02,790 --> 00:03:06,490
+اكبر element في ال sequence هاي او اعطيك مجموعة
+
+37
+00:03:06,490 --> 00:03:13,140
+setوارح اقولك هاتلي كل subset منها اللي احنا
+
+38
+00:03:13,140 --> 00:03:21,240
+سمناها ال power set مصبوط او بديك مجموعة من ال
+
+39
+00:03:21,240 --> 00:03:26,600
+integers و تروح ترتبلياهم ترتيب تصعدي او تنازليأو
+
+40
+00:03:26,600 --> 00:03:31,180
+بديك شبكة .. مجموعة من النقاط و بقولك اديني أقصر
+
+41
+00:03:31,180 --> 00:03:36,200
+طريق ما بين قطين .. أقصر طريق ما بين قطين .. هذه
+
+42
+00:03:36,200 --> 00:03:41,100
+هي المسائل اللي .. اللي هتتكلم عليها في الفصل او
+
+43
+00:03:41,100 --> 00:03:46,040
+ال chapter هذا لما بتكلم على ال algorithm معناته
+
+44
+00:03:46,040 --> 00:03:49,760
+انا بتكلم على طريقة للحل methodology و لما بتكلم
+
+45
+00:03:49,760 --> 00:03:54,830
+على ال methodology معناته انا بتكلم لازم ابنيموديل
+
+46
+00:03:54,830 --> 00:04:05,450
+موديل موديل موديل موديل موديل موديل موديل موديل
+
+47
+00:04:05,450 --> 00:04:10,070
+موديل موديل موديل نموذج نموذج نموذج نموذج نموذج
+
+48
+00:04:10,070 --> 00:04:13,550
+نموذج نموذج نموذج نموذج نموذج نموذج نموذج نموذج
+
+49
+00:04:13,550 --> 00:04:19,830
+نموذج نموذج نموذج نموذج نموذج نموذج نموذج نموذج
+
+50
+00:04:19,830 --> 00:04:20,710
+نموذج نموذج نموذج نموذج
+
+51
+00:04:23,230 --> 00:04:27,350
+لـ Mathematical Context لنص رياضي ليش نص رياضي او
+
+52
+00:04:27,350 --> 00:04:31,990
+رياضيات يا شباب لإن احنا شفنا سابقا .. شفنا سابقا
+
+53
+00:04:31,990 --> 00:04:36,490
+انه لما كنت بتكلم في مواصفات ال systems انه ممكن
+
+54
+00:04:36,490 --> 00:04:39,410
+ال system يحتمل تأويل النص اللي بالعربي او
+
+55
+00:04:39,410 --> 00:04:42,650
+بالانجليزي اللي بتوادل بين الناس ممكن نختلف في
+
+56
+00:04:42,650 --> 00:04:45,950
+معناه لأ كان قصدك كذا لأ القصد كان كذا لكن لما
+
+57
+00:04:45,950 --> 00:04:51,610
+بتتحول او ببنيها برياضيات زي ما شفنابالـ
+
+58
+00:04:51,610 --> 00:04:54,510
+quantifiers والـ predicates صارت مافيش مجال يا
+
+59
+00:04:54,510 --> 00:04:57,430
+true يا false مافيش اثنين بيختلفوا على ال values
+
+60
+00:04:57,430 --> 00:05:01,850
+تبعتها وبالتالي لما انا بحول او بحاول ابني من خلال
+
+61
+00:05:01,850 --> 00:05:06,430
+ال algorithm اللي عندي نموذج رياضي للمشكلة عشان
+
+62
+00:05:06,430 --> 00:05:11,190
+اقدر احلها اذا قدرت احول المشكلة او احور المشكلة
+
+63
+00:05:11,190 --> 00:05:15,290
+لموضوع رياضيات بتنحل وبالمناسبة معظم بحوث ال
+
+64
+00:05:15,290 --> 00:05:19,270
+computer science او ال IT اليوم الغالبية العظمى
+
+65
+00:05:19,270 --> 00:05:23,060
+بتتركز وين؟في موضوع الرياضيات سيبني من الناس اللي
+
+66
+00:05:23,060 --> 00:05:27,040
+بتشتغل تطبيقات على رغم أن أهميتها اللي غير مش هي
+
+67
+00:05:27,040 --> 00:05:31,000
+الأساس في التطور .. مش هي الأساس في التطور لكن
+
+68
+00:05:31,000 --> 00:05:36,740
+الرياضيات هي الأهم بعد ما تبني ال model تمام؟ بدك
+
+69
+00:05:36,740 --> 00:05:41,860
+تروح تبني طريقة أو تحدد خطواتعشان تحل الـ General
+
+70
+00:05:41,860 --> 00:05:45,860
+Problem باعتمادك على الموديل الموجود هذا باعتمادك
+
+71
+00:05:45,860 --> 00:05:48,820
+على الموديل اللي موجود طبعا هذا الكلام .. خلنا
+
+72
+00:05:48,820 --> 00:05:51,880
+نقول كلام إنشائي مش هركز عليه كتير ولا هسألك يعني
+
+73
+00:05:51,880 --> 00:05:54,500
+في اللحظة من اللحظات اكتبلي مواصفات ال methodology
+
+74
+00:05:54,500 --> 00:05:57,860
+واش هو ال model و الاخير لأ لأن المادة هي مادة
+
+75
+00:05:57,860 --> 00:06:03,900
+رياضيات و بدنا نروح عليها بشكل أساسي و بسيط معناته
+
+76
+00:06:03,900 --> 00:06:10,290
+أنت بحاجةلإجراء أو لخطوات تتبعها تمام لمسميها
+
+77
+00:06:10,290 --> 00:06:17,430
+procedure that follows a sequence of steps خطوات
+
+78
+00:06:17,430 --> 00:06:21,530
+متتالية أو متتالية من ال steps أو الخطوات عشان
+
+79
+00:06:21,530 --> 00:06:28,270
+تحصل وتؤدي إلى حل المشكلة الموجودة طبعا حد معاك
+
+80
+00:06:28,270 --> 00:06:35,380
+بمثال طريف تمامبواهدف انه فعليا انا ممكن احل
+
+81
+00:06:35,380 --> 00:06:41,140
+المشكلة اللي انا بقى بديها باكثر من طريقة لكن في
+
+82
+00:06:41,140 --> 00:06:46,280
+شغلات هنتفق عليها لازم تكون موجودة المثال بكل
+
+83
+00:06:46,280 --> 00:06:52,460
+بساطة لو انت فكرت تعمل فنجان قهوة تمام؟ ايش
+
+84
+00:06:52,460 --> 00:06:58,830
+الخطوات الخطوات اللي انت بتعملهاتمام؟ او تتبعها
+
+85
+00:06:58,830 --> 00:07:03,230
+عشان تنتج في الآخر او تحصل على فنجان جهوى المشكلة
+
+86
+00:07:03,230 --> 00:07:08,610
+.. المشكلة الآن ان انت مزاجك مش تمام بيدفعك لفنجان
+
+87
+00:07:08,610 --> 00:07:13,430
+جهوى الآن .. بدنا نعمل فنجان جهوى .. في حد بيقدر
+
+88
+00:07:13,430 --> 00:07:17,990
+يقولليش الخطوات؟ اه .. بعد الخيار اللي بيقولك اشوف
+
+89
+00:07:17,990 --> 00:07:22,280
+اذا في جهوى في الأولهذه ليست خطوة الجهاز لكي أعمل
+
+90
+00:07:22,280 --> 00:07:27,160
+في إنجان جهاز لازم يكون فيه جهاز لازم يكون فيه
+
+91
+00:07:27,160 --> 00:07:30,500
+مالجة لازم يكون فيه نار لازم يكون فيه ميّه وغلاق
+
+92
+00:07:30,500 --> 00:07:37,740
+كل الشغلات هذه احنا بيسميها input هذه المعطيات
+
+93
+00:07:37,740 --> 00:07:42,800
+تماما تماما مثل ما انا اجي اقولك هاي في عندك مثلث
+
+94
+00:07:42,800 --> 00:07:47,280
+و
+
+95
+00:07:47,280 --> 00:07:48,320
+بدي قولك قوله C
+
+96
+00:07:53,340 --> 00:07:58,260
+بتقدر تجيب طولة بلا C ولا أمرك بس إيش بلزمك؟ لو
+
+97
+00:07:58,260 --> 00:08:02,660
+أنت .. بدك بقوا قيادة عشان تقدر تبني حالك عليها لو
+
+98
+00:08:02,660 --> 00:08:06,980
+أنا بديتك ال A و ال C أو A و B عفوا كأضواء أطولة
+
+99
+00:08:06,980 --> 00:08:10,780
+بتجيبوا بالإضافة إذا قلتلك إن المثلث قائم الزاوية
+
+100
+00:08:10,780 --> 00:08:16,400
+لو مافيش بلعينه زامية ممكن أديكي ياهم و في الآخر
+
+101
+00:08:16,400 --> 00:08:21,190
+تحصل عليها لكن بدون ال inputبتقدرش تبني Algorithm
+
+102
+00:08:21,190 --> 00:08:24,010
+فحكاية ان انا بدي جهوة و بدي ميه و بدي كده هدى
+
+103
+00:08:24,010 --> 00:08:27,290
+كلها انساها هدى كلها متوفرة عندك الآن انا بدي
+
+104
+00:08:27,290 --> 00:08:35,050
+خطوات sequence of steps مجموعة من الخطوات توديني
+
+105
+00:08:35,050 --> 00:08:37,650
+او توصلني ان انا فعليا انشئ او اعمل فى انجل الجهة
+
+106
+00:08:37,650 --> 00:08:42,270
+اللى انا بديها عشان احل مشكلتي الآن خطوات سيبني من
+
+107
+00:08:42,270 --> 00:08:46,510
+ال ingredients المكونات كلها متوفرة عندك فضل خطوات
+
+108
+00:08:48,830 --> 00:08:53,550
+أحد بغلى الميه في خطوة قبلها بدي أضيف الميه في
+
+109
+00:08:53,550 --> 00:08:59,210
+الغلاية اتفضل رجعنا يشتري الجهوة صحي النوم يا
+
+110
+00:08:59,210 --> 00:09:03,350
+أستاذي احنا قولنا كل المكونات الحين حاطيتها قدامك
+
+111
+00:09:03,350 --> 00:09:11,130
+على الطاولة بحط بضخيها بسكر مفقتلك سكر تمل حاطينا
+
+112
+00:09:11,130 --> 00:09:15,530
+الميه في الغلاية وقالناها طيب احط الجهوة على الميه
+
+113
+00:09:15,530 --> 00:09:22,290
+بعد ما غليت احركها شويةجهزت، مصبوط؟ وصلنا لفنجان
+
+114
+00:09:22,290 --> 00:09:27,970
+الجهوة، ممتاز فى حد عنده خطوات تانية؟
+
+115
+00:09:27,970 --> 00:09:36,950
+شايفين انتوا الظرف جديش؟ طيب، الآن .. الآن ممكن
+
+116
+00:09:36,950 --> 00:09:41,750
+أنا أعيد الخطوات تانية بشكل مختلف أحط الجهوة، أدير
+
+117
+00:09:41,750 --> 00:09:44,570
+عليها المي باردة، بعدين أحطها على نار تقلل مع بعض
+
+118
+00:09:46,100 --> 00:09:51,520
+لاحظ انه انا بتكلم عن اختلاف الخطوات المحصلة في
+
+119
+00:09:51,520 --> 00:09:57,180
+الآخر فنجان جهوة بنفس المكونات اللي اعتمدت عليها
+
+120
+00:09:57,180 --> 00:10:01,480
+في الخطوات السابقة انا بدي اعتمد عليها ..لكن كلنا
+
+121
+00:10:01,480 --> 00:10:07,040
+بنجمع انه مستحيل احصل انا على فنجان الجهوة بدون ما
+
+122
+00:10:07,040 --> 00:10:11,330
+اغليالميّه .. لأ .. شوف شباب احنا اتفرجنا ان
+
+123
+00:10:11,330 --> 00:10:14,910
+المكونات الميّه والجهوه والنار وكده كلها دي موجود
+
+124
+00:10:14,910 --> 00:10:19,350
+واساسي عشان انا يقدر اعمل لان مستحيل كمان مرة اجي
+
+125
+00:10:19,350 --> 00:10:21,430
+اقول بدي اعمل جهوه وانا ماعنديش جهوه او بدي اعمل
+
+126
+00:10:21,430 --> 00:10:23,750
+جهوه وانا ماعنديش ميّه او بدي اعمل جهوه وانا
+
+127
+00:10:23,750 --> 00:10:27,740
+ماعنديش نارفهذه ال input كلها لازم تتوفر فانا
+
+128
+00:10:27,740 --> 00:10:31,860
+بتكلم على خطوات ال steps اللى انا بدى احصل فيها
+
+129
+00:10:31,860 --> 00:10:35,440
+على ال output تبعى بناء على ال input اللى عندي
+
+130
+00:10:35,440 --> 00:10:42,440
+المعطيات اللى عندي الان لو انت عندك كل المعطيات لو
+
+131
+00:10:42,440 --> 00:10:47,320
+انت عندك كل المعطيات و بتعرفش قانون في ثغوس بتقدر
+
+132
+00:10:47,320 --> 00:10:52,650
+تجيب قول الضلقلو انت ما تعرفش حساب وثلثات وعندك كل
+
+133
+00:10:52,650 --> 00:10:56,730
+الزوايا معروفة أو الأضلاع معروفة مع هذا الـC،
+
+134
+00:10:56,730 --> 00:11:03,150
+ماتقدرش تجيبه، مصبوط؟ فال input الأساسي، احنا مش
+
+135
+00:11:03,150 --> 00:11:06,690
+مختلفين عليه، انا بتكلم عن الخطوات اللي انت باك
+
+136
+00:11:06,690 --> 00:11:11,960
+تنفذها، وبالتالي اختلاف الخطواتتمام؟ ممكن يكون
+
+137
+00:11:11,960 --> 00:11:15,880
+صحيح .. ممكن يكون صحيح و يؤدي لنفس النتيجة لكن ولا
+
+138
+00:11:15,880 --> 00:11:20,380
+واحد فينا هيجي يقول والله أنا بدي أحط الجهوة في
+
+139
+00:11:20,380 --> 00:11:25,600
+الغلاية بدون الميه .. تمام؟ و أخليها تغلي و بعدين
+
+140
+00:11:25,600 --> 00:11:30,380
+أدفلها الميه .. ايه صارت الخطوة هذه؟ incense ..
+
+141
+00:11:30,380 --> 00:11:33,910
+الخطوة هذه مش منطقية الجهوة مابتغليشمصبوط؟ لأن
+
+142
+00:11:33,910 --> 00:11:37,310
+عشان تغلي لازم يكون في عندك الميّه موجودة وبالتالي
+
+143
+00:11:37,310 --> 00:11:40,330
+انت اختلف اتحقق الميّه في الأول و سبت تغلي لحالها
+
+144
+00:11:40,330 --> 00:11:43,150
+ولا خلّيت الجهو و الميّه و خلّيتهم يغلو مع بعض
+
+145
+00:11:43,150 --> 00:11:47,450
+بالمحصلة .. اعادة ترتيب للخطوات ضمن ال logic او
+
+146
+00:11:47,450 --> 00:11:50,950
+ضمن المنطق سليم من أجل الوصول لل output اللي عندك
+
+147
+00:11:50,950 --> 00:11:54,810
+إياه وبالتالي دائما المفروض انا بتكلم على
+
+148
+00:11:54,810 --> 00:11:59,310
+procedure مجموعة من الخطوات اتوديني
+
+149
+00:12:01,690 --> 00:12:05,150
+لمن؟ للحل اللي انا بدي اياه لنتيجة ال output اللي
+
+150
+00:12:05,150 --> 00:12:16,450
+انا .. اه لازم تديني الحل هو الا الفاضي ال
+
+151
+00:12:16,450 --> 00:12:18,390
+algorithm
+
+152
+00:12:20,860 --> 00:12:25,100
+تعريفه هو عبارة عن finite sets of precise
+
+153
+00:12:25,100 --> 00:12:30,520
+instructions أو steps مجموعة منتهية من الخطوات
+
+154
+00:12:30,520 --> 00:12:37,420
+الواضحة أو التعليمات الواضحة ليش؟ for performing
+
+155
+00:12:37,420 --> 00:12:44,330
+computation من أجل تنفيذ أو لتنفيذ عمليات حسابيةor
+
+156
+00:12:44,330 --> 00:12:49,230
+for solving a problem الان يا شباب ما تفهمليش
+
+157
+00:12:49,230 --> 00:12:53,270
+دائما كلمة مشكلة عن انها trouble تمام؟ انه انا في
+
+158
+00:12:53,270 --> 00:12:57,430
+عندى شغلة بدى اوصلها لنتيجة يعني مش دروري دائما
+
+159
+00:12:57,430 --> 00:13:02,310
+مصطلح مشكلة دائما سلبي تمام؟ ممكن تتعبر عن حاجة
+
+160
+00:13:02,310 --> 00:13:08,210
+تمام؟ بتقول عنها حلوان مشكلة طيب الان معناته ال
+
+161
+00:13:08,210 --> 00:13:15,140
+algorithm هذا هو عبارة عن finiteمجموعة منتهية من
+
+162
+00:13:15,140 --> 00:13:19,420
+الخطوات الواضحة او من التعليمات الواضحة من أجل
+
+163
+00:13:19,420 --> 00:13:28,960
+تنفيذ عملية حسابية او حل مشكلة معينة مثل لو انا
+
+164
+00:13:28,960 --> 00:13:32,800
+بدي algorithm يجيبلي اكبر قيمة موجودة في ال
+
+165
+00:13:32,800 --> 00:13:36,820
+sequence اكبر قيمة موجودة في ال sequence و ال
+
+166
+00:13:36,820 --> 00:13:42,840
+sequence هذه finite مثل لو اجينا قولناسبعة ..
+
+167
+00:13:42,840 --> 00:13:50,700
+تلاتة .. خمسة .. اتنين .. تمانية .. واحد .. عشرة و
+
+168
+00:13:50,700 --> 00:13:55,880
+دي اتسألتك ايش اكبر قيمة؟ عشرة .. كلكوا هتقولوا
+
+169
+00:13:55,880 --> 00:14:02,200
+عشرة طيب اذكر للخطوات .. اذكر للخطوات اللي انت
+
+170
+00:14:02,200 --> 00:14:08,890
+وصلت فيها للعشرةانت بتبقى مش بتدلفت انتباهك انه
+
+171
+00:14:08,890 --> 00:14:12,470
+أنا جاعت بكتب على الأرقام بكتب الأرقام ان ده عندك
+
+172
+00:14:12,470 --> 00:14:18,210
+علم على إيش أنا بدور على ال largest value وكل رقم
+
+173
+00:14:18,210 --> 00:14:23,230
+كنت أنا بكتبه انت كنت بتقارنه مع اللي جابله كتابة
+
+174
+00:14:23,230 --> 00:14:28,110
+سبعة فانت بتنتظر كنت الرقم التاني عشان تاخد
+
+175
+00:14:28,110 --> 00:14:32,790
+decision حتى انت بدون ما تشعر يعني انت مكلفتش نفسك
+
+176
+00:14:33,500 --> 00:14:36,940
+تمام؟ فالشغلة تلقائية صارت قرنت بين السبعة
+
+177
+00:14:36,940 --> 00:14:40,040
+والتلاتة فكانت السبعة هي الأكبر اللي بعدها لما
+
+178
+00:14:40,040 --> 00:14:44,180
+كتبت خمسة مازالت السبعة تمام؟ قرنت مع السبعة
+
+179
+00:14:44,180 --> 00:14:47,120
+مازالت السبعة تمانية مباشرة قلت لها التمانية
+
+180
+00:14:47,120 --> 00:14:52,120
+الأكبر ليش؟ أول حاجة لأن عملية ال compareالمقارنة
+
+181
+00:14:52,120 --> 00:14:56,020
+هذه binary لازم تقارن بين رقمين و رقمين وهذا ال
+
+182
+00:14:56,020 --> 00:14:59,780
+sequence اللي انت سويته لحد ما وصلت لمين كتبت اخر
+
+183
+00:14:59,780 --> 00:15:03,980
+رقم كتبت العشرة الان لو انا بدأ اكتب رقم هان
+
+184
+00:15:03,980 --> 00:15:09,560
+مباشرة هتروح تقارنه مع العشرة وبناء عليه تاخد ال
+
+185
+00:15:09,560 --> 00:15:13,260
+decision انه من الرقم الاكبر مظبوط؟ وبالتالي
+
+186
+00:15:13,260 --> 00:15:19,500
+الخطوات هذه ممكن تكون انت بتقدر تحلي المشكلة تمام؟
+
+187
+00:15:20,240 --> 00:15:24,600
+و عندك خبرة كويسة في التعامل معاها عشان هيك يجيولك
+
+188
+00:15:24,600 --> 00:15:29,820
+الناس و يقولك بس اكتب لنا طريقة تفكيرك كيف انت
+
+189
+00:15:29,820 --> 00:15:33,600
+وصلت للحل اللي موجود عشان هيك في معظم الانتحانات
+
+190
+00:15:33,600 --> 00:15:38,100
+اللي بتصير و قولك عشان انا بدي جواب نهائي و قوللي
+
+191
+00:15:38,100 --> 00:15:43,120
+كيف حليت الناس اللي بتعمل المسابقات تمام؟ بتروح
+
+192
+00:15:43,120 --> 00:15:48,890
+بيقولك okay وصلت لحل المطلوب بس وارتيني حلككيف
+
+193
+00:15:48,890 --> 00:15:52,930
+جبته؟ بناء على كيف فكرت؟ تمام؟ لأن هو مش معني ..
+
+194
+00:15:52,930 --> 00:15:56,790
+مش معني بالحالة فقط اللي انت اشتغلت عليها لأنه في
+
+195
+00:15:56,790 --> 00:15:59,910
+عنده general problem مشابه ممكن يبني عليها حل إذا
+
+196
+00:15:59,910 --> 00:16:04,650
+استوعب الحل اللي موجودوبالتالي المقدر أو الـ
+
+197
+00:16:04,650 --> 00:16:10,290
+Algorithm بحتاج لقدرة او لخبرة في غريقة صياغة ..
+
+198
+00:16:10,290 --> 00:16:14,430
+صياغة او كتابة الخطوات انت بتقدر تحل لكن في عندنا
+
+199
+00:16:14,430 --> 00:16:19,070
+مشكلة وين؟ في كتابة او صياغة الخطوات اللي انا بدي
+
+200
+00:16:19,070 --> 00:16:26,050
+اكتبها مثال على اخر شباب بتسمع ممكن أمك زوجتك أختك
+
+201
+00:16:26,050 --> 00:16:32,450
+بتعمل طبخة معينة تمام؟فجأة تجيب مثلا اتصلت على
+
+202
+00:16:32,450 --> 00:16:37,010
+أخالتك، على عمتك، جتله انت بتعمل كده، كيف؟ طب ما
+
+203
+00:16:37,010 --> 00:16:40,130
+هي بتطمخها، لكن لأن لاجئك فيه اختلاف في ال output
+
+204
+00:16:40,130 --> 00:16:44,670
+اللي ممكن للأفضل أو للأحسن، فقلدت منها الطريقة
+
+205
+00:16:44,670 --> 00:16:47,390
+اللي هي إيش؟ ال steps، مجموعة الخطوات اللي اشتغلت
+
+206
+00:16:47,390 --> 00:16:51,270
+عليها، طبعا احنا بنتكلم ال input هو نفس ال input،
+
+207
+00:16:51,270 --> 00:16:54,810
+لكن في الآخر ال sequence of steps هي اللي ممكن
+
+208
+00:16:54,810 --> 00:16:59,530
+تفرج في ال output اللي موجود عندهاعشان هيك بتلاقي
+
+209
+00:16:59,530 --> 00:17:03,450
+في كتير من المطاعم الكبيرةش بيقولك سر الصناعة،
+
+210
+00:17:03,450 --> 00:17:06,170
+يعني مثلا بيجي McDonald's أو غيرها، بيقولكاش إيش
+
+211
+00:17:06,170 --> 00:17:09,010
+هي الوصفة اللي بيستخدموها مثلا في جلة الجاج أو في
+
+212
+00:17:09,010 --> 00:17:12,530
+تحديد البطاطا إلى آخرى، فبالتالي هذه شغلات .. ليش؟
+
+213
+00:17:12,530 --> 00:17:15,990
+لأن هي .. و بفترض إذا انكشفت أو انعرفت، أنا هصيرلي
+
+214
+00:17:15,990 --> 00:17:19,190
+منافسين أكبر، وبالتالي بحافظ عليها، فالفكرة دائما
+
+215
+00:17:19,190 --> 00:17:23,950
+في وصولها مجموعة ال steps الصحيحة اللي بتقود لأفضل
+
+216
+00:17:23,950 --> 00:17:30,350
+حل ممكنالكلام اللى كتبناه قبل شوية لما كتبنا الـ
+
+217
+00:17:30,350 --> 00:17:35,710
+sequence هو نفس الخطوات هان من 1 ل 4 finite steps
+
+218
+00:17:35,710 --> 00:17:40,530
+مظبوط المفروض ال steps هتكون واضحة تعالى نقرأ بقول
+
+219
+00:17:40,530 --> 00:17:43,570
+6 temporary maximum number equal to the first
+
+220
+00:17:43,570 --> 00:17:47,550
+integer يعني افترض ان ال maximum يساوي أول element
+
+221
+00:17:48,740 --> 00:17:52,220
+وهذا اللي انت سويته لما كنت تكتب السبعة بعد هيك
+
+222
+00:17:52,220 --> 00:17:55,920
+compare the next integer in the sequence to the
+
+223
+00:17:55,920 --> 00:18:02,380
+temporary maximum قارنتها مع السبعة هل مصبوط؟ if
+
+224
+00:18:02,380 --> 00:18:07,720
+the larger لو كان الرقم أكبر مهراته بدل خلي ال
+
+225
+00:18:07,720 --> 00:18:13,480
+maximum تساوي كذا و هكذا و بتكررالـ Previous Step
+
+226
+00:18:13,480 --> 00:18:17,040
+مع الـ Next Integer لحد ما تصل لنهاية الـ Sequence
+
+227
+00:18:17,040 --> 00:18:23,700
+في الأخير انت هتوقف اذا كان مافيش No Integer مرة
+
+228
+00:18:23,700 --> 00:18:26,440
+يعني خلصت الـ Sequence تبعتك انت هتقف او تكون حصيت
+
+229
+00:18:26,440 --> 00:18:30,380
+على ال .. عفوا ال maximum او ال temporary maximum
+
+230
+00:18:30,380 --> 00:18:33,820
+number هو ال max integer اللي هيكون عندك هاي الـ
+
+231
+00:18:33,820 --> 00:18:37,300
+Precise Steps ممكن انت تروح تصيغها بصورة أطفف من
+
+232
+00:18:37,300 --> 00:18:41,320
+هيك كمانو كل ما كانت مقدرتك على كتابتها أو صيغتها
+
+233
+00:18:41,320 --> 00:18:45,900
+بشكل أبسط بكون ال algorithm تبعك أفضل و إذا كدرت
+
+234
+00:18:45,900 --> 00:18:51,620
+تكتبوا رياضيات بكون أفضل و أفضل لإيش؟ لأنه أنا
+
+235
+00:18:51,620 --> 00:18:55,360
+مابديش ييجي لي حد يقولي إيش يعني ال next integer
+
+236
+00:18:55,360 --> 00:19:00,640
+يعني بس إيه اتنين من ال sequence طيب لما أنا
+
+237
+00:19:00,640 --> 00:19:03,180
+روحانة و رجحتني يقولي repeat with the previous
+
+238
+00:19:03,180 --> 00:19:06,510
+stepطب انت ماقلتي ليه شهر انه تحرك ال pointer اللي
+
+239
+00:19:06,510 --> 00:19:10,250
+أمام خطوة؟ فانت بتدخل في حالة من انه ممكن ال
+
+240
+00:19:10,250 --> 00:19:14,030
+ambiguity او عدم الوضوح في ال steps اذا انا بعتمد
+
+241
+00:19:14,030 --> 00:19:17,670
+على ال natural language لغة الإنسان فبلجي ألانين
+
+242
+00:19:17,670 --> 00:19:22,730
+بحاول أصيغها بشكل رياضي عشان إيهاش تصير confirmed
+
+243
+00:19:22,730 --> 00:19:25,990
+واضحة 100% مابختلفوش عليها اتنين
+
+244
+00:19:28,660 --> 00:19:32,420
+من ضمن الصياغات البسيطة اللى عندي هان ان انا اكتب
+
+245
+00:19:32,420 --> 00:19:35,560
+ال algorithm ضمن special format بيسميه بينا بيسيدو
+
+246
+00:19:35,560 --> 00:19:42,640
+كود لغة .. لغة أعلى من لغة .. او عفوا أقل من لغة
+
+247
+00:19:42,640 --> 00:19:47,520
+البشر و أعلى من لغة الكمبيوتر ايش لغة الكمبيوتر؟
+
+248
+00:19:47,520 --> 00:19:51,060
+لغة البرمجة تمام؟ يعني تكتب ال بيسيدو كود في مرحلة
+
+249
+00:19:51,060 --> 00:19:55,960
+منتصف ما بين لغتك اللغة الرائعة اللي هي human
+
+250
+00:19:55,960 --> 00:20:01,760
+languages و لغة الآلةمثل ايش؟ بروح بعرف بقوله انا
+
+251
+00:20:01,760 --> 00:20:11,140
+بده اكتب ال procedure او ال algorithm اسمه
+
+252
+00:20:11,140 --> 00:20:17,320
+و بعطيله ال input اللي موجودين عندي finite
+
+253
+00:20:17,320 --> 00:20:22,240
+sequence يعني من a1 لحد am، بظبط؟ مش غير هيك هي
+
+254
+00:20:22,240 --> 00:20:25,200
+عشان تكون finite، بنفعش احط بالقبل ellipses و أسكت
+
+255
+00:20:25,200 --> 00:20:28,710
+معاه تهتد، بتقول إلى ما لا نهايةالخطوة التانية
+
+256
+00:20:28,710 --> 00:20:34,810
+كانت حط ال max بشكل مؤقت يساوي ال first element
+
+257
+00:20:34,810 --> 00:20:38,570
+اللي هي a واحد اللي عندى هنا بعد هيك اعمل four
+
+258
+00:20:38,570 --> 00:20:43,170
+جملة تكرار loop عشان هيك قلتلك لغة وسط ال
+
+259
+00:20:43,170 --> 00:20:47,890
+pseudocode هي عبارة عن لغة وسط ما بين لغة الآلة و
+
+260
+00:20:47,890 --> 00:20:53,120
+لغة الإنسان four ال Iبتساوى اتنين الـ next integer
+
+261
+00:20:53,120 --> 00:20:57,380
+الـ next position لو وجدت واحد يتسأل وين الـ I و
+
+262
+00:20:57,380 --> 00:21:03,400
+هي البيانات هيها؟ شايف وينها؟ عند الـ AI إيش AI؟
+
+263
+00:21:03,400 --> 00:21:06,040
+هي الـ A1 و A2 و A3 و A4 و A5 و A6 و A7 و A8 و A9
+
+264
+00:21:06,040 --> 00:21:07,300
+و A10 و A11 و A12 و A13 و A14 و A15 و A16 و A16 و
+
+265
+00:21:07,300 --> 00:21:13,020
+A17 و A18 و A19 و A20 و A21 و A22 و A22 و A22 و
+
+266
+00:21:13,020 --> 00:21:14,380
+A23 و A22 و A23 و A21 و A21 و A21 و A22 و A21 و
+
+267
+00:21:14,380 --> 00:21:14,660
+A21 و A21 و A21 و A21 و A21 و A21 و A21 و A21 و
+
+268
+00:21:14,660 --> 00:21:17,820
+A21 و A21 و A21 و A21 و A21 و A21 و A21 و A21 و
+
+269
+00:21:17,820 --> 00:21:18,160
+A21 و A21 و A21 و A21 و A21 و
+
+270
+00:21:21,330 --> 00:21:26,090
+المقارنة مش هي F statement لو كانت ال maximum أقل
+
+271
+00:21:26,090 --> 00:21:31,310
+من ال AI AI أول مرة كانت تساوي A2 مظبوط ثم ال
+
+272
+00:21:31,310 --> 00:21:38,010
+maximum يساوي AI وكرر العملية هذه لحد ما تنتهمتها
+
+273
+00:21:38,010 --> 00:21:42,050
+من ال sequence كلها يتها يعني هيك كل ما تنفذ هذا
+
+274
+00:21:42,050 --> 00:21:46,910
+الشرط او تنفذ هذه ارجع مرة تانية لحد ما توصل قيمة
+
+275
+00:21:46,910 --> 00:21:52,080
+ال I تساوي ال N بعد ال Nوقف، لا تكمل الشغل لأن
+
+276
+00:21:52,080 --> 00:21:57,400
+سيكون الـ sequence خلصت وبهك أنت تكون فعليا ال max
+
+277
+00:21:57,400 --> 00:22:03,700
+بتحتوي على أكبر element موجود في ال sequence ولو
+
+278
+00:22:03,700 --> 00:22:07,160
+طلعت الخطوات هذه كمان مرة هي نفس الخطوات اللي انت
+
+279
+00:22:07,160 --> 00:22:12,840
+سويتها أثناء كتابتي لل sequence ولو أنا .. لو
+
+280
+00:22:12,840 --> 00:22:17,420
+أظهرتلك ال sequence الآن بشكل مفاجئ تمام؟ وقلتلك
+
+281
+00:22:17,420 --> 00:22:21,970
+هاتلي أكبر element فيهاهتلقد المقارنات هذه بنفس
+
+282
+00:22:21,970 --> 00:22:26,790
+الترتيب بس طبعا صعب انك تدرك السرعة اللى الله وهبك
+
+283
+00:22:26,790 --> 00:22:30,650
+إياها تمام فى التحديد بمجرد انك عينيك بمر على
+
+284
+00:22:30,650 --> 00:22:35,950
+الأرقام دماغك كان بقارن و بحصل على ال output او
+
+285
+00:22:35,950 --> 00:22:39,130
+بقرر من ال max لحد ما تصل لأكبر element الموجود و
+
+286
+00:22:39,130 --> 00:22:43,910
+طبعا كل ما كانت ال sequence أطول هتحس ان النتيجة
+
+287
+00:22:43,910 --> 00:22:49,150
+تتأخر في الوصول لمينلأن مدى الرؤية تبعك .. مدى
+
+288
+00:22:49,150 --> 00:22:53,270
+الرؤية تبعك .. تمام؟ محدود .. يعني اعتقد ان في
+
+289
+00:22:53,270 --> 00:22:56,830
+اسكلمته تمانية بميز من تمانية لتسعة او من سبعة
+
+290
+00:22:56,830 --> 00:23:00,990
+لتسعة أرقام كل مرة .. كل مرة ال system .. ستة
+
+291
+00:23:00,990 --> 00:23:10,910
+لتمانية .. أكيد؟ في الأخر في عندك قدرتك محدودة لكن
+
+292
+00:23:10,910 --> 00:23:14,170
+ال computer .. ال computer بقدرش يعمل المقارنة هذه
+
+293
+00:23:14,170 --> 00:23:21,670
+مرة واحدة .. بشتغل؟إتنين إتنين طيب
+
+294
+00:23:21,670 --> 00:23:25,710
+و إذا بنتذكر .. نتذكر في عامل .. لما قولنا زمان أو
+
+295
+00:23:25,710 --> 00:23:28,730
+كانوا يعلمونا الحساب لما قولنا واحد زائد تلاتة
+
+296
+00:23:28,730 --> 00:23:34,350
+زائد خمسة زائد سبعة زائد تسعة و بدي ال output إيش
+
+297
+00:23:34,350 --> 00:23:40,070
+كنت بتساوي لما كانوا بدوا يعلمونا و ما زلنا لليوم؟
+
+298
+00:23:40,070 --> 00:23:48,100
+هانا أربعةزاد خمسة تسعة زاد السبعة ستة عشر زاد
+
+299
+00:23:48,100 --> 00:23:56,240
+التسعة خمسة وعشرين هذه المحصلة تقدرش تنفذ العملية
+
+300
+00:23:56,240 --> 00:24:03,100
+كلها مرة واحدة وبالتالي انت بتشتغل sequence ال
+
+301
+00:24:03,100 --> 00:24:08,320
+algorithm له مجموعة من الخصائص مجموعة من الخصائص
+
+302
+00:24:08,320 --> 00:24:14,230
+الخصية الأولى ال inputبتقدرش تبني algorithm بدون
+
+303
+00:24:14,230 --> 00:24:18,530
+معطيات تقدرش تحل المشكلة بدون ما يكون في عندك
+
+304
+00:24:18,530 --> 00:24:22,850
+input معطياتك الأساسية من المعطيات لما تقولنا بدنا
+
+305
+00:24:22,850 --> 00:24:25,830
+نجيب قطر المستطيل او عفوا قطر المثلث القائم
+
+306
+00:24:25,830 --> 00:24:30,290
+الزاوية هنا قاعد بقولك مثلث قائم الزاوية هذا موقع
+
+307
+00:24:30,290 --> 00:24:35,350
+طول الضلع كذا والزاوية كذا مع أن في عندك ضلع
+
+308
+00:24:35,350 --> 00:24:39,570
+وزاوية بتقدر تجيبه بناء على معرفتك القانون او
+
+309
+00:24:39,570 --> 00:24:43,870
+المثلث حسابة حساب المثلثات اللي موجود عندكو دائما
+
+310
+00:24:43,870 --> 00:24:49,830
+ال algorithm زي ما قلنا له input values حسب إيش ال
+
+311
+00:24:49,830 --> 00:24:54,190
+algorithm بده في المثال السابق لما قلنا جيب أكبر
+
+312
+00:24:54,190 --> 00:24:58,210
+element في ال list أكبر element في ال list إيش ال
+
+313
+00:24:58,210 --> 00:25:03,650
+input؟ ال list فقط تمام؟ هذا حد يختلف تماما لل
+
+314
+00:25:03,650 --> 00:25:07,850
+input لو أنا جيت قلتلك بدي تدورلي على element في
+
+315
+00:25:07,850 --> 00:25:12,430
+list بدي تشوف ال X موجودة ولا مش موجودةحصير ال
+
+316
+00:25:12,430 --> 00:25:20,070
+input عندك شغلتين ال list وال X اتنين ال output ال
+
+317
+00:25:20,070 --> 00:25:23,830
+output الشباب هو المفروض ايش يمثل؟ يمثل ال
+
+318
+00:25:23,830 --> 00:25:26,830
+solution المفروض ال output يمثل ال solution
+
+319
+00:25:26,830 --> 00:25:31,390
+النتيجة اللي انا بديها algorithm بدون نتيجة
+
+320
+00:25:31,390 --> 00:25:37,070
+مابلزمش algorithm بدون نتيجة مابلزمش لأنه فعليا لا
+
+321
+00:25:37,070 --> 00:25:41,170
+يشكل حل للمشكلة تبعتي لذا لازم اشوف منه output
+
+322
+00:25:47,850 --> 00:25:51,470
+definiteness تعريفه لازم يكون واضح تعريفه اش احنا
+
+323
+00:25:51,470 --> 00:25:54,510
+قبل شوية لما عرفنا ال algorithm بشكل عام قولنا هو
+
+324
+00:25:54,510 --> 00:25:59,750
+عبارة عن مجموع finite set
+
+325
+00:25:59,750 --> 00:26:05,830
+of precise set او steps عفوا كمان مرة عرفناه على
+
+326
+00:26:05,830 --> 00:26:11,990
+انهfinite set of precise steps أو instructions
+
+327
+00:26:11,990 --> 00:26:19,650
+مجموعة من الخطوات المتتالية و لا لأ وبالتالي لازم
+
+328
+00:26:19,650 --> 00:26:22,490
+يكون ال algorithm تبعتك الخطوات تبعتك تكون معرفة
+
+329
+00:26:22,490 --> 00:26:27,390
+بشكل واضح لازم تكون معرفة بشكل واضح لا يحتمل
+
+330
+00:26:27,390 --> 00:26:31,810
+التأويل correctness correctness صحة ال algorithm
+
+331
+00:26:31,810 --> 00:26:37,360
+لازم ال algorithm يعطيني نتيجة صحيحةبينفعش بأي حال
+
+332
+00:26:37,360 --> 00:26:43,020
+من الأحوال أجي أقولك أنا بدي ال maximum number و
+
+333
+00:26:43,020 --> 00:26:48,340
+تروح تقولي المجموع الأرقام 25 مش منطق فلازم يكون
+
+334
+00:26:48,340 --> 00:26:53,280
+ال algorithm بدي output صحيح correctness بعد هيك
+
+335
+00:26:53,280 --> 00:26:58,320
+finiteness الخطوات شو صفتها يا شباب؟ finite لازم
+
+336
+00:26:58,320 --> 00:27:02,400
+تكون محدودة مقدرش أبلي ماشي إلى مالة نهاية أضعها
+
+337
+00:27:02,400 --> 00:27:04,120
+فوق؟ أكيد
+
+338
+00:27:06,820 --> 00:27:09,920
+ممكن اقولك اعددلي تلاتة اعددلي اربعة اعرفلي ايش
+
+339
+00:27:09,920 --> 00:27:18,760
+كده؟ اه رياضيات Effectiveness فعال مؤثر ايش يعني
+
+340
+00:27:18,760 --> 00:27:23,100
+فعاله مؤثر؟ انه فعليا بتديني النتيجة ضمن فترة
+
+341
+00:27:23,100 --> 00:27:28,240
+زمانية مقبولةفترة زمانية finite كمان مرة شباب إذا
+
+342
+00:27:28,240 --> 00:27:33,780
+فيه بده يجيني حل المشكلة تمام؟ أو بعض المشاكل بدي
+
+343
+00:27:33,780 --> 00:27:39,260
+حلها الآن لو إجاني الحل بكرا بيلزمنيش؟ ولا لأ؟ زي
+
+344
+00:27:39,260 --> 00:27:41,640
+ما أنت بتكون عصابيه مثال في ال quiz زي يا أحمد
+
+345
+00:27:41,640 --> 00:27:45,940
+بيقولك أنا بستمر أي حد يحط إجابات ال quiz على ال
+
+346
+00:27:45,940 --> 00:27:50,560
+model أو على ال facebook قبل ما فترة ال quiz تخلص
+
+347
+00:27:50,560 --> 00:27:53,620
+أنت جات يا خالد حطيتليها بعد ما خلصنا؟ واش بده في
+
+348
+00:27:53,620 --> 00:27:57,480
+حلك أنا؟ما بصبتش .. وبالتالي أحيانا بعض ال
+
+349
+00:27:57,480 --> 00:28:01,560
+solutions لازم تكون ضمن فترة زمانية محددة
+
+350
+00:28:01,560 --> 00:28:08,520
+generality التعميم هل بقدر أعمم ال algorithm تبعي؟
+
+351
+00:28:08,520 --> 00:28:12,780
+generality لازم يكون ال algorithm .. لازم يكون ال
+
+352
+00:28:12,780 --> 00:28:17,180
+algorithm general عام يعني بقدر أعممه على مشكلة
+
+353
+00:28:17,180 --> 00:28:20,760
+مشابهة احنا الآن كانت المشكلة السابقة في ال
+
+354
+00:28:20,760 --> 00:28:26,060
+algorithm هذا أنه أنا أجيب أكبر elementبين integer
+
+355
+00:28:26,060 --> 00:28:31,140
+في ال sequence هذه لو قدّلت ال sequence لمجموعة من
+
+356
+00:28:31,140 --> 00:28:36,220
+ال strings مجموعة من الرصوص هل ال algorithm تبحر
+
+357
+00:28:36,220 --> 00:28:45,420
+بالفعل؟ ليش لأ؟ ليش لأ؟ هاي ال generality أنه بقدر
+
+358
+00:28:45,420 --> 00:28:49,040
+أعمل على مشكلة أكبر منه بنفس ال concept أه بقدر
+
+359
+00:28:49,040 --> 00:28:57,190
+الأن لو أنا سألتك علي و رانيحطيلي إشارة أكبر منه
+
+360
+00:28:57,190 --> 00:29:04,230
+وأصغر منه هذا
+
+361
+00:29:04,230 --> 00:29:10,010
+السؤال اللي بيطرح نفسه أنا باسألك بقدر أهمي الأصل
+
+362
+00:29:10,010 --> 00:29:13,930
+انت بتقولي اه أي شغلتين بتقارنوا مع بعض اه بينفع
+
+363
+00:29:13,930 --> 00:29:16,970
+ايش بعد هي شرط المقارنة في الأكبر و الأصغر من شغلك
+
+364
+00:29:16,970 --> 00:29:20,810
+أنا بقدر أقولك أنا بقدر أقارن بناء على ال value
+
+365
+00:29:20,810 --> 00:29:28,400
+لكل characterبتطلع راني أكبر لأن ال R أكبر من ال A
+
+366
+00:29:28,400 --> 00:29:33,560
+ال ask value تبع ال R أكبر من ال A وبالتالي باخد
+
+367
+00:29:33,560 --> 00:29:42,080
+decision لكن لو جينا علي و أحمد على
+
+368
+00:29:42,080 --> 00:29:48,040
+نفس ال concept السابق بتطلع علي .. علي أكبر من
+
+369
+00:29:48,040 --> 00:29:53,820
+أحمد لأن ال Lأكبر من ال H هذا ال algorithm و هذا
+
+370
+00:29:53,820 --> 00:29:57,200
+التفاصيل انت مش بالضرورة تعرفها بس الآن لما انا
+
+371
+00:29:57,200 --> 00:30:02,180
+بجب اقولك هل ال algorithm هذا قابل ال generality
+
+372
+00:30:02,180 --> 00:30:06,100
+قابل ان اعمله الاصل انت الوحيد اللي بيقدر تقولي اه
+
+373
+00:30:06,100 --> 00:30:09,640
+اي شغلتين بتقارنوا مع بعض و بقدر احدد ال maximum و
+
+374
+00:30:09,640 --> 00:30:13,240
+ال minimum ال algorithm تبقى بتطبق ما بينهم يعني
+
+375
+00:30:13,240 --> 00:30:18,520
+لو انا اجيتك و قلتلك في هنا عشر سيارات أحجامهم
+
+376
+00:30:18,520 --> 00:30:23,460
+مختلفةالـ Algorithm تبعك بتطبق عليهم؟ اه بتطبق
+
+377
+00:30:23,460 --> 00:30:26,760
+عليهم .. اذا انت بتبقى الأكبر حسب الحجم اه بقدر
+
+378
+00:30:26,760 --> 00:30:30,140
+احددك اي سيارة أكبر بنفس الخطوات باعتمدوا السيارة
+
+379
+00:30:30,140 --> 00:30:33,740
+الأولى هي الأكبر و بعدها بصير اقارن حجم السيارة مع
+
+380
+00:30:33,740 --> 00:30:38,960
+اللتي بعدها و كل ما لاقي أكبر بقول الأكبر سوى ال
+
+381
+00:30:38,960 --> 00:30:42,820
+max و هكذا لحد ما بصل لنتيجة و هذا احنا بنسميه ال
+
+382
+00:30:42,820 --> 00:30:49,830
+generality انه قابلة للتوسيع او التعميميعني انت في
+
+383
+00:30:49,830 --> 00:30:53,910
+عندك مجموعة من الخطوات input و output تعريف واضح
+
+384
+00:30:53,910 --> 00:30:58,410
+نتيجة واضحة او صحيحة finite steps و لازم response
+
+385
+00:30:58,410 --> 00:31:01,570
+في زمن مقبول effectiveness و ال generality انه
+
+386
+00:31:01,570 --> 00:31:09,750
+جاهز يكون اعمم ال algorithm اللي موجود عندى و
+
+387
+00:31:09,750 --> 00:31:13,990
+احنا ليش بنعمل قاعدين algorithm؟أحنا ليش بنعمل
+
+388
+00:31:13,990 --> 00:31:17,950
+algorithm؟ يعني المشكلة already موجودة، بس أنا
+
+389
+00:31:17,950 --> 00:31:21,550
+الآن بتكلم مش في مواصفات المشكلة، بتكلم في مواصفات
+
+390
+00:31:21,550 --> 00:31:26,590
+الحل اللي عندك، بدك مشاكل؟ فضل، رتبلي مصفوفة،
+
+391
+00:31:26,590 --> 00:31:30,970
+رتبلي مجموعة تراصل في المصفوفة،
+
+392
+00:31:30,970 --> 00:31:34,670
+ممتاز، ترتيب تصعدي،
+
+393
+00:31:40,930 --> 00:31:44,870
+ممتاز تماما الشباب هي نفس المثال الأول تبع فنجان
+
+394
+00:31:44,870 --> 00:31:48,850
+الجهوة انا في الآخر مشكلتي هتكون واضحة بالنسبالي و
+
+395
+00:31:48,850 --> 00:31:54,930
+بناء عليها .. بناء عليها بتتحدد المعطيات يعني مثل
+
+396
+00:31:54,930 --> 00:32:02,190
+.. ارجع كمان مرة للمثال المثلث ايش مشكلتي؟ بدي
+
+397
+00:32:02,190 --> 00:32:06,620
+قولك بلع مشكلتي ان انا بدي قولك بلع C ال waterالان
+
+398
+00:32:06,620 --> 00:32:13,220
+عشان تقدر تحل لازم يكون في عندك input بدون ال
+
+399
+00:32:13,220 --> 00:32:16,340
+input مش هتقدر تحل ماشي الحال زودتك بال input
+
+400
+00:32:16,340 --> 00:32:21,460
+مُثلَف قائم الزاوية وهي a و بيقول الأضلاع وفّرتلك
+
+401
+00:32:21,460 --> 00:32:27,520
+input ال algorithm تمام لازم تديني output تجي تقول
+
+402
+00:32:27,520 --> 00:32:33,540
+ان ال c equal كده و لطلع الخطوات تبعتك تعريف
+
+403
+00:32:33,540 --> 00:32:39,260
+خطواتك لازم تكون واضح و دقيقو Finite تديني output
+
+404
+00:32:39,260 --> 00:32:44,640
+صحيحة كل ما أغيرلك أنا في قيمة a و b الأصل تديني
+
+405
+00:32:44,640 --> 00:32:47,660
+نتيجة صحيحة مش في لحظة من اللحظات تقولي أنا مقدرش
+
+406
+00:32:47,660 --> 00:32:53,260
+أديك نتيجة Finiteness مش معقول تبقى تجرب إلى نهاية
+
+407
+00:32:53,260 --> 00:32:56,320
+و من خطوة لخطوة بدون أن الخطوات تتمتهي
+
+408
+00:32:56,320 --> 00:33:00,420
+Effectiveness لازم يكون في برنامجك أو ال algorithm
+
+409
+00:33:00,420 --> 00:33:06,920
+تبعتك الخطوات تبعتها فعالة بين جثين تتناسبمن ناحية
+
+410
+00:33:06,920 --> 00:33:10,400
+زمانية مع الحجم المُعطَى يعني لما أقول لك قارب من
+
+411
+00:33:10,400 --> 00:33:16,080
+خمس علاصر يقارب قارب من خمس تلاف أنصار دي نقالة
+
+412
+00:33:16,080 --> 00:33:21,400
+قابلة ان زي ما قلنا انوسعهم طيب الارهين algorithm
+
+413
+00:33:21,400 --> 00:33:27,280
+بقول لي مشكلتي ان انا بدي اوجد او بدي افحص هل ال X
+
+414
+00:33:27,280 --> 00:33:31,960
+موجودة في list of integers ولا لأ يعني بيديني list
+
+415
+00:33:31,960 --> 00:33:35,620
+of integers مجموعة من القيم وليكن على سبيل المثال
+
+416
+00:33:37,650 --> 00:33:45,630
+سبعة ثلاثة خمسة اتنين واحد عشرة تمانية اتنين اتنين
+
+417
+00:33:45,630 --> 00:33:51,510
+موجودة فلس اكيد الان
+
+418
+00:33:51,510 --> 00:33:54,890
+ال element اللي انا بديه بدي تقوللي هل هو موجود
+
+419
+00:33:54,890 --> 00:34:02,670
+ولا مش موجود طبعا طيب ايش دكتور هتساوي لاحظ طالما
+
+420
+00:34:02,670 --> 00:34:05,870
+انا مابلت ال cash ايش ال element اللي انا بدي ادور
+
+421
+00:34:05,870 --> 00:34:14,550
+عليهايه باك تساوي؟ اللي بينفعش .. اللي بينفعش تيجي
+
+422
+00:34:14,550 --> 00:34:18,550
+على بوابة الجامعة و تقول للأمن اللي موجود بالله
+
+423
+00:34:18,550 --> 00:34:24,210
+وين بلاجي الدكتور؟ من الدكتور اللي بدك إياه؟
+
+424
+00:34:24,210 --> 00:34:29,900
+الدكتور اللي .. بينفعش، إذا بدك تدور على شغلةلازم
+
+425
+00:34:29,900 --> 00:34:34,060
+يكون في إلها مواصفات واضحة عشان تقدر تدور عليها
+
+426
+00:34:34,060 --> 00:34:37,880
+وإلا فعليا أنت مكانك مش على باب الجامعة في مستشفى
+
+427
+00:34:37,880 --> 00:34:42,820
+المجانين هتكون هيك المنطق بقول يعني تقدرش تدور على
+
+428
+00:34:42,820 --> 00:34:47,680
+شغل أنت ما بتعرفهاش صح؟ صح يعني الآن لو أنا بدي
+
+429
+00:34:47,680 --> 00:34:53,860
+حازم بعرفش حازم من دار مين إذا ماكانش عالم موجود
+
+430
+00:34:53,860 --> 00:34:59,840
+معروف بينكوا شباب حازم وينه؟ مين حازم؟تمام؟
+
+431
+00:34:59,840 --> 00:35:02,560
+وبالتالي بدك تنتبه .. كويس .. عشان هيك إيش بيقول
+
+432
+00:35:02,560 --> 00:35:08,460
+هو .. لو قال لي locate X أنا بدي تكتبلي algorithm
+
+433
+00:35:08,460 --> 00:35:14,580
+يوجدلي أي قيمة في ال list اللي موجودة .. يوجدلي أي
+
+434
+00:35:14,580 --> 00:35:17,900
+قيمة أنا بدي كيها لاحقا .. هان إنت بدك تكتب
+
+435
+00:35:17,900 --> 00:35:20,840
+algorithm .. general algorithm .. يعني ال X تبدأ
+
+436
+00:35:20,840 --> 00:35:25,560
+تتغير .. بسيط ولا لأ؟ ال X تبدأ تتغير .. طيب إيش
+
+437
+00:35:25,560 --> 00:35:31,890
+الحل؟إنك تاخد في ال value تبع ال X و تقارنها مع كل
+
+438
+00:35:31,890 --> 00:35:37,710
+عناصر ال list واحد ورا التاني ال X بيتساوى سبعة و
+
+439
+00:35:37,710 --> 00:35:41,350
+هتاخد decision نعم او لا لو ال X بيتساوى سبعة
+
+440
+00:35:41,350 --> 00:35:45,790
+معناته مباشرة بدك توقف ال loop خلاص ما تكمل الشغل
+
+441
+00:35:45,790 --> 00:35:49,470
+جيتها هي ال position تباعتها واحد لو كانت ال X
+
+442
+00:35:49,470 --> 00:35:53,480
+اللي بتدور عليها اتنين اتنين تساوى سبعة لأتلاتة
+
+443
+00:35:53,480 --> 00:35:57,020
+تساوى سبعة لأ، خمسة تساوى سبعة لأ، سبعة تساوى
+
+444
+00:35:57,020 --> 00:36:00,340
+اتنين لأ، تلاتة تساوى اتنين لأ، خمسة تساوى اتنين
+
+445
+00:36:00,340 --> 00:36:05,740
+لأ، اتنين تساوى اتنين لأ، نعم، توقف، توقف، توقف،
+
+446
+00:36:05,740 --> 00:36:06,960
+توقف، توقف، توقف، توقف، توقف، توقف، توقف، توقف،
+
+447
+00:36:06,960 --> 00:36:09,760
+توقف، توقف، توقف، توقف، توقف، توقف، توقف، توقف،
+
+448
+00:36:09,760 --> 00:36:11,660
+توقف، توقف، توقف، توقف، توقف، توقف، توقف، توقف،
+
+449
+00:36:11,660 --> 00:36:13,780
+توقف، توقف، توقف، توقف، توقف،
+
+450
+00:36:15,570 --> 00:36:18,910
+تلاتة .. خمسة .. اتنين .. واحد .. عشرة .. تمانية
+
+451
+00:36:18,910 --> 00:36:22,750
+.. خلصت ال list وانت ما وجدتهوش معناته ال element
+
+452
+00:36:22,750 --> 00:36:31,030
+موجود على القائمة اللي موجودة إذا
+
+453
+00:36:31,030 --> 00:36:37,190
+انت موجود و في ال position الموقع تبقى بناء على ال
+
+454
+00:36:37,190 --> 00:36:40,170
+index .. واحد .. اتنين .. تلاتة .. اربعة .. خمسة
+
+455
+00:36:40,170 --> 00:36:43,650
+.. ستة .. سبعة .. بصفورت ال index بتجي تقول هو
+
+456
+00:36:43,650 --> 00:36:44,730
+عبارة عن ال location
+
+457
+00:36:48,180 --> 00:36:51,880
+في لحظات البرمجة أنا ماأتكلمش برمجة قاعد تمام؟
+
+458
+00:36:51,880 --> 00:36:55,120
+وشوفنا مع ال sequence وشوفنا مع ال sequence ال
+
+459
+00:36:55,120 --> 00:36:57,740
+index تبقى يمكن يبدأ من واحد ويبدأ من صفر ومافيش
+
+460
+00:36:57,740 --> 00:37:02,000
+عندي مشكلة في الموضوع تمام؟ و الأن ال sequence
+
+461
+00:37:02,000 --> 00:37:10,360
+المعرفة عندك هيها من a1 ل a n كم element؟ n من ال
+
+462
+00:37:10,360 --> 00:37:14,400
+.. من العناصر n من العناصر ال index من ون يبدأ؟ من
+
+463
+00:37:14,400 --> 00:37:17,700
+واحد هي ال algorithm
+
+464
+00:37:27,070 --> 00:37:39,570
+هي A1, A2, A3, A4, A5, A6, A7 السيكوانس اللي عندي
+
+465
+00:37:39,570 --> 00:37:44,910
+من سبعة أعصر وتخيل
+
+466
+00:37:44,910 --> 00:37:50,750
+أنا بدور على الخمسة X بتساوي خمسة من ال input لل
+
+467
+00:37:50,750 --> 00:37:55,720
+algorithm الآنالـ Sequence والـ X اللي أنا بدأ
+
+468
+00:37:55,720 --> 00:37:59,020
+أدور عليها الـ Sequence والـ X اللي أنا بدأ أدور
+
+469
+00:37:59,020 --> 00:38:06,940
+عليها قلت له هاي الـ X وهي الـ Sequence بعد اسم
+
+470
+00:38:06,940 --> 00:38:14,860
+الـ procedure I equal 1 I اللي هي 1 و 2 و 3 و 4 و
+
+471
+00:38:14,860 --> 00:38:17,760
+5 و 6 و 7 اللي هي العداد اللي بده يمشي خطوة خطوة
+
+472
+00:38:17,760 --> 00:38:25,390
+مع ال elements اللي عندي طالما Yالبروسيجر هي لغة
+
+473
+00:38:25,390 --> 00:38:30,430
+متوسطة بين الـ human language أو الـ natural
+
+474
+00:38:30,430 --> 00:38:34,570
+language والكمبيوتر language الـ I أقل أو تساوي ال
+
+475
+00:38:34,570 --> 00:38:34,830
+N
+
+476
+00:38:39,080 --> 00:38:42,340
+أخر index في الـ sequence أخر index في الـ
+
+477
+00:38:42,340 --> 00:38:46,540
+sequence والـ I أو الواحد أول index في الـ
+
+478
+00:38:46,540 --> 00:38:50,440
+sequence طالما أن الـ I أقل من ال N بوبينجو
+
+479
+00:38:50,440 --> 00:38:54,400
+سينطلما أنه الـ sequence أو ماوصلتش لنهاية الـ
+
+480
+00:38:54,400 --> 00:39:00,220
+sequence and ال X لا تساوي ال AI ال current
+
+481
+00:39:00,220 --> 00:39:03,600
+positive element اللي أنا موجود عليه اروح زيد ليه
+
+482
+00:39:03,600 --> 00:39:08,970
+هتضلك ماشي اللي هو بعد ما تحتجففي واحد من اتنين في
+
+483
+00:39:08,970 --> 00:39:12,850
+حالة من تنتين اما خلصت ال loop هذا ال condition
+
+484
+00:39:12,850 --> 00:39:23,870
+الاول تمام او لغا ال X الموجود نعم ليش ال R؟ ممتاز
+
+485
+00:39:23,870 --> 00:39:29,790
+R ايش يعني R؟ اذا واحد منهم ال true بقى لك نفذ ال
+
+486
+00:39:29,790 --> 00:39:33,610
+loop انا بقول جاهز متى بده يطلع من ال loop لما
+
+487
+00:39:33,610 --> 00:39:38,200
+واحد منهم يصير falseالـ loop دي ماتكيف هتبقى
+
+488
+00:39:38,200 --> 00:39:42,280
+المستمرة بلما الشرطين هدول .. بلما انت مالاجدش ال
+
+489
+00:39:42,280 --> 00:39:45,620
+element و لسه .. لسه فيها عناصر .. لما اتحققت
+
+490
+00:39:45,620 --> 00:39:50,780
+الشرطين ..
+
+491
+00:39:50,780 --> 00:39:54,500
+طيب .. if ال I أقل من ال N خلصت ال loop .. انت
+
+492
+00:39:54,500 --> 00:39:59,300
+اتنقلت من ال loop هذي الآن .. طب ليش اطلعت؟أطلعت
+
+493
+00:39:59,300 --> 00:40:05,580
+لواحد من السببين إما خلصت ال list تمام أو لجأت ال
+
+494
+00:40:05,580 --> 00:40:09,240
+X أنت في الآخر أطلعت من ال loop بدك تسأل ليش أنا
+
+495
+00:40:09,240 --> 00:40:15,240
+أطلعت إذا كانت ال I أقل أو تساوي ال N معناته هذا
+
+496
+00:40:15,240 --> 00:40:18,540
+ال condition هو اللي صار false يعني أنت فعليا لجأت
+
+497
+00:40:18,540 --> 00:40:21,260
+ال X اللي بدك إياها وبالتالي ال location تبعنا
+
+498
+00:40:21,260 --> 00:40:26,640
+تساوي I otherwise ال location equal0 دلالة على ان
+
+499
+00:40:26,640 --> 00:40:30,140
+ال element مالوش وجود ممكن تحقق بدلها صلب واحد
+
+500
+00:40:30,140 --> 00:40:35,400
+عشان الناس اللي بتبدأ بال index من صفر نعم نعم
+
+501
+00:40:35,400 --> 00:40:41,340
+مضطر تكتب مع ال pseudocode ده وبالتالي هاي ال
+
+502
+00:40:41,340 --> 00:40:45,840
+algorithm هذا ال algorithm تمام بنسميه linear
+
+503
+00:40:45,840 --> 00:40:50,500
+search ليش linear لأنه فعليا مش مع كل element خطوة
+
+504
+00:40:50,500 --> 00:40:52,040
+خطوة خطوة
+
+505
+00:40:56,390 --> 00:41:00,310
+في عند منهجية تانية في البحث اسمها ال binary
+
+506
+00:41:00,310 --> 00:41:04,570
+search اسمها ال binary search بس ال binary search
+
+507
+00:41:04,570 --> 00:41:09,830
+ايش بفترض بقوللي انا بشتغل فقط لما تكون ال list
+
+508
+00:41:09,830 --> 00:41:15,310
+عندي مرتبة ترتيب تصعدي او تنازلي ايش يعني مرتبة
+
+509
+00:41:15,310 --> 00:41:22,990
+يعني واحد اتنين تلاتة خمسة سبعة تمانية عشرة
+
+510
+00:41:27,190 --> 00:41:31,210
+كيف بيشتغل؟ خلصنا من اللي فوق الان ال binary
+
+511
+00:41:31,210 --> 00:41:36,510
+search منهجية تانية في البحث بيقول انا بأشتغل في
+
+512
+00:41:36,510 --> 00:41:40,310
+حالة ده كانت ال sequence امرتبة و ال concept
+
+513
+00:41:40,310 --> 00:41:44,370
+تباعتها بكل بساطة هيجي كالتالي ال sequence كام
+
+514
+00:41:44,370 --> 00:41:49,550
+element فيها؟ واحد اتنين تلاتة اربعة خمسة ستة سبعة
+
+515
+00:41:49,550 --> 00:41:56,780
+هيجسم ال sequence من النص هي النصياخدوا الـ
+
+516
+00:41:56,780 --> 00:42:00,500
+element اللي في المنتصف هل تساوي القيمة اللي بتدور
+
+517
+00:42:00,500 --> 00:42:07,840
+عليها؟ لأ إذا سواتها خلصت أنت جيبته من أول مرة لو
+
+518
+00:42:07,840 --> 00:42:12,600
+ما سواتهاش معناته بدك تكمل في البحث بس تكملتك في
+
+519
+00:42:12,600 --> 00:42:16,620
+البحث الآن هتاخد واحد أو نص المصفوفة أو نص ال list
+
+520
+00:42:16,620 --> 00:42:21,060
+اللي قدامك ليش؟ لأن هي مرتبة ترتيب تصعدي وبناء
+
+521
+00:42:21,060 --> 00:42:24,300
+عليها تخيل أنه أنا على سبيل المثال بدي أدور على
+
+522
+00:42:24,300 --> 00:42:31,320
+الأربعةبدي ادور على اربعة الان باجي بقارن الاربعة
+
+523
+00:42:31,320 --> 00:42:34,980
+تساوي خمسة؟ لأ طب .. خمس .. وبالتالي يمين ولا
+
+524
+00:42:34,980 --> 00:42:39,060
+يسار؟ بدي اروح ادور في الجزء اليسار بدي اخد نص
+
+525
+00:42:39,060 --> 00:42:44,080
+المصوفة اللي كان هيه ايش
+
+526
+00:42:44,080 --> 00:42:47,520
+ممكن تسوي فيها؟ كمان مرة بدي تجسم ال list من النص
+
+527
+00:42:47,520 --> 00:42:54,100
+عند مين؟ عند التنين و تقارن الاربعة تساوي اتنين؟
+
+528
+00:42:54,100 --> 00:43:00,880
+لأتمام؟ تمام .. الأربعة أكبر ولا أصغر؟ أكبر ..
+
+529
+00:43:00,880 --> 00:43:06,400
+أكبر .. أكبر
+
+530
+00:43:06,400 --> 00:43:09,500
+.. أكبر
+
+531
+00:43:09,500 --> 00:43:09,680
+.. أكبر .. أكبر .. أكبر .. أكبر .. أكبر .. أكبر ..
+
+532
+00:43:09,680 --> 00:43:09,840
+أكبر .. أكبر .. أكبر .. أكبر .. أكبر .. أكبر ..
+
+533
+00:43:09,840 --> 00:43:10,060
+أكبر .. أكبر .. أكبر .. أكبر .. أكبر .. أكبر ..
+
+534
+00:43:10,060 --> 00:43:19,980
+أكبر .. أكبر .. أكبر
+
+535
+00:43:19,980 --> 00:43:28,440
+.. أكبر .. أكبر .. أكتلات خطوات استني بس الان لو
+
+536
+00:43:28,440 --> 00:43:32,620
+قلتلك في ال linear search كام خطوة عشان تصل تقول
+
+537
+00:43:32,620 --> 00:43:39,220
+الاربع مش موجودة سبع خطوات مصبوط طيب تهالي نجرب
+
+538
+00:43:39,220 --> 00:43:45,840
+على element موجود محمد البيع زي ايش كنت بدك ممكن
+
+539
+00:43:45,840 --> 00:43:48,900
+يعني الاربع مكون مجلد و تاني الاربع يكون بعيد
+
+540
+00:43:48,900 --> 00:43:52,240
+ماشيش احنا عمال نقول يا صاحبي قول لل binary search
+
+541
+00:43:52,240 --> 00:43:54,300
+شرطه ان تكون ال list مرتبة
+
+542
+00:43:57,190 --> 00:44:01,210
+مش بيرتب القرية مانعش علاقة بترتيب القرية الشرط هو
+
+543
+00:44:01,210 --> 00:44:06,610
+binary search بقول انا بأصلح بنفع اشتغل مع list
+
+544
+00:44:06,610 --> 00:44:12,710
+مرتبة بس الان في ال linear search حتى لو اديتك ال
+
+545
+00:44:12,710 --> 00:44:17,970
+list مرتبة هيها وقلتلك ابحث linear search عليها
+
+546
+00:44:17,970 --> 00:44:22,710
+ايش هتساوي هتمشي السبع خطوات عشان الجول الأربع مش
+
+547
+00:44:22,710 --> 00:44:28,990
+موجودةلكن مع ضمان ان ال list هات مرتبة ال binary
+
+548
+00:44:28,990 --> 00:44:32,910
+search بقولك ما اتكمش حلقة هنورجيك شغل فايدة انها
+
+549
+00:44:32,910 --> 00:44:39,770
+كويسة تعالى ندور على التمانية نص اللصوفة خمسة
+
+550
+00:44:39,770 --> 00:44:48,430
+تمانية اكبر معناته النص هيك بينزماش الان بروح على
+
+551
+00:44:48,430 --> 00:44:52,740
+القائمة هادي و بجسمها من المتصفلجات التمانية
+
+552
+00:44:52,740 --> 00:44:56,720
+خطواتين طب تخيل انا بدي ادوى على السبعة او على
+
+553
+00:44:56,720 --> 00:45:01,800
+التلاتة .. السبعة او التلاتة او العشرة تلت خطوات
+
+554
+00:45:01,800 --> 00:45:07,160
+طيب تعال بس نتكلم على شغل اكبر تخيل ان لو كانت
+
+555
+00:45:07,160 --> 00:45:11,220
+عندك في القائمة الف و أربع و عشرين element و هلأ
+
+556
+00:45:11,220 --> 00:45:14,640
+بتبقى أقولك ليش الف و أربع و عشرين بالتحديد الف و
+
+557
+00:45:14,640 --> 00:45:19,480
+أربع و عشرين elementعشان تاخد decision فوق على
+
+558
+00:45:19,480 --> 00:45:23,540
+الـlinear search معناته بدك تشتغل ألف و أربع و
+
+559
+00:45:23,540 --> 00:45:29,200
+عشرين عملية مقارنة، مظبوط؟ طيب، بينما على
+
+560
+00:45:29,200 --> 00:45:32,840
+الـlinear search لما تكون البيانات نصفة انت بس
+
+561
+00:45:32,840 --> 00:45:37,140
+بحاجة تشتغل عشر مرة تفحص عشان إما تلاقي ال element
+
+562
+00:45:37,140 --> 00:45:43,450
+أو تقول مش موجود عشر خطوات كحد أقصىكيف هذا الكلام
+
+563
+00:45:43,450 --> 00:45:46,850
+اللي أنا بقوله؟ تعالى نحسبها بكل بساطة أول مرة
+
+564
+00:45:46,850 --> 00:45:51,830
+وفّرت عليه خمسين في المية من ال list صح ولا لأ؟ في
+
+565
+00:45:51,830 --> 00:45:56,410
+المرة اللي بعديها طيّرت
+
+566
+00:45:56,410 --> 00:46:02,150
+كمان ربع نهي نص النص ربع، مصبوط؟ و بعدين طيّرت تمن
+
+567
+00:46:02,150 --> 00:46:06,290
+و بعدين طيّرت واحد على ستناشر واحد على اتنين و
+
+568
+00:46:06,290 --> 00:46:12,780
+تلاتين واحد على اربع و ستين واحد علىمية تمانية
+
+569
+00:46:12,780 --> 00:46:17,440
+وعشرين واحد على متين ستة وخمسين واحد على خمسمية
+
+570
+00:46:17,440 --> 00:46:23,900
+واطمائش واحد على الف واربع عشر هذه عشر خطوات كل
+
+571
+00:46:23,900 --> 00:46:28,120
+مرة كنت بقى أخلص من النص اللي ضايل وهذه ال
+
+572
+00:46:28,120 --> 00:46:31,640
+sequence بدها تساوي log
+
+573
+00:46:34,230 --> 00:46:40,170
+الـ 1024 للأساس اتنين لأنه عملية binary ثنائي كل
+
+574
+00:46:40,170 --> 00:46:46,790
+مرة بخلص من النص اتنين مظبوط الـ 1024 هذه تساوي
+
+575
+00:46:46,790 --> 00:46:52,670
+اتنين أقصى عشرة وهذه
+
+576
+00:46:52,670 --> 00:47:02,470
+المحصلة تساوي عشرة هتلاحظ ان كل ما زاد الرقمكل
+
+577
+00:47:02,470 --> 00:47:07,690
+مجلة خطوات الحل يعني لو كان عندي من 512 element
+
+578
+00:47:07,690 --> 00:47:15,270
+عشان تجيب النتيجة كحت أقصى بدك 9 خطوات ألف و أربعة
+
+579
+00:47:15,270 --> 00:47:20,770
+و عشرين و ضعفها زنت خطوة واحدة بس في البحث الآن
+
+580
+00:47:20,770 --> 00:47:26,270
+ضعفها كمان مرة خطوة واحدة اللي هتزيد مش أكتر بس في
+
+581
+00:47:26,270 --> 00:47:32,450
+عين الرقم هذا بيكون ضعف مظبوط تصير ألفينوتمنية
+
+582
+00:47:32,450 --> 00:47:36,990
+واربعين وضل زي ذلك وبالتالي أصبح ال binary search
+
+583
+00:47:36,990 --> 00:47:43,290
+ممكن يشكل فرق لو أنا أتأكدت المصفوفة تبعتي مرتبة
+
+584
+00:47:43,290 --> 00:47:46,790
+طب لو ماكنتش مرتبة بقدر أطبق ال binary search لأ
+
+585
+00:47:46,790 --> 00:47:51,450
+طب أروح أرتبها واجف شوية تروح ترتبها معناته هتدخل
+
+586
+00:47:51,450 --> 00:47:55,030
+تكلفة تانية عملية ترتيب المصفوفة بحد ذاتها
+
+587
+00:47:55,030 --> 00:47:59,440
+algorithm بحد ذاتها مشكلة بدها حلوبالتالي احنا
+
+588
+00:47:59,440 --> 00:48:03,160
+جاعد انا بتكلم انا زوّدتك بمصفوفة وبدي تعمل ال
+
+589
+00:48:03,160 --> 00:48:07,280
+search في مجال public binary وفي مجال public
+
+590
+00:48:07,280 --> 00:48:13,300
+linear ايش تستخدم حسب وضع القرري اذا والله هي
+
+591
+00:48:13,300 --> 00:48:17,240
+مرتبة ترتيب تصاحب او تنازل بروح باتجاه ال binary
+
+592
+00:48:17,240 --> 00:48:23,240
+search شوف
+
+593
+00:48:23,240 --> 00:48:26,620
+انت مقارنة عشر خطوات عشان تاخد decision
+
+594
+00:48:30,950 --> 00:48:45,550
+هذه الخطوات كل
+
+595
+00:48:45,550 --> 00:48:50,110
+مرة تجسم الـ sequence لجزئينه وبتقرر أين تذهب وكل
+
+596
+00:48:50,110 --> 00:48:52,930
+مرة تنصف الـ sequence اللي موجود عندك لحد ما تصل
+
+597
+00:48:52,930 --> 00:48:58,000
+للحل ال algorithmProcedure binary search بدي الـ X
+
+598
+00:48:58,000 --> 00:49:00,920
+و بدي ال list نفس ال procedure السابق linear ك
+
+599
+00:49:00,920 --> 00:49:06,640
+input و افترضت ان ال I equal 1 تمام؟ و ال J equal
+
+600
+00:49:06,640 --> 00:49:12,900
+ال N ليش؟ عشان بدي احصر دايما الفترة تبعت بين I و
+
+601
+00:49:12,900 --> 00:49:18,200
+J I و Jأول مرة كانت فترة واحدة، مصبوط؟ لأن بعد ما
+
+602
+00:49:18,200 --> 00:49:21,160
+أنصفها بدي أقرر بدي أروح ليمين ولا شمال، فيا إما
+
+603
+00:49:21,160 --> 00:49:24,920
+بدي أحرك ال I للمتصف أو بدي أجيب ال J للمتصف عشان
+
+604
+00:49:24,920 --> 00:49:29,780
+أحافظ على الفترة اللي موجودة، يعني تخيل، هاي،
+
+605
+00:49:29,780 --> 00:49:37,540
+اتنين، سبعة، خمسة، تمانية، تسعة، هشرة، اتناشر،
+
+606
+00:49:37,540 --> 00:49:41,720
+اربعة، اتناشر، واحد، اتنين، تلاتة، اربعة، خمسة،
+
+607
+00:49:41,720 --> 00:49:48,100
+ستة، سبعة، هذا Iوهنا الـ J اللي هي السبعة لأن لما
+
+608
+00:49:48,100 --> 00:49:52,600
+انا بدي اجري هاي المنتصف اتيت عند التسعة لأن ال
+
+609
+00:49:52,600 --> 00:49:56,520
+element اللي انا بدور عليه الاربعة ايش هو المفروض
+
+610
+00:49:56,520 --> 00:49:59,900
+الساوي؟ بدي اروح باتجاه ال I يعني بدي احرك مين؟
+
+611
+00:49:59,900 --> 00:50:05,830
+اروح اقوله ان الـ J equalالـ Index أربعة ماليش تخل
+
+612
+00:50:05,830 --> 00:50:09,370
+في ال element تسعة أنا فحصه مش هو المطلوب خلاص بده
+
+613
+00:50:09,370 --> 00:50:12,870
+الآن بده أحصر ال interval بين ال I و 9 عشان
+
+614
+00:50:12,870 --> 00:50:17,750
+المنتصف تبعها كمان هي واحد او ال I زائد J على
+
+615
+00:50:17,750 --> 00:50:22,470
+اتنين مش كل مرة بده أجسم ال loop واحد زائد سبعة
+
+616
+00:50:22,470 --> 00:50:29,530
+تمانية على اتنين اربع عقل نص بعد هيك واحد زائد
+
+617
+00:50:29,530 --> 00:50:36,210
+اربعة خمسة على اتنينتنين و نص .. مافيش ال index
+
+618
+00:50:36,210 --> 00:50:41,250
+بالنص .. يا بتاخد الأعلى يا بتاخد الأقل .. يا
+
+619
+00:50:41,250 --> 00:50:45,130
+بتاخد ال ceiling أو بتاخد ال floor .. خدناهم ال
+
+620
+00:50:45,130 --> 00:50:48,410
+function .. او بتاخد ال ceiling او بتاخد ال floor
+
+621
+00:50:48,410 --> 00:50:53,030
+.. عشان تخلص من الكسر .. مش هتفرج معاك ولا حاجةهي
+
+622
+00:50:53,030 --> 00:50:56,210
+السجن في الأرضية وبالتالي بتصير تحرك في الـ
+
+623
+00:50:56,210 --> 00:50:59,650
+position pointer يمين وشمال كحب أقصى زي ما قلنا لك
+
+624
+00:50:59,650 --> 00:51:03,670
+بدك log الأن أنت تصل إلى العدد أو القيم الموجودة
+
+625
+00:51:03,670 --> 00:51:11,990
+عندك فكل مرة بتروح بتقارن طالما أن ال I أقل من ال
+
+626
+00:51:11,990 --> 00:51:18,370
+J لازم تبقى ال I أقل من ال J لحظة ما تسويها خلاص
+
+627
+00:51:18,370 --> 00:51:21,190
+انت صارت تنين مافيش عندك interval خلصة ال elements
+
+628
+00:51:21,190 --> 00:51:27,140
+اللي موجودةوبالتالي يجب أن تقارن ال condition إذا
+
+629
+00:51:27,140 --> 00:51:32,080
+كان ال X أكبر من A يعني أنني أحرك ال I إلا إذا
+
+630
+00:51:32,080 --> 00:51:37,280
+أحرك ال J لحد ما تصل إلى ال location إذا كان ال X
+
+631
+00:51:37,280 --> 00:51:42,640
+سوى AI فتقول خلاص ده هي يعني location يساوي I إلا
+
+632
+00:51:42,640 --> 00:51:48,900
+إذا كان ال element ليس موجودفي موضوع الترتيب مشكلة
+
+633
+00:51:48,900 --> 00:51:52,260
+تانية احنا دي كنا بتدور كنا على البحث في موضوع
+
+634
+00:51:52,260 --> 00:51:56,240
+الترتيب ترتيب ال elements زي ما قولنا هذه مشكلة
+
+635
+00:51:56,240 --> 00:52:02,340
+تانية غير مشكلة او مسئلة تانية غير مسئلة البحث
+
+636
+00:52:02,340 --> 00:52:11,800
+سبعة تلاتة خمسة اتنين واحد تمانية بدي ارتب العناصر
+
+637
+00:52:11,800 --> 00:52:20,970
+هدول انا كيبك ترتبهم؟تصعدي ارتب اليوم تصعدي شو
+
+638
+00:52:20,970 --> 00:52:27,530
+بقى تساوي؟ الان هتفكر كتالي قولي بدي اخد اول
+
+639
+00:52:27,530 --> 00:52:33,970
+element و بقى اقارنه مع كل اللي بعدين و كل ما لاجي
+
+640
+00:52:33,970 --> 00:52:37,930
+element اصغر منه اروح ابدله
+
+641
+00:52:41,680 --> 00:52:46,120
+يعني حاجة أقارن سبعة و تلاتة التلاتة أصغر بدي
+
+642
+00:52:46,120 --> 00:52:52,800
+أبدلهم صارت عندي هان تلاتة و هان سبعة تلاتة و خمسة
+
+643
+00:52:52,800 --> 00:53:01,300
+تلاتة و اتنين تلاتة
+
+644
+00:53:01,300 --> 00:53:10,710
+واحد و اتنين واحد و هان اتنينواحد و تمانية لأ
+
+645
+00:53:10,710 --> 00:53:15,670
+الواحد خلصت انت هيك ضمنت انه اول element هو اصغر
+
+646
+00:53:15,670 --> 00:53:20,490
+element بتسيبك منه و بتنتقل العنصر اللي بعده و
+
+647
+00:53:20,490 --> 00:53:29,830
+بتعيد نفس الكرة سبعة سبعة و خمسة خمسة حط الخمسة و
+
+648
+00:53:29,830 --> 00:53:33,790
+تبدل مع السبعة خمسة و تلاتة تلاتة
+
+649
+00:53:37,960 --> 00:53:43,740
+تلاتة و .. ايه؟ أنا خمسة عفوا تلاتة و اتنين ..
+
+650
+00:53:43,740 --> 00:53:49,140
+اتنين اتنين
+
+651
+00:53:49,140 --> 00:53:52,620
+و تمانية .. لأ اتنين صار التاني هو أصغر element
+
+652
+00:53:52,620 --> 00:53:57,860
+بقى في ال list بتنتقل للي بعده سبعة .. سبعة و خمسة
+
+653
+00:53:57,860 --> 00:54:01,400
+.. خمسة
+
+654
+00:54:01,400 --> 00:54:06,680
+و هي السبعة .. خمسة و تلاتة .. تلاتة
+
+655
+00:54:11,780 --> 00:54:17,820
+ثلاثة و تمانية ثلاثة خلصنا الآن اللي بعده سبعة
+
+656
+00:54:17,820 --> 00:54:25,980
+سبعة و خمسة خمسة خمسة
+
+657
+00:54:25,980 --> 00:54:30,420
+و تمانية الخمسة تيجي لللي بعده سبعة و تمانية سبعة
+
+658
+00:54:30,420 --> 00:54:33,640
+خلصت ال list خلصت الشغل مابالش next element
+
+659
+00:54:33,640 --> 00:54:41,800
+وبالتالي المصوفة تم ترتيبها هذا حل هذا حلواحد
+
+660
+00:54:41,800 --> 00:54:48,520
+بيحلمها بشكل تاني حد بتذكر إيش كانت في الأول سبعة
+
+661
+00:54:48,520 --> 00:54:52,440
+خمسة
+
+662
+00:54:52,440 --> 00:55:00,080
+ثلاثة اتنين واحد تمانية واحد هيفكر يشتغل كل اتنين
+
+663
+00:55:00,080 --> 00:55:05,680
+مع بعض كل اتنين مع بعض ويتبدلهم يعني انا بدي اخد
+
+664
+00:55:05,680 --> 00:55:08,780
+سبعة والخمسة
+
+665
+00:55:13,030 --> 00:55:20,210
+سبعة و خمسة ثلاثة و اتنين واحد و تمانية و ابدلهم
+
+666
+00:55:20,210 --> 00:55:26,230
+ايش بيصير اندي؟ خمسة و سبعة اتنين و تلاتة واحد و
+
+667
+00:55:26,230 --> 00:55:31,830
+تمانية زي ما هي طيب كمان مرة لان ايش بيتصرف اول
+
+668
+00:55:31,830 --> 00:55:37,450
+عنصر و اخر عنصر؟ هل حصل له نتيجة بالتبديل هذا؟ مش
+
+669
+00:55:37,450 --> 00:55:40,730
+شايف الحل انشو وصل له نتيجة بالشكل هذا بدون ما ايش
+
+670
+00:55:42,530 --> 00:55:44,890
+وبالتالي .. هاي .. لو أنا بدي أرجع أبدل .. هل
+
+671
+00:55:44,890 --> 00:55:48,650
+مافيش تغيير؟ هل مافيش تغيير؟ هل مافيش تغيير؟ بدي
+
+672
+00:55:48,650 --> 00:55:56,650
+أبدأ على مين؟ على الـ Next Element 2 و 7 .. 2 و 7
+
+673
+00:55:56,650 --> 00:56:01,410
+.. و أنا 1 و 3 .. يعني 5 .. 2 .. 7 .. 1 .. 3 .. هي
+
+674
+00:56:01,410 --> 00:56:08,800
+8 .. الآن .. في .. في تبديل .. بس أصبر شويةبين من
+
+675
+00:56:08,800 --> 00:56:12,960
+و مين؟ بين السبعة و التانية؟ خلاص هلاك سبعة و واحد
+
+676
+00:56:12,960 --> 00:56:17,040
+الخمسة
+
+677
+00:56:17,040 --> 00:56:21,020
+و الاتنين فانت فعليا ممكن بس في الآخر بدك تكتب عدد
+
+678
+00:56:21,020 --> 00:56:25,380
+خطوات او بدك تبدأ تفكر بخطوات ممكناش تكتبها بشكل
+
+679
+00:56:25,380 --> 00:56:28,880
+precise واضح يعني زي ما قلت قبل شوية مانفعش انا
+
+680
+00:56:28,880 --> 00:56:33,000
+اظل اشتغل إلى مال اللي هي لازم تكون خطواتيواضحة
+
+681
+00:56:33,000 --> 00:56:36,120
+لازم فكرة تكون واضحة و الناس ممكن تبقى اعتمد عليها
+
+682
+00:56:36,120 --> 00:56:41,740
+في حل من اشهر انواع ال sort الشغل اسمها ال bubble
+
+683
+00:56:41,740 --> 00:56:50,760
+sort اللي احنا اشتغلناه قبل شوية مع العناصر اللي
+
+684
+00:56:50,760 --> 00:56:58,080
+موجودة عندنا طبعا نموذج تالت للحل ممكن افكر انا هي
+
+685
+00:56:58,080 --> 00:57:03,170
+المصحوفة عندي اعتمد دائما اجيب ال minimumجلبت الـ
+
+686
+00:57:03,170 --> 00:57:08,050
+minimum و شطبته و حطه في list جديدة مظبوط ادور مرة
+
+687
+00:57:08,050 --> 00:57:10,770
+تانية اجيب ال minimum لاحظ كل مرة ال list ايش
+
+688
+00:57:10,770 --> 00:57:17,230
+بتساوي بتجيل واحد و احطه في ال list هذا برضه حل بس
+
+689
+00:57:17,230 --> 00:57:19,710
+في الآخر لما تكون جادر على كتابته في ال bubble
+
+690
+00:57:19,710 --> 00:57:24,650
+sort اللي احنا كتبناه في الأول بقارن كل element مع
+
+691
+00:57:24,650 --> 00:57:27,930
+اللي بعده و لما بكون فيه swap ببدل ال iteration
+
+692
+00:57:27,930 --> 00:57:31,250
+الأولى، التانية، التالتة، الرابع ماكون اوصل
+
+693
+00:57:31,250 --> 00:57:36,070
+تلاقياشللحل اللي موجود عندى هاي ال bubble sort بكل
+
+694
+00:57:36,070 --> 00:57:40,750
+بساطة مريت على عناصر من اللي عندى فقط عند ال list
+
+695
+00:57:40,750 --> 00:57:46,030
+و ال output هيكون list اللي هي مرتبة مريت على كل
+
+696
+00:57:46,030 --> 00:57:51,890
+عناصر المصوفة من الأول لجابلى الأخر لجابلى الأخر و
+
+697
+00:57:51,890 --> 00:57:57,160
+جرح و كمان لو كمان مرة من واحد لجابلى الاناللي هو
+
+698
+00:57:57,160 --> 00:58:03,260
+نقص I وكل ما بلاقي انه IG أكبر من AIG زائد واحد
+
+699
+00:58:03,260 --> 00:58:08,700
+بروح ببدل العناصر اللي موجودة عندى لحد ما بصل لل
+
+700
+00:58:08,700 --> 00:58:12,720
+list أو العناصر ال list اللي موجودة بعض ال
+
+701
+00:58:12,720 --> 00:58:16,820
+algorithm بنسميها greedy algorithmهنجف هنا مش
+
+702
+00:58:16,820 --> 00:58:20,780
+هنكمل نسميها greedy algorithms اللي هي ما نسميها
+
+703
+00:58:20,780 --> 00:58:24,620
+أو الخوارزمية الطناعة ايش الخوارزمية الطناعة
+
+704
+00:58:24,620 --> 00:58:29,080
+الفكرة فيها بكل بساطة انه انا بجيب حل لكن الحل هذا
+
+705
+00:58:29,080 --> 00:58:34,600
+مش افضل حل بناء على ايش؟ بناء على انه انا دائما
+
+706
+00:58:34,600 --> 00:58:38,940
+بانظر لأبسط او افضل حل في اللحظة الآنية ببقى اللي
+
+707
+00:58:38,940 --> 00:58:42,900
+بستشرفش المستقبلالمثال البسيط جدا اللي ممكن
+
+708
+00:58:42,900 --> 00:58:51,340
+اقدرحلك اياه تخيل ان في عندي مثلث بالشكل هذا A
+
+709
+00:58:51,340 --> 00:59:01,700
+B C وعندي كمان نقطة دي وهي الرسم هادي هيك وانت
+
+710
+00:59:01,700 --> 00:59:11,380
+واقف هنا عند ال A و بدك تروح ل D ايش اكثر طريق؟C
+
+711
+00:59:11,380 --> 00:59:15,680
+دي اقصر طريق بناء على انك الان واقف عند ال A و
+
+712
+00:59:15,680 --> 00:59:22,400
+حسبت ان ال A ل ال D و ال A ل ال C كمان اللي هي ال
+
+713
+00:59:22,400 --> 00:59:26,060
+water و هذا مستلف قائم الزاوية فال water هيكون
+
+714
+00:59:26,060 --> 00:59:29,360
+اقرب element اروح الطريق في ال grade algorithm
+
+715
+00:59:29,360 --> 00:59:32,800
+بتطلعش للحسبة اللي بعيدة ايش بياخد ال decision
+
+716
+00:59:32,800 --> 00:59:36,460
+بناء على ايش بناء ان انا الان من اقصر طريق ليه
+
+717
+00:59:36,460 --> 00:59:42,170
+اروح على B ولا اروح على Cمباشرة هيروح على ال B لأن
+
+718
+00:59:42,170 --> 00:59:46,850
+هو فعليا الآن شايفها أقصر طريق وبناء عليها هو أخد
+
+719
+00:59:46,850 --> 00:59:51,750
+ال decision وراح عليها الآن جدامه بدي يروح على ال
+
+720
+00:59:51,750 --> 00:59:56,930
+D يروح على ال C ولا يروح على ال D؟ هيروح على ال C
+
+721
+00:59:56,930 --> 01:00:04,190
+لأن ال C أقصر من ال D أصبت وبعدين مافيش جدامه لغير
+
+722
+01:00:04,190 --> 01:00:11,520
+روح على ال D فعليا هو سلك أطول طريقممكن ليش؟ لأنه
+
+723
+01:00:11,520 --> 01:00:15,400
+كان ياخد ال decision بناء على ال current situation
+
+724
+01:00:15,400 --> 01:00:19,620
+هو
+
+725
+01:00:19,620 --> 01:00:22,640
+دائما بياخد decision مقارنة بين اتنين، الآن مين
+
+726
+01:00:22,640 --> 01:00:26,960
+أحسن إليه؟ أروح يمين ولا أروح شمال؟ طيب أنا الآن
+
+727
+01:00:26,960 --> 01:00:35,040
+قاعد الجامعة و بدي أروح عرفح إيش أقصر الطرق اللي
+
+728
+01:00:35,040 --> 01:00:35,620
+بالنسبالي؟
+
+729
+01:00:44,510 --> 01:00:48,490
+المنطقي بيقول ان انا اروح على اقرب موقف بالنسبالي
+
+730
+01:00:48,490 --> 01:00:51,870
+مين اقرب موقف؟ اروح على الأزهر او على الشجاعية؟
+
+731
+01:00:51,870 --> 01:00:57,670
+على الأزهر طيب تخيل ان السيارة اللي في الأزهر او
+
+732
+01:00:57,670 --> 01:01:02,370
+على موقف الأزهر بدها تروح في أولا على الشجاعية
+
+733
+01:01:02,370 --> 01:01:07,250
+وبعدين بترجع تاني معينة وصارت فهذه الطريق؟ بقولش
+
+734
+01:01:07,250 --> 01:01:10,510
+اللي هو هذا الطمع لكن فعليا كانت decision مبني على
+
+735
+01:01:10,510 --> 01:01:16,380
+مين أقصر الطرقالموجودة عند هان احنا بنسميه كمان
+
+736
+01:01:16,380 --> 01:01:21,060
+مرة هو algorithm بتديني حل مش مابيدليش بوصللي لـ
+
+737
+01:01:21,060 --> 01:01:25,940
+output المطلوب لكن هذا الحل هل هو أفضل حل؟ لأ في
+
+738
+01:01:25,940 --> 01:01:28,240
+أحسن منه والله يعطيكوا العافية
+
diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/xXZat9maenA_raw.json b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/xXZat9maenA_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..5b1df093e20b6aedd5930be5cc6183214ea0bb79
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/xXZat9maenA_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4695, "start": 21.01, "end": 46.95, "text": "بسم الله والحمد لله والصلاة والسلام علي الرسول الله اليوم ان شاء الله يا شباب هنبدأ ب chapter تلاتة لو chapter ال algorithm ال chapter هيكون نوعا ما مريح بالنسبالي لأن مؤدام كو أخد برمجة واحد واخد برمجة اتنين واخد مقدمة تمام وفي ناس ختيرية في المنطقة وبالتالي ايش وضعهم تمام فاليوم احنا نتكلم على ال algorithms الخوارزميات", "tokens": [3555, 38251, 21984, 16070, 35571, 3215, 24976, 3224, 16070, 9381, 15040, 3660, 16070, 3794, 37440, 25894, 34892, 3794, 12610, 21984, 45595, 20498, 16472, 13412, 16606, 21984, 35186, 13412, 3555, 16758, 8032, 1863, 44510, 10721, 4724, 7187, 6055, 1211, 9307, 3660, 45164, 7187, 2423, 9284, 2423, 7187, 8032, 1829, 30544, 8717, 45367, 995, 19446, 3714, 16572, 5016, 20666, 1863, 35457, 6027, 1829, 5296, 33456, 3714, 33604, 3215, 10943, 9122, 2407, 5551, 9778, 3215, 4724, 2288, 2304, 7435, 3660, 36764, 24401, 4032, 47283, 3215, 4724, 2288, 2304, 7435, 3660, 1975, 2655, 1863, 9957, 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" علي", "probability": 0.7021484375}, {"start": 22.41, "end": 22.65, "word": " الرسول", "probability": 0.8434244791666666}, {"start": 22.65, "end": 22.83, "word": " الله", "probability": 0.52294921875}, {"start": 22.83, "end": 23.17, "word": " اليوم", "probability": 0.83984375}, {"start": 23.17, "end": 23.27, "word": " ان", "probability": 0.34130859375}, {"start": 23.27, "end": 23.39, "word": " شاء", "probability": 0.980712890625}, {"start": 23.39, "end": 23.39, "word": " الله", "probability": 0.93359375}, {"start": 23.39, "end": 23.53, "word": " يا", "probability": 0.49267578125}, {"start": 23.53, "end": 23.69, "word": " شباب", "probability": 0.9871419270833334}, {"start": 23.69, "end": 24.01, "word": " هنبدأ", "probability": 0.84521484375}, {"start": 24.01, "end": 24.09, "word": " ب", "probability": 0.65576171875}, {"start": 24.09, "end": 24.33, "word": " chapter", "probability": 0.62548828125}, {"start": 24.33, "end": 24.81, "word": " تلاتة", "probability": 0.7947998046875}, 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اللي انا .. اه لازم تديني الحل هو الا الفاضي ال algorithm", "tokens": [1211, 27842, 22807, 24976, 5016, 1211, 13672, 1829, 1975, 8315, 4724, 16254, 1975, 25528, 3224, 5296, 29399, 1829, 7435, 3660, 2423, 5598, 13672, 1829, 1975, 8315, 4386, 1975, 3224, 5296, 31377, 2304, 6055, 3215, 9957, 1829, 21542, 1211, 31439, 42963, 27188, 46958, 1829, 2423, 9284], "avg_logprob": -0.34018343233543896, "compression_ratio": 1.4152542372881356, "no_speech_prob": 0.0, "words": [{"start": 721.69, "end": 722.21, "word": "لمن؟", "probability": 0.5130208333333334}, {"start": 722.21, "end": 722.73, "word": " للحل", "probability": 0.8484700520833334}, {"start": 722.73, "end": 722.85, "word": " اللي", "probability": 0.691650390625}, {"start": 722.85, "end": 723.01, "word": " انا", "probability": 0.803955078125}, {"start": 723.01, "end": 723.19, "word": " بدي", "probability": 0.803955078125}, {"start": 723.19, "end": 723.57, "word": " اياه", "probability": 0.723388671875}, {"start": 723.57, "end": 724.35, 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element", "probability": 0.95654296875}], "temperature": 1.0}, {"id": 43, "seek": 109135, "start": 1068.74, "end": 1091.36, "text": "وهذا اللي انت سويته لما كنت تكتب السبعة بعد هيك compare the next integer in the sequence to the temporary maximum قارنتها مع السبعة هل مصبوط؟ if the larger لو كان الرقم أكبر مهراته بدل خلي ال maximum تساوي كذا و هكذا و بتكرر", "tokens": [2407, 3224, 15730, 13672, 1829, 16472, 2655, 8608, 2407, 36081, 3224, 5296, 15042, 9122, 29399, 6055, 4117, 2655, 3555, 21136, 3555, 27884, 39182, 39896, 4117, 6794, 264, 958, 24922, 294, 264, 8310, 281, 264, 13413, 6674, 12174, 9640, 29399, 11296, 20449, 21136, 3555, 27884, 8032, 1211, 3714, 9381, 3555, 2407, 9566, 22807, 498, 264, 4833, 45164, 25961, 34892, 4587, 2304, 5551, 4117, 26890, 3714, 3224, 2288, 9307, 3224, 47525, 1211, 16490, 20292, 2423, 6674, 6055, 3794, 995, 45865, 9122, 15730, 4032, 8032, 4117, 15730, 4032, 39894, 37983, 2288], "avg_logprob": -0.34216995453566645, "compression_ratio": 1.5159817351598173, 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ال .. عفوا ال maximum او ال temporary maximum number هو ال max integer اللي هيكون عندك هاي الـ Precise Steps ممكن انت تروح تصيغها بصورة أطفف من هيك كمان", "tokens": [6027, 39184, 6001, 1502, 5470, 20449, 2423, 39184, 3087, 5681, 30744, 5296, 24401, 19446, 6055, 36520, 5296, 1863, 11296, 10632, 2423, 39184, 46859, 655, 8978, 16247, 9778, 13546, 16472, 2655, 8032, 2655, 30543, 5172, 1975, 15730, 25961, 19446, 41185, 8592, 883, 5681, 30744, 3714, 25720, 37495, 22653, 16490, 1211, 9381, 2655, 2423, 39184, 46859, 655, 6055, 3555, 34268, 4117, 16472, 2655, 8032, 2655, 4587, 5172, 1975, 2407, 6055, 30544, 11331, 9381, 36081, 15844, 2423, 4386, 6225, 5172, 14407, 2423, 6674, 1975, 2407, 2423, 13413, 6674, 1230, 31439, 2423, 11469, 24922, 13672, 1829, 39896, 30544, 43242, 4117, 8032, 47302, 2423, 39184, 6001, 66, 908, 745, 10653, 3714, 43020, 16472, 2655, 6055, 32887, 5016, 6055, 9381, 1829, 17082, 11296, 4724, 9381, 13063, 3660, 5551, 9566, 5172, 5172, 9154, 39896, 4117, 9122, 2304, 7649], 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"probability": 0.83251953125}, {"start": 1106.76, "end": 1106.92, "word": " ..", "probability": 0.14599609375}, {"start": 1106.92, "end": 1108.4, "word": " عفوا", "probability": 0.6285807291666666}, {"start": 1108.4, "end": 1108.88, "word": " ال", "probability": 0.54345703125}, {"start": 1108.88, "end": 1109.36, "word": " maximum", "probability": 0.69921875}, {"start": 1109.36, "end": 1109.58, "word": " او", "probability": 0.7293701171875}, {"start": 1109.58, "end": 1109.68, "word": " ال", "probability": 0.6884765625}, {"start": 1109.68, "end": 1109.94, "word": " temporary", "probability": 0.83984375}, {"start": 1109.94, "end": 1110.38, "word": " maximum", "probability": 0.97314453125}, {"start": 1110.38, "end": 1110.72, "word": " number", "probability": 0.98291015625}, {"start": 1110.72, "end": 1111.0, "word": " هو", "probability": 0.98095703125}, {"start": 1111.0, "end": 1111.78, "word": " ال", "probability": 0.93310546875}, {"start": 1111.78, "end": 1112.02, "word": " max", "probability": 0.478271484375}, {"start": 1112.02, "end": 1112.38, "word": " integer", "probability": 0.88134765625}, {"start": 1112.38, "end": 1112.54, "word": " اللي", "probability": 0.94921875}, {"start": 1112.54, "end": 1112.76, "word": " هيكون", "probability": 0.6998291015625}, {"start": 1112.76, "end": 1113.16, "word": " عندك", "probability": 0.996826171875}, {"start": 1113.16, "end": 1113.72, "word": " هاي", "probability": 0.35040283203125}, {"start": 1113.72, "end": 1113.82, "word": " الـ", "probability": 0.52728271484375}, {"start": 1113.82, "end": 1114.2, "word": " Precise", "probability": 0.89013671875}, {"start": 1114.2, "end": 1114.58, "word": " Steps", "probability": 0.62744140625}, {"start": 1114.58, "end": 1115.56, "word": " ممكن", "probability": 0.92138671875}, {"start": 1115.56, "end": 1115.76, "word": " انت", "probability": 0.832763671875}, {"start": 1115.76, "end": 1116.0, "word": " تروح", "probability": 0.9905598958333334}, {"start": 1116.0, "end": 1116.48, "word": " تصيغها", "probability": 0.832421875}, {"start": 1116.48, "end": 1116.8, "word": " بصورة", "probability": 0.977783203125}, {"start": 1116.8, "end": 1117.16, "word": " أطفف", "probability": 0.716583251953125}, {"start": 1117.16, "end": 1117.3, "word": " من", "probability": 0.9873046875}, {"start": 1117.3, "end": 1117.48, "word": " هيك", "probability": 0.762451171875}, {"start": 1117.48, "end": 1117.74, "word": " كمان", "probability": 0.9894205729166666}], "temperature": 1.0}, {"id": 45, "seek": 114366, "start": 1118.66, "end": 1143.66, "text": "و كل ما كانت مقدرتك على كتابتها أو صيغتها بشكل أبسط بكون ال algorithm تبعك أفضل و إذا كدرت تكتبوا رياضيات بكون أفضل و أفضل لإيش؟ لأنه أنا مابديش ييجي لي حد يقولي إيش يعني ال next integer يعني بس إيه اتنين من ال sequence طيب لما أنا روحانة و رجحتني يقولي repeat with the previous step", "tokens": [2407, 28242, 19446, 25961, 2655, 3714, 28543, 43500, 4117, 15844, 9122, 2655, 16758, 2655, 11296, 34051, 20328, 1829, 17082, 2655, 11296, 4724, 8592, 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"end": 1394.17, "word": " هذه", "probability": 0.482421875}, {"start": 1394.17, "end": 1394.35, "word": " مرة", "probability": 0.981689453125}, {"start": 1394.35, "end": 1394.73, "word": " واحدة", "probability": 0.96728515625}, {"start": 1394.73, "end": 1395.23, "word": " ..", "probability": 0.564453125}, {"start": 1395.23, "end": 1395.87, "word": " بشتغل؟", "probability": 0.9291178385416666}], "temperature": 1.0}, {"id": 55, "seek": 142071, "start": 1396.25, "end": 1420.71, "text": "إتنين إتنين طيب و إذا بنتذكر .. نتذكر في عامل .. لما قولنا زمان أو كانوا يعلمونا الحساب لما قولنا واحد زائد تلاتة زائد خمسة زائد سبعة زائد تسعة و بدي ال output إيش كنت بتساوي لما كانوا بدوا يعلمونا و ما زلنا لليوم؟ هانا أربعة", "tokens": [28814, 2655, 1863, 9957, 11933, 2655, 1863, 9957, 23032, 1829, 3555, 4032, 11933, 15730, 4724, 29399, 8848, 37983, 4386, 8717, 2655, 8848, 37983, 8978, 6225, 10943, 1211, 4386, 5296, 15042, 12174, 12610, 8315, 30767, 2304, 7649, 34051, 25961, 14407, 37495, 19528, 2407, 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steps عفوا كمان مرة عرفناه على انه", "tokens": [1479, 5194, 6009, 442, 37279, 16572, 5172, 3224, 5296, 31377, 2304, 7251, 30544, 4032, 46958, 5016, 37279, 16572, 5172, 3224, 1975, 8592, 1975, 5016, 8315, 12174, 36150, 13412, 2407, 10632, 5296, 15042, 6225, 28480, 8315, 2423, 9284, 4724, 8592, 28820, 6225, 10943, 12174, 12610, 8315, 31439, 6225, 3555, 9640, 3660, 18871, 3714, 7435, 2304, 45367, 19362, 992, 295, 13600, 992, 1975, 2407, 4439, 6225, 5172, 14407, 9122, 2304, 7649, 3714, 25720, 6225, 28480, 8315, 3224, 15844, 16472, 3224], "avg_logprob": -0.23615506668634054, "compression_ratio": 1.5, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 1547.85, "end": 1548.61, "word": "definiteness", "probability": 0.80828857421875}, {"start": 1548.61, "end": 1549.37, "word": " تعريفه", "probability": 0.74554443359375}, {"start": 1549.37, "end": 1549.75, "word": " لازم", "probability": 0.8880208333333334}, {"start": 1549.75, "end": 1550.05, "word": " يكون", "probability": 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{"id": 128, "seek": 345173, "start": 3422.69, "end": 3451.73, "text": "جلبت الـ minimum و شطبته و حطه في list جديدة مظبوط ادور مرة تانية اجيب ال minimum لاحظ كل مرة ال list ايش بتساوي بتجيل واحد و احطه في ال list هذا برضه حل بس في الآخر لما تكون جادر على كتابته في ال bubble sort اللي احنا كتبناه في الأول بقارن كل element مع اللي بعده و لما بكون فيه swap ببدل ال iteration الأولى، التانية، التالتة، الرابع ماكون اوصل تلاقياش", "tokens": [7435, 46152, 2655, 2423, 39184, 7285, 4032, 13412, 9566, 3555, 47395, 4032, 11331, 9566, 3224, 8978, 1329, 10874, 16254, 41891, 3714, 19913, 3555, 2407, 9566, 1975, 3215, 13063, 3714, 25720, 6055, 7649, 10632, 1975, 7435, 1829, 3555, 2423, 7285, 20193, 5016, 19913, 28242, 3714, 25720, 2423, 1329, 1975, 1829, 8592, 39894, 3794, 995, 45865, 39894, 7435, 26895, 36764, 24401, 4032, 1975, 5016, 9566, 3224, 8978, 2423, 1329, 23758, 4724, 43042, 3224, 11331, 1211, 4724, 3794, 8978, 6024, 95, 34740, 5296, 15042, 6055, 30544, 10874, 18513, 2288, 15844, 9122, 2655, 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3424.27, "end": 3424.95, "word": " و", "probability": 0.77685546875}, {"start": 3424.95, "end": 3425.21, "word": " حطه", "probability": 0.667724609375}, {"start": 3425.21, "end": 3425.31, "word": " في", "probability": 0.75048828125}, {"start": 3425.31, "end": 3425.67, "word": " list", "probability": 0.55712890625}, {"start": 3425.67, "end": 3426.17, "word": " جديدة", "probability": 0.9127604166666666}, {"start": 3426.17, "end": 3426.95, "word": " مظبوط", "probability": 0.782763671875}, {"start": 3426.95, "end": 3427.81, "word": " ادور", "probability": 0.617919921875}, {"start": 3427.81, "end": 3428.05, "word": " مرة", "probability": 0.954345703125}, {"start": 3428.05, "end": 3428.31, "word": " تانية", "probability": 0.95068359375}, {"start": 3428.31, "end": 3428.53, "word": " اجيب", "probability": 0.8216552734375}, {"start": 3428.53, "end": 3428.63, "word": " ال", "probability": 0.93310546875}, {"start": 3428.63, "end": 3429.03, "word": " minimum", "probability": 0.908203125}, {"start": 3429.03, "end": 3429.89, "word": " لاحظ", "probability": 0.8636067708333334}, {"start": 3429.89, "end": 3430.09, "word": " كل", "probability": 0.60009765625}, {"start": 3430.09, "end": 3430.33, "word": " مرة", "probability": 0.985595703125}, {"start": 3430.33, "end": 3430.47, "word": " ال", "probability": 0.84521484375}, {"start": 3430.47, "end": 3430.65, "word": " list", "probability": 0.9453125}, {"start": 3430.65, "end": 3430.77, "word": " ايش", "probability": 0.6819661458333334}, {"start": 3430.77, "end": 3431.23, "word": " بتساوي", "probability": 0.924072265625}, {"start": 3431.23, "end": 3431.97, "word": " بتجيل", "probability": 0.6372884114583334}, {"start": 3431.97, "end": 3432.43, "word": " واحد", "probability": 0.81494140625}, {"start": 3432.43, "end": 3433.43, "word": " و", "probability": 0.83154296875}, {"start": 3433.43, "end": 3433.67, "word": " احطه", "probability": 0.81890869140625}, {"start": 3433.67, "end": 3433.75, "word": " في", "probability": 0.89404296875}, {"start": 3433.75, "end": 3433.79, "word": " ال", "probability": 0.916015625}, {"start": 3433.79, "end": 3433.99, "word": " list", "probability": 0.9619140625}, {"start": 3433.99, "end": 3434.57, "word": " هذا", "probability": 0.41015625}, {"start": 3434.57, "end": 3434.81, "word": " برضه", "probability": 0.9405924479166666}, {"start": 3434.81, "end": 3435.13, "word": " حل", "probability": 0.974365234375}, {"start": 3435.13, "end": 3437.23, "word": " بس", "probability": 0.58831787109375}, {"start": 3437.23, "end": 3437.33, "word": " في", "probability": 0.90283203125}, {"start": 3437.33, "end": 3437.53, "word": " الآخر", "probability": 0.8232421875}, {"start": 3437.53, "end": 3437.69, "word": " لما", "probability": 0.620361328125}, {"start": 3437.69, "end": 3437.93, "word": " تكون", "probability": 0.790283203125}, {"start": 3437.93, "end": 3438.23, "word": " جادر", "probability": 0.71728515625}, {"start": 3438.23, "end": 3438.35, "word": " على", "probability": 0.77001953125}, {"start": 3438.35, "end": 3438.83, "word": " كتابته", "probability": 0.9853515625}, {"start": 3438.83, "end": 3439.45, "word": " في", "probability": 0.87060546875}, {"start": 3439.45, "end": 3439.53, "word": " ال", "probability": 0.7587890625}, {"start": 3439.53, "end": 3439.71, "word": " bubble", "probability": 0.8564453125}, {"start": 3439.71, "end": 3440.13, "word": " sort", "probability": 0.87939453125}, {"start": 3440.13, "end": 3440.87, "word": " اللي", "probability": 0.8984375}, {"start": 3440.87, "end": 3441.03, "word": " احنا", "probability": 0.9415690104166666}, {"start": 3441.03, "end": 3441.83, "word": " كتبناه", "probability": 0.91318359375}, {"start": 3441.83, "end": 3441.91, "word": " في", "probability": 0.9345703125}, {"start": 3441.91, "end": 3442.21, "word": " الأول", "probability": 0.8916015625}, {"start": 3442.21, "end": 3442.73, "word": " بقارن", "probability": 0.979248046875}, {"start": 3442.73, "end": 3442.93, "word": " كل", "probability": 0.97802734375}, {"start": 3442.93, "end": 3443.45, "word": " element", "probability": 0.97509765625}, {"start": 3443.45, "end": 3444.65, "word": " مع", "probability": 0.953125}, {"start": 3444.65, "end": 3444.83, "word": " اللي", "probability": 0.934326171875}, {"start": 3444.83, "end": 3445.11, "word": " بعده", "probability": 0.94091796875}, {"start": 3445.11, "end": 3445.19, "word": " و", "probability": 0.68212890625}, {"start": 3445.19, "end": 3445.29, "word": " لما", "probability": 0.912841796875}, {"start": 3445.29, "end": 3445.53, "word": " بكون", "probability": 0.62255859375}, {"start": 3445.53, "end": 3445.75, "word": " فيه", "probability": 0.857666015625}, {"start": 3445.75, "end": 3446.01, "word": " swap", "probability": 0.346435546875}, {"start": 3446.01, "end": 3446.53, "word": " ببدل", "probability": 0.9576822916666666}, {"start": 3446.53, "end": 3447.67, "word": " ال", "probability": 0.41455078125}, {"start": 3447.67, "end": 3447.93, "word": " iteration", "probability": 0.4482421875}, {"start": 3447.93, "end": 3448.73, "word": " الأولى،", "probability": 0.724853515625}, {"start": 3448.73, "end": 3449.59, "word": " التانية،", "probability": 0.9537353515625}, {"start": 3449.59, "end": 3450.45, "word": " التالتة،", "probability": 0.953125}, {"start": 3450.45, "end": 3450.79, "word": " الرابع", "probability": 0.8343098958333334}, {"start": 3450.79, "end": 3451.01, "word": " ماكون", "probability": 0.531982421875}, {"start": 3451.01, "end": 3451.25, "word": " اوصل", "probability": 0.7499186197916666}, {"start": 3451.25, "end": 3451.73, "word": " تلاقياش", "probability": 0.65875244140625}], "temperature": 1.0}, {"id": 129, "seek": 347591, "start": 3452.59, "end": 3475.91, "text": "للحل اللي موجود عندى هاي ال bubble sort بكل بساطة مريت على عناصر من اللي عندى فقط عند ال list و ال output هيكون list اللي هي مرتبة مريت على كل عناصر المصوفة من الأول لجابلى الأخر لجابلى الأخر و جرح و كمان لو كمان مرة من واحد لجابلى الان", "tokens": [1211, 1211, 5016, 1211, 13672, 1829, 3714, 29245, 23328, 43242, 7578, 8032, 47302, 2423, 12212, 1333, 4724, 28820, 4724, 3794, 41193, 3660, 3714, 16572, 2655, 15844, 18871, 33546, 2288, 9154, 13672, 1829, 43242, 7578, 6156, 47432, 43242, 2423, 1329, 4032, 2423, 5598, 39896, 30544, 1329, 13672, 1829, 39896, 3714, 43500, 49401, 3714, 16572, 2655, 15844, 28242, 18871, 33546, 2288, 9673, 9381, 38688, 3660, 9154, 16247, 12610, 5296, 7435, 16758, 23942, 16247, 34740, 5296, 7435, 16758, 23942, 16247, 34740, 4032, 10874, 2288, 5016, 4032, 9122, 2304, 7649, 45164, 9122, 2304, 7649, 3714, 25720, 9154, 36764, 24401, 5296, 7435, 16758, 23942, 2423, 7649], "avg_logprob": -0.2081801431143985, "compression_ratio": 1.9655172413793103, "no_speech_prob": 5.364418029785156e-07, "words": [{"start": 3452.59, "end": 3453.17, "word": "للحل", "probability": 0.737060546875}, {"start": 3453.17, "end": 3453.49, "word": " اللي", "probability": 0.795166015625}, {"start": 3453.49, "end": 3453.85, "word": " موجود", "probability": 0.978515625}, {"start": 3453.85, "end": 3454.15, "word": " عندى", "probability": 0.84326171875}, {"start": 3454.15, "end": 3454.51, "word": " هاي", "probability": 0.3563232421875}, {"start": 3454.51, "end": 3454.61, "word": " ال", "probability": 0.9111328125}, {"start": 3454.61, "end": 3454.77, "word": " bubble", "probability": 0.8359375}, {"start": 3454.77, "end": 3455.21, "word": " sort", "probability": 0.8984375}, {"start": 3455.21, "end": 3456.07, "word": " بكل", "probability": 0.6131591796875}, {"start": 3456.07, "end": 3456.65, "word": " بساطة", "probability": 0.986328125}, {"start": 3456.65, "end": 3457.85, "word": " مريت", "probability": 0.8562825520833334}, {"start": 3457.85, "end": 3458.09, "word": " على", "probability": 0.845703125}, {"start": 3458.09, "end": 3458.97, "word": " عناصر", "probability": 0.9480794270833334}, {"start": 3458.97, "end": 3459.61, "word": " من", "probability": 0.93603515625}, {"start": 3459.61, "end": 3459.73, "word": " اللي", "probability": 0.87109375}, {"start": 3459.73, "end": 3459.95, "word": " عندى", "probability": 0.7861328125}, {"start": 3459.95, "end": 3460.17, "word": " فقط", "probability": 0.957275390625}, {"start": 3460.17, "end": 3460.35, "word": " عند", "probability": 0.67529296875}, {"start": 3460.35, "end": 3460.45, "word": " ال", "probability": 0.83740234375}, {"start": 3460.45, "end": 3460.75, "word": " list", "probability": 0.962890625}, {"start": 3460.75, "end": 3461.41, "word": " و", "probability": 0.5517578125}, {"start": 3461.41, "end": 3461.49, "word": " ال", "probability": 0.80859375}, {"start": 3461.49, "end": 3461.85, "word": " output", "probability": 0.9794921875}, {"start": 3461.85, "end": 3462.57, "word": " هيكون", "probability": 0.758544921875}, {"start": 3462.57, "end": 3463.51, "word": " list", "probability": 0.8681640625}, {"start": 3463.51, "end": 3463.83, "word": " اللي", "probability": 0.52947998046875}, {"start": 3463.83, "end": 3463.93, "word": " هي", "probability": 0.486328125}, {"start": 3463.93, "end": 3464.31, "word": " مرتبة", "probability": 0.8347981770833334}, {"start": 3464.31, "end": 3465.63, "word": " مريت", "probability": 0.9833984375}, {"start": 3465.63, "end": 3465.77, "word": " على", "probability": 0.93017578125}, {"start": 3465.77, "end": 3466.03, "word": " كل", "probability": 0.9912109375}, {"start": 3466.03, "end": 3466.45, "word": " عناصر", "probability": 0.9881184895833334}, {"start": 3466.45, "end": 3467.13, "word": " المصوفة", "probability": 0.88623046875}, {"start": 3467.13, "end": 3467.33, "word": " من", "probability": 0.9814453125}, {"start": 3467.33, "end": 3467.83, "word": " الأول", "probability": 0.910400390625}, {"start": 3467.83, "end": 3468.91, "word": " لجابلى", "probability": 0.68939208984375}, {"start": 3468.91, "end": 3469.39, "word": " الأخر", "probability": 0.8408203125}, {"start": 3469.39, "end": 3470.27, "word": " لجابلى", "probability": 0.9410400390625}, {"start": 3470.27, "end": 3470.69, "word": " الأخر", "probability": 0.968017578125}, {"start": 3470.69, "end": 3471.89, "word": " و", "probability": 0.92822265625}, {"start": 3471.89, "end": 3472.15, "word": " جرح", "probability": 0.7843424479166666}, {"start": 3472.15, "end": 3472.43, "word": " و", "probability": 0.54443359375}, {"start": 3472.43, "end": 3472.77, "word": " كمان", "probability": 0.8935546875}, {"start": 3472.77, "end": 3472.91, "word": " لو", "probability": 0.58349609375}, {"start": 3472.91, "end": 3473.21, "word": " كمان", "probability": 0.9632161458333334}, {"start": 3473.21, "end": 3473.59, "word": " مرة", "probability": 0.984375}, {"start": 3473.59, "end": 3474.29, "word": " من", "probability": 0.98828125}, {"start": 3474.29, "end": 3474.87, "word": " واحد", "probability": 0.916259765625}, {"start": 3474.87, "end": 3475.59, "word": " لجابلى", "probability": 0.96484375}, {"start": 3475.59, "end": 3475.91, "word": " الان", "probability": 0.5028076171875}], "temperature": 1.0}, {"id": 130, "seek": 349516, "start": 3476.82, "end": 3495.16, "text": "اللي هو نقص I وكل ما بلاقي انه IG أكبر من AIG زائد واحد بروح ببدل العناصر اللي موجودة عندى لحد ما بصل لل list أو العناصر ال list اللي موجودة بعض ال algorithm بنسميها greedy algorithm", "tokens": [6027, 20292, 31439, 8717, 4587, 9381, 286, 4032, 28820, 19446, 4724, 15040, 38436, 16472, 3224, 26367, 5551, 4117, 26890, 9154, 7318, 38, 30767, 16373, 3215, 36764, 24401, 4724, 32887, 5016, 4724, 44510, 1211, 18863, 8315, 9381, 2288, 13672, 1829, 3714, 29245, 23328, 3660, 43242, 7578, 5296, 24401, 19446, 4724, 36520, 24976, 1329, 34051, 18863, 8315, 9381, 2288, 2423, 1329, 13672, 1829, 3714, 29245, 23328, 3660, 45030, 11242, 2423, 9284, 44945, 38251, 1829, 11296, 28228, 9284], "avg_logprob": -0.2267680964187572, "compression_ratio": 1.6111111111111112, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 3476.82, "end": 3477.06, "word": "اللي", "probability": 0.5361328125}, {"start": 3477.06, "end": 3477.16, "word": " هو", "probability": 0.91943359375}, {"start": 3477.16, "end": 3477.48, "word": " نقص", "probability": 0.6982421875}, {"start": 3477.48, "end": 3477.76, "word": " I", "probability": 0.62109375}, {"start": 3477.76, "end": 3478.86, "word": " وكل", "probability": 0.65966796875}, {"start": 3478.86, "end": 3479.02, "word": " ما", "probability": 0.6748046875}, {"start": 3479.02, "end": 3479.38, "word": " بلاقي", "probability": 0.71923828125}, {"start": 3479.38, "end": 3479.68, "word": " انه", "probability": 0.591796875}, {"start": 3479.68, "end": 3480.16, "word": " IG", "probability": 0.41650390625}, {"start": 3480.16, "end": 3480.96, "word": " أكبر", "probability": 0.8763020833333334}, {"start": 3480.96, "end": 3481.22, "word": " من", "probability": 0.96337890625}, {"start": 3481.22, "end": 3482.44, "word": " AIG", "probability": 0.7115478515625}, {"start": 3482.44, "end": 3482.74, "word": " زائد", "probability": 0.6476236979166666}, {"start": 3482.74, "end": 3483.26, "word": " واحد", "probability": 0.786865234375}, {"start": 3483.26, "end": 3484.82, "word": " بروح", "probability": 0.91796875}, {"start": 3484.82, "end": 3485.42, "word": " ببدل", "probability": 0.8645833333333334}, {"start": 3485.42, "end": 3486.36, "word": " العناصر", "probability": 0.8538818359375}, {"start": 3486.36, "end": 3486.84, "word": " اللي", "probability": 0.630859375}, {"start": 3486.84, "end": 3487.16, "word": " موجودة", "probability": 0.930419921875}, {"start": 3487.16, "end": 3487.64, "word": " عندى", "probability": 0.83642578125}, {"start": 3487.64, "end": 3488.14, "word": " لحد", "probability": 0.954345703125}, {"start": 3488.14, "end": 3488.24, "word": " ما", "probability": 0.974609375}, {"start": 3488.24, "end": 3488.54, "word": " بصل", "probability": 0.7421875}, {"start": 3488.54, "end": 3488.7, "word": " لل", "probability": 0.7001953125}, {"start": 3488.7, "end": 3489.02, "word": " list", "probability": 0.90478515625}, {"start": 3489.02, "end": 3489.5, "word": " أو", "probability": 0.57421875}, {"start": 3489.5, "end": 3489.94, "word": " العناصر", "probability": 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ما نسميها أو الخوارزمية الطناعة ايش الخوارزمية الطناعة الفكرة فيها بكل بساطة انه انا بجيب حل لكن الحل هذا مش افضل حل بناء على ايش؟ بناء على انه انا دائما بانظر لأبسط او افضل حل في اللحظة الآنية ببقى اللي بستشرفش المستقبل", "tokens": [3224, 1863, 7435, 5172, 34105, 37893, 8032, 1863, 24793, 1211, 8717, 38251, 1829, 11296, 28228, 14642, 13672, 1829, 39896, 19446, 8717, 38251, 1829, 11296, 34051, 33962, 2407, 9640, 11622, 2304, 10632, 41950, 8315, 27884, 1975, 1829, 8592, 33962, 2407, 9640, 11622, 2304, 10632, 41950, 8315, 27884, 27188, 4117, 25720, 8978, 11296, 4724, 28820, 4724, 3794, 41193, 3660, 16472, 3224, 1975, 8315, 4724, 7435, 1829, 3555, 11331, 1211, 44381, 21542, 1211, 23758, 37893, 1975, 5172, 11242, 1211, 11331, 1211, 44945, 16606, 15844, 1975, 1829, 8592, 22807, 44945, 16606, 15844, 16472, 3224, 1975, 8315, 11778, 16373, 15042, 4724, 7649, 19913, 2288, 5296, 10721, 3555, 3794, 9566, 1975, 2407, 1975, 5172, 11242, 1211, 11331, 1211, 8978, 13672, 5016, 19913, 3660, 6024, 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"probability": 0.7869873046875}, {"start": 3650.49, "end": 3650.67, "word": " او", "probability": 0.838623046875}, {"start": 3650.67, "end": 3650.83, "word": " على", "probability": 0.26806640625}, {"start": 3650.83, "end": 3651.87, "word": " الشجاعية؟", "probability": 0.871484375}, {"start": 3651.87, "end": 3653.47, "word": " على", "probability": 0.7724609375}, {"start": 3653.47, "end": 3653.93, "word": " الأزهر", "probability": 0.9793701171875}, {"start": 3653.93, "end": 3654.71, "word": " طيب", "probability": 0.7635904947916666}, {"start": 3654.71, "end": 3655.47, "word": " تخيل", "probability": 0.9365234375}, {"start": 3655.47, "end": 3656.03, "word": " ان", "probability": 0.68505859375}, {"start": 3656.03, "end": 3656.55, "word": " السيارة", "probability": 0.984619140625}, {"start": 3656.55, "end": 3656.67, "word": " اللي", "probability": 0.844482421875}, {"start": 3656.67, "end": 3656.75, "word": " في", "probability": 0.90673828125}, {"start": 3656.75, "end": 3657.29, "word": " الأزهر", "probability": 0.9891357421875}, {"start": 3657.29, "end": 3657.67, "word": " او", "probability": 0.748291015625}, {"start": 3657.67, "end": 3657.81, "word": " على", "probability": 0.397216796875}, {"start": 3657.81, "end": 3658.03, "word": " موقف", "probability": 0.9864908854166666}, {"start": 3658.03, "end": 3658.63, "word": " الأزهر", "probability": 0.990478515625}, {"start": 3658.63, "end": 3659.29, "word": " بدها", "probability": 0.40130615234375}, {"start": 3659.29, "end": 3659.51, "word": " تروح", "probability": 0.99658203125}, {"start": 3659.51, "end": 3659.63, "word": " في", "probability": 0.7626953125}, {"start": 3659.63, "end": 3660.25, "word": " أولا", "probability": 0.8382161458333334}, {"start": 3660.25, "end": 3661.75, "word": " على", "probability": 0.7314453125}, {"start": 3661.75, "end": 3662.37, "word": " الشجاعية", "probability": 0.98779296875}, {"start": 3662.37, "end": 3663.13, "word": " وبعدين", "probability": 0.8085123697916666}, {"start": 3663.13, "end": 3663.57, "word": " بترجع", "probability": 0.8346354166666666}, {"start": 3663.57, "end": 3664.37, "word": " تاني", "probability": 0.8889973958333334}, {"start": 3664.37, "end": 3665.65, "word": " معينة", "probability": 0.5380452473958334}, {"start": 3665.65, "end": 3665.95, "word": " وصارت", "probability": 0.71051025390625}, {"start": 3665.95, "end": 3666.07, "word": " فهذه", "probability": 0.5182291666666666}, {"start": 3666.07, "end": 3666.89, "word": " الطريق؟", "probability": 0.830810546875}, {"start": 3666.89, "end": 3667.25, "word": " بقولش", "probability": 0.765625}, {"start": 3667.25, "end": 3667.35, "word": " اللي", "probability": 0.981201171875}, {"start": 3667.35, "end": 3667.43, "word": " هو", "probability": 0.916015625}, {"start": 3667.43, "end": 3667.53, "word": " هذا", "probability": 0.6376953125}, {"start": 3667.53, "end": 3667.81, "word": " الطمع", "probability": 0.8204752604166666}, {"start": 3667.81, "end": 3668.03, "word": " لكن", "probability": 0.8271484375}, {"start": 3668.03, "end": 3668.49, "word": " فعليا", "probability": 0.9407958984375}, {"start": 3668.49, "end": 3668.83, "word": " كانت", "probability": 0.79931640625}, {"start": 3668.83, "end": 3669.29, "word": " decision", "probability": 0.52783203125}, {"start": 3669.29, "end": 3670.27, "word": " مبني", "probability": 0.8924153645833334}, {"start": 3670.27, "end": 3670.51, "word": " على", "probability": 0.8017578125}, {"start": 3670.51, "end": 3670.79, "word": " مين", "probability": 0.977783203125}, {"start": 3670.79, "end": 3671.23, "word": " أقصر", "probability": 0.8846435546875}, {"start": 3671.23, "end": 3671.81, "word": " الطرق", "probability": 0.9498697916666666}], "temperature": 1.0}, {"id": 137, "seek": 368824, "start": 3672.94, "end": 3688.24, "text": "الموجودة عند هان احنا بنسميه كمان مرة هو algorithm بتديني حل مش مابيدليش بوصللي لـ output المطلوب لكن هذا الحل هل هو أفضل حل؟ لأ في أحسن منه والله يعطيكوا العافية", "tokens": [45340, 29245, 23328, 3660, 43242, 8032, 7649, 1975, 5016, 8315, 44945, 38251, 1829, 3224, 9122, 2304, 7649, 3714, 25720, 31439, 9284, 39894, 3215, 9957, 1829, 11331, 1211, 37893, 3714, 16758, 25708, 20292, 8592, 4724, 2407, 36520, 20292, 5296, 39184, 5598, 9673, 9566, 1211, 37746, 44381, 23758, 21542, 1211, 8032, 1211, 31439, 5551, 5172, 11242, 1211, 11331, 1211, 22807, 5296, 10721, 8978, 5551, 5016, 3794, 1863, 9154, 3224, 16070, 43761, 37495, 9566, 1829, 4117, 14407, 18863, 31845, 10632], "avg_logprob": -0.27864584288535976, "compression_ratio": 1.516304347826087, "no_speech_prob": 0.0002617835998535156, "words": [{"start": 3672.94, "end": 3673.78, "word": "الموجودة", "probability": 0.84588623046875}, {"start": 3673.78, "end": 3674.32, "word": " عند", "probability": 0.76123046875}, {"start": 3674.32, "end": 3674.62, "word": " هان", "probability": 0.489837646484375}, {"start": 3674.62, "end": 3675.16, "word": " احنا", "probability": 0.75146484375}, {"start": 3675.16, "end": 3675.86, "word": " بنسميه", "probability": 0.9078369140625}, {"start": 3675.86, "end": 3676.38, "word": " كمان", "probability": 0.9375}, {"start": 3676.38, "end": 3676.62, "word": " مرة", "probability": 0.972900390625}, {"start": 3676.62, "end": 3676.8, "word": " هو", "probability": 0.89697265625}, {"start": 3676.8, "end": 3677.28, "word": " algorithm", "probability": 0.85791015625}, {"start": 3677.28, "end": 3678.5, "word": " بتديني", "probability": 0.73114013671875}, {"start": 3678.5, "end": 3678.8, "word": " حل", "probability": 0.9921875}, {"start": 3678.8, "end": 3679.28, "word": " مش", "probability": 0.9228515625}, {"start": 3679.28, "end": 3679.92, "word": " مابيدليش", "probability": 0.69716796875}, {"start": 3679.92, "end": 3680.9, "word": " بوصللي", "probability": 0.65936279296875}, {"start": 3680.9, "end": 3681.06, "word": " لـ", "probability": 0.3690185546875}, {"start": 3681.06, "end": 3681.26, "word": " output", "probability": 0.583984375}, {"start": 3681.26, "end": 3681.94, "word": " المطلوب", "probability": 0.9510498046875}, {"start": 3681.94, "end": 3682.62, "word": " لكن", "probability": 0.873046875}, {"start": 3682.62, "end": 3682.98, "word": " هذا", "probability": 0.86474609375}, {"start": 3682.98, "end": 3683.32, "word": " الحل", "probability": 0.9814453125}, {"start": 3683.32, "end": 3683.54, "word": " هل", "probability": 0.83447265625}, {"start": 3683.54, "end": 3683.7, "word": " هو", "probability": 0.9853515625}, {"start": 3683.7, "end": 3684.12, "word": " أفضل", "probability": 0.95849609375}, {"start": 3684.12, "end": 3684.7, "word": " حل؟", "probability": 0.796875}, {"start": 3684.7, "end": 3685.68, "word": " لأ", "probability": 0.808837890625}, {"start": 3685.68, "end": 3685.94, "word": " في", "probability": 0.5048828125}, {"start": 3685.94, "end": 3686.28, "word": " أحسن", "probability": 0.9727783203125}, {"start": 3686.28, "end": 3686.62, "word": " منه", "probability": 0.991455078125}, {"start": 3686.62, "end": 3687.7, "word": " والله", "probability": 0.6881103515625}, {"start": 3687.7, "end": 3687.94, "word": " يعطيكوا", "probability": 0.728369140625}, {"start": 3687.94, "end": 3688.24, "word": " العافية", "probability": 0.718017578125}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3688.629125, "duration_after_vad": 3510.830624999986}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/xeTWnmt0OTo.srt b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/xeTWnmt0OTo.srt
new file mode 100644
index 0000000000000000000000000000000000000000..7c64e0fa9d9b8d0a5212c329bab04188416eeea4
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/xeTWnmt0OTo.srt
@@ -0,0 +1,1275 @@
+1
+00:00:21,310 --> 00:00:23,270
+بسم الله والحمد لله والصلاة والسلام على رسول الله
+
+2
+00:00:23,270 --> 00:00:26,470
+طيب شباب اليوم إن شاء الله هنكمل، ما زلنا في الـ
+
+3
+00:00:26,470 --> 00:00:30,130
+chapter الأول، ننتقل إلى الـ section الخامس، الـ nested
+
+4
+00:00:30,130 --> 00:00:34,020
+quantifiers لكن قبل ما نبدأ، لنعد إلى نفس الـ
+
+5
+00:00:34,020 --> 00:00:38,340
+quantifier، خلينا نسترجع مع بعض آخر مثالين والآخر
+
+6
+00:00:38,340 --> 00:00:42,080
+محاضرة بشكل سريع، قلنا في آخر محاضرة، تكلمت على الـ
+
+7
+00:00:42,080 --> 00:00:44,420
+predicate والـ quantifiers، تكلمنا على الـ
+
+8
+00:00:44,420 --> 00:00:48,360
+predicate والـ quantifiers، قلنا الـ predicate لما
+
+9
+00:00:48,360 --> 00:00:52,220
+يكون فيه عندي X أكبر من 3، قلنا الثلاثة هذه
+
+10
+00:00:52,220 --> 00:00:56,580
+مثابة الـ predicate أو القيمة المسندة اللي أنا
+
+11
+00:00:56,580 --> 00:01:00,360
+بناء عليها بدي أُحدد الـ truth value، قلنا في عندنا
+
+12
+00:01:00,360 --> 00:01:05,550
+predicate function، P of X، اللي بنرمز لها بـ X أكبر
+
+13
+00:01:05,550 --> 00:01:12,530
+من 3، وهذا سميناها predicate function، predicate
+
+14
+00:01:12,530 --> 00:01:15,830
+function، فالـ predicate function هنا ما بقدر أُعطيها
+
+15
+00:01:15,830 --> 00:01:20,550
+قيمة إلا لو حددت قيمة الـ X،  بأشيء، بقول P of واحد
+
+16
+00:01:20,550 --> 00:01:24,830
+هدا، قيمتها بأشيء، بقول واحد أكبر من ثلاثة، false،
+
+17
+00:01:24,830 --> 00:01:31,090
+معناته false، P of أربعة، true، لأن الأربعة أكبر من
+
+18
+00:01:31,090 --> 00:01:34,590
+ثلاثة، وبعد الـ predicate، هي تكلمنا على شغلة سميناها
+
+19
+00:01:34,590 --> 00:01:38,530
+quantifiers، والـ quantifiers طلب مني أن أنا أعرف
+
+20
+00:01:38,530 --> 00:01:44,070
+domain على كل عناصر الـ predicate function، صار في
+
+21
+00:01:44,070 --> 00:01:49,530
+عندي domain، أو اللي سميناه universal أو universe
+
+22
+00:01:49,530 --> 00:01:54,450
+of discourse، وقلنا في عندنا نوعين من الـ quantifiers
+
+23
+00:01:54,450 --> 00:02:05,670
+for all x,  ∀x، و there exists x، ∃x، بنقول صرنا
+
+24
+00:02:05,670 --> 00:02:08,850
+الآن بنقيم الـ predicate function أو الـ quantifier
+
+25
+00:02:08,850 --> 00:02:13,170
+هذا الـ predicate function، هذه is true لكل قيم الـ
+
+26
+00:02:13,170 --> 00:02:17,870
+domain، مثل
+
+27
+00:02:17,870 --> 00:02:22,450
+لو أنا قلت لك الـ domain هو الـ natural number، for
+
+28
+00:02:22,450 --> 00:02:28,360
+all x، كل قيم الـ domain هتكون أكبر من ثلاثة، false،
+
+29
+00:02:28,360 --> 00:02:34,420
+ليش؟ لأن عندي الواحد ينتمي للـ domain، والواحد أقل
+
+30
+00:02:34,420 --> 00:02:40,140
+من أو يساوي الثلاثة، اللي هي عكس هذه، صحيح؟ اللي هي
+
+31
+00:02:40,140 --> 00:02:44,520
+سميناها الـ counter example، there exists x، هناك على
+
+32
+00:02:44,520 --> 00:02:49,000
+الأقل x واحدة تحقق المعادلة بـ x أو الـ function بـ x
+
+33
+00:02:49,000 --> 00:02:54,590
+true، تمام؟ عندك سبعة، أربعة، أو خمسة، وأطلع إلى ما
+
+34
+00:02:54,590 --> 00:02:57,970
+لا نهاية، كلهم بيحققوا العناصر هذا، وآخر شغلة لما
+
+35
+00:02:57,970 --> 00:03:02,690
+تكلمنا على النفي، قلت لما أنا بأجي بأنفي، نفي
+
+36
+00:03:02,690 --> 00:03:12,550
+for all x، P(x)، تكافئ there exists x، not P(x)، نفي P of x
+
+37
+00:03:12,550 --> 00:03:20,110
+ونفي for there exists x، P(x)، هتصير تكافئ for all x،
+
+38
+00:03:20,740 --> 00:03:26,060
+not P(x)، وجينا قلنا for all X، يعني كل العناصر اللي
+
+39
+00:03:26,060 --> 00:03:31,980
+في الـ domain، نفيها، على الأقل هناك واحد في
+
+40
+00:03:31,980 --> 00:03:36,440
+الـ domain يحقق المعادلة، نفيها، كل عناصر الـ domain اللي
+
+41
+00:03:36,440 --> 00:03:42,570
+هتحقق المعادلة، و ننتقل بعد ذلك لموضوع الـ Translation
+
+42
+00:03:42,570 --> 00:03:47,290
+في موضوع الـ Quantifiers، وحاولنا أن نطبق أو نترجم
+
+43
+00:03:47,290 --> 00:03:52,270
+المثال اللي موجود عندنا هنا، بحيث قلنا لكل رسالة
+
+44
+00:03:52,270 --> 00:03:58,870
+حجمها أقل من واحد ميغا بايت، بدها تِتم تشفيرها، بقول
+
+45
+00:03:58,870 --> 00:04:04,030
+كيف نتعامل مع هذا المثال؟ بروح بتجسيم، every معناها for
+
+46
+00:04:04,030 --> 00:04:13,830
+all، خلصنا، Message X، أو المجهول تبعتنا، طيب إيش بده
+
+47
+00:04:13,830 --> 00:04:23,150
+يصير فيها، larger than، أكبر من one megabyte، المتغير
+
+48
+00:04:23,150 --> 00:04:30,530
+الثاني، واحد ميغا بايت، تمام، will be implies، والـ
+
+49
+00:04:30,530 --> 00:04:32,890
+compress، اللي هي هتكون المعادلة الثانية اللي
+
+50
+00:04:32,890 --> 00:04:38,380
+هنعملها على مين؟ على الـ M، يعني هي هتصير كمعادلة
+
+51
+00:04:38,380 --> 00:04:49,620
+لكل M، P of M، هيؤدي إلى C of M، إيش هذه P of M؟
+
+52
+00:04:49,620 --> 00:04:56,840
+لازم تتعرفها، الـ M is an email message، أو mail is
+
+53
+00:04:56,840 --> 00:05:03,380
+a mail message، P
+
+54
+00:05:03,380 --> 00:05:12,280
+of M، الـ M أكبر من واحد ميغا بايت، مظبوط، الـ C of
+
+55
+00:05:12,280 --> 00:05:21,200
+M، اللي هي الـ M will be compressed، وبالتالي هذه
+
+56
+00:05:21,200 --> 00:05:23,820
+المعادلة، هذه translation لـ specification اللي
+
+57
+00:05:23,820 --> 00:05:28,380
+موجودة عندنا، ممكن أتكلم على specification ثانية إذا
+
+58
+00:05:28,380 --> 00:05:31,740
+أنا قلت والله بدي أخلي الـ، الـ role هذا more
+
+59
+00:05:31,740 --> 00:05:35,260
+general، وأروح بدل الـ، وبدل الـ X أو بدل الـ واحد
+
+60
+00:05:35,260 --> 00:05:41,510
+أحط Y، بدل الواحد أحط Y، يعني لما تكون الـ M حجم
+
+61
+00:05:41,510 --> 00:05:46,290
+الرسالة أقل من أو أكبر من الـ Y، بتصير في عندي
+
+62
+00:05:46,290 --> 00:05:49,150
+hand، P of M، Y
+
+63
+00:05:51,780 --> 00:05:55,860
+وتحريف المعادلة هنا بصير بدل الواحد باستخدام الـ Y
+
+64
+00:05:55,860 --> 00:05:59,700
+اللي موجودة عندنا، وبالتالي ممكن أنا أحصل على أكثر
+
+65
+00:05:59,700 --> 00:06:03,400
+من definition أو أكثر من quantifier صحيح، إذا أنا
+
+66
+00:06:03,400 --> 00:06:07,000
+قدرت أترجم كل العناصر هذه بشكل مستقل بشكل صحيح
+
+67
+00:06:07,000 --> 00:06:10,120
+وبعدين أربطهم زي ما بدي، وشُفنا المثال الثاني اللي
+
+68
+00:06:10,120 --> 00:06:14,240
+كان نتكلم عن الـ connection وحليناها مع بعض وشُفنا
+
+69
+00:06:16,210 --> 00:06:19,370
+شو؟ يعني العلاقة ما بين الـ link والـ user، الـ
+
+70
+00:06:19,370 --> 00:06:23,590
+available، اليوم هنتقل لشغلة جديدة اللي هي nested
+
+71
+00:06:23,590 --> 00:06:28,830
+quantifiers، nested، احنا شفنا سابقًا لما تكلمنا
+
+72
+00:06:28,830 --> 00:06:32,610
+على الـ operators، الـ logical operators، قلنا P or
+
+73
+00:06:32,610 --> 00:06:43,750
+Q and R، أو بي نفي Q and P or R، فكل هذه
+
+74
+00:06:43,750 --> 00:06:47,230
+نسميها nested operators، لأنها تتداخل بين العناصر
+
+75
+00:06:47,230 --> 00:06:51,370
+الموجودة، وشُفنا أن النفي هذه لما تدخل تدخل على جوا
+
+76
+00:06:51,370 --> 00:06:57,750
+الجسم بالكامل، ولما شُفنا النفي في الـ quantifiers،
+
+77
+00:06:57,750 --> 00:07:04,490
+نفي for all x، P(x)، مررناها على كل العناصر صارت
+
+78
+00:07:04,490 --> 00:07:09,390
+there exists x، ونفينا الـ P(x)، لكن ما شفناش ولا
+
+79
+00:07:09,390 --> 00:07:14,680
+حالة من الـ nested quantifier
+
+80
+00:07:14,680 --> 00:07:19,060
+جايين وراء بعض، الآن لما أنا بتكلم على نفس الـ
+
+81
+00:07:19,060 --> 00:07:22,760
+quantifier، معناته أنا بتكلم إن الـ predicate function
+
+82
+00:07:22,760 --> 00:07:27,240
+تابعتي، زي في المثال السابق، بتعتمد على two variables
+
+83
+00:07:27,240 --> 00:07:35,300
+بس كل واحد فيهم له quantifier لحاله، بدي أتعامل
+
+84
+00:07:35,300 --> 00:07:39,700
+معاه لحاله، تعالَ نشوف أو نحاول نفهم الـ quantifier
+
+85
+00:07:39,700 --> 00:07:46,280
+اللي موجود قدامنا هنا، for all x، لأي x ينتمي للـ
+
+86
+00:07:46,280 --> 00:07:52,260
+domain، تمام، there exists y، بلاقيها على الأقل y
+
+87
+00:07:52,260 --> 00:07:55,480
+واحدة بتحقق الـ predicate function اللي موجودة عندي،
+
+88
+00:07:55,480 --> 00:08:01,400
+for all x، there exists y، بتحقق
+
+89
+00:08:02,540 --> 00:08:05,640
+الـ function، يعني تعالَ نشوفها، لو أنا أجيت قلت لك
+
+90
+00:08:05,640 --> 00:08:08,320
+الـ domain تبعتي اللي هي الـ natural number، الـ real
+
+91
+00:08:08,320 --> 00:08:17,340
+number، الـ domain، افترض أن الـ domain الأعداد
+
+92
+00:08:17,340 --> 00:08:24,640
+الحقيقية كلها، بالمثال هذا، for all x، لأي عدد
+
+93
+00:08:24,640 --> 00:08:34,650
+حقيقي، هناك على الأقل عنصر واحد، عدد حقيقي تمام، بحيث
+
+94
+00:08:34,650 --> 00:08:39,390
+إن لو جمعتهم الاثنين مع بعض يساووا صفر، true ولا
+
+95
+00:08:39,390 --> 00:08:42,870
+false؟  أُجيب
+
+96
+00:08:42,870 --> 00:08:46,910
+أقول صفر وصفر، وآخذ حالة واحدة فقط وأربط عليها
+
+97
+00:08:46,910 --> 00:08:54,490
+كأُسلوب، لحظة، إيش في الأول عندي؟ for all، لأي عدد حقيقي
+
+98
+00:08:55,430 --> 00:09:01,070
+ماذا يعني؟ لكل الأعداد الحقيقية، لأي عدد حقيقي، يعني
+
+99
+00:09:01,070 --> 00:09:06,770
+هذه المعادلة تبدأ تتطبق على كل الأعداد الحقيقية، إيش
+
+100
+00:09:06,770 --> 00:09:12,550
+ما آخذ عدد حقيقي، تمام؟ هتلاقيله عدد حقيقي آخر
+
+101
+00:09:12,550 --> 00:09:19,970
+واحد على الأقل لو جمعته يساوي صفر، true، العنصر
+
+102
+00:09:19,970 --> 00:09:29,400
+والسالب تبعه، النظير الجمعي، X زائد سالب X، لأن الشيء
+
+103
+00:09:29,400 --> 00:09:35,420
+اللي قاعد يقول لي خذ أي عنصر في الـ domain، for all X
+
+104
+00:09:35,420 --> 00:09:40,300
+in the domain، for any real number، there exists، يعني
+
+105
+00:09:40,300 --> 00:09:46,120
+إيش ما آخذ عدد، إيش ما آخذ عدد، هتلاقي عدد واحد
+
+106
+00:09:46,120 --> 00:09:50,200
+على الأقل لما تجمعهم الاثنين مع بعض بيديك صفر، true،
+
+107
+00:09:50,200 --> 00:09:59,200
+نشوف اللي بعدها، ليش برجعها؟ تمام، اختلفت الصورة تمامًا،
+
+108
+00:09:59,200 --> 00:10:07,560
+الآن تعالَ شوف there exists، هناك X واحدة على الأقل
+
+109
+00:10:07,560 --> 00:10:12,940
+في الـ domain، تُستخدم
+
+110
+00:10:12,940 --> 00:10:17,860
+مع كل عناصر اللي في الـ domain، تمام، بحيث إنها تحقق
+
+111
+00:10:17,860 --> 00:10:21,020
+المعادلة الموجودة، يعني الـ X هذه
+
+112
+00:10:23,550 --> 00:10:27,750
+ما فيش غيرها، أو على الأقل في X واحدة تظبط مع كل الـ X
+
+113
+00:10:27,750 --> 00:10:33,230
+حسب المعادلة، في المعادلة اللي عندي، هالـ، في المعادلة
+
+114
+00:10:33,230 --> 00:10:39,610
+اللي عندي، هالـ there exists X، لكل عناصر الـ Y، لكل
+
+115
+00:10:39,610 --> 00:10:42,850
+عناصر الـ domain، في الـ real number، لو ضربت X في Y
+
+116
+00:10:42,850 --> 00:10:49,980
+تديني صفر، true، الصفر، الصفر real number، ولو ضربته
+
+117
+00:10:49,980 --> 00:10:54,800
+في أي عدد حقيقي بحصل على صفر، بنجي نجيب الـ
+
+118
+00:10:54,800 --> 00:11:00,060
+quantifiers هدول، بحيث إننا نقول هان كالتالي: there
+
+119
+00:11:00,060 --> 00:11:09,480
+exists x، for all y، x زائد y يساوي صفر، وهان إيش
+
+120
+00:11:09,480 --> 00:11:16,530
+معناها الآن؟ هناك x واحدة، لو جمعتها لكل عناصر الـ domain
+
+121
+00:11:16,530 --> 00:11:20,870
+لكل عناصر الـ domain أو لأي عنصر في الـ domain هتديني
+
+122
+00:11:20,870 --> 00:11:27,170
+صفر، false، مستحيل تلاقي هيك معادلة، اختلاف أو إعادة
+
+123
+00:11:27,170 --> 00:11:31,830
+ترتيب الـ quantifiers أدى لاختلاف الـ output، تعالَ
+
+124
+00:11:31,830 --> 00:11:40,090
+نشوف هنا، for all x، there exists y، such that x ضرب
+
+125
+00:11:40,090 --> 00:11:51,820
+الـ y يساوي صفر، لكل X، لأي X في الـ domain، هتلاقيله Y
+
+126
+00:11:51,820 --> 00:11:57,960
+لو ضربتهم في بعض بِديك صفر، true، لأن الـ Y، لأن
+
+127
+00:11:57,960 --> 00:12:01,040
+عملية الضرب عملية إبدالية، وبالتالي الـ Y، بدي أعتمد
+
+128
+00:12:01,040 --> 00:12:04,900
+هذه الصفر، وبتقسم مع كل العناصر وبتقولي على الأقل
+
+129
+00:12:04,900 --> 00:12:10,380
+X واحدة وY واحدة ولا لأ؟ فبالتالي هذه كمان true،
+
+130
+00:12:10,380 --> 00:12:17,950
+طيب، تعالَ نشوف الجدول هذا، جمع مجموعة من الـ nested
+
+131
+00:12:17,950 --> 00:12:25,670
+quantifiers، وبحاول أترجم لهم، for all x، for all y،
+
+132
+00:12:25,670 --> 00:12:35,610
+P(x,y)، إيش يعني؟ لأي عددين في الـ domain، P(x,y) is true، أي
+
+133
+00:12:35,610 --> 00:12:38,930
+عددين في الـ domain بيحققوا الـ predicate function تبعتي،
+
+134
+00:12:38,930 --> 00:12:45,440
+هَيْ يعني لو أنا جاي قلت لك for all x، for all y، على
+
+135
+00:12:45,440 --> 00:12:54,360
+المثال السابق، x زائد y تساوي صفر، عرفنا معناها؟ بدك
+
+136
+00:12:54,360 --> 00:12:58,460
+تفترض أن في عندي real number وreal number، x بأبدأ
+
+137
+00:12:58,460 --> 00:13:04,740
+آخذها من هنا، والـ y بأبدأ آخذها من هنا، أي x هنا،
+
+138
+00:13:04,740 --> 00:13:12,590
+تمام؟ مع أي x هنا، جمعهم يساوي صفر، فـ، فـ،  مش
+
+139
+00:13:12,590 --> 00:13:18,550
+نفسها، ليش؟ لأنها بتكون true، لأن الاثنين متفقين،
+
+140
+00:13:18,550 --> 00:13:23,610
+الاثنين مع كل زوج مُرتّب، يعني هكذا أي x هنا بتكون
+
+141
+00:13:23,610 --> 00:13:28,770
+true مع كل عناصر الـ Y والعكس صحيح، أي Y هتكون true
+
+142
+00:13:28,770 --> 00:13:32,630
+مع كل عناصر الـ X، وهذا كلام مستحيل يصير حسب
+
+143
+00:13:32,630 --> 00:13:37,890
+المعادلة اللي مكتوبة هنا فوق، طيب، لاحظوا إننا بدّلنا
+
+144
+00:13:37,890 --> 00:13:44,090
+for all x وfor all y، نفس المعنى ما فرقتش، لأنه
+
+145
+00:13:44,090 --> 00:13:47,390
+بتكلم على نفس الـ quantifier، بتكلم على نفس الـ
+
+146
+00:13:47,390 --> 00:13:52,850
+quantifier، فلو قدمت أو أخرّجت مش فارق كتير عندي، اللي
+
+147
+00:13:52,850 --> 00:14:00,450
+بعده، متى هذا بيكون false؟ لو قدرت ألاقي فقط زوج
+
+148
+00:14:00,450 --> 00:14:04,880
+مرتب أو زوج من العناصر x و y اللي ما حققوش الـ
+
+149
+00:14:04,880 --> 00:14:09,680
+predicate function تبعها، إيش بتصير؟ false، طيب، for
+
+150
+00:14:09,680 --> 00:14:15,340
+all x، زي ما قلنا سابقًا، لأي عنصر في الـ domain فيه
+
+151
+00:14:15,340 --> 00:14:21,240
+هناك على الأقل عنصر واحد y يحقق المعادلة اللي
+
+152
+00:14:21,240 --> 00:14:26,520
+موجودة، متى بتكون false؟ لو ما لاقيتش الـ y لزوج واحد
+
+153
+00:14:26,520 --> 00:14:34,530
+على الأقل، there exists x، هناك x واحدة لو طبقتها مع
+
+154
+00:14:34,530 --> 00:14:38,690
+كل العناصر اللي في الـ domain بتعمل satisfied، متى هذا
+
+155
+00:14:38,690 --> 00:14:42,870
+الكلام بيكون false؟ لو قدرت ألاقي X وY كزوج مرتب واحد فقط
+
+156
+00:14:42,870 --> 00:14:47,270
+إن هذا ما حققتش المعادلة اللي عندي، there exists X،
+
+157
+00:14:47,270 --> 00:14:53,850
+there exists Y، هناك X، لـ Y واحدة، تمام، بتحقق المعادلة
+
+158
+00:14:53,850 --> 00:14:59,690
+اللي عندها، وترتيبهم ممكن يكون نفس النتيجة، متى
+
+159
+00:14:59,690 --> 00:15:05,540
+بتكون false؟ لو كانت المعادلة هذه false لكل الأزواج،
+
+160
+00:15:05,540 --> 00:15:12,520
+يعني هيك، لأي X لم أجد أي Y، تمام؟ عكسها تمامًا، طيب،
+
+161
+00:15:12,520 --> 00:15:20,060
+ننتقل للجزء اللي بعده، تعالَ نشوف، بقول لك نترجم نفس
+
+162
+00:15:20,060 --> 00:15:26,480
+الـ quantifier اللي موجود عندي هنا، أي
+
+163
+00:15:26,480 --> 00:15:27,040
+طالب،
+
+164
+00:15:33,320 --> 00:15:37,440
+or all students
+
+165
+00:15:37,440 --> 00:15:42,640
+الـ X لديه
+
+166
+00:15:42,640 --> 00:15:53,080
+كمبيوتر، P(x)، or has a friend that has a computer
+
+167
+00:15:53,080 --> 00:16:01,720
+الـ friend معناته Y، وP(y)، لديه كمبيوتر، ممكن هيك
+
+168
+00:16:01,720 --> 00:16:06,780
+تتعامل معاهم، يعني الآن أنا بكل بساطة، أي طالب في الـ
+
+169
+00:16:06,780 --> 00:16:11,840
+class هذا، إما هيكون عنده جهاز كمبيوتر أو  له
+
+170
+00:16:11,840 --> 00:16:18,640
+صديق مع جهاز كمبيوتر، تمام
+
+223
+00:22:01,450 --> 00:22:07,630
+هناك Y لأنه بتتكلم على نفس الـdomain أنا مازلت X
+
+224
+00:22:07,630 --> 00:22:15,090
+زائد Y تساوي صفر.  الشرط الأخير هذا تحت لكل X
+
+225
+00:22:15,090 --> 00:22:26,450
+مع أي Y، أي X مع أي Y في الـdomain X زائد Y تساوي Y
+
+226
+00:22:26,450 --> 00:22:34,620
+زائد X. لاحظ أن هنا قاعد بيقول لك بدك تأخذ كل العناصر
+
+227
+00:22:34,620 --> 00:22:40,780
+هتفترض X من R و Y من R،  الـR هنا real number
+
+228
+00:22:40,780 --> 00:22:47,080
+تأخذ كل عنصر في الـX تربط مع كل عناصر الـY والعكس
+
+229
+00:22:47,080 --> 00:22:51,600
+صحيح، كل عنصر في الـY بده يرتبط مع كل عناصر الـX
+
+230
+00:22:51,600 --> 00:22:58,490
+صار عندك مجموعة من الأزواج المرتبة، هيهم X و Y
+
+231
+00:22:58,490 --> 00:23:03,930
+زائد Y بدها تساوي Y زائد X، بدك تفهمها هيك، هذه
+
+232
+00:23:03,930 --> 00:23:09,970
+إحنا غالباً بنرمزها for all X, for all Y, P of X و
+
+233
+00:23:09,970 --> 00:23:13,070
+Y، هذا المكتوب تحت، هو هي العلاقة اللي ما بين
+
+234
+00:23:13,070 --> 00:23:15,450
+الـX والـY، الـpredicate function
+
+235
+00:23:26,450 --> 00:23:30,710
+ضروري تحدد شو علاقة الـcombination أو تحدد
+
+236
+00:23:30,710 --> 00:23:33,790
+العلاقة ما بين الـvariables اللي عندك عشان تقدر
+
+237
+00:23:33,790 --> 00:23:38,410
+تكتب الـquantifier صح، لأن إحنا اتفقنا قبل شوية من
+
+238
+00:23:38,410 --> 00:23:44,850
+خلال الأمثلة for all x there exist y مش بالضرورة
+
+239
+00:23:44,850 --> 00:23:52,150
+تكافئ There exists x for all y ولا بقى في اختلاف
+
+240
+00:23:52,150 --> 00:23:58,010
+تماماً في المعنى، وبالتالي لازم تفهم شو هي علاقة الـ
+
+241
+00:23:58,010 --> 00:24:03,210
+universal quantifier والـexistential مع العنصر
+
+242
+00:24:03,210 --> 00:24:07,170
+اللي عندك، خصوصاً إن هم الاثنين مش متساويات، ضروري
+
+243
+00:24:07,170 --> 00:24:11,390
+نفهمها بشكلٍ عنصر. تعالَ نشوف بالمثال اللي عندي هان
+
+244
+00:24:11,390 --> 00:24:18,530
+بقول الـpredicate XY هي عبارة عن X زائد Y تساوي صفر
+
+245
+00:24:18,530 --> 00:24:32,110
+هناك X لأي Y، P of XY، هناك X واحدة لو جمعتها مع أي
+
+246
+00:24:32,110 --> 00:24:40,730
+Y بتعطيني صفر. لكن تعالَ
+
+247
+00:24:40,730 --> 00:24:50,320
+نقول: لأي X أنت بتحددها، هتلاقي Y واحدة على الأقل لو
+
+248
+00:24:50,320 --> 00:24:54,420
+جمعتهم الاثنين مع بعض وبتعطيني صفر، true اللي هي
+
+249
+00:24:54,420 --> 00:25:02,960
+قولنا قيمة وسالب قيمتها
+
+250
+00:25:02,960 --> 00:25:07,320
+نفس الـquantifiers لما أنا بدي أنفيها، إحنا الآن
+
+251
+00:25:07,320 --> 00:25:14,750
+في عندي for all X for all Y، تخيل إن أنا بدي أنفيها
+
+252
+00:25:14,750 --> 00:25:21,830
+P of XY، إحنا
+
+253
+00:25:21,830 --> 00:25:26,670
+لما ننفي الـquantifier، قلنا بنمرر النافي تبعت الـ
+
+254
+00:25:26,670 --> 00:25:30,960
+universal quantifier بتصير existential وبعدين بتصير
+
+255
+00:25:30,960 --> 00:25:35,620
+النفي تبعت الـpredicate function، يعني نفي for all
+
+256
+00:25:35,620 --> 00:25:39,920
+x,  بتصير there exist x، هناك x واحدة على
+
+257
+00:25:39,920 --> 00:25:45,920
+الأقل لا تحقق الـP of X ولا لا؟ والنفي تبعت
+
+258
+00:25:45,920 --> 00:25:52,100
+there exist x، بتصير هناك x واحدة على الأقل تحقق
+
+259
+00:25:52,100 --> 00:26:00,140
+الـPx. نفيها: كل عناصر X لا تحقق الـPx. طيب، لما
+
+260
+00:26:00,140 --> 00:26:03,420
+يكون في عندي nested quantifier، شو بدي أسوي؟ بدك
+
+261
+00:26:03,420 --> 00:26:07,840
+تشتغل بنفس المنطق، بدك تشتغل بنفس المنطق، تبدأ
+
+262
+00:26:07,840 --> 00:26:12,720
+بمرور النفي على الـquantifier الأول للـquantifier
+
+263
+00:26:12,720 --> 00:26:17,080
+الثاني، لما تصل لمين؟ للـpredicate function للـB of
+
+264
+00:26:17,080 --> 00:26:20,280
+XY وتنفيها. بالمثال هذا
+
+265
+00:26:25,350 --> 00:26:32,870
+نفي for all x there exist y,  Pxy. خطوة رقم واحد، بدخل
+
+266
+00:26:32,870 --> 00:26:40,110
+النفي على for all x، بتصير there exist x لا تحقق
+
+267
+00:26:40,110 --> 00:26:46,970
+there exist y, P of xy. النفي بعد ذلك بتصير for all
+
+268
+00:26:46,970 --> 00:26:53,410
+y، بتصير هكذا: there exist x for all y
+
+269
+00:26:56,420 --> 00:27:04,260
+لما أنا بأجي أقول هيك: لكل x there exist y، x زائد y
+
+270
+00:27:04,260 --> 00:27:09,020
+equal 0، إيش كانت قيمتها الحقيقة (truth value)؟ true
+
+271
+00:27:09,020 --> 00:27:19,500
+ولا لا؟ طيب بدنا ننفيها، نفيها: there exist x for all
+
+272
+00:27:19,500 --> 00:27:29,950
+y such that x زائد y لا تساوي صفر.  إذن فيها هناك X
+
+273
+00:27:29,950 --> 00:27:42,750
+واحدة لو جمعتها مع كل عناصر أي Y لا تساوي صفر. طيب
+
+274
+00:27:42,750 --> 00:27:47,530
+وصفر؟ صفر زائد صفر شو؟ واضحة؟ صفر زائد صفر شو؟ واضحة؟
+
+275
+00:27:47,530 --> 00:27:55,070
+على الأقل أيوة، في نقص واحد بيساوي. لو سمعناه مرة
+
+276
+00:27:55,070 --> 00:27:59,800
+ثانية مثلًا:  مئة بالمئة يعني، تعالَ صفر زائد صفر
+
+277
+00:27:59,800 --> 00:28:07,260
+تساوي صفر، false
+
+278
+00:28:07,260 --> 00:28:13,880
+صفر زائد واحد لا تساوي صفر، true. بس الآن أصبح الـ
+
+279
+00:28:13,880 --> 00:28:18,720
+universal هذه، عفواً،  صافية. بقول على الأقل هناك x
+
+280
+00:28:18,720 --> 00:28:25,640
+واحدة لما تجمعها مع أي x مستحيل تلاقي ناتج عملية
+
+281
+00:28:25,640 --> 00:28:31,040
+الجمع بين الـx هذه والـy تعطيني صفر.  لأ، بس هنا  لجأت
+
+282
+00:28:31,040 --> 00:28:37,720
+للصفر وبالتالي هذه قيمتها false. شوف المثال اللي
+
+283
+00:28:37,720 --> 00:28:45,950
+بعده. في نفي for all x there exist y for all z, P
+
+284
+00:28:45,950 --> 00:28:54,850
+of x y. خطوة رقم واحد، بننفي يعني كمان مرة بالتدريج
+
+285
+00:28:54,850 --> 00:28:59,050
+بندخل النفي على واحد وراء الثاني quantifier وراء
+
+286
+00:28:59,050 --> 00:29:02,650
+الثاني لحد ما أصل لنفي الـpredicate function. there
+
+287
+00:29:02,650 --> 00:29:07,560
+exist x في الأولى، معناها في اللي بعديها for all i
+
+288
+00:29:07,560 --> 00:29:12,560
+نفي اللي بعديها there exist z ونفي الـpredicate
+
+289
+00:29:12,560 --> 00:29:26,400
+function اللي موجودة عندي: the sum
+
+290
+00:29:26,400 --> 00:29:33,260
+of two positive integer is always positive. سيبك من
+
+291
+00:29:33,260 --> 00:29:38,300
+الكلام المكتوب هذا. الآن هذا true. حاصل جمع أي عددين
+
+292
+00:29:38,300 --> 00:29:44,260
+موجبين ناتج موجب 100% true. تعالَ نكتبها as
+
+293
+00:29:44,260 --> 00:29:51,220
+quantifiers: the sum of any two positive integers
+
+294
+00:29:51,220 --> 00:29:58,880
+لأي رقمين: for all x for all y
+
+295
+00:29:58,880 --> 00:30:04,540
+لأنه قاعد بيقول لأي عددين، يعني تتخيل عندك مجموعتين
+
+296
+00:30:04,540 --> 00:30:09,560
+وعناصر الأولى مع كل عناصر الثانية، تمام؟ هذه مجموعة
+
+297
+00:30:09,560 --> 00:30:12,900
+الأزواج المرتبة اللي عندك كأزواج بيحققوا المعادلة
+
+298
+00:30:12,900 --> 00:30:22,520
+أن x زائد y أكبر من صفر. أكبر من صفر، مش هيك؟
+
+299
+00:30:30,510 --> 00:30:38,630
+أكبر أو تساوي؟ أكبر أو تساوي؟ أكبر أو تساوي؟ أكبر
+
+300
+00:30:38,630 --> 00:30:40,390
+أو تساوي؟ أكبر أو تساوي؟ أكبر أو تساوي؟ أكبر أو
+
+301
+00:30:40,390 --> 00:30:41,170
+تساوي؟ أكبر أو تساوي؟ أكبر أو تساوي؟ أكبر أو
+
+302
+00:30:41,170 --> 00:30:43,570
+تساوي؟ أكبر أو تساوي؟ أكبر أو تساوي؟ أكبر أو
+
+303
+00:30:43,570 --> 00:30:45,810
+تساوي؟ أكبر أو تساوي؟ أكبر أو تساوي؟ أكبر أو
+
+304
+00:30:45,810 --> 00:30:45,970
+تساوي؟ أكبر أو تساوي؟ أكبر أو تساوي؟ أكبر أو
+
+305
+00:30:45,970 --> 00:30:54,910
+تساوي؟ أكبر أو تساوي؟ أكبر أو تساوي؟ أكبر
+
+306
+00:30:54,910 --> 00:31:00,050
+أو تساوي. شوف الصيغة الموجودة في الكتاب أو في مثال
+
+307
+00:31:00,050 --> 00:31:07,530
+الكتاب: for all x for all y x أكبر من صفر، x and y
+
+308
+00:31:07,530 --> 00:31:13,570
+أكبر من صفر يؤدي إلى...
+
+309
+00:31:13,570 --> 00:31:17,390
+أو طبق الـdomain في الداخل. بما أن الـpredicate
+
+310
+00:31:17,390 --> 00:31:20,790
+function هي عبارة عن propositional function
+
+311
+00:31:20,790 --> 00:31:26,890
+بالتالي هذا الكلام صح، هذا proposition وهذا
+
+312
+00:31:26,890 --> 00:31:29,490
+proposition بدلالة مين يا شباب؟ الـproposition
+
+313
+00:31:29,490 --> 00:31:34,130
+بدلالة الـdomain، دلالة الـdomain ولا لأ؟ وهي كمان
+
+314
+00:31:34,130 --> 00:31:36,770
+الـproposition وهي الـimplication اللي بينهم
+
+315
+00:31:36,770 --> 00:31:41,830
+فبتكلم على compound proposition. لكن لحاله x
+
+316
+00:31:41,830 --> 00:31:45,810
+أكبر من صفر is not a proposition بدلالة الـ
+
+317
+00:31:45,810 --> 00:31:49,370
+quantifier. أصبحت proposition لكن بدون الـ
+
+318
+00:31:49,370 --> 00:31:51,630
+quantifier is not a proposition
+
+319
+00:31:54,690 --> 00:32:00,450
+المثال اللي بعده، تعالَ
+
+320
+00:32:00,450 --> 00:32:09,270
+نترجمه هذا: for all there exist x for any y x زائد y
+
+321
+00:32:09,270 --> 00:32:14,890
+تساوي y، لأي x
+
+322
+00:32:18,010 --> 00:32:27,710
+هناك X واحدة على الأقل لو جمعتها مع أي عدد بتعطيني
+
+323
+00:32:27,710 --> 00:32:34,610
+العدد نفسه، true. there exist an additive identity
+
+324
+00:32:34,610 --> 00:32:40,930
+المحايد الجمعي، for any real number، اللي هو الصفر
+
+325
+00:32:43,300 --> 00:32:46,380
+طيب، شو هذا المثال اللي بتقول؟ أو المثال الـ
+
+326
+00:32:46,380 --> 00:32:53,660
+quantifier اللي عندنا هنا؟ أيوة
+
+327
+00:32:53,660 --> 00:33:00,340
+for all x، شباب لما تشوف two for all يعني بتلك تتخيل
+
+328
+00:33:00,340 --> 00:33:05,860
+كل الأعداد مع بعضهم، المجموعتين، عناصر الأولى كل
+
+329
+00:33:05,860 --> 00:33:11,120
+عنصر في الأولى مع كل عناصر الثانية، تمام؟ x أكبر أو
+
+330
+00:33:11,120 --> 00:33:16,910
+تساوي صفر، and طبعاً هذه خاطئة، موجودة هنا مش مشكلة الـ
+
+331
+00:33:16,910 --> 00:33:25,810
+y أقل من صفر، يعني الـx موجبة والـy سالبة، لو
+
+332
+00:33:25,810 --> 00:33:32,150
+جمعتهم، حاصل الجمع هيكون أكبر من صفر، موجب. اعرف إن
+
+333
+00:33:32,150 --> 00:33:36,970
+لو طرحتهم، هيكون حاصل طرحهم أو الناتج أكبر من صفر،
+
+334
+00:33:36,970 --> 00:33:39,890
+false و true
+
+335
+00:33:43,060 --> 00:33:51,140
+نقص Y، ليش نقص Y؟ أنا حاططها هنا لأن الـY أقل
+
+336
+00:33:51,140 --> 00:33:56,940
+من صفر فهي سالبة، فالسالب مع السالب بيصير موجبة
+
+337
+00:33:56,940 --> 00:34:03,820
+فتكون العملية كلها موجبة، a
+
+338
+00:34:03,820 --> 00:34:08,840
+non negative number.  لا تعكس، لو عكست ممكن تختلف. لا تعكس
+
+339
+00:34:08,840 --> 00:34:18,980
+هذا، إيش اللي تعكس؟ Y ناقص X، حرام عليك! بتصير false، أما
+
+340
+00:34:18,980 --> 00:34:22,540
+عشان أقول لك، بقول لك لا تعكس، عشان تظل الأمور في نصابها
+
+341
+00:34:22,540 --> 00:34:25,520
+الصحيح، لا تتوه، أما الـnegative number هذا الكلام
+
+342
+00:34:25,520 --> 00:34:31,280
+هذا: minus negative number or positive number minus
+
+343
+00:34:31,280 --> 00:34:38,980
+negative number greater than zero. بعدها there
+
+344
+00:34:38,980 --> 00:34:44,290
+exist X، there exists Y، يعني على الأقل في المجموعتين
+
+345
+00:34:44,290 --> 00:34:49,970
+بدي أختار واحد هنا مع واحد من المجموعة الثانية بحيث
+
+346
+00:34:49,970 --> 00:34:55,750
+أنه لو كانت الأولى موجبة والثانية سالبة
+
+347
+00:34:55,750 --> 00:35:00,090
+و الثانية سالبة، حصل
+
+348
+00:35:00,090 --> 00:35:04,690
+طرحهم أكبر
+
+349
+00:35:04,690 --> 00:35:05,210
+من صفر
+
+350
+00:35:10,550 --> 00:35:16,610
+الاختلاف بين اثنين
+
+351
+00:35:16,610 --> 00:35:28,290
+أقل من صفر ليس بالضرورة يكون ناقص واحد ناقص اثنين
+
+352
+00:35:28,290 --> 00:35:31,830
+إيش يساوي واحد؟ أكبر من صفر
+
+353
+00:35:35,990 --> 00:35:41,110
+هتلاقي واحدة X وواحدة Y بتحقق المعادلة هذه، فالـ
+
+354
+00:35:41,110 --> 00:35:47,250
+quantifier تبعنا هذا true، هي
+
+355
+00:35:47,250 --> 00:35:57,530
+الآن X سالب واحد والـY سالب اثنين، هي، حط ناقص واحد
+
+356
+00:35:57,530 --> 00:36:03,430
+الله يعطيك الصحة إن شاء الله يا رب، ناقص ناقص اثنين
+
+357
+00:36:03,430 --> 00:36:08,970
+بتصير ناقص واحد زائد اثنين بتساوي واحد، صح؟ إنهم
+
+358
+00:36:08,970 --> 00:36:15,870
+طيب for all x for all y، إيش يعني for all for all؟
+
+359
+00:36:15,870 --> 00:36:20,630
+يعني كل عناصر الأولى مع كل عناصر الثانية، x لا
+
+360
+00:36:20,630 --> 00:36:29,070
+تساوي صفر والـy لا تساوي صفر، حاصل ضربهما لا يساوي
+
+361
+00:36:29,070 --> 00:36:30,530
+صفر، if and only if
+
+362
+00:36:33,970 --> 00:36:38,410
+The product of any two non-zero numbers is non-
+
+363
+00:36:38,410 --> 00:36:44,390
+zero number if and only if both factors are non-
+
+364
+00:36:44,390 --> 00:36:49,810
+zero، true. بس لاحظوا ما كنت قاعد بترجم بالعكس
+
+365
+00:36:49,810 --> 00:36:54,870
+بحاول أكتب الـquantifier بلغتنا. في المثال الأول
+
+366
+00:36:56,260 --> 00:37:01,500
+كنت بكتب من لغتنا للـquantifier لأن بحاول أشوف
+
+367
+00:37:01,500 --> 00:37:06,300
+الترجمة للعناصر اللي موجودة عندي. خلص الـsection
+
+368
+00:37:06,300 --> 00:37:11,420
+وبهيك بنكون خلصنا محاضرتنا لليوم وبيتبقى لنا
+
+369
+00:37:11,420 --> 00:37:15,420
+section واحد في الـchapter هذا، بنكمل المحاضرة اللي جاية
+
+370
+00:37:15,420 --> 00:37:17,320
+إن شاء الله تبارك وتعالى، لأن خلال الوقت اللي
+
+371
+00:37:17,320 --> 00:37:20,280
+بقي مش هقدر أخلصه. أعطيكم العافية
diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/xeTWnmt0OTo_postprocess.srt b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/xeTWnmt0OTo_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..419986e376b2695450cc4feeadd8d14fc4bbcebc
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/xeTWnmt0OTo_postprocess.srt
@@ -0,0 +1,1484 @@
+1
+00:00:21,310 --> 00:00:23,270
+بسم الله والحمد لله والصلاة والسلام على رسول الله
+
+2
+00:00:23,270 --> 00:00:26,470
+طيب شباب اليوم ان شاء الله هنكمل ما زلنا في ال
+
+3
+00:00:26,470 --> 00:00:30,130
+chapter الأول نقل على ال section الخامس ال misted
+
+4
+00:00:30,130 --> 00:00:34,020
+quantifiers لكن قبل ما ..الروح على نفس ال
+
+5
+00:00:34,020 --> 00:00:38,340
+quantifier خلينا نسترجع مع بعض اخر مثالين والاخر
+
+6
+00:00:38,340 --> 00:00:42,080
+محاضرة بشكل سريع قلنا في اخر محاضرة اتكلمت على ال
+
+7
+00:00:42,080 --> 00:00:44,420
+predicate و ال quantifiers اتكلمنا على ال
+
+8
+00:00:44,420 --> 00:00:48,360
+predicate و ال quantifiers قلنا ال predicate لما
+
+9
+00:00:48,360 --> 00:00:52,220
+انا بكون فيه عندي X أكبر من 3 قلنا التلاتة هذه
+
+10
+00:00:52,220 --> 00:00:56,580
+مثابة ال predicate او القيمة المسندلها اللي انا
+
+11
+00:00:56,580 --> 00:01:00,360
+بناء عليها بدي احدد ال truth value قلنا في عند
+
+12
+00:01:00,360 --> 00:01:05,550
+predicate function P of Xاللي بنرمزلها بـ X أكبر
+
+13
+00:01:05,550 --> 00:01:12,530
+من 3 وهذا سمناها predicate function predicate
+
+14
+00:01:12,530 --> 00:01:15,830
+function فالـ predicate function هنا ما بقدر أديها
+
+15
+00:01:15,830 --> 00:01:20,550
+قيمة إلا لو حددت قيمة الـ X باشي بقول بي أف واحد
+
+16
+00:01:20,550 --> 00:01:24,830
+هداش قيمتها باشي بقول واحد أكبر من تلاتة false
+
+17
+00:01:24,830 --> 00:01:31,090
+معناته false بي أف أربعةtrue لأن الأربعة أكبر من
+
+18
+00:01:31,090 --> 00:01:34,590
+تلاتة و بعد ال predicate هي تكلمنا على شغل سمناها
+
+19
+00:01:34,590 --> 00:01:38,530
+quantifiers و ال quantifiers طلب مني ان انا اعرف
+
+20
+00:01:38,530 --> 00:01:44,070
+domain على كل عناصر ال predicate function صار في
+
+21
+00:01:44,070 --> 00:01:49,530
+عندي دمين او اللي سمناه universal او universe
+
+22
+00:01:49,530 --> 00:01:54,450
+discourse و قلنا في عندي نوعين من ال quantifiers
+
+23
+00:01:54,450 --> 00:02:05,670
+for all x, b, xو there exists x بيكس بنقول صارنا
+
+24
+00:02:05,670 --> 00:02:08,850
+الآن بنقيم ال predicate function أو ال quantifier
+
+25
+00:02:08,850 --> 00:02:13,170
+هذا ال predicate function هذه is true لكل قيم ال
+
+26
+00:02:13,170 --> 00:02:17,870
+domain مثل
+
+27
+00:02:17,870 --> 00:02:22,450
+لو أنا قلتلك ال domain هو ال natural number for
+
+28
+00:02:22,450 --> 00:02:28,360
+all x كل قيم ال domainهتكون أكبر من تلاتة false
+
+29
+00:02:28,360 --> 00:02:34,420
+ليش؟ لأن عندي الواحد بتم تم لل domain والواحد أقل
+
+30
+00:02:34,420 --> 00:02:40,140
+أو يساوي التلاتة اللي هي عكس هذه مصبوط؟ اللي هي
+
+31
+00:02:40,140 --> 00:02:44,520
+سميناها ال counter example there exist x هناك على
+
+32
+00:02:44,520 --> 00:02:49,000
+الأقل x واحدة تحقق المعادلة ب x أو ال function ب x
+
+33
+00:02:49,000 --> 00:02:54,590
+trueتمام؟ عندك سبعة اربعة او خمسة واطلع الى مال
+
+34
+00:02:54,590 --> 00:02:57,970
+نهاية كلهم بيحققوا العناصر هذا واخر شغل لما
+
+35
+00:02:57,970 --> 00:03:02,690
+اتكلمنا على النفي قولت لما انا بيهاجي بانفي نفل
+
+36
+00:03:02,690 --> 00:03:12,550
+for all x bx تكافئ there exist x not bx نفل b of x
+
+37
+00:03:12,550 --> 00:03:20,110
+ونفل for there exist x bx هتصير تكافئ for all x
+
+38
+00:03:20,740 --> 00:03:26,060
+نقطة PX و جينا قلنا for all X يعني كل العناصر اللي
+
+39
+00:03:26,060 --> 00:03:31,980
+في الدمين نفيها على الأقل هناك واحد في
+
+40
+00:03:31,980 --> 00:03:36,440
+الدمين يحقق المعادلة نفيها كل عناصر الدمين اللي
+
+41
+00:03:36,440 --> 00:03:42,570
+هتحقق المعادلةونتقل بعد ذلك لموضوع الـ Translation
+
+42
+00:03:42,570 --> 00:03:47,290
+في موضوع الـ Quantifiers و حاولنا أن نطبق أو نترجم
+
+43
+00:03:47,290 --> 00:03:52,270
+المثال اللي موجود عندنا هنا بحيث قلنا لكل رسالة
+
+44
+00:03:52,270 --> 00:03:58,870
+حجمها أقل من واحد ميجا بايت بدو تم تشفيرها بقول
+
+45
+00:03:58,870 --> 00:04:04,030
+كيف نتعامل معك مثال؟ بروح بالتجسم every معته for
+
+46
+00:04:04,030 --> 00:04:13,830
+all خلصنا MessageX أو المجهول تبعتنا طيب ايش بده
+
+47
+00:04:13,830 --> 00:04:23,150
+يصير فيها larger than أكبر من one megabyte المتغير
+
+48
+00:04:23,150 --> 00:04:30,530
+التاني واحد ميجا بايت تمام will be implies و ال
+
+49
+00:04:30,530 --> 00:04:32,890
+compress اللي هي هتكون المعادلة التانية اللي
+
+50
+00:04:32,890 --> 00:04:38,380
+هنعملها على مين؟ على ال M يعني هي هتصير لكلمعادلة
+
+51
+00:04:38,380 --> 00:04:49,620
+لكل اك M P of M هيقد إلى C of M ايش هذه P of M
+
+52
+00:04:49,620 --> 00:04:56,840
+لازم تتعرفها ال M is an email message او mail is
+
+53
+00:04:56,840 --> 00:05:03,380
+mail message P
+
+54
+00:05:03,380 --> 00:05:12,280
+of M ال M أكبر من واحدميجا بايت مظبوط الـ C on
+
+55
+00:05:12,280 --> 00:05:21,200
+اللي هي ال M will be compressed وبالتالي هاي
+
+56
+00:05:21,200 --> 00:05:23,820
+المعادلة .. هاي translation لـ specification اللي
+
+57
+00:05:23,820 --> 00:05:28,380
+موجودة عندها ممكن أتكلم على specification تاني إذا
+
+58
+00:05:28,380 --> 00:05:31,740
+أنا قلت والله بدي أخلي ال .. ال role هذا more
+
+59
+00:05:31,740 --> 00:05:35,260
+general و أروح بدل ال و بدل ال X أو بدل ال واحد
+
+60
+00:05:35,260 --> 00:05:41,510
+أحط Yبدل الواحد احط Y يعني لما تكون ال M حجم
+
+61
+00:05:41,510 --> 00:05:46,290
+الرسالة اقل من او اعفم اكبر من ال Y بتصير في عندي
+
+62
+00:05:46,290 --> 00:05:49,150
+hand بي M Y
+
+63
+00:05:51,780 --> 00:05:55,860
+وتحريف المعادلة هنا بصير بدل الواحد باستخدام ال y
+
+64
+00:05:55,860 --> 00:05:59,700
+اللي موجودة عندها وبالتالي ممكن انا احصل على اكتر
+
+65
+00:05:59,700 --> 00:06:03,400
+من definition او اكتر من quantifier صحيح اذا انا
+
+66
+00:06:03,400 --> 00:06:07,000
+قدرت اترجم كل العناصر هذه بشكل مستقل بشكل صحيح
+
+67
+00:06:07,000 --> 00:06:10,120
+وبعدين اربقهم زي ما بدي وشوفنا المثال التاني اللي
+
+68
+00:06:10,120 --> 00:06:14,240
+كان نتكلم عن ال connection وحلناها مع بعض وشوفنا
+
+69
+00:06:16,210 --> 00:06:19,370
+شو؟ يعني العلاقة ما بين ال link و ال user ال
+
+70
+00:06:19,370 --> 00:06:23,590
+available اليوم هنتقل لشغلة جديدة اللي هي nested
+
+71
+00:06:23,590 --> 00:06:28,830
+quantifiers nested احنا شوفنا سابقا لما اتكلمنا
+
+72
+00:06:28,830 --> 00:06:32,610
+على ال operators ال logical operators قولنا PR
+
+73
+00:06:32,610 --> 00:06:43,750
+بفتح جوس Q and ال R أو بي نفي Q andP or R فكل هذه
+
+74
+00:06:43,750 --> 00:06:47,230
+نسميناها nested operators لأنها تتداخل بين العناصر
+
+75
+00:06:47,230 --> 00:06:51,370
+الموجودة وشوفنا أن النفي هذه لما تدخل تدخل على جوا
+
+76
+00:06:51,370 --> 00:06:57,750
+الجسم بالكامل ولمّا شوفنا النفي في ال quantifiers
+
+77
+00:06:57,750 --> 00:07:04,490
+نفي for all x P of X مررناها على كل العناصر صارت
+
+78
+00:07:04,490 --> 00:07:09,390
+there exist x ونفينا ال P of X لكن ماشوفناش ولا
+
+79
+00:07:09,390 --> 00:07:14,680
+حالةتو quantifier
+
+80
+00:07:14,680 --> 00:07:19,060
+جايين ورا بعض الان لما انا بتكلم على نفس ال
+
+81
+00:07:19,060 --> 00:07:22,760
+quantifier معناته انا بتكلم ان ال بريدكيت function
+
+82
+00:07:22,760 --> 00:07:27,240
+تبعتي زي في المثال السابق بتعتمد على two variables
+
+83
+00:07:27,240 --> 00:07:35,300
+بس كل واحد فيهمالو quantifier لحاله بدي أتعامل
+
+84
+00:07:35,300 --> 00:07:39,700
+معاه لحاله تعالى نشوف أو نحاول نفهم ال quantifier
+
+85
+00:07:39,700 --> 00:07:46,280
+اللي موجود قدامنا هنا for all x لأي x تنتني لل
+
+86
+00:07:46,280 --> 00:07:52,260
+domain تمام there exist y بلاجيها على الأقل y
+
+87
+00:07:52,260 --> 00:07:55,480
+واحدة بتحقق ال predicate function اللي موجودة عندي
+
+88
+00:07:55,480 --> 00:08:01,400
+for all x there exist y بتحقق
+
+89
+00:08:02,540 --> 00:08:05,640
+الـ function يعني تعالى نشوفها لو انا اجيت قولتلك
+
+90
+00:08:05,640 --> 00:08:08,320
+ال domain تبعتي اللي هي ال natural number ال real
+
+91
+00:08:08,320 --> 00:08:17,340
+number ال domain افترض ان ال domain الاعداد
+
+92
+00:08:17,340 --> 00:08:24,640
+الحقيقية كليتها بالمثال هذا for all x لأي عدد
+
+93
+00:08:24,640 --> 00:08:34,650
+حقيقي هناك على الأقل أنصر واحدعدد حقيقي تمام بحيث
+
+94
+00:08:34,650 --> 00:08:39,390
+ان لو جمعتهم التنين مع بعض يسووا صفر true ولا
+
+95
+00:08:39,390 --> 00:08:42,870
+false ازميل
+
+96
+00:08:42,870 --> 00:08:46,910
+أشجال صفر و صفر و أخد حالة واحدة فقط و ربط عليها
+
+97
+00:08:46,910 --> 00:08:54,490
+كلب لحظة ايش في الأول عندي for all لأي عدد حقيقي
+
+98
+00:08:55,430 --> 00:09:01,070
+ماذا يعني؟ لكل الأعداد الحقيقية لأي عدد حقيقي يعني
+
+99
+00:09:01,070 --> 00:09:06,770
+هذه المعادلة بدأ تتطبق على كل الأعداد الحقيقية أيش
+
+100
+00:09:06,770 --> 00:09:12,550
+ما تاخد عدد حقيقي تمام؟ هتلاقيله عدد حقيقي آخر
+
+101
+00:09:12,550 --> 00:09:19,970
+واحد على الأقل لو جمعته يساوي صفر true العنصر
+
+102
+00:09:19,970 --> 00:09:29,400
+والسالب تبعه النظير الجمعيX زائد نقص X لان الشيء
+
+103
+00:09:29,400 --> 00:09:35,420
+اللي قاعد يقوللي خد أي عنصر في ال domain for all X
+
+104
+00:09:35,420 --> 00:09:40,300
+in the domain for any real number there exist يعني
+
+105
+00:09:40,300 --> 00:09:46,120
+إيش ما تاخد عدد إيش ما تاخد عدد هتلاقي عدد واحد
+
+106
+00:09:46,120 --> 00:09:50,200
+على الأقل لما تجمعهم التنين مع بعض بديك صفر true
+
+107
+00:09:50,200 --> 00:09:59,200
+نشوف البعدهاليش برجعها؟ تمام اختلفت الصورة تماما
+
+108
+00:09:59,200 --> 00:10:07,560
+الان تعالى تشوف there exist هناك X واحدة على الأقل
+
+109
+00:10:07,560 --> 00:10:12,940
+في ال domain تستخدم
+
+110
+00:10:12,940 --> 00:10:17,860
+مع كل عناصر اللي في ال domain تمام بحيث انها تحقق
+
+111
+00:10:17,860 --> 00:10:21,020
+المعادلة الموجودة يعني ال X هذه
+
+112
+00:10:23,550 --> 00:10:27,750
+فيش غيرها أو على الأقل في X واحدة تظبط مع كل ال X
+
+113
+00:10:27,750 --> 00:10:33,230
+حسب المعادلة في المعادلة اللي عندي هال في المعادلة
+
+114
+00:10:33,230 --> 00:10:39,610
+اللي عندي هال there exist X لكل عناصر ال Y لكل
+
+115
+00:10:39,610 --> 00:10:42,850
+عناصر ال domain في ال real number لو ضربت X ال Y
+
+116
+00:10:42,850 --> 00:10:49,980
+تديني صفر true الصفرالصفر real number و لو ضربته
+
+117
+00:10:49,980 --> 00:10:54,800
+في أي عدد حقيقي بحصل على صفر ببتعالى نجلب ال
+
+118
+00:10:54,800 --> 00:11:00,060
+quantifiers هدول بحيث اننا نقول هان كتالي there
+
+119
+00:11:00,060 --> 00:11:09,480
+exist x for all y x زائد y يساوي صفر و هان ايش
+
+120
+00:11:09,480 --> 00:11:16,530
+متهدي الان هناك x واحدةلو جمعتها لكل عناصر الدومين
+
+121
+00:11:16,530 --> 00:11:20,870
+لكل عناصر الدومين او لأي عنصر في الدومين هتديني
+
+122
+00:11:20,870 --> 00:11:27,170
+صفر false مستحيل تلاقي هيك معادلة اختلاف او اعادة
+
+123
+00:11:27,170 --> 00:11:31,830
+ترتيب ال quantifiers ادى الاختلاف ال output تعالى
+
+124
+00:11:31,830 --> 00:11:40,090
+نشوف هنا for all x there exists y such that x ضرب
+
+125
+00:11:40,090 --> 00:11:51,820
+ال y يساوي صفرلكل X لأي X في ال domain هتلاقيلها Y
+
+126
+00:11:51,820 --> 00:11:57,960
+لو ضربتهم في بعض بدوني صفر true لأن ال Y .. لأن
+
+127
+00:11:57,960 --> 00:12:01,040
+عملية الضرب عملية إبدالية وبالتالي ال Y بدي اعتمد
+
+128
+00:12:01,040 --> 00:12:04,900
+هذه الصفر و بتقسم مع كل العناصر و بتقولي على الأقل
+
+129
+00:12:04,900 --> 00:12:10,380
+X واحدة و Y واحدة ولا لأ فبالتالي هذه كمان true
+
+130
+00:12:10,380 --> 00:12:17,950
+طيب تعالى نشوفالجدول هذا جمع مجموعة من الـ nested
+
+131
+00:12:17,950 --> 00:12:25,670
+quantifiers و بحاول اترجم ليهم for all x for all y
+
+132
+00:12:25,670 --> 00:12:35,610
+bxy ايش يعني؟ لأي عددين في الدمان bxy is true أي
+
+133
+00:12:35,610 --> 00:12:38,930
+عددين في الدمان بحققه ل predicate function تبعتي
+
+134
+00:12:38,930 --> 00:12:45,440
+هاييعني لو أنا جاي قلتلك for all x for all y على
+
+135
+00:12:45,440 --> 00:12:54,360
+المثال السابق x زائد y تساوي صفر عارفش معناها؟ بدك
+
+136
+00:12:54,360 --> 00:12:58,460
+تفترض أن في عندي real number و real number x بدأ
+
+137
+00:12:58,460 --> 00:13:04,740
+أخدها من هنا و ال y بدأ أخدها من هنا أي x هنا
+
+138
+00:13:04,740 --> 00:13:12,590
+تمام؟مع أي اكس هان جمعهم تساوي صفر فالس فالس مش
+
+139
+00:13:12,590 --> 00:13:18,550
+نفسها ليش لأنها بتكون true لأن الاتنين متفقين
+
+140
+00:13:18,550 --> 00:13:23,610
+الاتنين مع كل زوج مرتب يعني هيكد أي اكس هان بتكون
+
+141
+00:13:23,610 --> 00:13:28,770
+true مع كل عناصر ال Y و العكس صحيح اي Y هتكون true
+
+142
+00:13:28,770 --> 00:13:32,630
+مع كل عناصر ال X وهذا كلام مستحيل يصير حسب
+
+143
+00:13:32,630 --> 00:13:37,890
+المعادلة اللي مكتوبة هنا فوقطيب، لاحظوا إنما بدلنا
+
+144
+00:13:37,890 --> 00:13:44,090
+for all x و for all y نفس المعنى مافرجتش لأنه
+
+145
+00:13:44,090 --> 00:13:47,390
+بتكلم على نفس ال quantifier بتكلم على نفس ال
+
+146
+00:13:47,390 --> 00:13:52,850
+quantifier فلو قدمت أو أخرج مش فارق كتير عندي اللي
+
+147
+00:13:52,850 --> 00:14:00,450
+بعده، متى هذا بيكون false؟ لو جدرت ألاقي فقط زوج
+
+148
+00:14:00,450 --> 00:14:04,880
+مرتب أو زوج من العناصر x و yاللي محققوش ال
+
+149
+00:14:04,880 --> 00:14:09,680
+predicate function تبعها ايه بتصير؟ false طيب for
+
+150
+00:14:09,680 --> 00:14:15,340
+all x زي ما قلنا سابقا لأي عنصر في ال domain فيه
+
+151
+00:14:15,340 --> 00:14:21,240
+هناك على الأقل عنصر واحد y تحقق المعادلة اللي
+
+152
+00:14:21,240 --> 00:14:26,520
+موجودة متى بتكون false لو مالجتش ال y؟ لزوج واحد
+
+153
+00:14:26,520 --> 00:14:34,530
+على الأقل there exist x هناك xواحدة لو طبقتها مع
+
+154
+00:14:34,530 --> 00:14:38,690
+كل العناصر اللي في الدمية بتعمل satisfied متى هذا
+
+155
+00:14:38,690 --> 00:14:42,870
+الكلام بيكون لو قدرت ألاقي X وY كزوج مرتب واحد فقط
+
+156
+00:14:42,870 --> 00:14:47,270
+ان هذا ماتحققتش المعادلة اللي عندي there exist X
+
+157
+00:14:47,270 --> 00:14:53,850
+there exist Y هناك X ل Y واحدة تمام بتحقق المعادلة
+
+158
+00:14:53,850 --> 00:14:59,690
+اللي عندها و ترتيبهم ممكن يكون نفس النتيجة متى
+
+159
+00:14:59,690 --> 00:15:05,540
+بتكون falseلو كانت المعادلة هذه false لكل الأزواج
+
+160
+00:15:05,540 --> 00:15:12,520
+يعني هيك لأي X لم أجد أي Y تمام؟ عكسها تماما طيب
+
+161
+00:15:12,520 --> 00:15:20,060
+نمتقل للعصر اللي بعده تعالى نشوف بقول لترجم النفس
+
+162
+00:15:20,060 --> 00:15:26,480
+ال quantifier اللي موجود عندى هنا أي
+
+163
+00:15:26,480 --> 00:15:27,040
+طالب
+
+164
+00:15:33,320 --> 00:15:37,440
+or all student
+
+165
+00:15:37,440 --> 00:15:42,640
+ال X لديه
+
+166
+00:15:42,640 --> 00:15:53,080
+كمبيوتر B of X or has a friend that has a computer
+
+167
+00:15:53,080 --> 00:16:01,720
+ال friend معناته Y و B of Y لديه كمبيوترممكن هيك
+
+168
+00:16:01,720 --> 00:16:06,780
+تتعامل معاهم يعني الان انا بكل بساطة اي طالب في ال
+
+169
+00:16:06,780 --> 00:16:11,840
+class هذا اما هيكون عنده جهاز كمبيوتر او حاجه له
+
+170
+00:16:11,840 --> 00:16:18,640
+صديق مع جهاز كمبيوتر تمام؟ تعلمنا الكتابة as
+
+171
+00:16:18,640 --> 00:16:23,860
+nested quantifier لان عرفنا ال X وعرفنا ال Y ال X
+
+172
+00:16:23,860 --> 00:16:30,140
+هيك بتدهكي من البداية ال X student و
+
+173
+00:16:30,140 --> 00:16:30,520
+ال Y
+
+174
+00:16:33,260 --> 00:16:40,860
+friend of X friend
+
+175
+00:16:40,860 --> 00:16:55,820
+of X بي of X X has a computer مصبوط ولا يعني طيب
+
+176
+00:16:55,820 --> 00:17:03,650
+الأن بقدر أجي أقول أنا here for allX طبعا ال
+
+177
+00:17:03,650 --> 00:17:11,610
+domain تبقى مين هو يا شباب ال class الفصل for all
+
+178
+00:17:11,610 --> 00:17:19,190
+X there
+
+179
+00:17:19,190 --> 00:17:23,150
+exist Y
+
+180
+00:17:23,150 --> 00:17:26,890
+such
+
+181
+00:17:26,890 --> 00:17:38,920
+that B of Xأو P of Y تعالى بترجمها دى لان تبقى
+
+182
+00:17:38,920 --> 00:17:44,020
+للكلام اللى بيقوله لكل X لأى طالب فى ال class فى
+
+183
+00:17:44,020 --> 00:17:51,940
+الفصل there exist Y هناك صديق له تمام على الأقل
+
+184
+00:17:51,940 --> 00:18:00,630
+بحيث الهى ال bracket function ان P Xعرفتها هي X
+
+185
+00:18:00,630 --> 00:18:04,950
+has a computer او ال friend هذا has a computer
+
+186
+00:18:04,950 --> 00:18:10,610
+مصدود ولا لا؟ وبالتالي هذه ال statement مع العناصر
+
+187
+00:18:10,610 --> 00:18:13,670
+ال explanation هدول هي عبارة عن ترجمة لل
+
+188
+00:18:13,670 --> 00:18:17,290
+specification اللي فوق صحيحة؟ هل هو الحل الوحيد
+
+189
+00:18:17,290 --> 00:18:21,610
+اللي ممكن يكون عنده؟ لأ، بيعتمد كيف بدك تعرف
+
+190
+00:18:21,610 --> 00:18:25,290
+العناصر و علاقة المعادلة أو الدوال مع بعضهم دعونا
+
+191
+00:18:25,290 --> 00:18:28,370
+نشوف كيف جاء بالمثال اللي موجود عنده
+
+192
+00:18:32,700 --> 00:18:40,280
+كخطوة أولى راح
+
+193
+00:18:40,280 --> 00:18:48,100
+ترجم for any student x كما لهي for all for
+
+194
+00:18:48,100 --> 00:18:57,700
+all x x has a computer P of X or there is some
+
+195
+00:18:57,700 --> 00:18:58,580
+student y
+
+196
+00:19:02,930 --> 00:19:09,130
+Where ال Y has a computer and X and Y are friends
+
+197
+00:19:09,130 --> 00:19:18,050
+يعني هيك F of X و Y ربط ال X و ال Y مع بعضهم و
+
+198
+00:19:18,050 --> 00:19:27,850
+عرفليها كتالة X and Y are friends and
+
+199
+00:19:27,850 --> 00:19:31,090
+Y has a computer
+
+200
+00:19:36,090 --> 00:19:39,130
+حسب التفسير اللي اشتغله عليه و بدأ فصله بالشكل
+
+201
+00:19:39,130 --> 00:19:43,870
+اللي هي ده فكتب اللي هي ده تعالى نشوف اشرح كالحل
+
+202
+00:19:43,870 --> 00:19:52,830
+for all X for all X X is student CX
+
+203
+00:19:52,830 --> 00:19:59,110
+has a computer معناته for all X و راحظوا على كل
+
+204
+00:19:59,110 --> 00:20:03,050
+quantifier اللي موجود عندي هان C of X X has a
+
+205
+00:20:03,050 --> 00:20:05,230
+computer or
+
+206
+00:20:07,440 --> 00:20:14,120
+There exist Y such that Y has a computer نفس
+
+207
+00:20:14,120 --> 00:20:20,340
+الكلام اللي قلناه قبل شوية and ال friends F of XY
+
+208
+00:20:20,340 --> 00:20:28,300
+F of XY X and Y are friends هذه برضه ترجمة صحيحة
+
+209
+00:20:28,300 --> 00:20:37,580
+لل quantifier اللي موجود عندي طيب نشوف المثالأو
+
+210
+00:20:37,580 --> 00:20:47,720
+نشوف شغلة تانية واضح المثال يا شباب؟ بداك
+
+211
+00:20:47,720 --> 00:20:53,180
+تنتبه دائما ان فعليا كل شغلة في البربوسش انتباهك
+
+212
+00:20:53,180 --> 00:20:59,500
+تكون ضمن ال quantifier بشكل صحيح لما
+
+213
+00:20:59,500 --> 00:21:06,910
+انا باجي بقول for all x there exist yمعناته نجاحا
+
+214
+00:21:06,910 --> 00:21:13,250
+بقول for all x بتحقق ال x there exist y بتحقق
+
+215
+00:21:13,250 --> 00:21:18,950
+العلاقة ما بين x و y بنجو سين ال nested quantifier
+
+216
+00:21:18,950 --> 00:21:25,490
+بقدر أنظرله as two different quantifiers يعني الآن
+
+217
+00:21:25,490 --> 00:21:33,910
+for all معناته qxماذا يعني QX؟ لأي عنصر ينتمي؟ للـ
+
+218
+00:21:33,910 --> 00:21:40,190
+domain بأي عنصر ينتمي؟ للـ domain تمام؟ بدي ألاقي
+
+219
+00:21:40,190 --> 00:21:46,830
+there exists Y بتحقق علاقنا بين X وY هذا تفسير لـ
+
+220
+00:21:46,830 --> 00:21:50,890
+predicate اللي موجود عندها تعالى نشوف قيم أو
+
+221
+00:21:50,890 --> 00:21:54,790
+مجموعة من العراسر اللي موجودة عندهم تعالى ترجملي
+
+222
+00:21:54,790 --> 00:22:01,450
+هذه for all X there exists Yلأي X في ال domain
+
+223
+00:22:01,450 --> 00:22:07,630
+هناك Y لأنه بتتكلم على نفس ال domain أنا مازلت X
+
+224
+00:22:07,630 --> 00:22:15,090
+زائد Y تساوي صفر أصبعط تعالى الأخيرة هذه تحت لكل X
+
+225
+00:22:15,090 --> 00:22:26,450
+مع أي Y أي X مع أي Y في ال domain X زائد Y تساوي Y
+
+226
+00:22:26,450 --> 00:22:34,620
+زائد Xلاحظ ان هنا قاعد بيقولك بدك تاخد كل العناصر
+
+227
+00:22:34,620 --> 00:22:40,780
+هتفترض X من R واي من R واحد اللي هنا real number و
+
+228
+00:22:40,780 --> 00:22:47,080
+تاخد كل عنصر في ال X تربط مع كل عناصر ال Y و العكس
+
+229
+00:22:47,080 --> 00:22:51,600
+صحيح كل عنصر في ال Y بده يرتبط مع كل عناصر ال X
+
+230
+00:22:51,600 --> 00:22:58,490
+صار عندك مجموعة من الأزواد المرتبة هايهم X وYX
+
+231
+00:22:58,490 --> 00:23:03,930
+زائد Y بدها تساوي Y زائد X، بدك تفهمها هيك، هذه
+
+232
+00:23:03,930 --> 00:23:09,970
+احنا غالبا بنرمزها for all X, for all Y, P of X و
+
+233
+00:23:09,970 --> 00:23:13,070
+Y، هذا المكتوب تحت شهر هو هي العلاقة اللي ما بين
+
+234
+00:23:13,070 --> 00:23:15,450
+ال X و Y، ال predicate function
+
+235
+00:23:26,450 --> 00:23:30,710
+ضروري اتحدد شو علاقة ال combination او اتحدد
+
+236
+00:23:30,710 --> 00:23:33,790
+العلاقة ما بين ال variables اللى عندك عشان تقدر
+
+237
+00:23:33,790 --> 00:23:38,410
+تكتب ال quantifier صح لان احنا اتفاقن قبل شوية من
+
+238
+00:23:38,410 --> 00:23:44,850
+خلال الأمثلة for all x there exist y مش بالضرورة
+
+239
+00:23:44,850 --> 00:23:52,150
+تكافئThere exists x for all y و لا بقى في اختلاف
+
+240
+00:23:52,150 --> 00:23:58,010
+تماما في المعنى وبالتالي لازم تفهم شو هي علاقة ال
+
+241
+00:23:58,010 --> 00:24:03,210
+universal quantifier و ال existential مع العنصر
+
+242
+00:24:03,210 --> 00:24:07,170
+اللي عندي خصوصا ان هم التنتين مش متساويات فضروري
+
+243
+00:24:07,170 --> 00:24:11,390
+نفهمها بشكل عنصر تعالى نشوف بالمثال اللي عندي هان
+
+244
+00:24:11,390 --> 00:24:18,530
+بقول ال predicateXY هي عبارة عن X زائد Y تساوي صفر
+
+245
+00:24:18,530 --> 00:24:32,110
+هناك X لأي Y بي of XY هناك X واحدة لو جمعتها مع أي
+
+246
+00:24:32,110 --> 00:24:40,730
+في أولي الانظار أي Y تبديني صفر فالس لكن تعالى
+
+247
+00:24:40,730 --> 00:24:50,320
+نقوللأي X أنت بتحديها هتلاقي Y واحدة على الأقل لو
+
+248
+00:24:50,320 --> 00:24:54,420
+جمعتهم اتنين مع بعض و بتديني سفر true اللي هي
+
+249
+00:24:54,420 --> 00:25:02,960
+قولنا قيمة و قيمة السالبة تبعتها في
+
+250
+00:25:02,960 --> 00:25:07,320
+نفس ال quantifiers لما أنا بدي أجن فيها احنا الآن
+
+251
+00:25:07,320 --> 00:25:14,750
+في عندي for all X for allY تخيل ان انا بدي أنفيها
+
+252
+00:25:14,750 --> 00:25:21,830
+بي of XY احنا
+
+253
+00:25:21,830 --> 00:25:26,670
+لما نفيل ال quantifier قلنا بنمرر النافذ تبعت ال
+
+254
+00:25:26,670 --> 00:25:30,960
+universal quantifier بتصير existentialوبعدين بتصير
+
+255
+00:25:30,960 --> 00:25:35,620
+النفي تبعت ال predicate function يعني نفي for all
+
+256
+00:25:35,620 --> 00:25:39,920
+x,b,x في تساوي there exist x هناك x واحدة على
+
+257
+00:25:39,920 --> 00:25:45,920
+الأقل لا تحقق ال P of X ولا لا؟ و النفي التبعت ل
+
+258
+00:25:45,920 --> 00:25:52,100
+there exist x,b,x هناك x واحدة على الأقل تحقق تحقق
+
+259
+00:25:52,100 --> 00:26:00,140
+ال Pxنفيها كل عناصر و X لا تحقق الـ BX طيب، لما
+
+260
+00:26:00,140 --> 00:26:03,420
+يكون في عندي Analyzed Quantifier، شو بدي أسوي؟ بدك
+
+261
+00:26:03,420 --> 00:26:07,840
+تشتغل بنفس المنطق، بدك تشتغل بنفس المنطق، تبدأ
+
+262
+00:26:07,840 --> 00:26:12,720
+تمرر النفي على الـ Quantifier الأول لـ Quantifier
+
+263
+00:26:12,720 --> 00:26:17,080
+التاني لما تصل لمين؟ لـ Predicate Function لـ B of
+
+264
+00:26:17,080 --> 00:26:20,280
+XY وتنفيها بالمثال هذا
+
+265
+00:26:25,350 --> 00:26:32,870
+نفي for all x there exist y بxy خطوة رقم واحد بدخل
+
+266
+00:26:32,870 --> 00:26:40,110
+النفي على for all x بتصير there exist x لا تحقق
+
+267
+00:26:40,110 --> 00:26:46,970
+there exist y b of xy النفي بعد ذلك بتصير for all
+
+268
+00:26:46,970 --> 00:26:53,410
+y بتصير هندي هن there exist x for all y
+
+269
+00:26:56,420 --> 00:27:04,260
+لما انا باجب اقول هيك لكل x there exist y x زائد y
+
+270
+00:27:04,260 --> 00:27:09,020
+equal 0 ايش كانت قيمتها المعروفية ال number؟ true
+
+271
+00:27:09,020 --> 00:27:19,500
+ولا لا؟ طيب بدنا نفيها نفيها there exist x for all
+
+272
+00:27:19,500 --> 00:27:29,950
+y such that x زائد y لا تساوى صفرهينا فيها هناك X
+
+273
+00:27:29,950 --> 00:27:42,750
+واحدة لو جمعتها لكل علاصر لأي Y لاتساوي صفر طيب
+
+274
+00:27:42,750 --> 00:27:47,530
+و الصفر؟ صفر و صفر شو واضحة؟ صفر و صفر شو واضحة؟
+
+275
+00:27:47,530 --> 00:27:55,070
+على الأقل ايوة في نقص واحد بيساوي لو سمعناه مرة
+
+276
+00:27:55,070 --> 00:27:59,800
+تانية مثل عصرك مية المية يعنيتعالي صفر زائد صفر
+
+277
+00:27:59,800 --> 00:28:07,260
+سوى صفر فالس
+
+278
+00:28:07,260 --> 00:28:13,880
+صفر زائد واحد1 لا تساوي صفر true بس الأن أصبح ال
+
+279
+00:28:13,880 --> 00:28:18,720
+universal هذه عفوا صافيانة بقول على الأقل هناك x
+
+280
+00:28:18,720 --> 00:28:25,640
+واحدة لما تجمعها لأي x مستحيل تلاقي ناتج عملية
+
+281
+00:28:25,640 --> 00:28:31,040
+الجمع بين ال x هذه و ال y تديني صفر لأ بس هنا لجت
+
+282
+00:28:31,040 --> 00:28:37,720
+الصفر وبالتالي هذه قيمتها false شوف المثال اللي
+
+283
+00:28:37,720 --> 00:28:45,950
+بعدهفي النفي for all x there exist y for all z b
+
+284
+00:28:45,950 --> 00:28:54,850
+of x y خطوة رقم واحد بننفي يعني كمان مرة بالتدريج
+
+285
+00:28:54,850 --> 00:28:59,050
+بندخل النفي على واحد ورا التاني quantifier ورا
+
+286
+00:28:59,050 --> 00:29:02,650
+التاني لحد ما أصل لنفي ل predicate function there
+
+287
+00:29:02,650 --> 00:29:07,560
+exist x في الأولىمعناه في اللي بعديها for all i
+
+288
+00:29:07,560 --> 00:29:12,560
+نفي اللي بعديها there exist z ونفي اللي predicate
+
+289
+00:29:12,560 --> 00:29:26,400
+function اللي موجودة عندى the sum
+
+290
+00:29:26,400 --> 00:29:33,260
+of two positive integer is always positive سيبك من
+
+291
+00:29:33,260 --> 00:29:38,300
+الكلام المكتوب هذاالان هذا true حاصل جمع أي عددين
+
+292
+00:29:38,300 --> 00:29:44,260
+موجبين ناتج موجب 100% true تعالى نكتبها as
+
+293
+00:29:44,260 --> 00:29:51,220
+quantifiers the sum of two integers of any two
+
+294
+00:29:51,220 --> 00:29:58,880
+positive integers لأي رقمين for all xfor all y
+
+295
+00:29:58,880 --> 00:30:04,540
+لأنه قاعد يقول لأي عددين يعني تتخيل عندك مجموعتين
+
+296
+00:30:04,540 --> 00:30:09,560
+وعناصر الأولى مع كل عناصر التانية تمام هذه مجموعة
+
+297
+00:30:09,560 --> 00:30:12,900
+الأزواج المرتبة اللي عندك كأزواج بيحققوا المعادلة
+
+298
+00:30:12,900 --> 00:30:22,520
+ان x زائد y أكبر من صفر أكبر من صفر مش هيك
+
+299
+00:30:30,510 --> 00:30:38,630
+أكبر أو تساوي؟ أكبر أو تساوي؟ أكبر أو تساوي؟ أكبر
+
+300
+00:30:38,630 --> 00:30:40,390
+أو تساوي؟ أكبر أو تساوي؟ أكبر أو تساوي؟ أكبر أو
+
+301
+00:30:40,390 --> 00:30:41,170
+تساوي؟ أكبر أو تساوي؟ أكبر أو تساوي؟ أكبر أو
+
+302
+00:30:41,170 --> 00:30:43,570
+تساوي؟ أكبر أو تساوي؟ أكبر أو تساوي؟ أكبر أو
+
+303
+00:30:43,570 --> 00:30:45,810
+تساوي؟ أكبر أو تساوي؟ أكبر أو تساوي؟ أكبر أو
+
+304
+00:30:45,810 --> 00:30:45,970
+تساوي؟ أكبر أو تساوي؟ أكبر أو تساوي؟ أكبر أو
+
+305
+00:30:45,970 --> 00:30:54,910
+تساوي؟ أكبر أو تساوي؟ أكبر أو تساوي؟ أكبر
+
+306
+00:30:54,910 --> 00:31:00,050
+أو تساويشوف الصيغة الموجودة في الكتاب أو في مثال
+
+307
+00:31:00,050 --> 00:31:07,530
+الكتاب for all x for all y x أكبر من صفر x and y
+
+308
+00:31:07,530 --> 00:31:13,570
+أكبر من صفر يؤدي إلى نفط
+
+309
+00:31:13,570 --> 00:31:17,390
+أو طبق ال domain في الداخل بما أن ال predicate
+
+310
+00:31:17,390 --> 00:31:20,790
+function هي عبارة عن prepositional function
+
+311
+00:31:20,790 --> 00:31:26,890
+بالتالي هذا الكلام صحهذا proposition وهذا
+
+312
+00:31:26,890 --> 00:31:29,490
+proposition بدلالة مين يا شباب ال proposition
+
+313
+00:31:29,490 --> 00:31:34,130
+بدلالة ال domain دلالة ال domain ولا لأ وهي كمان
+
+314
+00:31:34,130 --> 00:31:36,770
+ال proposition وهي ال implication اللي بينهم
+
+315
+00:31:36,770 --> 00:31:41,830
+فبتكلم على compound ال proposition لكن لحاله x
+
+316
+00:31:41,830 --> 00:31:45,810
+أكبر من صفر is not a proposition بدلالة ال
+
+317
+00:31:45,810 --> 00:31:49,370
+quantifier أصبحت proposition لكن بدون بدون ال
+
+318
+00:31:49,370 --> 00:31:51,630
+quantifier is not a proposition
+
+319
+00:31:54,690 --> 00:32:00,450
+المثال اللي بعده تعالي
+
+320
+00:32:00,450 --> 00:32:09,270
+نترجم هذا for all there exist x for any y x زائد y
+
+321
+00:32:09,270 --> 00:32:14,890
+تسوى y لأي x
+
+322
+00:32:18,010 --> 00:32:27,710
+هناك X واحدة على الأقل لو جمعتها مع أي عدد بتديني
+
+323
+00:32:27,710 --> 00:32:34,610
+العدد نفسه true there exist an additive identity
+
+324
+00:32:34,610 --> 00:32:40,930
+المحايد الجمعي for any real number اللي هو الصفر
+
+325
+00:32:43,300 --> 00:32:46,380
+طيب، شو هذا المثال اللي بتقول؟ أو المثال الـ
+
+326
+00:32:46,380 --> 00:32:53,660
+Quantifier اللي عندنا هنا؟ أيوة
+
+327
+00:32:53,660 --> 00:33:00,340
+For all x شباب لما تشوف two for all يعني بلك تتخيل
+
+328
+00:33:00,340 --> 00:33:05,860
+كل الأعداد مع بعضهم المجموعتين، عناصر الأولى كل
+
+329
+00:33:05,860 --> 00:33:11,120
+عنصر في الأولى مع كل عناصر التانية تمام؟ x أكبر أو
+
+330
+00:33:11,120 --> 00:33:16,910
+تساوي صفرand طبعا هذه الخطأ موجودة هنا مش مشكلة ال
+
+331
+00:33:16,910 --> 00:33:25,810
+y أقل من صفر يعني ال x موجبة و ال y سالبة لو
+
+332
+00:33:25,810 --> 00:33:32,150
+جمعتهم حاصل الجمع هيكون أكبر من صفر موجب اعرف ان
+
+333
+00:33:32,150 --> 00:33:36,970
+لو طرحتهم هيكون حاصل طرحهم او الناتج أكبر من صفر
+
+334
+00:33:36,970 --> 00:33:39,890
+false و true
+
+335
+00:33:43,060 --> 00:33:51,140
+نقص نقص Y ليش نقص Y انا حاطيتها هنا لإن ال Y أقل
+
+336
+00:33:51,140 --> 00:33:56,940
+من صفر فهي سالبة فالسالب ماهي السالب بيصير موجبة
+
+337
+00:33:56,940 --> 00:34:03,820
+فبتكون العملية كلها موجبة a
+
+338
+00:34:03,820 --> 00:34:08,840
+non negative number تعكسش لو عكست ممكن تختلف تعكس
+
+339
+00:34:08,840 --> 00:34:18,980
+هذا ايش اللي تعكسY نقص X حرام عليك بتصير false اما
+
+340
+00:34:18,980 --> 00:34:22,540
+عشان اقولك بقولك ماتركسش عشان تظل الأمور في نصابها
+
+341
+00:34:22,540 --> 00:34:25,520
+الصحيحة ماتتوهش اما ال negative number هذا الكلام
+
+342
+00:34:25,520 --> 00:34:31,280
+هاي minus negative number or positive number minus
+
+343
+00:34:31,280 --> 00:34:38,980
+negative number greater than zero لبعدها there
+
+344
+00:34:38,980 --> 00:34:44,290
+exist XThere exists Y يعني على الأقل في المجموعتين
+
+345
+00:34:44,290 --> 00:34:49,970
+بدي أخلق واحد هنا مع واحد من المجموعة التانية بحيث
+
+346
+00:34:49,970 --> 00:34:55,750
+أنه لو كان الأولى موجب سالبة
+
+347
+00:34:55,750 --> 00:35:00,090
+و التانية سالبة حصل
+
+348
+00:35:00,090 --> 00:35:04,690
+طرحهم أكبر
+
+349
+00:35:04,690 --> 00:35:05,210
+من صفر
+
+350
+00:35:10,550 --> 00:35:16,610
+الاختلاف بين اتنين
+
+351
+00:35:16,610 --> 00:35:28,290
+أقل من صفر ليس بالضرورة يكون ناقص واحد ناقص اتنين
+
+352
+00:35:28,290 --> 00:35:31,830
+ايش يساوي واحد اكبر من صفر
+
+353
+00:35:35,990 --> 00:35:41,110
+هتلاقي واحدة X و واحدة Y بتحقق المعادلة هذه فال
+
+354
+00:35:41,110 --> 00:35:47,250
+quantifier تبعنا هذا true هيه
+
+355
+00:35:47,250 --> 00:35:57,530
+الآن X سالب واحد وال Y سالب اتنين هيه حط نقص واحد
+
+356
+00:35:57,530 --> 00:36:03,430
+الله يدك الصح ان شاء الله يا ربناقص ناقص اتنين
+
+357
+00:36:03,430 --> 00:36:08,970
+بتصير ناقص واحد زائد اتنين بتتساوي واحد صح انهم
+
+358
+00:36:08,970 --> 00:36:15,870
+طيب for all x for all y ايش يعني for all for all
+
+359
+00:36:15,870 --> 00:36:20,630
+يعني كل عناصر الأولى مع كل عناصر التانية x لا
+
+360
+00:36:20,630 --> 00:36:29,070
+تساوي صفر و ال y لا تساوي صفر حصل دربهم لا يساوي
+
+361
+00:36:29,070 --> 00:36:30,530
+صفر if and only if
+
+362
+00:36:33,970 --> 00:36:38,410
+The product of any two non-zero numbers is non
+
+363
+00:36:38,410 --> 00:36:44,390
+-zero number if and only if both factors are non
+
+364
+00:36:44,390 --> 00:36:49,810
+-zero true بس لاحظوا ما كنت قاعد بترجم بالعكس
+
+365
+00:36:49,810 --> 00:36:54,870
+بحاول أكتب ال quantifier بلغتنا في المأنثال الأولى
+
+366
+00:36:56,260 --> 00:37:01,500
+كنت بكتب من لغتنا لـ Quantifier لان بحاول أشوف
+
+367
+00:37:01,500 --> 00:37:06,300
+الترجمة للعناصر اللي موجودة عندي خلص ال section
+
+368
+00:37:06,300 --> 00:37:11,420
+وبهيك بنكون خلصنا محاضرتنا لليوم و بيبقى لنا
+
+369
+00:37:11,420 --> 00:37:15,420
+section واحد في الشبتر هذا بنكمل المحاضرة اللي جاي
+
+370
+00:37:15,420 --> 00:37:17,320
+ان شاء الله تبارك و تعالى لأنه خلال ال وقت اللي
+
+371
+00:37:17,320 --> 00:37:20,280
+بقال مش هقدر أخلصه اعطيكوا العافية
+
diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/xeTWnmt0OTo_raw.json b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/xeTWnmt0OTo_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..7c8a07364e4e133dd393036fbfa54393f741f4fd
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/xeTWnmt0OTo_raw.json
@@ -0,0 +1 @@
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universe", "probability": 0.54638671875}, {"start": 109.53, "end": 110.11, "word": " discourse", "probability": 0.748046875}, {"start": 110.11, "end": 111.11, "word": " و", "probability": 0.9326171875}, {"start": 111.11, "end": 111.45, "word": " قلنا", "probability": 0.7858072916666666}, {"start": 111.45, "end": 111.95, "word": " في", "probability": 0.8515625}, {"start": 111.95, "end": 112.81, "word": " عندي", "probability": 0.885009765625}, {"start": 112.81, "end": 113.27, "word": " نوعين", "probability": 0.9811197916666666}, {"start": 113.27, "end": 113.63, "word": " من", "probability": 0.9677734375}, {"start": 113.63, "end": 113.71, "word": " ال", "probability": 0.9716796875}, {"start": 113.71, "end": 114.45, "word": " quantifiers", "probability": 0.875732421875}, {"start": 114.45, "end": 115.13, "word": " for", "probability": 0.9599609375}, {"start": 115.13, "end": 115.65, "word": " all", "probability": 0.951171875}, {"start": 115.65, "end": 117.09, "word": " x,", "probability": 0.68408203125}, {"start": 117.47, "end": 117.61, "word": " b,", "probability": 0.474609375}, {"start": 117.89, "end": 118.01, "word": " x", "probability": 0.96533203125}], "temperature": 1.0}, {"id": 5, "seek": 14457, "start": 118.97, "end": 144.57, "text": "و there exists x بيكس بنقول صارنا الآن بنقيم ال predicate function أو ال quantifier هذا ال predicate function هذه is true لكل قيم ال domain مثل لو أنا قلتلك ال domain هو ال natural number for all x كل قيم ال domain", "tokens": [2407, 456, 8198, 2031, 4724, 1829, 4117, 3794, 44945, 39648, 20328, 9640, 8315, 6024, 48506, 44945, 4587, 32640, 2423, 3852, 8700, 2445, 34051, 2423, 4426, 9902, 23758, 2423, 3852, 8700, 2445, 29538, 307, 2074, 5296, 28820, 12174, 32640, 2423, 9274, 50113, 1211, 45164, 41850, 12174, 1211, 2655, 23275, 2423, 9274, 31439, 2423, 3303, 1230, 337, 439, 2031, 28242, 12174, 32640, 2423, 9274], "avg_logprob": -0.3779761819612412, "compression_ratio": 1.6342857142857143, "no_speech_prob": 5.960464477539063e-08, 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{"start": 162.92, "end": 163.38, "word": " exist", "probability": 0.57421875}, {"start": 163.38, "end": 163.74, "word": " x", "probability": 0.619140625}, {"start": 163.74, "end": 164.24, "word": " هناك", "probability": 0.923095703125}, {"start": 164.24, "end": 164.52, "word": " على", "probability": 0.92236328125}, {"start": 164.52, "end": 165.08, "word": " الأقل", "probability": 0.9933268229166666}, {"start": 165.08, "end": 165.46, "word": " x", "probability": 0.85693359375}, {"start": 165.46, "end": 166.3, "word": " واحدة", "probability": 0.9864908854166666}, {"start": 166.3, "end": 166.98, "word": " تحقق", "probability": 0.9754638671875}, {"start": 166.98, "end": 167.6, "word": " المعادلة", "probability": 0.9749755859375}, {"start": 167.6, "end": 167.78, "word": " ب", "probability": 0.77880859375}, {"start": 167.78, "end": 168.04, "word": " x", "probability": 0.255615234375}, {"start": 168.04, "end": 168.22, "word": " أو", "probability": 0.53759765625}, {"start": 168.22, "end": 168.32, "word": " ال", "probability": 0.837890625}, {"start": 168.32, "end": 168.56, "word": " function", "probability": 0.93115234375}, {"start": 168.56, "end": 168.74, "word": " ب", "probability": 0.87841796875}, {"start": 168.74, "end": 169.0, "word": " x", "probability": 0.904296875}, {"start": 169.0, "end": 169.84, "word": " true", "probability": 0.94287109375}], "temperature": 1.0}, {"id": 7, "seek": 20011, "start": 171.63, "end": 200.11, "text": "تمام؟ عندك سبعة اربعة او خمسة واطلع الى مال نهاية كلهم بيحققوا العناصر هذا واخر شغل لما اتكلمنا على النفي قولت لما انا بيهاجي بانفي نفل for all x bx تكافئ there exist x not bx نفل b of x ونفل for there exist x bx هتصير تكافئ for all x", "tokens": [39237, 10943, 22807, 43242, 4117, 8608, 3555, 27884, 1975, 25513, 27884, 1975, 2407, 16490, 2304, 3794, 3660, 4032, 41193, 1211, 3615, 2423, 7578, 3714, 6027, 8717, 11296, 10632, 28242, 16095, 4724, 1829, 5016, 4587, 4587, 14407, 18863, 1863, 33546, 2288, 23758, 4032, 47283, 2288, 13412, 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{"start": 395.99, "end": 396.41, "word": " بي", "probability": 0.6463623046875}, {"start": 396.41, "end": 398.05, "word": " نفي", "probability": 0.87158203125}, {"start": 398.05, "end": 399.49, "word": " Q", "probability": 0.79736328125}, {"start": 399.49, "end": 400.31, "word": " and", "probability": 0.9326171875}], "temperature": 1.0}, {"id": 16, "seek": 42997, "start": 401.81, "end": 429.97, "text": "P or R فكل هذه نسميناها nested operators لأنها تتداخل بين العناصر الموجودة وشوفنا أن النفي هذه لما تدخل تدخل على جوا الجسم بالكامل ولمّا شوفنا النفي في ال quantifiers نفي for all x P of X مررناها على كل العناصر صارت there exist x ونفينا ال P of X لكن ماشوفناش ولا حالة", "tokens": [47, 420, 497, 6156, 28820, 29538, 8717, 38251, 1829, 8315, 11296, 15646, 292, 19077, 5296, 33456, 11296, 6055, 2655, 3215, 47283, 1211, 49374, 18863, 1863, 33546, 2288, 9673, 29245, 23328, 3660, 4032, 8592, 38688, 8315, 14739, 28239, 41185, 29538, 5296, 15042, 6055, 3215, 9778, 1211, 6055, 3215, 9778, 1211, 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{"start": 424.49, "end": 424.65, "word": " there", "probability": 0.71142578125}, {"start": 424.65, "end": 424.99, "word": " exist", "probability": 0.50341796875}, {"start": 424.99, "end": 425.35, "word": " x", "probability": 0.70849609375}, {"start": 425.35, "end": 425.93, "word": " ونفينا", "probability": 0.7021484375}, {"start": 425.93, "end": 427.07, "word": " ال", "probability": 0.39599609375}, {"start": 427.07, "end": 427.21, "word": " P", "probability": 0.97314453125}, {"start": 427.21, "end": 427.39, "word": " of", "probability": 0.96630859375}, {"start": 427.39, "end": 427.65, "word": " X", "probability": 0.98095703125}, {"start": 427.65, "end": 428.67, "word": " لكن", "probability": 0.89111328125}, {"start": 428.67, "end": 429.17, "word": " ماشوفناش", "probability": 0.74658203125}, {"start": 429.17, "end": 429.39, "word": " ولا", "probability": 0.79833984375}, {"start": 429.39, "end": 429.97, "word": " حالة", "probability": 0.9947916666666666}], "temperature": 1.0}, {"id": 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"word": " على", "probability": 0.396484375}, {"start": 1897.61, "end": 1898.23, "word": " compound", "probability": 0.8388671875}, {"start": 1898.23, "end": 1899.17, "word": " ال", "probability": 0.2440185546875}, {"start": 1899.17, "end": 1899.51, "word": " proposition", "probability": 0.8427734375}, {"start": 1899.51, "end": 1900.05, "word": " لكن", "probability": 0.84130859375}, {"start": 1900.05, "end": 1900.77, "word": " لحاله", "probability": 0.9716796875}, {"start": 1900.77, "end": 1901.83, "word": " x", "probability": 0.46923828125}, {"start": 1901.83, "end": 1902.23, "word": " أكبر", "probability": 0.9444986979166666}, {"start": 1902.23, "end": 1902.41, "word": " من", "probability": 0.99609375}, {"start": 1902.41, "end": 1902.83, "word": " صفر", "probability": 0.89990234375}, {"start": 1902.83, "end": 1904.01, "word": " is", "probability": 0.74365234375}, {"start": 1904.01, "end": 1904.21, "word": " not", "probability": 0.96240234375}, {"start": 1904.21, "end": 1904.31, "word": " a", "probability": 0.8818359375}, {"start": 1904.31, "end": 1904.71, "word": " proposition", "probability": 0.837890625}, {"start": 1904.71, "end": 1905.73, "word": " بدلالة", "probability": 0.969482421875}, {"start": 1905.73, "end": 1905.81, "word": " ال", "probability": 0.8916015625}, {"start": 1905.81, "end": 1906.45, "word": " quantifier", "probability": 0.9736328125}, {"start": 1906.45, "end": 1906.89, "word": " أصبحت", "probability": 0.9114990234375}, {"start": 1906.89, "end": 1907.37, "word": " proposition", "probability": 0.75732421875}, {"start": 1907.37, "end": 1908.15, "word": " لكن", "probability": 0.8642578125}, {"start": 1908.15, "end": 1908.51, "word": " بدون", "probability": 0.986083984375}, {"start": 1908.51, "end": 1909.27, "word": " بدون", "probability": 0.6781005859375}, {"start": 1909.27, "end": 1909.37, "word": " ال", "probability": 0.9052734375}, {"start": 1909.37, "end": 1910.03, "word": " quantifier", "probability": 0.9892578125}, {"start": 1910.03, "end": 1911.07, "word": " is", "probability": 0.82958984375}, {"start": 1911.07, "end": 1911.25, "word": " not", "probability": 0.9599609375}, {"start": 1911.25, "end": 1911.39, "word": " a", "probability": 0.95849609375}, {"start": 1911.39, "end": 1911.63, "word": " proposition", "probability": 0.87451171875}], "temperature": 1.0}, {"id": 70, "seek": 193489, "start": 1914.69, "end": 1934.89, "text": "المثال اللي بعده تعالي نترجم هذا for all there exist x for any y x زائد y تسوى y لأي x", "tokens": [45340, 12984, 6027, 13672, 1829, 39182, 3224, 37279, 6027, 1829, 8717, 2655, 47341, 2304, 23758, 337, 439, 456, 2514, 2031, 337, 604, 288, 2031, 30767, 16373, 3215, 288, 6055, 3794, 2407, 7578, 288, 5296, 10721, 1829, 2031], "avg_logprob": -0.2621299475431442, "compression_ratio": 1.1272727272727272, "no_speech_prob": 0.0, "words": [{"start": 1914.69, "end": 1915.21, "word": "المثال", "probability": 0.85888671875}, {"start": 1915.21, "end": 1915.33, "word": " اللي", "probability": 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{"start": 1956.95, "end": 1958.55, "word": " الجمعي", "probability": 0.8516845703125}, {"start": 1958.55, "end": 1958.81, "word": " for", "probability": 0.955078125}, {"start": 1958.81, "end": 1959.09, "word": " any", "probability": 0.91748046875}, {"start": 1959.09, "end": 1959.39, "word": " real", "probability": 0.94482421875}, {"start": 1959.39, "end": 1959.81, "word": " number", "probability": 0.97021484375}, {"start": 1959.81, "end": 1960.39, "word": " اللي", "probability": 0.828857421875}, {"start": 1960.39, "end": 1960.51, "word": " هو", "probability": 0.98681640625}, {"start": 1960.51, "end": 1960.93, "word": " الصفر", "probability": 0.9114583333333334}], "temperature": 1.0}, {"id": 72, "seek": 199192, "start": 1963.3, "end": 1991.92, "text": "طيب، شو هذا المثال اللي بتقول؟ أو المثال الـ Quantifier اللي عندنا هنا؟ أيوة For all x شباب لما تشوف two for all يعني بلك تتخيل كل الأعداد مع بعضهم المجموعتين، عناصر الأولى كل عنصر في الأولى مع كل عناصر التانية تمام؟ x أكبر أو تساوي صفر", 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3547, 307, 2107, 12, 32226, 1230, 498, 293, 787, 498, 1293, 6771, 366, 2107, 12, 32226, 2074, 4724, 3794, 20193, 5016, 19913, 14407, 19446, 9122, 29399, 12174, 995, 22488, 39894, 47341, 2304, 20666, 3615, 4117, 3794, 4724, 5016, 995, 12610, 5551, 4117, 2655, 3555, 2423, 4426, 9902, 4724, 1211, 17082, 2655, 8315, 8978, 9673, 33456, 12984, 6027, 16247, 12610, 7578], "avg_logprob": -0.23822464459184287, "compression_ratio": 1.3567567567567567, "no_speech_prob": 0.0, "words": [{"start": 2193.97, "end": 2194.17, "word": "The", "probability": 0.0574951171875}, {"start": 2194.17, "end": 2194.69, "word": " product", "probability": 0.8896484375}, {"start": 2194.69, "end": 2195.11, "word": " of", "probability": 0.97705078125}, {"start": 2195.11, "end": 2196.25, "word": " any", "probability": 0.81884765625}, {"start": 2196.25, "end": 2196.59, "word": " two", "probability": 0.8359375}, {"start": 2196.59, "end": 2196.89, "word": " non", "probability": 0.96484375}, {"start": 2196.89, "end": 2197.17, "word": "-zero", "probability": 0.768798828125}, {"start": 2197.17, "end": 2197.73, "word": " numbers", "probability": 0.89501953125}, {"start": 2197.73, "end": 2198.17, "word": " is", "probability": 0.92822265625}, {"start": 2198.17, "end": 2198.41, "word": " non", "probability": 0.74169921875}, {"start": 2198.41, "end": 2198.69, "word": "-zero", "probability": 0.882568359375}, {"start": 2198.69, "end": 2199.19, "word": " number", "probability": 0.90966796875}, {"start": 2199.19, "end": 2200.05, "word": " if", "probability": 0.6630859375}, {"start": 2200.05, "end": 2200.33, "word": " and", "probability": 0.951171875}, {"start": 2200.33, "end": 2200.69, "word": " only", "probability": 0.9130859375}, {"start": 2200.69, "end": 2201.09, "word": " if", "probability": 0.97119140625}, {"start": 2201.09, "end": 2202.45, "word": " both", "probability": 0.859375}, {"start": 2202.45, "end": 2202.93, "word": " factors", "probability": 0.9345703125}, {"start": 2202.93, "end": 2203.35, "word": " are", "probability": 0.94384765625}, {"start": 2203.35, "end": 2204.39, "word": " non", "probability": 0.9609375}, {"start": 2204.39, "end": 2204.77, "word": "-zero", "probability": 0.87255859375}, {"start": 2204.77, "end": 2205.85, "word": " true", "probability": 0.07537841796875}, {"start": 2205.85, "end": 2207.21, "word": " بس", "probability": 0.7431640625}, {"start": 2207.21, "end": 2207.55, "word": " لاحظوا", "probability": 0.90771484375}, {"start": 2207.55, "end": 2207.69, "word": " ما", "probability": 0.366943359375}, {"start": 2207.69, "end": 2207.87, "word": " كنت", "probability": 0.861083984375}, {"start": 2207.87, "end": 2208.35, "word": " قاعد", "probability": 0.8077799479166666}, {"start": 2208.35, "end": 2209.15, "word": " بترجم", "probability": 0.9357096354166666}, {"start": 2209.15, "end": 2209.81, "word": " بالعكس", "probability": 0.9951171875}, {"start": 2209.81, "end": 2210.67, "word": " بحاول", "probability": 0.94677734375}, {"start": 2210.67, "end": 2211.27, "word": " أكتب", "probability": 0.91748046875}, {"start": 2211.27, "end": 2211.63, "word": " ال", "probability": 0.8798828125}, {"start": 2211.63, "end": 2212.47, "word": " quantifier", "probability": 0.919921875}, {"start": 2212.47, "end": 2213.63, "word": " بلغتنا", "probability": 0.9361328125}, {"start": 2213.63, "end": 2213.85, "word": " في", "probability": 0.7158203125}, {"start": 2213.85, "end": 2214.29, "word": " المأنثال", "probability": 0.609283447265625}, {"start": 2214.29, "end": 2214.87, "word": " الأولى", "probability": 0.9747721354166666}], "temperature": 1.0}, {"id": 81, "seek": 224028, "start": 2216.26, "end": 2240.28, "text": "كنت بكتب من لغتنا لـ Quantifier لان بحاول أشوف الترجمة للعناصر اللي موجودة عندي خلص ال section وبهيك بنكون خلصنا محاضرتنا لليوم و بيبقى لنا section واحد في الشبتر هذا بنكمل المحاضرة اللي جاي ان شاء الله تبارك و تعالى لأنه خلال ال وقت اللي بقال مش هقدر أخلصه اعطيكوا العافية", "tokens": [19452, 2655, 4724, 4117, 2655, 3555, 9154, 5296, 17082, 2655, 8315, 5296, 39184, 26968, 9902, 5296, 7649, 4724, 5016, 995, 12610, 5551, 8592, 38688, 16712, 47341, 46007, 24976, 3615, 1863, 33546, 2288, 13672, 1829, 3714, 29245, 23328, 3660, 18871, 16254, 16490, 1211, 9381, 2423, 3541, 46599, 3224, 1829, 4117, 44945, 30544, 16490, 1211, 9381, 8315, 3714, 5016, 46958, 43500, 8315, 5296, 20292, 20498, 4032, 4724, 1829, 3555, 4587, 7578, 5296, 8315, 3541, 36764, 24401, 8978, 25124, 3555, 2655, 2288, 23758, 44945, 24793, 1211, 9673, 5016, 46958, 25720, 13672, 1829, 10874, 47302, 16472, 13412, 16606, 21984, 6055, 3555, 9640, 4117, 4032, 37279, 6027, 7578, 5296, 33456, 3224, 16490, 1211, 6027, 2423, 4032, 38149, 13672, 1829, 4724, 4587, 6027, 37893, 8032, 28543, 2288, 5551, 9778, 1211, 9381, 3224, 1975, 3615, 9566, 1829, 4117, 14407, 18863, 31845, 10632], "avg_logprob": -0.25045955005814047, "compression_ratio": 1.7744360902255638, "no_speech_prob": 2.2649765014648438e-06, "words": [{"start": 2216.26, "end": 2216.6, "word": "كنت", "probability": 0.902099609375}, {"start": 2216.6, "end": 2217.16, "word": " بكتب", "probability": 0.9521484375}, {"start": 2217.16, "end": 2217.82, "word": " من", "probability": 0.96484375}, {"start": 2217.82, "end": 2218.22, "word": " لغتنا", "probability": 0.8687744140625}, {"start": 2218.22, "end": 2218.38, "word": " لـ", "probability": 0.5062255859375}, {"start": 2218.38, "end": 2219.06, "word": " Quantifier", "probability": 0.767822265625}, {"start": 2219.06, "end": 2219.62, "word": " لان", "probability": 0.28900146484375}, {"start": 2219.62, "end": 2221.32, "word": " بحاول", "probability": 0.8885498046875}, {"start": 2221.32, "end": 2221.5, "word": " أشوف", "probability": 0.8214518229166666}, {"start": 2221.5, "end": 2222.08, "word": " الترجمة", "probability": 0.9742838541666666}, {"start": 2222.08, "end": 2223.08, "word": " للعناصر", "probability": 0.853515625}, {"start": 2223.08, "end": 2223.2, "word": " اللي", "probability": 0.885009765625}, {"start": 2223.2, "end": 2223.56, "word": " موجودة", "probability": 0.9805908203125}, {"start": 2223.56, "end": 2223.84, "word": " عندي", "probability": 0.7841796875}, {"start": 2223.84, "end": 2225.92, "word": " خلص", "probability": 0.9088541666666666}, {"start": 2225.92, "end": 2226.04, "word": " ال", "probability": 0.5546875}, {"start": 2226.04, "end": 2226.3, "word": " section", "probability": 0.8115234375}, {"start": 2226.3, "end": 2227.2, "word": " وبهيك", "probability": 0.70269775390625}, {"start": 2227.2, "end": 2227.66, "word": " بنكون", "probability": 0.761474609375}, {"start": 2227.66, "end": 2228.78, "word": " خلصنا", "probability": 0.9447021484375}, {"start": 2228.78, "end": 2229.28, "word": " محاضرتنا", "probability": 0.91083984375}, {"start": 2229.28, "end": 2229.76, "word": " لليوم", "probability": 0.9327799479166666}, {"start": 2229.76, "end": 2231.08, "word": " و", "probability": 0.4599609375}, {"start": 2231.08, "end": 2231.24, "word": " بيبقى", "probability": 0.626708984375}, {"start": 2231.24, "end": 2231.42, "word": " لنا", "probability": 0.644287109375}, {"start": 2231.42, "end": 2231.76, "word": " section", "probability": 0.78857421875}, {"start": 2231.76, "end": 2232.28, "word": " واحد", "probability": 0.861328125}, {"start": 2232.28, "end": 2232.48, "word": " في", "probability": 0.88818359375}, {"start": 2232.48, "end": 2232.86, "word": " الشبتر", "probability": 0.660369873046875}, {"start": 2232.86, "end": 2233.2, "word": " هذا", "probability": 0.8662109375}, {"start": 2233.2, "end": 2234.66, "word": " بنكمل", "probability": 0.8468424479166666}, {"start": 2234.66, "end": 2235.12, "word": " المحاضرة", "probability": 0.9949951171875}, {"start": 2235.12, "end": 2235.26, "word": " اللي", "probability": 0.827392578125}, {"start": 2235.26, "end": 2235.42, "word": " جاي", "probability": 0.779541015625}, {"start": 2235.42, "end": 2235.56, "word": " ان", "probability": 0.73876953125}, {"start": 2235.56, "end": 2235.7, "word": " شاء", "probability": 0.94384765625}, {"start": 2235.7, "end": 2235.78, "word": " الله", "probability": 0.95849609375}, {"start": 2235.78, "end": 2236.12, "word": " تبارك", "probability": 0.82928466796875}, {"start": 2236.12, "end": 2236.2, "word": " و", "probability": 0.4521484375}, {"start": 2236.2, "end": 2236.48, "word": " تعالى", "probability": 0.9554036458333334}, {"start": 2236.48, "end": 2236.76, "word": " لأنه", "probability": 0.734130859375}, {"start": 2236.76, "end": 2236.96, "word": " خلال", "probability": 0.9860026041666666}, {"start": 2236.96, "end": 2237.08, "word": " ال", "probability": 0.98486328125}, {"start": 2237.08, "end": 2237.16, "word": " وقت", "probability": 0.6650390625}, {"start": 2237.16, "end": 2237.32, "word": " اللي", "probability": 0.984375}, {"start": 2237.32, "end": 2237.48, "word": " بقال", "probability": 0.677734375}, {"start": 2237.48, "end": 2237.6, "word": " مش", "probability": 0.90625}, {"start": 2237.6, "end": 2237.86, "word": " هقدر", "probability": 0.9488932291666666}, {"start": 2237.86, "end": 2238.28, "word": " أخلصه", "probability": 0.92197265625}, {"start": 2238.28, "end": 2239.96, "word": " اعطيكوا", "probability": 0.63037109375}, {"start": 2239.96, "end": 2240.28, "word": " العافية", "probability": 0.8181966145833334}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2240.5863125, "duration_after_vad": 2102.8274999999935}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/xeTWnmt0OTo_raw.srt b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/xeTWnmt0OTo_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..b3e082ed2c8b48b3dc181b2f6b6eeca2909119a6
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/xeTWnmt0OTo_raw.srt
@@ -0,0 +1,1488 @@
+1
+00:00:21,310 --> 00:00:23,270
+بسم الله والحمد لله والصلاة والسلام على رسول الله
+
+2
+00:00:23,270 --> 00:00:26,470
+طيب شباب اليوم ان شاء الله هنكمل ما زلنا في ال
+
+3
+00:00:26,470 --> 00:00:30,130
+chapter الأول نقل على ال section الخامس ال misted
+
+4
+00:00:30,130 --> 00:00:34,020
+quantifiers لكن قبل ما ..الروح على نفس ال
+
+5
+00:00:34,020 --> 00:00:38,340
+quantifier خلينا نسترجع مع بعض اخر مثالين والاخر
+
+6
+00:00:38,340 --> 00:00:42,080
+محاضرة بشكل سريع قلنا في اخر محاضرة اتكلمت على ال
+
+7
+00:00:42,080 --> 00:00:44,420
+predicate و ال quantifiers اتكلمنا على ال
+
+8
+00:00:44,420 --> 00:00:48,360
+predicate و ال quantifiers قلنا ال predicate لما
+
+9
+00:00:48,360 --> 00:00:52,220
+انا بكون فيه عندي X أكبر من 3 قلنا التلاتة هذه
+
+10
+00:00:52,220 --> 00:00:56,580
+مثابة ال predicate او القيمة المسندلها اللي انا
+
+11
+00:00:56,580 --> 00:01:00,360
+بناء عليها بدي احدد ال truth value قلنا في عند
+
+12
+00:01:00,360 --> 00:01:05,550
+predicate function P of Xاللي بنرمزلها بـ X أكبر
+
+13
+00:01:05,550 --> 00:01:12,530
+من 3 وهذا سمناها predicate function predicate
+
+14
+00:01:12,530 --> 00:01:15,830
+function فالـ predicate function هنا ما بقدر أديها
+
+15
+00:01:15,830 --> 00:01:20,550
+قيمة إلا لو حددت قيمة الـ X باشي بقول بي أف واحد
+
+16
+00:01:20,550 --> 00:01:24,830
+هداش قيمتها باشي بقول واحد أكبر من تلاتة false
+
+17
+00:01:24,830 --> 00:01:31,090
+معناته false بي أف أربعةtrue لأن الأربعة أكبر من
+
+18
+00:01:31,090 --> 00:01:34,590
+تلاتة و بعد ال predicate هي تكلمنا على شغل سمناها
+
+19
+00:01:34,590 --> 00:01:38,530
+quantifiers و ال quantifiers طلب مني ان انا اعرف
+
+20
+00:01:38,530 --> 00:01:44,070
+domain على كل عناصر ال predicate function صار في
+
+21
+00:01:44,070 --> 00:01:49,530
+عندي دمين او اللي سمناه universal او universe
+
+22
+00:01:49,530 --> 00:01:54,450
+discourse و قلنا في عندي نوعين من ال quantifiers
+
+23
+00:01:54,450 --> 00:02:05,670
+for all x, b, xو there exists x بيكس بنقول صارنا
+
+24
+00:02:05,670 --> 00:02:08,850
+الآن بنقيم ال predicate function أو ال quantifier
+
+25
+00:02:08,850 --> 00:02:13,170
+هذا ال predicate function هذه is true لكل قيم ال
+
+26
+00:02:13,170 --> 00:02:17,870
+domain مثل
+
+27
+00:02:17,870 --> 00:02:22,450
+لو أنا قلتلك ال domain هو ال natural number for
+
+28
+00:02:22,450 --> 00:02:28,360
+all x كل قيم ال domainهتكون أكبر من تلاتة false
+
+29
+00:02:28,360 --> 00:02:34,420
+ليش؟ لأن عندي الواحد بتم تم لل domain والواحد أقل
+
+30
+00:02:34,420 --> 00:02:40,140
+أو يساوي التلاتة اللي هي عكس هذه مصبوط؟ اللي هي
+
+31
+00:02:40,140 --> 00:02:44,520
+سميناها ال counter example there exist x هناك على
+
+32
+00:02:44,520 --> 00:02:49,000
+الأقل x واحدة تحقق المعادلة ب x أو ال function ب x
+
+33
+00:02:49,000 --> 00:02:54,590
+trueتمام؟ عندك سبعة اربعة او خمسة واطلع الى مال
+
+34
+00:02:54,590 --> 00:02:57,970
+نهاية كلهم بيحققوا العناصر هذا واخر شغل لما
+
+35
+00:02:57,970 --> 00:03:02,690
+اتكلمنا على النفي قولت لما انا بيهاجي بانفي نفل
+
+36
+00:03:02,690 --> 00:03:12,550
+for all x bx تكافئ there exist x not bx نفل b of x
+
+37
+00:03:12,550 --> 00:03:20,110
+ونفل for there exist x bx هتصير تكافئ for all x
+
+38
+00:03:20,740 --> 00:03:26,060
+نقطة PX و جينا قلنا for all X يعني كل العناصر اللي
+
+39
+00:03:26,060 --> 00:03:31,980
+في الدمين نفيها على الأقل هناك واحد في
+
+40
+00:03:31,980 --> 00:03:36,440
+الدمين يحقق المعادلة نفيها كل عناصر الدمين اللي
+
+41
+00:03:36,440 --> 00:03:42,570
+هتحقق المعادلةونتقل بعد ذلك لموضوع الـ Translation
+
+42
+00:03:42,570 --> 00:03:47,290
+في موضوع الـ Quantifiers و حاولنا أن نطبق أو نترجم
+
+43
+00:03:47,290 --> 00:03:52,270
+المثال اللي موجود عندنا هنا بحيث قلنا لكل رسالة
+
+44
+00:03:52,270 --> 00:03:58,870
+حجمها أقل من واحد ميجا بايت بدو تم تشفيرها بقول
+
+45
+00:03:58,870 --> 00:04:04,030
+كيف نتعامل معك مثال؟ بروح بالتجسم every معته for
+
+46
+00:04:04,030 --> 00:04:13,830
+all خلصنا MessageX أو المجهول تبعتنا طيب ايش بده
+
+47
+00:04:13,830 --> 00:04:23,150
+يصير فيها larger than أكبر من one megabyte المتغير
+
+48
+00:04:23,150 --> 00:04:30,530
+التاني واحد ميجا بايت تمام will be implies و ال
+
+49
+00:04:30,530 --> 00:04:32,890
+compress اللي هي هتكون المعادلة التانية اللي
+
+50
+00:04:32,890 --> 00:04:38,380
+هنعملها على مين؟ على ال M يعني هي هتصير لكلمعادلة
+
+51
+00:04:38,380 --> 00:04:49,620
+لكل اك M P of M هيقد إلى C of M ايش هذه P of M
+
+52
+00:04:49,620 --> 00:04:56,840
+لازم تتعرفها ال M is an email message او mail is
+
+53
+00:04:56,840 --> 00:05:03,380
+mail message P
+
+54
+00:05:03,380 --> 00:05:12,280
+of M ال M أكبر من واحدميجا بايت مظبوط الـ C on
+
+55
+00:05:12,280 --> 00:05:21,200
+اللي هي ال M will be compressed وبالتالي هاي
+
+56
+00:05:21,200 --> 00:05:23,820
+المعادلة .. هاي translation لـ specification اللي
+
+57
+00:05:23,820 --> 00:05:28,380
+موجودة عندها ممكن أتكلم على specification تاني إذا
+
+58
+00:05:28,380 --> 00:05:31,740
+أنا قلت والله بدي أخلي ال .. ال role هذا more
+
+59
+00:05:31,740 --> 00:05:35,260
+general و أروح بدل ال و بدل ال X أو بدل ال واحد
+
+60
+00:05:35,260 --> 00:05:41,510
+أحط Yبدل الواحد احط Y يعني لما تكون ال M حجم
+
+61
+00:05:41,510 --> 00:05:46,290
+الرسالة اقل من او اعفم اكبر من ال Y بتصير في عندي
+
+62
+00:05:46,290 --> 00:05:49,150
+hand بي M Y
+
+63
+00:05:51,780 --> 00:05:55,860
+وتحريف المعادلة هنا بصير بدل الواحد باستخدام ال y
+
+64
+00:05:55,860 --> 00:05:59,700
+اللي موجودة عندها وبالتالي ممكن انا احصل على اكتر
+
+65
+00:05:59,700 --> 00:06:03,400
+من definition او اكتر من quantifier صحيح اذا انا
+
+66
+00:06:03,400 --> 00:06:07,000
+قدرت اترجم كل العناصر هذه بشكل مستقل بشكل صحيح
+
+67
+00:06:07,000 --> 00:06:10,120
+وبعدين اربقهم زي ما بدي وشوفنا المثال التاني اللي
+
+68
+00:06:10,120 --> 00:06:14,240
+كان نتكلم عن ال connection وحلناها مع بعض وشوفنا
+
+69
+00:06:16,210 --> 00:06:19,370
+شو؟ يعني العلاقة ما بين ال link و ال user ال
+
+70
+00:06:19,370 --> 00:06:23,590
+available اليوم هنتقل لشغلة جديدة اللي هي nested
+
+71
+00:06:23,590 --> 00:06:28,830
+quantifiers nested احنا شوفنا سابقا لما اتكلمنا
+
+72
+00:06:28,830 --> 00:06:32,610
+على ال operators ال logical operators قولنا PR
+
+73
+00:06:32,610 --> 00:06:43,750
+بفتح جوس Q and ال R أو بي نفي Q andP or R فكل هذه
+
+74
+00:06:43,750 --> 00:06:47,230
+نسميناها nested operators لأنها تتداخل بين العناصر
+
+75
+00:06:47,230 --> 00:06:51,370
+الموجودة وشوفنا أن النفي هذه لما تدخل تدخل على جوا
+
+76
+00:06:51,370 --> 00:06:57,750
+الجسم بالكامل ولمّا شوفنا النفي في ال quantifiers
+
+77
+00:06:57,750 --> 00:07:04,490
+نفي for all x P of X مررناها على كل العناصر صارت
+
+78
+00:07:04,490 --> 00:07:09,390
+there exist x ونفينا ال P of X لكن ماشوفناش ولا
+
+79
+00:07:09,390 --> 00:07:14,680
+حالةتو quantifier
+
+80
+00:07:14,680 --> 00:07:19,060
+جايين ورا بعض الان لما انا بتكلم على نفس ال
+
+81
+00:07:19,060 --> 00:07:22,760
+quantifier معناته انا بتكلم ان ال بريدكيت function
+
+82
+00:07:22,760 --> 00:07:27,240
+تبعتي زي في المثال السابق بتعتمد على two variables
+
+83
+00:07:27,240 --> 00:07:35,300
+بس كل واحد فيهمالو quantifier لحاله بدي أتعامل
+
+84
+00:07:35,300 --> 00:07:39,700
+معاه لحاله تعالى نشوف أو نحاول نفهم ال quantifier
+
+85
+00:07:39,700 --> 00:07:46,280
+اللي موجود قدامنا هنا for all x لأي x تنتني لل
+
+86
+00:07:46,280 --> 00:07:52,260
+domain تمام there exist y بلاجيها على الأقل y
+
+87
+00:07:52,260 --> 00:07:55,480
+واحدة بتحقق ال predicate function اللي موجودة عندي
+
+88
+00:07:55,480 --> 00:08:01,400
+for all x there exist y بتحقق
+
+89
+00:08:02,540 --> 00:08:05,640
+الـ function يعني تعالى نشوفها لو انا اجيت قولتلك
+
+90
+00:08:05,640 --> 00:08:08,320
+ال domain تبعتي اللي هي ال natural number ال real
+
+91
+00:08:08,320 --> 00:08:17,340
+number ال domain افترض ان ال domain الاعداد
+
+92
+00:08:17,340 --> 00:08:24,640
+الحقيقية كليتها بالمثال هذا for all x لأي عدد
+
+93
+00:08:24,640 --> 00:08:34,650
+حقيقي هناك على الأقل أنصر واحدعدد حقيقي تمام بحيث
+
+94
+00:08:34,650 --> 00:08:39,390
+ان لو جمعتهم التنين مع بعض يسووا صفر true ولا
+
+95
+00:08:39,390 --> 00:08:42,870
+false ازميل
+
+96
+00:08:42,870 --> 00:08:46,910
+أشجال صفر و صفر و أخد حالة واحدة فقط و ربط عليها
+
+97
+00:08:46,910 --> 00:08:54,490
+كلب لحظة ايش في الأول عندي for all لأي عدد حقيقي
+
+98
+00:08:55,430 --> 00:09:01,070
+ماذا يعني؟ لكل الأعداد الحقيقية لأي عدد حقيقي يعني
+
+99
+00:09:01,070 --> 00:09:06,770
+هذه المعادلة بدأ تتطبق على كل الأعداد الحقيقية أيش
+
+100
+00:09:06,770 --> 00:09:12,550
+ما تاخد عدد حقيقي تمام؟ هتلاقيله عدد حقيقي آخر
+
+101
+00:09:12,550 --> 00:09:19,970
+واحد على الأقل لو جمعته يساوي صفر true العنصر
+
+102
+00:09:19,970 --> 00:09:29,400
+والسالب تبعه النظير الجمعيX زائد نقص X لان الشيء
+
+103
+00:09:29,400 --> 00:09:35,420
+اللي قاعد يقوللي خد أي عنصر في ال domain for all X
+
+104
+00:09:35,420 --> 00:09:40,300
+in the domain for any real number there exist يعني
+
+105
+00:09:40,300 --> 00:09:46,120
+إيش ما تاخد عدد إيش ما تاخد عدد هتلاقي عدد واحد
+
+106
+00:09:46,120 --> 00:09:50,200
+على الأقل لما تجمعهم التنين مع بعض بديك صفر true
+
+107
+00:09:50,200 --> 00:09:59,200
+نشوف البعدهاليش برجعها؟ تمام اختلفت الصورة تماما
+
+108
+00:09:59,200 --> 00:10:07,560
+الان تعالى تشوف there exist هناك X واحدة على الأقل
+
+109
+00:10:07,560 --> 00:10:12,940
+في ال domain تستخدم
+
+110
+00:10:12,940 --> 00:10:17,860
+مع كل عناصر اللي في ال domain تمام بحيث انها تحقق
+
+111
+00:10:17,860 --> 00:10:21,020
+المعادلة الموجودة يعني ال X هذه
+
+112
+00:10:23,550 --> 00:10:27,750
+فيش غيرها أو على الأقل في X واحدة تظبط مع كل ال X
+
+113
+00:10:27,750 --> 00:10:33,230
+حسب المعادلة في المعادلة اللي عندي هال في المعادلة
+
+114
+00:10:33,230 --> 00:10:39,610
+اللي عندي هال there exist X لكل عناصر ال Y لكل
+
+115
+00:10:39,610 --> 00:10:42,850
+عناصر ال domain في ال real number لو ضربت X ال Y
+
+116
+00:10:42,850 --> 00:10:49,980
+تديني صفر true الصفرالصفر real number و لو ضربته
+
+117
+00:10:49,980 --> 00:10:54,800
+في أي عدد حقيقي بحصل على صفر ببتعالى نجلب ال
+
+118
+00:10:54,800 --> 00:11:00,060
+quantifiers هدول بحيث اننا نقول هان كتالي there
+
+119
+00:11:00,060 --> 00:11:09,480
+exist x for all y x زائد y يساوي صفر و هان ايش
+
+120
+00:11:09,480 --> 00:11:16,530
+متهدي الان هناك x واحدةلو جمعتها لكل عناصر الدومين
+
+121
+00:11:16,530 --> 00:11:20,870
+لكل عناصر الدومين او لأي عنصر في الدومين هتديني
+
+122
+00:11:20,870 --> 00:11:27,170
+صفر false مستحيل تلاقي هيك معادلة اختلاف او اعادة
+
+123
+00:11:27,170 --> 00:11:31,830
+ترتيب ال quantifiers ادى الاختلاف ال output تعالى
+
+124
+00:11:31,830 --> 00:11:40,090
+نشوف هنا for all x there exists y such that x ضرب
+
+125
+00:11:40,090 --> 00:11:51,820
+ال y يساوي صفرلكل X لأي X في ال domain هتلاقيلها Y
+
+126
+00:11:51,820 --> 00:11:57,960
+لو ضربتهم في بعض بدوني صفر true لأن ال Y .. لأن
+
+127
+00:11:57,960 --> 00:12:01,040
+عملية الضرب عملية إبدالية وبالتالي ال Y بدي اعتمد
+
+128
+00:12:01,040 --> 00:12:04,900
+هذه الصفر و بتقسم مع كل العناصر و بتقولي على الأقل
+
+129
+00:12:04,900 --> 00:12:10,380
+X واحدة و Y واحدة ولا لأ فبالتالي هذه كمان true
+
+130
+00:12:10,380 --> 00:12:17,950
+طيب تعالى نشوفالجدول هذا جمع مجموعة من الـ nested
+
+131
+00:12:17,950 --> 00:12:25,670
+quantifiers و بحاول اترجم ليهم for all x for all y
+
+132
+00:12:25,670 --> 00:12:35,610
+bxy ايش يعني؟ لأي عددين في الدمان bxy is true أي
+
+133
+00:12:35,610 --> 00:12:38,930
+عددين في الدمان بحققه ل predicate function تبعتي
+
+134
+00:12:38,930 --> 00:12:45,440
+هاييعني لو أنا جاي قلتلك for all x for all y على
+
+135
+00:12:45,440 --> 00:12:54,360
+المثال السابق x زائد y تساوي صفر عارفش معناها؟ بدك
+
+136
+00:12:54,360 --> 00:12:58,460
+تفترض أن في عندي real number و real number x بدأ
+
+137
+00:12:58,460 --> 00:13:04,740
+أخدها من هنا و ال y بدأ أخدها من هنا أي x هنا
+
+138
+00:13:04,740 --> 00:13:12,590
+تمام؟مع أي اكس هان جمعهم تساوي صفر فالس فالس مش
+
+139
+00:13:12,590 --> 00:13:18,550
+نفسها ليش لأنها بتكون true لأن الاتنين متفقين
+
+140
+00:13:18,550 --> 00:13:23,610
+الاتنين مع كل زوج مرتب يعني هيكد أي اكس هان بتكون
+
+141
+00:13:23,610 --> 00:13:28,770
+true مع كل عناصر ال Y و العكس صحيح اي Y هتكون true
+
+142
+00:13:28,770 --> 00:13:32,630
+مع كل عناصر ال X وهذا كلام مستحيل يصير حسب
+
+143
+00:13:32,630 --> 00:13:37,890
+المعادلة اللي مكتوبة هنا فوقطيب، لاحظوا إنما بدلنا
+
+144
+00:13:37,890 --> 00:13:44,090
+for all x و for all y نفس المعنى مافرجتش لأنه
+
+145
+00:13:44,090 --> 00:13:47,390
+بتكلم على نفس ال quantifier بتكلم على نفس ال
+
+146
+00:13:47,390 --> 00:13:52,850
+quantifier فلو قدمت أو أخرج مش فارق كتير عندي اللي
+
+147
+00:13:52,850 --> 00:14:00,450
+بعده، متى هذا بيكون false؟ لو جدرت ألاقي فقط زوج
+
+148
+00:14:00,450 --> 00:14:04,880
+مرتب أو زوج من العناصر x و yاللي محققوش ال
+
+149
+00:14:04,880 --> 00:14:09,680
+predicate function تبعها ايه بتصير؟ false طيب for
+
+150
+00:14:09,680 --> 00:14:15,340
+all x زي ما قلنا سابقا لأي عنصر في ال domain فيه
+
+151
+00:14:15,340 --> 00:14:21,240
+هناك على الأقل عنصر واحد y تحقق المعادلة اللي
+
+152
+00:14:21,240 --> 00:14:26,520
+موجودة متى بتكون false لو مالجتش ال y؟ لزوج واحد
+
+153
+00:14:26,520 --> 00:14:34,530
+على الأقل there exist x هناك xواحدة لو طبقتها مع
+
+154
+00:14:34,530 --> 00:14:38,690
+كل العناصر اللي في الدمية بتعمل satisfied متى هذا
+
+155
+00:14:38,690 --> 00:14:42,870
+الكلام بيكون لو قدرت ألاقي X وY كزوج مرتب واحد فقط
+
+156
+00:14:42,870 --> 00:14:47,270
+ان هذا ماتحققتش المعادلة اللي عندي there exist X
+
+157
+00:14:47,270 --> 00:14:53,850
+there exist Y هناك X ل Y واحدة تمام بتحقق المعادلة
+
+158
+00:14:53,850 --> 00:14:59,690
+اللي عندها و ترتيبهم ممكن يكون نفس النتيجة متى
+
+159
+00:14:59,690 --> 00:15:05,540
+بتكون falseلو كانت المعادلة هذه false لكل الأزواج
+
+160
+00:15:05,540 --> 00:15:12,520
+يعني هيك لأي X لم أجد أي Y تمام؟ عكسها تماما طيب
+
+161
+00:15:12,520 --> 00:15:20,060
+نمتقل للعصر اللي بعده تعالى نشوف بقول لترجم النفس
+
+162
+00:15:20,060 --> 00:15:26,480
+ال quantifier اللي موجود عندى هنا أي
+
+163
+00:15:26,480 --> 00:15:27,040
+طالب
+
+164
+00:15:33,320 --> 00:15:37,440
+or all student
+
+165
+00:15:37,440 --> 00:15:42,640
+ال X لديه
+
+166
+00:15:42,640 --> 00:15:53,080
+كمبيوتر B of X or has a friend that has a computer
+
+167
+00:15:53,080 --> 00:16:01,720
+ال friend معناته Y و B of Y لديه كمبيوترممكن هيك
+
+168
+00:16:01,720 --> 00:16:06,780
+تتعامل معاهم يعني الان انا بكل بساطة اي طالب في ال
+
+169
+00:16:06,780 --> 00:16:11,840
+class هذا اما هيكون عنده جهاز كمبيوتر او حاجه له
+
+170
+00:16:11,840 --> 00:16:18,640
+صديق مع جهاز كمبيوتر تمام؟ تعلمنا الكتابة as
+
+171
+00:16:18,640 --> 00:16:23,860
+nested quantifier لان عرفنا ال X وعرفنا ال Y ال X
+
+172
+00:16:23,860 --> 00:16:30,140
+هيك بتدهكي من البداية ال X student و
+
+173
+00:16:30,140 --> 00:16:30,520
+ال Y
+
+174
+00:16:33,260 --> 00:16:40,860
+friend of X friend
+
+175
+00:16:40,860 --> 00:16:55,820
+of X بي of X X has a computer مصبوط ولا يعني طيب
+
+176
+00:16:55,820 --> 00:17:03,650
+الأن بقدر أجي أقول أنا here for allX طبعا ال
+
+177
+00:17:03,650 --> 00:17:11,610
+domain تبقى مين هو يا شباب ال class الفصل for all
+
+178
+00:17:11,610 --> 00:17:19,190
+X there
+
+179
+00:17:19,190 --> 00:17:23,150
+exist Y
+
+180
+00:17:23,150 --> 00:17:26,890
+such
+
+181
+00:17:26,890 --> 00:17:38,920
+that B of Xأو P of Y تعالى بترجمها دى لان تبقى
+
+182
+00:17:38,920 --> 00:17:44,020
+للكلام اللى بيقوله لكل X لأى طالب فى ال class فى
+
+183
+00:17:44,020 --> 00:17:51,940
+الفصل there exist Y هناك صديق له تمام على الأقل
+
+184
+00:17:51,940 --> 00:18:00,630
+بحيث الهى ال bracket function ان P Xعرفتها هي X
+
+185
+00:18:00,630 --> 00:18:04,950
+has a computer او ال friend هذا has a computer
+
+186
+00:18:04,950 --> 00:18:10,610
+مصدود ولا لا؟ وبالتالي هذه ال statement مع العناصر
+
+187
+00:18:10,610 --> 00:18:13,670
+ال explanation هدول هي عبارة عن ترجمة لل
+
+188
+00:18:13,670 --> 00:18:17,290
+specification اللي فوق صحيحة؟ هل هو الحل الوحيد
+
+189
+00:18:17,290 --> 00:18:21,610
+اللي ممكن يكون عنده؟ لأ، بيعتمد كيف بدك تعرف
+
+190
+00:18:21,610 --> 00:18:25,290
+العناصر و علاقة المعادلة أو الدوال مع بعضهم دعونا
+
+191
+00:18:25,290 --> 00:18:28,370
+نشوف كيف جاء بالمثال اللي موجود عنده
+
+192
+00:18:32,700 --> 00:18:40,280
+كخطوة أولى راح
+
+193
+00:18:40,280 --> 00:18:48,100
+ترجم for any student x كما لهي for all for
+
+194
+00:18:48,100 --> 00:18:57,700
+all x x has a computer P of X or there is some
+
+195
+00:18:57,700 --> 00:18:58,580
+student y
+
+196
+00:19:02,930 --> 00:19:09,130
+Where ال Y has a computer and X and Y are friends
+
+197
+00:19:09,130 --> 00:19:18,050
+يعني هيك F of X و Y ربط ال X و ال Y مع بعضهم و
+
+198
+00:19:18,050 --> 00:19:27,850
+عرفليها كتالة X and Y are friends and
+
+199
+00:19:27,850 --> 00:19:31,090
+Y has a computer
+
+200
+00:19:36,090 --> 00:19:39,130
+حسب التفسير اللي اشتغله عليه و بدأ فصله بالشكل
+
+201
+00:19:39,130 --> 00:19:43,870
+اللي هي ده فكتب اللي هي ده تعالى نشوف اشرح كالحل
+
+202
+00:19:43,870 --> 00:19:52,830
+for all X for all X X is student CX
+
+203
+00:19:52,830 --> 00:19:59,110
+has a computer معناته for all X و راحظوا على كل
+
+204
+00:19:59,110 --> 00:20:03,050
+quantifier اللي موجود عندي هان C of X X has a
+
+205
+00:20:03,050 --> 00:20:05,230
+computer or
+
+206
+00:20:07,440 --> 00:20:14,120
+There exist Y such that Y has a computer نفس
+
+207
+00:20:14,120 --> 00:20:20,340
+الكلام اللي قلناه قبل شوية and ال friends F of XY
+
+208
+00:20:20,340 --> 00:20:28,300
+F of XY X and Y are friends هذه برضه ترجمة صحيحة
+
+209
+00:20:28,300 --> 00:20:37,580
+لل quantifier اللي موجود عندي طيب نشوف المثالأو
+
+210
+00:20:37,580 --> 00:20:47,720
+نشوف شغلة تانية واضح المثال يا شباب؟ بداك
+
+211
+00:20:47,720 --> 00:20:53,180
+تنتبه دائما ان فعليا كل شغلة في البربوسش انتباهك
+
+212
+00:20:53,180 --> 00:20:59,500
+تكون ضمن ال quantifier بشكل صحيح لما
+
+213
+00:20:59,500 --> 00:21:06,910
+انا باجي بقول for all x there exist yمعناته نجاحا
+
+214
+00:21:06,910 --> 00:21:13,250
+بقول for all x بتحقق ال x there exist y بتحقق
+
+215
+00:21:13,250 --> 00:21:18,950
+العلاقة ما بين x و y بنجو سين ال nested quantifier
+
+216
+00:21:18,950 --> 00:21:25,490
+بقدر أنظرله as two different quantifiers يعني الآن
+
+217
+00:21:25,490 --> 00:21:33,910
+for all معناته qxماذا يعني QX؟ لأي عنصر ينتمي؟ للـ
+
+218
+00:21:33,910 --> 00:21:40,190
+domain بأي عنصر ينتمي؟ للـ domain تمام؟ بدي ألاقي
+
+219
+00:21:40,190 --> 00:21:46,830
+there exists Y بتحقق علاقنا بين X وY هذا تفسير لـ
+
+220
+00:21:46,830 --> 00:21:50,890
+predicate اللي موجود عندها تعالى نشوف قيم أو
+
+221
+00:21:50,890 --> 00:21:54,790
+مجموعة من العراسر اللي موجودة عندهم تعالى ترجملي
+
+222
+00:21:54,790 --> 00:22:01,450
+هذه for all X there exists Yلأي X في ال domain
+
+223
+00:22:01,450 --> 00:22:07,630
+هناك Y لأنه بتتكلم على نفس ال domain أنا مازلت X
+
+224
+00:22:07,630 --> 00:22:15,090
+زائد Y تساوي صفر أصبعط تعالى الأخيرة هذه تحت لكل X
+
+225
+00:22:15,090 --> 00:22:26,450
+مع أي Y أي X مع أي Y في ال domain X زائد Y تساوي Y
+
+226
+00:22:26,450 --> 00:22:34,620
+زائد Xلاحظ ان هنا قاعد بيقولك بدك تاخد كل العناصر
+
+227
+00:22:34,620 --> 00:22:40,780
+هتفترض X من R واي من R واحد اللي هنا real number و
+
+228
+00:22:40,780 --> 00:22:47,080
+تاخد كل عنصر في ال X تربط مع كل عناصر ال Y و العكس
+
+229
+00:22:47,080 --> 00:22:51,600
+صحيح كل عنصر في ال Y بده يرتبط مع كل عناصر ال X
+
+230
+00:22:51,600 --> 00:22:58,490
+صار عندك مجموعة من الأزواد المرتبة هايهم X وYX
+
+231
+00:22:58,490 --> 00:23:03,930
+زائد Y بدها تساوي Y زائد X، بدك تفهمها هيك، هذه
+
+232
+00:23:03,930 --> 00:23:09,970
+احنا غالبا بنرمزها for all X, for all Y, P of X و
+
+233
+00:23:09,970 --> 00:23:13,070
+Y، هذا المكتوب تحت شهر هو هي العلاقة اللي ما بين
+
+234
+00:23:13,070 --> 00:23:15,450
+ال X و Y، ال predicate function
+
+235
+00:23:26,450 --> 00:23:30,710
+ضروري اتحدد شو علاقة ال combination او اتحدد
+
+236
+00:23:30,710 --> 00:23:33,790
+العلاقة ما بين ال variables اللى عندك عشان تقدر
+
+237
+00:23:33,790 --> 00:23:38,410
+تكتب ال quantifier صح لان احنا اتفاقن قبل شوية من
+
+238
+00:23:38,410 --> 00:23:44,850
+خلال الأمثلة for all x there exist y مش بالضرورة
+
+239
+00:23:44,850 --> 00:23:52,150
+تكافئThere exists x for all y و لا بقى في اختلاف
+
+240
+00:23:52,150 --> 00:23:58,010
+تماما في المعنى وبالتالي لازم تفهم شو هي علاقة ال
+
+241
+00:23:58,010 --> 00:24:03,210
+universal quantifier و ال existential مع العنصر
+
+242
+00:24:03,210 --> 00:24:07,170
+اللي عندي خصوصا ان هم التنتين مش متساويات فضروري
+
+243
+00:24:07,170 --> 00:24:11,390
+نفهمها بشكل عنصر تعالى نشوف بالمثال اللي عندي هان
+
+244
+00:24:11,390 --> 00:24:18,530
+بقول ال predicateXY هي عبارة عن X زائد Y تساوي صفر
+
+245
+00:24:18,530 --> 00:24:32,110
+هناك X لأي Y بي of XY هناك X واحدة لو جمعتها مع أي
+
+246
+00:24:32,110 --> 00:24:40,730
+في أولي الانظار أي Y تبديني صفر فالس لكن تعالى
+
+247
+00:24:40,730 --> 00:24:50,320
+نقوللأي X أنت بتحديها هتلاقي Y واحدة على الأقل لو
+
+248
+00:24:50,320 --> 00:24:54,420
+جمعتهم اتنين مع بعض و بتديني سفر true اللي هي
+
+249
+00:24:54,420 --> 00:25:02,960
+قولنا قيمة و قيمة السالبة تبعتها في
+
+250
+00:25:02,960 --> 00:25:07,320
+نفس ال quantifiers لما أنا بدي أجن فيها احنا الآن
+
+251
+00:25:07,320 --> 00:25:14,750
+في عندي for all X for allY تخيل ان انا بدي أنفيها
+
+252
+00:25:14,750 --> 00:25:21,830
+بي of XY احنا
+
+253
+00:25:21,830 --> 00:25:26,670
+لما نفيل ال quantifier قلنا بنمرر النافذ تبعت ال
+
+254
+00:25:26,670 --> 00:25:30,960
+universal quantifier بتصير existentialوبعدين بتصير
+
+255
+00:25:30,960 --> 00:25:35,620
+النفي تبعت ال predicate function يعني نفي for all
+
+256
+00:25:35,620 --> 00:25:39,920
+x,b,x في تساوي there exist x هناك x واحدة على
+
+257
+00:25:39,920 --> 00:25:45,920
+الأقل لا تحقق ال P of X ولا لا؟ و النفي التبعت ل
+
+258
+00:25:45,920 --> 00:25:52,100
+there exist x,b,x هناك x واحدة على الأقل تحقق تحقق
+
+259
+00:25:52,100 --> 00:26:00,140
+ال Pxنفيها كل عناصر و X لا تحقق الـ BX طيب، لما
+
+260
+00:26:00,140 --> 00:26:03,420
+يكون في عندي Analyzed Quantifier، شو بدي أسوي؟ بدك
+
+261
+00:26:03,420 --> 00:26:07,840
+تشتغل بنفس المنطق، بدك تشتغل بنفس المنطق، تبدأ
+
+262
+00:26:07,840 --> 00:26:12,720
+تمرر النفي على الـ Quantifier الأول لـ Quantifier
+
+263
+00:26:12,720 --> 00:26:17,080
+التاني لما تصل لمين؟ لـ Predicate Function لـ B of
+
+264
+00:26:17,080 --> 00:26:20,280
+XY وتنفيها بالمثال هذا
+
+265
+00:26:25,350 --> 00:26:32,870
+نفي for all x there exist y بxy خطوة رقم واحد بدخل
+
+266
+00:26:32,870 --> 00:26:40,110
+النفي على for all x بتصير there exist x لا تحقق
+
+267
+00:26:40,110 --> 00:26:46,970
+there exist y b of xy النفي بعد ذلك بتصير for all
+
+268
+00:26:46,970 --> 00:26:53,410
+y بتصير هندي هن there exist x for all y
+
+269
+00:26:56,420 --> 00:27:04,260
+لما انا باجب اقول هيك لكل x there exist y x زائد y
+
+270
+00:27:04,260 --> 00:27:09,020
+equal 0 ايش كانت قيمتها المعروفية ال number؟ true
+
+271
+00:27:09,020 --> 00:27:19,500
+ولا لا؟ طيب بدنا نفيها نفيها there exist x for all
+
+272
+00:27:19,500 --> 00:27:29,950
+y such that x زائد y لا تساوى صفرهينا فيها هناك X
+
+273
+00:27:29,950 --> 00:27:42,750
+واحدة لو جمعتها لكل علاصر لأي Y لاتساوي صفر طيب
+
+274
+00:27:42,750 --> 00:27:47,530
+و الصفر؟ صفر و صفر شو واضحة؟ صفر و صفر شو واضحة؟
+
+275
+00:27:47,530 --> 00:27:55,070
+على الأقل ايوة في نقص واحد بيساوي لو سمعناه مرة
+
+276
+00:27:55,070 --> 00:27:59,800
+تانية مثل عصرك مية المية يعنيتعالي صفر زائد صفر
+
+277
+00:27:59,800 --> 00:28:07,260
+سوى صفر فالس
+
+278
+00:28:07,260 --> 00:28:13,880
+صفر زائد واحد1 لا تساوي صفر true بس الأن أصبح ال
+
+279
+00:28:13,880 --> 00:28:18,720
+universal هذه عفوا صافيانة بقول على الأقل هناك x
+
+280
+00:28:18,720 --> 00:28:25,640
+واحدة لما تجمعها لأي x مستحيل تلاقي ناتج عملية
+
+281
+00:28:25,640 --> 00:28:31,040
+الجمع بين ال x هذه و ال y تديني صفر لأ بس هنا لجت
+
+282
+00:28:31,040 --> 00:28:37,720
+الصفر وبالتالي هذه قيمتها false شوف المثال اللي
+
+283
+00:28:37,720 --> 00:28:45,950
+بعدهفي النفي for all x there exist y for all z b
+
+284
+00:28:45,950 --> 00:28:54,850
+of x y خطوة رقم واحد بننفي يعني كمان مرة بالتدريج
+
+285
+00:28:54,850 --> 00:28:59,050
+بندخل النفي على واحد ورا التاني quantifier ورا
+
+286
+00:28:59,050 --> 00:29:02,650
+التاني لحد ما أصل لنفي ل predicate function there
+
+287
+00:29:02,650 --> 00:29:07,560
+exist x في الأولىمعناه في اللي بعديها for all i
+
+288
+00:29:07,560 --> 00:29:12,560
+نفي اللي بعديها there exist z ونفي اللي predicate
+
+289
+00:29:12,560 --> 00:29:26,400
+function اللي موجودة عندى the sum
+
+290
+00:29:26,400 --> 00:29:33,260
+of two positive integer is always positive سيبك من
+
+291
+00:29:33,260 --> 00:29:38,300
+الكلام المكتوب هذاالان هذا true حاصل جمع أي عددين
+
+292
+00:29:38,300 --> 00:29:44,260
+موجبين ناتج موجب 100% true تعالى نكتبها as
+
+293
+00:29:44,260 --> 00:29:51,220
+quantifiers the sum of two integers of any two
+
+294
+00:29:51,220 --> 00:29:58,880
+positive integers لأي رقمين for all xfor all y
+
+295
+00:29:58,880 --> 00:30:04,540
+لأنه قاعد يقول لأي عددين يعني تتخيل عندك مجموعتين
+
+296
+00:30:04,540 --> 00:30:09,560
+وعناصر الأولى مع كل عناصر التانية تمام هذه مجموعة
+
+297
+00:30:09,560 --> 00:30:12,900
+الأزواج المرتبة اللي عندك كأزواج بيحققوا المعادلة
+
+298
+00:30:12,900 --> 00:30:22,520
+ان x زائد y أكبر من صفر أكبر من صفر مش هيك
+
+299
+00:30:30,510 --> 00:30:38,630
+أكبر أو تساوي؟ أكبر أو تساوي؟ أكبر أو تساوي؟ أكبر
+
+300
+00:30:38,630 --> 00:30:40,390
+أو تساوي؟ أكبر أو تساوي؟ أكبر أو تساوي؟ أكبر أو
+
+301
+00:30:40,390 --> 00:30:41,170
+تساوي؟ أكبر أو تساوي؟ أكبر أو تساوي؟ أكبر أو
+
+302
+00:30:41,170 --> 00:30:43,570
+تساوي؟ أكبر أو تساوي؟ أكبر أو تساوي؟ أكبر أو
+
+303
+00:30:43,570 --> 00:30:45,810
+تساوي؟ أكبر أو تساوي؟ أكبر أو تساوي؟ أكبر أو
+
+304
+00:30:45,810 --> 00:30:45,810
+تساوي؟ أكبر أو تساوي؟ أكبر أو تساوي؟ أكبر أو
+
+305
+00:30:45,810 --> 00:30:45,970
+تساوي؟ أكبر أو تساوي؟ أكبر أو تساوي؟ أكبر أو
+
+306
+00:30:45,970 --> 00:30:54,910
+تساوي؟ أكبر أو تساوي؟ أكبر أو تساوي؟ أكبر
+
+307
+00:30:54,910 --> 00:31:00,050
+أو تساويشوف الصيغة الموجودة في الكتاب أو في مثال
+
+308
+00:31:00,050 --> 00:31:07,530
+الكتاب for all x for all y x أكبر من صفر x and y
+
+309
+00:31:07,530 --> 00:31:13,570
+أكبر من صفر يؤدي إلى نفط
+
+310
+00:31:13,570 --> 00:31:17,390
+أو طبق ال domain في الداخل بما أن ال predicate
+
+311
+00:31:17,390 --> 00:31:20,790
+function هي عبارة عن prepositional function
+
+312
+00:31:20,790 --> 00:31:26,890
+بالتالي هذا الكلام صحهذا proposition وهذا
+
+313
+00:31:26,890 --> 00:31:29,490
+proposition بدلالة مين يا شباب ال proposition
+
+314
+00:31:29,490 --> 00:31:34,130
+بدلالة ال domain دلالة ال domain ولا لأ وهي كمان
+
+315
+00:31:34,130 --> 00:31:36,770
+ال proposition وهي ال implication اللي بينهم
+
+316
+00:31:36,770 --> 00:31:41,830
+فبتكلم على compound ال proposition لكن لحاله x
+
+317
+00:31:41,830 --> 00:31:45,810
+أكبر من صفر is not a proposition بدلالة ال
+
+318
+00:31:45,810 --> 00:31:49,370
+quantifier أصبحت proposition لكن بدون بدون ال
+
+319
+00:31:49,370 --> 00:31:51,630
+quantifier is not a proposition
+
+320
+00:31:54,690 --> 00:32:00,450
+المثال اللي بعده تعالي
+
+321
+00:32:00,450 --> 00:32:09,270
+نترجم هذا for all there exist x for any y x زائد y
+
+322
+00:32:09,270 --> 00:32:14,890
+تسوى y لأي x
+
+323
+00:32:18,010 --> 00:32:27,710
+هناك X واحدة على الأقل لو جمعتها مع أي عدد بتديني
+
+324
+00:32:27,710 --> 00:32:34,610
+العدد نفسه true there exist an additive identity
+
+325
+00:32:34,610 --> 00:32:40,930
+المحايد الجمعي for any real number اللي هو الصفر
+
+326
+00:32:43,300 --> 00:32:46,380
+طيب، شو هذا المثال اللي بتقول؟ أو المثال الـ
+
+327
+00:32:46,380 --> 00:32:53,660
+Quantifier اللي عندنا هنا؟ أيوة
+
+328
+00:32:53,660 --> 00:33:00,340
+For all x شباب لما تشوف two for all يعني بلك تتخيل
+
+329
+00:33:00,340 --> 00:33:05,860
+كل الأعداد مع بعضهم المجموعتين، عناصر الأولى كل
+
+330
+00:33:05,860 --> 00:33:11,120
+عنصر في الأولى مع كل عناصر التانية تمام؟ x أكبر أو
+
+331
+00:33:11,120 --> 00:33:16,910
+تساوي صفرand طبعا هذه الخطأ موجودة هنا مش مشكلة ال
+
+332
+00:33:16,910 --> 00:33:25,810
+y أقل من صفر يعني ال x موجبة و ال y سالبة لو
+
+333
+00:33:25,810 --> 00:33:32,150
+جمعتهم حاصل الجمع هيكون أكبر من صفر موجب اعرف ان
+
+334
+00:33:32,150 --> 00:33:36,970
+لو طرحتهم هيكون حاصل طرحهم او الناتج أكبر من صفر
+
+335
+00:33:36,970 --> 00:33:39,890
+false و true
+
+336
+00:33:43,060 --> 00:33:51,140
+نقص نقص Y ليش نقص Y انا حاطيتها هنا لإن ال Y أقل
+
+337
+00:33:51,140 --> 00:33:56,940
+من صفر فهي سالبة فالسالب ماهي السالب بيصير موجبة
+
+338
+00:33:56,940 --> 00:34:03,820
+فبتكون العملية كلها موجبة a
+
+339
+00:34:03,820 --> 00:34:08,840
+non negative number تعكسش لو عكست ممكن تختلف تعكس
+
+340
+00:34:08,840 --> 00:34:18,980
+هذا ايش اللي تعكسY نقص X حرام عليك بتصير false اما
+
+341
+00:34:18,980 --> 00:34:22,540
+عشان اقولك بقولك ماتركسش عشان تظل الأمور في نصابها
+
+342
+00:34:22,540 --> 00:34:25,520
+الصحيحة ماتتوهش اما ال negative number هذا الكلام
+
+343
+00:34:25,520 --> 00:34:31,280
+هاي minus negative number or positive number minus
+
+344
+00:34:31,280 --> 00:34:38,980
+negative number greater than zero لبعدها there
+
+345
+00:34:38,980 --> 00:34:44,290
+exist XThere exists Y يعني على الأقل في المجموعتين
+
+346
+00:34:44,290 --> 00:34:49,970
+بدي أخلق واحد هنا مع واحد من المجموعة التانية بحيث
+
+347
+00:34:49,970 --> 00:34:55,750
+أنه لو كان الأولى موجب سالبة
+
+348
+00:34:55,750 --> 00:35:00,090
+و التانية سالبة حصل
+
+349
+00:35:00,090 --> 00:35:04,690
+طرحهم أكبر
+
+350
+00:35:04,690 --> 00:35:05,210
+من صفر
+
+351
+00:35:10,550 --> 00:35:16,610
+الاختلاف بين اتنين
+
+352
+00:35:16,610 --> 00:35:28,290
+أقل من صفر ليس بالضرورة يكون ناقص واحد ناقص اتنين
+
+353
+00:35:28,290 --> 00:35:31,830
+ايش يساوي واحد اكبر من صفر
+
+354
+00:35:35,990 --> 00:35:41,110
+هتلاقي واحدة X و واحدة Y بتحقق المعادلة هذه فال
+
+355
+00:35:41,110 --> 00:35:47,250
+quantifier تبعنا هذا true هيه
+
+356
+00:35:47,250 --> 00:35:57,530
+الآن X سالب واحد وال Y سالب اتنين هيه حط نقص واحد
+
+357
+00:35:57,530 --> 00:36:03,430
+الله يدك الصح ان شاء الله يا ربناقص ناقص اتنين
+
+358
+00:36:03,430 --> 00:36:08,970
+بتصير ناقص واحد زائد اتنين بتتساوي واحد صح انهم
+
+359
+00:36:08,970 --> 00:36:15,870
+طيب for all x for all y ايش يعني for all for all
+
+360
+00:36:15,870 --> 00:36:20,630
+يعني كل عناصر الأولى مع كل عناصر التانية x لا
+
+361
+00:36:20,630 --> 00:36:29,070
+تساوي صفر و ال y لا تساوي صفر حصل دربهم لا يساوي
+
+362
+00:36:29,070 --> 00:36:30,530
+صفر if and only if
+
+363
+00:36:33,970 --> 00:36:38,410
+The product of any two non-zero numbers is non
+
+364
+00:36:38,410 --> 00:36:44,390
+-zero number if and only if both factors are non
+
+365
+00:36:44,390 --> 00:36:49,810
+-zero true بس لاحظوا ما كنت قاعد بترجم بالعكس
+
+366
+00:36:49,810 --> 00:36:54,870
+بحاول أكتب ال quantifier بلغتنا في المأنثال الأولى
+
+367
+00:36:56,260 --> 00:37:01,500
+كنت بكتب من لغتنا لـ Quantifier لان بحاول أشوف
+
+368
+00:37:01,500 --> 00:37:06,300
+الترجمة للعناصر اللي موجودة عندي خلص ال section
+
+369
+00:37:06,300 --> 00:37:11,420
+وبهيك بنكون خلصنا محاضرتنا لليوم و بيبقى لنا
+
+370
+00:37:11,420 --> 00:37:15,420
+section واحد في الشبتر هذا بنكمل المحاضرة اللي جاي
+
+371
+00:37:15,420 --> 00:37:17,320
+ان شاء الله تبارك و تعالى لأنه خلال ال وقت اللي
+
+372
+00:37:17,320 --> 00:37:20,280
+بقال مش هقدر أخلصه اعطيكوا العافية
+
diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/yo5uTs-agBQ.srt b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/yo5uTs-agBQ.srt
new file mode 100644
index 0000000000000000000000000000000000000000..39b6b2905efb70909f6f71ec0c2b772a08b362e2
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/yo5uTs-agBQ.srt
@@ -0,0 +1,2173 @@
+1
+00:00:21,040 --> 00:00:22,900
+بسم الله والحمد لله والصلاة والسلام علي رسول الله
+
+2
+00:00:22,900 --> 00:00:26,960
+اليوم إن شاء الله يا شباب، هننتقل للموضوع الثاني في
+
+3
+00:00:26,960 --> 00:00:30,580
+الـ chapter الثاني اللي هو الـ structures، وهنتكلم
+
+4
+00:00:30,580 --> 00:00:34,400
+على الـ function، لكن مش هتلاقي أن الموضوع بعيد عن
+
+5
+00:00:34,400 --> 00:00:40,280
+موضوع المجموعات، وعلاقة المجموعات مع بعضها. خلينا
+
+6
+00:00:40,280 --> 00:00:42,760
+نبدأ بـ definition، وهنعيد  الـ slide
+
+7
+00:00:42,760 --> 00:00:47,540
+اللي بعدها. لو كان في عندي مجموعتين non-empty، يعني
+
+8
+00:00:47,540 --> 00:00:52,490
+مش فارغات، فيهم عناصر. يعني،  التخدمنيش في هيك مجال أو
+
+9
+00:00:52,490 --> 00:00:58,870
+في الـ functions، الـ function f from a to b، يعني الـ
+
+10
+00:00:58,870 --> 00:01:03,650
+function هتكون هي عبارة عن انتقال من عناصر a لـ b، و
+
+11
+00:01:03,650 --> 00:01:07,210
+بنرمزها بالشكل هذا: a implies b is an assignment
+
+12
+00:01:07,210 --> 00:01:17,250
+تخصيص كل عنصر في a، of each element in a، to exactly
+
+13
+00:01:17,250 --> 00:01:24,340
+one element of B. يعني بدك تخصص أو تربط أو تعمل
+
+14
+00:01:24,340 --> 00:01:29,780
+اقتران بين كل عنصر في A مع عنصر واحد فقط من الـ B.
+
+15
+00:01:29,780 --> 00:01:35,140
+عشان الكلام هذا، بدي ارجع معاك لاختصار الـ Cartesian أو
+
+16
+00:01:35,140 --> 00:01:38,960
+الـ cross product في المحاضرة الماضية. لما اجينا
+
+17
+00:01:38,960 --> 00:01:44,100
+قلنا لو كان أنا في عندي مجموعتين A، بده تساوي A و
+
+18
+00:01:44,100 --> 00:01:49,960
+B، والـ B المجموعة الثانية كانت واحد واثنين و
+
+19
+00:01:49,960 --> 00:01:56,330
+ثلاثة. جينا قلنا أن a cross الـ b هي عبارة عن
+
+20
+00:01:56,330 --> 00:02:01,010
+المجموعة اللي بتنتج أزواج مرتبة، العنصر فيها الأول
+
+21
+00:02:01,010 --> 00:02:15,630
+من a، والعنصر الثاني من الـ b: a1 a2 و a3، b1 b2 b3 في
+
+22
+00:02:15,630 --> 00:02:21,250
+غير هيك، إن هذا الـ definition تبع الـ Cartesian
+
+23
+00:02:21,250 --> 00:02:26,410
+product هو عبارة عن assignment، تخصيص لكل عنصر في A
+
+24
+00:02:26,410 --> 00:02:31,910
+مع كل عناصر الـ B. فإذن في عندي الـ function هي
+
+25
+00:02:31,910 --> 00:02:36,450
+عبارة عن حالة خاصة من الـ Cartesian. هنا بقول أنا
+
+26
+00:02:36,450 --> 00:02:40,670
+بدي أخصص كل عنصر في الـ A. لاحظ هنا هو نفسه كل عنصر
+
+27
+00:02:40,670 --> 00:02:45,970
+في A مرتبط مع عنصر واحد فقط من الـ B. يعني لا يريد
+
+28
+00:02:45,970 --> 00:02:50,090
+أن يرتبط معهم كلهم، يريد أن يرتبط مع عنصر واحد فقط
+
+29
+00:02:50,090 --> 00:02:54,110
+وليس أكثر من ذلك. لو ارتبط بعنصرين أو أكثر فهو
+
+30
+00:02:54,110 --> 00:02:58,890
+ليست  function. فبالتالي الـ function هي عبارة
+
+31
+00:02:58,890 --> 00:03:02,870
+عن حالة خاصة من الـ cross product. الـ function هي
+
+32
+00:03:02,870 --> 00:03:09,210
+عبارة عن حالة خاصة من الـ cross product. أيوة، الاثنين
+
+33
+00:03:09,210 --> 00:03:15,460
+على سبيل المثال، function من a لـ b حسب الـ definition
+
+34
+00:03:15,460 --> 00:03:25,700
+اللي عندي: a واحد، b واحد. صح؟ function لازم كل عناصر
+
+35
+00:03:25,700 --> 00:03:32,300
+الـ a كلها موجودات، وكل عنصر مرتبط مع عنصر واحد في b.
+
+36
+00:03:32,300 --> 00:03:42,400
+الآن لو أنا قلت a واحد، أو أو سكتت هيك لحالها، هذا
+
+37
+00:03:42,400 --> 00:03:46,020
+ليس function. هذا ليس function. لماذا؟ لأنه بالـ
+
+38
+00:03:46,020 --> 00:03:50,220
+function لازم يكون لكل العناصر. طيب، لو أنا اجيت
+
+39
+00:03:50,220 --> 00:03:59,760
+قلت كمان مرة A .. عفواً، A واحد و A اثنين برضه
+
+40
+00:03:59,760 --> 00:04:05,020
+هذا ليس function. لماذا؟ لأن الـ A هذا ارتبط مع
+
+41
+00:04:05,020 --> 00:04:11,150
+عنصرين مختلفين في B، وبالتالي ليس function. اصبر يا
+
+42
+00:04:11,150 --> 00:04:18,990
+أحمد شوية. a واحد، b واثنين، a واحد، function.
+
+43
+00:04:18,990 --> 00:04:23,050
+function. ليش؟ لأن الـ function هي عبارة عن مجموعة
+
+44
+00:04:23,050 --> 00:04:27,770
+والعنصر هذا هو نفسه العنصر هذا، مكرر. فبالتالي هذا
+
+45
+00:04:27,770 --> 00:04:32,130
+التكرار ملوش معنى عندنا. تمام؟ نرجع نقيد تاني على
+
+46
+00:04:32,130 --> 00:04:36,330
+السريع، الـ definition تبع الـ function عشان نكمل.
+
+47
+00:04:36,330 --> 00:04:43,330
+وبالتالي الـ function من a لـ b is an assignment،
+
+48
+00:04:43,330 --> 00:04:50,650
+تخصيص لكل عنصر في A to exactly one element في B.
+
+49
+00:04:50,650 --> 00:04:59,690
+طيب، الآن لو افترضنا الطلاب والعلامات، هل ينفع أقول
+
+50
+00:04:59,690 --> 00:05:05,590
+إسمك محمد؟ أخد امتياز، أو حصل على امتياز في رياضيات
+
+51
+00:05:05,590 --> 00:05:12,900
+منفصلة وجيد جداً. فعش مش معقول، يعني هو يا امتياز، يا
+
+52
+00:05:12,900 --> 00:05:17,420
+جيد جداً، مافيش الاثنين. مصبوط؟ وبالتالي، هتلاقي
+
+53
+00:05:17,420 --> 00:05:24,600
+أن كل عنصر مرتبط بعنصر واحد فقط. هل ممكن أكثر من
+
+54
+00:05:24,600 --> 00:05:28,220
+عنصر يرتبطوا بنفس العنصر الثاني؟ اه، ينفع، مافيش
+
+55
+00:05:28,220 --> 00:05:31,460
+مشكلة، يكون في عندي أكثر من واحد، لامتياز، مافيش
+
+56
+00:05:31,460 --> 00:05:35,240
+مشكلة في الموضوع. وبالتالي، يعني الأمثلة اللي احنا
+
+57
+00:05:35,240 --> 00:05:42,610
+شفناها: F A1 وB1 عبارة عن function. كذلك الـ
+
+58
+00:05:42,610 --> 00:05:47,110
+function هي تُعرف علي أنها binary relation. ليش
+
+59
+00:05:47,110 --> 00:05:50,950
+binary relation؟ لأن أنا أتكلم على مجموعتين، two
+
+60
+00:05:50,950 --> 00:05:57,670
+sets، والـ binary relation بتنتج أزواج مرتبة. زوج
+
+61
+00:05:57,670 --> 00:06:01,750
+مرتب a و b، x و y، a و b، x ينتمي للمجموعة
+
+62
+00:06:01,750 --> 00:06:07,030
+الأولى a، والـ y ينتمي للمجموعة الثانية b، وشرطها
+
+63
+00:06:07,030 --> 00:06:11,820
+هنا في الـ function، في الـ relation هذه، أن كل عنصر في
+
+64
+00:06:11,820 --> 00:06:16,960
+A بيرتبط to exactly one element in B، مش أكثر.
+
+65
+00:06:16,960 --> 00:06:21,620
+وبالتالي الـ definition أصبح معروف، وهذه هي الـ
+
+66
+00:06:21,620 --> 00:06:25,780
+elements اللي بتنتمي للـ function. لاحظ: element
+
+67
+00:06:25,780 --> 00:06:31,360
+ينتمي إلى function. بتفهم أن الـ function عبارة عن
+
+68
+00:06:31,360 --> 00:06:34,240
+مجموعة. يعني لو في صح وغلط جيت سألتك لحظة، ولـ
+
+69
+00:06:34,240 --> 00:06:42,650
+لحظات: الـ function is a set، true، مش غلط. صح؟ كل
+
+70
+00:06:42,650 --> 00:06:46,810
+function عبارة عن مجموعة، بس مش كل مجموعة function.
+
+71
+00:06:46,810 --> 00:06:51,790
+الـ function هذه عبارة عن مجموعة من الأزواج المرتبة
+
+72
+00:06:51,790 --> 00:06:57,050
+اللي بتعمل اقترانات ما بين الـ a والـ b، وحسب
+
+73
+00:06:57,050 --> 00:07:02,410
+definition، واحد فقط. أحياناً بنسمي الـ function
+
+74
+00:07:02,410 --> 00:07:06,450
+mapping، أو
+
+75
+00:07:06,450 --> 00:07:13,740
+بنسميها transformation، انتقال. انتقال منين؟ للعنصر A
+
+76
+00:07:13,740 --> 00:07:17,760
+لـ B، بحيث أنه أخذ شكل جديد بعد تطبيق الـ function
+
+77
+00:07:17,760 --> 00:07:26,680
+هذه عليه. عادةً
+
+78
+00:07:26,680 --> 00:07:32,820
+بنرمز للزوج المرتب هذا: F of A أو A و B، F of A،
+
+79
+00:07:32,820 --> 00:07:41,120
+بنكتبه على صورة الزوج المرتب هذا: F of A equal B. طبعاً
+
+80
+00:07:41,120 --> 00:07:46,140
+هذا بنسميه element، وهذا
+
+81
+00:07:46,140 --> 00:07:51,660
+بنسميه الـ image أو الصورة حسب الـ definition اللي
+
+82
+00:07:51,660 --> 00:07:55,980
+بيعتمد عليه. هيا
+
+83
+00:07:55,980 --> 00:08:00,460
+عندي a و b كمجموعات، وبقول لي: افحص هل الـ relation
+
+84
+00:08:00,460 --> 00:08:04,940
+هاي، الـ relation هاي عبارة عن function. مباشرة أول
+
+85
+00:08:04,940 --> 00:08:12,340
+شغلة، أتأكد إن كل عناصر a موجودة. A, B, C، عناصرهم
+
+86
+00:08:12,340 --> 00:08:17,440
+موجودة. الشغل الثاني، كل عنصر في A ارتباطه مرة
+
+87
+00:08:17,440 --> 00:08:27,200
+واحدة فقط، مية بالمية. وبالتالي، function G
+
+88
+00:08:27,200 --> 00:08:31,440
+is not a function. ليش؟ لأن الـ C، الـ C مش موجودة
+
+89
+00:08:31,440 --> 00:08:35,160
+عنصر من عناصر الـ A، مش موجود في الـ relation هادي.
+
+90
+00:08:35,160 --> 00:08:39,420
+وبالتالي، it's not a function. الأخيرة،
+
+91
+00:08:42,140 --> 00:08:49,860
+H: A1 B2 C1 A2 A2. معناته هذا العنصر هي موجود
+
+92
+00:08:49,860 --> 00:08:53,440
+وبالتالي مش function. لكن لاحظ لو .. هيختلف الـ
+
+93
+00:08:53,440 --> 00:08:57,620
+decision تبعي، لو كانت هذه واحد، معناته أنا بكرر
+
+94
+00:08:57,620 --> 00:09:03,640
+العنصر جاية في مجموعة الـ B.
+
+95
+00:09:03,640 --> 00:09:08,760
+بيقول عنها: لما يكون عندي F of A equal B، بنقول عن
+
+96
+00:09:08,760 --> 00:09:12,220
+الـ B، الـ Image. عارفين أن دي مجموعة من الـ
+
+97
+00:09:12,220 --> 00:09:16,940
+Definition مهمة. الـ B Image، الـ A كمجموعة هي ..
+
+98
+00:09:16,940 --> 00:09:21,760
+بنسميها domain، المجال. كانوا بيعلمونا ايه في
+
+99
+00:09:21,760 --> 00:09:28,760
+الثانوية بمصطلح المجال. بالنسبي لـ B، سميناها المجال
+
+100
+00:09:28,760 --> 00:09:34,580
+المقابل، أو الـ target، الـ codomain، أو المدى. لأ، مش
+
+101
+00:09:34,580 --> 00:09:38,730
+المدى. المجال المقابل، المدى هي عبارة عن مجموعة جزئية
+
+102
+00:09:38,730 --> 00:09:43,790
+من المجال المقابل. مجموعة الصور، الـ range أو المدى.
+
+103
+00:09:43,790 --> 00:09:48,770
+تمام؟ من a و b هي عبارة عن all images of element of
+
+104
+00:09:48,770 --> 00:09:52,210
+a. مجموعة الصور، وهلا بنجيب لك بالأمثلة كيف أنه
+
+105
+00:09:52,210 --> 00:09:57,710
+بتفرق عن بعضها. وبالتالي الـ range هي عبارة، أو المدى
+
+106
+00:09:57,710 --> 00:10:02,010
+هي عبارة عن مجموعة جزئية من الـ b، من الـ definition
+
+107
+00:10:02,010 --> 00:10:09,010
+الكل. تأكيد: B تنتمي إلى B حيث F of A equal B، يعني الـ
+
+108
+00:10:09,010 --> 00:10:12,210
+B لازم تكون عبارة عن صورة، وبالأمثلة السابقة لما
+
+109
+00:10:12,210 --> 00:10:19,530
+قلنا A بدها تساوي A و B، والـ B قلنا واحد واثنين
+
+110
+00:10:19,530 --> 00:10:25,870
+وثلاثة، وجيت قلت الـ F بدها تساوي الـ relation: A
+
+111
+00:10:25,870 --> 00:10:32,370
+واثنين، و B، وثلاثة. الآن،
+
+112
+00:10:33,200 --> 00:10:37,900
+لو أنا جيت سألتك حسب الـ definition هذا، من الـ
+
+113
+00:10:37,900 --> 00:10:41,880
+domain هاي الـ function، وهي الـ two sets، من الـ
+
+114
+00:10:41,880 --> 00:10:48,200
+domain الـ a، من
+
+115
+00:10:48,200 --> 00:10:54,080
+الـ codomain أو الـ target. عارف ليش سموها target؟ لأن
+
+116
+00:10:54,080 --> 00:11:00,240
+كل عنصر من الـ a بيستهدف عنصر في الـ b. الآن، هاي الـ
+
+117
+00:11:00,240 --> 00:11:01,700
+function، ضال في الـ end، الـ range
+
+118
+00:11:04,470 --> 00:11:09,550
+هي عبارة عن مجموعة جزئية من B، وهي بتجتمع مجموعة
+
+119
+00:11:09,550 --> 00:11:12,270
+الصور المقتنعة مع عناصر الـ A، اللي هم في المثال
+
+120
+00:11:12,270 --> 00:11:16,210
+هذا: اثنين وثلاثة، أو اثنين وثلاثة. مجموعة جزئية زي
+
+121
+00:11:16,210 --> 00:11:20,270
+ما قلنا من الـ B، ولا تساويها، أو proper subset من
+
+122
+00:11:20,270 --> 00:11:28,550
+الـ B. كل
+
+123
+00:11:28,550 --> 00:11:31,850
+عناصر
+
+124
+00:11:31,850 --> 00:11:35,880
+الـ A. احنا نهي المثال. عاماً، لما نروح، هنا قلنا هذه
+
+125
+00:11:35,880 --> 00:11:42,560
+function، وهذه لأ. لماذا؟ لأن الـ C كعنصر في الـ A
+
+126
+00:11:42,560 --> 00:11:46,780
+لا يوجد مكان هنا في الـ function، في المجموعة هذه.
+
+127
+00:11:46,780 --> 00:11:50,780
+وبالتالي هذه ليست function. وبالتالي أول حاجة قلت لك
+
+128
+00:11:50,780 --> 00:11:55,380
+تتأكد إن أنا فعلياً كل عناصر المجموعة موجودة عندي.
+
+129
+00:11:55,380 --> 00:11:59,940
+عناصر أي مجموعة، عناصر الـ domain اللي هي الـ A.
+
+130
+00:12:03,950 --> 00:12:09,330
+هي دالة: a, b, c، الـ a و الـ set: واحد، اثنين، ثلاثة،
+
+131
+00:12:09,330 --> 00:12:15,550
+وهي الاقتران اللي بينهم: f of a .. f .. a واحد، b و
+
+132
+00:12:15,550 --> 00:12:23,970
+اثنين، c واحد. الآن، هي من مجموعة الصور. دماغ ايه؟ هذه
+
+133
+00:12:23,970 --> 00:12:31,050
+function. مظبوط؟ الـ target كل الـ b. ايش الـ range؟ واحد
+
+134
+00:12:31,050 --> 00:12:34,330
+واثنين. مش كل الصور اللي موجودة عندي هنا، أو مش كل
+
+135
+00:12:34,330 --> 00:12:40,250
+العناصر اللي في الـ B عبارة عن صور. okay. الآن وأنا
+
+136
+00:12:40,250 --> 00:12:44,050
+جيت من الأمثلة اللي موجودة على الـ functions، ارتباط
+
+137
+00:12:44,050 --> 00:12:49,810
+الطالب بالتخصص. ارتباط الطالب بالتخصص. يعني إذا قلت
+
+138
+00:12:49,810 --> 00:12:53,890
+إن أنا في عندي function F: الـ student والـ major
+
+139
+00:12:53,890 --> 00:12:57,610
+تبعه. الطلاب اللي عندي: مونة، وأحمد، وسالي، ورامي،
+
+140
+00:12:58,270 --> 00:13:01,930
+والتخصصات اللي عندي أربعة: computer science، الـ IT، و
+
+141
+00:13:01,930 --> 00:13:05,830
+الـ software development، والـ computer engineering.
+
+142
+00:13:05,830 --> 00:13:18,110
+الآن، الطالب كم تخصص إله في الجامعة؟ تخصص واحد. بدك
+
+143
+00:13:18,110 --> 00:13:23,460
+تخصص ثاني، معناته إما بدك تغير الـ track كله، وبالتالي
+
+144
+00:13:23,460 --> 00:13:27,260
+تحتفظ بتخصص واحد لولي جديد، أو تتسجل في الجامعة
+
+145
+00:13:27,260 --> 00:13:33,620
+كطالب جديد، وتدرس من تخصص جديد. بس في الآخر، بس في
+
+146
+00:13:33,620 --> 00:13:38,200
+الآخر، الطالب بينجو سيني اللي بمثل الرقم الجامعي لا
+
+147
+00:13:38,200 --> 00:13:42,980
+يحتمل إلا ارتباط بتخصص واحد فقط. وبالتالي، هل
+
+148
+00:13:42,980 --> 00:13:46,040
+ممكن يكون فيه أكثر من تخصص طلاب؟ اه، ممكن، مافيش مشكلة
+
+149
+00:13:46,040 --> 00:13:50,660
+في الموضوع. يعني الآن، اقتران هذا ممكن أنا أمثله
+
+150
+00:13:50,660 --> 00:13:57,450
+بجدول زي ما هو قدامي هنا، أو أروح أمثله بالأسهم، عشان
+
+151
+00:13:57,450 --> 00:14:01,990
+أبين الـ relation اللي موجودة عندي هنا. من السهم، هي
+
+152
+00:14:01,990 --> 00:14:06,330
+الطالب، وهي الـ major. مونة ايش تخصصها؟ computer
+
+153
+00:14:06,330 --> 00:14:10,470
+engineering. رامي ايش تخصصه؟ computer science. ونفس
+
+154
+00:14:10,470 --> 00:14:12,690
+الكلام، نفس المعلومة هذه، أنا بقدر أخدها من الجدول
+
+155
+00:14:12,690 --> 00:14:18,630
+هنا. أنا لا أتكلم على طريقة تمثيل العناصر، أكتبها
+
+156
+00:14:18,630 --> 00:14:21,270
+بأزواج مرتبة، أكتبها من خلال جدول، أو أمثلها
+
+157
+00:14:21,270 --> 00:14:24,270
+بالأسهم، أو بالـ relation اللي موجودة عندها، القدر
+
+158
+00:14:24,270 --> 00:14:28,110
+اللي عندي. أنا لازم أفهم أنه لما أتكلم على function، كل
+
+159
+00:14:28,110 --> 00:14:30,370
+عناصر الـ domain لازم يكون لها ارتباط.
+
+160
+00:14:36,450 --> 00:14:39,550
+طيب، الآن انتقلنا من تعريف الـ function، بعد ما
+
+161
+00:14:39,550 --> 00:14:42,190
+عرفنا الـ function والأمور تمام. الآن بدي أنتقل
+
+162
+00:14:42,190 --> 00:14:48,590
+لخصائص الـ function. خصائص الـ function: أول حاجة
+
+163
+00:14:48,590 --> 00:14:54,930
+بنقول عن الـ function onto أو surjective، لما يكون
+
+164
+00:14:54,930 --> 00:14:59,630
+الـ range، لما يكون الـ range اللي هي مجموعة الصور
+
+165
+00:14:59,630 --> 00:15:06,070
+تساوي الـ Target Set أو تساوي الـ Codomain. بقول عن
+
+166
+00:15:06,070 --> 00:15:12,390
+الـ Function تبعتها Onto. لما كمان مرة بتكون عناصر
+
+167
+00:15:12,390 --> 00:15:19,970
+المدى هي تساوي كل عناصر المجال المقابل. لما تكون
+
+168
+00:15:19,970 --> 00:15:25,610
+عند الـ range تبعت الـ F تساوي كل الـ B، تساوي كل الـ B.
+
+169
+00:15:29,560 --> 00:15:32,460
+بالمثال اللي عندنا هنا، يعني على الـ slide: A و B و C،
+
+170
+00:15:32,460 --> 00:15:39,240
+على رأس المجموعة A، على رأس المجموعة B: واحد واثنين.
+
+171
+00:15:39,240 --> 00:15:47,360
+الآن: F of واحد: A واحد، B واثنين، C واحد. الآن ايش الـ
+
+172
+00:15:47,360 -->
+
+223
+00:20:12,740 --> 00:20:16,740
+ال domain  هدى الدالة حققت المواصفات هدى بتكون
+
+224
+00:20:16,740 --> 00:20:20,520
+objective تعالى شوف المثال اللي موجود عندي هنا هو
+
+225
+00:20:20,520 --> 00:20:28,350
+ال a  {a, b, c}  و ال b {1, 2, 3} وهي ال function f
+
+226
+00:20:28,350 --> 00:20:36,450
+a واحد، b  اثنين، c ثلاثة، الان one to one الصور
+
+227
+00:20:36,450 --> 00:20:39,450
+كل صورة موجودة مع عنصر واحد أو بتمثل اقتراح لعنصر
+
+228
+00:20:39,450 --> 00:20:46,070
+واحد فقط صحيح، و on to، on to  معاه by adjective الآن
+
+229
+00:20:46,070 --> 00:20:49,390
+يا شباب لما أتكلم على one to one و on to أو by
+
+230
+00:20:49,390 --> 00:20:52,890
+adjective function مباشرة، الـ Function بدها تكون ..
+
+231
+00:20:52,890 --> 00:20:55,170
+أو عفوا الـ Cardinality للمجموعة الـ A للـ domain
+
+232
+00:20:55,170 --> 00:20:59,290
+لازم يساوي Cardinality للثانية وإلا عمره ما هذا
+
+233
+00:20:59,290 --> 00:21:02,530
+الكلام حيصير لو أتيت في لحظة من اللحظات سألتك هل
+
+234
+00:21:02,530 --> 00:21:06,930
+الـ Function هذه one to one أو on to مباشرة بتقدر
+
+235
+00:21:06,930 --> 00:21:10,830
+تحكم أو objective تحكم عليها من عدد، ايش؟ اختلاف عدد
+
+236
+00:21:10,830 --> 00:21:14,890
+العناصر، بالطبع، بتقدر تنفيه لو عدد العناصر
+
+237
+00:21:14,890 --> 00:21:18,770
+مختلف بتقدر تنفيه أو تثبته، أجي أقولك والله في عندي
+
+238
+00:21:18,770 --> 00:21:21,890
+دالة Function أو الـ Function اللي عندي هنا ..
+
+239
+00:21:21,890 --> 00:21:26,770
+الثلاثة مش موجودة تمام؟ وبعدين بقولك الـ function
+
+240
+00:21:26,770 --> 00:21:30,170
+هذه bijective؟
+
+241
+00:21:30,170 --> 00:21:35,970
+لا .. مستحيل .. ليش؟ لأن حتما عنصر من العناصر هذه
+
+242
+00:21:35,970 --> 00:21:40,590
+اللي هي الـ C لازم تتعرف والثلاثة مش موجودة، إما
+
+243
+00:21:40,590 --> 00:21:44,070
+بدي أغيرها باثنين أو بدي أغيرها بواحد وهيك أنا
+
+244
+00:21:44,070 --> 00:21:48,710
+ضيعت خاصية اللي هي ال one to one، خاصية ال one to
+
+245
+00:21:48,710 --> 00:21:53,240
+one وبالتالي بطلت by adjective، خاصية الـ one to one
+
+246
+00:21:53,240 --> 00:22:00,560
+وبطلت by adjective كذلك، لو كان عدد عناصر
+
+247
+00:22:00,560 --> 00:22:06,900
+الـ B أكبر زي ما كان فيهم الأربعة، تمام، هذه function
+
+248
+00:22:06,900 --> 00:22:13,340
+one to one بس مش onto، تمام؟ لأن الأربعة موجودة في
+
+249
+00:22:13,340 --> 00:22:16,520
+الـ domain، عفوا في الـ codomain  ومش موجودة في الـ
+
+250
+00:22:16,520 --> 00:22:21,900
+range وبالتالي is not onto، عليه كده بحياته أنا
+
+251
+00:22:21,900 --> 00:22:25,140
+بقدر أتكلم أنه عشان تكون الـ .. لو كانت الدالة
+
+252
+00:22:25,140 --> 00:22:29,040
+bijective مباشرة، الـ cardinality للـ A بده تساوي الـ
+
+253
+00:22:29,040 --> 00:22:35,780
+cardinality للـ B، التخصصات
+
+254
+00:22:35,780 --> 00:22:39,220
+اللي عندنا قبل شوية ذكرناها، computer science،
+
+255
+00:22:39,220 --> 00:22:44,960
+computer engineering، IT، software development، أربع
+
+256
+00:22:44,960 --> 00:22:45,680
+تخصصات
+
+257
+00:22:48,610 --> 00:22:52,450
+شوف الدالة هذه، F of Muna، Computer Engineering، تخصص
+
+258
+00:22:52,450 --> 00:22:54,770
+Muna، Computer Engineering، أحمد، Computer Science،
+
+259
+00:22:54,770 --> 00:22:59,070
+سالي و راني، Computer Science، هل الدالة هذه one to
+
+260
+00:22:59,070 --> 00:23:05,090
+one؟ لأ، one to one لإيش؟ لأن في عند أحمد و راني
+
+261
+00:23:05,090 --> 00:23:09,410
+اللي هم نفس التخصص أو بينتموا لنفس التخصص اللي
+
+262
+00:23:09,410 --> 00:23:14,690
+موجود، بينتموا لنفس الصورة، لأ أنا ما سألتش على ال on
+
+263
+00:23:14,690 --> 00:23:26,370
+to، الآن أنا بسأل على one to one، هذه الدالة
+
+264
+00:23:26,370 --> 00:23:35,250
+ليست one to one، لأن كل طالب له تخصص مختلف، الدالة
+
+265
+00:23:35,250 --> 00:23:41,710
+بقول عنها identity function لو كانت معرفة من
+
+266
+00:23:44,020 --> 00:23:48,540
+هي عبارة عن relation بين عناصر مجموعة واحدة من ال
+
+267
+00:23:48,540 --> 00:23:54,140
+A إلى ال A، بيسميها identity function، لو كان كل F
+
+268
+00:23:54,140 --> 00:23:59,920
+of a بيتساوي a، يعني مش بس هيك، لو كانت الـ F من الـ A
+
+269
+00:23:59,920 --> 00:24:07,680
+إلى الـ A و f of a equal a، هذه بقول عنها
+
+270
+00:24:07,680 --> 00:24:21,240
+identity، ولا لأ، bijective function لما
+
+271
+00:24:21,240 --> 00:24:27,120
+بيكون الـ function اللي عندي بتتكلم فيها على مجموعة
+
+272
+00:24:27,120 --> 00:24:30,400
+أكبر من تلت أو خمس أرقام، لما أتكلم على الـ real
+
+273
+00:24:30,400 --> 00:24:34,060
+number أو الـ integer number أو الـ natural number
+
+274
+00:24:34,060 --> 00:24:37,910
+بصير أعتمد على مين؟ على الرموز اللي اتبعتي وبتصير
+
+275
+00:24:37,910 --> 00:24:41,330
+الدالة لها معنى آخر أو أعرف الدالة بشكل آخر
+
+276
+00:24:41,330 --> 00:24:45,190
+صعب أن أحصره بالأزواج المرتبة، بلجأ لمين؟ للـ
+
+277
+00:24:45,190 --> 00:24:48,230
+definition أو الخواص اللي احنا شفناها سابقا، لما
+
+278
+00:24:48,230 --> 00:24:52,450
+بلجأ، بقول: هاي في عندي function معرفة من R إلى ال R
+
+279
+00:24:52,450 --> 00:24:55,970
+ما أقدرش أقول عنها identity function اللي قلنا لو
+
+280
+00:24:55,970 --> 00:25:01,910
+كانت F of X بتساوي X، تمام، من الـ R إلى الـ R، يعني
+
+281
+00:25:01,910 --> 00:25:07,050
+بينتمي الـ domain أعداد حقيقية والـ target عدد
+
+282
+00:25:07,050 --> 00:25:14,130
+حقيقي، F of X بيتساوي الـ 2X، F of X بيتساوي 2X و
+
+283
+00:25:14,130 --> 00:25:17,890
+بيكمل، طبعا بكتب الدالة، الصورة تبعها، هيها: F of واحد
+
+284
+00:25:17,890 --> 00:25:20,990
+تساوي اثنين، F of ثلاثة، ستة، F of سالب ثلاثة، سالب
+
+285
+00:25:20,990 --> 00:25:25,790
+ستة، بنبنيها على مين؟ على الـ Definition الآن، F of
+
+286
+00:25:25,790 --> 00:25:26,810
+جذر الاثنين،
+
+287
+00:25:33,090 --> 00:25:38,910
+هل بقدر أحكم على هيك دالة one to one أنتم؟ حرام
+
+288
+00:25:38,910 --> 00:25:41,070
+عليك، تقدر، ممكن، نعم،
+
+289
+00:25:44,410 --> 00:25:49,270
+أيوه، الآن، أول ما تبدأ تفكر إذا أنت بتفكر باتجاهها
+
+290
+00:25:49,270 --> 00:25:52,610
+أن الدالة هذه مش onto أو مش by adjective أو مش
+
+291
+00:25:52,610 --> 00:25:56,630
+one to one، بتروح تجيب .. تفكر .. تجيب مثال واحد
+
+292
+00:25:56,630 --> 00:26:02,030
+يُدلل على أنَّها دالة مش صحيحة، مثلا لو أنا جيت قلت لك
+
+293
+00:26:02,030 --> 00:26:05,090
+f
+
+294
+00:26:05,090 --> 00:26:11,870
+of x بده يساوي x تربيع، f of x بده تساوي x تربيع
+
+295
+00:26:13,050 --> 00:26:23,670
+الدالة هذه، هل هي is F one to one؟ هل الـ F دالة one
+
+296
+00:26:23,670 --> 00:26:28,350
+to one؟ لأ، لإيش؟
+
+297
+00:26:28,350 --> 00:26:33,170
+لأن عندي أنا الآن الاثنين بتنتمي للـ real number as
+
+298
+00:26:33,170 --> 00:26:40,070
+image، صح؟ الاثنين؟ أو الأربعة عشان نريح حالنا، الـ
+
+299
+00:26:40,070 --> 00:26:48,100
+image as image، one image  ترتبط بعنصرين، F of سالب اثنين
+
+300
+00:26:48,100 --> 00:26:55,440
+تساوي أربعة، و F of اثنين تساوي أربعة، والاثنين لا تساوي
+
+301
+00:26:55,440 --> 00:27:02,080
+السالب اثنين، وبالتالي صار في عندي one image، تمام
+
+302
+00:27:02,080 --> 00:27:07,760
+مرتبطة مع two different elements، في عندي one image
+
+303
+00:27:07,760 --> 00:27:13,120
+لـ two different elements، وبالتالي one to one is not
+
+304
+00:27:13,120 --> 00:27:18,080
+one to one، هل هي bijective؟ عفوا، bijective، نعم، هل هي
+
+305
+00:27:18,080 --> 00:27:22,040
+bijective؟ لأ، خلصنا، ما عادش نطول، one to one is
+
+306
+00:27:22,040 --> 00:27:25,960
+not bijective، هل هي onto؟ صحيح، ممكن تكونوا، هل هي
+
+307
+00:27:25,960 --> 00:27:29,600
+onto؟ ممكن تكونوا، الآن لو فكرت تجيب counter
+
+308
+00:27:29,600 --> 00:27:33,200
+example مش هتقدر، معناته بيبقى تروح باتجاه العكس
+
+309
+00:27:33,200 --> 00:27:38,440
+تثبت أن الدالة هذه is not onto، هتوصلوا
+
+310
+00:27:38,440 --> 00:27:43,300
+contradiction في الآخر، السؤال الآن كمان مرة، is
+
+311
+00:27:43,300 --> 00:27:49,700
+أمته .. هل هي onto؟ يعني، ببساطة، هل الـ range
+
+312
+00:27:49,700 --> 00:27:58,620
+يساوي الـ R؟ هل الـ range يساوي الـ R؟ هل الـ range
+
+313
+00:27:58,620 --> 00:28:03,820
+يساوي الـ R يا شباب؟ اه .. اه .. اه .. اه ..
+
+314
+00:28:03,820 --> 00:28:09,440
+ما بتحتاجش .. ما بتحتاجش شطارة كتير، الآن الفكرة كانت
+
+315
+00:28:09,440 --> 00:28:13,960
+التالي، عشان تثبت إنها onto، تفترض أن في عندك
+
+316
+00:28:13,960 --> 00:28:20,600
+element بينتمي لمجموعة الصور، وإذا قدرت تكتب على
+
+317
+00:28:20,600 --> 00:28:25,480
+صورة أو لجيت له X تنتمي للـ R، معناته عبارة عن onto
+
+318
+00:28:25,480 --> 00:28:36,260
+يعني هكذا، ستقول مثلا الـ X تنتمي للـ R، الـ range
+
+319
+00:28:36,260 --> 00:28:40,600
+تمام؟
+
+320
+00:28:40,600 --> 00:28:43,760
+إذا كانت الـ X بتنتمي للـ range، معناته there
+
+321
+00:28:43,760 --> 00:28:55,580
+exist some Y تنتمي للـ R للـ domain such
+
+322
+00:28:55,580 --> 00:29:05,780
+that F of Y يساوي X، الآن لو كانت الدالة onto، لو
+
+323
+00:29:05,780 --> 00:29:08,660
+كانت الدالة onto، معناته .. أنا قاعد بقولك التالي:
+
+324
+00:29:08,660 --> 00:29:12,880
+هاي فيه عندي صورة، الصورة هذه لازم .. أي عنصر ..
+
+325
+00:29:12,880 --> 00:29:17,700
+random number، معناته فيه عنصر في الـ Y أو عفوا في
+
+326
+00:29:17,700 --> 00:29:21,800
+الـ R اللي هي بالـ domain بحيث أن F of Y بتساوي X، طيب
+
+327
+00:29:21,800 --> 00:29:26,900
+F of Y ايش بتساوي يا شباب؟ اثنين Y، مضبوط؟ حسب الـ
+
+328
+00:29:26,900 --> 00:29:33,960
+definition، أو عفوا Y تربيع .. آسف، F of Y بيبقى
+
+329
+00:29:33,960 --> 00:29:40,540
+تساوي Y تربيع، بيبقى تساوي X، الـ
+
+330
+00:29:40,540 --> 00:29:49,040
+Y ايش بتساوي؟ جذر الـ X، تنتمي للـ R؟ مش
+
+331
+00:29:49,040 --> 00:29:57,860
+بالضرورة، ليش؟ سالب، الآن لو أنا أخدت رقم سالب من
+
+332
+00:29:57,860 --> 00:30:03,950
+الـ R، مضبوط؟ هيك، الآن السالب ينتمي لرئيس الـ
+
+333
+00:30:03,950 --> 00:30:09,930
+number ولا لا ينتمي؟ ينتمي، تمام؟ ينتمي، معناته أنا
+
+334
+00:30:09,930 --> 00:30:15,890
+في عندي هيك، في عندي اثنين أو في عندي X، اثنين X
+
+335
+00:30:15,890 --> 00:30:22,630
+يساوي سالب واحد، هل بقدر لقيمة أوجد، أفرض X تربيع بـ
+
+336
+00:30:22,630 --> 00:30:28,980
+تساوي سالب واحد، هل في عندي رقم، لما أنا برجع في الـ
+
+337
+00:30:28,980 --> 00:30:32,500
+number بالـ R، السالب واحد، لأ، ما عنديش، معناته ده
+
+338
+00:30:32,500 --> 00:30:37,040
+اللي هي دي is not onto، هكذا، شوف لما أنا مشيت مع
+
+339
+00:30:37,040 --> 00:30:40,740
+المثال أو مع الـ definition خطوة خطوة، وصلت و لحاله
+
+340
+00:30:40,740 --> 00:30:43,380
+قال: اتفضل، هاي الـ counter example بين يديك، باختصار
+
+341
+00:30:43,380 --> 00:30:47,540
+تسبق معك الأمور، نعم، ايه كيف؟
+
+342
+00:30:52,890 --> 00:30:55,290
+أه، بس ممتاز من حيث الـ definition، جاي بقولك من R لـ
+
+343
+00:30:55,290 --> 00:31:00,230
+R مش على كيفك، أيامك، تكييف المسألة، أنا جاي بقولك
+
+344
+00:31:00,230 --> 00:31:05,790
+هي المسألة، بقولك R لـ R ما قلت لكش لـ R positive، لو
+
+345
+00:31:05,790 --> 00:31:13,010
+قلت لك لـ R positive، معناته هي onto، ممتاز
+
+346
+00:31:13,010 --> 00:31:16,650
+وهي الـ onto، ايش معناها؟ أن الـ range يساوي كل
+
+347
+00:31:18,960 --> 00:31:22,660
+يساوي كل، أنت بقى بتقول أن والله الـ range هي عبارة
+
+348
+00:31:22,660 --> 00:31:26,460
+عن positive real number، والـ positive real
+
+349
+00:31:26,460 --> 00:31:30,360
+number هي عبارة عن مجموعة proper subset، okay، مش
+
+350
+00:31:30,360 --> 00:31:34,520
+مشكلة، نفس المعنى في الآخر، لكن عند النفي يا شباب
+
+351
+00:31:34,520 --> 00:31:38,160
+دايما بنلجأ لشغل اسمها الـ counter example، بتجيب
+
+352
+00:31:38,160 --> 00:31:41,600
+المثال اللي بينفي الموضوع، بتجيب المثال اللي بينفي
+
+353
+00:31:41,600 --> 00:31:47,200
+الموضوع من
+
+354
+00:31:47,200 --> 00:31:54,440
+الدوال، من الدوال المهمة اللي بتلزمنا في شغلنا
+
+355
+00:31:54,440 --> 00:31:57,640
+فاحنا في الـ computer science أو related discipline
+
+356
+00:31:57,640 --> 00:32:01,500
+الـ floor والـ ceiling، الـ floor والـ ceiling
+
+357
+00:32:01,500 --> 00:32:06,800
+الأرضية والسقف، الـ ceiling سقف، الـ floor أرضية
+
+358
+00:32:06,800 --> 00:32:10,660
+طبعا هذه الدالة أو الدوال هذه معرفة من real
+
+359
+00:32:10,660 --> 00:32:11,140
+number
+
+360
+00:32:14,380 --> 00:32:17,880
+لـ Integer، من الـ Real Number لـ Integer، وعشان
+
+361
+00:32:17,880 --> 00:32:21,340
+أتخلص من الغموض أو اللبس اللي ممكن يصير فيه عندك في
+
+362
+00:32:21,340 --> 00:32:25,680
+الـ Definition، دائما استحضر أن شريط الأعداد أو خط
+
+363
+00:32:25,680 --> 00:32:30,780
+الأعداد، اعمله بدل ما هو أفقي، اعمله عمودي، صفر، واحد،
+
+364
+00:32:30,780 --> 00:32:36,240
+اثنين، هي سالب واحد، وسالب اثنين، وبضل ماشي إلى ما
+
+365
+00:32:36,240 --> 00:32:44,020
+لانهاية، الآن لو أنا جيت قلت الـ floor للواحد فاصلة
+
+366
+00:32:44,020 --> 00:32:51,760
+سبعة خمسة، مش بياخد real number؟ واحد .. واحد ..
+
+367
+00:32:51,760 --> 00:32:52,020
+واحد .. واحد .. واحد .. واحد .. واحد .. واحد ..
+
+368
+00:32:52,020 --> 00:32:53,400
+واحد .. واحد .. واحد .. واحد .. واحد .. واحد ..
+
+369
+00:32:53,400 --> 00:32:54,320
+واحد .. واحد .. واحد .. واحد .. واحد .. واحد ..
+
+370
+00:32:54,320 --> 00:32:55,020
+واحد .. واحد .. واحد .. واحد .. واحد .. واحد ..
+
+371
+00:32:55,020 --> 00:32:58,000
+واحد .. واحد .. واحد .. واحد .. واحد .. واحد ..
+
+372
+00:32:58,000 --> 00:32:58,040
+واحد .. واحد .. واحد .. واحد .. واحد .. واحد ..
+
+373
+00:32:58,040 --> 00:32:58,440
+واحد .. واحد .. واحد .. واحد .. واحد .. واحد ..
+
+374
+00:32:58,440 --> 00:33:06,000
+واحد .. واحد .. واحد .. واحد ..
+
+375
+00:33:06,000 --> 00:33:14,060
+واحد .. والـ floor هي عبارة عن أكبر عدد صحيح أصغر
+
+376
+00:33:14,060 --> 00:33:18,360
+من القيمة الحقيقية الموضوعة لك أو يساويها، طبعا عشان
+
+377
+00:33:18,360 --> 00:33:23,340
+تكون دائما في نفس المستوى، يعني هيك المفروض الـ
+
+378
+00:33:23,340 --> 00:33:27,920
+floor هي
+
+379
+00:33:27,920 --> 00:33:28,900
+الـ largest
+
+380
+00:33:31,570 --> 00:33:35,510
+Integer أو عدد صحيح بحيث أن الـ Z هتكون أكبر أو
+
+381
+00:33:35,510 --> 00:33:40,670
+عفوا، أقل أو تساوي الـ R، أقل أو تساوي الـ R، الآن لما
+
+382
+00:33:40,670 --> 00:33:44,870
+أنا بدي أجي هنا واحد خمسة وسبعين، هيها هنا تقريبا الـ
+
+383
+00:33:44,870 --> 00:33:48,110
+الـ
+
+384
+00:33:48,110 --> 00:33:57,670
+floor تبعها، أكبر عدد صحيح أقل منها، واحد، لو اجيت
+
+385
+00:33:57,670 --> 00:34:01,230
+مع السالب مثلا،
+
+386
+00:34:01,700 --> 00:34:09,560
+سالب واحد فاصلة خمسة وسبعين، الـ floor تبعها سالب
+
+387
+00:34:09,560 --> 00:34:17,460
+اثنين، الـ floor تبعها سالب اثنين، أكبر عدد صحيح أقل
+
+388
+00:34:17,460 --> 00:34:25,400
+منها سالب اثنين، يعني هنا قلنا واحد، لما قلنا هنا
+
+389
+00:34:25,400 --> 00:34:28,900
+سالب سبعة وخمسة
+
+390
+00:34:31,340 --> 00:34:35,020
+سالب اثنين، لأنه، ليش أنا ركزت على المثال هذا هيك
+
+391
+00:34:35,020 --> 00:34:39,320
+وقلت لك دائما خلي خط الأعداد عمودي، بسهل عليك حكاية
+
+392
+00:34:39,320 --> 00:34:42,940
+floor و ceiling، الآن كثير من الشباب لما بيغلطوا في
+
+393
+00:34:42,940 --> 00:34:48,280
+مثال زي هذا، ايش هو بيساوي؟ إذا كانت هذه واحد، فهذه
+
+394
+00:34:48,280 --> 00:34:52,580
+سالب واحد، وكان الله بالسر عليهم، لا يا صاحبي
+
+445
+00:40:08,640 --> 00:40:13,100
+ده إيش، بدنا نأخره شوية، أحسن، بس هنشوف الفكرة أين
+
+446
+00:40:13,100 --> 00:40:16,940
+بدك تمشي، بدك تحاول تشتغل على الـ definition، بدك
+
+447
+00:40:16,940 --> 00:40:20,380
+تشتغل على الـ definition، الفكرة في هو أن هي الـ
+
+448
+00:40:20,380 --> 00:40:20,720
+definition
+
+449
+00:40:23,690 --> 00:40:28,110
+فإذا أنا بدي آخذ عنصرين مختلفين من الـ range لازم
+
+450
+00:40:28,110 --> 00:40:32,090
+يكونوا عنصرين مختلفين في الـ domain، و إلا يعني
+
+451
+00:40:32,090 --> 00:40:35,230
+هيك لو قلت أن في عندي صورتين مختلفتين F of X لا
+
+452
+00:40:35,230 --> 00:40:40,950
+تساوي F of Y، معناته حتما X لا تساوي Y، هذا تعريف الـ
+
+453
+00:40:40,950 --> 00:40:43,430
+one to one، وبالتالي أنا بدي أمشي بالـ definition
+
+454
+00:40:43,430 --> 00:40:47,430
+لحد ما أصل لمين؟ للكلام اللي مولود هان، سيبونا منه
+
+455
+00:40:47,430 --> 00:40:49,590
+لحد ما نصل لموضوع الـ definition أو الإثبات اللي
+
+456
+00:40:49,590 --> 00:40:53,380
+بنتكلم فيه، إن شاء الله تعالى، ننتقل لخاصية بعدها وهي
+
+457
+00:40:53,380 --> 00:40:57,440
+خاصية أو موضوع الـ composition، الـ composition هي
+
+458
+00:40:57,440 --> 00:41:02,040
+عبارة عن function أو انتقال للـ function اللي موجود
+
+459
+00:41:02,040 --> 00:41:08,700
+عندي، لو كنت بتكلم على two functions f و g، جي معرفة
+
+460
+00:41:08,700 --> 00:41:17,600
+من الـ A للـ B، و الـ f معرفة من الـ B للـ C، يعني بين
+
+461
+00:41:17,600 --> 00:41:24,510
+جثتين، بين جثتين، الـ target set تبعتي الأولى تمثل الـ
+
+462
+00:41:24,510 --> 00:41:31,070
+domain تبعتي الثانية بالضبط، ممكن أحصل على function
+
+463
+00:41:31,070 --> 00:41:37,170
+من A لـ C، ممكن أحصل على function من A لـ C اللي احنا
+
+464
+00:41:37,170 --> 00:41:43,710
+بنسميها composition f circle g أو fog، اللي هي الـ
+
+465
+00:41:43,710 --> 00:41:46,430
+composition تبع الـ g، و اللي هي بتساوي
+
+466
+00:41:50,180 --> 00:41:58,040
+G of A، الآن F of، إيش اللي لازم يكون جوا الجثة هنا
+
+467
+00:41:58,040 --> 00:42:02,060
+يا شباب؟ إيش العنصر هذا؟ لازم يكون ينتمي لمين؟
+
+468
+00:42:02,060 --> 00:42:05,380
+العنصر
+
+469
+00:42:05,380 --> 00:42:09,520
+اللي لازم يكون جوا الجثة بينتمي لمين؟ بينتمي للـ B
+
+470
+00:42:09,520 --> 00:42:16,400
+للـ domain تبع الـ F، بينتمي للـ domain، كمان مرة لما
+
+471
+00:42:16,400 --> 00:42:21,060
+أنا كنت بقول هاي الـ F معرفة من الـ A إلى الـ B، سيبك
+
+472
+00:42:21,060 --> 00:42:25,480
+من المثال هذا، و دي هتقول اللي قلت لك الـ F of بده
+
+473
+00:42:25,480 --> 00:42:31,540
+تساوي كده، العناصر اللي هنا من الـ domain، مصبوط، و
+
+474
+00:42:31,540 --> 00:42:35,880
+هذه العناصر اللي هنا بتكون الـ image أو الـ code
+
+475
+00:42:35,880 --> 00:42:41,280
+domain ولا لأ؟ نفس الكلام اللي أنا بدي أسقطه هنا من
+
+476
+00:42:41,280 --> 00:42:45,930
+العنصر اللي بده يكون هنا من عناصر الـ domain، domain
+
+477
+00:42:45,930 --> 00:42:57,650
+الـ F اللي هي B، مصبوط؟ طيب G of الـ A إيش بتساوي؟
+
+478
+00:42:57,650 --> 00:43:04,810
+B، اللي هي بتنتمي لمين؟ للـ code domain تبعتي الـ B
+
+479
+00:43:04,810 --> 00:43:09,530
+وبالتالي هذه المعادلة بتكون صحيحة، هيك يعني، الآن
+
+480
+00:43:09,530 --> 00:43:13,150
+الدالة تبعتي عشان تكون معرفة صح، لازم يكون كل
+
+481
+00:43:13,150 --> 00:43:18,160
+element، بمثل عناصر من الـ domain تبعتها، من الـ
+
+482
+00:43:18,160 --> 00:43:23,340
+V، وبما أن الدالة هي  from the inside، F of A أو G of
+
+483
+00:43:23,340 --> 00:43:28,200
+A، عفوا الـ G of A هي عبارة عن صورة، يعني هي عبارة عن
+
+484
+00:43:28,200 --> 00:43:34,120
+عنصر موجود في مين؟ موجود في B، وبالتالي الـ
+
+485
+00:43:34,120 --> 00:43:37,420
+definition تبعت الـ composition صحيحة، ما فيش فيه
+
+486
+00:43:37,420 --> 00:43:37,800
+مشكلة
+
+487
+00:43:47,500 --> 00:43:53,300
+كيف؟ لأ أنا حصلت على دالة جديدة من A لـ C، أنا حصلت
+
+488
+00:43:53,300 --> 00:44:00,940
+على دالة جديدة من A لـ C، الدالة اسمها F circle G، F
+
+489
+00:44:00,940 --> 00:44:08,420
+circle G، ومن اسمها أن هذه عبارة عن F of G of X
+
+490
+00:44:20,710 --> 00:44:24,250
+تعال نشوف، نعمل composition، أوكي، بدي أعمل
+
+491
+00:44:24,250 --> 00:44:28,910
+composition بين دالتين، لو فرضنا هي F و G موجودة عندكم
+
+492
+00:44:28,910 --> 00:44:35,070
+معرفات من الـ R للـ R، إيش يعني R للـ R؟ يعني هذه هي نفسها
+
+493
+00:44:35,070 --> 00:44:42,730
+هذه، وبالتالي بقدر أحصل على composition من الـ R للـ R
+
+494
+00:44:42,730 --> 00:44:47,690
+الـ composition، تابعها مفادها يا شباب، الـ composition
+
+495
+00:44:47,690 --> 00:45:02,960
+تابعها مفادها F of G of X، بشكل هذا، يعني أنا ممكن
+
+496
+00:45:02,960 --> 00:45:06,080
+أطبق الـ G of X في الأول، الـ G، وبعدين ممكن أطبق من
+
+497
+00:45:06,080 --> 00:45:14,880
+الـ F، طيب لو أنا قلت لك F circle G of 2 إيش تساوي؟
+
+498
+00:45:14,880 --> 00:45:21,830
+معناه F of G of 2، جي أوف اثنين شو بتساوي حسب الـ
+
+499
+00:45:21,830 --> 00:45:28,330
+definition؟ هي 6، مصبوط، اف أوف اثنين ضرب ثلاثة أو
+
+500
+00:45:28,330 --> 00:45:35,770
+ثلاثة ضرب اثنين، ستة، معناته اف ستة، واف ستة هي
+
+501
+00:45:35,770 --> 00:45:39,730
+بتساوي سبعة في ستة ناقص أربعة، سبعة في ستة، اثنين
+
+502
+00:45:39,730 --> 00:45:49,130
+وأربعين ناقص أربعة، ثمانية وثلاثين، كيف؟
+
+503
+00:45:50,670 --> 00:45:54,430
+هيك بتحل أنت، بس الفكرة أنه أنا مش هستنى أن أعمل
+
+504
+00:45:54,430 --> 00:46:00,950
+الكلام هذا أو الـ function بالشكل هذا، ليش؟ بما أنه
+
+505
+00:46:00,950 --> 00:46:05,550
+أنا بدي آخذ الـ G of X في الداخل هيك، طب ليش ما آخذ
+
+506
+00:46:05,550 --> 00:46:12,050
+كل X هنا وأعوض عنها بالدالة اللي هنا؟ وبتصير عندي
+
+507
+00:46:12,050 --> 00:46:20,080
+هنا الدالة F circle G of X، بدها تساوي 7، أو خلينا
+
+508
+00:46:20,080 --> 00:46:27,880
+نفصلها كمان مرة، F of G of X، وبدها تساوي 7، مكان كل
+
+509
+00:46:27,880 --> 00:46:36,460
+X بدي أحط GX، إيش قيمة الـ GX؟ 3X ناقص 4، بدها تساوي
+
+510
+00:46:36,460 --> 00:46:50,350
+21X ناقص 4، طيب دعنا نشوف F circle G of 2 تساوي 21
+
+511
+00:46:50,350 --> 00:47:02,260
+في 2 ناقص 4، 42 ناقص 4، يساوي 38، ثمانية وثلاثين
+
+512
+00:47:02,260 --> 00:47:05,220
+فعليا هذا اللي أنا بدي أعمل composition، أنا ما بديش
+
+513
+00:47:05,220 --> 00:47:09,580
+أطبق بالطريقة العقيمة السابقة، بقصد أنه، أو الهدف
+
+514
+00:47:09,580 --> 00:47:12,840
+اللي أنا بدي إياه أن بالـ composition بحصل على function
+
+515
+00:47:12,840 --> 00:47:17,260
+جديدة، بحصل على function جديدة بتكون عبارة عن
+
+516
+00:47:17,260 --> 00:47:22,980
+applicable function من domain الأولى، domain الأولى
+
+517
+00:47:22,980 --> 00:47:28,020
+لـ target الثانية، كيف يعني two elements؟
+
+518
+00:47:28,900 --> 00:47:32,040
+X و Y، حسب المهمة، تحافظ على الـ definition يكون
+
+519
+00:47:32,040 --> 00:47:41,280
+صحيح بدون أي مشاكل، الآن
+
+520
+00:47:41,280 --> 00:47:49,620
+لما احنا نتكلم عن الـ bijective، معناته
+
+521
+00:47:49,620 --> 00:47:55,150
+أنا في عندي F من الـ A للـ B، one to one و one to two
+
+522
+00:47:55,150 --> 00:47:59,190
+هذا بيعطيني مباشرة أن هناك دالة عكسية تماما
+
+523
+00:47:59,190 --> 00:48:05,590
+بنسميها F inverse، معرفة من الـ B إلى الـ A، ومن هنا
+
+524
+00:48:05,590 --> 00:48:11,310
+اسمها inverse، من الـ B للـ A، بترجع الـ element لأصله
+
+525
+00:48:11,310 --> 00:48:15,390
+الآن لو أنا بدي أعمل composition أو أجمع كل دالة
+
+526
+00:48:15,390 --> 00:48:19,690
+مع الـ inverse تبعها، بحصل على مين؟ بحصل على الـ
+
+527
+00:48:19,690 --> 00:48:25,040
+element، بحصل على الـ element، تعال نشوف مثال موجود
+
+528
+00:48:25,040 --> 00:48:28,300
+عندي هنا، طبعا الـ composition مع الدالة ما بين
+
+529
+00:48:28,300 --> 00:48:31,520
+الدالة والـ inverse تبعها بتديني identity function
+
+530
+00:48:31,520 --> 00:48:36,760
+بتديني identity function، بقول
+
+531
+00:48:36,760 --> 00:48:43,200
+ليش؟ هي في عندي two functions F و G، معرفات، الـ F من R
+
+532
+00:48:43,200 --> 00:48:48,540
+إلى واحد إلى ما لا نهاية، اللي بين جثتين، ممكن نقولها R
+
+533
+00:48:48,540 --> 00:48:54,700
+plus، معادلة صفر ومعادلة واحد، okay، وبالتالي والـ G
+
+534
+00:48:54,700 --> 00:49:03,300
+معرفة من كده لكده، الآن جاوبني نعم أو لا، F circle G
+
+535
+00:49:03,300 --> 00:49:13,560
+of X exist، F circle G exist، F circle G كده، لأ
+
+536
+00:49:13,560 --> 00:49:16,660
+معرفة حسب التعريف السابق ولا لأ؟
+
+537
+00:49:28,550 --> 00:49:32,030
+عشان تقول معرفة أو لا، اذكر الـ definition، هذا إذا
+
+538
+00:49:32,030 --> 00:49:37,370
+كان الـ target تبعت الثانية، عفوا اللي تبعت الـ G
+
+539
+00:49:37,370 --> 00:49:42,270
+تمام؟ هو نفسه تبعت الـ domain، بتكون معرفة، وأين الـ
+
+540
+00:49:42,270 --> 00:49:47,390
+target تبعت الـ G؟ الـ R، الـ
+
+541
+00:49:47,390 --> 00:49:53,170
+R هي نفسها الـ domain تبعت الـ F؟ تمام، لو أنا قلت G
+
+542
+00:49:53,170 --> 00:50:03,940
+circle F of X، معناته g of f of x، مفهومها أن الـ
+
+543
+00:50:03,940 --> 00:50:09,340
+target تبعت الـ f لازم يكون نفس الـ domain تبعت الـ g
+
+544
+00:50:09,340 --> 00:50:13,060
+target الـ f هيها، والـ domain تبعت الـ g هيها
+
+545
+00:50:13,060 --> 00:50:17,280
+وبالتالي هذه exist، بتكون موجودة حسب الـ definition
+
+546
+00:50:17,280 --> 00:50:19,260
+الموجودة عندنا، تمام
+
+547
+00:50:24,470 --> 00:50:30,510
+بقول أن في دالتين، F of X معرفة على أنها ثلاثة أقصى
+
+548
+00:50:30,510 --> 00:50:37,370
+اثنين X زائد واحد، والـ G of X بتساوي نصف log X ناقص
+
+549
+00:50:37,370 --> 00:50:41,890
+واحد للأساس ثلاثة، وبدي أعمل composition بين
+
+550
+00:50:41,890 --> 00:50:46,470
+الاثنين، بدي أعمل composition ما بين الاثنين، بدي
+
+551
+00:50:46,470 --> 00:50:52,570
+أحسب F circle G of X، إيش بتساوي؟ معناته بتساوي
+
+552
+00:50:52,570 --> 00:50:53,350
+ثلاثة
+
+553
+00:50:56,210 --> 00:51:03,970
+مرفوعة على اثنين مضروبة في نصف log الـ X ناقص واحد
+
+554
+00:51:03,970 --> 00:51:09,590
+للاساس ثلاثة، الكل زائد واحد، بيقول هذا كلام أنا
+
+555
+00:51:09,590 --> 00:51:14,430
+جبته، قلت بدي أشتغل حسب الـ definition هذا، بدي أعوض
+
+556
+00:51:14,430 --> 00:51:20,170
+عن كل X في الـ F بقيمة G of X، هاي الـ composition
+
+557
+00:51:22,790 --> 00:51:27,310
+تعال نحلل، بروح وأنا الـ X هي الـ X اللي هنا، بده
+
+558
+00:51:27,310 --> 00:51:32,210
+أروح أستبدلها بهذه، الآن
+
+559
+00:51:32,210 --> 00:51:39,610
+الاثنين والنصف بيروحوا مع بعض، بتصفر
+
+560
+00:51:39,610 --> 00:51:49,770
+عندي المسألة ثلاثة أس log X ناقص واحد للثلاثة
+
+561
+00:51:49,770 --> 00:51:58,450
+زائد واحد، الآن log x
+
+562
+00:51:58,450 --> 00:52:04,310
+ناقص واحد للاساس ثلاثة، تساوي X ناقص واحد في واحد
+
+563
+00:52:04,310 --> 00:52:09,550
+زائد واحد، الآن
+
+564
+00:52:09,550 --> 00:52:15,710
+ثلاثة قوس log x للأساس ثلاثة، تساوي x، في واحد، أنا
+
+565
+00:52:15,710 --> 00:52:19,680
+عندي X ناقص واحد زي ما هي، هيك X ناقص واحد في واحد
+
+566
+00:52:19,680 --> 00:52:26,360
+يعني بين قوسين هيك يا شباب، القانون عندي A أس log X
+
+567
+00:52:26,360 --> 00:52:33,980
+للأساس A تساوي X، تساوي X، لأن صفت عندي المسألة تساوي
+
+568
+00:52:33,980 --> 00:52:39,940
+X ناقص واحد زائد واحد، وتساوي X، معناته هذه inverse
+
+569
+00:52:39,940 --> 00:52:47,170
+لهذه، معناته هذه هي عبارة عن المعكوس تبع الدالة اللي
+
+570
+00:52:47,170 --> 00:52:50,450
+موجودة عندنا هنا، و ليش حكمنا عليها إنفرس  اللي
+
+571
+00:52:50,450 --> 00:52:54,670
+احنا؟ لأنها
+
+572
+00:52:54,670 --> 00:53:00,390
+عبارة عن دالة عكسية، كانت قولنا identity function
+
+573
+00:53:00,390 --> 00:53:03,250
+لما أنا بعمل composition مع الـ inverse الأصلي
+
+574
+00:53:03,250 --> 00:53:06,610
+بيديني الـ element نفسه، هي الـ composition function
+
+575
+00:53:06,610 --> 00:53:11,510
+اللي موجودة عندنا، وهذا خلانا نفتح موضوع الـ inverse
+
+576
+00:53:11,510 --> 00:53:14,190
+function، لو كان في عندي أي دالة معرفة وبدي أحصل
+
+577
+00:53:14,190 --> 00:53:17,710
+للـ inverse function، الـ inverse function لازم تكون
+
+578
+00:53:17,710 --> 00:53:20,490
+الـ F عندي bijective، إيش يعني bijective يا
+
+579
+00:53:20,490 --> 00:53:28,110
+شباب؟ يعني one to one و onto، يعني كل عنصر في المدى
+
+580
+00:53:28,110 --> 00:53:34,450
+يكون مرتبط أو بيمثل صورة لعنصر واحد في الدومين
+
+581
+00:53:35,530 --> 00:53:39,150
+وعناصر، والمدى اللي هو الـ range، مجموعة الصور، تساوي
+
+582
+00:53:39,150 --> 00:53:45,190
+كل الـ target، كل عناصر الـ code domain، عشان لما آجي
+
+583
+00:53:45,190 --> 00:53:49,870
+أقول لك العكس لازم تكون function، كمان مرة، لو أنا
+
+584
+00:53:49,870 --> 00:53:57,490
+قلت F معرفة من A لـ B، F inverse المفروض تكون من B
+
+585
+00:53:59,060 --> 00:54:03,820
+لـ A، راح ننتبه معها شوية، ومش بس هيك يا شباب، عارف ليش
+
+586
+00:54:03,820 --> 00:54:09,320
+لازم تكون هنا onto؟ عشان لما بدي أعمل العكس، لو
+
+587
+00:54:09,320 --> 00:54:15,880
+كان في عنصر واحد من الـ B لا ينتمي للـ range، مش
+
+588
+00:54:15,880 --> 00:54:19,120
+هتكون الدالة معرفة، هتصير في عندي مشكلة في تعريف
+
+589
+00:54:19,120 --> 00:54:23,040
+عنصر واحد، وكل، عشان تصير function لازم يكون كل
+
+590
+00:54:23,040 --> 00:54:27,440
+العناصر تبع الـ domain موجودة، وبالتالي هذه الـ...
+
+591
+00:54:27,440 --> 00:54:30,260
+لازم الدالة تبعتنا تكون bijective عشان أولد الـ
+
+592
+00:54:30,260 --> 00:54:34,380
+inverse تبعتها، ولما بتكون الـ inverse تبعتها هيهم
+
+593
+00:54:34,380 --> 00:54:39,640
+مثلا، التوزيع تبعتي للتخصصات هي bijective، مصبوط؟
+
+594
+00:54:39,640 --> 00:54:43,340
+وبالتالي أنا بقدر أتكلم على الـ inverse بالشكل هذا
+
+595
+00:54:43,340 --> 00:54:50,460
+من التخصص للطالب، يعني مثلا في الأول بدي أقول لك إيش
+
+596
+00:54:50,460 --> 00:54:55,450
+تخصص أحمد؟ Computer Science، طب لو أنا قلت لك من
+
+597
+00:54:55,450 --> 00:54:57,590
+الطالب اللي في تخصص الـ computer الـ software
+
+598
+00:54:57,590 --> 00:55:02,330
+development، لما بتعرف أن الدالة one to one و one
+
+599
+00:55:02,330 --> 00:55:05,370
+to onto، و bijective، بتقدر تقولي Sally، أصبحت
+
+600
+00:55:05,370 --> 00:55:09,130
+وبالتالي أنا بقدر أصار أعتمد على القيم تبعت الـ
+
+601
+00:55:09,130 --> 00:55:13,170
+code main أو الـ range اللي موجود عندي هنا بشكل عام
+
+602
+00:55:13,170 --> 00:55:17,170
+يا صاحبي، تعال نشتغل رياضيات بشكل أفضل، لو أنا في
+
+603
+00:55:17,170 --> 00:55:21,530
+عندي دالة وبدي أجيبها، الدالة تبعتي F is a
+
+604
+00:55:21,530 --> 00:55:24,230
+bijective، وبدي أجيب الـ inverse تبعتها، في عندي
+
+605
+00:55:24,230 --> 00:55:28,850
+خطوات بسيطة وبدنا نعتمد عليهم، الخطوة رقم واحد
+
+606
+00:55:28,850 --> 00:55:34,390
+استبدل F of X،  طب عشان نطبق على المثال مع بعضنا، لو
+
+607
+00:55:34,390 --> 00:55:41,190
+افترضت أن أنا F of X بدها تساوي X زائد واحد، أو
+
+608
+00:55:41,190 --> 00:55:44,970
+اثنين X زائد واحد، وأنسى الـ domain وأنسى الـ range
+
+609
+00:55:44,970 --> 00:55:49,740
+الآن، وافترض أن الدالة هذه bijective، افترض أن
+
+610
+00:55:49,740 --> 00:55:53,580
+الدالة هذه bijective عشان ما أخلّكش في موضوع
+
+611
+00:55:53,580 --> 00:55:57,360
+الـ range والـ domain، بقول الخطوة... بدي أجيب الـ
+
+612
+00:55:57,360 --> 00:56:01,260
+inverse، بقول الخطوة رقم واحد، استبدل الـ Y بـ f of X
+
+613
+00:
+
+667
+01:00:59,610 --> 01:01:05,040
+المثال الأخير، بالمثال الأخير الآن، ما هو؟ عشان جبت لك
+
+668
+01:01:05,040 --> 01:01:09,180
+واحد فيه ضرب، وواحد جمع، وواحد طرح، وواحد فيه log
+
+669
+01:01:09,180 --> 01:01:14,780
+بلاش منه، بلاش منه. طيب، ليش؟ قانون الـ log بسيط جدا يا
+
+670
+01:01:14,780 --> 01:01:26,640
+شباب. log الـ a للأساس a = 1. a<sup>log<sub>a</sub>x</sup>
+
+671
+01:01:26,640 --> 01:01:37,940
+للأساس a = x. والعكس صحيح. الـ log<sub>a</sub> a<sup>x</sup> للأساس a
+
+672
+01:01:37,940 --> 01:01:42,260
+= x. حسب القانون اللي فوق. عندي هم، وعندي كمان
+
+673
+01:01:42,260 --> 01:01:53,900
+قانون بسيط. log<sub>a</sub> (x × y) = log<sub>a</sub> x
+
+674
+01:01:53,900 --> 01:01:58,680
+للأساس a + log<sub>a</sub> y. ولو كانت العملية
+
+675
+01:01:58,680 --> 01:02:04,810
+طرح، لو كانت طرح، بتصير طرح. هذه قوانين الـ أو
+
+676
+01:02:04,810 --> 01:02:11,430
+قوانين الـ log السهلة اللي ممكن تتذكرها. تعالى، y بدأت
+
+677
+01:02:11,430 --> 01:02:20,150
+= log<sub>2</sub>(x + 1) للأساس 2. بدل x بدأت
+
+678
+01:02:20,150 --> 01:02:26,160
+= log<sub>2</sub>(y + 1) للأساس 2. الآن، أنا
+
+679
+01:02:26,160 --> 01:02:29,480
+بدي أخلص من مين؟ بدي أخلص من الـ log من الـ
+
+680
+01:02:29,480 --> 01:02:32,940
+logarithm. إيش الـ base تبعته؟ 2. يعني أنا لو
+
+681
+01:02:32,940 --> 01:02:36,360
+رفعتها للأساس 2، بخلص منه بكل بساطة، حسب القانون
+
+682
+01:02:36,360 --> 01:02:43,980
+هي. ده معناته بقول: 2<sup>x</sup> = 2<sup>log<sub>2</sub>(y+1)</sup>
+
+683
+01:02:43,980 --> 01:02:50,130
+log<sub>2</sub> الـ x، الـ y عفواً، زائد 1 للأساس 2، وبدها
+
+684
+01:02:50,130 --> 01:02:55,450
+= y + 1. يعني هذا الكلام اللي بس بكتبه
+
+685
+01:02:55,450 --> 01:03:00,750
+عشان أقول هيها مظبوط؟ هذا، هي أنا قُلت: رفعت الـ 2
+
+686
+01:03:00,750 --> 01:03:05,510
+للطرفين المعادلة، لأن الشغل بسيط جداً يا شباب. أي
+
+687
+01:03:05,510 --> 01:03:09,150
+عملية بدك تنفذها على أحد الطرفين، بدك تنفذها على
+
+688
+01:03:09,150 --> 01:03:12,650
+الطرف الثاني، عشان تبقى المعادلة متساوية. فأنا رفعت
+
+689
+01:03:12,650 --> 01:03:22,440
+الـ 2 للأساس 2. الآن صارت عندي: 2<sup>x</sup> -
+
+690
+01:03:22,440 --> 01:03:32,820
+1 = y. معناته f<sup>-1</sup>(x) بدها
+
+691
+01:03:32,820 --> 01:03:40,120
+= 2<sup>x</sup> - 1. الآن هذا الكلام يكون صحيح لو
+
+692
+01:03:40,120 --> 01:03:44,280
+عملت الـ composition معها، دي الدالة، وعطاني x. ما نحن
+
+693
+01:03:44,280 --> 01:03:48,060
+قبل شوية عاملين ولا لا؟ في المثال السابق. هيا، خذ عن
+
+694
+01:03:48,060 --> 01:03:55,180
+2<sup>x</sup> هنا، وعوضها. 2<sup>x</sup> - 1. الواحد بروح مع
+
+695
+01:03:55,180 --> 01:04:04,120
+الواحد. بصفي عندي log<sub>2</sub> 2<sup>x</sup> للأساس 2، وليه بتساوي
+
+696
+01:04:04,120 --> 01:04:08,400
+x. وبالتالي، الـ inverse تبعتنا هنا صحيحة 100%
+
+697
+01:04:15,990 --> 01:04:18,970
+في أي سؤال يا شباب؟ كدا؟ الله يعطيكم العافية
diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/yo5uTs-agBQ_postprocess.srt b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/yo5uTs-agBQ_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..d54e4804000d3b274d8883888221e28af8300d28
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/yo5uTs-agBQ_postprocess.srt
@@ -0,0 +1,2788 @@
+1
+00:00:21,040 --> 00:00:22,900
+بسم الله والحمد لله والصلاة والسلام علي رسول الله
+
+2
+00:00:22,900 --> 00:00:26,960
+اليوم ان شاء الله يا شباب هنترق لموضوع الثاني في
+
+3
+00:00:26,960 --> 00:00:30,580
+ال chapter التاني اللي هو ال structures و هنتكلم
+
+4
+00:00:30,580 --> 00:00:34,400
+على ال function لكن مش هتلاقي ان الموضوع بعيد عن
+
+5
+00:00:34,400 --> 00:00:40,280
+موضوع المجموعات و علاقة المجموعات مع بعضها خلينا
+
+6
+00:00:40,280 --> 00:00:42,760
+نبدأ ب definition و هنعيد السيارة تانية ال slide
+
+7
+00:00:42,760 --> 00:00:47,540
+اللي بعدها لو كان في عندي مجموعتين non-empty يعني
+
+8
+00:00:47,540 --> 00:00:52,490
+مش فارغات فيهم عناصر يعني التخدمنيش في هيك مجال او
+
+9
+00:00:52,490 --> 00:00:58,870
+في ال functions ال function f from a to b يعني ال
+
+10
+00:00:58,870 --> 00:01:03,650
+function هتكون هي عبارة عن انتقال من عناصر a ل b و
+
+11
+00:01:03,650 --> 00:01:07,210
+بنرمزها بالشكل هذا a implies b is an assignment
+
+12
+00:01:07,210 --> 00:01:17,250
+تخصيص كل عنصر في a of each element in a to exactly
+
+13
+00:01:17,250 --> 00:01:24,340
+one elementof B يعني بدك تخصص او تربط او تعمل
+
+14
+00:01:24,340 --> 00:01:29,780
+اقتران بين كل عنصر في A مع عنصر واحد فقط من ال B
+
+15
+00:01:29,780 --> 00:01:35,140
+عشان الكلام هذا بدي ارجع معاك لاخت لل Cartesian او
+
+16
+00:01:35,140 --> 00:01:38,960
+ال cross product في المحاضرة الماضية لما اجينا
+
+17
+00:01:38,960 --> 00:01:44,100
+قولنا لو كان انا في عندى مجموعتين A بده تساوي A و
+
+18
+00:01:44,100 --> 00:01:49,960
+B و ال B المجموعة التانية كانت واحد و اتنين و
+
+19
+00:01:49,960 --> 00:01:56,330
+تلاتةهجينا قولنا ان a cross ال b هي عبارة عن
+
+20
+00:01:56,330 --> 00:02:01,010
+المجموعة اللى بتنتج أزواج مركبة العنصر فيها الأول
+
+21
+00:02:01,010 --> 00:02:15,630
+من a والعنصر التاني من ال b a1 a2 و a3 b1 b2 b3 فى
+
+22
+00:02:15,630 --> 00:02:21,250
+غير هيك الانهذا الـ definition تبع الـ Cartesian
+
+23
+00:02:21,250 --> 00:02:26,410
+product هو عبارة عن assignment تخصيص لكل عنصر في A
+
+24
+00:02:26,410 --> 00:02:31,910
+مع كل عناصر ال B فأتيت في عندي ال function هي
+
+25
+00:02:31,910 --> 00:02:36,450
+عبارة عن حالة خاصة من ال Cartesian هنا بقولي أنا
+
+26
+00:02:36,450 --> 00:02:40,670
+بدي أخصص كل عنصر في ال A لاحظ هنا هو نفسه كل عنصر
+
+27
+00:02:40,670 --> 00:02:45,970
+في Aمرتبط مع عنصر واحد فقط من الـ B يعني لا يريد
+
+28
+00:02:45,970 --> 00:02:50,090
+أن يرتبط معهم كلهم يريد ان يرتبط مع عنصر واحد فقط
+
+29
+00:02:50,090 --> 00:02:54,110
+وليس اكثر من ذلك لو ارتبط بعنصرين او اكثر فهو
+
+30
+00:02:54,110 --> 00:02:58,890
+يتبقى بالـ function فبالتالي الـ function هي عبارة
+
+31
+00:02:58,890 --> 00:03:02,870
+عن حالة خاصة من الـ cross product الـ function هي
+
+32
+00:03:02,870 --> 00:03:09,210
+عبارة عن حالة خاصة من الـ cross product ايوة الاين
+
+33
+00:03:09,210 --> 00:03:15,460
+على سبيل المثال functionمن a ل b حسب ال definition
+
+34
+00:03:15,460 --> 00:03:25,700
+اللي عندي a واحد b واحد صح function لازم كل عناصر
+
+35
+00:03:25,700 --> 00:03:32,300
+ال a كله موجودات و كل عنصر مرتبط مع عنصر واحد في b
+
+36
+00:03:32,300 --> 00:03:42,400
+الآن لو أنا قلت a واحد او او سكتت هيك لحالهاهذا
+
+37
+00:03:42,400 --> 00:03:46,020
+ليس فانكشن هذا ليس فانكشن لماذا؟ لأنه بالـ
+
+38
+00:03:46,020 --> 00:03:50,220
+function لازم يكون عند كل العناصر طيب، لو أنا اجيت
+
+39
+00:03:50,220 --> 00:03:59,760
+قولت كمان مرة A .. عفوان A واحد و A و اتنين برضه
+
+40
+00:03:59,760 --> 00:04:05,020
+هذا ليس فانكشن لماذا؟ لأن الـ A هذا ارتبط مع
+
+41
+00:04:05,020 --> 00:04:11,150
+عنصرين مختلفين في B وبالتالي ليس فانكشناصبر يا
+
+42
+00:04:11,150 --> 00:04:18,990
+أحمد شوية a واحد b و اتنين a واحد function
+
+43
+00:04:18,990 --> 00:04:23,050
+function ليش لأن ال function هي عبارة عن مجموعة
+
+44
+00:04:23,050 --> 00:04:27,770
+والعنصر هذا هو نفسه العنصر هذا مكرر فبالتالي هذا
+
+45
+00:04:27,770 --> 00:04:32,130
+التكرار مليش معناه عندنا تمام نرجع نقيد تاني على
+
+46
+00:04:32,130 --> 00:04:36,330
+السريع ال definition تبع ال function عشان نكمل
+
+47
+00:04:36,330 --> 00:04:43,330
+وبالتالي ال function من a ل bis an assignment
+
+48
+00:04:43,330 --> 00:04:50,650
+تخصيص لكل عنصر في A to exactly one element في B
+
+49
+00:04:50,650 --> 00:04:59,690
+طيب الآن لو فترضت الطلاب والعلامات هل بنفعاش اقول
+
+50
+00:04:59,690 --> 00:05:05,590
+اش اسمك محمد اخد امتياز او حصل امتياز في رياضيات
+
+51
+00:05:05,590 --> 00:05:12,900
+منفصلة وجيد جدا فعش مش معقوليعني هو يا امتياز، يا
+
+52
+00:05:12,900 --> 00:05:17,420
+جيد جدا، مافيه عشان تنتين، مصبوط؟ وبالتالي، هتلاقي
+
+53
+00:05:17,420 --> 00:05:24,600
+أن كل عنصر مرتبط بأنصر واحد فقط، هل ممكن أكثر من
+
+54
+00:05:24,600 --> 00:05:28,220
+عنصر يرتبطوا مع نفس الانصر تاني؟ أه، بنفع، مافي
+
+55
+00:05:28,220 --> 00:05:31,460
+مشكلة، يكون في عندي أكثر من واحد، لا بامتياز، مافي
+
+56
+00:05:31,460 --> 00:05:35,240
+مشكلة في الموضوع، وبالتالي، يعني الأمثلة اللي احنا
+
+57
+00:05:35,240 --> 00:05:42,610
+شوفناها F A1 وB1 عبارة عن functionكذلك الـ
+
+58
+00:05:42,610 --> 00:05:47,110
+function هي تعرف علي إنها binary relation ليش
+
+59
+00:05:47,110 --> 00:05:50,950
+binary relation؟ لأن أنا أتكلم على مجموعتين two
+
+60
+00:05:50,950 --> 00:05:57,670
+sets و ال binary relation بتنتج أزواج مرتبة .. زوج
+
+61
+00:05:57,670 --> 00:06:01,750
+مرتب a و b .. x و y a و b .. x انتمي للمجموعة
+
+62
+00:06:01,750 --> 00:06:07,030
+الأولى a و ال y انتمي للمجموعة التانية b و شرطها
+
+63
+00:06:07,030 --> 00:06:11,820
+هنا في ال function في ال relation هذهأن كل عنصر في
+
+64
+00:06:11,820 --> 00:06:16,960
+A بيرتبط to exactly one element in B مش أكتر
+
+65
+00:06:16,960 --> 00:06:21,620
+وبالتالي ال definition أصبح معروف وهذه هي ال
+
+66
+00:06:21,620 --> 00:06:25,780
+elements اللي بتنتمي لل function لاحظ element
+
+67
+00:06:25,780 --> 00:06:31,360
+ينتمي إلى function بتفهم أن ال function عبارة عن
+
+68
+00:06:31,360 --> 00:06:34,240
+مجموعة يعني لو في الصح و غلط جيت سألتك لحظة و
+
+69
+00:06:34,240 --> 00:06:42,650
+للحظات ال function is a settrue مش غلط صح كل
+
+70
+00:06:42,650 --> 00:06:46,810
+function عبارة عن مجموعة بس مش كل مجموعة function
+
+71
+00:06:46,810 --> 00:06:51,790
+ال function هذه عبارة عن مجموعة من الأزواج المرتبة
+
+72
+00:06:51,790 --> 00:06:57,050
+اللي بتعمل اقترانات ما بين ال a و ال b و حسب
+
+73
+00:06:57,050 --> 00:07:02,410
+definition واحد فقط احيانا بنسمي ال function
+
+74
+00:07:02,410 --> 00:07:06,450
+mapping او
+
+75
+00:07:06,450 --> 00:07:13,740
+بنسميها transformationانتقال انتقال لمين للعنصر A
+
+76
+00:07:13,740 --> 00:07:17,760
+ل B بحيث انه اخد شكل جديد بعد تطبيق ال function
+
+77
+00:07:17,760 --> 00:07:26,680
+هذه عليه عادة
+
+78
+00:07:26,680 --> 00:07:32,820
+بنرمز الزوج المرتب هذا F of A او A و B F of A
+
+79
+00:07:32,820 --> 00:07:41,120
+بنكتب على صورة الزوج المرتب هذا F of A equal Bطبعا
+
+80
+00:07:41,120 --> 00:07:46,140
+هذا بنسميه element وهذا
+
+81
+00:07:46,140 --> 00:07:51,660
+بنسميه ال image أو الصورة حسب ال definition اللي
+
+82
+00:07:51,660 --> 00:07:55,980
+بيعتمد عليه هيا
+
+83
+00:07:55,980 --> 00:08:00,460
+عندي a و b كمجموعات و بقوللي افحص هل ال relation
+
+84
+00:08:00,460 --> 00:08:04,940
+هاي ال relation هاي عبارة عن function مباشرة أول
+
+85
+00:08:04,940 --> 00:08:12,340
+شغلة اتأكد ان كل عناصر a موجودةA,B,C عناصرهم
+
+86
+00:08:12,340 --> 00:08:17,440
+موجودات الشغل التاني كل عنصر في A ارتباطه مرة
+
+87
+00:08:17,440 --> 00:08:27,200
+واحدة فقط مية المية وبالتالي function G
+
+88
+00:08:27,200 --> 00:08:31,440
+is not a function ليش؟ لأن ال C .. ال C مش موجودة
+
+89
+00:08:31,440 --> 00:08:35,160
+عنصر من عناصر ال A مش موجود في ال relation هادي
+
+90
+00:08:35,160 --> 00:08:39,420
+وبالتالي it's not a function الأخيرة
+
+91
+00:08:42,140 --> 00:08:49,860
+H A1 B2 C1 A2 A2 معناته هذا العنصر هي موجود
+
+92
+00:08:49,860 --> 00:08:53,440
+وبالتالي مش function لكن لاحظ لو .. هيختلف ال
+
+93
+00:08:53,440 --> 00:08:57,620
+decision تبعتي لو كانت هذه الواحد معناته أنا بكرر
+
+94
+00:08:57,620 --> 00:09:03,640
+العنصر جاية في مجموعة ال B
+
+95
+00:09:03,640 --> 00:09:08,760
+بيقول عنها لما يكون عندي F of AEqual B بنقول عن
+
+96
+00:09:08,760 --> 00:09:12,220
+الـ B الـ Image عارفى أن دي مجموعة من الـ
+
+97
+00:09:12,220 --> 00:09:16,940
+Definition مهمة الـ B Image الـ A كمجموعة هي ..
+
+98
+00:09:16,940 --> 00:09:21,760
+نسميها domain المجال كانوا بتعلمونا ايه في
+
+99
+00:09:21,760 --> 00:09:28,760
+الثانوية بمصطلح المجال لمباجي للـ B سميناها المجال
+
+100
+00:09:28,760 --> 00:09:34,580
+المقابل أو ال target ال code domain أو المدى لأ مش
+
+101
+00:09:34,580 --> 00:09:38,730
+المدىالمجال المقابل المدى هي عبارة عن مجموعة جزئية
+
+102
+00:09:38,730 --> 00:09:43,790
+من المجال المقابل مجموعة الصور ال range أو المدى
+
+103
+00:09:43,790 --> 00:09:48,770
+تمام من a و b هي عبارة عن all images of element of
+
+104
+00:09:48,770 --> 00:09:52,210
+a مجموعة الصور و هلا بنجيبلك بالأمثلة كيف أنه
+
+105
+00:09:52,210 --> 00:09:57,710
+بتفرج عن بعضها وبالتالي ال range هي عبارة أو المدى
+
+106
+00:09:57,710 --> 00:10:02,010
+هي عبارة عن مجموعة جزئية من ال b من ال definition
+
+107
+00:10:02,010 --> 00:10:09,010
+الكل تأكيدB تنتمي إلى B حيث F و A equal B يعني الـ
+
+108
+00:10:09,010 --> 00:10:12,210
+B لازم تكون عبارة عن صورة و بالأمثل السابقة لما
+
+109
+00:10:12,210 --> 00:10:19,530
+قلنا A بدها تساوي A و B و الـ B قلنا واحد و اتنين
+
+110
+00:10:19,530 --> 00:10:25,870
+و تلاتة و جيتها قلت الـ F بدها تساوي ال relation A
+
+111
+00:10:25,870 --> 00:10:32,370
+و اتنين و B و تلاتة الآن
+
+112
+00:10:33,200 --> 00:10:37,900
+لو انا اجيت سألتك حسب ال definition هذا من ال
+
+113
+00:10:37,900 --> 00:10:41,880
+domain هاي ال function وهي ال two sets من ال
+
+114
+00:10:41,880 --> 00:10:48,200
+domain ال a من
+
+115
+00:10:48,200 --> 00:10:54,080
+ال codomain او ال target عارف ليش سموها target لأن
+
+116
+00:10:54,080 --> 00:11:00,240
+كل عنصر من ال a بيستهدف عنصر في ال b الآن هاي ال
+
+117
+00:11:00,240 --> 00:11:01,700
+function ضال في end ال range
+
+118
+00:11:04,470 --> 00:11:09,550
+هي عبارة عن مجموعة جزئية من B وهي بين جثيم مجموعة
+
+119
+00:11:09,550 --> 00:11:12,270
+الصور المقتنعة مع عناصر الـ A اللي هم في المثال
+
+120
+00:11:12,270 --> 00:11:16,210
+هذا اتنين و تلاتة او اتنين و تلاتة مجموعة جزئية زي
+
+121
+00:11:16,210 --> 00:11:20,270
+ما قلنا من الـ B ولا تسويها او proper subset من
+
+122
+00:11:20,270 --> 00:11:28,550
+الـ B كل
+
+123
+00:11:28,550 --> 00:11:31,850
+عناصر
+
+124
+00:11:31,850 --> 00:11:35,880
+الـ A .. احنا نهي المثال عاما لما نروحهنا قلنا هذه
+
+125
+00:11:35,880 --> 00:11:42,560
+function وهذه لأ لماذا؟ لأن الـC كأنصر في الـA
+
+126
+00:11:42,560 --> 00:11:46,780
+لايوجد مكان هنا في الـfunction في المجموعة هذه
+
+127
+00:11:46,780 --> 00:11:50,780
+وبالتالي هذه ليست function وبالتالي أول حاجة قلتلك
+
+128
+00:11:50,780 --> 00:11:55,380
+تتأكد إن أنا فعليا كل عراسر المجموعة موجودة عندى
+
+129
+00:11:55,380 --> 00:11:59,940
+عراسر أي مجموعة عراسر ال domain اللي هي الـA
+
+130
+00:12:03,950 --> 00:12:09,330
+هي دالة a,b,c الـ a و ال set p واحد اتنين تلاتة
+
+131
+00:12:09,330 --> 00:12:15,550
+وهي الاقتران اللي بينهم f of a .. f .. a واحد b و
+
+132
+00:12:15,550 --> 00:12:23,970
+اتنين c واحد الان هي من مجموعة الصوت دماغ ايه؟ هذه
+
+133
+00:12:23,970 --> 00:12:31,050
+function مظبوط ال target كل ال b ايش ال range؟واحد
+
+134
+00:12:31,050 --> 00:12:34,330
+و اتنين مش كل الصور اللي موجودة عندى هنا او مش كل
+
+135
+00:12:34,330 --> 00:12:40,250
+العناصر اللي في ال B عبارة عن صور okay الان و انا
+
+136
+00:12:40,250 --> 00:12:44,050
+جيت من الامثلة اللي موجودة على ال functions ارتباط
+
+137
+00:12:44,050 --> 00:12:49,810
+الطالب بالتخصص ارتباط الطالب بالتخصص يعني اذا قلت
+
+138
+00:12:49,810 --> 00:12:53,890
+ان انا في عندى function F ال student و ال major
+
+139
+00:12:53,890 --> 00:12:57,610
+تبعه طلاب اللي عندى مونة و أحمد و سالي و رامي
+
+140
+00:12:58,270 --> 00:13:01,930
+والتخصصات اللي عندي أربعة computer science ال IT و
+
+141
+00:13:01,930 --> 00:13:05,830
+ال software development و ال computer engineering
+
+142
+00:13:05,830 --> 00:13:18,110
+الآن الطالب كام تخصص إله في الجامعة تخصص واحد بدك
+
+143
+00:13:18,110 --> 00:13:23,460
+تخصص تاني معناته إما بدك تغير ال track كلهوبالتالي
+
+144
+00:13:23,460 --> 00:13:27,260
+تحتفظ بتخصص واحد لولي جديد او تتسجل في الجامعة
+
+145
+00:13:27,260 --> 00:13:33,620
+كطالب جديد وتدرس من تخصص جديد بس في الآخر .. بس في
+
+146
+00:13:33,620 --> 00:13:38,200
+الآخر الطالب بينجو سيني اللي بمثل الرقم الجامعي لا
+
+147
+00:13:38,200 --> 00:13:42,980
+يحتمل الا غير اتباط بتخصص واحد فقط وبالتالي هل
+
+148
+00:13:42,980 --> 00:13:46,040
+ممكن يكون فيه اندي تخصص طلاب؟ اه ممكن مافيش مشكلة
+
+149
+00:13:46,040 --> 00:13:50,660
+في الموضوع يعني الان اقتران هذا ممكن انا امثله
+
+150
+00:13:50,660 --> 00:13:57,450
+بجدولزي ما هو قدامي هان او اروح امثله بالاسهم عشان
+
+151
+00:13:57,450 --> 00:14:01,990
+ابين ال relation اللي موجودة عندي هان من السهم هي
+
+152
+00:14:01,990 --> 00:14:06,330
+الطالب وهي ال major مونة ايش تخصصها computer
+
+153
+00:14:06,330 --> 00:14:10,470
+engineering رامي ايش تخصصه computer science ونفس
+
+154
+00:14:10,470 --> 00:14:12,690
+الكلام نفس المعلومة هذه انا بقدر اخدها من الجدول
+
+155
+00:14:12,690 --> 00:14:18,630
+هانأنا لا أتكلم على طريقة تمثيل العناصر، أكتبها
+
+156
+00:14:18,630 --> 00:14:21,270
+بزوادي مرتبة، أكتبها من خلال جدول أو أمثلها
+
+157
+00:14:21,270 --> 00:14:24,270
+بالأسهم أو بال relation اللي موجودة عندها، القدر
+
+158
+00:14:24,270 --> 00:14:28,110
+ما أني أنا لازم أفهم أنه لما أتكلم على function كل
+
+159
+00:14:28,110 --> 00:14:30,370
+عناصر ال domain لازم يكون لها ارتباط
+
+160
+00:14:36,450 --> 00:14:39,550
+طيب، الآن انتقلنا من تعريف الـ function بعد ما
+
+161
+00:14:39,550 --> 00:14:42,190
+أعرفنا الـ function و الأمور تمام الآن بدي أنتقل
+
+162
+00:14:42,190 --> 00:14:48,590
+لخصائص الـ function الخصائص الـ function أول حاجة
+
+163
+00:14:48,590 --> 00:14:54,930
+بنقول عن الـ function onto أو subjective لما يكون
+
+164
+00:14:54,930 --> 00:14:59,630
+ال range لما يكون ال range اللي هي مجموعة الصور
+
+165
+00:14:59,630 --> 00:15:06,070
+تساويالـ Target Set أو تساوي الـ Codomain بقول عن
+
+166
+00:15:06,070 --> 00:15:12,390
+الـ Function تبعتها Onto لما كمان مرة بتكون عناصر
+
+167
+00:15:12,390 --> 00:15:19,970
+المدى هي تساوي كل عناصر المجال المقابل لما تكون
+
+168
+00:15:19,970 --> 00:15:25,610
+عند ال range تبعت ال F تساوي كل ال B تساوي كل ال B
+
+169
+00:15:29,560 --> 00:15:32,460
+بالمثال اللي عندناها يعني على الـ slide A و B و C
+
+170
+00:15:32,460 --> 00:15:39,240
+على رأس المجموعة A على رأس المجموعة B واحد و اتنين
+
+171
+00:15:39,240 --> 00:15:47,360
+الان F of واحد A واحد B و اتنين C واحد الان ايش ال
+
+172
+00:15:47,360 --> 00:15:55,440
+range واحد و اتنين تساوي ال B معناته ال F is onto
+
+173
+00:15:55,440 --> 00:16:07,000
+لو انا افترضتإن الـ G equal A1B1C1
+
+174
+00:16:07,000 --> 00:16:13,800
+فنشن فنشن و عادة بالشكل هذا بنسميها constant
+
+175
+00:16:13,800 --> 00:16:18,480
+function لأن كل ال element فيها بيتساوي واحد لكن
+
+176
+00:16:18,480 --> 00:16:23,800
+has not onto كل هذه الدلة onto اللي فوق اللي تحت
+
+177
+00:16:23,800 --> 00:16:27,840
+is not onto تمام؟
+
+178
+00:16:28,820 --> 00:16:34,240
+يعني لما انا بلاج أنه المدى مجموعة الصور اللي
+
+179
+00:16:34,240 --> 00:16:38,360
+تنتجت عنها ال function ساوت كل ال target set او ال
+
+180
+00:16:38,360 --> 00:16:41,180
+co-domain set يعني ان انا بتكلم عن الدالة on to
+
+181
+00:16:41,180 --> 00:16:46,080
+لما
+
+182
+00:16:46,080 --> 00:16:50,630
+بتكون الدالة او الصفة التانية one to oneماذا يعني
+
+183
+00:16:50,630 --> 00:16:56,630
+one-to-one؟ إن كل عنصر في الـA مقترن فقط بأنصر
+
+184
+00:16:56,630 --> 00:17:00,210
+واحد في الـB، غلط لأنه أساساً المقترن بأكتر من
+
+185
+00:17:00,210 --> 00:17:05,190
+عنصر بقبطة الـfunction هو كل صورة أو كل عنصر في
+
+186
+00:17:05,190 --> 00:17:10,190
+الـB يمثل صورة لعنصر واحد فقط من الـA وهذا تعريف
+
+187
+00:17:10,190 --> 00:17:14,970
+الصح الأول ما تجعش إذا انت قلت كل عنصر في A له
+
+188
+00:17:14,970 --> 00:17:17,570
+صورة واحدة فقط، ما هو أساسا لو كان صورتين is not a
+
+189
+00:17:17,570 --> 00:17:22,480
+functionتمام؟ لأ هو التعريف الصح انه كل أنصر في
+
+190
+00:17:22,480 --> 00:17:25,620
+الـB اللي هو بمثل الصورة تمام؟ في الـCodomain أو
+
+191
+00:17:25,620 --> 00:17:31,140
+في الـRange بشكل أدق يمثل صورة لأنصر مختلفة في
+
+192
+00:17:31,140 --> 00:17:34,660
+الـDomain طيب،
+
+193
+00:17:34,660 --> 00:17:42,980
+الآن A و 1 B و 3 و C و 2 لاحظ، أنا باتكلم مش على
+
+194
+00:17:42,980 --> 00:17:48,320
+Onto أنا بتكلم على one to one يعني بين جسيمكل عنصر
+
+195
+00:17:48,320 --> 00:17:52,420
+من الصور مرتبط بانصر و مختلف من العناصر الـA
+
+196
+00:17:52,420 --> 00:17:56,500
+الواحد هي هيك الواحد مظهرش ولا مرة بعد هيك فمن وقت
+
+197
+00:17:56,500 --> 00:17:59,620
+الصور التلاتة مظهرتش لغير مرة واحدة والتانية مرة
+
+198
+00:17:59,620 --> 00:18:05,020
+واحدة معناته الدالة ها دي one to one الاربعة مش من
+
+199
+00:18:05,020 --> 00:18:09,720
+حسب Tالاربع مش من اهتمامي .. ليش؟ لأن هي ليست
+
+200
+00:18:09,720 --> 00:18:14,100
+مجموعة من مجموعة الصور .. مش عنصر موجود في مجموعة
+
+201
+00:18:14,100 --> 00:18:19,040
+الصور .. وبالتالي أنا بتكلم عن عناصر المدى ..
+
+202
+00:18:19,040 --> 00:18:24,780
+عناصر المدى .. لما تكون كل عنصر في المدى بمثل صورة
+
+203
+00:18:24,780 --> 00:18:30,760
+.. صورة لعنصر واحد فقط من عناصر الدماء .. الآن
+
+204
+00:18:30,760 --> 00:18:38,660
+high function تانية .. G .. A1ب و واحد سي و اتنين
+
+205
+00:18:38,660 --> 00:18:44,600
+هذه function لكنها
+
+206
+00:18:44,600 --> 00:18:53,100
+ليست one to one ليش
+
+207
+00:18:53,100 --> 00:18:59,380
+ليست one to one لأن ال a و ال b لهم نفس الصورة او
+
+208
+00:18:59,380 --> 00:19:04,990
+بين جثين في عندي الواحد كصورةهي أبعاد صورة عن صورة
+
+209
+00:19:04,990 --> 00:19:08,790
+واحدة لأنصرين مختلفين من ال domain وبالتالي ليست
+
+210
+00:19:08,790 --> 00:19:15,190
+one to one بدي أسأل الآن نعم أما
+
+211
+00:19:15,190 --> 00:19:18,330
+ليه هيك بدي أجيك في السؤال ممكن الدالة تجمع خاصية
+
+212
+00:19:18,330 --> 00:19:21,190
+ال on one to one و ال on two مع بعض؟ أه ممكن بس
+
+213
+00:19:21,190 --> 00:19:27,570
+بحاجة تطبق الآن هل الدالة اللي فوق on two؟ لأ لأن
+
+214
+00:19:27,570 --> 00:19:31,410
+الأربعة تنتمي لل D ولا تنتمي لل range
+
+215
+00:19:34,130 --> 00:19:36,590
+لو الأربعة مش موجودة بنفع أقول عنها one to one
+
+216
+00:19:36,590 --> 00:19:40,330
+وunto تمام؟ ما شاء الله عليكم و هيكم بدأتوا
+
+217
+00:19:40,330 --> 00:19:43,450
+تشتغلوا وهي ال slide اللي بعدها شرحتوها على حالكوا
+
+218
+00:19:43,450 --> 00:19:48,930
+الدالة بنقول عنها by adjective لو كانت فيها
+
+219
+00:19:48,930 --> 00:19:54,770
+الخصيتين one to one وunto one to one وunto إيش
+
+220
+00:19:54,770 --> 00:19:59,930
+يعني one to one وunto؟ إن ال range أو المدى يساوي
+
+221
+00:20:02,140 --> 00:20:06,840
+Codomain هدى إيش بتسميناها one to one to one كل
+
+222
+00:20:06,840 --> 00:20:12,740
+عنصر في ال range يمثل يمثل صورة لعنصر واحد فقط من
+
+223
+00:20:12,740 --> 00:20:16,740
+ال domain هدى الدلز حققت المواصفات هدى بتكون
+
+224
+00:20:16,740 --> 00:20:20,520
+objective تعالى شوف المثال اللى موجود عندى هان هى
+
+225
+00:20:20,520 --> 00:20:28,350
+ال a a b c و ال bاحد اتنين تلاتة وهي ال function f
+
+226
+00:20:28,350 --> 00:20:36,450
+a واحد b و اتنين c و تلاتة الان one to one الصور
+
+227
+00:20:36,450 --> 00:20:39,450
+كل صورة موجودة مع أنصر واحد او بتمثل اقتراح لأنصر
+
+228
+00:20:39,450 --> 00:20:46,070
+واحد فقط صحيح و on to on to معاه by adjective الآن
+
+229
+00:20:46,070 --> 00:20:49,390
+يا شباب لما اتكلم على one to one و on to او by
+
+230
+00:20:49,390 --> 00:20:52,890
+adjective function مباشرةالـ Function بدها تكون ..
+
+231
+00:20:52,890 --> 00:20:55,170
+أو عفوا الـ Cardinality للمجموع الـ A للـ domain
+
+232
+00:20:55,170 --> 00:20:59,290
+لازم يساوي Cardinality للتانية وإلا ولا عمرو هذا
+
+233
+00:20:59,290 --> 00:21:02,530
+الكلام حيصير لو اتيت في لحظة من اللحظات سألتك هل
+
+234
+00:21:02,530 --> 00:21:06,930
+الـ Function هذي one to one او on two مباشرة بتقدر
+
+235
+00:21:06,930 --> 00:21:10,830
+تحكم او objective تحكم عليها من عدد ايش اختلاف عدد
+
+236
+00:21:10,830 --> 00:21:14,890
+العناصر بالنافي طبعا بتقدر تنفيه لو العدد العناصر
+
+237
+00:21:14,890 --> 00:21:18,770
+مختلف بتقدر تنفيه او تثبت اجي اقولك والله في عندي
+
+238
+00:21:18,770 --> 00:21:21,890
+دالة Function او الـ Function اللي عندي هانهك ..
+
+239
+00:21:21,890 --> 00:21:26,770
+التلاتة مش موجودة تمام؟ وبعدين بقولك الـ function
+
+240
+00:21:26,770 --> 00:21:30,170
+هذي bijective؟
+
+241
+00:21:30,170 --> 00:21:35,970
+لا .. مستحيل .. ليش؟ لأن حتما عصر من العناصر هذه
+
+242
+00:21:35,970 --> 00:21:40,590
+اللي لازم الـ C لازم تتعرف والتلاتة مش موجودة إما
+
+243
+00:21:40,590 --> 00:21:44,070
+بدي أغيرها باتنين أو بدي أغيرها من واحد وهيك أنا
+
+244
+00:21:44,070 --> 00:21:48,710
+ضيعت خاصية اللي هي ال one to one خاصية ال one to
+
+245
+00:21:48,710 --> 00:21:53,240
+one وبالتالي بطلتby adjective خاصية الـ one to one
+
+246
+00:21:53,240 --> 00:22:00,560
+و بطلات by adjective كذلك لو كان عدد عناصر
+
+247
+00:22:00,560 --> 00:22:06,900
+ال B أكبر زي ما كان فيهم الأربعة تمام هذه function
+
+248
+00:22:06,900 --> 00:22:13,340
+one to one بس مش unto تمام لأن الأربعة موجودة في
+
+249
+00:22:13,340 --> 00:22:16,520
+ال domain عفوا في ال code domain و مش موجودة في ال
+
+250
+00:22:16,520 --> 00:22:21,900
+range و بالتاليis not onto عليه كده بحياته انا
+
+251
+00:22:21,900 --> 00:22:25,140
+بقدر اتكلم انه عشان تكون ال .. لو كانت الدالة
+
+252
+00:22:25,140 --> 00:22:29,040
+bijective مباشرة ال cardinality لل a بده تساوي ال
+
+253
+00:22:29,040 --> 00:22:35,780
+cardinality لل b التخصصات
+
+254
+00:22:35,780 --> 00:22:39,220
+اللي عندنا قبل شوية ذكرناها computer science
+
+255
+00:22:39,220 --> 00:22:44,960
+computer engineering IT software development اربع
+
+256
+00:22:44,960 --> 00:22:45,680
+تخصصات
+
+257
+00:22:48,610 --> 00:22:52,450
+شوف الدالة هذه F of Muna Computer Engineering تخصص
+
+258
+00:22:52,450 --> 00:22:54,770
+Muna Computer Engineering أحمد Computer Science
+
+259
+00:22:54,770 --> 00:22:59,070
+سالي و راني Computer Science هل الدالة هذه one to
+
+260
+00:22:59,070 --> 00:23:05,090
+one؟ لأ one to one لإيش؟ لأن في عند أحمد و راني
+
+261
+00:23:05,090 --> 00:23:09,410
+اللي هم نفس التخصص أو بينتموا لنفس التخصص اللي
+
+262
+00:23:09,410 --> 00:23:14,690
+موجود لبين جسيم نفس الصورة لأنا ماسألتش على ال on
+
+263
+00:23:14,690 --> 00:23:26,370
+to الأن أنا بسأل على one to oneهذا الدالة
+
+264
+00:23:26,370 --> 00:23:35,250
+جي one to one لأن كل طالب له تخصص مختلف الدالة
+
+265
+00:23:35,250 --> 00:23:41,710
+بقول عنها identity function لو كانت معرفة من
+
+266
+00:23:44,020 --> 00:23:48,540
+هي عبارة عن relation بين عناصر مجموعة واحدة من ال
+
+267
+00:23:48,540 --> 00:23:54,140
+a إلى ال a بيسميها identity function لو كان كل f
+
+268
+00:23:54,140 --> 00:23:59,920
+of a بيتساوي a يعني مش بس هيك لو كانت ال f من ال a
+
+269
+00:23:59,920 --> 00:24:07,680
+إلى ال a و f of a equal a هيذهكت بقول عنها
+
+270
+00:24:07,680 --> 00:24:21,240
+identityولا لأ بيجيكتف function لما
+
+271
+00:24:21,240 --> 00:24:27,120
+بيكون ال function اللي عندي بتتكلم فيها على مجموعة
+
+272
+00:24:27,120 --> 00:24:30,400
+أكبر من تلت أو خمس أرقام لما أتكلم على ال real
+
+273
+00:24:30,400 --> 00:24:34,060
+number أو ال integer number أو ال natural number
+
+274
+00:24:34,060 --> 00:24:37,910
+بصير اعتمد على مينعلى الرموز اللي اتبعتي و بتصير
+
+275
+00:24:37,910 --> 00:24:41,330
+الدالة اللي لها معنى اخر او تعرف الدالة بشكل اخر
+
+276
+00:24:41,330 --> 00:24:45,190
+صعب ان احصره بالازواج المرتبة بلجأ لمين لل
+
+277
+00:24:45,190 --> 00:24:48,230
+definition او الخواصة اللي احنا شوفناها سابقا لما
+
+278
+00:24:48,230 --> 00:24:52,450
+بلجأ بقول هاي في عندي function معرفة من R إلى ال R
+
+279
+00:24:52,450 --> 00:24:55,970
+ماقدرش اقول عنها identity function اللي جال لو
+
+280
+00:24:55,970 --> 00:25:01,910
+كانت F of X بتساوي X تمام من ال R إلى ال R يعني
+
+281
+00:25:01,910 --> 00:25:07,050
+بين جسيم ال end domain اعداد حقيقيةوالـ Target عدد
+
+282
+00:25:07,050 --> 00:25:14,130
+حقيقية F of X بيتساوي الـ 2X F of X بيتساوي 2X و
+
+283
+00:25:14,130 --> 00:25:17,890
+بيكسر طبعا بكتب الدالة الصورة تبعت هيها F of واحد
+
+284
+00:25:17,890 --> 00:25:20,990
+تساوي اتنين F of تلاتة ستة F of سالب تلاتة سالب
+
+285
+00:25:20,990 --> 00:25:25,790
+ستة بنانا على مين؟ على الـ Definition الان F of
+
+286
+00:25:25,790 --> 00:25:26,810
+جذر الاتنين
+
+287
+00:25:33,090 --> 00:25:38,910
+هل بقدر احكم على هيك ديالة one to one وانتوا؟ حرام
+
+288
+00:25:38,910 --> 00:25:41,070
+عليك تقدر ممكن نعم
+
+289
+00:25:44,410 --> 00:25:49,270
+أيوة الان اول ما تبدأ تفكر اذا انت بتفكر باتجاهها
+
+290
+00:25:49,270 --> 00:25:52,610
+ان الدالة هذه مش on to او مش by adjective او مش
+
+291
+00:25:52,610 --> 00:25:56,630
+one to one بتروح تجيب .. تفكر .. تجيب لمثال واحد
+
+292
+00:25:56,630 --> 00:26:02,030
+بدلل على انها دالة مش صحيحة مثلا لو انا اجد قلتلك
+
+293
+00:26:02,030 --> 00:26:05,090
+f
+
+294
+00:26:05,090 --> 00:26:11,870
+of x بده يساوي x تربيع f of x بده تساوي x تربيع
+
+295
+00:26:13,050 --> 00:26:23,670
+الدالة هذه هل هي is F one to one؟ هل ال F دالة one
+
+296
+00:26:23,670 --> 00:26:28,350
+to one؟ لأ لإيش؟
+
+297
+00:26:28,350 --> 00:26:33,170
+لأن عندي أنا الآن التنين بتنتمل ال real number as
+
+298
+00:26:33,170 --> 00:26:40,070
+image صح؟ التنين؟ او الاربعة عشان نريح حالنا ال
+
+299
+00:26:40,070 --> 00:26:48,100
+image as imageone image ترتبط بأنصرين F of سالب 2
+
+300
+00:26:48,100 --> 00:26:55,440
+تساوي أربعة و F of 2 تساوي أربعة و التنين لا تساوي
+
+301
+00:26:55,440 --> 00:27:02,080
+السالب تنين وبالتالي صار في عندي one image تمام
+
+302
+00:27:02,080 --> 00:27:07,760
+مرتبطة مع two different elements في عندي one image
+
+303
+00:27:07,760 --> 00:27:13,120
+ل two different elements وبالتاليone to one is not
+
+304
+00:27:13,120 --> 00:27:18,080
+one to one هل هي bijective؟ عفوا بيجيكتف نعم هل هي
+
+305
+00:27:18,080 --> 00:27:22,040
+بيجيكتف؟ لأ خلصنا بلا ماعنش نطلوا one to one is
+
+306
+00:27:22,040 --> 00:27:25,960
+not bijective هل هي on to؟ صحيح ممكن تكونوا هل هي
+
+307
+00:27:25,960 --> 00:27:29,600
+on to؟ ممكن تكونوا الان لو فكرت تجيب counter
+
+308
+00:27:29,600 --> 00:27:33,200
+example مش هتقدر معناته بيبقى تروح باتجاه العكس
+
+309
+00:27:33,200 --> 00:27:38,440
+تثبت أن الدالة هذه is not on toهتصلكوا
+
+310
+00:27:38,440 --> 00:27:43,300
+contradiction في الآخر السؤال الآن كمان مرة is
+
+311
+00:27:43,300 --> 00:27:49,700
+أمته .. هل هي أمته؟ يعني بين قصين هل ال range
+
+312
+00:27:49,700 --> 00:27:58,620
+يساوي ال R؟ هل ال range يساوي ال R؟ هل ال range
+
+313
+00:27:58,620 --> 00:28:03,820
+يساوي ال R يا شباب؟ اه .. اه .. اه .. اه ..
+
+314
+00:28:03,820 --> 00:28:09,440
+مابتهاش .. مابتهاش شطارة كتير الآنالفكرة كانت
+
+315
+00:28:09,440 --> 00:28:13,960
+تالية عشان تثبت انها on to تفترض ان في عندك
+
+316
+00:28:13,960 --> 00:28:20,600
+element بينتمي لمجموعة الصور وإذا قدرت تكتب على
+
+317
+00:28:20,600 --> 00:28:25,480
+صورة او لجيتله X تنتمي لل R معناته عبارة عن on to
+
+318
+00:28:25,480 --> 00:28:36,260
+يعني هكذا ستقول لك مثلا ال X تنتمي لل Rالـ Range
+
+319
+00:28:36,260 --> 00:28:40,600
+تمام؟
+
+320
+00:28:40,600 --> 00:28:43,760
+إذا كانت الـ X بتنتمي للـ Range معناها to there
+
+321
+00:28:43,760 --> 00:28:55,580
+exist some Y كنتمي لل R لل domain such
+
+322
+00:28:55,580 --> 00:29:05,780
+that F of Y يساوي Xالان لو كانت الدالة on two لو
+
+323
+00:29:05,780 --> 00:29:08,660
+كانت الدالة on two معناته .. انا قاعد بقولك التالي
+
+324
+00:29:08,660 --> 00:29:12,880
+هاي فيه عندي صورة الصورة هذه لازم .. اي عنصر ..
+
+325
+00:29:12,880 --> 00:29:17,700
+random number معناته فيه عنصر في ال Y او عفوا في
+
+326
+00:29:17,700 --> 00:29:21,800
+ال R اللي هي بال domain بحيث ان F of Y بتسوي X طيب
+
+327
+00:29:21,800 --> 00:29:26,900
+F of Y ايش بتسوي يا شباب؟ اتنين Y مصبوط؟ حسب ال
+
+328
+00:29:26,900 --> 00:29:33,960
+definition او عفوا Y تربيع .. آسفأف of Y بيبقى
+
+329
+00:29:33,960 --> 00:29:40,540
+تساوي Y تربيه بيبقى تساوي X ال
+
+330
+00:29:40,540 --> 00:29:49,040
+Y إيش بتساوي؟ جذر ال X تن تن إلى ال R؟ مش
+
+331
+00:29:49,040 --> 00:29:57,860
+بالضرورة، ليش؟ سالب، الآن لو أنا أخدت رقم سالب من
+
+332
+00:29:57,860 --> 00:30:03,950
+ال rentبصبوط؟ هيكد الآن السالب ينتمي لرئيس ال
+
+333
+00:30:03,950 --> 00:30:09,930
+number ولا لا ينتمي؟ ينتمي تمام؟ ينتمي معناته انا
+
+334
+00:30:09,930 --> 00:30:15,890
+في عندي هيكد في عندي اتنين او في عندي X اتنين X
+
+335
+00:30:15,890 --> 00:30:22,630
+يساوي سالب واحد هل بقدر لقيمة اوصل افر X تربيه بيه
+
+336
+00:30:22,630 --> 00:30:28,980
+تساوي سالب واحد هل في عندي رقملما انا بربق في ال
+
+337
+00:30:28,980 --> 00:30:32,500
+number بالدين السالب واحد، لأ ماعنديش، معناته ده
+
+338
+00:30:32,500 --> 00:30:37,040
+اللي هي دي is not onto هكذا، شوف لما انا مشيت مع
+
+339
+00:30:37,040 --> 00:30:40,740
+المثال أو مع ال definition خطوة خطوة وصلت و لحاله
+
+340
+00:30:40,740 --> 00:30:43,380
+قال اتفضل هاي ال counter example بين ايديك، باطمل
+
+341
+00:30:43,380 --> 00:30:47,540
+تصبق معاك الأمور، نعم، ايه كيف؟
+
+342
+00:30:52,890 --> 00:30:55,290
+أه بس ممتاز من حيث ال definition جاعل بقولك من R ل
+
+343
+00:30:55,290 --> 00:31:00,230
+R مش على كيفك لإيامك تكيفي المسألة انا جاعل بقولك
+
+344
+00:31:00,230 --> 00:31:05,790
+هي المسألة بقولك R ل R ماقولتلكاش ل R positive لو
+
+345
+00:31:05,790 --> 00:31:13,010
+قولتلك ل R positive معناته هي on to ممتاز
+
+346
+00:31:13,010 --> 00:31:16,650
+و هي ال on to ايش معناتها ان ال range يساوي كل
+
+347
+00:31:18,960 --> 00:31:22,660
+يساوي كل انت بقى بتقول ان والله ال range هي عبارة
+
+348
+00:31:22,660 --> 00:31:26,460
+عن positive and real number وال positive real
+
+349
+00:31:26,460 --> 00:31:30,360
+number هي عبارة عن مجموعة proper subset okay مش
+
+350
+00:31:30,360 --> 00:31:34,520
+مشكلة نفس المعنى في الآخر لكن عند النفي يا شباب
+
+351
+00:31:34,520 --> 00:31:38,160
+دايما بنلجأ لشغل اسمها ال counter example بتجيب
+
+352
+00:31:38,160 --> 00:31:41,600
+المثال اللي بينفي الموضوع بتجيب المثال اللي بينفي
+
+353
+00:31:41,600 --> 00:31:47,200
+الموضوع من
+
+354
+00:31:47,200 --> 00:31:54,440
+الدوالمن الدوالة المهمة اللى بتلزمها فى شغلنا
+
+355
+00:31:54,440 --> 00:31:57,640
+فاحنا فى ال computer science او related discipline
+
+356
+00:31:57,640 --> 00:32:01,500
+ال floor و ال ceiling ال floor و ال ceiling
+
+357
+00:32:01,500 --> 00:32:06,800
+الأرضية و السقف ال ceiling سقف ال floor الأرضية
+
+358
+00:32:06,800 --> 00:32:10,660
+طبعا هذه الدالة او الدوالة هذه معرفة من real
+
+359
+00:32:10,660 --> 00:32:11,140
+number
+
+360
+00:32:14,380 --> 00:32:17,880
+لـ Integer من الـ Real Number لـ Integer وعشان
+
+361
+00:32:17,880 --> 00:32:21,340
+اتحل الغموض او اللبس اللي ممكن يصير فيه عندك في
+
+362
+00:32:21,340 --> 00:32:25,680
+الـ Definition دائما استحضر ان شريط الأعداد او خط
+
+363
+00:32:25,680 --> 00:32:30,780
+الأعداد اعمله بدل ما هو أفقي اعمله عمودي صفر واحد
+
+364
+00:32:30,780 --> 00:32:36,240
+اتنين هي سالب واحد و سالب اتنين و بضل ماشي إلى ملا
+
+365
+00:32:36,240 --> 00:32:44,020
+نهاية الآن لو انا جيت جولت ال floorللواحد فاصلة
+
+366
+00:32:44,020 --> 00:32:51,760
+سبعة خمسة مش بياخد real number؟ واحد .. واحد ..
+
+367
+00:32:51,760 --> 00:32:52,020
+واحد .. واحد .. واحد .. واحد .. واحد .. واحد ..
+
+368
+00:32:52,020 --> 00:32:53,400
+واحد .. واحد .. واحد .. واحد .. واحد .. واحد ..
+
+369
+00:32:53,400 --> 00:32:54,320
+واحد .. واحد .. واحد .. واحد .. واحد .. واحد ..
+
+370
+00:32:54,320 --> 00:32:55,020
+واحد .. واحد .. واحد .. واحد .. واحد .. واحد ..
+
+371
+00:32:55,020 --> 00:32:58,000
+واحد .. واحد .. واحد .. واحد .. واحد .. واحد ..
+
+372
+00:32:58,000 --> 00:32:58,040
+واحد .. واحد .. واحد .. واحد .. واحد .. واحد ..
+
+373
+00:32:58,040 --> 00:32:58,440
+واحد .. واحد .. واحد .. واحد .. واحد .. واحد ..
+
+374
+00:32:58,440 --> 00:33:06,000
+واحد .. واحد .. واحد .. واحد ..
+
+375
+00:33:06,000 --> 00:33:14,060
+واحد .. واالـ floor هي عبارة عن أكبر عدد صحيح أصغر
+
+376
+00:33:14,060 --> 00:33:18,360
+من القيمة الحقيقية الموضعة لك أو يسويها طبعا عشان
+
+377
+00:33:18,360 --> 00:33:23,340
+تكون دائما في نفس المستوى يعني هيك المفروض ال
+
+378
+00:33:23,340 --> 00:33:27,920
+floor هي
+
+379
+00:33:27,920 --> 00:33:28,900
+ال largest
+
+380
+00:33:31,570 --> 00:33:35,510
+Integer او عدد صحيح بحيث ان الـ Z هتكون اكبر او
+
+381
+00:33:35,510 --> 00:33:40,670
+عفوا اقل او تساوي ال R اقل او تساوي ال R الان لما
+
+382
+00:33:40,670 --> 00:33:44,870
+انا بدي اجي هان واحد خمسة و سبعين هيها هان تقريبا
+
+383
+00:33:44,870 --> 00:33:48,110
+ال
+
+384
+00:33:48,110 --> 00:33:57,670
+floor تبعتها اكبر عدد صحيح اقل منها واحد لو اجيت
+
+385
+00:33:57,670 --> 00:34:01,230
+مع السالب مثلا
+
+386
+00:34:01,700 --> 00:34:09,560
+سالب سالب واحد وخمسة وسبعين ال floor تبعتها سالب
+
+387
+00:34:09,560 --> 00:34:17,460
+اتنين ال floor تبعتها سالب اتنين اكبر عدد صحيح اقل
+
+388
+00:34:17,460 --> 00:34:25,400
+منها سالب اتنين يعني هنا قلنا واحد لما قلنا هنا
+
+389
+00:34:25,400 --> 00:34:28,900
+سالب سبعة وخمسة
+
+390
+00:34:31,340 --> 00:34:35,020
+سالب اتنين لانه ليش انا ركزت على المثال هدا هيك
+
+391
+00:34:35,020 --> 00:34:39,320
+وقلتلك دايما خلي خط الاعداد عمودي بسهل عليك حكاية
+
+392
+00:34:39,320 --> 00:34:42,940
+floor و ceiling الان كتير من الشباب لما بيغلقوا في
+
+393
+00:34:42,940 --> 00:34:48,280
+مثال زي هذا ايش هو بيساوي اذا كانت هذه واحد فهذه
+
+394
+00:34:48,280 --> 00:34:52,580
+سالب واحد وكان الله بالسر عليهم لا يا صاحبي اياك
+
+395
+00:34:52,580 --> 00:35:02,110
+تخطئ في هيكالـ Ceiling function نفس الكلام نتكلم
+
+396
+00:35:02,110 --> 00:35:08,030
+عن أصغر عدد صحيح أكبر من القيمة عندهان Smallest
+
+397
+00:35:08,030 --> 00:35:14,430
+integer أكبر أو تساوي الرقم اللي موجود عندهان مين
+
+398
+00:35:14,430 --> 00:35:23,360
+الـ Ceiling للواحد فاصلة خمسة وسبعين؟ ساقف تبعهامن
+
+399
+00:35:23,360 --> 00:35:31,520
+السيلنج لـ 1.75؟ سالب واحد سالب واحد هي السيلنج
+
+400
+00:35:31,520 --> 00:35:42,260
+تبعيها لبعده ما شاء الله شباب
+
+401
+00:35:42,260 --> 00:35:44,580
+الكلام اللي أنا بقوله مافيش فيه شيء جديد المفروض
+
+402
+00:35:44,580 --> 00:35:49,280
+أضمر عليك في الثانوية ولا عمرك شفته في الثانوية؟
+
+403
+00:36:01,600 --> 00:36:07,720
+أول اللحظة أنا بتتكلم على ceiling السجف بقولنا ال
+
+404
+00:36:07,720 --> 00:36:12,720
+ceiling هي عبارة عن أصغر عدد صحيح أكبر من الرقم
+
+405
+00:36:12,720 --> 00:36:20,150
+هذا لأن الواحد أكبر من هذاالصفر أكبر من هذا لكنه
+
+406
+00:36:20,150 --> 00:36:25,350
+في واحد أصغر منهم لو السالب واحد أكبر من الرقم هذا
+
+407
+00:36:25,350 --> 00:36:28,590
+وفي نفس الوقت أصغر من الأرقام التانية كلها كانت
+
+408
+00:36:28,590 --> 00:36:35,790
+رقم صحيح فكانت النتيجة سالب واحد من
+
+409
+00:36:35,790 --> 00:36:42,770
+خصائص ال functions أنه لو كانت معرفة من a ل r أو
+
+410
+00:36:42,770 --> 00:36:45,270
+من a ل b يعني بين جثين لو كان في عندي two
+
+411
+00:36:45,270 --> 00:36:51,200
+functions معرفاتعلى نفس ال set نفس المجموعات عشان
+
+412
+00:36:51,200 --> 00:36:55,280
+اضمن انهم نفس ال domain و نفس ال target ال
+
+413
+00:36:55,280 --> 00:37:00,120
+function ممكن اناعش اجمعهم او اضوبهم في بعض و احصل
+
+414
+00:37:00,120 --> 00:37:05,260
+على نتيجة يعني لو قدجينا قولنا f of x بدي تساوي 2x
+
+415
+00:37:05,260 --> 00:37:14,630
+f of 1x و f of او f2 of x بدي تساوي x زائد 1وجد
+
+416
+00:37:14,630 --> 00:37:22,730
+قلتلك F1 زائد F2 of X ايش تساوي؟ بدك تروح تجمع
+
+417
+00:37:22,730 --> 00:37:28,110
+الدالتين هدول مع بعض الدالة الأولى F of X الاتنين
+
+418
+00:37:28,110 --> 00:37:34,850
+X زائد الدالة التانية X زائد واحد وتساوي تلاتة X
+
+419
+00:37:34,850 --> 00:37:43,330
+زائد واحد عند عملية الضرب F1
+
+420
+00:37:44,070 --> 00:37:49,670
+أف اتنين of X بدها تساوي اتنين X اللي هي الدالة
+
+421
+00:37:49,670 --> 00:37:57,050
+الأولى مضروبة في X زائد واحد هو تساوي اتنين X
+
+422
+00:37:57,050 --> 00:38:10,310
+تربيع زائد اتنين X تمام
+
+423
+00:38:16,150 --> 00:38:20,330
+لو احنا فكرنا نثبت انه ده الـ one to one او one to
+
+424
+00:38:20,330 --> 00:38:24,090
+احنا بنحاول نمشي مع ال definition لكن نمشي مع ال
+
+425
+00:38:24,090 --> 00:38:27,170
+definition دائما exactly ولا ممكن يكون فيه تغيير
+
+426
+00:38:27,170 --> 00:38:30,890
+تعالى نشوف التعبير هذا احنا ايش قولنا one to one
+
+427
+00:38:30,890 --> 00:38:38,090
+يا شباب؟ ايش قولنا one to one؟ كل عنصر في ال range
+
+428
+00:38:38,090 --> 00:38:42,730
+كل عنصر في ال range هو عبارة عن صورة ل element
+
+429
+00:38:42,730 --> 00:38:50,630
+واحد فقط من عناصر ال domainfor all x و y تنتمي لل
+
+430
+00:38:50,630 --> 00:38:55,350
+a لو أخدت أي عنصرين مختلفين في ال a
+
+431
+00:38:58,370 --> 00:39:03,370
+فى مفهوم مين؟ فى مفهوم الـ one to one و لو لجيت F
+
+432
+00:39:03,370 --> 00:39:06,350
+of X بيتساوي F of Y ايش يعني F of X بيتساوي F of
+
+433
+00:39:06,350 --> 00:39:10,910
+Y؟ يعني العنصرين اللي هم نفس ال image معناته X
+
+434
+00:39:10,910 --> 00:39:15,130
+بيتساوي Y هدى فى مفهوم مين؟ مفهوم ال one to one
+
+435
+00:39:15,130 --> 00:39:20,850
+يعني لو أخدت أي عنصرين من الدمان اي عنصرين من
+
+436
+00:39:20,850 --> 00:39:26,950
+الدمان و لجيت F of X بيتساوي F of Y و الدالة one
+
+437
+00:39:26,950 --> 00:39:32,210
+to oneمعناته ال X بيبقى تساوي Y وبغير هيك الكلام
+
+438
+00:39:32,210 --> 00:39:37,010
+بيكون مصحيح وقولنا دائما بنركز على ال counter
+
+439
+00:39:37,010 --> 00:39:43,550
+example اللي مشيناه قبل شوية في الشغل طيب الآن
+
+440
+00:39:43,550 --> 00:39:47,270
+بييجي بيقولي هاي الدالة F of X بيبقى تساوي تلاتة X
+
+441
+00:39:47,270 --> 00:39:54,230
+هل هي الدالة هادي one to one ايه F of X بيبقى
+
+442
+00:39:54,230 --> 00:39:59,940
+تساوي تلاتة Xهندال هذه one to one الفكرة يا شباب
+
+443
+00:39:59,940 --> 00:40:05,440
+إذا بدنا نقول اه مانفعش أشتغل بأرقام، بدك تثبت،
+
+444
+00:40:05,440 --> 00:40:08,640
+بدك تروح مرحلة إثبات رياضة و احنا قولنا الإثبات هي
+
+445
+00:40:08,640 --> 00:40:13,100
+ده إيش، بدنا نأخره شوية، أحسن، بس هنشوف الفكرة أين
+
+446
+00:40:13,100 --> 00:40:16,940
+بدك تمشي، بدك تحاول تشتغل على ال definition، بدك
+
+447
+00:40:16,940 --> 00:40:20,380
+تشتغل على ال definition، الفكرة في هو أن هي ال
+
+448
+00:40:20,380 --> 00:40:20,720
+definition
+
+449
+00:40:23,690 --> 00:40:28,110
+فإذا انا بدى اخد عنصرين مختلفين من ال range لازم
+
+450
+00:40:28,110 --> 00:40:32,090
+يكونهم عنصرين مختلفين في ال domain و لا لا يعني
+
+451
+00:40:32,090 --> 00:40:35,230
+هيك لو قلت ان في عندي صورتين مختلفتين F of X لا
+
+452
+00:40:35,230 --> 00:40:40,950
+تساوي F of Y معناته حتما X لا تساوي Y هذا تعريف ال
+
+453
+00:40:40,950 --> 00:40:43,430
+one to one وبالتالي انا بدى امشي بال definition
+
+454
+00:40:43,430 --> 00:40:47,430
+لحد ما اصل لمين للكلام اللى مولود هان سيبونا منه
+
+455
+00:40:47,430 --> 00:40:49,590
+لحد ما يصل لموضوع ال definition او الاثبات اللى
+
+456
+00:40:49,590 --> 00:40:53,380
+بنتكلم فيه ان شاء الله تعالىننتقل لخاصية بعدها وهي
+
+457
+00:40:53,380 --> 00:40:57,440
+خاصية او موضوع ال composition ال composition هي
+
+458
+00:40:57,440 --> 00:41:02,040
+عبارة عن function او انتقال لل function اللي موجود
+
+459
+00:41:02,040 --> 00:41:08,700
+عندى لو كنت بتكلم على two functions f و g جي معرفة
+
+460
+00:41:08,700 --> 00:41:17,600
+من ال a لل b و ال f معرفة من ال b لل c يعني بين
+
+461
+00:41:17,600 --> 00:41:24,510
+جثين بين جثينان ال target set تبعتي الأولى مثلت ال
+
+462
+00:41:24,510 --> 00:41:31,070
+domain تبعتي التانية بالضبط ممكن احصل على function
+
+463
+00:41:31,070 --> 00:41:37,170
+من a ل c ممكن احصل على function من a ل c اللي احنا
+
+464
+00:41:37,170 --> 00:41:43,710
+بنسميها composition f circle g او fog اللي هي ال
+
+465
+00:41:43,710 --> 00:41:46,430
+composition تبع الجي و اللي هي بتتساوي
+
+466
+00:41:50,180 --> 00:41:58,040
+G of A الان F of ايش اللي لازم يكون جوا الجثة هنا
+
+467
+00:41:58,040 --> 00:42:02,060
+يا شباب؟ ايش العنصر هذا لازم يكون ينتمي لمين؟
+
+468
+00:42:02,060 --> 00:42:05,380
+العنصر
+
+469
+00:42:05,380 --> 00:42:09,520
+اللي لازم يكون جوا الجثة بينتمي لمين؟ بينتمي لل B
+
+470
+00:42:09,520 --> 00:42:16,400
+لل domain تبع ال F بينتمي لل domainكمان مرة لما
+
+471
+00:42:16,400 --> 00:42:21,060
+انا كنت بقول هاي ال F معرفة من ال A الى ال B سيبك
+
+472
+00:42:21,060 --> 00:42:25,480
+من المثال هذا و دي هتقول اللي قلتلك ال F of بده
+
+473
+00:42:25,480 --> 00:42:31,540
+تساوي كده العناصر اللي هان من ال domain مصبوط و
+
+474
+00:42:31,540 --> 00:42:35,880
+هذه العناصر اللي هان بتكون ال image او ال code
+
+475
+00:42:35,880 --> 00:42:41,280
+domain ولا لأ نفس الكلام اللي انا بده اسقطه هان من
+
+476
+00:42:41,280 --> 00:42:45,930
+العنصر اللي بده يكون هان من عناصر ال domaindomain
+
+477
+00:42:45,930 --> 00:42:57,650
+الـ F اللي هي B بصبوط؟ طيب G of الـ A إيش بتتساوي؟
+
+478
+00:42:57,650 --> 00:43:04,810
+B اللي هي بتنتمي لمين؟ لل code domain تبعتي الـ B
+
+479
+00:43:04,810 --> 00:43:09,530
+وبالتالي هذه المعادلة بتكون صحيحة هيك يعني الآن
+
+480
+00:43:09,530 --> 00:43:13,150
+الدالة تبعتي عشان تكون معرفة صح لازم يكون كل
+
+481
+00:43:13,150 --> 00:43:18,160
+element Mبمثّل عناصر من الـ domain تبعتها، من الـ
+
+482
+00:43:18,160 --> 00:43:23,340
+V وبما أن الدالة هيوم جلف من الداخل F of A أو G of
+
+483
+00:43:23,340 --> 00:43:28,200
+A عفوا الـ G of A هي عبارة عن صوة يعني هي عبارة عن
+
+484
+00:43:28,200 --> 00:43:34,120
+عنصر موجود في مين؟ موجود في B وبالتالي ال
+
+485
+00:43:34,120 --> 00:43:37,420
+definition تبعت ال composition صحيح، مافيش فيه
+
+486
+00:43:37,420 --> 00:43:37,800
+مشكلة
+
+487
+00:43:47,500 --> 00:43:53,300
+كيف؟ لأ انا حصلت على دالة جديدة من A ل C انا حصلت
+
+488
+00:43:53,300 --> 00:44:00,940
+على دالة جديدة من A ل C الدالة اسمها F circle G F
+
+489
+00:44:00,940 --> 00:44:08,420
+circle G و من اسمها ان هذه عبارة عن F of G of X
+
+490
+00:44:20,710 --> 00:44:24,250
+تعالى نشوف نعمل composition اوكى بدي اعمل
+
+491
+00:44:24,250 --> 00:44:28,910
+composition بين دلتين لو فجل هي F و G موجودة عندكم
+
+492
+00:44:28,910 --> 00:44:35,070
+عرفات من ال R ل R اش يعني R ل R يعني هذه هي نفسها
+
+493
+00:44:35,070 --> 00:44:42,730
+هذه وبالتالي بقدر احصل على composition من ال R ل R
+
+494
+00:44:42,730 --> 00:44:47,690
+ال composition تابعيش مفاده يا شباب ال composition
+
+495
+00:44:47,690 --> 00:45:02,960
+تابعيش مفادهF of G of X بشكل هذا يعني انا ممكن
+
+496
+00:45:02,960 --> 00:45:06,080
+اطبق ال G of X في الأول ال G و بعدين ممكن اطبق من
+
+497
+00:45:06,080 --> 00:45:14,880
+ال F طيب لو انا قلتلك F circle G of 2 ايش تساوي؟
+
+498
+00:45:14,880 --> 00:45:21,830
+معناه F of G of 2جيوف اتنين اشتو ساوي حسب ال
+
+499
+00:45:21,830 --> 00:45:28,330
+definition هي ده ستة بصبوط اف اف اتنين ضرب تلات او
+
+500
+00:45:28,330 --> 00:45:35,770
+تلاخد ضرب اتنين ستة معناته اف ستة و اف ستة هي
+
+501
+00:45:35,770 --> 00:45:39,730
+تساوي سبعة في ستة ناقص اربعة سبعة في ستة اتنين
+
+502
+00:45:39,730 --> 00:45:49,130
+واربعين ناقص اربعة تمانية و تلاتين كيف؟
+
+503
+00:45:50,670 --> 00:45:54,430
+هك بتحل انت بس الفكرة انه انا مش هستنى ان اعمل
+
+504
+00:45:54,430 --> 00:46:00,950
+الكلام هذا او ال function بالشكل هذا ليش؟ بما انه
+
+505
+00:46:00,950 --> 00:46:05,550
+انا بدي اخد ال G of X في الداخل هيك طب ليش ما اخد
+
+506
+00:46:05,550 --> 00:46:12,050
+كل X هان و اعوض عنها بالدلة اللي هان؟ و بتصير عندي
+
+507
+00:46:12,050 --> 00:46:20,080
+هان المدلة F circle G of Xبدا تساوي 7 او خلينا
+
+508
+00:46:20,080 --> 00:46:27,880
+نفصلها كمان مرة F of G of X و بدا تساوي 7 مكان كل
+
+509
+00:46:27,880 --> 00:46:36,460
+X بدي احط GX ايش قيمة الـ GX 3X ناقص 4 بدا تساوي
+
+510
+00:46:36,460 --> 00:46:50,350
+21X ناقص 4 طيب دعنا نشوف FCircle G of 2 تساوي 21
+
+511
+00:46:50,350 --> 00:47:02,260
+في 2 ناقص 4 42 ناقص 4 يساوي 48تمانية و تلاتين
+
+512
+00:47:02,260 --> 00:47:05,220
+فعليا هذا اللي انا بدي اعمل composition انا مابديش
+
+513
+00:47:05,220 --> 00:47:09,580
+اطبق بالطريقة العقيمة السابقة بقصد انه او الهدف
+
+514
+00:47:09,580 --> 00:47:12,840
+اللي انا بديه ان بال composition بحصل على function
+
+515
+00:47:12,840 --> 00:47:17,260
+جديدة بحصل على function جديدة بتكون عبارة عن
+
+516
+00:47:17,260 --> 00:47:22,980
+applicable function من domain الأولى domain الأولى
+
+517
+00:47:22,980 --> 00:47:28,020
+ل target التانية كيف يعني two elements؟
+
+518
+00:47:28,900 --> 00:47:32,040
+اكس و واي حسب المهمة تحافظ على ال definition يكون
+
+519
+00:47:32,040 --> 00:47:41,280
+صحيح بدون اي مشاكل الان
+
+520
+00:47:41,280 --> 00:47:49,620
+لما احنا نتكلم عن ال by adjective معناته
+
+521
+00:47:49,620 --> 00:47:55,150
+انا في عندي F من ال Aلل B one to one و one to two
+
+522
+00:47:55,150 --> 00:47:59,190
+هذا بيعطيني مباشرة ان هناك دالة عكسية تماما
+
+523
+00:47:59,190 --> 00:48:05,590
+بنسميها F inverse معرفة من ال B إلى ال A و من هنا
+
+524
+00:48:05,590 --> 00:48:11,310
+اسمها inverse من ال B لل A بترجع ال element لأصله
+
+525
+00:48:11,310 --> 00:48:15,390
+الآن لو أنا بدي أعمل composition أو أجمع كل دالة
+
+526
+00:48:15,390 --> 00:48:19,690
+مع ال inverse تبعها بحصل على مين؟ بحصل على ال
+
+527
+00:48:19,690 --> 00:48:25,040
+element بحصل على ال elementتعالى نشوف مثال موجود
+
+528
+00:48:25,040 --> 00:48:28,300
+عندى هنا طبعا ال composition مع الدالة ما بين
+
+529
+00:48:28,300 --> 00:48:31,520
+الدالة و ال inverse سبعها بتديني identity function
+
+530
+00:48:31,520 --> 00:48:36,760
+بتديني identity function بقول
+
+531
+00:48:36,760 --> 00:48:43,200
+لي هى فى عندي two functions F و G معرفات ال F من R
+
+532
+00:48:43,200 --> 00:48:48,540
+إلى 1 إلى ملا نهاية اللى بين جثين ممكن نقولها R
+
+533
+00:48:48,540 --> 00:48:54,700
+plus معادل صفر و معادل واحدOkay وبالتالي و الجي
+
+534
+00:48:54,700 --> 00:49:03,300
+معرفة من كده لكده الآن جاوبني نعم او لا F circle G
+
+535
+00:49:03,300 --> 00:49:13,560
+of X exist F circle G exist F circle G كده لأ
+
+536
+00:49:13,560 --> 00:49:16,660
+معرفة حسب التعريف السابق ولا لأ؟
+
+537
+00:49:28,550 --> 00:49:32,030
+عشان تقول معرفة او لا اذكر ال definition هذا اذا
+
+538
+00:49:32,030 --> 00:49:37,370
+كان ال target تبعت التانية عفوا اللي تبعت ال G
+
+539
+00:49:37,370 --> 00:49:42,270
+تمام؟ هو نفسه تبعت ال domain بتكون معرفة و اين ال
+
+540
+00:49:42,270 --> 00:49:47,390
+target تبعت ال G؟ ال R ال
+
+541
+00:49:47,390 --> 00:49:53,170
+R هي نفسها ال domain تبعت ال F؟ تمام لو انا قلت G
+
+542
+00:49:53,170 --> 00:50:03,940
+circle F of Xمعناته g of f of x مفهومها إن ال
+
+543
+00:50:03,940 --> 00:50:09,340
+target تبعت ال f لازم يكون نفس ال domain تبعت ال g
+
+544
+00:50:09,340 --> 00:50:13,060
+target ال f هيها و ال domain تبعت ال g هيها
+
+545
+00:50:13,060 --> 00:50:17,280
+وبالتالي هذه exist تنتهي موجودة حسب ال definition
+
+546
+00:50:17,280 --> 00:50:19,260
+الموجودة عندنا تمام
+
+547
+00:50:24,470 --> 00:50:30,510
+بقول إن في دلتين F of X معرفة على أنها ثلاثة أقصى
+
+548
+00:50:30,510 --> 00:50:37,370
+اتنين X زائد واحد والـ G of X بتساوي نص log X نقص
+
+549
+00:50:37,370 --> 00:50:41,890
+واحد للأساس ثلاثة وبدي أعمل composition بين
+
+550
+00:50:41,890 --> 00:50:46,470
+التنتين بدي أعمل composition ما بين التنتين بدي
+
+551
+00:50:46,470 --> 00:50:52,570
+أحسب F circle G of X أيش بتساوي معناته بتساوي
+
+552
+00:50:52,570 --> 00:50:53,350
+تلاتة
+
+553
+00:50:56,210 --> 00:51:03,970
+مرفوعة على اتنين مضروبة فيه نص log ال X ناقص واحد
+
+554
+00:51:03,970 --> 00:51:09,590
+ده الأساس تلاتة الكل زائد واحد بيقول هذا كلام أنا
+
+555
+00:51:09,590 --> 00:51:14,430
+جبته قولت بدي أهرف حسب ال definition هذا بدي أعوض
+
+556
+00:51:14,430 --> 00:51:20,170
+عن كل X في ال F بقيمة G of X هاي ال composition
+
+557
+00:51:22,790 --> 00:51:27,310
+تعالى نحلل فروحت وان ال X هي ال X اللي هنا بده
+
+558
+00:51:27,310 --> 00:51:32,210
+أروح أستبدلها بهدون الان
+
+559
+00:51:32,210 --> 00:51:39,610
+تنين و النص بيروحوا مع بعض بتصفر
+
+560
+00:51:39,610 --> 00:51:49,770
+عندي المسألة تلاتة أس log X ناقص واحد للتلاتة
+
+561
+00:51:49,770 --> 00:51:58,450
+زائد واحدالان log x
+
+562
+00:51:58,450 --> 00:52:04,310
+ناقص واحد للأساس تلاتة تساوي x ناقص واحد في واحد
+
+563
+00:52:04,310 --> 00:52:09,550
+زائد واحد الان
+
+564
+00:52:09,550 --> 00:52:15,710
+تلاتة قص log x للأساس تلاتة تساوي x في واحد انا
+
+565
+00:52:15,710 --> 00:52:19,680
+عند x ناقص واحد زي ما هي هيكX ناقص واحد في واحد
+
+566
+00:52:19,680 --> 00:52:26,360
+يعني بين قصين هيك يا شباب القانون عندي A أُس log X
+
+567
+00:52:26,360 --> 00:52:33,980
+للأساس A تساوي X تساوي X لأن صفت عند المسألة تساوي
+
+568
+00:52:33,980 --> 00:52:39,940
+X ناقص واحد زائد واحد وتساوي X معناته هذه inverse
+
+569
+00:52:39,940 --> 00:52:47,170
+لهذهمعناته هذه هي عبارة عن المعكوس تبع الدالة اللى
+
+570
+00:52:47,170 --> 00:52:50,450
+موجودة عندنا هن و ليش حكمنا علي انفرستون اللي
+
+571
+00:52:50,450 --> 00:52:54,670
+نحنا؟ لأنها
+
+572
+00:52:54,670 --> 00:53:00,390
+عبارة عن دالة عكسية كانت قولنا identity function
+
+573
+00:53:00,390 --> 00:53:03,250
+لما انا بعمل composition مع ال inverse الاصل
+
+574
+00:53:03,250 --> 00:53:06,610
+بيديني ال element نفسه هي ال composition function
+
+575
+00:53:06,610 --> 00:53:11,510
+اللى موجودة عندناوهذا خلّانا نفتح موضوع ال inverse
+
+576
+00:53:11,510 --> 00:53:14,190
+function لو كان في عندي أي دالة معرفة و بدي أحصل
+
+577
+00:53:14,190 --> 00:53:17,710
+لل inverse function ال inverse function لازم تكون
+
+578
+00:53:17,710 --> 00:53:20,490
+ال F عندي by adjective ايش يعني by adjective يا
+
+579
+00:53:20,490 --> 00:53:28,110
+شباب؟ يعني one to one و onto يعني كل عنصر في المدى
+
+580
+00:53:28,110 --> 00:53:34,450
+يكون مرتبط أو بيمثل صورة لعنصر واحد في الدمين
+
+581
+00:53:35,530 --> 00:53:39,150
+وعراصر و المدى اللي هو ال range عمومة الصور تساوي
+
+582
+00:53:39,150 --> 00:53:45,190
+كل ال target كل عراصر ال code domain عشان لما أجي
+
+583
+00:53:45,190 --> 00:53:49,870
+أقولك العكس لازم تكون function كمان مرة لو أنا
+
+584
+00:53:49,870 --> 00:53:57,490
+قولت F معرفة من A ل B F inverse المفروض تكون من B
+
+585
+00:53:59,060 --> 00:54:03,820
+لأيه؟ راح انتبه معاه شوية ومش بس هيك شباب عارف ليش
+
+586
+00:54:03,820 --> 00:54:09,320
+لازم تكون هنا on two؟ عشان لما بدي أعمل العكس لو
+
+587
+00:54:09,320 --> 00:54:15,880
+كان في عنصر واحد من ال B لا ينتمي لل range مش
+
+588
+00:54:15,880 --> 00:54:19,120
+هتكون الدالة معرفة، هصير في عندي مشكلة في تعريف
+
+589
+00:54:19,120 --> 00:54:23,040
+عنصر واحد وكل عشان تصير function لازم يكون كل
+
+590
+00:54:23,040 --> 00:54:27,440
+العراسر تبع ال domain موجودةوبالتالي هذه الـ ..
+
+591
+00:54:27,440 --> 00:54:30,260
+لازم الدالة تبعتنا تكون objective عشان أولد ال
+
+592
+00:54:30,260 --> 00:54:34,380
+inverse تبعتها ولمّا بتكون ال inverse تبعتها هيهم
+
+593
+00:54:34,380 --> 00:54:39,640
+مثلا التوزيع تبعتي للتخصصات هي objective مظبوط؟
+
+594
+00:54:39,640 --> 00:54:43,340
+وبالتالي أنا بقدر أتكلم على ال inverse بالشكل هذا
+
+595
+00:54:43,340 --> 00:54:50,460
+من التخصص للطالب يعني مثلا في الأول بدي أقولك إيش
+
+596
+00:54:50,460 --> 00:54:55,450
+تخصص أحمد؟Computer Science طب لو أنا قلتلك من
+
+597
+00:54:55,450 --> 00:54:57,590
+الطالب اللي في تخصص ال computer ال software
+
+598
+00:54:57,590 --> 00:55:02,330
+development لما بتعرف أن الدالة one to one و one
+
+599
+00:55:02,330 --> 00:55:05,370
+to up و simple adjective بتقدر تقولي Sally أصبت
+
+600
+00:55:05,370 --> 00:55:09,130
+وبالتالي أنا بقدر أصير أعتمد على القيم تبعت ال
+
+601
+00:55:09,130 --> 00:55:13,170
+code main أو ال range اللي موجود عندي هن بشكل عام
+
+602
+00:55:13,170 --> 00:55:17,170
+يا صاحبي تعالي نشتغل رياضيات بشكل أفضل لو أنا في
+
+603
+00:55:17,170 --> 00:55:21,530
+عندي دالة و بدي أجيبها الدالة تبعتي Fis a
+
+604
+00:55:21,530 --> 00:55:24,230
+bijective و بدي أجيب ال inverse تبعتها في عندي
+
+605
+00:55:24,230 --> 00:55:28,850
+خطوات بسيطات و بدنا نعتمد عليهم الخطوة رقم واحد
+
+606
+00:55:28,850 --> 00:55:34,390
+استبدل F of X طب عشان نطبق على المثال مع بعضنا لو
+
+607
+00:55:34,390 --> 00:55:41,190
+افترضت ان انا F of X بدها تساوي X زائد واحد او
+
+608
+00:55:41,190 --> 00:55:44,970
+اتنين X زائد واحد وانسال ال domain وانسال ال range
+
+609
+00:55:44,970 --> 00:55:49,740
+الآن وافترض ان الدالة هادي bijectiveأفترض أن
+
+610
+00:55:49,740 --> 00:55:53,580
+الدالة هذه by adjective عشان ما ألخمكاش في موضوع
+
+611
+00:55:53,580 --> 00:55:57,360
+ال range و ال domain بقول الخطوة .. بود أجيب ال
+
+612
+00:55:57,360 --> 00:56:01,260
+inverse بقول الخطوة رقم واحد استبدل ال Y بقفل X
+
+613
+00:56:01,260 --> 00:56:06,140
+يعني Y بدها تساوي اتنين X زائد واحد خطوة رقم واحد
+
+614
+00:56:06,140 --> 00:56:11,520
+الخطوة التانية استبدل كل X ب Y و كل Y ب X يعني بدل
+
+615
+00:56:11,520 --> 00:56:17,300
+مكان بعض معناه الخطوة رقم اتنين X بدها تساوي اتنين
+
+616
+00:56:17,300 --> 00:56:23,600
+Yزائد واحد الخطوة رقم تلاتة حل المسألة بحيث انك
+
+617
+00:56:23,600 --> 00:56:30,900
+تجيب قيمة ال Y الان بدك تجيب قيمة Y معناته تلاتة
+
+618
+00:56:30,900 --> 00:56:36,780
+او X ناقص واحد بدها تساوي اتنين Y مظبوط؟ اضافت
+
+619
+00:56:36,780 --> 00:56:40,340
+واحد علي الطرفين الان بدي اخلص من التنين هنا
+
+620
+00:56:40,340 --> 00:56:44,960
+معناته ال Y بدها تساوي X ناقص واحد على اتنين اللي
+
+621
+00:56:44,960 --> 00:56:49,470
+هي بين جسيم نص مضروبة في X ناقص واحد مظبوط؟الان
+
+622
+00:56:49,470 --> 00:56:55,170
+اذا انا قدرت اعمل composition بين هذه و هذه و احصل
+
+623
+00:56:55,170 --> 00:56:59,910
+على x بيكون ال inverse تبعي صحيح 100% لان ال
+
+624
+00:56:59,910 --> 00:57:02,590
+composition ما بين ال function و ال inverse تبعتها
+
+625
+00:57:02,590 --> 00:57:06,010
+عبارة عن identity function بتديني ال x تعالى
+
+626
+00:57:06,010 --> 00:57:13,390
+نعوضها هي f of g of x على فرض ان ال g of x هي ال
+
+627
+00:57:13,390 --> 00:57:20,380
+inverse أصبت بدها تساويقلنا مكان كل x بيحط g of x
+
+628
+00:57:20,380 --> 00:57:29,400
+نص في x ناقص واحد زائد واحد الآن التنين مع النص و
+
+629
+00:57:29,400 --> 00:57:34,800
+بتتصف في المثل x ناقص واحد زائد واحد و بيتساوي x
+
+630
+00:57:34,800 --> 00:57:37,900
+ميهاتو ال inverse تبعتي سليمة مية في المية
+
+631
+00:57:44,450 --> 00:57:49,610
+حلنا زي ما بدنا اشياه تعالى نشوف اللى بعده هداك هو
+
+632
+00:57:49,610 --> 00:57:53,670
+المثال هذا
+
+633
+00:57:53,670 --> 00:57:57,870
+F
+
+634
+00:57:57,870 --> 00:58:04,550
+of X بيتساوي ستة ناقص X على اتنين ستة ناقص X على
+
+635
+00:58:04,550 --> 00:58:12,350
+اتنين Y بيتساوي ستة ناقص X على اتنين X بيتساوي لا
+
+636
+00:58:12,350 --> 00:58:19,430
+مش سالب هذا الشرط الترقيميستة ناقص Y على اتنين Y
+
+637
+00:58:19,430 --> 00:58:25,770
+على اتنين بدها تساوي X ناقص ستة مصبوط انا بس هذه
+
+638
+00:58:25,770 --> 00:58:29,990
+المسألة هيك المفروض تكون X ناقص ستة بتساوي Y على
+
+639
+00:58:29,990 --> 00:58:37,810
+اتنين صح استنى
+
+640
+00:58:37,810 --> 00:58:44,170
+شوية أستاذي الآن المفروض ال X زائد زائدزائد ستة
+
+641
+00:58:44,170 --> 00:58:50,010
+وهدى سالب هدى سالب Y على اتنين اروح اضربت في
+
+642
+00:58:50,010 --> 00:58:54,170
+السالب اضربت
+
+643
+00:58:54,170 --> 00:58:55,530
+الطرفين في سالب واحد
+
+644
+00:58:58,770 --> 00:59:02,210
+خلّيها زي ما هي خلّيها زي ما هي فاش مشكلة تعالي
+
+645
+00:59:02,210 --> 00:59:05,670
+نشوف زي ما انت تعرفه أسهل لك خلّينا معانا بكل
+
+646
+00:59:05,670 --> 00:59:09,850
+بساطة الآن بدي أنا أقول الستة اللي أبرق ستة ششرتها
+
+647
+00:59:09,850 --> 00:59:16,990
+موجبة X ناقص ستة بدأ تساوي ناقص Y على اتنين الآن
+
+648
+00:59:16,990 --> 00:59:21,130
+بدي أخلص من السالب نص هذه بدي أضرب في سالب اتنين
+
+649
+00:59:21,130 --> 00:59:27,300
+اتوا سالب اتنيندرب X ناقص ستة بيتساوي سالب اتنين
+
+650
+00:59:27,300 --> 00:59:32,440
+في ناقص او في Y على اتنين عشان نخلص منهم الآن
+
+651
+00:59:32,440 --> 00:59:37,220
+بيصير في عندي ناقص اتنين X زائد اتناشه انه سالب
+
+652
+00:59:37,220 --> 00:59:44,500
+اتنين في سالب ستة ناشه بيتساوي ال Y خلصنا او بين
+
+653
+00:59:44,500 --> 00:59:50,700
+جثيم بيعدلها ال Y بيتساوي اتناشه ناقص اتنين X هذا
+
+654
+00:59:50,700 --> 00:59:54,470
+ال inverse تبعت الدالة اللي فوقهذا الانفارس تبعت
+
+655
+00:59:54,470 --> 01:00:01,890
+الدالة اللي فوق المثال اللي بعده
+
+656
+01:00:01,890 --> 01:00:05,530
+تلاتة
+
+657
+01:00:05,530 --> 01:00:13,580
+X تربية زائد واحد Y بتتساويتلاتة X تربيع زائد واحد
+
+658
+01:00:13,580 --> 01:00:19,040
+X بيتساوي تلاتة Y تربيع زائد واحد هذا خطوة رقم
+
+659
+01:00:19,040 --> 01:00:22,040
+واحد الآن بدي أبدأ أحل المسألة عشان بدي ال Y
+
+660
+01:00:22,040 --> 01:00:28,580
+لحالها X ناقص واحد بيتساوي تلاتة Y تربيع الآن بدي
+
+661
+01:00:28,580 --> 01:00:34,420
+أخلص من التلاتة X ناقص واحد على تلاتة بيتساوي Y
+
+662
+01:00:34,420 --> 01:00:41,510
+تربيع الآن ال Yبدي اتساوي الجدري التربيعي ل X ناقص
+
+663
+01:00:41,510 --> 01:00:47,910
+واحد على تلاتة كيف؟
+
+664
+01:00:47,910 --> 01:00:51,250
+مافيقول؟
+
+665
+01:00:51,250 --> 01:00:54,710
+الله
+
+666
+01:00:54,710 --> 01:00:59,610
+يسامحه طيب
+
+667
+01:00:59,610 --> 01:01:05,040
+المثال الأخير بالمثال الأخيرالان ما هو عشان جبتلك
+
+668
+01:01:05,040 --> 01:01:09,180
+واحد فيه ضرب و واحد جمع و واحد القص و واحد فيه log
+
+669
+01:01:09,180 --> 01:01:14,780
+بلاش منه بلاش منه طيب ليش قانون ال log بسيط جدا يا
+
+670
+01:01:14,780 --> 01:01:26,640
+شباب log ال a للأساس a equal واحد a أسط log x
+
+671
+01:01:26,640 --> 01:01:37,940
+للأساس a x و العكس صحيح ال logالـ A أُس X للأساس A
+
+672
+01:01:37,940 --> 01:01:42,260
+بيتساوي X حسب القانون اللي فوق عندي هم وعندي كمان
+
+673
+01:01:42,260 --> 01:01:53,900
+قانون بسيط Log X ضرب ال Y للأساس A يساوي Log X
+
+674
+01:01:53,900 --> 01:01:58,680
+للأساس A زائد Log Y للأساس A ولو كانت العملية
+
+675
+01:01:58,680 --> 01:02:04,810
+طريحة لو كانت جسمي بتصير طريحةهذه قوانين الاص أو
+
+676
+01:02:04,810 --> 01:02:11,430
+قوانين ال log السهلة اللي ممكن تتذكرها تعالى y بدت
+
+677
+01:02:11,430 --> 01:02:20,150
+ساوي log تنير او x زائد واحد للاساس تنير بدل x بدت
+
+678
+01:02:20,150 --> 01:02:26,160
+ساوي logالـ y زائد واحد ده الأساسي اتنين الان أنا
+
+679
+01:02:26,160 --> 01:02:29,480
+بدي أخلص من مين؟ بدي أخلص من ال log من ال
+
+680
+01:02:29,480 --> 01:02:32,940
+logarithm ايش ال base تبعته؟ اتنين يعني انا لو
+
+681
+01:02:32,940 --> 01:02:36,360
+وفعته للأساسي اتنين بخلص منه كل بساطة حسب القانون
+
+682
+01:02:36,360 --> 01:02:43,980
+هي ده معناته بقول اتنين قص x بدها تساوي اتنين قص
+
+683
+01:02:43,980 --> 01:02:50,130
+logالـ X الـ Y عفوا زائد واحد الأساس اتنين و بدها
+
+684
+01:02:50,130 --> 01:02:55,450
+تساوي Y زائد واحد يعني هذا القطة اللي بس بكتبها
+
+685
+01:02:55,450 --> 01:03:00,750
+عشان أقول هيها مظبوط؟ هدا هي أنا قولت رفعت التنين
+
+686
+01:03:00,750 --> 01:03:05,510
+الطرفين المعادلة لأن الشغف بسيط جدا يا شباب أي
+
+687
+01:03:05,510 --> 01:03:09,150
+عملية بدك تنفذها على احد الطرفين بدك تنفذها على
+
+688
+01:03:09,150 --> 01:03:12,650
+الطرف التاني عشان تبقى المعادلة متساوية فان رفعت
+
+689
+01:03:12,650 --> 01:03:22,440
+التنين الأساستنين الان صارت يعندي اتنين X ناقص
+
+690
+01:03:22,440 --> 01:03:32,820
+واحد بدها تساوي ال Y معناته F inverse لل X بدها
+
+691
+01:03:32,820 --> 01:03:40,120
+تساوي اتنين X ناقص واحد الان هذا الكلام يكون صحلو
+
+692
+01:03:40,120 --> 01:03:44,280
+عملت ال composition معها دي الدالة وعطاني X ماحنا
+
+693
+01:03:44,280 --> 01:03:48,060
+قبل شوية عاملين ولا لا في المثال السابق هيا خد عن
+
+694
+01:03:48,060 --> 01:03:55,180
+2 X هان وعوضها 2 أُس X ماقص واحد الواحد بروح مع
+
+695
+01:03:55,180 --> 01:04:04,120
+الواحد بصف عندي log 2 أُس X للأساس 2 وليه بتتساوي
+
+696
+01:04:04,120 --> 01:04:08,400
+X وبالتالي ال inverse تبعتنا هان صحيحة 100%
+
+697
+01:04:15,990 --> 01:04:18,970
+في أي سؤال يا شباب؟ كدا؟ الله يعطيكوا العافية
+
diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/zrkaFn0izUk.srt b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/zrkaFn0izUk.srt
new file mode 100644
index 0000000000000000000000000000000000000000..7500daa449de2116ee7cf03b0c4763ed6143587f
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/zrkaFn0izUk.srt
@@ -0,0 +1,2444 @@
+1
+00:00:21,090 --> 00:00:23,190
+بسم الله والحمد لله والصلاة والسلام على رسول الله
+
+2
+00:00:23,190 --> 00:00:27,590
+كنا في المحاضرة الماضية يا شباب، اتكلمنا على مجموعة من
+
+3
+00:00:27,590 --> 00:00:30,330
+المهمة.. مجموعة مهمة من الـ definitions فيما يتعلق
+
+4
+00:00:30,330 --> 00:00:34,750
+بموضوع الـ graphs. اتكلمنا على الـ walk، وهو عبارة عن
+
+5
+00:00:34,750 --> 00:00:38,050
+مجموعة أو sequence، مجموعة من الـ vertices والـ edges
+
+6
+00:00:38,050 --> 00:00:41,590
+المتتالية، لازم يكون في بينها ربط، والـ length تبع
+
+7
+00:00:41,590 --> 00:00:45,110
+الـ walk يمثل بعدد الـ edges. وقلنا الـ walk مكون
+
+8
+00:00:45,110 --> 00:00:49,600
+closed لما بيبدأ وينتهي عند نفس النقطة، وعكسها
+
+9
+00:00:49,600 --> 00:00:52,960
+بيكون open. في عنده definition للـ walk آخر اسمه
+
+10
+00:00:52,960 --> 00:00:56,180
+trail، لما بيكون هذا الـ walk بيحتوي على distinct
+
+11
+00:00:56,180 --> 00:01:01,500
+edges، بيحتوي على جسور مختلفة، و بسميه path لما بكون
+
+12
+00:01:01,500 --> 00:01:06,500
+الـ path لما بيكون عندي بيحتوي على vertices مختلفة، و
+
+13
+00:01:06,500 --> 00:01:09,740
+لما يكون هذا trail closed، يعني بدأ وانتهى بنفس
+
+14
+00:01:09,740 --> 00:01:13,820
+النقاط وكل الجسور اللي فيه مختلفة، بسميه circuit، و
+
+15
+00:01:13,820 --> 00:01:18,460
+لما بيكون الـ path اللي عندي بينتهي بنفس النقطة
+
+16
+00:01:18,460 --> 00:01:24,980
+باستثناء، سميناها cycle. وشوفنا المثال هذا وحلينا منه
+
+17
+00:01:24,980 --> 00:01:28,420
+في المحاضرة الماضية. اليوم إن شاء الله تعالى هنبدأ مع
+
+18
+00:01:28,420 --> 00:01:32,180
+definition جديد، نسميه Euler circuit و Euler path.
+
+19
+00:01:32,180 --> 00:01:37,920
+في لبس أحيانًا بيصير في موضوع اللي فهمناه، الـ Euler
+
+20
+00:01:37,920 --> 00:01:42,240
+circuit والـ Euler path، خصوصًا لما اتكلم على الـ path.
+
+21
+00:01:42,240 --> 00:01:48,060
+بداية في قرية في روسيا أو في مدينة في روسيا،
+
+22
+00:01:48,060 --> 00:01:51,960
+Königsberg، أعتقد إذا أنا مش غلطان في الاسم، في الـ
+
+23
+00:01:51,960 --> 00:01:56,100
+1800، ومش عارف جدًّا، كانوا ناس بتحب تتنزه حول
+
+24
+00:01:57,030 --> 00:01:59,810
+النهر، المبني عليه السبع جسور الموجودة اللي احنا
+
+25
+00:01:59,810 --> 00:02:04,730
+شايفينها قدامنا هنا، وكانت الناس دائمًا بتتساءل هل
+
+26
+00:02:04,730 --> 00:02:08,590
+بإمكاني أنا أعمل جولة، الـ walk تبعتي، المسار تبعي
+
+27
+00:02:08,590 --> 00:02:14,190
+أمر فيه على كل الجسور بدون ما أمر في جسر واحد أو
+
+28
+00:02:14,190 --> 00:02:20,320
+جسر معين مرتين أو ما شابه. فكان الكلام هذا أخذ وضلّ
+
+29
+00:02:20,320 --> 00:02:23,500
+التساؤل قائمًا، لأنه ما حدش كان بيجرب بشكل عام، لإيه
+
+30
+00:02:23,500 --> 00:02:27,820
+اللي بيغير طريقه، يرجع يمر على جسر مرة ثانية، في نهاية
+
+31
+00:02:27,820 --> 00:02:36,340
+الـ 1800، وبعدها بكم سنة، اجى عالم سويدي، أويلر، و
+
+32
+00:02:36,340 --> 00:02:41,490
+راح درس المنطقة، و مثّل الـ graph اللي انتم شايفينه
+
+33
+00:02:41,490 --> 00:02:45,270
+بالخريطة اللي موجودة هنا، وكانت نظريته بتقول كالتالي:
+
+34
+00:02:45,270 --> 00:02:49,990
+من خلالها عرف الـ Euler circuit والـ Euler path،
+
+35
+00:02:49,990 --> 00:02:53,090
+بناءً على الـ definition اللي موجود، النظرية كانت
+
+36
+00:02:53,090 --> 00:02:58,170
+بتقول كالتالي: إن الـ Euler circuit هي عبارة عن
+
+37
+00:02:58,170 --> 00:03:02,610
+simple circuit.  ونشوف هنا simple circuit، شو يعني
+
+38
+00:03:02,610 --> 00:03:08,230
+simple circuit؟ closed walk
+
+39
+00:03:08,230 --> 00:03:09,630
+أو closed trail،
+
+40
+00:03:12,590 --> 00:03:20,530
+closed circuit، يعني closed trail containing every
+
+41
+00:03:20,530 --> 00:03:25,350
+edge في الـ graph اللي جاي، يعني إذا أنا قدرت أعمل
+
+42
+00:03:25,350 --> 00:03:31,050
+closed trail أو circuit بتحتوي على كل الجسور اللي
+
+43
+00:03:31,050 --> 00:03:36,530
+موجودة في الـ graph، بسميها إيش؟ Euler circuit، و
+
+44
+00:03:36,530 --> 00:03:42,290
+أويلر هذا أثبت الكلام التالي: قال: إذا كان الـ graph
+
+45
+00:03:42,290 --> 00:03:48,690
+هذا، كل الـ vertices اللي موجودة فيه، كل النقاط اللي
+
+46
+00:03:48,690 --> 00:03:55,620
+موجودة فيه لها درجة زوجية، إيش يعني درجة زوجية؟ يعني
+
+47
+00:03:55,620 --> 00:04:00,500
+عدد الجسور اللي جاية على الـ vertex عدد زوجي،
+
+48
+00:04:00,500 --> 00:04:05,440
+تمام؟ معناته بتقدر تلاقي في الـ graph Euler circuit.
+
+49
+00:04:05,440 --> 00:04:11,200
+طب لو ما كانش، لو لقيت واحد من الـ vertices هذه عدد
+
+50
+00:04:11,200 --> 00:04:15,780
+درجته فردية، درجة فردية، انسى الموضوع، ما فيش هيكون
+
+51
+00:04:15,780 --> 00:04:16,780
+circuit.
+
+52
+00:04:21,190 --> 00:04:26,350
+والـ Euler path، بقول كالتالي: simple path، لكن للأسف
+
+53
+00:04:26,350 --> 00:04:30,730
+كلمة path هنا مش بمعناها الحقيقي path حسب الـ
+
+54
+00:04:30,730 --> 00:04:36,170
+definition تبع الكتاب، بقدر ما هي إيش؟ walk، simple
+
+55
+00:04:36,170 --> 00:04:41,210
+walk containing every edge.
+
+56
+00:04:44,410 --> 00:04:49,970
+احنا بنعرف إن الـ path بيحتوي على طرق مختلفة، وأنا
+
+57
+00:04:49,970 --> 00:04:53,230
+بقول إن هذا الشيء اللي بيحتوي على كل الـ edges، يعني
+
+58
+00:04:53,230 --> 00:04:56,150
+الفرق بين هذا وهذا إنّه إيش بيكون يا شباب؟ الـ
+
+59
+00:04:56,150 --> 00:05:01,270
+closing فقط. طيب، أويلر قال بالنسبة للـ path، قال:
+
+60
+00:05:01,270 --> 00:05:07,720
+إذا كانت الرسمة اللي موجودة عندك بتحتوي على اثنتين
+
+61
+00:05:07,720 --> 00:05:13,080
+فقط، exactly two vertices of odd degrees، of odd
+
+62
+00:05:13,080 --> 00:05:18,540
+degree، بتلاقي Euler path. كمان مرة نعيد: قال لك الـ
+
+63
+00:05:18,540 --> 00:05:22,040
+Euler circuit بتلاقيها لو كانت كل الـ degree تحت الـ
+
+64
+00:05:22,040 --> 00:05:26,800
+vertices even، درجات زوجية، وبتلاقي الـ Euler path
+
+65
+00:05:26,800 --> 00:05:33,180
+موجود لو كان فقط عندك اثنين، اثنين فقط، درجتهم
+
+66
+00:05:33,180 --> 00:05:37,980
+درجة فردية. فلو وجدت واحدة، ما فيش Euler بقى، فلو
+
+67
+00:05:37,980 --> 00:05:41,560
+وجدت ثلاث، ما فيش Euler بقى. تعالوا نرجع للرسمة
+
+68
+00:05:41,560 --> 00:05:48,420
+السابقة،  بنجي نقول: أويلر كان بيقول لهم، من المستحيل
+
+69
+00:05:48,420 --> 00:05:55,860
+إنك تعمل جولة، تمام؟ تمر فيها على كل الجسور بدون ما
+
+70
+00:05:55,860 --> 00:06:00,590
+تمر على جسر مرتين. لماذا؟ لكي نجيب الـ vertices في
+
+71
+00:06:00,590 --> 00:06:05,870
+الرسمة، ونسقط نظرية الـ Euler. رتب C كم يا
+
+72
+00:06:05,870 --> 00:06:15,410
+شباب؟ ثلاثة؟ خمسة؟
+
+73
+00:06:15,410 --> 00:06:18,130
+Euler circuit كان بيقول إنه لازم تكون كل vertices
+
+74
+00:06:18,130 --> 00:06:22,490
+درجتها زوجية، عشان تلاقي الـ Euler circuit، زوجية، عفواً، كل
+
+75
+00:06:22,490 --> 00:06:25,430
+vertices لازم تكون درجتها زوجية عشان تلاقي الـ Euler
+
+76
+00:06:25,430 --> 00:06:30,090
+circuit. طب، كل vertices اللي عندها درجة فردية، يبقى ما فيش
+
+77
+00:06:30,090 --> 00:06:34,290
+على الرسمة هنا Euler circuit.. does not exist. الـ
+
+78
+00:06:34,290 --> 00:06:38,050
+Euler path، بقول: بتلاقي الـ Euler path في حالة
+
+79
+00:06:38,050 --> 00:06:42,350
+إذا كان في الـ graph فقط اثنين درجتهما درجة فردية.
+
+80
+00:06:42,350 --> 00:06:46,890
+بقى بقى خمسة وكلهم فرديات، معناته الـ Euler path
+
+81
+00:06:46,890 --> 00:06:51,250
+does not exist. تعالى نشوف الأمثلة اللي موجودة
+
+82
+00:06:51,250 --> 00:06:55,910
+عندنا، ونسقط عليها الكلام ده، ونسأل نفسنا: هل الـ
+
+83
+00:06:55,910 --> 00:06:59,630
+Euler path والـ Euler circuit exist ولا لأ؟ نبدأ مع
+
+84
+00:06:59,630 --> 00:07:05,290
+G1، وأنا بدي اختصر، أحاول أقول Euler circuit و Euler
+
+85
+00:07:07,040 --> 00:07:11,500
+Euler Circuit مع الـ G1، الـ vertices  كم يا شباب؟ 2،
+
+86
+00:07:11,500 --> 00:07:18,420
+2، 2، 4، 4، 4، 4، 4، 4، 4، 4،
+
+87
+00:07:18,420 --> 00:07:18,500
+4، 4، 4، 4، 4، 4، 4، 4، 4، 4،
+
+88
+00:07:18,500 --> 00:07:19,100
+4، 4، 4، 4، 4، 4، 4، 4، 4، 4،
+
+89
+00:07:19,100 --> 00:07:19,160
+4، 4، 4، 4، 4، 4، 4، 4، 4، 4،
+
+90
+00:07:19,160 --> 00:07:19,180
+4، 4، 4، 4، 4، 4، 4، 4، 4، 4،
+
+91
+00:07:19,180 --> 00:07:19,680
+4، 4، 4، 4، 4، 4، 4، 4، 4، 4،
+
+92
+00:07:19,680 --> 00:07:28,280
+..
+
+93
+00:07:31,320 --> 00:07:36,340
+D، C، E، A، لأنه لو تنساش، circuit لازم تبدأ وتنتهي
+
+94
+00:07:36,340 --> 00:07:43,920
+بنفس النقطة. أنا بتكلم كم مرة؟ A، D.. بالضبط هي
+
+95
+00:07:43,920 --> 00:07:54,560
+اللي احنا بدنا نوصلها. C أو A، B، E، D، C، E، A، لو مفهوم،
+
+96
+00:07:54,560 --> 00:07:58,660
+إن الـ vertices ممنوع تتكرر، بنقع في مشكلة الآن،
+
+97
+00:07:58,660 --> 00:08:02,980
+إن الـ circuit هذا إيش؟ مش موجودة، تمام؟ الآن هي الـ
+
+98
+00:08:02,980 --> 00:08:05,740
+Euler circuit. طبعًا ممكن تلاقي أكثر من واحدة، تبدأ من
+
+99
+00:08:05,740 --> 00:08:08,840
+عند الـ C، وتبدأ باتجاه آخر، هتلاقي الـ Euler circuit
+
+100
+00:08:08,840 --> 00:08:13,100
+موجودة. الـ Euler path إيش؟ الـ Euler path بقول: بقول
+
+101
+00:08:13,100 --> 00:08:18,900
+إنّه لازم تكون اثنتين فقط درجتهما فردية، ما فيش عنده درجة
+
+102
+00:08:18,900 --> 00:08:22,300
+فردية، كلها درجات زوجية، وبالتالي ما فيش Euler path.
+
+103
+00:08:23,530 --> 00:08:32,770
+ما فيش.  ND، Euler path، تمام؟ اللي بعدها؟ ثلاثة،
+
+104
+00:08:32,770 --> 00:08:42,670
+ثلاثة، ثلاثة، ثلاثة، أربعة، Euler circuit، Euler
+
+105
+00:08:42,670 --> 00:08:48,520
+path، Euler circuit موجودة؟ بقول: كل vertices يجب أن
+
+106
+00:08:48,520 --> 00:08:52,900
+تكون زوجية عشان الـ circuit، والـ Euler path، يجب أن
+
+107
+00:08:52,900 --> 00:08:59,740
+يكون في عندك اثنين vertices درجتهما فردية. الأخير،
+
+108
+00:08:59,740 --> 00:09:12,820
+ثلاثة، ثلاثة، أربعة، أربعة، أربعة،
+
+109
+00:09:12,820 --> 00:09:13,540
+أربعة، أربعة، أربعة، أربعة، أربعة، أربعة، أربعة، أربعة،
+
+110
+00:09:13,540 --> 00:09:13,900
+أربعة، أربعة، أربعة، أربعة، أربعة، أربعة، أربعة، أربعة،
+
+111
+00:09:13,900 --> 00:09:14,280
+أربعة، أربعة، أربعة، أربعة، أربعة، أربعة، أربعة، أربعة،
+
+112
+00:09:14,280 --> 00:09:14,300
+أربعة، أربعة، أربعة، أربعة، أربعة، أربعة، أربعة، أربعة،
+
+113
+00:09:14,300 --> 00:09:14,600
+أربعة، أربعة، أربعة، أربعة، أربعة، أربعة، أربعة، أربعة،
+
+114
+00:09:14,600 --> 00:09:17,570
+أربعة، أربعة، أربعة. مش موجودة، لأن في عنده درجات فردية،
+
+115
+00:09:17,570 --> 00:09:22,450
+وهو بيقول لازم تكون كل الدرجات زوجية. Euler path
+
+116
+00:09:22,450 --> 00:09:28,350
+موجودة؟ موجودة، لأنه بيقول تكون عندك اثنتين من الـ
+
+117
+00:09:28,350 --> 00:09:31,790
+vertices ودرجتهما فردية، موجود. تعالوا نشوف الـ Euler
+
+118
+00:09:31,790 --> 00:09:41,570
+path: A، B، E، D،
+
+119
+00:09:45,220 --> 00:09:51,700
+أطلع فوق؟ أيوة. طيب، ممكن ألاقي بيكتب المسار مرة
+
+120
+00:09:51,700 --> 00:09:57,280
+ثانية: A، B، D، A،
+
+121
+00:09:57,280 --> 00:09:58,400
+B، D،
+
+122
+00:10:06,200 --> 00:10:09,920
+لأ، ارجع عليه كمان مرة، مش هتظبط. الآن أنا في قاعدة
+
+123
+00:10:09,920 --> 00:10:13,920
+وأنا بأجرب، متأكد إن الـ Euler path exist، بس بقعد
+
+124
+00:10:13,920 --> 00:10:24,560
+أدور عليه، أشوف إزاي أجيبه، مرات يعني نعم.  واحد،
+
+125
+00:10:24,560 --> 00:10:32,440
+اثنين، ثلاثة، أربعة، بس لحظة شوي، اللي يصبر علي، أربعة،
+
+126
+00:10:33,470 --> 00:10:41,030
+خمسة.. ستة.. سبعة. صح ولا غلط؟ طبعًا، لو كان
+
+127
+00:10:41,030 --> 00:10:44,290
+بيقول لك موجود، ممكن تلاقي أكثر من واحد، ما يحددش الـ
+
+128
+00:10:44,290 --> 00:10:47,570
+case إن هو واحد ولا أكثر. أنا الآن بقعد بأقترح إنّه
+
+129
+00:10:47,570 --> 00:10:56,350
+هيك: واحد من A لـ B، من A لـ C، من C لـ D، من D لـ E، من E
+
+130
+00:10:56,350 --> 00:11:08,180
+لـ D، من B لـ D، من D لـ A، ومن A لـ B، وألاحظ إن المسار
+
+131
+00:11:08,180 --> 00:11:12,720
+اللي كتبته هذا حقق، من وجهة نظري، كل الجسور اللي موجودة
+
+132
+00:11:12,720 --> 00:11:19,360
+عندي على الرسمة، بدون أي مشاكل.. بدون أي مشاكل.
+
+133
+00:11:19,360 --> 00:11:26,200
+إيش كنت تقول يا حازم؟ مسار ثاني؟ في
+
+134
+00:11:26,200 --> 00:11:30,340
+الأخير أنت بتلاقي، بما أنه حسب النظرية إن الـ vertices اللي
+
+135
+00:11:30,340 --> 00:11:34,640
+موجودة بيبقى عليها أي شيء، أدقق ولا إيش بقى أجيب
+
+136
+00:11:34,640 --> 00:11:42,560
+المسار اللي موجود عندي، بتمشي الأمور تمام، على
+
+137
+00:11:42,560 --> 00:11:50,660
+غرار، أولًا، عندي الـ Hamiltonian، راح أقول Hamiltonian path، و
+
+138
+00:11:50,660 --> 00:11:55,500
+Hamiltonian circuit. نعم. إذا كان مضمون مثلاً أنه في نقاط
+
+139
+00:11:58,490 --> 00:12:02,450
+بتسقط النظرية بالكامل، النظرية بتتحقق لما أقول لك:
+
+140
+00:12:02,450 --> 00:12:07,290
+اثنين فقط odd vertices،  معينة بتلاقي الـ Euler path.
+
+141
+00:12:07,290 --> 00:12:13,930
+كلها even vertices أو even degree، معينة بتلاقي الـ
+
+142
+00:12:13,930 --> 00:12:18,930
+Euler circuits. طيب.. الآن لو جيت.. هذه فيها..
+
+143
+00:12:18,930 --> 00:12:25,150
+لقيت فيها خمسة، اثنين منهم odd وثلاثة even، الـ path
+
+144
+00:12:25,150 --> 00:12:29,200
+موجود لكن الـ circuit مش موجودة. هذا المفروض منه، يعني
+
+145
+00:12:29,200 --> 00:12:33,480
+إذا لوجد الـ circuit، مش ضروري، مش هتلاقي الـ path، وإذا
+
+146
+00:12:33,480 --> 00:12:36,700
+لوجد الـ path، مش هتلاقي الـ circuit، لأنه في بينهم
+
+147
+00:12:36,700 --> 00:12:42,640
+تبعيات في الـ definition. الـ Hamiltonian path إيش بيقول؟
+
+148
+00:12:42,640 --> 00:12:46,500
+لاحظوا إيش كان الـ Euler يا شباب؟ containing
+
+149
+00:12:46,500 --> 00:12:55,270
+every edge، containing every edge، تمام؟ هاملتون لما
+
+150
+00:12:55,270 --> 00:12:59,890
+جاء، تكلم، قال: لا يا عمي، أنا أنا بدي أعرف إذا قدرنا
+
+151
+00:12:59,890 --> 00:13:08,250
+نوجد مسار بيحتوي على كل الـ vertices، كل
+
+152
+00:13:08,250 --> 00:13:13,610
+الـ vertices في دورة واحدة. لاحظ، هو أكد إن أنا عديت
+
+153
+00:13:13,610 --> 00:13:23,080
+two definitions. الـ path  بدور في كل النقاط. والآن
+
+154
+00:13:23,080 --> 00:13:26,640
+بتسقط معنى الـ path بالمعنى الحرفي، على خلال الـ
+
+155
+00:13:26,640 --> 00:13:33,300
+walk، وبتكلم الآن إن هذا بيجيبه في مسار واحد. عارف
+
+156
+00:13:33,300 --> 00:13:35,400
+إيش أنا في مسار واحد؟ يعني أنا غالبًا مش هأرجع
+
+157
+00:13:35,400 --> 00:13:41,460
+ثاني، مش هأرجع على النقطة مرة ثانية. تعالى نشوف الـ
+
+158
+00:13:41,460 --> 00:13:44,320
+pentagon والـ hexagon، الرسومات اللي موجودة هنا، هي
+
+159
+00:13:44,320 --> 00:13:49,230
+الشكل الخماسي والشكل السداسي. الآن،  في الشكل الخماسي،
+
+160
+00:13:49,230 --> 00:13:54,850
+موجود واحد، اثنين، ثلاثة، تمام؟ الآن، الـ author.. أو
+
+161
+00:13:54,850 --> 00:13:59,950
+عفواً، الـ Hamiltonian path هو عبارة عن مسار بيحتوي على
+
+162
+00:13:59,950 --> 00:14:04,710
+كل النقاط في لفة واحدة، اللي هو أنا محدد لك إياه
+
+163
+00:14:04,710 --> 00:14:05,830
+باللون الأحمر. بدأت من هنا.
+
+164
+00:14:18,550 --> 00:14:24,390
+إذا وقفت لحد الـ hand،  ميلاده غيبار، مصبور؟ و
+
+165
+00:14:24,390 --> 00:14:30,750
+سكرته، أصبح circuit، مصبور؟ تسيبه مفتوح، ميلاده، و
+
+166
+00:14:30,750 --> 00:14:36,340
+تتكلم على مين؟ على path وأتكلم على circuit. طب،
+
+167
+00:14:36,340 --> 00:14:40,000
+circuit ولا cycle أسميها؟ هو سماها circuit ليش؟
+
+168
+00:14:40,000 --> 00:14:44,640
+لأن كل الجسور اللي فيها جسور مختلفة، كل الجسور اللي
+
+169
+00:14:44,640
+
+223
+00:20:02,130 --> 00:20:06,190
+لـِ Graph عشان أنتَ تشتغل أو تطبّق برنامج بتعامل مع
+
+224
+00:20:06,190 --> 00:20:10,410
+الـ Graph بيلزمك تمثّل الـ Graph هذا في شغل سهلة
+
+225
+00:20:10,410 --> 00:20:13,670
+تقدر تتعامل مع الكمبيوتر ببساطة، والتمثيل هذا هيكون
+
+226
+00:20:13,670 --> 00:20:19,370
+من خلال مصفوفة الجوار، مصفوفة بنسمّيها مصفوفة الجوار
+
+227
+00:20:19,370 --> 00:20:25,270
+مصفوفة بنسمّيها مصفوفة الجوار. الآن، في مصفوفة الجوار
+
+228
+00:20:25,270 --> 00:20:30,150
+هي عبارة عن مصفوفة مربّعة. ماذا يعني مربّعة؟ 1000xN
+
+229
+00:20:30,150 --> 00:20:35,690
+عدد الصفوف فيها يساوي عدد الأعمدة يساوي عدد النقاط
+
+230
+00:20:35,690 --> 00:20:41,350
+الّلي موجودة في الرسمة، يعني
+
+231
+00:20:41,350 --> 00:20:49,010
+لو أنا جئتُ وقلتُ والله هذه الرسمة الّلي عندي A
+
+232
+00:20:49,010 --> 00:20:58,570
+,B,C وبدّي أمثّلها. كم حجم المصفوفة؟ ثلاثة
+
+233
+00:20:58,570 --> 00:21:03,730
+ثلاثة في ثلاثة. ليش ثلاثة؟ لأنّ عدد النقاط
+
+234
+00:21:03,730 --> 00:21:07,110
+الّلي موجودة عندي ثلاثة. وأهمّ شغلة في التمثيل يا
+
+235
+00:21:07,110 --> 00:21:11,390
+شباب، تنتبهوا للكلام الّلي أنا بدّي أقوله. ثلاثة أعمدة
+
+236
+00:21:11,390 --> 00:21:16,070
+هيمثّل ثلاثة نقاط، وثلاثة صفوف كذلك هيمثّل ثلاثة نقاط. أنا
+
+237
+00:21:16,070 --> 00:21:24,170
+الآن، الصفّ الأوّل A، B، C. الأعمدة والصفوف هتأخذ نفس
+
+238
+00:21:24,170 --> 00:21:26,650
+الترتيب الّلي عملته فوق.
+
+239
+00:21:45,010 --> 00:21:50,890
+الترتيب الّلي أنا اعتمده هو نفسه يعتمد على الصفوف
+
+240
+00:21:51,910 --> 00:21:54,930
+ما ينفع كل واحد يشتغل فيه ترتيب... عفواً... ما ينفع
+
+241
+00:21:54,930 --> 00:21:58,810
+يستخدم كل ترتيب مختلف مع كل الصفوف... من كل الصفوف
+
+242
+00:21:58,810 --> 00:22:03,530
+والأعمدة. تمام. هذا رقم واحد. الآن، اثنين. أيّة قيم بتروح
+
+243
+00:22:03,530 --> 00:22:08,290
+تساوي؟ أيّة values موجودة؟ على أساس
+
+244
+00:22:08,290 --> 00:22:12,730
+graph، بتكلّم على binary value. يا صفر يا واحد، يعني
+
+245
+00:22:12,730 --> 00:22:20,390
+ما في مسار أو ما فيش من C لـ C؟ صفر. بمثّلها بصفر. من
+
+246
+00:22:20,390 --> 00:22:21,390
+C لـ D؟
+
+247
+00:22:28,610 --> 00:22:35,410
+من B لـ B صفر.
+
+248
+00:22:35,410 --> 00:22:47,070
+من B لـ A واحد. من A لـ C صفر. من A لـ B واحد. ومن A لـ
+
+249
+00:22:47,070 --> 00:22:54,030
+C صفر. هذه المصفوفة بنسمّيها مصفوفة الجوار الّلي تمثّل
+
+250
+00:22:54,030 --> 00:22:57,810
+الـ graph البسيط الّلي عندنا. تمثّل الـ graph البسيط
+
+251
+00:22:57,810 --> 00:22:59,010
+الّلي عندنا.
+
+252
+00:23:01,170 --> 00:23:05,610
+الـ Graph هذا، أنا بقدر أصل من خلاله أو أتعرف هل في
+
+253
+00:23:05,610 --> 00:23:08,530
+connection ولا ما فيش. لو أنا جئتُ وقلتُ
+
+254
+00:23:08,530 --> 00:23:12,490
+الرسم هنا، وجئتُ وسألتُ: هل في طريق ما بين النقطة A
+
+255
+00:23:12,490 --> 00:23:16,770
+و C؟ باجي مباشرة وأين الصفّ الّلي فيه A؟
+
+256
+00:23:16,770 --> 00:23:21,350
+ها هي، وأين الـ C؟ ها هي. صفر، يعني ما فيش طريق، ما فيش
+
+257
+00:23:21,350 --> 00:23:28,810
+جسر. طيب، من B لـ A؟ ها هي B وها هي A، واحد، فيه
+
+258
+00:23:29,930 --> 00:23:33,870
+وبالتالي، هذه المصفوفة هي الّلي مثّلت الـ graph أيّ
+
+259
+00:23:33,870 --> 00:23:36,870
+ما وجد عندها. لو أنا بدّي أكبّر الـ graph شويّة
+
+260
+00:23:36,870 --> 00:23:42,530
+أجعله أصعب
+
+261
+00:23:42,530 --> 00:23:46,010
+A، B، C، D
+
+262
+00:23:59,600 --> 00:24:14,360
+المصفوفة الّلي هستخدمها أربعة في أربعة. A، B، C، D
+
+263
+00:24:14,360 --> 00:24:18,120
+A، B، C، D
+
+264
+00:24:18,120 --> 00:24:21,660
+أحرف، زي ما قلنا، في الترتيب. لكنّ الترتيب الّلي
+
+265
+00:24:21,660 --> 00:24:27,060
+بتعتمدها في الصفوف هو نفسه بتعتمدها مع الأعمدة. من A
+
+266
+00:24:27,060 --> 00:24:37,410
+لـ A صفر. من A لـ B؟ واحد. A لـ C؟ صفر. A لـ D؟ واحد. B لـ A؟
+
+267
+00:24:37,410 --> 00:24:48,430
+واحد. B لـ C؟ واحد. B لـ D واحد. من C لـ A؟ صفر. من C لـ B،
+
+268
+00:24:48,430 --> 00:24:53,330
+واحد. من C لـ C، صفر. ومن C لـ D، واحد. من D لـ A،
+
+269
+00:24:53,330 --> 00:25:01,850
+واحد. من D لـ B، واحد. من D لـ C، واحد. وصفر من D لـ
+
+270
+00:25:01,850 --> 00:25:06,730
+D، صفر. الآن يا شباب، في عندنا ملاحظة مهمّة جداً في
+
+271
+00:25:06,730 --> 00:25:11,030
+موضوع الـ Graph. عناصر القطر الرئيسي، صفر.
+
+272
+00:25:16,100 --> 00:25:20,400
+بس اصبر شويّة... اصبر شويّة... لما أنا بتكلّم على
+
+273
+00:25:20,400 --> 00:25:26,980
+simple graph، عناصر القطر الرئيسي صفر. ليش؟ لأنّ
+
+274
+00:25:26,980 --> 00:25:30,680
+ما فيش loop، ما فيش... عندي loop، مصبوط. لو فيه
+
+275
+00:25:30,680 --> 00:25:33,740
+دائرة، بيصير... سمّيناها بـ zero graph إحنا، مصبوط ولا
+
+276
+00:25:33,740 --> 00:25:38,020
+لا؟ الـ basic graph ما فيش عناصر المصفوفة فيه أو
+
+277
+00:25:38,020 --> 00:25:43,580
+عناصر القطر الرئيسي فيه صفر. هذه واحد، اثنين. المصفوفة
+
+278
+00:25:43,580 --> 00:25:48,080
+للـ basic graph متماثلة. شو يعني متماثلة؟ لو
+
+279
+00:25:48,080 --> 00:25:55,280
+أخذت المثلّثين هيك وقلبتهم على بعض، فيها a<sub>ij</sub> تساوي
+
+280
+00:25:55,280 --> 00:26:05,840
+a<sub>ji</sub>. الواحد
+
+281
+00:26:05,840 --> 00:26:17,050
+اثنين تساوي اثنين. E<sub>12</sub> هي تساوي E<sub>21</sub>. E<sub>32</sub> هي
+
+282
+00:26:17,050 --> 00:26:25,730
+تساوي E<sub>23</sub>. هي متماثلة، بنسمّيها symmetric matrix.
+
+283
+00:26:35,110 --> 00:26:40,150
+هذا نفس الكلام الموجود عندي هنا، لأنّه basic graph.
+
+284
+00:26:40,150 --> 00:26:44,650
+إذا الـ graph الّلي عندي هذا صار pseudo graph. إيش
+
+285
+00:26:44,650 --> 00:26:50,470
+يعني pseudo graph؟ يعني صار في عندي loop أو
+
+286
+00:26:50,470 --> 00:26:55,030
+multiple edge. الـ
+
+287
+00:26:55,030 --> 00:27:02,530
+pseudo graph يعني إمّا في عندي loop أو multiple. ماذا
+
+288
+00:27:02,530 --> 00:27:06,670
+يعني؟ أيش الّلي بيغيّر في الرسمة أو في المصفوفة؟
+
+289
+00:27:06,670 --> 00:27:14,690
+هتبطّل 0، 1. هتبطّل 0، 1، تمام؟ هتصير من الـ D لـ C 2، وين
+
+290
+00:27:14,690 --> 00:27:23,360
+DC؟ هذه C و هذه D، هتصير 2. ومن C ومن D لـ C برضه
+
+291
+00:27:23,360 --> 00:27:27,560
+اثنين. هتبقى المصفوفة متماثلة، ومش بس هيك، هتصير
+
+292
+00:27:27,560 --> 00:27:31,680
+عناصر القطر الرئيسي بطّلت صفر لأنّ صار في عندك جسر
+
+293
+00:27:31,680 --> 00:27:38,260
+من D لـ B. صارت في عندك واحد. وبهيك صرت أنا بقدر أقول
+
+294
+00:27:38,260 --> 00:27:43,860
+بكلّات. إذا أنا شفت عناصر القطر الرئيسي لا تساوي صفر
+
+295
+00:27:44,630 --> 00:27:48,150
+أو واحد من عناصر قطر الرئيسي لا تساوي صفر، ما يعتبر
+
+296
+00:27:48,150 --> 00:27:51,310
+أنّ عندي loop. في عندي loop edge موجود في الرسمة
+
+297
+00:27:51,310 --> 00:27:57,250
+طبعاً؟ طيب، وإذا شفت عناصر أكثر من واحد أو أكبر من
+
+298
+00:27:57,250 --> 00:28:00,230
+واحد في value، ما يعتبر أن عندي multiple edge موجود
+
+299
+00:28:00,230 --> 00:28:03,490
+وين؟ بالرسم. ما يعتبر أن عندي multiple edge موجود
+
+300
+00:28:03,490 --> 00:28:08,350
+في الرسم. الآن، بما أن أنا اتكلّمت على Undirected
+
+301
+00:28:08,350 --> 00:28:11,990
+Graph، بدّي أعمل representation بنفس الكيفيّة، بس إيش
+
+302
+00:28:11,990 --> 00:28:17,400
+الفرق؟ أنّها مش هتكون Symmetric. الآن، في الـ Directed
+
+303
+00:28:17,400 --> 00:28:32,020
+Graph، لو أنا أعطيتك هذين الـ Graph، هذا Directed
+
+304
+00:28:32,020 --> 00:28:40,240
+Graph. يعني، الشباب بيمشي مع مين؟ مع الـ Sam. A،
+
+305
+00:28:40,280 --> 00:28:52,870
+B، C، D. وأنا بدّي أمثّل المصفوفة. الآن، هي المصفوفة A، B،
+
+306
+00:28:52,870 --> 00:29:00,630
+C، D، A، B، C، D. هتختلف
+
+307
+00:29:00,630 --> 00:29:05,090
+تماماً عن المصفوفة الّلي هنا. هتبقى Symmetric لأنّ أنا
+
+308
+00:29:05,090 --> 00:29:09,010
+بدّي أمشي من وين يا حسن؟ السهل، لأنّ في الرسم هنا من A
+
+309
+00:29:09,010 --> 00:29:19,690
+لـ A صفر. من A لـ B ما فيش، أيّة صفر. من A لـ C واحد. ومن A
+
+310
+00:29:19,690 --> 00:29:29,430
+لـ D واحد. من B لـ A واحد. من B لـ B صفر. من B لـ C صفر.
+
+311
+00:29:29,430 --> 00:29:41,010
+من B لـ D صفر. من C لـ A صفر. من
+
+312
+00:29:41,010 --> 00:29:49,220
+C لـ B واحد. من C لـ C صفر. من C لـ D واحد. من D لـ A صفر.
+
+313
+00:29:49,220 --> 00:29:56,300
+من D لـ B صفر. من D لـ C صفر. من D لـ D صفر. ولو أطلعتُ
+
+314
+00:29:56,300 --> 00:30:02,180
+في عناصر القطر الرئيسي، أصفار، ليس فيها مشكلة لأنّها
+
+315
+00:30:02,180 --> 00:30:07,040
+basic graph، لكنّها ليست Symmetric. هي الـ value هذه
+
+316
+00:30:09,490 --> 00:30:16,910
+هذه A<sub>1</sub> أربعة وهذه A<sub>4</sub> واحد. يعني لو
+
+317
+00:30:16,910 --> 00:30:20,910
+أنا شفت الـ graph أو شفت المصفوفة، بيصير أقدر أحدّد
+
+318
+00:30:20,910 --> 00:30:24,510
+شو نوع الـ graph. هل هو pseudo graph ولا
+
+319
+00:30:24,510 --> 00:30:29,150
+directed graph. ومش بس هيك، بقدر أرسمه بغضّ النظر إيش
+
+320
+00:30:29,150 --> 00:30:33,870
+كان. بقدر أرسم الـ graph بغضّ النظر إيش كان. ما بيجي وأقول لك:
+
+321
+00:30:33,870 --> 00:30:40,700
+هاي عندك أربع نقاط، أربع نقاط. هذه العلاقات
+
+322
+00:30:40,700 --> 00:30:44,680
+الموجودة بينهم. يعني: هل يوجد جسر أو جسرين؟ هل يوجد
+
+323
+00:30:44,680 --> 00:30:48,320
+loop أو لا loop؟ هل باتجاه واحد أو باتجاهين؟
+
+324
+00:30:48,320 --> 00:30:51,760
+وبالتالي، تستطيع ترسم من رسمتك، وهكذا يحصل في
+
+325
+00:30:51,760 --> 00:30:54,600
+برامج الخرائط الّلي بتحصل على الجوالات وعلى اللابتوب
+
+326
+00:30:54,600 --> 00:31:00,490
+كلّ هذا يحصل. هي تمثّل المنطقة كمجموعة من مين؟ مجموعة
+
+327
+00:31:00,490 --> 00:31:05,130
+من النقاط والطرق المعرفة بينهم. هي بتمثّل الجسور و
+
+328
+00:31:05,130 --> 00:31:08,490
+كلّ ما بتتحرّك السيارة أو الـ mobile، عفواً، وبحدّد
+
+329
+00:31:08,490 --> 00:31:11,310
+الموبايل الجديد بالـ GPS، شو بيصير بيعمل؟ بيروح بيعمل
+
+330
+00:31:11,310 --> 00:31:15,610
+shift للنقاط. يعني دائماً بيعمل زيوم للخريطة أو بيصغّر
+
+331
+00:31:15,610 --> 00:31:19,730
+المصفوفة عشان تمثّل حسب العرض أو حجم العرض الّلي
+
+332
+00:31:19,730 --> 00:31:24,270
+موجود عندك. anyway، في الآخر، المصفوفة دي بتمثّل إيش؟
+
+333
+00:31:24,530 --> 00:31:30,290
+بتمثّل Graph بشكل صحيح ومناسب، وجدّاً مناسب. في أيّ سؤال
+
+334
+00:31:30,290 --> 00:31:33,430
+يا شباب؟ في تعريف المصفوفات هنا؟ سواء كانت Directed
+
+335
+00:31:33,430 --> 00:31:37,730
+Graph أو لا؟
+
+336
+00:31:37,730 --> 00:31:44,470
+Okay.
+
+337
+00:31:44,470 --> 00:31:50,530
+بدّنا نروح ننتقل لموضوع shortest path. في shortest
+
+338
+00:31:50,530 --> 00:31:56,340
+path، من أهمّ التطبيقات تبع الـ graphs الّلي هي
+
+339
+00:31:56,340 --> 00:32:00,380
+الوصول بين الـ two points بأقصر الطرق. الوصول إلى الـ two
+
+340
+00:32:00,380 --> 00:32:05,460
+points، أو المسافة بين الـ two points بأقصر الطرق. طب
+
+341
+00:32:05,460 --> 00:32:09,580
+إحنا سابقاً في كلّ الـ graphs ما كان في عندنا شغل بتدلّ
+
+342
+00:32:09,580 --> 00:32:15,650
+عليه. الـ Cost، التكلفة. لكن لنكتلم عن القصر، لاحظ، بجينا
+
+343
+00:32:15,650 --> 00:32:19,210
+نكتب الخطّ أو نرسم الخطّ بدون ولا حاجة. الّلي هيتغيّر
+
+344
+00:32:19,210 --> 00:32:23,350
+عندي في الـ graph، لما أتكلم عن الـ shortest path، بدو
+
+345
+00:32:23,350 --> 00:32:28,350
+يصير كلّ خطّ مربوط ومحسوب عليه التكلفة تبعته. كلّ خطّ
+
+346
+00:32:28,350 --> 00:32:32,990
+بدو ينحسب عليه التكلفة تبعته. السؤال الّلي بيطرح نفسه:
+
+347
+00:32:32,990 --> 00:32:38,570
+هل التكلفة تكلفة نقديّة؟ لا، مش ضروري. ممكن التكلفة
+
+348
+00:32:38,570 --> 00:32:44,360
+وقت، تمام؟ مسافة، جهد، أيّ تكلفة بدها تكون...
+
+349
+00:32:44,360 --> 00:32:47,580
+أنا ما بعني لشو وحدة التكلفة الموجودة... بس في
+
+350
+00:32:47,580 --> 00:32:52,160
+الآخر، الرقم الّلي بيكتب فوق الجسر هو مقدار التكلفة
+
+351
+00:32:52,160 --> 00:32:55,560
+... بوحدة معيّنة... لأنّ أنا ممكن أقول 650
+
+352
+00:32:55,560 --> 00:33:00,440
+شيء... مثلاً... تكلفة السفر من غزّة لرام الله... بينما
+
+353
+00:33:00,440 --> 00:33:05,230
+القصّة كلّفتها 700 شيء... مثلاً... ممكن تقول إنّك بتأخذ
+
+354
+00:33:05,230 --> 00:33:16,570
+650 ملّ بنزين أو سولار، مثلاً، بتأخذ 650 دقيقة. حسب، لكلّ
+
+355
+00:33:16,570 --> 00:33:21,510
+unit بتفرق. لكن في شغلي هنا، لما بتكلّم
+
+356
+00:33:21,510 --> 00:33:27,570
+على الـ shortest path، بتكلّم على مسار بأقلّ تكلفة...
+
+357
+00:33:27,570 --> 00:33:32,690
+بأقلّ تكلفة... أقلّ value مرسوم على مين؟ على الخطّ
+
+358
+00:33:32,690 --> 00:33:36,430
+الّلي موجود عنده، تمام؟ ما إليّ دخل بإيش اليونيت،
+
+359
+00:33:36,430 --> 00:33:38,650
+أقلّ تكلفة ممكنة.
+
+360
+00:33:40,900 --> 00:33:45,060
+من أهمّ الـ Algorithms الّلي بتستخدم في موضوع
+
+361
+00:33:45,060 --> 00:33:48,160
+shortest path، وأبسطها، الّلي هو الـ Dijkstra
+
+362
+00:33:48,160 --> 00:33:51,200
+Algorithm.
+
+363
+00:33:51,200 --> 00:33:55,600
+فالـ graph زي هذا... هلاّقيته عشان أوضّح لك الصورة،
+
+364
+00:33:55,600 --> 00:34:00,100
+الآن، أنا بدّي أتحرّك ما بين نقطتين. ما ينفع أقول أنا
+
+365
+00:34:00,100 --> 00:34:04,160
+والله ما أعرف الـ target تبعي، لأنّ إذا أنا ما عرفتش
+
+366
+00:34:04,160 --> 00:34:07,950
+الـ target، ما بقدر أروح، ما بقدر أروح. ما بقدر أرسم
+
+367
+00:34:07,950 --> 00:34:12,310
+المسار الّلي أنا بدّي إياه. كذلك، على الرسم السابق هنا،
+
+368
+00:34:12,310 --> 00:34:15,850
+لما أنا بدّي أقول بدّي أروح من غزّة للقدس، إيش
+
+369
+00:34:15,850 --> 00:34:20,910
+المسارات الّلي يجب أن تدخل في المقارنة؟ الطريق
+
+370
+00:34:20,910 --> 00:34:25,570
+المباشر أو الطريق الّلي بيمرّ بالخليل؟ ما ينفع أقول
+
+371
+00:34:25,570 --> 00:34:28,190
+بدّي أروح على رام الله وبعدين بدّي أروح على القدس، لأنّه
+
+372
+00:34:28,190 --> 00:34:33,190
+حسب المادة الّلي عندي هنا، ما فيش طريق. تمام؟ وبالتالي،
+
+373
+00:34:33,190 --> 00:34:38,150
+اختيار الـ shortest path بيكون تبع إيش؟ هل المسار
+
+374
+00:34:38,150 --> 00:34:42,290
+موجود في الأول من الـ start point للـ end point، و
+
+375
+00:34:42,290 --> 00:34:46,270
+بعدين ببدأ أقرّن إيش التكلفة. تعالَ نشوف الرسمة، هاي
+
+376
+00:34:46,270 --> 00:34:48,930
+الّلي عندي. إيش في الرسمة هاي الّلي بيقول إيه؟ بيقول
+
+377
+00:34:48,930 --> 00:34:54,190
+حسب لي أو هات الـ shortest path عشان أجيب ما بين أو
+
+378
+00:34:54,190 --> 00:34:58,570
+أوصل للـ vertex E؟ يعني، هذا الـ target تبعي from
+
+379
+00:34:58,570 --> 00:35:09,890
+the vertex. يعني هو بدّه يتحرّك من الـ A للـ E. يعني
+
+380
+00:35:09,890 --> 00:35:20,210
+هنا نقطة البداية وبدّه يجي من وين؟ بدّه يجي من هنا. إذا
+
+381
+00:35:20,210 --> 00:35:29,490
+اتّجه من هنا 100%. الآن، كان مسار موجود كثير: A، B، D، F، E.
+
+382
+00:35:30,180 --> 00:35:48,220
+A، B، D، F، E. A، B، D، C، E. مظبوط؟ A، B، C، E. A، C، B، D، F، E. A، C، B،
+
+383
+00:35:48,220 --> 00:35:55,240
+D، E. A، C... لحظة شويّة... A، C... ما فيش. خلاص، الـ B خلصت، ما ينفع
+
+384
+00:35:55,240 --> 00:35
+
+445
+00:41:14,170 --> 00:41:17,290
+النظر عشان أمثل الـ graph كله كيف أجيب الـ shortest
+
+446
+00:41:17,290 --> 00:41:21,930
+path لازم يكون الـ graph عندي بمصفوفة، والـ course
+
+447
+00:41:21,930 --> 00:41:27,210
+تبعه في مصفوفة عشان كل مسار أنا برسمه أروح أرسم
+
+448
+00:41:27,210 --> 00:41:32,730
+الـ course تبعه لما أكون  دارس نفس الفكرة أنه
+
+449
+00:41:32,730 --> 00:41:36,570
+مصفوفين، والمصفوفتين التاليتين لازم تكون موجودات الآن
+
+450
+00:41:36,570 --> 00:41:45,810
+B إلى C واحد، B إلى D خمسة، B إلى E صفر، ما فيش لأنه
+
+451
+00:41:45,810 --> 00:41:51,670
+طريق، الآن B إلى C، من C إلى B واحد، من C إلى C صفر، من
+
+452
+00:41:51,670 --> 00:41:55,390
+الـ  vertex بتاعه واحدة، هيها الـ cost هيها، تمام، من C إلى
+
+453
+00:41:55,390 --> 00:41:57,950
+D ثمانية
+
+454
+00:42:00,230 --> 00:42:08,490
+ومن C إلى E؟ عشرة، من D إلى B؟ خمسة، هذا التباعد من
+
+455
+00:42:08,490 --> 00:42:20,230
+D إلى C؟ ثمانية، صفر، ومن D إلى E؟ اثنين، الآن،
+
+456
+00:42:20,230 --> 00:42:27,810
+اكمل، صفر، خمسة، واحد، صفر
+
+457
+00:42:32,390 --> 00:42:37,230
+هذه غلط، كيف غلط؟ هذه صفر، أكيد هذه لازم تكون اثنين
+
+458
+00:42:37,230 --> 00:42:46,850
+هذه عشرة وهذه صفر لأن
+
+459
+00:42:46,850 --> 00:42:51,630
+المفروض هذا الصف هي اثنين، عشرة، صفر، هي التماثل اللي
+
+460
+00:42:51,630 --> 00:42:55,190
+موجود عندها، إذا ما الصفين هدول موجودات، سبّت كل
+
+461
+00:42:55,190 --> 00:43:00,040
+شيء، بقول: هل في طريق؟ وقديش تكلفته؟ بصير تبدأ عمليّة
+
+462
+00:43:00,040 --> 00:43:05,480
+تراكمية من أجل الوصول على العناصر اللي موجودة
+
+463
+00:43:05,480 --> 00:43:10,340
+عندنا في
+
+464
+00:43:10,340 --> 00:43:14,620
+أن المصطلح الشجرة
+
+465
+00:43:14,620 --> 00:43:19,520
+الـ tree هي عبارة عن special graph، هي عبارة عن
+
+466
+00:43:19,520 --> 00:43:24,960
+special graph، الشبكة دي كلها مصطلحات
+
+467
+00:43:29,870 --> 00:43:33,530
+Connected يعني كل النقاط اللي فيه متصلة، ما فيش فيه
+
+468
+00:43:33,530 --> 00:43:38,350
+isolated point، وإلّا هتكونش tree، Undirected، ما فيش
+
+469
+00:43:38,350 --> 00:43:45,430
+أسهم، graph contains no circuits، ما فيش أي شغلة
+
+470
+00:43:45,430 --> 00:43:48,490
+مغلقة، دائماً مسارات مفتوحة، كل المسارات اللي
+
+471
+00:43:48,490 --> 00:43:50,210
+فيها مفتوحة
+
+472
+00:43:57,380 --> 00:44:00,280
+ما فيش circuit ولا cycles؟ ما خلاص ما فيش circuit
+
+473
+00:44:00,280 --> 00:44:03,920
+يعني ما فيش closed walk، ما فيش closed trail، كلها
+
+474
+00:44:03,920 --> 00:44:07,280
+بيعتمد، لأن هذا الرسم simple graph، simple graph،
+
+475
+00:44:07,280 --> 00:44:11,360
+simple graph، أي واحد فيهم بيمثل الـ tree، كلنا
+
+476
+00:44:11,360 --> 00:44:15,020
+نتكلم على الـ tree، وقلنا هذه كل حياتها بتمثل الـ
+
+477
+00:44:15,020 --> 00:44:18,640
+trees، فكرة الـ tree connected .. simply connected
+
+478
+00:44:18,640 --> 00:44:19,200
+graph
+
+479
+00:44:29,930 --> 00:44:33,650
+مفهوم الـ circuit أن نقطة البداية تصير نقطة النهاية
+
+480
+00:44:33,650 --> 00:44:42,150
+وبالتالي لو أنت طلعت بين أي نقطتين هتلاقي في عندك
+
+481
+00:44:42,150 --> 00:44:46,250
+مسار واحد فقط، بين أي نقطتين عشان تصل لهم بما أنه ما فيش
+
+482
+00:44:46,250 --> 00:44:49,410
+cross أو ما فيش تقاطع، بما أنك تتكلم أنك دائماً في
+
+483
+00:44:49,410 --> 00:44:53,610
+مسار واحد بين النقطتين، لو أنت هنا وبنكسة اللي هنا
+
+484
+00:44:53,610 --> 00:45:01,210
+مستحيل اللي غير تمر بالمسار هذا، وفي مش غيره، تمام؟
+
+485
+00:45:01,210 --> 00:45:06,530
+وبذلك صارت في عندي، أنا بتكلم على الـ tree الآن بشكل
+
+486
+00:45:06,530 --> 00:45:11,800
+عام، بقى الـ trees، استخداماتها مهمة في الكمبيوتر
+
+487
+00:45:11,800 --> 00:45:15,960
+وبتشوف أنت على سبيل المثال الـ road folder تبع الـ C
+
+488
+00:45:15,960 --> 00:45:19,940
+و D عندك على الجهاز، storage هو بيمثل الـ tree، الـ C
+
+489
+00:45:19,940 --> 00:45:23,660
+بتمثل الـ road، المجلدات اللي موجودة على الـ C بتمثل
+
+490
+00:45:23,660 --> 00:45:27,040
+الـ level الأول، والمجلدات اللي موجودة تمثل الـ
+
+491
+00:45:27,040 --> 00:45:29,560
+leaves اللي موجودة على الـ level الأول، بعد هيك
+
+492
+00:45:29,560 --> 00:45:35,870
+بتبدأ تتفرع بالشجرة اللي عندك، لأن المعروف في مصطلح
+
+493
+00:45:35,870 --> 00:45:40,370
+الـ trees لازم يكون فيها root، لأن ما فيش شجرة طايرة
+
+494
+00:45:40,370 --> 00:45:45,430
+في الهوا، ولا لا؟ كل شجرة فيها جذر ثابت وواضح، حتى
+
+495
+00:45:45,430 --> 00:45:50,310
+بالـ graph هذا، المثال السابق، هدول لو ما فيش لازم
+
+496
+00:45:50,310 --> 00:45:54,550
+أنت تختار واحد منهم يكون root، أي واحد بينفع يكون
+
+497
+00:45:54,550 --> 00:45:59,770
+root، ومع اختلاف الـ root هتختلف شكل الشجرة، يعني لو
+
+498
+00:45:59,770 --> 00:46:03,860
+أنا افترضت أن هذا هو الـ root، كمبدأ، تصير الشجرة
+
+499
+00:46:03,860 --> 00:46:10,960
+هيها، في عندي a و b are siblings، إخوة، هذا leaf، و
+
+500
+00:46:10,960 --> 00:46:15,940
+هذا في عنده تفرعات، لو أنا أجيت أخدت هذه root، أو
+
+501
+00:46:15,940 --> 00:46:20,760
+أخذت هذا root، هتختلف الشجرة، لو أخدت هذا root، هتصير
+
+502
+00:46:20,760 --> 00:46:26,520
+في عنده تلات أولاد، مظبوط، three siblings، ولو أخدت
+
+503
+00:46:26,520 --> 00:46:29,880
+هذا root، هتصير في عندها واحد، فأنت في الآخر في كل
+
+504
+00:46:29,880 --> 00:46:36,130
+tree لازم يكون لها root، لازم يكون لها جذر، هذه نفس
+
+505
+00:46:36,130 --> 00:46:41,530
+الـ graph، لكن الـ root هنا A، والـ root هنا B، هي الـ
+
+506
+00:46:41,530 --> 00:46:51,970
+B لحظة ما أخذتها root، هي شكل الشجرة اختلف تماماً في
+
+507
+00:46:51,970 --> 00:46:57,810
+موضوع الـ root، أنا بتكلم على parent و siblings
+
+508
+00:46:57,810 --> 00:47:02,560
+parent و siblings، الـ siblings اللي هم مين يا شباب؟
+
+509
+00:47:02,560 --> 00:47:08,480
+التفرعات اللي موجودة عندهم، الآن الـ parent بتاعت الـ a
+
+510
+00:47:08,480 --> 00:47:13,500
+ب هي a، والـ parent بتاعت الـ c هي a، معناته أنا باجي
+
+511
+00:47:13,500 --> 00:47:20,580
+بقول b و c are siblings .. siblings .. إخوة ..
+
+512
+00:47:20,580 --> 00:47:26,120
+تمام؟ الـ parent بتاعت الـ e هي b، والـ parent بتاعت الـ d
+
+513
+00:47:26,120 --> 00:47:29,340
+هي b، معناته الـ b والـ d .. الـ d والـ e
+
+514
+00:47:29,340 --> 00:47:29,660
+siblings
+
+515
+00:47:37,050 --> 00:47:40,650
+الآن في عندي مصطلح الـ Leaf، الـ Leaf، و
+
+516
+00:47:40,650 --> 00:47:46,610
+Internal Vertex، في الـ Leaf، مين الـ Leafs؟ c هي
+
+517
+00:47:46,610 --> 00:47:52,450
+النقطة اللي ما فيش إلا تفرعت بنسميها إيش؟ Leaf، c، e،
+
+518
+00:47:52,450 --> 00:47:59,730
+و f، c و e و f هدول إيش؟ Leafs، أوراق، الآن دي إيه
+
+519
+00:47:59,730 --> 00:48:04,280
+بنسميها Internal Vertex، أو Parent؟ b، Internal
+
+520
+00:48:04,280 --> 00:48:09,820
+Vertex، أو Parent، لأن الـ b Parent للـ d، والـ d
+
+521
+00:48:09,820 --> 00:48:16,700
+Parent للـ e، Internal
+
+522
+00:48:16,700 --> 00:48:20,360
+يعني أن هناك الـ parent، وهناك الـ parent، وهناك الـ
+
+523
+00:48:20,360 --> 00:48:20,520
+parent، وهناك الـ parent، وهناك الـ parent، وهناك الـ
+
+524
+00:48:20,520 --> 00:48:21,820
+parent، وهناك الـ parent، وهناك الـ parent، وهناك الـ
+
+525
+00:48:21,820 --> 00:48:25,560
+parent، وهناك الـ parent، وهناك الـ parent، وهناك الـ
+
+526
+00:48:25,560 --> 00:48:26,960
+parent، وهناك الـ parent، وهناك الـ parent، وهناك الـ
+
+527
+00:48:26,960 --> 00:48:29,940
+parent، وهناك الـ parent، وهناك الـ parent، وهناك الـ
+
+528
+00:48:29,940 --> 00:48:34,250
+parent، وهناك الـ  ، الآن لما اتكلمنا عن الـ sub graph
+
+529
+00:48:34,250 --> 00:48:37,890
+تتذكر الـ sub graph هو عبارة عن جزء من الـ graph، ومع
+
+530
+00:48:37,890 --> 00:48:42,290
+أن الـ tree هي graph، فبقدر أتكلم على sub tree، sub
+
+531
+00:48:42,290 --> 00:48:49,530
+tree هي شجرة فرعية، يعني الـ sub graph أو الـ sub
+
+532
+00:48:49,530 --> 00:48:53,910
+tree هي عبارة عن sub graph من الـ tree، هي الـ b هذا
+
+533
+00:48:53,910 --> 00:48:57,670
+هي أخدت الجزء هذا لحاله، ولو أخدت الجزء هذا هيك
+
+534
+00:48:57,670 --> 00:49:00,790
+لحاله بيمشي الحال، ولو أخدت الجزء هذا هيك لحاله
+
+535
+00:49:00,790 --> 00:49:05,030
+بيمشي الحال، دائماً لما اتكلمنا في الـ sub graph قلنا
+
+536
+00:49:05,030 --> 00:49:08,030
+مجموعة الـ vertices، مجموعة جزئية من المجموعة
+
+537
+00:49:08,030 --> 00:49:11,690
+الأساسية، ومجموعة الجسور، مجموعة جزئية من مجموعة
+
+538
+00:49:11,690 --> 00:49:19,110
+الجسور الأساسية، فهي أن مصطلح الـ level، إذا أنا
+
+539
+00:49:19,110 --> 00:49:22,800
+أخذت الـ a، الـ c لحالها، وقدرت أقول عنها sub tree، هو الـ
+
+540
+00:49:22,800 --> 00:49:26,240
+Subtree، الـ a والـ c، لفهمك؟ آه، آه، لفهمك، إيه الـ a
+
+541
+00:49:26,240 --> 00:49:29,480
+والـ c، الـ Subgraph، وهو المشكلة في الموضوع إيه؟
+
+542
+00:49:29,480 --> 00:49:32,860
+الشرط بتاعنا أن الـ vertices subset من الـ vertices
+
+543
+00:49:32,860 --> 00:49:36,140
+الـ a والـ c subset من المجموعة الكلية لنقاط، و
+
+544
+00:49:36,140 --> 00:49:40,840
+الجسر اللي بينهم، a و c subset من مجموعة الجسور
+
+545
+00:49:40,840 --> 00:49:46,670
+الكلية، فهي Subtree، الشرط عضو من نقاطك ونقاطك، بس
+
+546
+00:49:46,670 --> 00:49:50,110
+عدد النقاط على الأقل بيكون تنتهي من التّصلات، لو أنك
+
+547
+00:49:50,110 --> 00:49:55,630
+بتطبق بالـ letter a، أصبت؟ أيوة، فيه أن المصطلح الـ
+
+548
+00:49:55,630 --> 00:49:59,510
+level، المستوى، الـ road ده من الـ level بتاعته إيه؟
+
+549
+00:49:59,510 --> 00:50:03,410
+zero، والـ height أو الـ depth بتاعت الـ letter e
+
+550
+00:50:03,410 --> 00:50:09,690
+بتمثل إيه؟ عدد الجسور ما بين الـ road لحد آخر leaf
+
+551
+00:50:09,690 --> 00:50:15,110
+لحد أعمق leaf، الـ height، الـ a level zero، b و c
+
+552
+00:50:15,110 --> 00:50:21,570
+level one، دي، وإيه level 3، level 2 عفواً، و f level
+
+553
+00:50:21,570 --> 00:50:25,270
+3، جداش الـ depth، جداش الـ height، جداش ارتفاع الشجرة؟
+
+554
+00:50:25,270 --> 00:50:32,710
+واحد، اثنين، تلاتة، تلات جسور، بتقعد أطول غُمُوق موجود
+
+555
+00:50:32,710 --> 00:50:36,510
+عندك في الشجرة، واحد، اثنين، تلاتة، اللي هو الـ maximum
+
+556
+00:50:36,510 --> 00:50:44,170
+level موجود عندك، يعني بالـ tree هاي، اثنين، صفر، واحد
+
+557
+00:50:46,030 --> 00:50:50,930
+ما يغركاش يا شباب إنه ممكن أنا أروح أجسر الرسم هادي
+
+558
+00:50:50,930 --> 00:51:00,710
+وأجيب لك الإجابة، لو
+
+559
+00:51:00,710 --> 00:51:06,330
+أنا جيت سألتك إيش الـ level بتاع الـ f؟ بدك تعدّي
+
+560
+00:51:06,330 --> 00:51:10,830
+الجسور اللي بينها وبين الـ root، تعدّي الجسور لحد
+
+561
+00:51:10,830 --> 00:51:15,510
+ما توصل الـ root، وتوصل الـ level واحد، اثنين، وصلت الـ
+
+562
+00:51:15,510 --> 00:51:19,370
+root، ما هي بتبدأ في level؟ اثنين، لأن level zero
+
+563
+00:51:19,370 --> 00:51:25,270
+level واحد، level اثنين، بقى لو طلت أو جسّرت مالهاش
+
+564
+00:51:25,270 --> 00:51:31,410
+علاقة، مالهاش علاقة، ليش؟
+
+565
+00:51:31,410 --> 00:51:35,390
+نفس الكلام، الـ level بتاعت الـ c هي عبارة عن عدد
+
+566
+00:51:35,390 --> 00:51:36,870
+الجسور اللي بينها وبين الـ root
+
+567
+00:51:43,130 --> 00:51:54,890
+أول الـ edge ما بين الـ points مالوش شبه بالعمليات
+
+568
+00:51:54,890 --> 00:52:00,700
+الحسابية، بتتمثل بـ tree، والمجلدات على الـ operating
+
+569
+00:52:00,700 --> 00:52:04,980
+system زي اللينكس، على الـ root عندك، الـ c، على الـ
+
+570
+00:52:04,980 --> 00:52:09,300
+ويندوز، الـ user إلى آخره، هذه المجلدات، وهذا الموضوع
+
+571
+00:52:09,300 --> 00:52:15,960
+للعمليات الحسابية بتمثل بتريس، x + y * x not
+
+572
+00:52:15,960 --> 00:52:21,920
+plus y، x + z، عفواً، من وين جبت هنا؟ لأن x أو y و
+
+573
+00:52:21,920 --> 00:52:27,900
+z، الـ parent بتاعتهم من عملية الجمع، الـ x والـ y الـ
+
+574
+00:52:27,900 --> 00:52:33,640
+parent بتاعتهم، مارح، والـ parent للعمليتين الضرب
+
+575
+00:52:33,640 --> 00:52:43,560
+فهذه عبارة عن x أو y + z مضروبة في x، ما قص Y هي
+
+576
+00:52:43,560 --> 00:52:47,000
+الأولويات اللي بتحكم في العملية، أولويات العملية
+
+577
+00:52:47,000 --> 00:53:04,440
+الحسابية في الـ trees، في عند مصطلح binary
+
+578
+00:53:04,440 --> 00:53:17,180
+و مممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممم
+
+579
+00:53:22,870 --> 00:53:27,690
+two children، لما أتكلم على الـ ternary أتكلم على تلاتة،
+
+580
+00:53:27,690 --> 00:53:32,590
+تمام، ternary معناته أتكلم على تلاتة، unary أتكلم على
+
+581
+00:53:32,590 --> 00:53:36,190
+واحد، وهذه صارت single path، عمرو ما بتصير شجرة بشتغل
+
+582
+00:53:36,190 --> 00:53:39,890
+بتفرعات، فالآن أتكلم على binary، على ternary، وها حسب
+
+583
+00:53:39,890 --> 00:53:47,330
+الحاجة، لما أنا باجي بقول full binary tree، full
+
+584
+00:53:47,330 --> 00:53:52,090
+binary tree، إيش يعني؟ يعني كل الـ parents عندهم
+
+585
+00:53:52,090 --> 00:54:00,610
+اثنين، ما بتوقف عندهم اثنين، طيب
+
+586
+00:54:00,610 --> 00:54:10,990
+ماشي، الحل، من أهم التطبيقات اللي موجودة عندي أنا الـ
+
+587
+00:54:10,990 --> 00:54:15,130
+binary tree، من أهم التطبيقات اللي موجودة عندي أنا
+
+588
+00:54:15,130 --> 00:54:21,030
+في الـ binary tree، وبدي أشتغل معك في استخدامات
+
+589
+00:54:21,030 --> 00:54:24,270
+الـ binary tree، قبل ما أروح بالمثال هذا، بدي أروح
+
+590
+00:54:24,270 --> 00:54:29,670
+باتجاه مثال أبسط، وهو أنا فيه عندي أرقام أو
+
+591
+00:54:29,670 --> 00:54:39,450
+sequence، خمسة، سبعة، أربعة، تلاتة، ستة، واحد
+
+592
+00:54:52,040 --> 00:54:57,040
+عادة بأخذ أول element يمثل الـ root
+
+593
+00:55:02,280 --> 00:55:08,780
+ثنائي، يعني كحد أقصى، كحد أقصى عند كل parent two
+
+594
+00:55:08,780 --> 00:55:17,180
+nodes، تمام، باجي بعد هيك الآن السابعة، الآن إذا كانت
+
+595
+00:55:17,180 --> 00:55:20,840
+الـ value أكبر من الـ parent node، بتروح بتضيفها على
+
+596
+00:55:20,840 --> 00:55:24,760
+يمينها، على اليمين، لو كانت أقل منها بتضيفها على
+
+597
+00:55:24,760 --> 00:55:29,600
+الشمال، باجي السابعة، أكبر، حطها على اليمين، هي
+
+598
+00:55:29,600 --> 00:55:35,340
+السبعة، باجي للأربعة، ببدأ أقارنها مع الخمسة، أقل من
+
+599
+00:55:35,340 --> 00:55:42,240
+الخمسة، بروح على الشمال، أربعة، باجي للتلاتة، تلاتة
+
+600
+00:55:42,240 --> 00:55:51,080
+على شمال الخمسة، على شمال الأربعة، باجي للستة، أكبر
+
+601
+00:55:51,080 --> 00:55:54,160
+من الخمسة، يعني على يمينها، باجي للسبعة، أقل من
+
+602
+00:55:54,160 --> 00:55:56,360
+السبعة، على شمال السبعة
+
+603
+00:56:01,190 --> 00:56:08,630
+هذه، ستة، واحد، على شمال الخمسة، شمال الأربعة، شمال
+
+604
+00:56:08,630 --> 00:56:21,030
+التلاتة، واحد، اثنين، شمال الخمسة، شمال شمال، يمين
+
+605
+00:56:21,030 --> 00:56:24,790
+الواحد، الآن
+
+606
+00:56:24,790 --> 00:56:30,350
+ثمانية، يمين الخمسة، يمين السبعة
+
+607
+00:56:37,540 --> 00:56:44,800
+وبهيك بتبني الـ binary tree، ببنائها، الفكرة دائماً الـ
+
+608
+00:56:44,800 --> 00:56:49,440
+value الأكبر على اليمين، الأصغر على الشمال، واحد
+
+609
+00:56:49,440 --> 00:56:53,200
+يقول القيم المتساوية، أو السادس مالهاش وجود على
+
+610
+00:56:53,200 --> 00:56:57,940
+يمين إيه؟ ممتاز، أنا ببدأ أكملها، ثمانية، أكبر من
+
+611
+00:56:57,940 --> 00:5
+
+667
+01:01:42,510 --> 01:01:53,910
+بساطة جدتي تقولي تهيأ A
+
+668
+01:01:53,910 --> 01:02:03,910
+B C D هذا مين؟ هي graph الآن باجي بقول ال spanning
+
+669
+01:02:03,910 --> 01:02:10,110
+tree طبعا هي عبارة عن sub graph من ال graph هذا
+
+670
+01:02:10,110 --> 01:02:15,850
+يمثل ال tree طبعا هو عبارة عن ال tree  بتحتوي على
+
+671
+01:02:15,850 --> 01:02:21,010
+كل النقاط اللي موجودة في الرسمة، ايش يعني كل النقاط
+
+672
+01:02:21,010 --> 01:02:24,990
+اللي موجودة في الرسمة؟ يعني ممكن أنا أعملها هيك
+
+673
+01:02:24,990 --> 01:02:30,870
+أيه؟
+
+674
+01:02:31,680 --> 01:02:39,540
+D C B هذي تجارب ترى، ترى ولا مش ترى؟ هاي ترى بناء
+
+675
+01:02:39,540 --> 01:02:44,140
+على إيش؟ بناء على إنها connected graph، simple
+
+676
+01:02:44,140 --> 01:02:51,640
+connected graph has no circuit، بصبوط، هايها ترى لأن
+
+677
+01:02:51,640 --> 01:02:56,760
+هذي sub graph من هذي، صح ولا لأ؟ مجموعة نقاط، subset
+
+678
+01:02:56,760 --> 01:03:03,540
+من مجموعة نقاط، لأ لأ لأ لأ أنا
+
+679
+01:03:03,540 --> 01:03:07,880
+جلبت ال ..
+
+680
+01:03:07,880 --> 01:03:19,980
+D B ال .. وهنا في عندك ال A وهنا عندك ال C، طبعا؟
+
+681
+01:03:19,980 --> 01:03:26,500
+الآن sub graph، sub graph، النقاط subset من النقاط
+
+682
+01:03:26,500 --> 01:03:31,220
+والجسور subset من الجسور اللي موجودة، Has no circuit
+
+683
+01:03:31,220 --> 01:03:34,640
+فهي Tree، وبما أنها تحتوي على كل النقاط اللي في
+
+684
+01:03:34,640 --> 01:03:39,500
+الرسمة الأساسية، يعني ال V التي هي تساوي ال V التي هي
+
+685
+01:03:39,500 --> 01:03:46,000
+ما هي تسميها؟ أيش؟ Spanning Tree، شجرة ممتدة، تجتمل
+
+686
+01:03:46,000 --> 01:03:48,840
+على كل العناصر اللي موجودة اللي عندها، وفي كل
+
+687
+01:03:48,840 --> 01:03:54,320
+Spanning Tree، عدد الجسور يساوي عدد النقاط ناقص
+
+688
+01:03:54,320 --> 01:04:01,590
+واحد، عدد الجسور يساوي عدد النقاط ناقص واحد، كم
+
+689
+01:04:01,590 --> 01:04:04,990
+النقاط اللي عندي هان؟ أربعة، الجسور اللي عندي فيها
+
+690
+01:04:04,990 --> 01:04:08,610
+هتكون ثلاثة، في أي spanning tree، في أي spanning tree
+
+691
+01:04:08,610 --> 01:04:11,790
+بغض النظر كيف كان شكلها، عدد الجسور يساوي عدد
+
+692
+01:04:11,790 --> 01:04:19,030
+النقاط ناقص واحد، الآن
+
+693
+01:04:19,030 --> 01:04:23,390
+من الأشكال اللي عندنا دول، تبقى لل G1
+
+694
+01:04:28,660 --> 01:04:33,300
+هل هذا spanning tree؟ لأ، فيه circuit، هل هذا
+
+695
+01:04:33,300 --> 01:04:39,420
+spanning tree؟ yes، هل هذا spanning tree؟ yes، هل
+
+696
+01:04:39,420 --> 01:04:43,040
+هذا spanning tree؟ no، ليش؟ لأنه فيه عندي isolated
+
+697
+01:04:43,040 --> 01:04:46,260
+point، وهو راح يقول أن ال tree لازم تكون connected
+
+698
+01:04:46,260 --> 01:04:57,790
+لازم تكون متصلة، اه، ونعتبرها true، true، خلاص، وين ميزة الـ
+
+699
+01:04:57,790 --> 01:05:02,950
+Spanning Tree يا شباب؟ الآية دي، تخيل هي K6، إيش
+
+700
+01:05:02,950 --> 01:05:07,290
+يعني K6؟ Complete Graph من ست نقاط، هيك ال
+
+701
+01:05:07,290 --> 01:05:11,970
+connection، كل واحد متصل مع الخمس نقاط الثانية،
+
+702
+01:05:11,970 --> 01:05:14,850
+الآية، ميزة ال Complete Graph والـ Spanning Tree
+
+703
+01:05:14,850 --> 01:05:19,550
+بتلزمني عشان أنا أعرف كل ال possible paths اللي
+
+704
+01:05:19,550 --> 01:05:23,350
+بتوصلني لمين، أو بدي أبني unique paths عشان أصل من
+
+705
+01:05:23,350 --> 01:05:28,350
+نقطة لنقطة، هيك كل النقاط بتوصل لبعضها، فأنا بدي أعمل
+
+706
+01:05:28,350 --> 01:05:31,830
+minimize للشجرة هذه، أو لل graph هذا، بدي اختصره
+
+707
+01:05:31,830 --> 01:05:36,630
+بشجرة بحيث إنه ما يتركش ولا graph، أو عفوا ولا vertex
+
+708
+01:05:36,630 --> 01:05:40,150
+يبقى برا بدون connection، فبيخدمني في الموضوع مين؟
+
+709
+01:05:40,150 --> 01:05:43,790
+spanning tree، فممكن أتكلم، هي spanning tree من
+
+710
+01:05:43,790 --> 01:05:48,430
+الرسم السابق، ست نقاط، هي ست نقاط موجودة، وهي
+
+711
+01:05:48,430 --> 01:05:52,380
+connected، وهي كمان spanning tree من الرسم السابق،
+
+712
+01:05:52,380 --> 01:05:56,380
+الفكرة هو إن بدل من أدور على كل ال connections
+
+713
+01:05:56,380 --> 01:06:00,280
+هدول، بصير أدور على connection واحدة، خصوصا لما
+
+714
+01:06:00,280 --> 01:06:04,860
+التكلفة .. التكلفة بتكون مالهاش معيار عندي لما
+
+715
+01:06:04,860 --> 01:06:07,720
+التكلفة بتصير مالهاش معيار عندي، بصير أدور على
+
+716
+01:06:07,720 --> 01:06:12,520
+spanning tree عشان أصل لعناصر اللي موجودة عندها،
+
+717
+01:06:12,520 --> 01:06:16,940
+كيف
+
+718
+01:06:16,940 --> 01:06:24,070
+بدي أوجد ال minimum spanning tree؟ أصغر .. أصغر
+
+719
+01:06:24,070 --> 01:06:28,630
+شبكة تجمع كل النقاط اللي موجودة عنها .. بأقل تكلفة
+
+720
+01:06:28,630 --> 01:06:31,510
+طبعا .. الآن أنا في عندي spanning tree، إيش اسمها؟
+
+721
+01:06:31,510 --> 01:06:35,250
+دولة spanning tree .. صارت في عندي شجرات بتحتوي
+
+722
+01:06:35,250 --> 01:06:39,570
+على كل النقاط .. لما بدخل ال cost في الموضوع ..
+
+723
+01:06:39,570 --> 01:06:43,310
+بدخل ال cost في الموضوع .. بصير أدور على مين؟ على
+
+724
+01:06:43,310 --> 01:06:46,950
+ال minimum .. minimum spanning tree .. الآن في أي
+
+725
+01:06:46,950 --> 01:06:51,510
+رسمة، سأقول هي هذي spanning tree وهذه spanning tree
+
+726
+01:06:51,510 --> 01:06:55,150
+لكن مين أقل فيهم؟ أنا ما أعرفش، لأنه فعليا ما تكلمتش
+
+727
+01:06:55,150 --> 01:06:59,210
+على تكلفة، بال minimum spanning tree، بقول كالتالي: هي
+
+728
+01:06:59,210 --> 01:07:02,750
+ال minimum spanning tree بتحتوي على أقل weight، أقل
+
+729
+01:07:02,750 --> 01:07:06,730
+تكلفة، أقل cost، يعني ال cost لازم تكون موجودة عندها
+
+730
+01:07:06,730 --> 01:07:11,370
+فرسمتها البسيطة يا شباب، في عندي two algorithms، في
+
+731
+01:07:11,370 --> 01:07:15,470
+عند ال Prim وفي عند ال Kruskal algorithms، فرسمت
+
+732
+01:07:15,470 --> 01:07:24,300
+بكل البساطة، ده الكالتالي: أنا بدي أشغل هيك، بغض النظر
+
+733
+01:07:24,300 --> 01:07:30,900
+إيش ال algorithm اللي مُستخدم، هاي
+
+734
+01:07:30,900 --> 01:07:39,940
+ال graph، عشان نلهي، تخلصنا A B C D، هنتكلفة خمسة هنا
+
+735
+01:07:39,940 --> 01:07:49,050
+واحد هنا، ثلاثة هنا، أربعة هنا، اثنين هنا، خمسة، الآن
+
+736
+01:07:49,050 --> 01:07:52,010
+عندما تحصل على الـ Minimum Spanning Tree، يعني أنك
+
+737
+01:07:52,010 --> 01:08:00,630
+تريد الأربع نقاط اللي موجودة، هذه الأربع نقاط A
+
+738
+01:08:00,630 --> 01:08:09,670
+,B,C,D، أول ما بترسم، بترسم الخطوط اللي أقل تكلفة
+
+739
+01:08:09,670 --> 01:08:15,750
+احنا حطينا قد ايش؟ اوكي، اثنين فيهم، خمسات، اوكي، بس
+
+740
+01:08:15,750 --> 01:08:17,990
+بعد إذنك، بدي أحط هذه كمان، مرة، اثنين
+
+741
+01:08:22,160 --> 01:08:29,340
+الآن بتاخد أقل تكلفة، مين أقل تكلفة؟ AC، ها هو أول خط
+
+742
+01:08:29,340 --> 01:08:39,520
+بواحد، بعد هيك بتاخد AB، أخدت AB، اثنين، اللي بعده BC،
+
+743
+01:08:39,520 --> 01:08:44,450
+لو أنا ارسمت ال BC هنا، شباب، صار في عندي circle، صار
+
+744
+01:08:44,450 --> 01:08:48,390
+في عندي circuit، بطل ال three، فأنا آسف، مش هاخد هذا
+
+745
+01:08:48,390 --> 01:08:54,230
+بيه، اثنين، هاخد مين؟ هاخد اللي بعده، لأ، هو واحد، بين
+
+746
+01:08:54,230 --> 01:09:00,810
+كانوا .. ماشي
+
+747
+01:09:00,810 --> 01:09:07,230
+الحال، هي واحد، واحد، وأنا أربعة، طبعا، الآن بدي أخد
+
+748
+01:09:07,230 --> 01:09:16,680
+مين؟ بدي أخد، خلصت هذا ما بديش إياه، بدي أخد الأربعة،
+
+749
+01:09:16,680 --> 01:09:23,640
+هاي أربعة، طيب، كم دي صارت عندي أنا؟ ثلاثة،
+
+750
+01:09:23,640 --> 01:09:29,860
+وعدد النقاط؟ أنا مش بحاجة للجسور بعد هيك،
+
+751
+01:09:29,860 --> 01:09:35,750
+وينها؟ وينها؟ ما فيش circuit، ما فيش، لو فيه نقطة في النص
+
+752
+01:09:35,750 --> 01:09:39,090
+كان اختلفت الأمور، السؤال اللي بيطرح نفسه الآن: ليش
+
+753
+01:09:39,090 --> 01:09:43,630
+أنا وقفت ما كملتش؟ لأن ال spanning tree عدد الجسور
+
+754
+01:09:43,630 --> 01:09:47,390
+فيها يساوي عدد النقاط ناقص واحد، وأنا بدي بس ثلاثة
+
+755
+01:09:47,390 --> 01:09:51,370
+نقاط، فهي اتكملت بالثلاث نقاط وخلصنا، وبهيك أنت
+
+756
+01:09:51,370 --> 01:09:55,950
+بترسم، أو بتقدر تحصل على ال minimum spanning
+
+757
+01:09:55,950 --> 01:09:56,810
+tree
+
+758
+01:10:02,620 --> 01:10:07,480
+الأسماء لـ Algorithm، لرسم، التعامل، أو الوصول للـ
+
+759
+01:10:07,480 --> 01:10:11,360
+Tree، خلاص، بس أنت بدك تعرف الأسماء، مش أكثر من هيك
+
+760
+01:10:11,360 --> 01:10:17,000
+تسميهم، بدك تعرف إن في عندك two algorithms كمان من
+
+761
+01:10:17,000 --> 01:10:20,100
+أجل الوصول لـ ال minimum spanning trees، هيهم
+
+762
+01:10:20,100 --> 01:10:24,040
+Kruskal و Prim algorithms، لكن الطريقة اللي أنا ..
+
+763
+01:10:24,040 --> 01:10:26,720
+لو قلت لك، هتل ال minimum spanning tree، أشغل
+
+764
+01:10:26,720 --> 01:10:31,670
+بالطريقة اللي أنا قلت لك عنها .. طيب، وبهيك الشباب، مع
+
+765
+01:10:31,670 --> 01:10:35,230
+ال Kruskal algorithm، نكون انتهينا من ال chapter
+
+766
+01:10:35,230 --> 01:10:40,190
+الأخير في المساق، للفصل هذا، هو فعليا أنا ال .. هذا
+
+767
+01:10:40,190 --> 01:10:43,990
+المفروض ال Tree في ال chapter سبعة، فاحنا فعليا
+
+768
+01:10:43,990 --> 01:10:46,030
+طلعنا من الستة وروحنا على سبعة وجبنا اللي
+
+769
+01:10:46,030 --> 01:10:49,950
+بدنا إياه، وبهيك نكون خلصنا الفصل بالكامل، إن شاء الله
+
+770
+01:10:49,950 --> 01:10:54,530
+تعالوا إذا في حد عنده أي سؤال، احنا جاهزين في المكتب
+
+771
+01:10:54,530 --> 01:10:56,310
+باستماعكم خلال الأسبوع اللي جاي، إن شاء الله، جايين
+
+772
+01:10:56,310 --> 01:11:01,720
+للامتحان، حضّر نفسك، راجع، ما تجينيش إن
+
+773
+01:11:01,720 --> 01:11:05,880
+أشرح لك المادة من الصفر، لازم أشوفك فعلا أنت بذلت
+
+774
+01:11:05,880 --> 01:11:10,080
+جهود، وجايين إن أنا أشوف إنك فاهم الشغل اللي أنت
+
+775
+01:11:10,080 --> 01:11:13,160
+ما قدرت توصل له، وإن شاء الله هنكون بانتظارك، بإذن
+
+776
+01:11:13,160 --> 01:11:16,280
+الله تبارك وتعالى، بس الحال هيك بكون نهينا محاضرتنا،
+
+777
+01:11:16,280 --> 01:11:19,000
+ونهينا الفصل، سبحانك اللهم وبحمدك، نشهد أن لا إله إلا
+
+778
+01:11:19,000 --> 01:11:21,820
+أنت، ونستغفرك، ونَتوب إليك، و سامحونا إذا نحن
+
+779
+01:11:21,820 --> 01:11:25,700
+أخللنا .. إذا  أُخِذَت محاضرة هكذا، الله يعطي كل واحد عافية إن
+
+780
+01:11:25,700 --> 01:11:25,800
+شاء الله
diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/zrkaFn0izUk_postprocess.srt b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/zrkaFn0izUk_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..58fda5a7ce13696c92c43729e9010c68d79879e5
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/zrkaFn0izUk_postprocess.srt
@@ -0,0 +1,3120 @@
+1
+00:00:21,090 --> 00:00:23,190
+بسم الله والحمد لله والصلاة والسلام علي رسول الله
+
+2
+00:00:23,190 --> 00:00:27,590
+كنا المحاضرة الماضي شباب اتكلمنا على مجموعة من
+
+3
+00:00:27,590 --> 00:00:30,330
+المهمة .. مجموعة مهمة من ال definitions فيما تعلق
+
+4
+00:00:30,330 --> 00:00:34,750
+بموضوع ال graphs اتكلمنا على ال walk هو عبارة عن
+
+5
+00:00:34,750 --> 00:00:38,050
+مجموعة او sequence مجموعة من ال vertices و اليسور
+
+6
+00:00:38,050 --> 00:00:41,590
+المتتالية لازم يكون في بينها ربط و ال length تبع
+
+7
+00:00:41,590 --> 00:00:45,110
+ال walk تمثل بعدد اليسور وقولنا ال walk مكون
+
+8
+00:00:45,110 --> 00:00:49,600
+closed لما بيبدأ و بينتهي عند نفس النقطةوعكسها
+
+9
+00:00:49,600 --> 00:00:52,960
+بيكون open في عنده definition لل walk اخر اسمه
+
+10
+00:00:52,960 --> 00:00:56,180
+trail لما بيكون هذا ال walk بيحتوي على distinct
+
+11
+00:00:56,180 --> 00:01:01,500
+edge بيحتوي على جسور مختلفة و بسميه path لما بكون
+
+12
+00:01:01,500 --> 00:01:06,500
+و path لما بكون عندي بيحتوي على vertices مختلفة و
+
+13
+00:01:06,500 --> 00:01:09,740
+لما بكل trail هذا closed يعني بدأ و انتهى بنفس
+
+14
+00:01:09,740 --> 00:01:13,820
+النقاط و كل الجسور اللي فيه مختلفة بسميه circuit و
+
+15
+00:01:13,820 --> 00:01:18,460
+لما بيكون ال path اللي عنديبينتهي بنفس النقطة
+
+16
+00:01:18,460 --> 00:01:24,980
+استثناء سمناها cycle وشوفنا المثال هذا وحلينا منه
+
+17
+00:01:24,980 --> 00:01:28,420
+المحاضرة الماضيةاليوم ان شاء الله تعالى هنبدأ مع
+
+18
+00:01:28,420 --> 00:01:32,180
+definition جديد نسميه Euler circuit و Euler path
+
+19
+00:01:32,180 --> 00:01:37,920
+في لبس أحيانا بيصير في موضوع اللي فهمناه ال Euler
+
+20
+00:01:37,920 --> 00:01:42,240
+circuit و Euler path خصوصا لما اتكلم على ال path
+
+21
+00:01:42,240 --> 00:01:48,060
+بداية في قرية في روسيا او في المدينة في روسيا
+
+22
+00:01:48,060 --> 00:01:51,960
+Konigsberg اعتقد اذا انا مش غلطان في الاسم في ال
+
+23
+00:01:51,960 --> 00:01:56,100
+1800 و مش عارف جداش كانوا ناس بتحب تتنزح عوالين
+
+24
+00:01:57,030 --> 00:01:59,810
+النهر المبني عليه السبع جسور الموجودة اللي احنا
+
+25
+00:01:59,810 --> 00:02:04,730
+شايفينهم قدامنا هنا وكانت الناس دائما بتتساءل هل
+
+26
+00:02:04,730 --> 00:02:08,590
+بإمكاني انا اعمل جولة ال walk تبعتي المسار تبعي
+
+27
+00:02:08,590 --> 00:02:14,190
+امر فيه على كل الجسور بدون مبر امر في جسر واحد او
+
+28
+00:02:14,190 --> 00:02:20,320
+جسر معين مرتين او ما شابه فكان الكلام هذاأخد وضل
+
+29
+00:02:20,320 --> 00:02:23,500
+التساوي قائم لأنه ماحدش كان يجرب بشكل عام لإيه
+
+30
+00:02:23,500 --> 00:02:27,820
+اللي غير يجيه رجع يمر على جسر مرة تانية في نهاية
+
+31
+00:02:27,820 --> 00:02:36,340
+ال 1800 و بعديها بقى كام سنة اجى عالم سويدي أيلر و
+
+32
+00:02:36,340 --> 00:02:41,490
+راح درس المنطقة ومثل ال graphاللي انها مثلة
+
+33
+00:02:41,490 --> 00:02:45,270
+بالخريطة اللي موجودة هنا وكانت نظريته بتقول كالشكل
+
+34
+00:02:45,270 --> 00:02:49,990
+التالي من خلال عرف ال oiler circuit وال oiler path
+
+35
+00:02:49,990 --> 00:02:53,090
+بناء على ال definition اللي موجود النظرية كانت
+
+36
+00:02:53,090 --> 00:02:58,170
+بتقول كالتالي ان ال oiler circuit هي عبارة عن
+
+37
+00:02:58,170 --> 00:03:02,610
+simple circuit ونجف هنا simple circuit شو يعني
+
+38
+00:03:02,610 --> 00:03:08,230
+simple circuit closed walk
+
+39
+00:03:08,230 --> 00:03:09,630
+او closed trail
+
+40
+00:03:12,590 --> 00:03:20,530
+closed circuit يعني closed trail containing every
+
+41
+00:03:20,530 --> 00:03:25,350
+edge في الgraph اللي جيه يعني إذا أنا كدفت أعمل
+
+42
+00:03:25,350 --> 00:03:31,050
+closed trailأو circuit بتحتوي على كل الجسور اللي
+
+43
+00:03:31,050 --> 00:03:36,530
+موجودة في ال graph بسميها ايش؟ Oiler circuit و
+
+44
+00:03:36,530 --> 00:03:42,290
+oiler هذا أثبت الكلام التالي جال إذا كان ال graph
+
+45
+00:03:42,290 --> 00:03:48,690
+هذا كل ال vertices اللي موجودة فيه كل النقاط اللي
+
+46
+00:03:48,690 --> 00:03:55,620
+موجودة فيهلها رطبة زوجية ايش يعني رطبة زوجية؟ يعني
+
+47
+00:03:55,620 --> 00:04:00,500
+عدد الجسور اللي جاية على ال vertex عدد زوجية،
+
+48
+00:04:00,500 --> 00:04:05,440
+كمان؟ معناته بتقدر تلاقي في ال graph Oiler circuit
+
+49
+00:04:05,440 --> 00:04:11,200
+طب لو ماكانش، لو لجيت واحد من ال vertices هذه عدد
+
+50
+00:04:11,200 --> 00:04:15,780
+او رطبة كبار رطبة فردية انسى الموضوع، مافيش هيش
+
+51
+00:04:15,780 --> 00:04:16,780
+circuit
+
+52
+00:04:21,190 --> 00:04:26,350
+والأولى باث بقول كالتالي simple path لكن للأسف
+
+53
+00:04:26,350 --> 00:04:30,730
+كلمة path هان مش بمعناها الحقيقي path حسب ال
+
+54
+00:04:30,730 --> 00:04:36,170
+definition تبع الكتاب بقدر ما هي ايش walk simple
+
+55
+00:04:36,170 --> 00:04:41,210
+walk containing every edge
+
+56
+00:04:44,410 --> 00:04:49,970
+أحنا نعرف أن الـ path بيحتوي عن طرق مختلفة وانا
+
+57
+00:04:49,970 --> 00:04:53,230
+بقول أن هذه الشيء اللي بيحتوي على كل اليسار، يعني
+
+58
+00:04:53,230 --> 00:04:56,150
+الفرق بين هذه و هذه انها إيش تكون يا شباب؟ ال
+
+59
+00:04:56,150 --> 00:05:01,270
+closing فقط، طيب اويدراش جال بالنسبة لل path جال
+
+60
+00:05:01,270 --> 00:05:07,720
+إذا كانتالرسمة اللى موجود عندك بتحتوي على تنتين
+
+61
+00:05:07,720 --> 00:05:13,080
+فقط exactly two vertices of odd degrees of odd
+
+62
+00:05:13,080 --> 00:05:18,540
+degree بتلاقي Euler path كمان مرة نعيد قالك ال
+
+63
+00:05:18,540 --> 00:05:22,040
+Euler circuit بتلاقيها لو كانت كل ال degree تحت ال
+
+64
+00:05:22,040 --> 00:05:26,800
+vertices even احداث زوجية و بتلاقي ال Euler path
+
+65
+00:05:26,800 --> 00:05:33,180
+موجود لو كان فقط عندك اتنين اتنين فقطالرطبة تبعتهم
+
+66
+00:05:33,180 --> 00:05:37,980
+رطبة فردية، فلو وجدت واحد، مافيش Euler بقى، فلو
+
+67
+00:05:37,980 --> 00:05:41,560
+وجدت تلاتة، مافيش Euler بقى. تعالى نرجع للرسمة
+
+68
+00:05:41,560 --> 00:05:48,420
+السابقة، بينجوسين، Euler كان بيقولهم، من المستحيل
+
+69
+00:05:48,420 --> 00:05:55,860
+انك تعمل جولة تمام؟ تمر فيها على كل الجسور بدون ما
+
+70
+00:05:55,860 --> 00:06:00,590
+تطلع على جسر؟مرتين، لماذا؟ لكي نجيب البوتر في
+
+71
+00:06:00,590 --> 00:06:05,870
+العناصر و نسقط النظرية تبع الـ Euler ربط C كم
+
+72
+00:06:05,870 --> 00:06:15,410
+شباب؟ تلاتة؟ خمس؟
+
+73
+00:06:15,410 --> 00:06:18,130
+Euler circuit كان بيقول إنه لازم تكون كل بوتر
+
+74
+00:06:18,130 --> 00:06:22,490
+فردية عشان تلاقي الـ Euler circuit زوجية عفواً كل
+
+75
+00:06:22,490 --> 00:06:25,430
+بوتر لازم تكون بوتر زوجية عشان تلاقي الـ Euler
+
+76
+00:06:25,430 --> 00:06:30,090
+circuitطب كل رتب اللي عنده رتب فردية بالتاني مافيش
+
+77
+00:06:30,090 --> 00:06:34,290
+على الرسم هان oiler circuit .. does not exist ال
+
+78
+00:06:34,290 --> 00:06:38,050
+oiler path بقول .. بتلاقي ال oiler path في حالة
+
+79
+00:06:38,050 --> 00:06:42,350
+إذا كان في ال graph فقط اتنينورتبته مرتبة فردية
+
+80
+00:06:42,350 --> 00:06:46,890
+بقى بقى خمسة وكلهم فرديات معناته ال oiler bath
+
+81
+00:06:46,890 --> 00:06:51,250
+does not exist تعالى نشوف الأمثلات اللى موجودة
+
+82
+00:06:51,250 --> 00:06:55,910
+عندها ونسقط عليها الكلام الصادق ونسأل نفسنا هل ال
+
+83
+00:06:55,910 --> 00:06:59,630
+oiler bath و ال oiler circuit exist ولا لأ نبدأ مع
+
+84
+00:06:59,630 --> 00:07:05,290
+G1 وانا بدي اختصر احاول اقول oiler circuit و oiler
+
+85
+00:07:07,040 --> 00:07:11,500
+Oiler Circuit مع الـ G1 الروت برنجل دي الشباب؟ 2
+
+86
+00:07:11,500 --> 00:07:18,420
+.. 2 .. 2 .. 4 .. 4 .. 4 .. 4 .. 4 .. 4 .. 4 .. 4
+
+87
+00:07:18,420 --> 00:07:18,500
+.. 4 .. 4 .. 4 .. 4 .. 4 .. 4 .. 4 .. 4 .. 4 .. 4
+
+88
+00:07:18,500 --> 00:07:19,100
+.. 4 .. 4 .. 4 .. 4 .. 4 .. 4 .. 4 .. 4 .. 4 .. 4
+
+89
+00:07:19,100 --> 00:07:19,160
+.. 4 .. 4 .. 4 .. 4 .. 4 .. 4 .. 4 .. 4 .. 4 .. 4
+
+90
+00:07:19,160 --> 00:07:19,180
+.. 4 .. 4 .. 4 .. 4 .. 4 .. 4 .. 4 .. 4 .. 4 .. 4
+
+91
+00:07:19,180 --> 00:07:19,680
+.. 4 .. 4 .. 4 .. 4 .. 4 .. 4 .. 4 .. 4 .. 4 .. 4
+
+92
+00:07:19,680 --> 00:07:28,280
+..
+
+93
+00:07:31,320 --> 00:07:36,340
+D C E A لأنه لو تنساش circuit لازم تبدأ وتنتهي
+
+94
+00:07:36,340 --> 00:07:43,920
+بنفس المقمة انا بتبقى أكتر كم مرة A D .. بالضبط هي
+
+95
+00:07:43,920 --> 00:07:54,560
+اللي احنا بدنا نوصلها C أو A B E D C E Aلو مفهوم
+
+96
+00:07:54,560 --> 00:07:58,660
+ان الـ Vertices ممنوع تتكرر كروحنا في مشكلة الآن
+
+97
+00:07:58,660 --> 00:08:02,980
+ان ال circuit هاد ايش مش موجودة تمام الان هي ال
+
+98
+00:08:02,980 --> 00:08:05,740
+Euler circuit طبعا ممكن تعرف اكثر من واحدة تبدأ من
+
+99
+00:08:05,740 --> 00:08:08,840
+عند ال C و تبدأ بايب اتجاه هتلاقي ال Euler circuit
+
+100
+00:08:08,840 --> 00:08:13,100
+موجودة ال Euler path ايش ال Euler path بقول؟ بقول
+
+101
+00:08:13,100 --> 00:08:18,900
+انه لازم تكون تنتين فقط رتبة فردية مافيش عنده رتبة
+
+102
+00:08:18,900 --> 00:08:22,300
+فردية كلها قانون زوجية وبالتالي مافيش Euler path
+
+103
+00:08:23,530 --> 00:08:32,770
+مافيش ND، oiler bath، تمام؟ اللي بعديها؟ تلاتة،
+
+104
+00:08:32,770 --> 00:08:42,670
+تلاتة، تلاتة، تلاتة، أربعة، oiler circuit، oiler
+
+105
+00:08:42,670 --> 00:08:48,520
+bath، oiler circuit موجودة؟بقول كل غطبك يجب ان
+
+106
+00:08:48,520 --> 00:08:52,900
+تكون زوجي عشان كل ال circuit وال all or بقى يجب ان
+
+107
+00:08:52,900 --> 00:08:59,740
+يكون في عندك تلتير غطبتهم فردية الاخير
+
+108
+00:08:59,740 --> 00:09:12,820
+تلاتة تلاتة اربعة اربعة اربعة
+
+109
+00:09:12,820 --> 00:09:13,540
+اربعة اربعة اربعة اربعة اربعة اربعة اربعة اربعة
+
+110
+00:09:13,540 --> 00:09:13,900
+اربعة اربعة اربعة اربعة اربعة اربعة اربعة اربعة
+
+111
+00:09:13,900 --> 00:09:14,280
+اربعة اربعة اربعة اربعة اربعة اربعة اربعة اربعة
+
+112
+00:09:14,280 --> 00:09:14,300
+اربعة اربعة اربعة اربعة اربعة اربعة اربعة اربعة
+
+113
+00:09:14,300 --> 00:09:14,600
+اربعة اربعة اربعة اربعة اربعة اربعة اربعة اربعة
+
+114
+00:09:14,600 --> 00:09:17,570
+اربعة اربعة اربعةمش موجودة لأنه في عنده رتب فردية
+
+115
+00:09:17,570 --> 00:09:22,450
+و هو بيقول لازم تكون كل الرتب زوجيا اويلر باف
+
+116
+00:09:22,450 --> 00:09:28,350
+موجودة؟ موجودة لأنه بيقول تكون عندك تلتين من ال
+
+117
+00:09:28,350 --> 00:09:31,790
+vertices و رتبهم فردية موجود تعالي نقف بال اويلر
+
+118
+00:09:31,790 --> 00:09:41,570
+باف A B E D
+
+119
+00:09:45,220 --> 00:09:51,700
+أطلع فوق؟ أيوة طيب ممكن ألاق بيكتب المسار مرة
+
+120
+00:09:51,700 --> 00:09:57,280
+تانية A B D A
+
+121
+00:09:57,280 --> 00:09:58,400
+B D
+
+122
+00:10:06,200 --> 00:10:09,920
+لأ ارجع عليه كمان مرة مش هتظبط الان انا في قاعد
+
+123
+00:10:09,920 --> 00:10:13,920
+وانا بجرب متأكد ان ال oiler bath exist بس بقالي
+
+124
+00:10:13,920 --> 00:10:24,560
+عليهاش ان اجيبه مرات يعني نعم احد
+
+125
+00:10:24,560 --> 00:10:32,440
+اتنين تلاتة اربعة بس لحظة شوي اللي يصبر علي اربعة
+
+126
+00:10:33,470 --> 00:10:41,030
+خمسة .. ستة .. سبعة صح ولا غلط؟ طبعا لو كونه
+
+127
+00:10:41,030 --> 00:10:44,290
+بيقولك موجود ممكن تلاقي اكتر من واحد مايحدد ال
+
+128
+00:10:44,290 --> 00:10:47,570
+cash ان هو واحد ولا اكتر انا الان بقعد بقترح انه
+
+129
+00:10:47,570 --> 00:10:56,350
+هيك واحد من A ل B من A ل C من C ل D من D ل E من E
+
+130
+00:10:56,350 --> 00:11:08,180
+ل D من B ل D من D ل Aو من A ل B و احظ ان المسار
+
+131
+00:11:08,180 --> 00:11:12,720
+اللى كتبته هذا حقق من وجهه كل الجسور اللى موجودة
+
+132
+00:11:12,720 --> 00:11:19,360
+وين عندي على الرصمة بدون اي مشاكل .. بدون اي مشاكل
+
+133
+00:11:19,360 --> 00:11:26,200
+ايش كنت تقولي حازم؟ مسار تاني؟ في
+
+134
+00:11:26,200 --> 00:11:30,340
+الآخر انت بتلاقي كونه حسب النظرية ان ال vert اللى
+
+135
+00:11:30,340 --> 00:11:34,640
+موجود بضل عليه اي شساويأدقق ولا إيش بقى أجيب
+
+136
+00:11:34,640 --> 00:11:42,560
+المسار اللي موجود عندي بتمشي الأمور تمام على
+
+137
+00:11:42,560 --> 00:11:50,660
+غرار أولا في اندي الهاملتون راح أرف هاملتون باخ و
+
+138
+00:11:50,660 --> 00:11:55,500
+هاملتون circle نعم إذا كان ماضينا مثلا أنه في نقاط
+
+139
+00:11:58,490 --> 00:12:02,450
+بتسقط النظرية بالكامل النظرية تتحقق لما أقولك
+
+140
+00:12:02,450 --> 00:12:07,290
+اتنين فقط odd vertices معينة بتلاقي ال oiler path
+
+141
+00:12:07,290 --> 00:12:13,930
+كلهم even vertices او even degree معينة بتلاقي ال
+
+142
+00:12:13,930 --> 00:12:18,930
+oiler circuits طيب ..الان لو لجيت .. هذه فيها ..
+
+143
+00:12:18,930 --> 00:12:25,150
+لجيت فيها خمسة اتنين منهم odd و تلاتة even ال path
+
+144
+00:12:25,150 --> 00:12:29,200
+موجود لكن ال circuit مش موجودةهذا المفروض منه يعني
+
+145
+00:12:29,200 --> 00:12:33,480
+إذا لوجد ال circuit مش ضروري مش هتلاقي البعض وإذا
+
+146
+00:12:33,480 --> 00:12:36,700
+لوجد البعض مش هتلاقي ال circuit لأنه في بينهم
+
+147
+00:12:36,700 --> 00:12:42,640
+تبعات في ال definition ال hamilton path إيش بيقول؟
+
+148
+00:12:42,640 --> 00:12:46,500
+لاحظوا إيش كان ال oiler في مركز الشباب containing
+
+149
+00:12:46,500 --> 00:12:55,270
+every edge containing every edge تمام؟هاملتون لما
+
+150
+00:12:55,270 --> 00:12:59,890
+جاء تكلم قال لا يا عمي انا انا بدى اعرف اذا قدرنا
+
+151
+00:12:59,890 --> 00:13:08,250
+نوجد مسار بيحتوي على كل ال vertices كل
+
+152
+00:13:08,250 --> 00:13:13,610
+ال vertices في دورة واحدة لاحظ هو اكد ان انا عديت
+
+153
+00:13:13,610 --> 00:13:23,080
+two definitions ال path بدمر في كل النقاطوالآن
+
+154
+00:13:23,080 --> 00:13:26,640
+تسقط معنى الـ path بالمعنى الحرفي على خلال الـ
+
+155
+00:13:26,640 --> 00:13:33,300
+walk وبتكلم الآن إن هذا بتجيبه في مسار واحد، عارف
+
+156
+00:13:33,300 --> 00:13:35,400
+إيش أنا في مسار واحد؟ يعني أنا غالباً مش هارجي
+
+157
+00:13:35,400 --> 00:13:41,460
+عايش، مش هارجي على النقطة مرة تانية تعالى نشوف ال
+
+158
+00:13:41,460 --> 00:13:44,320
+vintage و الhexagon الرسمات اللي موجودة هنا هي
+
+159
+00:13:44,320 --> 00:13:49,230
+الشكل الخماسي والشكل السوداسيالان كمشكات الخماسي
+
+160
+00:13:49,230 --> 00:13:54,850
+موجود واحد اتنين ثلاثة تمام؟ الان ال author .. او
+
+161
+00:13:54,850 --> 00:13:59,950
+عفوا ال Hamilton path هو عبارة عن مسار بيحتوي على
+
+162
+00:13:59,950 --> 00:14:04,710
+كل النقاط في لفة واحدة اللي هو انا محدد لك ايه
+
+163
+00:14:04,710 --> 00:14:05,830
+باللون الأحمر بدأت من هنا
+
+164
+00:14:18,550 --> 00:14:24,390
+إذا وقفت لحد الـ hand، ميلاده غيبار، مصبور؟ و
+
+165
+00:14:24,390 --> 00:14:30,750
+سكرته، أصبح circuit، مصبور؟ تسيبه مفتوح ميلاده و
+
+166
+00:14:30,750 --> 00:14:36,340
+تتكلم على مين؟ على باهسكت و أتكلم على circuit طب
+
+167
+00:14:36,340 --> 00:14:40,000
+circuit و لا cycle أسميها هو سماها circuit ليش؟
+
+168
+00:14:40,000 --> 00:14:44,640
+لأن كل الجسور اللي فيها جسور مختلفة كل الجسور اللي
+
+169
+00:14:44,640 --> 00:14:48,740
+فيها جسور مختلفة السؤال اللي بيطرح نفسه هل هو مسار
+
+170
+00:14:48,740 --> 00:14:55,020
+واحد اللي موجود حقنا لأ ابدأ نقطة بداية تانية تمام
+
+171
+00:14:55,020 --> 00:14:58,880
+ابدأ من هنا مش
+
+172
+00:14:58,880 --> 00:15:03,580
+هيكون في عندك مشكلةبالضبط كل مطبخ ستقدر تديك مسار
+
+173
+00:15:03,580 --> 00:15:09,520
+مختلف هدف
+
+174
+00:15:09,520 --> 00:15:13,040
+الشكل الخماسي والشكل السلاسي هذا الشكل هو نفس
+
+175
+00:15:13,040 --> 00:15:16,400
+الشكل فانا قلتلك عليه two different paths two
+
+176
+00:15:16,400 --> 00:15:21,500
+different hamilton paths أصبح الأخضر والأزرق لاحظ
+
+177
+00:15:21,500 --> 00:15:30,990
+بمجرد أن هذه الأشيرة بتكلم علي بقى سكت الخطبتكلم
+
+178
+00:15:30,990 --> 00:15:36,350
+على circuit واضح الأمر يا شباب أه؟ تمام خلّيني
+
+179
+00:15:36,350 --> 00:15:42,770
+ننتقل لنقطة أهم من ال ILR و ال Hamilton في موضوع
+
+180
+00:15:42,770 --> 00:15:47,890
+ال graphs كل graphs اللي أسميها سابقا الشباب كانت
+
+181
+00:15:47,890 --> 00:15:52,110
+undirected graph إيش يعني undirected؟ غير مباشرة
+
+182
+00:15:52,110 --> 00:15:58,530
+أو غير موجهة undirected غير موجهة
+
+183
+00:16:02,190 --> 00:16:09,790
+عندما أقول a,b,c,d هل
+
+184
+00:16:09,790 --> 00:16:15,890
+هناك طريق من a إلى b؟ موجود، فمن b إلى a؟ موجود،
+
+185
+00:16:15,890 --> 00:16:20,930
+لماذا؟ لأنه لا يوجد سهم يحدد الاتجاه وعندما كنا
+
+186
+00:16:20,930 --> 00:16:28,470
+نمثل هذا الجراف، كنت أقول إن v هي مجموعة النقاط a
+
+187
+00:16:28,470 --> 00:16:34,550
+,b,cو D مظبوط و مجموعة ال ديسور ايش كانت تساوي
+
+188
+00:16:34,550 --> 00:16:44,330
+الشباب A B B C C و D و A D او دي او دي ايه مش قضية
+
+189
+00:16:44,330 --> 00:16:53,150
+كتير او A C مظبوط يعني او A C لان ماكانش تفرج
+
+190
+00:16:53,150 --> 00:16:58,530
+معايا اكتب B C ولا اكتب C B مظبوط اكتب A D ولا D A
+
+191
+00:16:59,590 --> 00:17:03,470
+ليش؟ لأنه انخط الجسر موجود بين نقطين، يعني أنه
+
+192
+00:17:03,470 --> 00:17:07,630
+مسموح يتحرك بين اتجاهين.باقلهم في الـdirected
+
+193
+00:17:07,630 --> 00:17:12,650
+graph، هذا الكلام صحيح، بيصير الحركة باتجاه السهم
+
+194
+00:17:12,650 --> 00:17:17,170
+فقط، عشان هيك اسمه directed graph، directed أو
+
+195
+00:17:17,170 --> 00:17:21,230
+direct graph، وفي ال direct graph الفرق بينه و بين
+
+196
+00:17:21,230 --> 00:17:24,490
+ال undirected graph، انه انا بدي اكتر مجموعة
+
+197
+00:17:24,490 --> 00:17:31,010
+الجسور على شكل أزواج مرتبة،و احنا بنعرف في الزوج
+
+198
+00:17:31,010 --> 00:17:39,690
+المرتب XY لا تساوي YX أصبت؟ وبالتالي انا ببيعصير
+
+199
+00:17:39,690 --> 00:17:45,890
+اتكلم حسب اتجاه السهم بالرسمة هذه هل في طريق من A
+
+200
+00:17:45,890 --> 00:17:49,750
+ل D؟
+
+201
+00:17:49,750 --> 00:17:56,750
+ليس مجال انا بدي اتبع عصير اتبع السهم هل من ال A
+
+202
+00:17:56,750 --> 00:18:03,780
+ممكن اصل ال D؟لأ مافيش مجال وبالتالي بصير انا بشغل
+
+203
+00:18:03,780 --> 00:18:09,020
+عالمين حسب الأسهم اللي موجودة عندى كمان مرة بنقول
+
+204
+00:18:09,020 --> 00:18:12,040
+في ال directed graph أو في ال direct graph بدنا
+
+205
+00:18:12,040 --> 00:18:17,300
+نصير نقطة للجسور بأزواج مرتبة النقطة الأولى في
+
+206
+00:18:17,300 --> 00:18:22,100
+الزواج المرتبة بتمثل starting vertex نقطة البداية
+
+207
+00:18:22,100 --> 00:18:26,720
+والنقطة التانية بتمثل ال end vertex أو ال target
+
+208
+00:18:26,720 --> 00:18:27,300
+vertex
+
+209
+00:18:32,420 --> 00:18:39,760
+في موضوع الـ Undirected Graph كنت بتكلم على الجوار
+
+210
+00:18:39,760 --> 00:18:43,600
+قلنا إنه بتكون فيه عندى نقاطين متجاورتين لمّا
+
+211
+00:18:43,600 --> 00:18:49,140
+بيكون فيه بينهم جسم يعني بقول من النقاط المجاورة
+
+212
+00:18:49,140 --> 00:18:54,620
+للـD هي كل النقاط اللي بتلتق معاها مع جسور A و B و
+
+213
+00:18:54,620 --> 00:18:59,140
+C مصدوق احمد؟ من النقاط اللي مجاورة للـB
+
+214
+00:19:01,760 --> 00:19:09,520
+A و D من النقاط المجاورة للـC A و D و هكذا طيب لكن
+
+215
+00:19:09,520 --> 00:19:13,440
+مع ال Direct Graph بقلت أتكلم عليه الـJson
+
+216
+00:19:13,440 --> 00:19:18,920
+Vertices أتكلم عليه Terminal Vertices اللي أنا
+
+217
+00:19:18,920 --> 00:19:22,700
+رايح له من ال Target Vertices من ال Terminal تبعت
+
+218
+00:19:22,700 --> 00:19:29,820
+الـDA و B و C بناء على السهم من ال term اللي تبعت
+
+219
+00:19:29,820 --> 00:19:37,220
+ال A؟ C لحالها بس باتجاه السهم فقط B من ال term
+
+220
+00:19:37,220 --> 00:19:42,840
+اللي تبعت ال B؟ ال A من ال term اللي تبعت ال C؟
+
+221
+00:19:42,840 --> 00:19:53,400
+ماعناش تمام، تستجبل و لا تعطيش واضح الأمور؟ تمام
+
+222
+00:19:58,930 --> 00:20:02,130
+بدي اتكلم في الموضوع اسمه الـ Representation تمثيل
+
+223
+00:20:02,130 --> 00:20:06,190
+لـ Graph عشان انت تشتغل او تطبق برنامج بتعامل مع
+
+224
+00:20:06,190 --> 00:20:10,410
+الـ Graph بيلزمك اتمثل لـ Graph هذا في شغل سهلة
+
+225
+00:20:10,410 --> 00:20:13,670
+تقدر تتعامل مع الكمبيوتر ببساطة والتمثيل هذا هيكون
+
+226
+00:20:13,670 --> 00:20:19,370
+من خلال مصفوفة الجوار مصفوفة بنسميها مصفوفة الجوار
+
+227
+00:20:19,370 --> 00:20:25,270
+مصفوفة بنسميها مصفوفة الجوار الآن في مصفوفة الجوار
+
+228
+00:20:25,270 --> 00:20:30,150
+هي عبارة عن مصفوفة مربعةماذا يعني مربعة؟ 1000xN
+
+229
+00:20:30,150 --> 00:20:35,690
+عدد الصفوف فيها يساوي عدد الأعمدة يساوي عدد النقاط
+
+230
+00:20:35,690 --> 00:20:41,350
+اللي موجودة في الرسمة يعني
+
+231
+00:20:41,350 --> 00:20:49,010
+لو أنا إجيت وقلت والله هذه الرسمة اللي عندي A
+
+232
+00:20:49,010 --> 00:20:58,570
+,B,C وبدي أمثلها حوال أعمى المصفوفة كم حجبها؟تلاتة
+
+233
+00:20:58,570 --> 00:21:03,730
+في تلاتة تلاتة في تلاتة ليش تلاتة؟ لأن عدد النقاط
+
+234
+00:21:03,730 --> 00:21:07,110
+اللي موجودة عندي تلاتة و أهم شغلة في التمثيل يا
+
+235
+00:21:07,110 --> 00:21:11,390
+شباب تنتبه للكلام اللي انا بدي أقوله تلت أعمدة
+
+236
+00:21:11,390 --> 00:21:16,070
+هيمثل تلت نقاط و تلت صفوف كذلك هيمثل تلت نقاط انا
+
+237
+00:21:16,070 --> 00:21:24,170
+الآن الصف الأول A D C الأعمدة الصفوف هياخد نفس
+
+238
+00:21:24,170 --> 00:21:26,650
+الترتيب اللي عملته فوق
+
+239
+00:21:45,010 --> 00:21:50,890
+الترتيب اللي انا اعتمده هو نفسه يعتمد على الصفوف
+
+240
+00:21:51,910 --> 00:21:54,930
+بنفعش كل واحد اشتغل فيه ترتيب .. عفوا .. بنفعش
+
+241
+00:21:54,930 --> 00:21:58,810
+استخدم كل ترتيب مختلف مع كل الصفوف .. من كل الصفوف
+
+242
+00:21:58,810 --> 00:22:03,530
+والأعمدة تمام هذا رقم واحد الآن اتنين ايه بتروح
+
+243
+00:22:03,530 --> 00:22:08,290
+تساوي؟ ايش ال values اللي موجودة؟ على ال basic
+
+244
+00:22:08,290 --> 00:22:12,730
+graph بتكلم على binary value يا صفر يا واحد يعني
+
+245
+00:22:12,730 --> 00:22:20,390
+مافي مسار او مافيش من C ل C؟ Zero بمثلها ب Zero من
+
+246
+00:22:20,390 --> 00:22:21,390
+C ل D؟
+
+247
+00:22:28,610 --> 00:22:35,410
+من B ل B صفر
+
+248
+00:22:35,410 --> 00:22:47,070
+من B ل A واحد من A ل C Zero من A ل B واحد و من A ل
+
+249
+00:22:47,070 --> 00:22:54,030
+C Zeroهذه المصفوفة بنسميها مصفوفة الجوار اللى تمثل
+
+250
+00:22:54,030 --> 00:22:57,810
+ال graph البسيط اللى عندناها تمثل ال graph البسيط
+
+251
+00:22:57,810 --> 00:22:59,010
+اللى عندناها
+
+252
+00:23:01,170 --> 00:23:05,610
+الـ Graph هذا أنا بقدر أصل من خلاله أو أتعرف هل في
+
+253
+00:23:05,610 --> 00:23:08,530
+connection ولا مافيش لو أنا إجيت إنسان اللي قلت
+
+254
+00:23:08,530 --> 00:23:12,490
+الرسم هنا و إجيت سألت هل في طريق ما بين النقطة A
+
+255
+00:23:12,490 --> 00:23:16,770
+واحد من A ل C باجي مباشرة و أين الصف اللي في A؟
+
+256
+00:23:16,770 --> 00:23:21,350
+هايه و أين ال C؟ هايها Zero يعني مافيش طريق، مافيش
+
+257
+00:23:21,350 --> 00:23:28,810
+جسر طيب، من B ل A؟ هاي B وهي ال A، واحد، فيه
+
+258
+00:23:29,930 --> 00:23:33,870
+وبالتالي هذه المصحوفة هي اللي مثلت ال graph أي
+
+259
+00:23:33,870 --> 00:23:36,870
+ماوجد عندها لو انا بدي اكبر ال graph كمان شوية
+
+260
+00:23:36,870 --> 00:23:42,530
+خليه أصعب
+
+261
+00:23:42,530 --> 00:23:46,010
+ABCD
+
+262
+00:23:59,600 --> 00:24:14,360
+المصفوف اللى هستخدمه ايه اربع فاربع ABCD
+
+263
+00:24:14,360 --> 00:24:18,120
+ABCD
+
+264
+00:24:18,120 --> 00:24:21,660
+انت حروف زى ما قلنا فى الترتيب لكن الترتيب اللى
+
+265
+00:24:21,660 --> 00:24:27,060
+بتعتمده فى الصفوف هو نفسه بتعتمده مع الأعمدة من A
+
+266
+00:24:27,060 --> 00:24:37,410
+ل A0 من A ل B؟ واحد A ل C؟ صفر A ل D؟ واحد B ل A؟
+
+267
+00:24:37,410 --> 00:24:48,430
+واحد صفر ل C؟ واحد ل D واحد من C ل A؟ صفرمن C ل B،
+
+268
+00:24:48,430 --> 00:24:53,330
+واحد، من C ل C، صفر، ومن C ل D، واحد، من D ل A،
+
+269
+00:24:53,330 --> 00:25:01,850
+واحد، من D ل B، واحد، من D ل C، واحد، وصفر، من D ل
+
+270
+00:25:01,850 --> 00:25:06,730
+D، صفر. الآن يا شباب، في عندنا ملاحظة مهمة جدا في
+
+271
+00:25:06,730 --> 00:25:11,030
+موضوع الـ Graph عاصر القطر الرئيسي، Zero
+
+272
+00:25:16,100 --> 00:25:20,400
+بس اصبر شوية .. اصبر شوية .. لما انا بتكلم على
+
+273
+00:25:20,400 --> 00:25:26,980
+simple graph عناصر القطر الرئيسي صفر، ليش؟ لأن
+
+274
+00:25:26,980 --> 00:25:30,680
+مافيش loop، مافيش .. عندي loop، مصبوط، لو فيه
+
+275
+00:25:30,680 --> 00:25:33,740
+دائرة، بصير .. سمناها ب zero graph احنا، مصبوط ولا
+
+276
+00:25:33,740 --> 00:25:38,020
+لا؟ ال basic graph مافيش عناصر المصحوفة فيه أو
+
+277
+00:25:38,020 --> 00:25:43,580
+عناصر القطر الرئيسي فيه صفرهذه واحد اتنين المصحوفة
+
+278
+00:25:43,580 --> 00:25:48,080
+لل basic graph متطابقة شو يعني متمثل او متطابقة لو
+
+279
+00:25:48,080 --> 00:25:55,280
+أخدت المثلثين هيك و قبلتهم على بعض فيها aij تساوي
+
+280
+00:25:55,280 --> 00:26:05,840
+aji الواحد
+
+281
+00:26:05,840 --> 00:26:17,050
+اتنين تساوي اتنين واحدE12 هي تساوي E21 E32 هي
+
+282
+00:26:17,050 --> 00:26:25,730
+تساوي E23 هي متماثلة بنسميها symmetric matrix
+
+283
+00:26:35,110 --> 00:26:40,150
+هذا نفس الكلام الموجود عندي هنا لانه basic graph
+
+284
+00:26:40,150 --> 00:26:44,650
+إذا ال graph اللي عندي هذا صار بيسيدو graph إيش
+
+285
+00:26:44,650 --> 00:26:50,470
+يعني بيسيدو graph؟ يعني صار في عندي loop أو
+
+286
+00:26:50,470 --> 00:26:55,030
+multiple edge ال
+
+287
+00:26:55,030 --> 00:27:02,530
+بيسيدو graph يعني إما في عندي loop أو multipleماذا
+
+288
+00:27:02,530 --> 00:27:06,670
+يعني؟ ايش اللي بيغير في الرسمة أو في المصفوفة؟
+
+289
+00:27:06,670 --> 00:27:14,690
+هتبطل 01، هتبطل 01، تمام؟ هتصير من الـD لـC 2، وين
+
+290
+00:27:14,690 --> 00:27:23,360
+DC؟ هذي C و دي D، هتصير 2ومن C ومن D لـ C برضه
+
+291
+00:27:23,360 --> 00:27:27,560
+اتنين هتبقى المصفوفة متماتلة ومش بس هيك هتصير
+
+292
+00:27:27,560 --> 00:27:31,680
+عناصر القكر الرئيسي بطل صفر لإن أصار في عندك يسر
+
+293
+00:27:31,680 --> 00:27:38,260
+من D لB أصارت في عندك واحد وبهيك صرت أنا بقدر أقول
+
+294
+00:27:38,260 --> 00:27:43,860
+كتالة إذا أنا شفت عناصر القكر الرئيسي لا تساوي صفر
+
+295
+00:27:44,630 --> 00:27:48,150
+أو واحد من عناصر قطر الرئيسي لا تساوي صفر ما يعتبر
+
+296
+00:27:48,150 --> 00:27:51,310
+ان عندي Loop في عندي Loop Edge موجود في الرسمة
+
+297
+00:27:51,310 --> 00:27:57,250
+طبعا؟ طيب، وإذا شوفت عناصر أكتر من واحد أو أكبر من
+
+298
+00:27:57,250 --> 00:28:00,230
+واحد في Value ما يعتبر أن عندي Multiple Edge موجود
+
+299
+00:28:00,230 --> 00:28:03,490
+وين؟ بالرسم ما يعتبر أن عندي Multiple Edge موجود
+
+300
+00:28:03,490 --> 00:28:08,350
+في الرسم الآن، بما أن أنا اتكلمت على Undirected
+
+301
+00:28:08,350 --> 00:28:11,990
+Graph بدي أعمل representation بنفس الكيفية، بس إيش
+
+302
+00:28:11,990 --> 00:28:17,400
+الفرق؟إنها مش هتكون Symmetric الآن في ال Directed
+
+303
+00:28:17,400 --> 00:28:32,020
+Graph لو أنا ادويت لك همين ال Graph هان Directed
+
+304
+00:28:32,020 --> 00:28:40,240
+Graph يعني الشباب بمشي مع مين؟ مع ال Sam A,
+
+305
+00:28:40,280 --> 00:28:52,870
+B, C, Dوانا بدي امثل المصفوفة الآن هي المصفوفة a b
+
+306
+00:28:52,870 --> 00:29:00,630
+c d a b c d هتختلف
+
+307
+00:29:00,630 --> 00:29:05,090
+تماما عن المصفوفة اللي هان هتبقى symmetric لان انا
+
+308
+00:29:05,090 --> 00:29:09,010
+بدي امشي من وين يا حسن السهل لان في الرسم هان من a
+
+309
+00:29:09,010 --> 00:29:19,690
+ل a صفر من a ل bمافيش ايه صفر من a ل c واحد ومن a
+
+310
+00:29:19,690 --> 00:29:29,430
+ل d واحد من b ل a واحد من b ل b صفر من b ل c صفر
+
+311
+00:29:29,430 --> 00:29:41,010
+من b ل d صفر من c ل a صفر من
+
+312
+00:29:41,010 --> 00:29:49,220
+c ل bو احد من C ل C صفر من C ل D واحد من D ل A صفر
+
+313
+00:29:49,220 --> 00:29:56,300
+من D ل D صفر من D ل C صفر من D ل D صفر و لو أطلعنا
+
+314
+00:29:56,300 --> 00:30:02,180
+في عناصر القطر الرئيسي أصفر ليس فيها مشكلة لأنها
+
+315
+00:30:02,180 --> 00:30:07,040
+basic graph لكنها ليست symmetric هي ال value هذه
+
+316
+00:30:09,490 --> 00:30:16,910
+هذه A1 أربعة وهذه A4 واحد يعني لو
+
+317
+00:30:16,910 --> 00:30:20,910
+أنا شُفت ال graph أو شُفت المصفوفة بصير أقدر أحدد
+
+318
+00:30:20,910 --> 00:30:24,510
+شو أبقى بيعت ال graph هل هو precedo graph ولا
+
+319
+00:30:24,510 --> 00:30:29,150
+direct graph ومش بس هيك بقدر أرسمه بغض النظر إيش
+
+320
+00:30:29,150 --> 00:30:33,870
+كان بقدر أرسم ال graph بغض النظر إيش كان مابيجي و
+
+321
+00:30:33,870 --> 00:30:40,700
+أقولك هاي عندك أربع لقات أربع لقاتوهذه العلاقات
+
+322
+00:30:40,700 --> 00:30:44,680
+الموجودة بينهم يعني هل يوجد جسر او جسرين؟ هل يوجد
+
+323
+00:30:44,680 --> 00:30:48,320
+لوب او لا لوب؟ هل باتجاه واحد او باتجاهين؟
+
+324
+00:30:48,320 --> 00:30:51,760
+وبالتالي تستطيع ترسم من كرسمة تبعك وهكذا يحصل في
+
+325
+00:30:51,760 --> 00:30:54,600
+برانج الخرايق اللي يحصل على الجوالات وعلى اللابتوب
+
+326
+00:30:54,600 --> 00:31:00,490
+كل هكذا يحصلهي تمثل المنطقة مجموعا من مين؟ مجموعا
+
+327
+00:31:00,490 --> 00:31:05,130
+من النقاط و الطرق المعرفة بينهم هي بتمثل الجسور و
+
+328
+00:31:05,130 --> 00:31:08,490
+كل ما بتتحرك السيارة أو ال mobile عفوا و بحدد
+
+329
+00:31:08,490 --> 00:31:11,310
+الموبايل الجديد بال GPS شو روح بساوي؟ بروح بعمل
+
+330
+00:31:11,310 --> 00:31:15,610
+shift للنقاط يعني دايما بعمل زيوبة الخريطة أو بزغر
+
+331
+00:31:15,610 --> 00:31:19,730
+المصفوفة عشان تتمثل حسب العرض أو حجم العرض اللي
+
+332
+00:31:19,730 --> 00:31:24,270
+موجود عندك anyway في الآخر المصفوفة دي بتمثل إيش؟
+
+333
+00:31:24,530 --> 00:31:30,290
+بتمثل Graph بشكل صحيح ومناسب ومناسب جدا في أي سؤال
+
+334
+00:31:30,290 --> 00:31:33,430
+يا شباب في تعريف المصفوف هنا؟ سواء كانت Directly
+
+335
+00:31:33,430 --> 00:31:37,730
+Graph او لا؟
+
+336
+00:31:37,730 --> 00:31:44,470
+okay
+
+337
+00:31:44,470 --> 00:31:50,530
+بدنا نروح ننتقل لموضوع shortest path في shortest
+
+338
+00:31:50,530 --> 00:31:56,340
+pathأنا من أهم التطبيقات تبع ال graphs اللي هي
+
+339
+00:31:56,340 --> 00:32:00,380
+الوصول بين ال two points بأقصر الطرق الوصول ال two
+
+340
+00:32:00,380 --> 00:32:05,460
+points أو المسافة بين ال two points بأقصر الطرق طب
+
+341
+00:32:05,460 --> 00:32:09,580
+احنا سابقا في كل graphs ماكانش في عيننا شغل تدلل
+
+342
+00:32:09,580 --> 00:32:15,650
+عليهالـ Cost التكلفة لكي نتكلم عن القصر لاحظ بجينا
+
+343
+00:32:15,650 --> 00:32:19,210
+نكتب الخط أو نرسم الخط بدون ولا حاجة اللي هيتغير
+
+344
+00:32:19,210 --> 00:32:23,350
+عندي في ال graph لما أتكلم عن ال shortest path بدو
+
+345
+00:32:23,350 --> 00:32:28,350
+يصير كل خط مربوط ومحسوب عليه التكلفة تبعته كل خط
+
+346
+00:32:28,350 --> 00:32:32,990
+بدو ينحسب عليه التكلفة تبعته السؤال اللي يبرح نفسه
+
+347
+00:32:32,990 --> 00:32:38,570
+هل التكلفة تكلفة نقدية؟ لأ مش ضروري ممكن التكلفة
+
+348
+00:32:38,570 --> 00:32:44,360
+كل وقت؟تمام؟ مسافة .. جعد .. أي تكلفة بدها تكون ..
+
+349
+00:32:44,360 --> 00:32:47,580
+أنا ما بعني لشو وحدة التكلفة اللي موجودة .. بس في
+
+350
+00:32:47,580 --> 00:32:52,160
+الآخر الرقم اللي بيكتب فوق الجسر هو مقدار التكلفة
+
+351
+00:32:52,160 --> 00:32:55,560
+.. بليونة المتعرف عليها .. لإن أنا ممكن أقل 650
+
+352
+00:32:55,560 --> 00:33:00,440
+شكل .. مثلا .. تكلفة السفر من غزة لرمالة .. بينما
+
+353
+00:33:00,440 --> 00:33:05,230
+القصة كلفتها 700 شكل .. مثلا ..ممكن تقول انك بتاخد
+
+354
+00:33:05,230 --> 00:33:16,570
+650 مل بنزين او سولار مثلا بتاخد 650 دقيقة حسب فكل
+
+355
+00:33:16,570 --> 00:33:21,510
+unit بتفرق لكن في شغل مش كاركة انا هان لما بتكلم
+
+356
+00:33:21,510 --> 00:33:27,570
+على ال shortest pathبتكلم على مسار بأقل تكلفة ..
+
+357
+00:33:27,570 --> 00:33:32,690
+بأقل تكلفة .. أقل value مرسوم على مين؟ على الخط
+
+358
+00:33:32,690 --> 00:33:36,430
+اللي موجود عندهان، تمام؟ ماليش دخل بإيش اليونيت،
+
+359
+00:33:36,430 --> 00:33:38,650
+أقل تكلفة ممكنة
+
+360
+00:33:40,900 --> 00:33:45,060
+من أهم الـ Algorithms اللي تستخدم في موضوع
+
+361
+00:33:45,060 --> 00:33:48,160
+shortest path و أبسطها اللي هو الـ Dijkstra
+
+362
+00:33:48,160 --> 00:33:51,200
+Algorithm
+
+363
+00:33:51,200 --> 00:33:55,600
+فالـ graph زي هذا .. هلاقيته عشان أوضح لك الصورة،
+
+364
+00:33:55,600 --> 00:34:00,100
+الآن أنا بدي أتحرك ما بين نقمتين، بنفعش أقول أنا
+
+365
+00:34:00,100 --> 00:34:04,160
+والله مش عارف ال target تبعتي، لأن إذا أنا ماعرفتش
+
+366
+00:34:04,160 --> 00:34:07,950
+ال targetمش هقدر أروح ما بدر أروح، مش هقدر أرسم
+
+367
+00:34:07,950 --> 00:34:12,310
+المسار اللي أنا بدياه، كذلك على الرسم السابق هنا،
+
+368
+00:34:12,310 --> 00:34:15,850
+لما أنا بدي أقول بدي أروح من غزة لقدس، إيش
+
+369
+00:34:15,850 --> 00:34:20,910
+المسارات اللي يجب أن تدخل في المقارنة؟ الطريق
+
+370
+00:34:20,910 --> 00:34:25,570
+المباشر أو الطريق أبو المرور بالخليل؟ بنفعش أقول
+
+371
+00:34:25,570 --> 00:34:28,190
+بدي أروح على ماما و بعدين بدي أروح على قدس، لأنه
+
+372
+00:34:28,190 --> 00:34:33,190
+حسب المادة اللي عندي هنا، مافيش طريقتمام؟ وبالتالي
+
+373
+00:34:33,190 --> 00:34:38,150
+اختيار ال shortest path بيكون تبع ليش هل المسار
+
+374
+00:34:38,150 --> 00:34:42,290
+موجود في الأول من ال start point ل ال end point و
+
+375
+00:34:42,290 --> 00:34:46,270
+بعدين ببدأ اقارن ايش التكلفة تعالى نشوف الرسم هاي
+
+376
+00:34:46,270 --> 00:34:48,930
+اللي عندي ايش في الرسم هاي اللي بيقول ايه؟ بيقول
+
+377
+00:34:48,930 --> 00:34:54,190
+حسبلي او هات ال shortest path عشان اجيب ما بين او
+
+378
+00:34:54,190 --> 00:34:58,570
+اقفل ال vertex ايه؟ يعني هذا ال target تبعتي from
+
+379
+00:34:58,570 --> 00:35:09,890
+the vertexيعني هو بدى يتحرك من ال A لل E يعني
+
+380
+00:35:09,890 --> 00:35:20,210
+هان نقطة البداية و بدى يجي من اين؟ بدى يجي هن اذا
+
+381
+00:35:20,210 --> 00:35:29,490
+استيقظ من هنا 100% الان كان مسار موجود كتير abdfe
+
+382
+00:35:30,180 --> 00:35:48,220
+A B D A A B D C A مظبوط؟ A B C A A C B D F A A C B
+
+383
+00:35:48,220 --> 00:35:55,240
+D A A لحظة شوية A C مافيش خلاص ال B خلصت مانفعش
+
+384
+00:35:55,240 --> 00:35:59,070
+اضحك دي كمان مرة مظبوط؟الان ايه لان اذا روحت على
+
+385
+00:35:59,070 --> 00:36:06,090
+دي كلمة مرة هتبرجحها هتبقى بالباب بصبع ايه ايه ايه
+
+386
+00:36:06,090 --> 00:36:08,510
+ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه
+
+387
+00:36:08,510 --> 00:36:10,510
+ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه
+
+388
+00:36:10,510 --> 00:36:10,530
+ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه
+
+389
+00:36:10,530 --> 00:36:12,090
+ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه
+
+390
+00:36:12,090 --> 00:36:16,130
+ايه ايه ايه ايه ايه ايه ايه ايه ايه
+
+391
+00:36:16,130 --> 00:36:20,250
+ايه
+
+392
+00:36:20,250 --> 00:36:23,010
+ايه
+
+393
+00:36:23,340 --> 00:36:26,900
+بتروح تحسب التكلفة، من وين؟ على سبيل المثال،
+
+394
+00:36:26,900 --> 00:36:31,620
+التكلفة تبقى في المسار الأول A,B,D,F,E جداش
+
+395
+00:36:31,620 --> 00:36:38,240
+تكلفتها؟ أربعة، تسعة، خلصتاش، تلت ماشي المسار اللي
+
+396
+00:36:38,240 --> 00:36:48,860
+بعده، على سبيل المثال A,C,E ماشي تمام؟ بينما A,C,D
+
+397
+00:36:48,860 --> 00:36:50,980
+,E,D,E
+
+398
+00:36:53,730 --> 00:37:00,750
+تلاتة .. تمانية .. عشرة .. اه بيخدّيبهم كلهم طبعا
+
+399
+00:37:00,750 --> 00:37:04,610
+الميزة ان هو هذا الكلام مش انت اللي بتعمله هذا ال
+
+400
+00:37:04,610 --> 00:37:08,070
+algorithm هو ايش اللي بيساوي فيه بمر على المصفوفة
+
+401
+00:37:08,070 --> 00:37:13,010
+ال adjacent matrix الان لو انا بدي اعمل مصفوفة
+
+402
+00:37:13,010 --> 00:37:17,950
+الجواهر ليه ليش حاجة لها .. لل graph هذا .. ستة في
+
+403
+00:37:17,950 --> 00:37:23,030
+ستةستة و ستة، تمام؟ وش بقى ال C بتساوي؟ بتقول
+
+404
+00:37:23,030 --> 00:37:29,050
+والله الآن من A ل B و من A ل C، مع الخيارات
+
+405
+00:37:29,050 --> 00:37:33,590
+الوصولي لل E مافيش عندي خط مباشر، في عندي خط مع
+
+406
+00:37:33,590 --> 00:37:39,090
+مين؟ مع ال B و مع ال C، بروح بعد هيك، بشوف ال C
+
+407
+00:37:39,090 --> 00:37:44,740
+وين بتوديني؟وبشوف ال B وين بتوديني وبنقل بمشي مع
+
+408
+00:37:44,740 --> 00:37:47,280
+المساعد اللي موجود عندي هنا فده عشان ايه اسمه
+
+409
+00:37:47,280 --> 00:37:50,740
+algorithm هو عبارة عن اللي بفحص هالطريق موجود او
+
+410
+00:37:50,740 --> 00:37:56,060
+لا و بكمل لكن هذا هو فكرة ال algorithm هذه فكرة ال
+
+411
+00:37:56,060 --> 00:38:02,020
+algorithm بعد ما انت بتذكر المساعد تمام؟ ايش بروح
+
+412
+00:38:02,020 --> 00:38:08,280
+بنساوي؟ بنحسب التكلف على كل واحد فيه كمان مرة A,B
+
+413
+00:38:08,280 --> 00:38:15,850
+,D,F,E جدش قولنا A,B؟أربعة PD خمسة هي تسعة DF ستة
+
+414
+00:38:15,850 --> 00:38:24,830
+هي خمستاشر وتلاتة تمانتاشر بينما ACE جدش تكلفتها
+
+415
+00:38:24,830 --> 00:38:34,810
+هنا تين وهنا عشرة معاشر قلنا ACE BDE
+
+416
+00:38:40,680 --> 00:38:47,620
+وبالتالي انا ال shortest ده التبعي هيو تمام؟ بناء
+
+417
+00:38:47,620 --> 00:38:52,320
+على إيش؟ بناء على التكلفة اللي موجودة على الخريطة
+
+418
+00:38:52,320 --> 00:38:57,280
+بقدرش أخترع من عندي أرقام أنا تمام؟ وإذا بتتذكر من
+
+419
+00:38:57,280 --> 00:39:01,960
+البداية قلتلك طول الجسم مابثرش معايا رسمته بين
+
+420
+00:39:01,960 --> 00:39:06,760
+مقطينها الجد و لا رسمته هيك مابفرجش كتير معايا
+
+421
+00:39:06,760 --> 00:39:11,330
+اللي بتفرج معايا إيش هي ال value اللي بيتمثلالجراف
+
+422
+00:39:11,330 --> 00:39:16,190
+عشان هيك يا شباب هانش بروح بنساوي احنا بنمثل
+
+423
+00:39:16,190 --> 00:39:23,210
+الجراف هذا ك connection كجراف بنحطه في مصفوفة بدأ
+
+424
+00:39:23,210 --> 00:39:29,910
+أعمل تخيل فقط بس المربع هذا عشان أوريك شغلة بسيطة
+
+425
+00:39:29,910 --> 00:39:34,450
+و ننهي من النقوة هاي الآن بدأ امثل الجراف هذا 4x4
+
+426
+00:39:34,450 --> 00:39:34,970
+مصبوط
+
+427
+00:39:40,000 --> 00:39:49,480
+ب و سي و دي و ايه ب سي دي ايه ب ب ب ب ب ب ب ب ب ب
+
+428
+00:39:49,480 --> 00:39:53,960
+ب ب ب ب
+
+429
+00:39:53,960 --> 00:39:55,340
+ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب
+
+430
+00:39:55,340 --> 00:40:00,120
+ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب
+
+431
+00:40:00,120 --> 00:40:01,140
+ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب
+
+432
+00:40:01,140 --> 00:40:02,260
+ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب
+
+433
+00:40:02,260 --> 00:40:09,280
+ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب
+
+434
+00:40:09,280 --> 00:40:23,870
+ب ب بواحد صفر واحد الاخيرة صفر واحد واحد صفر بخرب
+
+435
+00:40:23,870 --> 00:40:27,430
+12 اللي
+
+436
+00:40:27,430 --> 00:40:30,430
+وراك مش مشكلة انت عارف ايش كنت لما انت كنت بتقول
+
+437
+00:40:30,430 --> 00:40:33,490
+كده الأرقام انا ماكنتش معاك كنت بطلع في الرقم بسمع
+
+438
+00:40:33,490 --> 00:40:37,450
+الرقم اللي انت بتقولهوبأتمنى على وين؟ على الرقم
+
+439
+00:40:37,450 --> 00:40:40,390
+المقابل اللي أنا بكتبه لإنه Symmetric Basic Graph
+
+440
+00:40:40,390 --> 00:40:45,130
+يعني Symmetric أصبت؟ تمام هاد احنا كنا بنسميها ال
+
+441
+00:40:45,130 --> 00:40:51,010
+Graph هاد الرسم فالمقابل كان في عندي مصفوفة تانية
+
+442
+00:40:51,010 --> 00:40:57,210
+بتنعمل اسمها ال Cost إيش المصفوفة؟ اللي هي التكلفة
+
+443
+00:40:57,210 --> 00:41:03,790
+بتحدد التكلفة وبنفس الترتيب اللي موجود هنا B C D E
+
+444
+00:41:03,790 --> 00:41:14,170
+BC D E الان هتكون undirected بغض النظر .. بغض
+
+445
+00:41:14,170 --> 00:41:17,290
+النظر عشان امثل ال graph كله كيف اجيب ال shortest
+
+446
+00:41:17,290 --> 00:41:21,930
+path لازم يكون ال graph عندى بمصفوفة و ال course
+
+447
+00:41:21,930 --> 00:41:27,210
+تبعته في مصفوفة عشان كل مسار انا برسمه اروح بدرحسم
+
+448
+00:41:27,210 --> 00:41:32,730
+ال course تبعتهو لما أكون دارحت نفس الفكرة أنه
+
+449
+00:41:32,730 --> 00:41:36,570
+مصفوفيان و مصفوفان التلتيان لازم تكون موجودات الان
+
+450
+00:41:36,570 --> 00:41:45,810
+B ل C واحد واحد B ل D خمسة B ل E صفر مافيش لانه
+
+451
+00:41:45,810 --> 00:41:51,670
+طريق الان B ل C من C ل B واحد من C ل C صفر من
+
+452
+00:41:51,670 --> 00:41:55,390
+الوينكي بتاوة واحدة هيها ال cost هيها تمام من C ل
+
+453
+00:41:55,390 --> 00:41:57,950
+D تمانية
+
+454
+00:42:00,230 --> 00:42:08,490
+ومن C إلى E؟ عشرة من D إلى B؟ خمسة، هذا التباخل من
+
+455
+00:42:08,490 --> 00:42:20,230
+D إلى C؟ تمانية صفر ومن D إلى E؟ اتنين الآن،
+
+456
+00:42:20,230 --> 00:42:27,810
+كمل، صفر، خمسة، واحد، صفر
+
+457
+00:42:32,390 --> 00:42:37,230
+هذه غلط كيف غلط هذه صفر أكيد هذه لازم تكون اتنين
+
+458
+00:42:37,230 --> 00:42:46,850
+هذه عشرة وهذه صفر لأن
+
+459
+00:42:46,850 --> 00:42:51,630
+المفروض هذا الصف هي اتنين عشرة صفر هي التماثل اللي
+
+460
+00:42:51,630 --> 00:42:55,190
+موجود عندها إذا ما الصفتين هدول موجودات سبت كل
+
+461
+00:42:55,190 --> 00:43:00,040
+بصحبة بقول هل في طريق وقدش تكلفتهبصير تبدأ عملياش
+
+462
+00:43:00,040 --> 00:43:05,480
+تراكمية من أجل الوصول على العناصر اللي موجودة
+
+463
+00:43:05,480 --> 00:43:10,340
+عندنا في
+
+464
+00:43:10,340 --> 00:43:14,620
+أن المصطلح الشجرة
+
+465
+00:43:14,620 --> 00:43:19,520
+ال tree هي عبارة عن special graph هي عبارة عن
+
+466
+00:43:19,520 --> 00:43:24,960
+special graph الشبكة ده كلها مصطلحات
+
+467
+00:43:29,870 --> 00:43:33,530
+Connected يعني كل النقاب اللي فيه متصلة، مافيش فيه
+
+468
+00:43:33,530 --> 00:43:38,350
+isolated point و إلا هتكونش three Undirected مافيش
+
+469
+00:43:38,350 --> 00:43:45,430
+أسهم، graph contains no circuits مافيش أي شغلة
+
+470
+00:43:45,430 --> 00:43:48,490
+مسكرة دايما كلاش مسارات مفتوحة، كل المسارات اللي
+
+471
+00:43:48,490 --> 00:43:50,210
+فيها مفتوحة
+
+472
+00:43:57,380 --> 00:44:00,280
+مافيش circuit ولا cycles؟ ماخلاص مافيش circuit
+
+473
+00:44:00,280 --> 00:44:03,920
+يعني مافيش closed walk مافيش closed trail، كلها
+
+474
+00:44:03,920 --> 00:44:07,280
+بيعتسم، لأن هذا الرسم، simple graph، simple graph،
+
+475
+00:44:07,280 --> 00:44:11,360
+simple graph، أي واحد فيهم بيمثل ال tree، كلنا
+
+476
+00:44:11,360 --> 00:44:15,020
+بنتكلم على ال tree وقلنا هذه كل حياتها بتمثل ال
+
+477
+00:44:15,020 --> 00:44:18,640
+trees، فكرة ال tree connected .. simple connected
+
+478
+00:44:18,640 --> 00:44:19,200
+graph
+
+479
+00:44:29,930 --> 00:44:33,650
+مفهوم ال circuit أن نقطة البداية تصير نقطة نهاية
+
+480
+00:44:33,650 --> 00:44:42,150
+وبالتالي لو انت طلعت بين أي نقطتين هتلاقي في عندك
+
+481
+00:44:42,150 --> 00:44:46,250
+مسار واحد فقطبالأي نقطين عشان تصللهم بما أنه مافيش
+
+482
+00:44:46,250 --> 00:44:49,410
+cross أو مافيش تقاطع بما أنك تتكلم أنك دائما في
+
+483
+00:44:49,410 --> 00:44:53,610
+مسار واحد بالنقطين لو أنت هنا وبالنكسة اللي هنا
+
+484
+00:44:53,610 --> 00:45:01,210
+مستحيل اللي غير تمر بالمسار هذا وفيه مش غيره تمام؟
+
+485
+00:45:01,210 --> 00:45:06,530
+وبذلك صارت في عندي أنا بتكلم على ال tree الآن بشكل
+
+486
+00:45:06,530 --> 00:45:11,800
+عام بقى ال treesاستخداماتها مهمة في الكمبيوتر
+
+487
+00:45:11,800 --> 00:45:15,960
+وبتشوف انت على سبيل المثال ال road folder تبع ال C
+
+488
+00:45:15,960 --> 00:45:19,940
+وD عندك على الجهاز storage هو بيمثل ال tree ال C
+
+489
+00:45:19,940 --> 00:45:23,660
+بتمثل ال road المجلدات اللي موجودة على ال C بتمثل
+
+490
+00:45:23,660 --> 00:45:27,040
+ال level الأول والميافات اللي موجودة تمثل ال
+
+491
+00:45:27,040 --> 00:45:29,560
+leaves اللي موجودة على ال level الأول بعد هيك
+
+492
+00:45:29,560 --> 00:45:35,870
+بتبدأ تتفرع بالشجرة اللي عندكلأن العروف في مصطلح
+
+493
+00:45:35,870 --> 00:45:40,370
+الـtrees لازم يكون فيها روت لأن مافيش شجرة طايرة
+
+494
+00:45:40,370 --> 00:45:45,430
+في الهوا ولا لا كل شجرة فيها جدر ثابت وواضح حتى
+
+495
+00:45:45,430 --> 00:45:50,310
+بالـ graph هذا الأمثل السابق هادول لو مافيش لازم
+
+496
+00:45:50,310 --> 00:45:54,550
+انت تختار واحد منهم يكون root أي واحد بينفع يكون
+
+497
+00:45:54,550 --> 00:45:59,770
+root ومع اختلاف ال root هتختلف شكل شجرة يعني لو
+
+498
+00:45:59,770 --> 00:46:03,860
+انا افترضت ان هذا هو ال root كمعهدهتصير الشجرة
+
+499
+00:46:03,860 --> 00:46:10,960
+هايها في عندي a و b are siblings اخوة هذا ليف و
+
+500
+00:46:10,960 --> 00:46:15,940
+هذا في عنده تفريحة لو انا اجيت اخدت هذه روت او
+
+501
+00:46:15,940 --> 00:46:20,760
+اخدت هذا روت هتختلف الشجرة لو اخدت هذا روت هتصير
+
+502
+00:46:20,760 --> 00:46:26,520
+في عنده تلت اولاد مظبوط three siblings و لو اخدت
+
+503
+00:46:26,520 --> 00:46:29,880
+هذا روت هتصير في عندها واحد فانت في الاخر في كل
+
+504
+00:46:29,880 --> 00:46:36,130
+three لازم يكون لهاRoot لازم يكون لها جذر هذه نفس
+
+505
+00:46:36,130 --> 00:46:41,530
+ال graph لكن ال root هنا A و ال root هنا B هاي ال
+
+506
+00:46:41,530 --> 00:46:51,970
+B لحظة ماخدتها root هاي شكل الشجرة اختلف تماما في
+
+507
+00:46:51,970 --> 00:46:57,810
+موضوع ال root انا بتكلم على parent و siblings
+
+508
+00:46:57,810 --> 00:47:02,560
+parent و siblingsالـ siblings اللي هم مين يا شباب؟
+
+509
+00:47:02,560 --> 00:47:08,480
+التفرعات اللي موجودة عندهم الآن ال بيرن تبعت ال a
+
+510
+00:47:08,480 --> 00:47:13,500
+بي ايه؟ و ال بيرن تبعت ال c ايه؟ معناته أنا باجي
+
+511
+00:47:13,500 --> 00:47:20,580
+بقول بي و سي are siblings .. siblings .. إخوة ..
+
+512
+00:47:20,580 --> 00:47:26,120
+تمام؟ ال بيرن تبعت ال e بي .. و ال بيرن تبعت ال d
+
+513
+00:47:26,120 --> 00:47:29,340
+بي .. معناته ال b و ال d .. ال d عفر و ال e
+
+514
+00:47:29,340 --> 00:47:29,660
+siblings
+
+515
+00:47:37,050 --> 00:47:40,650
+الان في عندى مصطلح الـ Leaf ال Leaf Leaf و
+
+516
+00:47:40,650 --> 00:47:46,610
+Internal Vertex في ال Leaf مين ال Leafs؟ C هي
+
+517
+00:47:46,610 --> 00:47:52,450
+النقطة اللى مافيش الا تفرعت بنسميها إيش؟ Leaf C E
+
+518
+00:47:52,450 --> 00:47:59,730
+و F C و E و F هدول إيش؟ Leafs أوراق الان دى إيه
+
+519
+00:47:59,730 --> 00:48:04,280
+بنسميها Internal Vertex أو Parent؟B Internal
+
+520
+00:48:04,280 --> 00:48:09,820
+Vertex او Parent لأن الـ B Parent للـ D والـ D
+
+521
+00:48:09,820 --> 00:48:16,700
+Parent للـ S Internal
+
+522
+00:48:16,700 --> 00:48:20,360
+يعني أن هناك اله بيرنت و هناك اله بيرنت و هناك اله
+
+523
+00:48:20,360 --> 00:48:20,520
+بيرنت و هناك اله بيرنت و هناك اله بيرنت و هناك اله
+
+524
+00:48:20,520 --> 00:48:21,820
+بيرنت و هناك اله بيرنت و هناك اله بيرنت و هناك اله
+
+525
+00:48:21,820 --> 00:48:25,560
+بيرنت و هناك اله بيرنت و هناك اله بيرنت و هناك اله
+
+526
+00:48:25,560 --> 00:48:26,960
+بيرنت و هناك اله بيرنت و هناك اله بيرنت و هناك اله
+
+527
+00:48:26,960 --> 00:48:29,940
+بيرنت و هناك اله بيرنت و هناك اله بيرنت و هناك اله
+
+528
+00:48:29,940 --> 00:48:34,250
+بيرنت و هناك اله بالان لما اتكلمنا عن ال sub graph
+
+529
+00:48:34,250 --> 00:48:37,890
+تتذكر ال sub graph هو عبارة عن جزء من ال graph ومع
+
+530
+00:48:37,890 --> 00:48:42,290
+ان ال tree هي graph فبقدر اتكلم على sub tree sub
+
+531
+00:48:42,290 --> 00:48:49,530
+tree هي شجرة فرعية يعني ال sub graph او ال sub
+
+532
+00:48:49,530 --> 00:48:53,910
+tree هي عبارة عن sub graph من ال treeهي ال بي هذا
+
+533
+00:48:53,910 --> 00:48:57,670
+هي أخدت الجزء هذا لوحده و لو أخدت الجزء هذا هيك
+
+534
+00:48:57,670 --> 00:49:00,790
+لحاله بمشي الحال و لو أخدت الجزء هذا هيك لحاله
+
+535
+00:49:00,790 --> 00:49:05,030
+بمشي الحال دائما لما اتكلمنا في ال sub graph قلنا
+
+536
+00:49:05,030 --> 00:49:08,030
+مجموعة ال vertices مجموعة جزئية من المجموعة
+
+537
+00:49:08,030 --> 00:49:11,690
+الأساسية و مجموعة الجسور مجموعة جزئية من مجموعة
+
+538
+00:49:11,690 --> 00:49:19,110
+الجسور الأساسية فهي اني مصطلح ال level اذا انا
+
+539
+00:49:19,110 --> 00:49:22,800
+أخدت ال AOC لحالة و قدر اقول عنها sub treeهو الـ
+
+540
+00:49:22,800 --> 00:49:26,240
+Subtree الـ A و الـ C لفهمك؟ اه اه لفهمك ايه الـ A
+
+541
+00:49:26,240 --> 00:49:29,480
+و الـ C الـ Subgraph و هو المشكلة في الموضوع ايه
+
+542
+00:49:29,480 --> 00:49:32,860
+الشرط بتاعنا ان ال vertices subset من ال vertices
+
+543
+00:49:32,860 --> 00:49:36,140
+ال A و ال C subset من المجموعة الكلية لنقاط و
+
+544
+00:49:36,140 --> 00:49:40,840
+الجسر اللي بينهم A و C subset من مجموعة الجسور
+
+545
+00:49:40,840 --> 00:49:46,670
+الكلية فهي Subtree الشرط عضو من نقاطك و نقاطكبس
+
+546
+00:49:46,670 --> 00:49:50,110
+عدد النقاب على الأقل بيكون تنتهي من التصلات لو انك
+
+547
+00:49:50,110 --> 00:49:55,630
+بتطبق بال letter A أصبت؟ أيوة فيه أن المصطلح ال
+
+548
+00:49:55,630 --> 00:49:59,510
+level المستوى ال road ده من ال level تبعته إيه؟
+
+549
+00:49:59,510 --> 00:50:03,410
+Zero و ال height أو ال depth تبعته ال letter E
+
+550
+00:50:03,410 --> 00:50:09,690
+بتمثل إيه؟ عدد الجسور ما بين ال road لحد آخر leaf
+
+551
+00:50:09,690 --> 00:50:15,110
+لحد أعمق leaf ال height ال A level zero B و C
+
+552
+00:50:15,110 --> 00:50:21,570
+level oneدى و ايه level 3 level 2 عفوا و اف level
+
+553
+00:50:21,570 --> 00:50:25,270
+3 جداش الـ depth جداش الخيط جداش ارتفاع الشجرة
+
+554
+00:50:25,270 --> 00:50:32,710
+واحد اتنين تلاتة تلات جسور بتقعد اطول الغموق موجود
+
+555
+00:50:32,710 --> 00:50:36,510
+عندك في الشجرة واحد اتنين تلاتة اللي هو ال maximum
+
+556
+00:50:36,510 --> 00:50:44,170
+level موجود عندك يعنى بال three هاي اتنين صفر واحد
+
+557
+00:50:46,030 --> 00:50:50,930
+مايغركاش يا شباب انه ممكن انا اروح اجسر الرسم هادى
+
+558
+00:50:50,930 --> 00:51:00,710
+واجيبك الافهام لو
+
+559
+00:51:00,710 --> 00:51:06,330
+انا جيت سألتك ايش ال level كبار ال F؟ بدك تعدى
+
+560
+00:51:06,330 --> 00:51:10,830
+الجسور اللى بينها و بين ال route تعدى الجسور لحد
+
+561
+00:51:10,830 --> 00:51:15,510
+ما تصل ال route و تصل ال level واحدتنين اوصلت ال
+
+562
+00:51:15,510 --> 00:51:19,370
+route ما هي تبدي في level؟ تنين لان level zero
+
+563
+00:51:19,370 --> 00:51:25,270
+level واحد level اتنين بقى لو طلت او جسرت مالهاش
+
+564
+00:51:25,270 --> 00:51:31,410
+علاقة مالهاش علاقة ليش؟
+
+565
+00:51:31,410 --> 00:51:35,390
+نفس الكلام ال level تبعت ال C هي عبارة عن عرب
+
+566
+00:51:35,390 --> 00:51:36,870
+الجسور اللي بناه هو بين ال route
+
+567
+00:51:43,130 --> 00:51:54,890
+أول الـ edge ما بين ال points مالوش شبهنا العمليات
+
+568
+00:51:54,890 --> 00:52:00,700
+الحسابية بتتمثل بـ treeوالمجلدات على ال operating
+
+569
+00:52:00,700 --> 00:52:04,980
+system زي الينيكس على الروت عندك ال C على ال
+
+570
+00:52:04,980 --> 00:52:09,300
+ويندوز ال user إلى آخره هذه المجلدات وهذه الموضوع
+
+571
+00:52:09,300 --> 00:52:15,960
+للعمليات الحسابية تمثل بتريس X زائد Y ضرب X not
+
+572
+00:52:15,960 --> 00:52:21,920
+plus Y X زائد Z عفوا من وين جبت هنا؟ لأن X أو Y و
+
+573
+00:52:21,920 --> 00:52:27,900
+Z ال بيرم تبعتهم من عملية الجمعالـ X والـ Y الـ
+
+574
+00:52:27,900 --> 00:52:33,640
+parent تبعتهم مارح والـ parent للعمليتين الضرب
+
+575
+00:52:33,640 --> 00:52:43,560
+فهذه عبارة عن X أو Y زائد Z مضغوبة في X ماقص Y هي
+
+576
+00:52:43,560 --> 00:52:47,000
+الأولويات اللي بتحكم في العملية أولويات العملية
+
+577
+00:52:47,000 --> 00:53:04,440
+الحسابية في ال trees في عند مصبلحم-اري
+
+578
+00:53:04,440 --> 00:53:17,180
+وممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممم
+
+579
+00:53:22,870 --> 00:53:27,690
+TWO CHILDREN لما أتكلم على ال تريري اتكلم على ترى
+
+580
+00:53:27,690 --> 00:53:32,590
+تمام فوريري معناه اتكلم على أربعة يونيري اتكلم على
+
+581
+00:53:32,590 --> 00:53:36,190
+واحد وهذه صارت single path عمروحاش بتصير شجرة بيش
+
+582
+00:53:36,190 --> 00:53:39,890
+تفرعات فالان اتكلم على باينري على تريري وها كان
+
+583
+00:53:39,890 --> 00:53:47,330
+حسب الحاجة لما أنا باجي بقول full binary tree full
+
+584
+00:53:47,330 --> 00:53:52,090
+binary tree ايش يعني يعني كل ال parents عندهم
+
+585
+00:53:52,090 --> 00:54:00,610
+اتنينمش توقف عندهم اتنين طيب
+
+586
+00:54:00,610 --> 00:54:10,990
+ماشي الحل من اهم التطبيقات اللى موجودة عندى اناالـ
+
+587
+00:54:10,990 --> 00:54:15,130
+binary tree من أهم التطبيقات اللي موجودة عندي أنا
+
+588
+00:54:15,130 --> 00:54:21,030
+في ال binary ال tree و بدي أشتغل معاك في استخدامات
+
+589
+00:54:21,030 --> 00:54:24,270
+ال binary ال tree قبل ما أروح بالمثال هذا بدي أروح
+
+590
+00:54:24,270 --> 00:54:29,670
+باتجاه مثال أبسط و هو أنا فيه عندي أرقام أو
+
+591
+00:54:29,670 --> 00:54:39,450
+sequence خمسة سبعة أربعة تلاتة ستة واحد
+
+592
+00:54:52,040 --> 00:54:57,040
+عادة باخد أول element يمثل الـ root
+
+593
+00:55:02,280 --> 00:55:08,780
+ثلائي يعني كحد أقصى كحد أقصى عند كل parent two
+
+594
+00:55:08,780 --> 00:55:17,180
+nodes تمام باجي بعد هيك الآن السابعة الآن إذا كانت
+
+595
+00:55:17,180 --> 00:55:20,840
+ال value أكبر من ال parent node بتروح بتضيفها على
+
+596
+00:55:20,840 --> 00:55:24,760
+يمينها على اليمين لو كانت أقل منها بتضيفها على
+
+597
+00:55:24,760 --> 00:55:29,600
+الشمال باجي السابعة أكبر حطها على اليمين هي
+
+598
+00:55:29,600 --> 00:55:35,340
+السابعةباجل الأربعة ببدأ أقارنها مع الخمسة أقل من
+
+599
+00:55:35,340 --> 00:55:42,240
+الخمسة هروح على الشمال أربعة باجل التلاتة تلاتة
+
+600
+00:55:42,240 --> 00:55:51,080
+على شمال الخمسة على شمال الأربعة باجل الستة أكبر
+
+601
+00:55:51,080 --> 00:55:54,160
+من الخمسة يعني على يمينها باجل السبعة أقل من
+
+602
+00:55:54,160 --> 00:55:56,360
+السبعة على شمال السبعة
+
+603
+00:56:01,190 --> 00:56:08,630
+هذه ستة واحد على شمال الخمسة شمال الأربعة شمال
+
+604
+00:56:08,630 --> 00:56:21,030
+التلاتة واحد اتنين شمال الخمسة شمال شمال يمين
+
+605
+00:56:21,030 --> 00:56:24,790
+الواحد الآن
+
+606
+00:56:24,790 --> 00:56:30,350
+تمانية يمين الخمسة يمين السبعة
+
+607
+00:56:37,540 --> 00:56:44,800
+وبهك تبني ال binary tree ببنائها الفكرة دائما ال
+
+608
+00:56:44,800 --> 00:56:49,440
+value الأكبر على اليمين الأصغر على الشمال واحد
+
+609
+00:56:49,440 --> 00:56:53,200
+يقول القيم المتساوية أو السادس مالهاش وجود على
+
+610
+00:56:53,200 --> 00:56:57,940
+يمين ايه؟ ممتاز انا بدأ اكملها تمانى أكبر من
+
+611
+00:56:57,940 --> 00:57:01,870
+السبعة بالخمسة ولا أصغرأكبر و روحت .. روحت على
+
+612
+00:57:01,870 --> 00:57:05,650
+يمين لجت فيه node عشان أقرر أروح على يمين أو يسار
+
+613
+00:57:05,650 --> 00:57:08,810
+السبعة أقرر السبعة أو التمانية تمانية أكبر من
+
+614
+00:57:08,810 --> 00:57:13,030
+السبعة أو الأقل أكبر مانعته بروح على يمين السبعة
+
+615
+00:57:13,030 --> 00:57:17,650
+فش node برسم لها node جديدة الآن لو بدي أجيب تسعة
+
+616
+00:57:21,250 --> 00:57:25,210
+ماذا سأفعل؟ خمسة التسعة أكبر من الخمسة على اليمين
+
+617
+00:57:25,210 --> 00:57:29,810
+أكبر من السبعة على اليمين أكبر من التمانية على
+
+618
+00:57:29,810 --> 00:57:36,270
+يمين التمانية بمثالي في الكتاب يقول إعمل binary
+
+619
+00:57:36,270 --> 00:57:44,010
+tree من ال text اللي موجود عندي string math
+
+620
+00:57:44,010 --> 00:57:52,870
+computer powerNorth zebra dentist book نفس الكلام
+
+621
+00:57:52,870 --> 00:57:55,550
+مش على عدد الحرف، على الحرف الأول، على ترتيب
+
+622
+00:57:55,550 --> 00:58:01,230
+الأبجادية، على الأبجادية أول واحد ال math هي ال
+
+623
+00:58:01,230 --> 00:58:07,230
+route ال math هي ال route اللي بعدها computer ال C
+
+624
+00:58:07,230 --> 00:58:12,730
+أصغر من ال M ولا أكبر؟ أصغر فهتيجي وين؟ هتيجي شمال
+
+625
+00:58:14,270 --> 00:58:22,070
+الأن power P أكبر من ال C على اليمين North أكبر من
+
+626
+00:58:22,070 --> 00:58:30,070
+ال M M N O M N O فبتيجي الأن وين أكبر هتروح على
+
+627
+00:58:30,070 --> 00:58:37,930
+يمين الماهة أقل من ال B بتيجي ع شمالها Z Zebra
+
+628
+00:58:37,930 --> 00:58:42,010
+أكبر من ال M أكبر من ال B على يمين ال power
+
+629
+00:58:46,810 --> 00:58:52,890
+D أصغر من ال M تيجي على اليسار أكبر من ال C تيجي
+
+630
+00:58:52,890 --> 00:59:00,550
+على يمينها أخر كلمة عندي بك ال B أصغر من ال M تيجي
+
+631
+00:59:00,550 --> 00:59:05,930
+على اليسار أصغر من ال C تيجي على الشمال full
+
+632
+00:59:05,930 --> 00:59:08,530
+binary tree
+
+633
+00:59:13,500 --> 00:59:17,360
+طبعا من أهم تطبيقات تبع ال binary tree يا شباب
+
+634
+00:59:17,360 --> 00:59:21,220
+اللي هو من تبع ال tree اللي هي ال binary tree او
+
+635
+00:59:21,220 --> 00:59:25,380
+ال search في ال search في البحث الان على المثال
+
+636
+00:59:25,380 --> 00:59:29,720
+اللي وصلناه سابقا لما حطيت الأرقام لو انا اجيت و
+
+637
+00:59:29,720 --> 00:59:34,180
+قلتلك تسعة موجود ولا مش موجود ايش هتروح تساوي تسعة
+
+638
+00:59:34,180 --> 00:59:37,520
+اكبر من خمسة بروح على اليامين اكبر من السبعة بروح
+
+639
+00:59:37,520 --> 00:59:42,590
+على اليامين اكبر من التمانيةبروح على اليمين، في
+
+640
+00:59:42,590 --> 00:59:47,390
+عناصر بقارنها، مافيش .. إذا في الإضافة بأضيفها،
+
+641
+00:59:47,390 --> 00:59:49,910
+لكن أنا بقولك التسعة موجودة ولا مش موجودة، أخر
+
+642
+00:59:49,910 --> 00:59:53,470
+element عند التمانية، Leaf، مابقدرش رشش على
+
+643
+00:59:53,470 --> 00:59:56,690
+اليمينها، مايعتبر بـ stop، بقول التسعة إياش، مش
+
+644
+00:59:56,690 --> 01:00:01,070
+موجودة، تسعة مش موجودة، وهكذا في عملية ال search،
+
+645
+01:00:01,070 --> 01:00:04,590
+فالآن عملية من أهم التطبيقات تبع ال binary tree،
+
+646
+01:00:04,590 --> 01:00:10,310
+اللي هي ال binary search treeعادة لأ الان في ال
+
+647
+01:00:10,310 --> 01:00:13,390
+binary tree احنا ايش بنروح بنساوي بنحول المجموعة
+
+648
+01:00:13,390 --> 01:00:17,870
+اللي عندي ل set تمام؟ ايش يعني set؟ يعني مافيش
+
+649
+01:00:17,870 --> 01:00:21,230
+تكرار بالعراصر و بصير انا ايش اساوي اضيف ال
+
+650
+01:00:21,230 --> 01:00:24,890
+element عارف ليش هتصير منك مشكلة؟ الان تخيل هي
+
+651
+01:00:24,890 --> 01:00:30,290
+عندي خمسة خمسة بعد ما حطيت هنا سبعة و حطيت هنا
+
+652
+01:00:30,290 --> 01:00:34,510
+اربعة اتجتني كمان مرة خمسة وين بده احطها؟
+
+653
+01:00:36,990 --> 01:00:43,130
+هي تخيل ان انا بتضيفها داخل ال tree اما القانون
+
+654
+01:00:43,130 --> 01:00:47,510
+بيقول كالتالي اللي على الشمال أصغر و اللي على
+
+655
+01:00:47,510 --> 01:00:50,530
+اليمين أكبر بقادته ساوي مالهاش وجود عشان هيك
+
+656
+01:00:50,530 --> 01:00:53,350
+التكرار مالهاش .. عشان هيك أول شي باخد ال list
+
+657
+01:00:53,350 --> 01:00:58,290
+بحولها لمجموعة أشيل عناصر مكررة و بروح بابنين لل
+
+658
+01:00:58,290 --> 01:00:59,870
+tree اللي موجودة عندك
+
+659
+01:01:05,920 --> 01:01:10,380
+من أهم التطبيقات في الموضوع الـ Trees شغل اسمها
+
+660
+01:01:10,380 --> 01:01:14,440
+الـ Spanning Tree من
+
+661
+01:01:14,440 --> 01:01:18,520
+التطبيقات تبع الـ Tree الـ Minimum Spanning Tree و
+
+662
+01:01:18,520 --> 01:01:22,460
+الـ Decision Tree و الـ Half Man Code Trees احنا
+
+663
+01:01:22,460 --> 01:01:27,400
+هتكلم على Spanning Tree Spanning Tree هي عبارة عن
+
+664
+01:01:27,400 --> 01:01:29,160
+Graph
+
+665
+01:01:31,490 --> 01:01:35,970
+أو sub graph بيحتوي على كل النقاط اللي فى الرسمة
+
+666
+01:01:35,970 --> 01:01:42,510
+بيحتوي على كل النقاط اللي فى الرسمة طيب لو انا بكل
+
+667
+01:01:42,510 --> 01:01:53,910
+بساطة جدتي تقولي تهيأ A
+
+668
+01:01:53,910 --> 01:02:03,910
+B C D هذا مين؟ هى graphالان باجي بقول ال spanning
+
+669
+01:02:03,910 --> 01:02:10,110
+tree طبعا هي عبارة عن sub graph من ال graph هذا
+
+670
+01:02:10,110 --> 01:02:15,850
+يمثل ال tree طبعا هو عبارة عن ال tree بتحتوي على
+
+671
+01:02:15,850 --> 01:02:21,010
+كل النقاط اللي موجودة في الرسمة ايش يعني كل النقاط
+
+672
+01:02:21,010 --> 01:02:24,990
+اللي موجودة في الرسمة يعني ممكن انا اعملها هيك
+
+673
+01:02:24,990 --> 01:02:30,870
+ايه؟
+
+674
+01:02:31,680 --> 01:02:39,540
+دي سي بي هذي تجارب ترى ترى ولا مش ترى هاي ترى بناء
+
+675
+01:02:39,540 --> 01:02:44,140
+على إيش؟ بناء على إنها connected graph simple
+
+676
+01:02:44,140 --> 01:02:51,640
+connected graph has no circuit بصبوط هايها ترى لأن
+
+677
+01:02:51,640 --> 01:02:56,760
+هذي sub graph من هذي صح ولا لأ مجموعة نقاط subset
+
+678
+01:02:56,760 --> 01:03:03,540
+من مجموعة نقاطلأ لأ لأ لأ انا
+
+679
+01:03:03,540 --> 01:03:07,880
+جلبت ال ..
+
+680
+01:03:07,880 --> 01:03:19,980
+دي بي ال .. وهنا في عندك ال a وهنا عندك ال c طبعا؟
+
+681
+01:03:19,980 --> 01:03:26,500
+الآن sub graph sub graphالنقاط سبسط من النقاط
+
+682
+01:03:26,500 --> 01:03:31,220
+والجسور سبسط من الجسور اللي موجودة Has no circuit
+
+683
+01:03:31,220 --> 01:03:34,640
+فهي Tree وبما أنها تحتوي على كل النقاط اللي في
+
+684
+01:03:34,640 --> 01:03:39,500
+الرصمة الأساسيةيعني ال V التي هي تساوي V التي هي
+
+685
+01:03:39,500 --> 01:03:46,000
+ما هي تسميها أيش Spanning Tree شجرة ممتدة تجتمل
+
+686
+01:03:46,000 --> 01:03:48,840
+على كل العناصر اللي موجودة اللي عندها و في كل
+
+687
+01:03:48,840 --> 01:03:54,320
+Spanning Tree عدد الجسور يساوي عدد النقاط ناقص
+
+688
+01:03:54,320 --> 01:04:01,590
+واحدعدد الجسور يساوي عدد النقاط ناقص واحد كم
+
+689
+01:04:01,590 --> 01:04:04,990
+النقاط اللي عندي هان؟ أربعة الجسور اللي عندي فيها
+
+690
+01:04:04,990 --> 01:04:08,610
+هتكون تلت في أي spanning tree في أي spanning tree
+
+691
+01:04:08,610 --> 01:04:11,790
+بغض النظر كيف كان شكلها عدد الجسور يساوي عدد
+
+692
+01:04:11,790 --> 01:04:19,030
+النقاط ناقص واحد الأن
+
+693
+01:04:19,030 --> 01:04:23,390
+من الأشكال اللي عناها دول تبقى لل G1
+
+694
+01:04:28,660 --> 01:04:33,300
+هل هذا spanning tree؟ لأ فى circuit هل هذا
+
+695
+01:04:33,300 --> 01:04:39,420
+spanning tree؟ yes هل هذا spanning tree؟ yes هل
+
+696
+01:04:39,420 --> 01:04:43,040
+هذا spanning tree؟ no ليش؟ لأنه فى عندى isolated
+
+697
+01:04:43,040 --> 01:04:46,260
+point وهو راح يقول أن ال tree لازم تكون connected
+
+698
+01:04:46,260 --> 01:04:57,790
+لازم تكون متصلة اه ونعت true true خلاصوين ميزة الـ
+
+699
+01:04:57,790 --> 01:05:02,950
+Spanning Tree يا شباب؟ الآية دي تخيل هي K6، إيش
+
+700
+01:05:02,950 --> 01:05:07,290
+يعني K6؟ Complete Graph من ست نقاط، هيك ال
+
+701
+01:05:07,290 --> 01:05:11,970
+connection، كل واحد متصل مع الخمس نقاط التانين،
+
+702
+01:05:11,970 --> 01:05:14,850
+الآية ميزة الـ Complete Graph و الـ Spanning Tree
+
+703
+01:05:14,850 --> 01:05:19,550
+بتلزمني عشان انا اعرف كل ال possible path's اللي
+
+704
+01:05:19,550 --> 01:05:23,350
+بتوصلني لمين أو بدي أبني unique path's عشان أصل من
+
+705
+01:05:23,350 --> 01:05:28,350
+نقطة لنقطةهك كل النقاط بتوصل لبعضها فانا بدي اعمل
+
+706
+01:05:28,350 --> 01:05:31,830
+minimize للشجرة هذه او لل graph هذا بدي اختصره
+
+707
+01:05:31,830 --> 01:05:36,630
+بشجرة بحيث انه ماتركش ولا graph او عفوا ولا vertex
+
+708
+01:05:36,630 --> 01:05:40,150
+يبقى برا بدون connection فبيخدمني في الموضوع مين
+
+709
+01:05:40,150 --> 01:05:43,790
+spanning tree فممكن اتكلم هى spanning tree من
+
+710
+01:05:43,790 --> 01:05:48,430
+الرسم السابق ست نقاط هى ست نقاط موجودات وهى
+
+711
+01:05:48,430 --> 01:05:52,380
+connected وهى كمان spanning treeمن الرسم السابق
+
+712
+01:05:52,380 --> 01:05:56,380
+الفكرة هو ان بدل من دوري على كل ال connections
+
+713
+01:05:56,380 --> 01:06:00,280
+هدول بصير بدوري على connection واحدة خصوصا لما
+
+714
+01:06:00,280 --> 01:06:04,860
+التكلفة .. التكلفة بتكون مالهاش معيار عندي لما
+
+715
+01:06:04,860 --> 01:06:07,720
+التكلفة بتصير مالهاش معيار عندي بصير بدوري على
+
+716
+01:06:07,720 --> 01:06:12,520
+spanning tree عشان اصل لعناصر اللي موجودة عندها
+
+717
+01:06:12,520 --> 01:06:16,940
+كيف
+
+718
+01:06:16,940 --> 01:06:24,070
+بدى اوجد ال minimum spanning tree؟أصغر .. أصغر
+
+719
+01:06:24,070 --> 01:06:28,630
+شبكة تجمع كل النقاط اللي موجودة عنها .. بأقل تكلفة
+
+720
+01:06:28,630 --> 01:06:31,510
+طبعا .. الآن أنا في عندي spanning tree ايش اسمها؟
+
+721
+01:06:31,510 --> 01:06:35,250
+دولة spanning tree .. صارت في عندي شجرات بتحتوي
+
+722
+01:06:35,250 --> 01:06:39,570
+على كل النقاط .. لما بدخل ال cost في الموضوع ..
+
+723
+01:06:39,570 --> 01:06:43,310
+بدخل ال cost في الموضوع .. بصير أدور على مين؟ على
+
+724
+01:06:43,310 --> 01:06:46,950
+ال minimum .. minimum spanning tree .. الآن في أي
+
+725
+01:06:46,950 --> 01:06:51,510
+رسمةسأقول هي هذي spanning tree وهذه spanning tree
+
+726
+01:06:51,510 --> 01:06:55,150
+لكن مين أقل فيهم أنا ماعرفش لأنه فعليا ماتكلمتش
+
+727
+01:06:55,150 --> 01:06:59,210
+على تكلفة بال minimum spanning tree بقول كتالي هي
+
+728
+01:06:59,210 --> 01:07:02,750
+ال minimum spanning tree بتحتوى على أقل weight أقل
+
+729
+01:07:02,750 --> 01:07:06,730
+تكلفة أقل cost يعني ال cost لازم تكون موجودة عندها
+
+730
+01:07:06,730 --> 01:07:11,370
+فرسمتها البسيطة يا شباب في عندي two algorithms في
+
+731
+01:07:11,370 --> 01:07:15,470
+عند ال Brim وفي عند ال cost curve algorithms فرسمت
+
+732
+01:07:15,470 --> 01:07:24,300
+بكل البساطة ده الكتاليأنا بدي أشغل هيك بغض النظر
+
+733
+01:07:24,300 --> 01:07:30,900
+إيش ال algorithm اللي مستخدم هاي
+
+734
+01:07:30,900 --> 01:07:39,940
+ال graph عشان نلهي تخلصنا A B C D هنتكلفة خمسة هنا
+
+735
+01:07:39,940 --> 01:07:49,050
+واحد هنا تلاتة هنا أربعة هنا اتنين هنا خمسةالان
+
+736
+01:07:49,050 --> 01:07:52,010
+عندما تحصل على الـ Minimum Spanning Tree يعني أنك
+
+737
+01:07:52,010 --> 01:08:00,630
+تريد الأربع نقاط اللي موجودة هذه الأربع نقاط A
+
+738
+01:08:00,630 --> 01:08:09,670
+,B,C,D أول ما بترسم، بترسم الخطوط اللي أقل تكلفة
+
+739
+01:08:09,670 --> 01:08:15,750
+احنا حطينا جديش؟ اوكي، اتنين فيهم، خمسات اوكي، بس
+
+740
+01:08:15,750 --> 01:08:17,990
+بعد إذنك، بدي أحط هذه كمان مرة اتنين
+
+741
+01:08:22,160 --> 01:08:29,340
+الان بتاخد أقل تكلفة مين أقل تكلفة؟ AC هايو أول خط
+
+742
+01:08:29,340 --> 01:08:39,520
+بواحد بعد هيك بتاخد AB اخدت AB اتنين اللي بعده BC
+
+743
+01:08:39,520 --> 01:08:44,450
+لو انا اترسمت ال BC هنا شباب صار في عندي circleصار
+
+744
+01:08:44,450 --> 01:08:48,390
+في عندي circuit بطلة ال three فانا أسف مش هاخد هذا
+
+745
+01:08:48,390 --> 01:08:54,230
+بيه اتنين هاخد مين؟ هاخد اللي بعده لأ هو واحد بين
+
+746
+01:08:54,230 --> 01:09:00,810
+كانوا .. ماشي
+
+747
+01:09:00,810 --> 01:09:07,230
+الحال هي واحد واحد وانا أربعة طبعا الان بدي أخد
+
+748
+01:09:07,230 --> 01:09:16,680
+مين؟ بدي أخد خلصت هذا مابديش إياهبدي أخد الأربعة،
+
+749
+01:09:16,680 --> 01:09:23,640
+هاي أربعة، طيب كام دي سر عندي أنا صاروا؟ تلاتة،
+
+750
+01:09:23,640 --> 01:09:29,860
+وعدد النقاط؟ أنا مش بحاجة للجسور بعد هيك،
+
+751
+01:09:29,860 --> 01:09:35,750
+وينها؟ وينها؟ مافيش circuitمافيش لو فيه تقطة فالنص
+
+752
+01:09:35,750 --> 01:09:39,090
+كان اختلفت الأمور السؤال اللي بيقرح نفسه الآن ليش
+
+753
+01:09:39,090 --> 01:09:43,630
+أنا وقفت ماكملتش؟ لأن ال spanning tree عدد الجسور
+
+754
+01:09:43,630 --> 01:09:47,390
+فيها يساوي عدد النقاط ماتس واحد وانا بدي بس ثلاث
+
+755
+01:09:47,390 --> 01:09:51,370
+نقاط فهي اتكملت بالثلاث نقاط وخلصنا وبهيك انت
+
+756
+01:09:51,370 --> 01:09:55,950
+بترسم على أو بتقدر تحصل على ال minimum spanning
+
+757
+01:09:55,950 --> 01:09:56,810
+tree
+
+758
+01:10:02,620 --> 01:10:07,480
+الأسماء لـ Algorithm لرسم التتعامل أو الوصول للـ
+
+759
+01:10:07,480 --> 01:10:11,360
+Tree خلاص بس انت بدك تعرف الأسماء مش اكتر من هيك
+
+760
+01:10:11,360 --> 01:10:17,000
+تمويها بدك تعرف ان في عندك two algorithms كمان من
+
+761
+01:10:17,000 --> 01:10:20,100
+أجل الوصول ل ال minimum spanning trees هيهم
+
+762
+01:10:20,100 --> 01:10:24,040
+crosscan و prim algorithms لكن الطريقة اللي انا ..
+
+763
+01:10:24,040 --> 01:10:26,720
+لو قلتلك هتل ال minimum spanning tree اشغل
+
+764
+01:10:26,720 --> 01:10:31,670
+بالطريقة اللي اناقلتلك عنها ..طيب وبهيك الشباب مع
+
+765
+01:10:31,670 --> 01:10:35,230
+ال crosscut algorithm نكون انتهينا من ال chapter
+
+766
+01:10:35,230 --> 01:10:40,190
+الأخير في المساق للفصل هذا هو فعليا انا ال .. هذا
+
+767
+01:10:40,190 --> 01:10:43,990
+المفروض ال three في ال chapter سبعة فاحنا فعليا
+
+768
+01:10:43,990 --> 01:10:46,030
+طلعنا من الستة و روحنا على سبعة و جيبنا اللي
+
+769
+01:10:46,030 --> 01:10:49,950
+بدنايا وبهيك نكون خلصنا الفصل بالكامل ان شاء الله
+
+770
+01:10:49,950 --> 01:10:54,530
+تعالى اذا في حد عنده اي سؤال احنا جاهزين في المكتب
+
+771
+01:10:54,530 --> 01:10:56,310
+باستماعه خلال الأسبوع اللي جاي ان شاء الله جابيه
+
+772
+01:10:56,310 --> 01:11:01,720
+لاياشيقبل الامتحان تحضر نفسك تدراجع ماتجينيش ان
+
+773
+01:11:01,720 --> 01:11:05,880
+اشرحلك المادة من الصفر لازم أشوفك فعلا انت بذالك
+
+774
+01:11:05,880 --> 01:11:10,080
+جهود و جايين ان انا اعيش ان فاهمك الشغل اللي انت
+
+775
+01:11:10,080 --> 01:11:13,160
+ماقدرتش توصل لها و ان شاء الله هنكون بانتظارك بإذن
+
+776
+01:11:13,160 --> 01:11:16,280
+الله تبارك وتعالى بس الحال هيك بكون نهينا محاضرتنا
+
+777
+01:11:16,280 --> 01:11:19,000
+و نهينا الفصل سبحانك اللهم وبحمدك نشهد ولا إله إلا
+
+778
+01:11:19,000 --> 01:11:21,820
+أنت و نستغفرك و أتوب إليك و سامحونا إذا ان احنا
+
+779
+01:11:21,820 --> 01:11:25,700
+عايش .. إذا ناكل محاضرة هكذا الله يعطي كل عافية إن
+
+780
+01:11:25,700 --> 01:11:25,800
+شاء الله
+
diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/zrkaFn0izUk_raw.json b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/zrkaFn0izUk_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..d5877c9da050d69ee1630a657e32db7edd767915
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/zrkaFn0izUk_raw.json
@@ -0,0 +1 @@
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النظرية تبع الـ Euler ربط C كم شباب؟ تلاتة؟ خمس؟ Euler circuit كان بيقول إنه لازم تكون كل بوتر فردية عشان تلاقي الـ Euler circuit زوجية عفواً كل بوتر لازم تكون بوتر زوجية عشان تلاقي الـ Euler circuit", "tokens": [2304, 43500, 9957, 12399, 32767, 45636, 995, 22807, 5296, 4117, 1829, 8717, 7435, 1829, 3555, 29739, 35473, 2288, 8978, 18863, 8315, 9381, 2288, 4032, 8717, 3794, 47432, 28239, 19913, 2288, 10632, 6055, 3555, 3615, 2423, 39184, 462, 26318, 12602, 3555, 9566, 383, 9122, 2304, 13412, 3555, 16758, 22807, 6055, 1211, 9307, 3660, 22807, 16490, 2304, 3794, 22807, 462, 26318, 9048, 25961, 4724, 1829, 39648, 36145, 3224, 5296, 31377, 2304, 6055, 30544, 28242, 4724, 35473, 2288, 6156, 2288, 3215, 10632, 6225, 8592, 7649, 6055, 15040, 38436, 2423, 39184, 462, 26318, 9048, 30767, 29245, 10632, 6225, 5172, 14407, 14111, 28242, 4724, 35473, 2288, 5296, 31377, 2304, 6055, 30544, 4724, 35473, 2288, 30767, 29245, 10632, 6225, 8592, 7649, 6055, 15040, 38436, 2423, 39184, 462, 26318, 9048], 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385.43, "end": 385.89, "word": " circuit", "probability": 0.94384765625}], "temperature": 1.0}, {"id": 16, "seek": 40023, "start": 387.35, "end": 400.23, "text": "طب كل رتب اللي عنده رتب فردية بالتاني مافيش على الرسم هان oiler circuit .. does not exist ال oiler path بقول .. بتلاقي ال oiler path في حالة إذا كان في ال graph فقط اتنين", "tokens": [9566, 3555, 28242, 12602, 2655, 3555, 13672, 1829, 43242, 3224, 12602, 2655, 3555, 6156, 2288, 3215, 10632, 20666, 2655, 7649, 1829, 19446, 41185, 8592, 15844, 34892, 38251, 8032, 7649, 3184, 260, 9048, 4386, 775, 406, 2514, 2423, 3184, 260, 3100, 4724, 39648, 4386, 39894, 15040, 38436, 2423, 3184, 260, 3100, 8978, 11331, 6027, 3660, 11933, 15730, 25961, 8978, 2423, 4295, 6156, 47432, 1975, 2655, 1863, 9957], "avg_logprob": -0.3299906725314126, "compression_ratio": 1.4682080924855492, "no_speech_prob": 0.0, "words": [{"start": 387.35, "end": 387.57, "word": "طب", "probability": 0.5672607421875}, {"start": 387.57, "end": 387.77, "word": " كل", 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edge تمام؟", "tokens": [3224, 15730, 9673, 5172, 32887, 11242, 9154, 3224, 37495, 22653, 11933, 15730, 45164, 7435, 3215, 2423, 9048, 37893, 48812, 2288, 13063, 1829, 37893, 8032, 2655, 15040, 38436, 29739, 3615, 11242, 4032, 28814, 15730, 45164, 7435, 3215, 29739, 3615, 11242, 37893, 8032, 2655, 15040, 38436, 2423, 9048, 5296, 33456, 3224, 8978, 49374, 16095, 6055, 3555, 3615, 9307, 8978, 2423, 7123, 2423, 7852, 15200, 3100, 11933, 1829, 8592, 4724, 1829, 39648, 22807, 20193, 5016, 19913, 14407, 11933, 1829, 8592, 25961, 2423, 3184, 260, 8978, 3714, 31747, 11622, 25124, 3555, 16758, 19273, 633, 4691, 19273, 633, 4691, 46811, 10943, 22807], "avg_logprob": -0.3158482063789757, "compression_ratio": 1.7671232876712328, "no_speech_prob": 3.5762786865234375e-07, "words": [{"start": 748.0, "end": 748.28, "word": "هذا", "probability": 0.673583984375}, {"start": 748.28, "end": 748.56, "word": " المفروض", "probability": 0.96337890625}, {"start": 748.56, "end": 748.84, "word": " منه", 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"text": "بس عدد النقاب على الأقل بيكون تنتهي من التصلات لو انك بتطبق بال letter A أصبت؟ أيوة فيه أن المصطلح ال level المستوى ال road ده من ال level تبعته إيه؟ Zero و ال height أو ال depth تبعته ال letter E بتمثل إيه؟ عدد الجسور ما بين ال road لحد آخر leaf لحد أعمق leaf ال height ال A level zero B و C level one", "tokens": [3555, 3794, 6225, 3215, 3215, 28239, 4587, 16758, 15844, 16247, 4587, 1211, 4724, 1829, 30544, 6055, 29399, 3224, 1829, 9154, 16712, 36520, 9307, 45164, 16472, 4117, 39894, 9566, 3555, 4587, 20666, 5063, 316, 5551, 9381, 3555, 2655, 22807, 36632, 2407, 3660, 8978, 3224, 14739, 9673, 9381, 9566, 1211, 5016, 2423, 1496, 9673, 14851, 2407, 7578, 2423, 3060, 11778, 3224, 9154, 2423, 1496, 6055, 3555, 34268, 3224, 11933, 1829, 3224, 22807, 17182, 4032, 2423, 6681, 34051, 2423, 7161, 6055, 3555, 34268, 3224, 2423, 5063, 462, 39894, 2304, 12984, 1211, 11933, 1829, 3224, 22807, 6225, 3215, 3215, 25724, 3794, 13063, 19446, 49374, 2423, 3060, 5296, 24401, 19753, 34740, 10871, 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"word": " connected", "probability": 0.91455078125}, {"start": 3764.68, "end": 3765.28, "word": " graph", "probability": 0.96484375}, {"start": 3765.28, "end": 3765.82, "word": " has", "probability": 0.57275390625}, {"start": 3765.82, "end": 3766.08, "word": " no", "probability": 0.9443359375}, {"start": 3766.08, "end": 3766.66, "word": " circuit", "probability": 0.90625}, {"start": 3766.66, "end": 3767.48, "word": " بصبوط", "probability": 0.634423828125}, {"start": 3767.48, "end": 3768.96, "word": " هايها", "probability": 0.5215657552083334}, {"start": 3768.96, "end": 3770.56, "word": " ترى", "probability": 0.7228190104166666}, {"start": 3770.56, "end": 3771.64, "word": " لأن", "probability": 0.7236328125}, {"start": 3771.64, "end": 3772.28, "word": " هذي", "probability": 0.70654296875}, {"start": 3772.28, "end": 3772.46, "word": " sub", "probability": 0.68212890625}, {"start": 3772.46, "end": 3772.88, "word": " graph", "probability": 0.88232421875}, {"start": 3772.88, "end": 3773.04, 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عندك ال a وهنا عندك ال c طبعا؟ الآن sub graph sub graph", "tokens": [1211, 10721, 5296, 10721, 5296, 10721, 5296, 10721, 1975, 8315, 10874, 46152, 2655, 2423, 4386, 11778, 1829, 4724, 1829, 2423, 4386, 37037, 8315, 8978, 43242, 4117, 2423, 257, 37037, 8315, 43242, 4117, 2423, 269, 23032, 3555, 3615, 995, 22807, 6024, 48506, 1422, 4295, 1422, 4295], "avg_logprob": -0.26545516498710797, "compression_ratio": 1.5294117647058822, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 3778.88, "end": 3779.58, "word": "لأ", "probability": 0.82861328125}, {"start": 3779.58, "end": 3780.02, "word": " لأ", "probability": 0.787353515625}, {"start": 3780.02, "end": 3780.16, "word": " لأ", "probability": 0.951171875}, {"start": 3780.16, "end": 3780.36, "word": " لأ", "probability": 0.869384765625}, {"start": 3780.36, "end": 3783.54, "word": " انا", "probability": 0.6767578125}, {"start": 3783.54, "end": 3783.9, "word": " جلبت", "probability": 0.97900390625}, {"start": 3783.9, "end": 3784.46, 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"probability": 0.97607421875}, {"start": 3797.46, "end": 3797.62, "word": " ال", "probability": 0.98388671875}, {"start": 3797.62, "end": 3797.82, "word": " c", "probability": 0.923828125}, {"start": 3797.82, "end": 3799.98, "word": " طبعا؟", "probability": 0.733203125}, {"start": 3799.98, "end": 3800.52, "word": " الآن", "probability": 0.6558837890625}, {"start": 3800.52, "end": 3801.58, "word": " sub", "probability": 0.6474609375}, {"start": 3801.58, "end": 3801.98, "word": " graph", "probability": 0.54541015625}, {"start": 3801.98, "end": 3802.24, "word": " sub", "probability": 0.66845703125}, {"start": 3802.24, "end": 3802.7, "word": " graph", "probability": 0.97705078125}], "temperature": 1.0}, {"id": 143, "seek": 381556, "start": 3804.04, "end": 3815.56, "text": "النقاط سبسط من النقاط والجسور سبسط من الجسور اللي موجودة Has no circuit فهي Tree وبما أنها تحتوي على كل النقاط اللي في الرصمة الأساسية", "tokens": [6027, 1863, 4587, 41193, 8608, 3555, 3794, 9566, 9154, 28239, 4587, 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/zrkaFn0izUk_raw.srt b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/zrkaFn0izUk_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..2ab3f930b50c682de456ce2e4f0c905340fa9be9
--- /dev/null
+++ b/PL9fwy3NUQKwbTb0jzhfbgpcbRPhRsoGhi/zrkaFn0izUk_raw.srt
@@ -0,0 +1,3160 @@
+1
+00:00:21,090 --> 00:00:23,190
+بسم الله والحمد لله والصلاة والسلام علي رسول الله
+
+2
+00:00:23,190 --> 00:00:27,590
+كنا المحاضرة الماضي شباب اتكلمنا على مجموعة من
+
+3
+00:00:27,590 --> 00:00:30,330
+المهمة .. مجموعة مهمة من ال definitions فيما تعلق
+
+4
+00:00:30,330 --> 00:00:34,750
+بموضوع ال graphs اتكلمنا على ال walk هو عبارة عن
+
+5
+00:00:34,750 --> 00:00:38,050
+مجموعة او sequence مجموعة من ال vertices و اليسور
+
+6
+00:00:38,050 --> 00:00:41,590
+المتتالية لازم يكون في بينها ربط و ال length تبع
+
+7
+00:00:41,590 --> 00:00:45,110
+ال walk تمثل بعدد اليسور وقولنا ال walk مكون
+
+8
+00:00:45,110 --> 00:00:49,600
+closed لما بيبدأ و بينتهي عند نفس النقطةوعكسها
+
+9
+00:00:49,600 --> 00:00:52,960
+بيكون open في عنده definition لل walk اخر اسمه
+
+10
+00:00:52,960 --> 00:00:56,180
+trail لما بيكون هذا ال walk بيحتوي على distinct
+
+11
+00:00:56,180 --> 00:01:01,500
+edge بيحتوي على جسور مختلفة و بسميه path لما بكون
+
+12
+00:01:01,500 --> 00:01:06,500
+و path لما بكون عندي بيحتوي على vertices مختلفة و
+
+13
+00:01:06,500 --> 00:01:09,740
+لما بكل trail هذا closed يعني بدأ و انتهى بنفس
+
+14
+00:01:09,740 --> 00:01:13,820
+النقاط و كل الجسور اللي فيه مختلفة بسميه circuit و
+
+15
+00:01:13,820 --> 00:01:18,460
+لما بيكون ال path اللي عنديبينتهي بنفس النقطة
+
+16
+00:01:18,460 --> 00:01:24,980
+استثناء سمناها cycle وشوفنا المثال هذا وحلينا منه
+
+17
+00:01:24,980 --> 00:01:28,420
+المحاضرة الماضيةاليوم ان شاء الله تعالى هنبدأ مع
+
+18
+00:01:28,420 --> 00:01:32,180
+definition جديد نسميه Euler circuit و Euler path
+
+19
+00:01:32,180 --> 00:01:37,920
+في لبس أحيانا بيصير في موضوع اللي فهمناه ال Euler
+
+20
+00:01:37,920 --> 00:01:42,240
+circuit و Euler path خصوصا لما اتكلم على ال path
+
+21
+00:01:42,240 --> 00:01:48,060
+بداية في قرية في روسيا او في المدينة في روسيا
+
+22
+00:01:48,060 --> 00:01:51,960
+Konigsberg اعتقد اذا انا مش غلطان في الاسم في ال
+
+23
+00:01:51,960 --> 00:01:56,100
+1800 و مش عارف جداش كانوا ناس بتحب تتنزح عوالين
+
+24
+00:01:57,030 --> 00:01:59,810
+النهر المبني عليه السبع جسور الموجودة اللي احنا
+
+25
+00:01:59,810 --> 00:02:04,730
+شايفينهم قدامنا هنا وكانت الناس دائما بتتساءل هل
+
+26
+00:02:04,730 --> 00:02:08,590
+بإمكاني انا اعمل جولة ال walk تبعتي المسار تبعي
+
+27
+00:02:08,590 --> 00:02:14,190
+امر فيه على كل الجسور بدون مبر امر في جسر واحد او
+
+28
+00:02:14,190 --> 00:02:20,320
+جسر معين مرتين او ما شابه فكان الكلام هذاأخد وضل
+
+29
+00:02:20,320 --> 00:02:23,500
+التساوي قائم لأنه ماحدش كان يجرب بشكل عام لإيه
+
+30
+00:02:23,500 --> 00:02:27,820
+اللي غير يجيه رجع يمر على جسر مرة تانية في نهاية
+
+31
+00:02:27,820 --> 00:02:36,340
+ال 1800 و بعديها بقى كام سنة اجى عالم سويدي أيلر و
+
+32
+00:02:36,340 --> 00:02:41,490
+راح درس المنطقة ومثل ال graphاللي انها مثلة
+
+33
+00:02:41,490 --> 00:02:45,270
+بالخريطة اللي موجودة هنا وكانت نظريته بتقول كالشكل
+
+34
+00:02:45,270 --> 00:02:49,990
+التالي من خلال عرف ال oiler circuit وال oiler path
+
+35
+00:02:49,990 --> 00:02:53,090
+بناء على ال definition اللي موجود النظرية كانت
+
+36
+00:02:53,090 --> 00:02:58,170
+بتقول كالتالي ان ال oiler circuit هي عبارة عن
+
+37
+00:02:58,170 --> 00:03:02,610
+simple circuit ونجف هنا simple circuit شو يعني
+
+38
+00:03:02,610 --> 00:03:08,230
+simple circuit closed walk
+
+39
+00:03:08,230 --> 00:03:09,630
+او closed trail
+
+40
+00:03:12,590 --> 00:03:20,530
+closed circuit يعني closed trail containing every
+
+41
+00:03:20,530 --> 00:03:25,350
+edge في الgraph اللي جيه يعني إذا أنا كدفت أعمل
+
+42
+00:03:25,350 --> 00:03:31,050
+closed trailأو circuit بتحتوي على كل الجسور اللي
+
+43
+00:03:31,050 --> 00:03:36,530
+موجودة في ال graph بسميها ايش؟ Oiler circuit و
+
+44
+00:03:36,530 --> 00:03:42,290
+oiler هذا أثبت الكلام التالي جال إذا كان ال graph
+
+45
+00:03:42,290 --> 00:03:48,690
+هذا كل ال vertices اللي موجودة فيه كل النقاط اللي
+
+46
+00:03:48,690 --> 00:03:55,620
+موجودة فيهلها رطبة زوجية ايش يعني رطبة زوجية؟ يعني
+
+47
+00:03:55,620 --> 00:04:00,500
+عدد الجسور اللي جاية على ال vertex عدد زوجية،
+
+48
+00:04:00,500 --> 00:04:05,440
+كمان؟ معناته بتقدر تلاقي في ال graph Oiler circuit
+
+49
+00:04:05,440 --> 00:04:11,200
+طب لو ماكانش، لو لجيت واحد من ال vertices هذه عدد
+
+50
+00:04:11,200 --> 00:04:15,780
+او رطبة كبار رطبة فردية انسى الموضوع، مافيش هيش
+
+51
+00:04:15,780 --> 00:04:16,780
+circuit
+
+52
+00:04:21,190 --> 00:04:26,350
+والأولى باث بقول كالتالي simple path لكن للأسف
+
+53
+00:04:26,350 --> 00:04:30,730
+كلمة path هان مش بمعناها الحقيقي path حسب ال
+
+54
+00:04:30,730 --> 00:04:36,170
+definition تبع الكتاب بقدر ما هي ايش walk simple
+
+55
+00:04:36,170 --> 00:04:41,210
+walk containing every edge
+
+56
+00:04:44,410 --> 00:04:49,970
+أحنا نعرف أن الـ path بيحتوي عن طرق مختلفة وانا
+
+57
+00:04:49,970 --> 00:04:53,230
+بقول أن هذه الشيء اللي بيحتوي على كل اليسار، يعني
+
+58
+00:04:53,230 --> 00:04:56,150
+الفرق بين هذه و هذه انها إيش تكون يا شباب؟ ال
+
+59
+00:04:56,150 --> 00:05:01,270
+closing فقط، طيب اويدراش جال بالنسبة لل path جال
+
+60
+00:05:01,270 --> 00:05:07,720
+إذا كانتالرسمة اللى موجود عندك بتحتوي على تنتين
+
+61
+00:05:07,720 --> 00:05:13,080
+فقط exactly two vertices of odd degrees of odd
+
+62
+00:05:13,080 --> 00:05:18,540
+degree بتلاقي Euler path كمان مرة نعيد قالك ال
+
+63
+00:05:18,540 --> 00:05:22,040
+Euler circuit بتلاقيها لو كانت كل ال degree تحت ال
+
+64
+00:05:22,040 --> 00:05:26,800
+vertices even احداث زوجية و بتلاقي ال Euler path
+
+65
+00:05:26,800 --> 00:05:33,180
+موجود لو كان فقط عندك اتنين اتنين فقطالرطبة تبعتهم
+
+66
+00:05:33,180 --> 00:05:37,980
+رطبة فردية، فلو وجدت واحد، مافيش Euler بقى، فلو
+
+67
+00:05:37,980 --> 00:05:41,560
+وجدت تلاتة، مافيش Euler بقى. تعالى نرجع للرسمة
+
+68
+00:05:41,560 --> 00:05:48,420
+السابقة، بينجوسين، Euler كان بيقولهم، من المستحيل
+
+69
+00:05:48,420 --> 00:05:55,860
+انك تعمل جولة تمام؟ تمر فيها على كل الجسور بدون ما
+
+70
+00:05:55,860 --> 00:06:00,590
+تطلع على جسر؟مرتين، لماذا؟ لكي نجيب البوتر في
+
+71
+00:06:00,590 --> 00:06:05,870
+العناصر و نسقط النظرية تبع الـ Euler ربط C كم
+
+72
+00:06:05,870 --> 00:06:15,410
+شباب؟ تلاتة؟ خمس؟
+
+73
+00:06:15,410 --> 00:06:18,130
+Euler circuit كان بيقول إنه لازم تكون كل بوتر
+
+74
+00:06:18,130 --> 00:06:22,490
+فردية عشان تلاقي الـ Euler circuit زوجية عفواً كل
+
+75
+00:06:22,490 --> 00:06:25,430
+بوتر لازم تكون بوتر زوجية عشان تلاقي الـ Euler
+
+76
+00:06:25,430 --> 00:06:30,090
+circuitطب كل رتب اللي عنده رتب فردية بالتاني مافيش
+
+77
+00:06:30,090 --> 00:06:34,290
+على الرسم هان oiler circuit .. does not exist ال
+
+78
+00:06:34,290 --> 00:06:38,050
+oiler path بقول .. بتلاقي ال oiler path في حالة
+
+79
+00:06:38,050 --> 00:06:42,350
+إذا كان في ال graph فقط اتنينورتبته مرتبة فردية
+
+80
+00:06:42,350 --> 00:06:46,890
+بقى بقى خمسة وكلهم فرديات معناته ال oiler bath
+
+81
+00:06:46,890 --> 00:06:51,250
+does not exist تعالى نشوف الأمثلات اللى موجودة
+
+82
+00:06:51,250 --> 00:06:55,910
+عندها ونسقط عليها الكلام الصادق ونسأل نفسنا هل ال
+
+83
+00:06:55,910 --> 00:06:59,630
+oiler bath و ال oiler circuit exist ولا لأ نبدأ مع
+
+84
+00:06:59,630 --> 00:07:05,290
+G1 وانا بدي اختصر احاول اقول oiler circuit و oiler
+
+85
+00:07:07,040 --> 00:07:11,500
+Oiler Circuit مع الـ G1 الروت برنجل دي الشباب؟ 2
+
+86
+00:07:11,500 --> 00:07:18,420
+.. 2 .. 2 .. 4 .. 4 .. 4 .. 4 .. 4 .. 4 .. 4 .. 4
+
+87
+00:07:18,420 --> 00:07:18,500
+.. 4 .. 4 .. 4 .. 4 .. 4 .. 4 .. 4 .. 4 .. 4 .. 4
+
+88
+00:07:18,500 --> 00:07:19,100
+.. 4 .. 4 .. 4 .. 4 .. 4 .. 4 .. 4 .. 4 .. 4 .. 4
+
+89
+00:07:19,100 --> 00:07:19,100
+.. 4 .. 4 .. 4 .. 4 .. 4 .. 4 .. 4 .. 4 .. 4 .. 4
+
+90
+00:07:19,100 --> 00:07:19,160
+.. 4 .. 4 .. 4 .. 4 .. 4 .. 4 .. 4 .. 4 .. 4 .. 4
+
+91
+00:07:19,160 --> 00:07:19,160
+.. 4 .. 4 .. 4 .. 4 .. 4 .. 4 .. 4 .. 4 .. 4 .. 4
+
+92
+00:07:19,160 --> 00:07:19,180
+.. 4 .. 4 .. 4 .. 4 .. 4 .. 4 .. 4 .. 4 .. 4 .. 4
+
+93
+00:07:19,180 --> 00:07:19,180
+.. 4 .. 4 .. 4 .. 4 .. 4 .. 4 .. 4 .. 4 .. 4 .. 4
+
+94
+00:07:19,180 --> 00:07:19,180
+.. 4 .. 4 .. 4 .. 4 .. 4 .. 4 .. 4 .. 4 .. 4 .. 4
+
+95
+00:07:19,180 --> 00:07:19,680
+.. 4 .. 4 .. 4 .. 4 .. 4 .. 4 .. 4 .. 4 .. 4 .. 4
+
+96
+00:07:19,680 --> 00:07:28,280
+..
+
+97
+00:07:31,320 --> 00:07:36,340
+D C E A لأنه لو تنساش circuit لازم تبدأ وتنتهي
+
+98
+00:07:36,340 --> 00:07:43,920
+بنفس المقمة انا بتبقى أكتر كم مرة A D .. بالضبط هي
+
+99
+00:07:43,920 --> 00:07:54,560
+اللي احنا بدنا نوصلها C أو A B E D C E Aلو مفهوم
+
+100
+00:07:54,560 --> 00:07:58,660
+ان الـ Vertices ممنوع تتكرر كروحنا في مشكلة الآن
+
+101
+00:07:58,660 --> 00:08:02,980
+ان ال circuit هاد ايش مش موجودة تمام الان هي ال
+
+102
+00:08:02,980 --> 00:08:05,740
+Euler circuit طبعا ممكن تعرف اكثر من واحدة تبدأ من
+
+103
+00:08:05,740 --> 00:08:08,840
+عند ال C و تبدأ بايب اتجاه هتلاقي ال Euler circuit
+
+104
+00:08:08,840 --> 00:08:13,100
+موجودة ال Euler path ايش ال Euler path بقول؟ بقول
+
+105
+00:08:13,100 --> 00:08:18,900
+انه لازم تكون تنتين فقط رتبة فردية مافيش عنده رتبة
+
+106
+00:08:18,900 --> 00:08:22,300
+فردية كلها قانون زوجية وبالتالي مافيش Euler path
+
+107
+00:08:23,530 --> 00:08:32,770
+مافيش ND، oiler bath، تمام؟ اللي بعديها؟ تلاتة،
+
+108
+00:08:32,770 --> 00:08:42,670
+تلاتة، تلاتة، تلاتة، أربعة، oiler circuit، oiler
+
+109
+00:08:42,670 --> 00:08:48,520
+bath، oiler circuit موجودة؟بقول كل غطبك يجب ان
+
+110
+00:08:48,520 --> 00:08:52,900
+تكون زوجي عشان كل ال circuit وال all or بقى يجب ان
+
+111
+00:08:52,900 --> 00:08:59,740
+يكون في عندك تلتير غطبتهم فردية الاخير
+
+112
+00:08:59,740 --> 00:09:12,820
+تلاتة تلاتة اربعة اربعة اربعة
+
+113
+00:09:12,820 --> 00:09:13,540
+اربعة اربعة اربعة اربعة اربعة اربعة اربعة اربعة
+
+114
+00:09:13,540 --> 00:09:13,900
+اربعة اربعة اربعة اربعة اربعة اربعة اربعة اربعة
+
+115
+00:09:13,900 --> 00:09:14,280
+اربعة اربعة اربعة اربعة اربعة اربعة اربعة اربعة
+
+116
+00:09:14,280 --> 00:09:14,300
+اربعة اربعة اربعة اربعة اربعة اربعة اربعة اربعة
+
+117
+00:09:14,300 --> 00:09:14,600
+اربعة اربعة اربعة اربعة اربعة اربعة اربعة اربعة
+
+118
+00:09:14,600 --> 00:09:14,600
+اربعة اربعة اربعة اربعة اربعة اربعة اربعة اربعة
+
+119
+00:09:14,600 --> 00:09:17,570
+اربعة اربعة اربعةمش موجودة لأنه في عنده رتب فردية
+
+120
+00:09:17,570 --> 00:09:22,450
+و هو بيقول لازم تكون كل الرتب زوجيا اويلر باف
+
+121
+00:09:22,450 --> 00:09:28,350
+موجودة؟ موجودة لأنه بيقول تكون عندك تلتين من ال
+
+122
+00:09:28,350 --> 00:09:31,790
+vertices و رتبهم فردية موجود تعالي نقف بال اويلر
+
+123
+00:09:31,790 --> 00:09:41,570
+باف A B E D
+
+124
+00:09:45,220 --> 00:09:51,700
+أطلع فوق؟ أيوة طيب ممكن ألاق بيكتب المسار مرة
+
+125
+00:09:51,700 --> 00:09:57,280
+تانية A B D A
+
+126
+00:09:57,280 --> 00:09:58,400
+B D
+
+127
+00:10:06,200 --> 00:10:09,920
+لأ ارجع عليه كمان مرة مش هتظبط الان انا في قاعد
+
+128
+00:10:09,920 --> 00:10:13,920
+وانا بجرب متأكد ان ال oiler bath exist بس بقالي
+
+129
+00:10:13,920 --> 00:10:24,560
+عليهاش ان اجيبه مرات يعني نعم احد
+
+130
+00:10:24,560 --> 00:10:32,440
+اتنين تلاتة اربعة بس لحظة شوي اللي يصبر علي اربعة
+
+131
+00:10:33,470 --> 00:10:41,030
+خمسة .. ستة .. سبعة صح ولا غلط؟ طبعا لو كونه
+
+132
+00:10:41,030 --> 00:10:44,290
+بيقولك موجود ممكن تلاقي اكتر من واحد مايحدد ال
+
+133
+00:10:44,290 --> 00:10:47,570
+cash ان هو واحد ولا اكتر انا الان بقعد بقترح انه
+
+134
+00:10:47,570 --> 00:10:56,350
+هيك واحد من A ل B من A ل C من C ل D من D ل E من E
+
+135
+00:10:56,350 --> 00:11:08,180
+ل D من B ل D من D ل Aو من A ل B و احظ ان المسار
+
+136
+00:11:08,180 --> 00:11:12,720
+اللى كتبته هذا حقق من وجهه كل الجسور اللى موجودة
+
+137
+00:11:12,720 --> 00:11:19,360
+وين عندي على الرصمة بدون اي مشاكل .. بدون اي مشاكل
+
+138
+00:11:19,360 --> 00:11:26,200
+ايش كنت تقولي حازم؟ مسار تاني؟ في
+
+139
+00:11:26,200 --> 00:11:30,340
+الآخر انت بتلاقي كونه حسب النظرية ان ال vert اللى
+
+140
+00:11:30,340 --> 00:11:34,640
+موجود بضل عليه اي شساويأدقق ولا إيش بقى أجيب
+
+141
+00:11:34,640 --> 00:11:42,560
+المسار اللي موجود عندي بتمشي الأمور تمام على
+
+142
+00:11:42,560 --> 00:11:50,660
+غرار أولا في اندي الهاملتون راح أرف هاملتون باخ و
+
+143
+00:11:50,660 --> 00:11:55,500
+هاملتون circle نعم إذا كان ماضينا مثلا أنه في نقاط
+
+144
+00:11:58,490 --> 00:12:02,450
+بتسقط النظرية بالكامل النظرية تتحقق لما أقولك
+
+145
+00:12:02,450 --> 00:12:07,290
+اتنين فقط odd vertices معينة بتلاقي ال oiler path
+
+146
+00:12:07,290 --> 00:12:13,930
+كلهم even vertices او even degree معينة بتلاقي ال
+
+147
+00:12:13,930 --> 00:12:18,930
+oiler circuits طيب ..الان لو لجيت .. هذه فيها ..
+
+148
+00:12:18,930 --> 00:12:25,150
+لجيت فيها خمسة اتنين منهم odd و تلاتة even ال path
+
+149
+00:12:25,150 --> 00:12:29,200
+موجود لكن ال circuit مش موجودةهذا المفروض منه يعني
+
+150
+00:12:29,200 --> 00:12:33,480
+إذا لوجد ال circuit مش ضروري مش هتلاقي البعض وإذا
+
+151
+00:12:33,480 --> 00:12:36,700
+لوجد البعض مش هتلاقي ال circuit لأنه في بينهم
+
+152
+00:12:36,700 --> 00:12:42,640
+تبعات في ال definition ال hamilton path إيش بيقول؟
+
+153
+00:12:42,640 --> 00:12:46,500
+لاحظوا إيش كان ال oiler في مركز الشباب containing
+
+154
+00:12:46,500 --> 00:12:55,270
+every edge containing every edge تمام؟هاملتون لما
+
+155
+00:12:55,270 --> 00:12:59,890
+جاء تكلم قال لا يا عمي انا انا بدى اعرف اذا قدرنا
+
+156
+00:12:59,890 --> 00:13:08,250
+نوجد مسار بيحتوي على كل ال vertices كل
+
+157
+00:13:08,250 --> 00:13:13,610
+ال vertices في دورة واحدة لاحظ هو اكد ان انا عديت
+
+158
+00:13:13,610 --> 00:13:23,080
+two definitions ال path بدمر في كل النقاطوالآن
+
+159
+00:13:23,080 --> 00:13:26,640
+تسقط معنى الـ path بالمعنى الحرفي على خلال الـ
+
+160
+00:13:26,640 --> 00:13:33,300
+walk وبتكلم الآن إن هذا بتجيبه في مسار واحد، عارف
+
+161
+00:13:33,300 --> 00:13:35,400
+إيش أنا في مسار واحد؟ يعني أنا غالباً مش هارجي
+
+162
+00:13:35,400 --> 00:13:41,460
+عايش، مش هارجي على النقطة مرة تانية تعالى نشوف ال
+
+163
+00:13:41,460 --> 00:13:44,320
+vintage و الhexagon الرسمات اللي موجودة هنا هي
+
+164
+00:13:44,320 --> 00:13:49,230
+الشكل الخماسي والشكل السوداسيالان كمشكات الخماسي
+
+165
+00:13:49,230 --> 00:13:54,850
+موجود واحد اتنين ثلاثة تمام؟ الان ال author .. او
+
+166
+00:13:54,850 --> 00:13:59,950
+عفوا ال Hamilton path هو عبارة عن مسار بيحتوي على
+
+167
+00:13:59,950 --> 00:14:04,710
+كل النقاط في لفة واحدة اللي هو انا محدد لك ايه
+
+168
+00:14:04,710 --> 00:14:05,830
+باللون الأحمر بدأت من هنا
+
+169
+00:14:18,550 --> 00:14:24,390
+إذا وقفت لحد الـ hand، ميلاده غيبار، مصبور؟ و
+
+170
+00:14:24,390 --> 00:14:30,750
+سكرته، أصبح circuit، مصبور؟ تسيبه مفتوح ميلاده و
+
+171
+00:14:30,750 --> 00:14:36,340
+تتكلم على مين؟ على باهسكت و أتكلم على circuit طب
+
+172
+00:14:36,340 --> 00:14:40,000
+circuit و لا cycle أسميها هو سماها circuit ليش؟
+
+173
+00:14:40,000 --> 00:14:44,640
+لأن كل الجسور اللي فيها جسور مختلفة كل الجسور اللي
+
+174
+00:14:44,640 --> 00:14:48,740
+فيها جسور مختلفة السؤال اللي بيطرح نفسه هل هو مسار
+
+175
+00:14:48,740 --> 00:14:55,020
+واحد اللي موجود حقنا لأ ابدأ نقطة بداية تانية تمام
+
+176
+00:14:55,020 --> 00:14:58,880
+ابدأ من هنا مش
+
+177
+00:14:58,880 --> 00:15:03,580
+هيكون في عندك مشكلةبالضبط كل مطبخ ستقدر تديك مسار
+
+178
+00:15:03,580 --> 00:15:09,520
+مختلف هدف
+
+179
+00:15:09,520 --> 00:15:13,040
+الشكل الخماسي والشكل السلاسي هذا الشكل هو نفس
+
+180
+00:15:13,040 --> 00:15:16,400
+الشكل فانا قلتلك عليه two different paths two
+
+181
+00:15:16,400 --> 00:15:21,500
+different hamilton paths أصبح الأخضر والأزرق لاحظ
+
+182
+00:15:21,500 --> 00:15:30,990
+بمجرد أن هذه الأشيرة بتكلم علي بقى سكت الخطبتكلم
+
+183
+00:15:30,990 --> 00:15:36,350
+على circuit واضح الأمر يا شباب أه؟ تمام خلّيني
+
+184
+00:15:36,350 --> 00:15:42,770
+ننتقل لنقطة أهم من ال ILR و ال Hamilton في موضوع
+
+185
+00:15:42,770 --> 00:15:47,890
+ال graphs كل graphs اللي أسميها سابقا الشباب كانت
+
+186
+00:15:47,890 --> 00:15:52,110
+undirected graph إيش يعني undirected؟ غير مباشرة
+
+187
+00:15:52,110 --> 00:15:58,530
+أو غير موجهة undirected غير موجهة
+
+188
+00:16:02,190 --> 00:16:09,790
+عندما أقول a,b,c,d هل
+
+189
+00:16:09,790 --> 00:16:15,890
+هناك طريق من a إلى b؟ موجود، فمن b إلى a؟ موجود،
+
+190
+00:16:15,890 --> 00:16:20,930
+لماذا؟ لأنه لا يوجد سهم يحدد الاتجاه وعندما كنا
+
+191
+00:16:20,930 --> 00:16:28,470
+نمثل هذا الجراف، كنت أقول إن v هي مجموعة النقاط a
+
+192
+00:16:28,470 --> 00:16:34,550
+,b,cو D مظبوط و مجموعة ال ديسور ايش كانت تساوي
+
+193
+00:16:34,550 --> 00:16:44,330
+الشباب A B B C C و D و A D او دي او دي ايه مش قضية
+
+194
+00:16:44,330 --> 00:16:53,150
+كتير او A C مظبوط يعني او A C لان ماكانش تفرج
+
+195
+00:16:53,150 --> 00:16:58,530
+معايا اكتب B C ولا اكتب C B مظبوط اكتب A D ولا D A
+
+196
+00:16:59,590 --> 00:17:03,470
+ليش؟ لأنه انخط الجسر موجود بين نقطين، يعني أنه
+
+197
+00:17:03,470 --> 00:17:07,630
+مسموح يتحرك بين اتجاهين.باقلهم في الـdirected
+
+198
+00:17:07,630 --> 00:17:12,650
+graph، هذا الكلام صحيح، بيصير الحركة باتجاه السهم
+
+199
+00:17:12,650 --> 00:17:17,170
+فقط، عشان هيك اسمه directed graph، directed أو
+
+200
+00:17:17,170 --> 00:17:21,230
+direct graph، وفي ال direct graph الفرق بينه و بين
+
+201
+00:17:21,230 --> 00:17:24,490
+ال undirected graph، انه انا بدي اكتر مجموعة
+
+202
+00:17:24,490 --> 00:17:31,010
+الجسور على شكل أزواج مرتبة،و احنا بنعرف في الزوج
+
+203
+00:17:31,010 --> 00:17:39,690
+المرتب XY لا تساوي YX أصبت؟ وبالتالي انا ببيعصير
+
+204
+00:17:39,690 --> 00:17:45,890
+اتكلم حسب اتجاه السهم بالرسمة هذه هل في طريق من A
+
+205
+00:17:45,890 --> 00:17:49,750
+ل D؟
+
+206
+00:17:49,750 --> 00:17:56,750
+ليس مجال انا بدي اتبع عصير اتبع السهم هل من ال A
+
+207
+00:17:56,750 --> 00:18:03,780
+ممكن اصل ال D؟لأ مافيش مجال وبالتالي بصير انا بشغل
+
+208
+00:18:03,780 --> 00:18:09,020
+عالمين حسب الأسهم اللي موجودة عندى كمان مرة بنقول
+
+209
+00:18:09,020 --> 00:18:12,040
+في ال directed graph أو في ال direct graph بدنا
+
+210
+00:18:12,040 --> 00:18:17,300
+نصير نقطة للجسور بأزواج مرتبة النقطة الأولى في
+
+211
+00:18:17,300 --> 00:18:22,100
+الزواج المرتبة بتمثل starting vertex نقطة البداية
+
+212
+00:18:22,100 --> 00:18:26,720
+والنقطة التانية بتمثل ال end vertex أو ال target
+
+213
+00:18:26,720 --> 00:18:27,300
+vertex
+
+214
+00:18:32,420 --> 00:18:39,760
+في موضوع الـ Undirected Graph كنت بتكلم على الجوار
+
+215
+00:18:39,760 --> 00:18:43,600
+قلنا إنه بتكون فيه عندى نقاطين متجاورتين لمّا
+
+216
+00:18:43,600 --> 00:18:49,140
+بيكون فيه بينهم جسم يعني بقول من النقاط المجاورة
+
+217
+00:18:49,140 --> 00:18:54,620
+للـD هي كل النقاط اللي بتلتق معاها مع جسور A و B و
+
+218
+00:18:54,620 --> 00:18:59,140
+C مصدوق احمد؟ من النقاط اللي مجاورة للـB
+
+219
+00:19:01,760 --> 00:19:09,520
+A و D من النقاط المجاورة للـC A و D و هكذا طيب لكن
+
+220
+00:19:09,520 --> 00:19:13,440
+مع ال Direct Graph بقلت أتكلم عليه الـJson
+
+221
+00:19:13,440 --> 00:19:18,920
+Vertices أتكلم عليه Terminal Vertices اللي أنا
+
+222
+00:19:18,920 --> 00:19:22,700
+رايح له من ال Target Vertices من ال Terminal تبعت
+
+223
+00:19:22,700 --> 00:19:29,820
+الـDA و B و C بناء على السهم من ال term اللي تبعت
+
+224
+00:19:29,820 --> 00:19:37,220
+ال A؟ C لحالها بس باتجاه السهم فقط B من ال term
+
+225
+00:19:37,220 --> 00:19:42,840
+اللي تبعت ال B؟ ال A من ال term اللي تبعت ال C؟
+
+226
+00:19:42,840 --> 00:19:53,400
+ماعناش تمام، تستجبل و لا تعطيش واضح الأمور؟ تمام
+
+227
+00:19:58,930 --> 00:20:02,130
+بدي اتكلم في الموضوع اسمه الـ Representation تمثيل
+
+228
+00:20:02,130 --> 00:20:06,190
+لـ Graph عشان انت تشتغل او تطبق برنامج بتعامل مع
+
+229
+00:20:06,190 --> 00:20:10,410
+الـ Graph بيلزمك اتمثل لـ Graph هذا في شغل سهلة
+
+230
+00:20:10,410 --> 00:20:13,670
+تقدر تتعامل مع الكمبيوتر ببساطة والتمثيل هذا هيكون
+
+231
+00:20:13,670 --> 00:20:19,370
+من خلال مصفوفة الجوار مصفوفة بنسميها مصفوفة الجوار
+
+232
+00:20:19,370 --> 00:20:25,270
+مصفوفة بنسميها مصفوفة الجوار الآن في مصفوفة الجوار
+
+233
+00:20:25,270 --> 00:20:30,150
+هي عبارة عن مصفوفة مربعةماذا يعني مربعة؟ 1000xN
+
+234
+00:20:30,150 --> 00:20:35,690
+عدد الصفوف فيها يساوي عدد الأعمدة يساوي عدد النقاط
+
+235
+00:20:35,690 --> 00:20:41,350
+اللي موجودة في الرسمة يعني
+
+236
+00:20:41,350 --> 00:20:49,010
+لو أنا إجيت وقلت والله هذه الرسمة اللي عندي A
+
+237
+00:20:49,010 --> 00:20:58,570
+,B,C وبدي أمثلها حوال أعمى المصفوفة كم حجبها؟تلاتة
+
+238
+00:20:58,570 --> 00:21:03,730
+في تلاتة تلاتة في تلاتة ليش تلاتة؟ لأن عدد النقاط
+
+239
+00:21:03,730 --> 00:21:07,110
+اللي موجودة عندي تلاتة و أهم شغلة في التمثيل يا
+
+240
+00:21:07,110 --> 00:21:11,390
+شباب تنتبه للكلام اللي انا بدي أقوله تلت أعمدة
+
+241
+00:21:11,390 --> 00:21:16,070
+هيمثل تلت نقاط و تلت صفوف كذلك هيمثل تلت نقاط انا
+
+242
+00:21:16,070 --> 00:21:24,170
+الآن الصف الأول A D C الأعمدة الصفوف هياخد نفس
+
+243
+00:21:24,170 --> 00:21:26,650
+الترتيب اللي عملته فوق
+
+244
+00:21:45,010 --> 00:21:50,890
+الترتيب اللي انا اعتمده هو نفسه يعتمد على الصفوف
+
+245
+00:21:51,910 --> 00:21:54,930
+بنفعش كل واحد اشتغل فيه ترتيب .. عفوا .. بنفعش
+
+246
+00:21:54,930 --> 00:21:58,810
+استخدم كل ترتيب مختلف مع كل الصفوف .. من كل الصفوف
+
+247
+00:21:58,810 --> 00:22:03,530
+والأعمدة تمام هذا رقم واحد الآن اتنين ايه بتروح
+
+248
+00:22:03,530 --> 00:22:08,290
+تساوي؟ ايش ال values اللي موجودة؟ على ال basic
+
+249
+00:22:08,290 --> 00:22:12,730
+graph بتكلم على binary value يا صفر يا واحد يعني
+
+250
+00:22:12,730 --> 00:22:20,390
+مافي مسار او مافيش من C ل C؟ Zero بمثلها ب Zero من
+
+251
+00:22:20,390 --> 00:22:21,390
+C ل D؟
+
+252
+00:22:28,610 --> 00:22:35,410
+من B ل B صفر
+
+253
+00:22:35,410 --> 00:22:47,070
+من B ل A واحد من A ل C Zero من A ل B واحد و من A ل
+
+254
+00:22:47,070 --> 00:22:54,030
+C Zeroهذه المصفوفة بنسميها مصفوفة الجوار اللى تمثل
+
+255
+00:22:54,030 --> 00:22:57,810
+ال graph البسيط اللى عندناها تمثل ال graph البسيط
+
+256
+00:22:57,810 --> 00:22:59,010
+اللى عندناها
+
+257
+00:23:01,170 --> 00:23:05,610
+الـ Graph هذا أنا بقدر أصل من خلاله أو أتعرف هل في
+
+258
+00:23:05,610 --> 00:23:08,530
+connection ولا مافيش لو أنا إجيت إنسان اللي قلت
+
+259
+00:23:08,530 --> 00:23:12,490
+الرسم هنا و إجيت سألت هل في طريق ما بين النقطة A
+
+260
+00:23:12,490 --> 00:23:16,770
+واحد من A ل C باجي مباشرة و أين الصف اللي في A؟
+
+261
+00:23:16,770 --> 00:23:21,350
+هايه و أين ال C؟ هايها Zero يعني مافيش طريق، مافيش
+
+262
+00:23:21,350 --> 00:23:28,810
+جسر طيب، من B ل A؟ هاي B وهي ال A، واحد، فيه
+
+263
+00:23:29,930 --> 00:23:33,870
+وبالتالي هذه المصحوفة هي اللي مثلت ال graph أي
+
+264
+00:23:33,870 --> 00:23:36,870
+ماوجد عندها لو انا بدي اكبر ال graph كمان شوية
+
+265
+00:23:36,870 --> 00:23:42,530
+خليه أصعب
+
+266
+00:23:42,530 --> 00:23:46,010
+ABCD
+
+267
+00:23:59,600 --> 00:24:14,360
+المصفوف اللى هستخدمه ايه اربع فاربع ABCD
+
+268
+00:24:14,360 --> 00:24:18,120
+ABCD
+
+269
+00:24:18,120 --> 00:24:21,660
+انت حروف زى ما قلنا فى الترتيب لكن الترتيب اللى
+
+270
+00:24:21,660 --> 00:24:27,060
+بتعتمده فى الصفوف هو نفسه بتعتمده مع الأعمدة من A
+
+271
+00:24:27,060 --> 00:24:37,410
+ل A0 من A ل B؟ واحد A ل C؟ صفر A ل D؟ واحد B ل A؟
+
+272
+00:24:37,410 --> 00:24:48,430
+واحد صفر ل C؟ واحد ل D واحد من C ل A؟ صفرمن C ل B،
+
+273
+00:24:48,430 --> 00:24:53,330
+واحد، من C ل C، صفر، ومن C ل D، واحد، من D ل A،
+
+274
+00:24:53,330 --> 00:25:01,850
+واحد، من D ل B، واحد، من D ل C، واحد، وصفر، من D ل
+
+275
+00:25:01,850 --> 00:25:06,730
+D، صفر. الآن يا شباب، في عندنا ملاحظة مهمة جدا في
+
+276
+00:25:06,730 --> 00:25:11,030
+موضوع الـ Graph عاصر القطر الرئيسي، Zero
+
+277
+00:25:16,100 --> 00:25:20,400
+بس اصبر شوية .. اصبر شوية .. لما انا بتكلم على
+
+278
+00:25:20,400 --> 00:25:26,980
+simple graph عناصر القطر الرئيسي صفر، ليش؟ لأن
+
+279
+00:25:26,980 --> 00:25:30,680
+مافيش loop، مافيش .. عندي loop، مصبوط، لو فيه
+
+280
+00:25:30,680 --> 00:25:33,740
+دائرة، بصير .. سمناها ب zero graph احنا، مصبوط ولا
+
+281
+00:25:33,740 --> 00:25:38,020
+لا؟ ال basic graph مافيش عناصر المصحوفة فيه أو
+
+282
+00:25:38,020 --> 00:25:43,580
+عناصر القطر الرئيسي فيه صفرهذه واحد اتنين المصحوفة
+
+283
+00:25:43,580 --> 00:25:48,080
+لل basic graph متطابقة شو يعني متمثل او متطابقة لو
+
+284
+00:25:48,080 --> 00:25:55,280
+أخدت المثلثين هيك و قبلتهم على بعض فيها aij تساوي
+
+285
+00:25:55,280 --> 00:26:05,840
+aji الواحد
+
+286
+00:26:05,840 --> 00:26:17,050
+اتنين تساوي اتنين واحدE12 هي تساوي E21 E32 هي
+
+287
+00:26:17,050 --> 00:26:25,730
+تساوي E23 هي متماثلة بنسميها symmetric matrix
+
+288
+00:26:35,110 --> 00:26:40,150
+هذا نفس الكلام الموجود عندي هنا لانه basic graph
+
+289
+00:26:40,150 --> 00:26:44,650
+إذا ال graph اللي عندي هذا صار بيسيدو graph إيش
+
+290
+00:26:44,650 --> 00:26:50,470
+يعني بيسيدو graph؟ يعني صار في عندي loop أو
+
+291
+00:26:50,470 --> 00:26:55,030
+multiple edge ال
+
+292
+00:26:55,030 --> 00:27:02,530
+بيسيدو graph يعني إما في عندي loop أو multipleماذا
+
+293
+00:27:02,530 --> 00:27:06,670
+يعني؟ ايش اللي بيغير في الرسمة أو في المصفوفة؟
+
+294
+00:27:06,670 --> 00:27:14,690
+هتبطل 01، هتبطل 01، تمام؟ هتصير من الـD لـC 2، وين
+
+295
+00:27:14,690 --> 00:27:23,360
+DC؟ هذي C و دي D، هتصير 2ومن C ومن D لـ C برضه
+
+296
+00:27:23,360 --> 00:27:27,560
+اتنين هتبقى المصفوفة متماتلة ومش بس هيك هتصير
+
+297
+00:27:27,560 --> 00:27:31,680
+عناصر القكر الرئيسي بطل صفر لإن أصار في عندك يسر
+
+298
+00:27:31,680 --> 00:27:38,260
+من D لB أصارت في عندك واحد وبهيك صرت أنا بقدر أقول
+
+299
+00:27:38,260 --> 00:27:43,860
+كتالة إذا أنا شفت عناصر القكر الرئيسي لا تساوي صفر
+
+300
+00:27:44,630 --> 00:27:48,150
+أو واحد من عناصر قطر الرئيسي لا تساوي صفر ما يعتبر
+
+301
+00:27:48,150 --> 00:27:51,310
+ان عندي Loop في عندي Loop Edge موجود في الرسمة
+
+302
+00:27:51,310 --> 00:27:57,250
+طبعا؟ طيب، وإذا شوفت عناصر أكتر من واحد أو أكبر من
+
+303
+00:27:57,250 --> 00:28:00,230
+واحد في Value ما يعتبر أن عندي Multiple Edge موجود
+
+304
+00:28:00,230 --> 00:28:03,490
+وين؟ بالرسم ما يعتبر أن عندي Multiple Edge موجود
+
+305
+00:28:03,490 --> 00:28:08,350
+في الرسم الآن، بما أن أنا اتكلمت على Undirected
+
+306
+00:28:08,350 --> 00:28:11,990
+Graph بدي أعمل representation بنفس الكيفية، بس إيش
+
+307
+00:28:11,990 --> 00:28:17,400
+الفرق؟إنها مش هتكون Symmetric الآن في ال Directed
+
+308
+00:28:17,400 --> 00:28:32,020
+Graph لو أنا ادويت لك همين ال Graph هان Directed
+
+309
+00:28:32,020 --> 00:28:40,240
+Graph يعني الشباب بمشي مع مين؟ مع ال Sam A,
+
+310
+00:28:40,280 --> 00:28:52,870
+B, C, Dوانا بدي امثل المصفوفة الآن هي المصفوفة a b
+
+311
+00:28:52,870 --> 00:29:00,630
+c d a b c d هتختلف
+
+312
+00:29:00,630 --> 00:29:05,090
+تماما عن المصفوفة اللي هان هتبقى symmetric لان انا
+
+313
+00:29:05,090 --> 00:29:09,010
+بدي امشي من وين يا حسن السهل لان في الرسم هان من a
+
+314
+00:29:09,010 --> 00:29:19,690
+ل a صفر من a ل bمافيش ايه صفر من a ل c واحد ومن a
+
+315
+00:29:19,690 --> 00:29:29,430
+ل d واحد من b ل a واحد من b ل b صفر من b ل c صفر
+
+316
+00:29:29,430 --> 00:29:41,010
+من b ل d صفر من c ل a صفر من
+
+317
+00:29:41,010 --> 00:29:49,220
+c ل bو احد من C ل C صفر من C ل D واحد من D ل A صفر
+
+318
+00:29:49,220 --> 00:29:56,300
+من D ل D صفر من D ل C صفر من D ل D صفر و لو أطلعنا
+
+319
+00:29:56,300 --> 00:30:02,180
+في عناصر القطر الرئيسي أصفر ليس فيها مشكلة لأنها
+
+320
+00:30:02,180 --> 00:30:07,040
+basic graph لكنها ليست symmetric هي ال value هذه
+
+321
+00:30:09,490 --> 00:30:16,910
+هذه A1 أربعة وهذه A4 واحد يعني لو
+
+322
+00:30:16,910 --> 00:30:20,910
+أنا شُفت ال graph أو شُفت المصفوفة بصير أقدر أحدد
+
+323
+00:30:20,910 --> 00:30:24,510
+شو أبقى بيعت ال graph هل هو precedo graph ولا
+
+324
+00:30:24,510 --> 00:30:29,150
+direct graph ومش بس هيك بقدر أرسمه بغض النظر إيش
+
+325
+00:30:29,150 --> 00:30:33,870
+كان بقدر أرسم ال graph بغض النظر إيش كان مابيجي و
+
+326
+00:30:33,870 --> 00:30:40,700
+أقولك هاي عندك أربع لقات أربع لقاتوهذه العلاقات
+
+327
+00:30:40,700 --> 00:30:44,680
+الموجودة بينهم يعني هل يوجد جسر او جسرين؟ هل يوجد
+
+328
+00:30:44,680 --> 00:30:48,320
+لوب او لا لوب؟ هل باتجاه واحد او باتجاهين؟
+
+329
+00:30:48,320 --> 00:30:51,760
+وبالتالي تستطيع ترسم من كرسمة تبعك وهكذا يحصل في
+
+330
+00:30:51,760 --> 00:30:54,600
+برانج الخرايق اللي يحصل على الجوالات وعلى اللابتوب
+
+331
+00:30:54,600 --> 00:31:00,490
+كل هكذا يحصلهي تمثل المنطقة مجموعا من مين؟ مجموعا
+
+332
+00:31:00,490 --> 00:31:05,130
+من النقاط و الطرق المعرفة بينهم هي بتمثل الجسور و
+
+333
+00:31:05,130 --> 00:31:08,490
+كل ما بتتحرك السيارة أو ال mobile عفوا و بحدد
+
+334
+00:31:08,490 --> 00:31:11,310
+الموبايل الجديد بال GPS شو روح بساوي؟ بروح بعمل
+
+335
+00:31:11,310 --> 00:31:15,610
+shift للنقاط يعني دايما بعمل زيوبة الخريطة أو بزغر
+
+336
+00:31:15,610 --> 00:31:19,730
+المصفوفة عشان تتمثل حسب العرض أو حجم العرض اللي
+
+337
+00:31:19,730 --> 00:31:24,270
+موجود عندك anyway في الآخر المصفوفة دي بتمثل إيش؟
+
+338
+00:31:24,530 --> 00:31:30,290
+بتمثل Graph بشكل صحيح ومناسب ومناسب جدا في أي سؤال
+
+339
+00:31:30,290 --> 00:31:33,430
+يا شباب في تعريف المصفوف هنا؟ سواء كانت Directly
+
+340
+00:31:33,430 --> 00:31:37,730
+Graph او لا؟
+
+341
+00:31:37,730 --> 00:31:44,470
+okay
+
+342
+00:31:44,470 --> 00:31:50,530
+بدنا نروح ننتقل لموضوع shortest path في shortest
+
+343
+00:31:50,530 --> 00:31:56,340
+pathأنا من أهم التطبيقات تبع ال graphs اللي هي
+
+344
+00:31:56,340 --> 00:32:00,380
+الوصول بين ال two points بأقصر الطرق الوصول ال two
+
+345
+00:32:00,380 --> 00:32:05,460
+points أو المسافة بين ال two points بأقصر الطرق طب
+
+346
+00:32:05,460 --> 00:32:09,580
+احنا سابقا في كل graphs ماكانش في عيننا شغل تدلل
+
+347
+00:32:09,580 --> 00:32:15,650
+عليهالـ Cost التكلفة لكي نتكلم عن القصر لاحظ بجينا
+
+348
+00:32:15,650 --> 00:32:19,210
+نكتب الخط أو نرسم الخط بدون ولا حاجة اللي هيتغير
+
+349
+00:32:19,210 --> 00:32:23,350
+عندي في ال graph لما أتكلم عن ال shortest path بدو
+
+350
+00:32:23,350 --> 00:32:28,350
+يصير كل خط مربوط ومحسوب عليه التكلفة تبعته كل خط
+
+351
+00:32:28,350 --> 00:32:32,990
+بدو ينحسب عليه التكلفة تبعته السؤال اللي يبرح نفسه
+
+352
+00:32:32,990 --> 00:32:38,570
+هل التكلفة تكلفة نقدية؟ لأ مش ضروري ممكن التكلفة
+
+353
+00:32:38,570 --> 00:32:44,360
+كل وقت؟تمام؟ مسافة .. جعد .. أي تكلفة بدها تكون ..
+
+354
+00:32:44,360 --> 00:32:47,580
+أنا ما بعني لشو وحدة التكلفة اللي موجودة .. بس في
+
+355
+00:32:47,580 --> 00:32:52,160
+الآخر الرقم اللي بيكتب فوق الجسر هو مقدار التكلفة
+
+356
+00:32:52,160 --> 00:32:55,560
+.. بليونة المتعرف عليها .. لإن أنا ممكن أقل 650
+
+357
+00:32:55,560 --> 00:33:00,440
+شكل .. مثلا .. تكلفة السفر من غزة لرمالة .. بينما
+
+358
+00:33:00,440 --> 00:33:05,230
+القصة كلفتها 700 شكل .. مثلا ..ممكن تقول انك بتاخد
+
+359
+00:33:05,230 --> 00:33:16,570
+650 مل بنزين او سولار مثلا بتاخد 650 دقيقة حسب فكل
+
+360
+00:33:16,570 --> 00:33:21,510
+unit بتفرق لكن في شغل مش كاركة انا هان لما بتكلم
+
+361
+00:33:21,510 --> 00:33:27,570
+على ال shortest pathبتكلم على مسار بأقل تكلفة ..
+
+362
+00:33:27,570 --> 00:33:32,690
+بأقل تكلفة .. أقل value مرسوم على مين؟ على الخط
+
+363
+00:33:32,690 --> 00:33:36,430
+اللي موجود عندهان، تمام؟ ماليش دخل بإيش اليونيت،
+
+364
+00:33:36,430 --> 00:33:38,650
+أقل تكلفة ممكنة
+
+365
+00:33:40,900 --> 00:33:45,060
+من أهم الـ Algorithms اللي تستخدم في موضوع
+
+366
+00:33:45,060 --> 00:33:48,160
+shortest path و أبسطها اللي هو الـ Dijkstra
+
+367
+00:33:48,160 --> 00:33:51,200
+Algorithm
+
+368
+00:33:51,200 --> 00:33:55,600
+فالـ graph زي هذا .. هلاقيته عشان أوضح لك الصورة،
+
+369
+00:33:55,600 --> 00:34:00,100
+الآن أنا بدي أتحرك ما بين نقمتين، بنفعش أقول أنا
+
+370
+00:34:00,100 --> 00:34:04,160
+والله مش عارف ال target تبعتي، لأن إذا أنا ماعرفتش
+
+371
+00:34:04,160 --> 00:34:07,950
+ال targetمش هقدر أروح ما بدر أروح، مش هقدر أرسم
+
+372
+00:34:07,950 --> 00:34:12,310
+المسار اللي أنا بدياه، كذلك على الرسم السابق هنا،
+
+373
+00:34:12,310 --> 00:34:15,850
+لما أنا بدي أقول بدي أروح من غزة لقدس، إيش
+
+374
+00:34:15,850 --> 00:34:20,910
+المسارات اللي يجب أن تدخل في المقارنة؟ الطريق
+
+375
+00:34:20,910 --> 00:34:25,570
+المباشر أو الطريق أبو المرور بالخليل؟ بنفعش أقول
+
+376
+00:34:25,570 --> 00:34:28,190
+بدي أروح على ماما و بعدين بدي أروح على قدس، لأنه
+
+377
+00:34:28,190 --> 00:34:33,190
+حسب المادة اللي عندي هنا، مافيش طريقتمام؟ وبالتالي
+
+378
+00:34:33,190 --> 00:34:38,150
+اختيار ال shortest path بيكون تبع ليش هل المسار
+
+379
+00:34:38,150 --> 00:34:42,290
+موجود في الأول من ال start point ل ال end point و
+
+380
+00:34:42,290 --> 00:34:46,270
+بعدين ببدأ اقارن ايش التكلفة تعالى نشوف الرسم هاي
+
+381
+00:34:46,270 --> 00:34:48,930
+اللي عندي ايش في الرسم هاي اللي بيقول ايه؟ بيقول
+
+382
+00:34:48,930 --> 00:34:54,190
+حسبلي او هات ال shortest path عشان اجيب ما بين او
+
+383
+00:34:54,190 --> 00:34:58,570
+اقفل ال vertex ايه؟ يعني هذا ال target تبعتي from
+
+384
+00:34:58,570 --> 00:35:09,890
+the vertexيعني هو بدى يتحرك من ال A لل E يعني
+
+385
+00:35:09,890 --> 00:35:20,210
+هان نقطة البداية و بدى يجي من اين؟ بدى يجي هن اذا
+
+386
+00:35:20,210 --> 00:35:29,490
+استيقظ من هنا 100% الان كان مسار موجود كتير abdfe
+
+387
+00:35:30,180 --> 00:35:48,220
+A B D A A B D C A مظبوط؟ A B C A A C B D F A A C B
+
+388
+00:35:48,220 --> 00:35:55,240
+D A A لحظة شوية A C مافيش خلاص ال B خلصت مانفعش
+
+389
+00:35:55,240 --> 00:35:59,070
+اضحك دي كمان مرة مظبوط؟الان ايه لان اذا روحت على
+
+390
+00:35:59,070 --> 00:36:06,090
+دي كلمة مرة هتبرجحها هتبقى بالباب بصبع ايه ايه ايه
+
+391
+00:36:06,090 --> 00:36:08,510
+ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه
+
+392
+00:36:08,510 --> 00:36:10,510
+ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه
+
+393
+00:36:10,510 --> 00:36:10,530
+ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه
+
+394
+00:36:10,530 --> 00:36:12,090
+ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه ايه
+
+395
+00:36:12,090 --> 00:36:16,130
+ايه ايه ايه ايه ايه ايه ايه ايه ايه
+
+396
+00:36:16,130 --> 00:36:20,250
+ايه
+
+397
+00:36:20,250 --> 00:36:23,010
+ايه
+
+398
+00:36:23,340 --> 00:36:26,900
+بتروح تحسب التكلفة، من وين؟ على سبيل المثال،
+
+399
+00:36:26,900 --> 00:36:31,620
+التكلفة تبقى في المسار الأول A,B,D,F,E جداش
+
+400
+00:36:31,620 --> 00:36:38,240
+تكلفتها؟ أربعة، تسعة، خلصتاش، تلت ماشي المسار اللي
+
+401
+00:36:38,240 --> 00:36:48,860
+بعده، على سبيل المثال A,C,E ماشي تمام؟ بينما A,C,D
+
+402
+00:36:48,860 --> 00:36:50,980
+,E,D,E
+
+403
+00:36:53,730 --> 00:37:00,750
+تلاتة .. تمانية .. عشرة .. اه بيخدّيبهم كلهم طبعا
+
+404
+00:37:00,750 --> 00:37:04,610
+الميزة ان هو هذا الكلام مش انت اللي بتعمله هذا ال
+
+405
+00:37:04,610 --> 00:37:08,070
+algorithm هو ايش اللي بيساوي فيه بمر على المصفوفة
+
+406
+00:37:08,070 --> 00:37:13,010
+ال adjacent matrix الان لو انا بدي اعمل مصفوفة
+
+407
+00:37:13,010 --> 00:37:17,950
+الجواهر ليه ليش حاجة لها .. لل graph هذا .. ستة في
+
+408
+00:37:17,950 --> 00:37:23,030
+ستةستة و ستة، تمام؟ وش بقى ال C بتساوي؟ بتقول
+
+409
+00:37:23,030 --> 00:37:29,050
+والله الآن من A ل B و من A ل C، مع الخيارات
+
+410
+00:37:29,050 --> 00:37:33,590
+الوصولي لل E مافيش عندي خط مباشر، في عندي خط مع
+
+411
+00:37:33,590 --> 00:37:39,090
+مين؟ مع ال B و مع ال C، بروح بعد هيك، بشوف ال C
+
+412
+00:37:39,090 --> 00:37:44,740
+وين بتوديني؟وبشوف ال B وين بتوديني وبنقل بمشي مع
+
+413
+00:37:44,740 --> 00:37:47,280
+المساعد اللي موجود عندي هنا فده عشان ايه اسمه
+
+414
+00:37:47,280 --> 00:37:50,740
+algorithm هو عبارة عن اللي بفحص هالطريق موجود او
+
+415
+00:37:50,740 --> 00:37:56,060
+لا و بكمل لكن هذا هو فكرة ال algorithm هذه فكرة ال
+
+416
+00:37:56,060 --> 00:38:02,020
+algorithm بعد ما انت بتذكر المساعد تمام؟ ايش بروح
+
+417
+00:38:02,020 --> 00:38:08,280
+بنساوي؟ بنحسب التكلف على كل واحد فيه كمان مرة A,B
+
+418
+00:38:08,280 --> 00:38:15,850
+,D,F,E جدش قولنا A,B؟أربعة PD خمسة هي تسعة DF ستة
+
+419
+00:38:15,850 --> 00:38:24,830
+هي خمستاشر وتلاتة تمانتاشر بينما ACE جدش تكلفتها
+
+420
+00:38:24,830 --> 00:38:34,810
+هنا تين وهنا عشرة معاشر قلنا ACE BDE
+
+421
+00:38:40,680 --> 00:38:47,620
+وبالتالي انا ال shortest ده التبعي هيو تمام؟ بناء
+
+422
+00:38:47,620 --> 00:38:52,320
+على إيش؟ بناء على التكلفة اللي موجودة على الخريطة
+
+423
+00:38:52,320 --> 00:38:57,280
+بقدرش أخترع من عندي أرقام أنا تمام؟ وإذا بتتذكر من
+
+424
+00:38:57,280 --> 00:39:01,960
+البداية قلتلك طول الجسم مابثرش معايا رسمته بين
+
+425
+00:39:01,960 --> 00:39:06,760
+مقطينها الجد و لا رسمته هيك مابفرجش كتير معايا
+
+426
+00:39:06,760 --> 00:39:11,330
+اللي بتفرج معايا إيش هي ال value اللي بيتمثلالجراف
+
+427
+00:39:11,330 --> 00:39:16,190
+عشان هيك يا شباب هانش بروح بنساوي احنا بنمثل
+
+428
+00:39:16,190 --> 00:39:23,210
+الجراف هذا ك connection كجراف بنحطه في مصفوفة بدأ
+
+429
+00:39:23,210 --> 00:39:29,910
+أعمل تخيل فقط بس المربع هذا عشان أوريك شغلة بسيطة
+
+430
+00:39:29,910 --> 00:39:34,450
+و ننهي من النقوة هاي الآن بدأ امثل الجراف هذا 4x4
+
+431
+00:39:34,450 --> 00:39:34,970
+مصبوط
+
+432
+00:39:40,000 --> 00:39:49,480
+ب و سي و دي و ايه ب سي دي ايه ب ب ب ب ب ب ب ب ب ب
+
+433
+00:39:49,480 --> 00:39:53,960
+ب ب ب ب
+
+434
+00:39:53,960 --> 00:39:55,340
+ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب
+
+435
+00:39:55,340 --> 00:40:00,120
+ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب
+
+436
+00:40:00,120 --> 00:40:01,140
+ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب
+
+437
+00:40:01,140 --> 00:40:02,260
+ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب
+
+438
+00:40:02,260 --> 00:40:02,260
+ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب
+
+439
+00:40:02,260 --> 00:40:02,260
+ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب
+
+440
+00:40:02,260 --> 00:40:02,260
+ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب
+
+441
+00:40:02,260 --> 00:40:09,280
+ب ب ب ب ب ب ب ب ب ب ب ب ب ب ب
+
+442
+00:40:09,280 --> 00:40:23,870
+ب ب بواحد صفر واحد الاخيرة صفر واحد واحد صفر بخرب
+
+443
+00:40:23,870 --> 00:40:27,430
+12 اللي
+
+444
+00:40:27,430 --> 00:40:30,430
+وراك مش مشكلة انت عارف ايش كنت لما انت كنت بتقول
+
+445
+00:40:30,430 --> 00:40:33,490
+كده الأرقام انا ماكنتش معاك كنت بطلع في الرقم بسمع
+
+446
+00:40:33,490 --> 00:40:37,450
+الرقم اللي انت بتقولهوبأتمنى على وين؟ على الرقم
+
+447
+00:40:37,450 --> 00:40:40,390
+المقابل اللي أنا بكتبه لإنه Symmetric Basic Graph
+
+448
+00:40:40,390 --> 00:40:45,130
+يعني Symmetric أصبت؟ تمام هاد احنا كنا بنسميها ال
+
+449
+00:40:45,130 --> 00:40:51,010
+Graph هاد الرسم فالمقابل كان في عندي مصفوفة تانية
+
+450
+00:40:51,010 --> 00:40:57,210
+بتنعمل اسمها ال Cost إيش المصفوفة؟ اللي هي التكلفة
+
+451
+00:40:57,210 --> 00:41:03,790
+بتحدد التكلفة وبنفس الترتيب اللي موجود هنا B C D E
+
+452
+00:41:03,790 --> 00:41:14,170
+BC D E الان هتكون undirected بغض النظر .. بغض
+
+453
+00:41:14,170 --> 00:41:17,290
+النظر عشان امثل ال graph كله كيف اجيب ال shortest
+
+454
+00:41:17,290 --> 00:41:21,930
+path لازم يكون ال graph عندى بمصفوفة و ال course
+
+455
+00:41:21,930 --> 00:41:27,210
+تبعته في مصفوفة عشان كل مسار انا برسمه اروح بدرحسم
+
+456
+00:41:27,210 --> 00:41:32,730
+ال course تبعتهو لما أكون دارحت نفس الفكرة أنه
+
+457
+00:41:32,730 --> 00:41:36,570
+مصفوفيان و مصفوفان التلتيان لازم تكون موجودات الان
+
+458
+00:41:36,570 --> 00:41:45,810
+B ل C واحد واحد B ل D خمسة B ل E صفر مافيش لانه
+
+459
+00:41:45,810 --> 00:41:51,670
+طريق الان B ل C من C ل B واحد من C ل C صفر من
+
+460
+00:41:51,670 --> 00:41:55,390
+الوينكي بتاوة واحدة هيها ال cost هيها تمام من C ل
+
+461
+00:41:55,390 --> 00:41:57,950
+D تمانية
+
+462
+00:42:00,230 --> 00:42:08,490
+ومن C إلى E؟ عشرة من D إلى B؟ خمسة، هذا التباخل من
+
+463
+00:42:08,490 --> 00:42:20,230
+D إلى C؟ تمانية صفر ومن D إلى E؟ اتنين الآن،
+
+464
+00:42:20,230 --> 00:42:27,810
+كمل، صفر، خمسة، واحد، صفر
+
+465
+00:42:32,390 --> 00:42:37,230
+هذه غلط كيف غلط هذه صفر أكيد هذه لازم تكون اتنين
+
+466
+00:42:37,230 --> 00:42:46,850
+هذه عشرة وهذه صفر لأن
+
+467
+00:42:46,850 --> 00:42:51,630
+المفروض هذا الصف هي اتنين عشرة صفر هي التماثل اللي
+
+468
+00:42:51,630 --> 00:42:55,190
+موجود عندها إذا ما الصفتين هدول موجودات سبت كل
+
+469
+00:42:55,190 --> 00:43:00,040
+بصحبة بقول هل في طريق وقدش تكلفتهبصير تبدأ عملياش
+
+470
+00:43:00,040 --> 00:43:05,480
+تراكمية من أجل الوصول على العناصر اللي موجودة
+
+471
+00:43:05,480 --> 00:43:10,340
+عندنا في
+
+472
+00:43:10,340 --> 00:43:14,620
+أن المصطلح الشجرة
+
+473
+00:43:14,620 --> 00:43:19,520
+ال tree هي عبارة عن special graph هي عبارة عن
+
+474
+00:43:19,520 --> 00:43:24,960
+special graph الشبكة ده كلها مصطلحات
+
+475
+00:43:29,870 --> 00:43:33,530
+Connected يعني كل النقاب اللي فيه متصلة، مافيش فيه
+
+476
+00:43:33,530 --> 00:43:38,350
+isolated point و إلا هتكونش three Undirected مافيش
+
+477
+00:43:38,350 --> 00:43:45,430
+أسهم، graph contains no circuits مافيش أي شغلة
+
+478
+00:43:45,430 --> 00:43:48,490
+مسكرة دايما كلاش مسارات مفتوحة، كل المسارات اللي
+
+479
+00:43:48,490 --> 00:43:50,210
+فيها مفتوحة
+
+480
+00:43:57,380 --> 00:44:00,280
+مافيش circuit ولا cycles؟ ماخلاص مافيش circuit
+
+481
+00:44:00,280 --> 00:44:03,920
+يعني مافيش closed walk مافيش closed trail، كلها
+
+482
+00:44:03,920 --> 00:44:07,280
+بيعتسم، لأن هذا الرسم، simple graph، simple graph،
+
+483
+00:44:07,280 --> 00:44:11,360
+simple graph، أي واحد فيهم بيمثل ال tree، كلنا
+
+484
+00:44:11,360 --> 00:44:15,020
+بنتكلم على ال tree وقلنا هذه كل حياتها بتمثل ال
+
+485
+00:44:15,020 --> 00:44:18,640
+trees، فكرة ال tree connected .. simple connected
+
+486
+00:44:18,640 --> 00:44:19,200
+graph
+
+487
+00:44:29,930 --> 00:44:33,650
+مفهوم ال circuit أن نقطة البداية تصير نقطة نهاية
+
+488
+00:44:33,650 --> 00:44:42,150
+وبالتالي لو انت طلعت بين أي نقطتين هتلاقي في عندك
+
+489
+00:44:42,150 --> 00:44:46,250
+مسار واحد فقطبالأي نقطين عشان تصللهم بما أنه مافيش
+
+490
+00:44:46,250 --> 00:44:49,410
+cross أو مافيش تقاطع بما أنك تتكلم أنك دائما في
+
+491
+00:44:49,410 --> 00:44:53,610
+مسار واحد بالنقطين لو أنت هنا وبالنكسة اللي هنا
+
+492
+00:44:53,610 --> 00:45:01,210
+مستحيل اللي غير تمر بالمسار هذا وفيه مش غيره تمام؟
+
+493
+00:45:01,210 --> 00:45:06,530
+وبذلك صارت في عندي أنا بتكلم على ال tree الآن بشكل
+
+494
+00:45:06,530 --> 00:45:11,800
+عام بقى ال treesاستخداماتها مهمة في الكمبيوتر
+
+495
+00:45:11,800 --> 00:45:15,960
+وبتشوف انت على سبيل المثال ال road folder تبع ال C
+
+496
+00:45:15,960 --> 00:45:19,940
+وD عندك على الجهاز storage هو بيمثل ال tree ال C
+
+497
+00:45:19,940 --> 00:45:23,660
+بتمثل ال road المجلدات اللي موجودة على ال C بتمثل
+
+498
+00:45:23,660 --> 00:45:27,040
+ال level الأول والميافات اللي موجودة تمثل ال
+
+499
+00:45:27,040 --> 00:45:29,560
+leaves اللي موجودة على ال level الأول بعد هيك
+
+500
+00:45:29,560 --> 00:45:35,870
+بتبدأ تتفرع بالشجرة اللي عندكلأن العروف في مصطلح
+
+501
+00:45:35,870 --> 00:45:40,370
+الـtrees لازم يكون فيها روت لأن مافيش شجرة طايرة
+
+502
+00:45:40,370 --> 00:45:45,430
+في الهوا ولا لا كل شجرة فيها جدر ثابت وواضح حتى
+
+503
+00:45:45,430 --> 00:45:50,310
+بالـ graph هذا الأمثل السابق هادول لو مافيش لازم
+
+504
+00:45:50,310 --> 00:45:54,550
+انت تختار واحد منهم يكون root أي واحد بينفع يكون
+
+505
+00:45:54,550 --> 00:45:59,770
+root ومع اختلاف ال root هتختلف شكل شجرة يعني لو
+
+506
+00:45:59,770 --> 00:46:03,860
+انا افترضت ان هذا هو ال root كمعهدهتصير الشجرة
+
+507
+00:46:03,860 --> 00:46:10,960
+هايها في عندي a و b are siblings اخوة هذا ليف و
+
+508
+00:46:10,960 --> 00:46:15,940
+هذا في عنده تفريحة لو انا اجيت اخدت هذه روت او
+
+509
+00:46:15,940 --> 00:46:20,760
+اخدت هذا روت هتختلف الشجرة لو اخدت هذا روت هتصير
+
+510
+00:46:20,760 --> 00:46:26,520
+في عنده تلت اولاد مظبوط three siblings و لو اخدت
+
+511
+00:46:26,520 --> 00:46:29,880
+هذا روت هتصير في عندها واحد فانت في الاخر في كل
+
+512
+00:46:29,880 --> 00:46:36,130
+three لازم يكون لهاRoot لازم يكون لها جذر هذه نفس
+
+513
+00:46:36,130 --> 00:46:41,530
+ال graph لكن ال root هنا A و ال root هنا B هاي ال
+
+514
+00:46:41,530 --> 00:46:51,970
+B لحظة ماخدتها root هاي شكل الشجرة اختلف تماما في
+
+515
+00:46:51,970 --> 00:46:57,810
+موضوع ال root انا بتكلم على parent و siblings
+
+516
+00:46:57,810 --> 00:47:02,560
+parent و siblingsالـ siblings اللي هم مين يا شباب؟
+
+517
+00:47:02,560 --> 00:47:08,480
+التفرعات اللي موجودة عندهم الآن ال بيرن تبعت ال a
+
+518
+00:47:08,480 --> 00:47:13,500
+بي ايه؟ و ال بيرن تبعت ال c ايه؟ معناته أنا باجي
+
+519
+00:47:13,500 --> 00:47:20,580
+بقول بي و سي are siblings .. siblings .. إخوة ..
+
+520
+00:47:20,580 --> 00:47:26,120
+تمام؟ ال بيرن تبعت ال e بي .. و ال بيرن تبعت ال d
+
+521
+00:47:26,120 --> 00:47:29,340
+بي .. معناته ال b و ال d .. ال d عفر و ال e
+
+522
+00:47:29,340 --> 00:47:29,660
+siblings
+
+523
+00:47:37,050 --> 00:47:40,650
+الان في عندى مصطلح الـ Leaf ال Leaf Leaf و
+
+524
+00:47:40,650 --> 00:47:46,610
+Internal Vertex في ال Leaf مين ال Leafs؟ C هي
+
+525
+00:47:46,610 --> 00:47:52,450
+النقطة اللى مافيش الا تفرعت بنسميها إيش؟ Leaf C E
+
+526
+00:47:52,450 --> 00:47:59,730
+و F C و E و F هدول إيش؟ Leafs أوراق الان دى إيه
+
+527
+00:47:59,730 --> 00:48:04,280
+بنسميها Internal Vertex أو Parent؟B Internal
+
+528
+00:48:04,280 --> 00:48:09,820
+Vertex او Parent لأن الـ B Parent للـ D والـ D
+
+529
+00:48:09,820 --> 00:48:16,700
+Parent للـ S Internal
+
+530
+00:48:16,700 --> 00:48:20,360
+يعني أن هناك اله بيرنت و هناك اله بيرنت و هناك اله
+
+531
+00:48:20,360 --> 00:48:20,520
+بيرنت و هناك اله بيرنت و هناك اله بيرنت و هناك اله
+
+532
+00:48:20,520 --> 00:48:21,820
+بيرنت و هناك اله بيرنت و هناك اله بيرنت و هناك اله
+
+533
+00:48:21,820 --> 00:48:25,560
+بيرنت و هناك اله بيرنت و هناك اله بيرنت و هناك اله
+
+534
+00:48:25,560 --> 00:48:26,960
+بيرنت و هناك اله بيرنت و هناك اله بيرنت و هناك اله
+
+535
+00:48:26,960 --> 00:48:26,960
+بيرنت و هناك اله بيرنت و هناك اله بيرنت و هناك اله
+
+536
+00:48:26,960 --> 00:48:26,960
+بيرنت و هناك اله بيرنت و هناك اله بيرنت و هناك اله
+
+537
+00:48:26,960 --> 00:48:29,940
+بيرنت و هناك اله بيرنت و هناك اله بيرنت و هناك اله
+
+538
+00:48:29,940 --> 00:48:34,250
+بيرنت و هناك اله بالان لما اتكلمنا عن ال sub graph
+
+539
+00:48:34,250 --> 00:48:37,890
+تتذكر ال sub graph هو عبارة عن جزء من ال graph ومع
+
+540
+00:48:37,890 --> 00:48:42,290
+ان ال tree هي graph فبقدر اتكلم على sub tree sub
+
+541
+00:48:42,290 --> 00:48:49,530
+tree هي شجرة فرعية يعني ال sub graph او ال sub
+
+542
+00:48:49,530 --> 00:48:53,910
+tree هي عبارة عن sub graph من ال treeهي ال بي هذا
+
+543
+00:48:53,910 --> 00:48:57,670
+هي أخدت الجزء هذا لوحده و لو أخدت الجزء هذا هيك
+
+544
+00:48:57,670 --> 00:49:00,790
+لحاله بمشي الحال و لو أخدت الجزء هذا هيك لحاله
+
+545
+00:49:00,790 --> 00:49:05,030
+بمشي الحال دائما لما اتكلمنا في ال sub graph قلنا
+
+546
+00:49:05,030 --> 00:49:08,030
+مجموعة ال vertices مجموعة جزئية من المجموعة
+
+547
+00:49:08,030 --> 00:49:11,690
+الأساسية و مجموعة الجسور مجموعة جزئية من مجموعة
+
+548
+00:49:11,690 --> 00:49:19,110
+الجسور الأساسية فهي اني مصطلح ال level اذا انا
+
+549
+00:49:19,110 --> 00:49:22,800
+أخدت ال AOC لحالة و قدر اقول عنها sub treeهو الـ
+
+550
+00:49:22,800 --> 00:49:26,240
+Subtree الـ A و الـ C لفهمك؟ اه اه لفهمك ايه الـ A
+
+551
+00:49:26,240 --> 00:49:29,480
+و الـ C الـ Subgraph و هو المشكلة في الموضوع ايه
+
+552
+00:49:29,480 --> 00:49:32,860
+الشرط بتاعنا ان ال vertices subset من ال vertices
+
+553
+00:49:32,860 --> 00:49:36,140
+ال A و ال C subset من المجموعة الكلية لنقاط و
+
+554
+00:49:36,140 --> 00:49:40,840
+الجسر اللي بينهم A و C subset من مجموعة الجسور
+
+555
+00:49:40,840 --> 00:49:46,670
+الكلية فهي Subtree الشرط عضو من نقاطك و نقاطكبس
+
+556
+00:49:46,670 --> 00:49:50,110
+عدد النقاب على الأقل بيكون تنتهي من التصلات لو انك
+
+557
+00:49:50,110 --> 00:49:55,630
+بتطبق بال letter A أصبت؟ أيوة فيه أن المصطلح ال
+
+558
+00:49:55,630 --> 00:49:59,510
+level المستوى ال road ده من ال level تبعته إيه؟
+
+559
+00:49:59,510 --> 00:50:03,410
+Zero و ال height أو ال depth تبعته ال letter E
+
+560
+00:50:03,410 --> 00:50:09,690
+بتمثل إيه؟ عدد الجسور ما بين ال road لحد آخر leaf
+
+561
+00:50:09,690 --> 00:50:15,110
+لحد أعمق leaf ال height ال A level zero B و C
+
+562
+00:50:15,110 --> 00:50:21,570
+level oneدى و ايه level 3 level 2 عفوا و اف level
+
+563
+00:50:21,570 --> 00:50:25,270
+3 جداش الـ depth جداش الخيط جداش ارتفاع الشجرة
+
+564
+00:50:25,270 --> 00:50:32,710
+واحد اتنين تلاتة تلات جسور بتقعد اطول الغموق موجود
+
+565
+00:50:32,710 --> 00:50:36,510
+عندك في الشجرة واحد اتنين تلاتة اللي هو ال maximum
+
+566
+00:50:36,510 --> 00:50:44,170
+level موجود عندك يعنى بال three هاي اتنين صفر واحد
+
+567
+00:50:46,030 --> 00:50:50,930
+مايغركاش يا شباب انه ممكن انا اروح اجسر الرسم هادى
+
+568
+00:50:50,930 --> 00:51:00,710
+واجيبك الافهام لو
+
+569
+00:51:00,710 --> 00:51:06,330
+انا جيت سألتك ايش ال level كبار ال F؟ بدك تعدى
+
+570
+00:51:06,330 --> 00:51:10,830
+الجسور اللى بينها و بين ال route تعدى الجسور لحد
+
+571
+00:51:10,830 --> 00:51:15,510
+ما تصل ال route و تصل ال level واحدتنين اوصلت ال
+
+572
+00:51:15,510 --> 00:51:19,370
+route ما هي تبدي في level؟ تنين لان level zero
+
+573
+00:51:19,370 --> 00:51:25,270
+level واحد level اتنين بقى لو طلت او جسرت مالهاش
+
+574
+00:51:25,270 --> 00:51:31,410
+علاقة مالهاش علاقة ليش؟
+
+575
+00:51:31,410 --> 00:51:35,390
+نفس الكلام ال level تبعت ال C هي عبارة عن عرب
+
+576
+00:51:35,390 --> 00:51:36,870
+الجسور اللي بناه هو بين ال route
+
+577
+00:51:43,130 --> 00:51:54,890
+أول الـ edge ما بين ال points مالوش شبهنا العمليات
+
+578
+00:51:54,890 --> 00:52:00,700
+الحسابية بتتمثل بـ treeوالمجلدات على ال operating
+
+579
+00:52:00,700 --> 00:52:04,980
+system زي الينيكس على الروت عندك ال C على ال
+
+580
+00:52:04,980 --> 00:52:09,300
+ويندوز ال user إلى آخره هذه المجلدات وهذه الموضوع
+
+581
+00:52:09,300 --> 00:52:15,960
+للعمليات الحسابية تمثل بتريس X زائد Y ضرب X not
+
+582
+00:52:15,960 --> 00:52:21,920
+plus Y X زائد Z عفوا من وين جبت هنا؟ لأن X أو Y و
+
+583
+00:52:21,920 --> 00:52:27,900
+Z ال بيرم تبعتهم من عملية الجمعالـ X والـ Y الـ
+
+584
+00:52:27,900 --> 00:52:33,640
+parent تبعتهم مارح والـ parent للعمليتين الضرب
+
+585
+00:52:33,640 --> 00:52:43,560
+فهذه عبارة عن X أو Y زائد Z مضغوبة في X ماقص Y هي
+
+586
+00:52:43,560 --> 00:52:47,000
+الأولويات اللي بتحكم في العملية أولويات العملية
+
+587
+00:52:47,000 --> 00:53:04,440
+الحسابية في ال trees في عند مصبلحم-اري
+
+588
+00:53:04,440 --> 00:53:17,180
+وممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممممم
+
+589
+00:53:22,870 --> 00:53:27,690
+TWO CHILDREN لما أتكلم على ال تريري اتكلم على ترى
+
+590
+00:53:27,690 --> 00:53:32,590
+تمام فوريري معناه اتكلم على أربعة يونيري اتكلم على
+
+591
+00:53:32,590 --> 00:53:36,190
+واحد وهذه صارت single path عمروحاش بتصير شجرة بيش
+
+592
+00:53:36,190 --> 00:53:39,890
+تفرعات فالان اتكلم على باينري على تريري وها كان
+
+593
+00:53:39,890 --> 00:53:47,330
+حسب الحاجة لما أنا باجي بقول full binary tree full
+
+594
+00:53:47,330 --> 00:53:52,090
+binary tree ايش يعني يعني كل ال parents عندهم
+
+595
+00:53:52,090 --> 00:54:00,610
+اتنينمش توقف عندهم اتنين طيب
+
+596
+00:54:00,610 --> 00:54:10,990
+ماشي الحل من اهم التطبيقات اللى موجودة عندى اناالـ
+
+597
+00:54:10,990 --> 00:54:15,130
+binary tree من أهم التطبيقات اللي موجودة عندي أنا
+
+598
+00:54:15,130 --> 00:54:21,030
+في ال binary ال tree و بدي أشتغل معاك في استخدامات
+
+599
+00:54:21,030 --> 00:54:24,270
+ال binary ال tree قبل ما أروح بالمثال هذا بدي أروح
+
+600
+00:54:24,270 --> 00:54:29,670
+باتجاه مثال أبسط و هو أنا فيه عندي أرقام أو
+
+601
+00:54:29,670 --> 00:54:39,450
+sequence خمسة سبعة أربعة تلاتة ستة واحد
+
+602
+00:54:52,040 --> 00:54:57,040
+عادة باخد أول element يمثل الـ root
+
+603
+00:55:02,280 --> 00:55:08,780
+ثلائي يعني كحد أقصى كحد أقصى عند كل parent two
+
+604
+00:55:08,780 --> 00:55:17,180
+nodes تمام باجي بعد هيك الآن السابعة الآن إذا كانت
+
+605
+00:55:17,180 --> 00:55:20,840
+ال value أكبر من ال parent node بتروح بتضيفها على
+
+606
+00:55:20,840 --> 00:55:24,760
+يمينها على اليمين لو كانت أقل منها بتضيفها على
+
+607
+00:55:24,760 --> 00:55:29,600
+الشمال باجي السابعة أكبر حطها على اليمين هي
+
+608
+00:55:29,600 --> 00:55:35,340
+السابعةباجل الأربعة ببدأ أقارنها مع الخمسة أقل من
+
+609
+00:55:35,340 --> 00:55:42,240
+الخمسة هروح على الشمال أربعة باجل التلاتة تلاتة
+
+610
+00:55:42,240 --> 00:55:51,080
+على شمال الخمسة على شمال الأربعة باجل الستة أكبر
+
+611
+00:55:51,080 --> 00:55:54,160
+من الخمسة يعني على يمينها باجل السبعة أقل من
+
+612
+00:55:54,160 --> 00:55:56,360
+السبعة على شمال السبعة
+
+613
+00:56:01,190 --> 00:56:08,630
+هذه ستة واحد على شمال الخمسة شمال الأربعة شمال
+
+614
+00:56:08,630 --> 00:56:21,030
+التلاتة واحد اتنين شمال الخمسة شمال شمال يمين
+
+615
+00:56:21,030 --> 00:56:24,790
+الواحد الآن
+
+616
+00:56:24,790 --> 00:56:30,350
+تمانية يمين الخمسة يمين السبعة
+
+617
+00:56:37,540 --> 00:56:44,800
+وبهك تبني ال binary tree ببنائها الفكرة دائما ال
+
+618
+00:56:44,800 --> 00:56:49,440
+value الأكبر على اليمين الأصغر على الشمال واحد
+
+619
+00:56:49,440 --> 00:56:53,200
+يقول القيم المتساوية أو السادس مالهاش وجود على
+
+620
+00:56:53,200 --> 00:56:57,940
+يمين ايه؟ ممتاز انا بدأ اكملها تمانى أكبر من
+
+621
+00:56:57,940 --> 00:57:01,870
+السبعة بالخمسة ولا أصغرأكبر و روحت .. روحت على
+
+622
+00:57:01,870 --> 00:57:05,650
+يمين لجت فيه node عشان أقرر أروح على يمين أو يسار
+
+623
+00:57:05,650 --> 00:57:08,810
+السبعة أقرر السبعة أو التمانية تمانية أكبر من
+
+624
+00:57:08,810 --> 00:57:13,030
+السبعة أو الأقل أكبر مانعته بروح على يمين السبعة
+
+625
+00:57:13,030 --> 00:57:17,650
+فش node برسم لها node جديدة الآن لو بدي أجيب تسعة
+
+626
+00:57:21,250 --> 00:57:25,210
+ماذا سأفعل؟ خمسة التسعة أكبر من الخمسة على اليمين
+
+627
+00:57:25,210 --> 00:57:29,810
+أكبر من السبعة على اليمين أكبر من التمانية على
+
+628
+00:57:29,810 --> 00:57:36,270
+يمين التمانية بمثالي في الكتاب يقول إعمل binary
+
+629
+00:57:36,270 --> 00:57:44,010
+tree من ال text اللي موجود عندي string math
+
+630
+00:57:44,010 --> 00:57:52,870
+computer powerNorth zebra dentist book نفس الكلام
+
+631
+00:57:52,870 --> 00:57:55,550
+مش على عدد الحرف، على الحرف الأول، على ترتيب
+
+632
+00:57:55,550 --> 00:58:01,230
+الأبجادية، على الأبجادية أول واحد ال math هي ال
+
+633
+00:58:01,230 --> 00:58:07,230
+route ال math هي ال route اللي بعدها computer ال C
+
+634
+00:58:07,230 --> 00:58:12,730
+أصغر من ال M ولا أكبر؟ أصغر فهتيجي وين؟ هتيجي شمال
+
+635
+00:58:14,270 --> 00:58:22,070
+الأن power P أكبر من ال C على اليمين North أكبر من
+
+636
+00:58:22,070 --> 00:58:30,070
+ال M M N O M N O فبتيجي الأن وين أكبر هتروح على
+
+637
+00:58:30,070 --> 00:58:37,930
+يمين الماهة أقل من ال B بتيجي ع شمالها Z Zebra
+
+638
+00:58:37,930 --> 00:58:42,010
+أكبر من ال M أكبر من ال B على يمين ال power
+
+639
+00:58:46,810 --> 00:58:52,890
+D أصغر من ال M تيجي على اليسار أكبر من ال C تيجي
+
+640
+00:58:52,890 --> 00:59:00,550
+على يمينها أخر كلمة عندي بك ال B أصغر من ال M تيجي
+
+641
+00:59:00,550 --> 00:59:05,930
+على اليسار أصغر من ال C تيجي على الشمال full
+
+642
+00:59:05,930 --> 00:59:08,530
+binary tree
+
+643
+00:59:13,500 --> 00:59:17,360
+طبعا من أهم تطبيقات تبع ال binary tree يا شباب
+
+644
+00:59:17,360 --> 00:59:21,220
+اللي هو من تبع ال tree اللي هي ال binary tree او
+
+645
+00:59:21,220 --> 00:59:25,380
+ال search في ال search في البحث الان على المثال
+
+646
+00:59:25,380 --> 00:59:29,720
+اللي وصلناه سابقا لما حطيت الأرقام لو انا اجيت و
+
+647
+00:59:29,720 --> 00:59:34,180
+قلتلك تسعة موجود ولا مش موجود ايش هتروح تساوي تسعة
+
+648
+00:59:34,180 --> 00:59:37,520
+اكبر من خمسة بروح على اليامين اكبر من السبعة بروح
+
+649
+00:59:37,520 --> 00:59:42,590
+على اليامين اكبر من التمانيةبروح على اليمين، في
+
+650
+00:59:42,590 --> 00:59:47,390
+عناصر بقارنها، مافيش .. إذا في الإضافة بأضيفها،
+
+651
+00:59:47,390 --> 00:59:49,910
+لكن أنا بقولك التسعة موجودة ولا مش موجودة، أخر
+
+652
+00:59:49,910 --> 00:59:53,470
+element عند التمانية، Leaf، مابقدرش رشش على
+
+653
+00:59:53,470 --> 00:59:56,690
+اليمينها، مايعتبر بـ stop، بقول التسعة إياش، مش
+
+654
+00:59:56,690 --> 01:00:01,070
+موجودة، تسعة مش موجودة، وهكذا في عملية ال search،
+
+655
+01:00:01,070 --> 01:00:04,590
+فالآن عملية من أهم التطبيقات تبع ال binary tree،
+
+656
+01:00:04,590 --> 01:00:10,310
+اللي هي ال binary search treeعادة لأ الان في ال
+
+657
+01:00:10,310 --> 01:00:13,390
+binary tree احنا ايش بنروح بنساوي بنحول المجموعة
+
+658
+01:00:13,390 --> 01:00:17,870
+اللي عندي ل set تمام؟ ايش يعني set؟ يعني مافيش
+
+659
+01:00:17,870 --> 01:00:21,230
+تكرار بالعراصر و بصير انا ايش اساوي اضيف ال
+
+660
+01:00:21,230 --> 01:00:24,890
+element عارف ليش هتصير منك مشكلة؟ الان تخيل هي
+
+661
+01:00:24,890 --> 01:00:30,290
+عندي خمسة خمسة بعد ما حطيت هنا سبعة و حطيت هنا
+
+662
+01:00:30,290 --> 01:00:34,510
+اربعة اتجتني كمان مرة خمسة وين بده احطها؟
+
+663
+01:00:36,990 --> 01:00:43,130
+هي تخيل ان انا بتضيفها داخل ال tree اما القانون
+
+664
+01:00:43,130 --> 01:00:47,510
+بيقول كالتالي اللي على الشمال أصغر و اللي على
+
+665
+01:00:47,510 --> 01:00:50,530
+اليمين أكبر بقادته ساوي مالهاش وجود عشان هيك
+
+666
+01:00:50,530 --> 01:00:53,350
+التكرار مالهاش .. عشان هيك أول شي باخد ال list
+
+667
+01:00:53,350 --> 01:00:58,290
+بحولها لمجموعة أشيل عناصر مكررة و بروح بابنين لل
+
+668
+01:00:58,290 --> 01:00:59,870
+tree اللي موجودة عندك
+
+669
+01:01:05,920 --> 01:01:10,380
+من أهم التطبيقات في الموضوع الـ Trees شغل اسمها
+
+670
+01:01:10,380 --> 01:01:14,440
+الـ Spanning Tree من
+
+671
+01:01:14,440 --> 01:01:18,520
+التطبيقات تبع الـ Tree الـ Minimum Spanning Tree و
+
+672
+01:01:18,520 --> 01:01:22,460
+الـ Decision Tree و الـ Half Man Code Trees احنا
+
+673
+01:01:22,460 --> 01:01:27,400
+هتكلم على Spanning Tree Spanning Tree هي عبارة عن
+
+674
+01:01:27,400 --> 01:01:29,160
+Graph
+
+675
+01:01:31,490 --> 01:01:35,970
+أو sub graph بيحتوي على كل النقاط اللي فى الرسمة
+
+676
+01:01:35,970 --> 01:01:42,510
+بيحتوي على كل النقاط اللي فى الرسمة طيب لو انا بكل
+
+677
+01:01:42,510 --> 01:01:53,910
+بساطة جدتي تقولي تهيأ A
+
+678
+01:01:53,910 --> 01:02:03,910
+B C D هذا مين؟ هى graphالان باجي بقول ال spanning
+
+679
+01:02:03,910 --> 01:02:10,110
+tree طبعا هي عبارة عن sub graph من ال graph هذا
+
+680
+01:02:10,110 --> 01:02:15,850
+يمثل ال tree طبعا هو عبارة عن ال tree بتحتوي على
+
+681
+01:02:15,850 --> 01:02:21,010
+كل النقاط اللي موجودة في الرسمة ايش يعني كل النقاط
+
+682
+01:02:21,010 --> 01:02:24,990
+اللي موجودة في الرسمة يعني ممكن انا اعملها هيك
+
+683
+01:02:24,990 --> 01:02:30,870
+ايه؟
+
+684
+01:02:31,680 --> 01:02:39,540
+دي سي بي هذي تجارب ترى ترى ولا مش ترى هاي ترى بناء
+
+685
+01:02:39,540 --> 01:02:44,140
+على إيش؟ بناء على إنها connected graph simple
+
+686
+01:02:44,140 --> 01:02:51,640
+connected graph has no circuit بصبوط هايها ترى لأن
+
+687
+01:02:51,640 --> 01:02:56,760
+هذي sub graph من هذي صح ولا لأ مجموعة نقاط subset
+
+688
+01:02:56,760 --> 01:03:03,540
+من مجموعة نقاطلأ لأ لأ لأ انا
+
+689
+01:03:03,540 --> 01:03:07,880
+جلبت ال ..
+
+690
+01:03:07,880 --> 01:03:19,980
+دي بي ال .. وهنا في عندك ال a وهنا عندك ال c طبعا؟
+
+691
+01:03:19,980 --> 01:03:26,500
+الآن sub graph sub graphالنقاط سبسط من النقاط
+
+692
+01:03:26,500 --> 01:03:31,220
+والجسور سبسط من الجسور اللي موجودة Has no circuit
+
+693
+01:03:31,220 --> 01:03:34,640
+فهي Tree وبما أنها تحتوي على كل النقاط اللي في
+
+694
+01:03:34,640 --> 01:03:39,500
+الرصمة الأساسيةيعني ال V التي هي تساوي V التي هي
+
+695
+01:03:39,500 --> 01:03:46,000
+ما هي تسميها أيش Spanning Tree شجرة ممتدة تجتمل
+
+696
+01:03:46,000 --> 01:03:48,840
+على كل العناصر اللي موجودة اللي عندها و في كل
+
+697
+01:03:48,840 --> 01:03:54,320
+Spanning Tree عدد الجسور يساوي عدد النقاط ناقص
+
+698
+01:03:54,320 --> 01:04:01,590
+واحدعدد الجسور يساوي عدد النقاط ناقص واحد كم
+
+699
+01:04:01,590 --> 01:04:04,990
+النقاط اللي عندي هان؟ أربعة الجسور اللي عندي فيها
+
+700
+01:04:04,990 --> 01:04:08,610
+هتكون تلت في أي spanning tree في أي spanning tree
+
+701
+01:04:08,610 --> 01:04:11,790
+بغض النظر كيف كان شكلها عدد الجسور يساوي عدد
+
+702
+01:04:11,790 --> 01:04:19,030
+النقاط ناقص واحد الأن
+
+703
+01:04:19,030 --> 01:04:23,390
+من الأشكال اللي عناها دول تبقى لل G1
+
+704
+01:04:28,660 --> 01:04:33,300
+هل هذا spanning tree؟ لأ فى circuit هل هذا
+
+705
+01:04:33,300 --> 01:04:39,420
+spanning tree؟ yes هل هذا spanning tree؟ yes هل
+
+706
+01:04:39,420 --> 01:04:43,040
+هذا spanning tree؟ no ليش؟ لأنه فى عندى isolated
+
+707
+01:04:43,040 --> 01:04:46,260
+point وهو راح يقول أن ال tree لازم تكون connected
+
+708
+01:04:46,260 --> 01:04:57,790
+لازم تكون متصلة اه ونعت true true خلاصوين ميزة الـ
+
+709
+01:04:57,790 --> 01:05:02,950
+Spanning Tree يا شباب؟ الآية دي تخيل هي K6، إيش
+
+710
+01:05:02,950 --> 01:05:07,290
+يعني K6؟ Complete Graph من ست نقاط، هيك ال
+
+711
+01:05:07,290 --> 01:05:11,970
+connection، كل واحد متصل مع الخمس نقاط التانين،
+
+712
+01:05:11,970 --> 01:05:14,850
+الآية ميزة الـ Complete Graph و الـ Spanning Tree
+
+713
+01:05:14,850 --> 01:05:19,550
+بتلزمني عشان انا اعرف كل ال possible path's اللي
+
+714
+01:05:19,550 --> 01:05:23,350
+بتوصلني لمين أو بدي أبني unique path's عشان أصل من
+
+715
+01:05:23,350 --> 01:05:28,350
+نقطة لنقطةهك كل النقاط بتوصل لبعضها فانا بدي اعمل
+
+716
+01:05:28,350 --> 01:05:31,830
+minimize للشجرة هذه او لل graph هذا بدي اختصره
+
+717
+01:05:31,830 --> 01:05:36,630
+بشجرة بحيث انه ماتركش ولا graph او عفوا ولا vertex
+
+718
+01:05:36,630 --> 01:05:40,150
+يبقى برا بدون connection فبيخدمني في الموضوع مين
+
+719
+01:05:40,150 --> 01:05:43,790
+spanning tree فممكن اتكلم هى spanning tree من
+
+720
+01:05:43,790 --> 01:05:48,430
+الرسم السابق ست نقاط هى ست نقاط موجودات وهى
+
+721
+01:05:48,430 --> 01:05:52,380
+connected وهى كمان spanning treeمن الرسم السابق
+
+722
+01:05:52,380 --> 01:05:56,380
+الفكرة هو ان بدل من دوري على كل ال connections
+
+723
+01:05:56,380 --> 01:06:00,280
+هدول بصير بدوري على connection واحدة خصوصا لما
+
+724
+01:06:00,280 --> 01:06:04,860
+التكلفة .. التكلفة بتكون مالهاش معيار عندي لما
+
+725
+01:06:04,860 --> 01:06:07,720
+التكلفة بتصير مالهاش معيار عندي بصير بدوري على
+
+726
+01:06:07,720 --> 01:06:12,520
+spanning tree عشان اصل لعناصر اللي موجودة عندها
+
+727
+01:06:12,520 --> 01:06:16,940
+كيف
+
+728
+01:06:16,940 --> 01:06:24,070
+بدى اوجد ال minimum spanning tree؟أصغر .. أصغر
+
+729
+01:06:24,070 --> 01:06:28,630
+شبكة تجمع كل النقاط اللي موجودة عنها .. بأقل تكلفة
+
+730
+01:06:28,630 --> 01:06:31,510
+طبعا .. الآن أنا في عندي spanning tree ايش اسمها؟
+
+731
+01:06:31,510 --> 01:06:35,250
+دولة spanning tree .. صارت في عندي شجرات بتحتوي
+
+732
+01:06:35,250 --> 01:06:39,570
+على كل النقاط .. لما بدخل ال cost في الموضوع ..
+
+733
+01:06:39,570 --> 01:06:43,310
+بدخل ال cost في الموضوع .. بصير أدور على مين؟ على
+
+734
+01:06:43,310 --> 01:06:46,950
+ال minimum .. minimum spanning tree .. الآن في أي
+
+735
+01:06:46,950 --> 01:06:51,510
+رسمةسأقول هي هذي spanning tree وهذه spanning tree
+
+736
+01:06:51,510 --> 01:06:55,150
+لكن مين أقل فيهم أنا ماعرفش لأنه فعليا ماتكلمتش
+
+737
+01:06:55,150 --> 01:06:59,210
+على تكلفة بال minimum spanning tree بقول كتالي هي
+
+738
+01:06:59,210 --> 01:07:02,750
+ال minimum spanning tree بتحتوى على أقل weight أقل
+
+739
+01:07:02,750 --> 01:07:06,730
+تكلفة أقل cost يعني ال cost لازم تكون موجودة عندها
+
+740
+01:07:06,730 --> 01:07:11,370
+فرسمتها البسيطة يا شباب في عندي two algorithms في
+
+741
+01:07:11,370 --> 01:07:15,470
+عند ال Brim وفي عند ال cost curve algorithms فرسمت
+
+742
+01:07:15,470 --> 01:07:24,300
+بكل البساطة ده الكتاليأنا بدي أشغل هيك بغض النظر
+
+743
+01:07:24,300 --> 01:07:30,900
+إيش ال algorithm اللي مستخدم هاي
+
+744
+01:07:30,900 --> 01:07:39,940
+ال graph عشان نلهي تخلصنا A B C D هنتكلفة خمسة هنا
+
+745
+01:07:39,940 --> 01:07:49,050
+واحد هنا تلاتة هنا أربعة هنا اتنين هنا خمسةالان
+
+746
+01:07:49,050 --> 01:07:52,010
+عندما تحصل على الـ Minimum Spanning Tree يعني أنك
+
+747
+01:07:52,010 --> 01:08:00,630
+تريد الأربع نقاط اللي موجودة هذه الأربع نقاط A
+
+748
+01:08:00,630 --> 01:08:09,670
+,B,C,D أول ما بترسم، بترسم الخطوط اللي أقل تكلفة
+
+749
+01:08:09,670 --> 01:08:15,750
+احنا حطينا جديش؟ اوكي، اتنين فيهم، خمسات اوكي، بس
+
+750
+01:08:15,750 --> 01:08:17,990
+بعد إذنك، بدي أحط هذه كمان مرة اتنين
+
+751
+01:08:22,160 --> 01:08:29,340
+الان بتاخد أقل تكلفة مين أقل تكلفة؟ AC هايو أول خط
+
+752
+01:08:29,340 --> 01:08:39,520
+بواحد بعد هيك بتاخد AB اخدت AB اتنين اللي بعده BC
+
+753
+01:08:39,520 --> 01:08:44,450
+لو انا اترسمت ال BC هنا شباب صار في عندي circleصار
+
+754
+01:08:44,450 --> 01:08:48,390
+في عندي circuit بطلة ال three فانا أسف مش هاخد هذا
+
+755
+01:08:48,390 --> 01:08:54,230
+بيه اتنين هاخد مين؟ هاخد اللي بعده لأ هو واحد بين
+
+756
+01:08:54,230 --> 01:09:00,810
+كانوا .. ماشي
+
+757
+01:09:00,810 --> 01:09:07,230
+الحال هي واحد واحد وانا أربعة طبعا الان بدي أخد
+
+758
+01:09:07,230 --> 01:09:16,680
+مين؟ بدي أخد خلصت هذا مابديش إياهبدي أخد الأربعة،
+
+759
+01:09:16,680 --> 01:09:23,640
+هاي أربعة، طيب كام دي سر عندي أنا صاروا؟ تلاتة،
+
+760
+01:09:23,640 --> 01:09:29,860
+وعدد النقاط؟ أنا مش بحاجة للجسور بعد هيك،
+
+761
+01:09:29,860 --> 01:09:35,750
+وينها؟ وينها؟ مافيش circuitمافيش لو فيه تقطة فالنص
+
+762
+01:09:35,750 --> 01:09:39,090
+كان اختلفت الأمور السؤال اللي بيقرح نفسه الآن ليش
+
+763
+01:09:39,090 --> 01:09:43,630
+أنا وقفت ماكملتش؟ لأن ال spanning tree عدد الجسور
+
+764
+01:09:43,630 --> 01:09:47,390
+فيها يساوي عدد النقاط ماتس واحد وانا بدي بس ثلاث
+
+765
+01:09:47,390 --> 01:09:51,370
+نقاط فهي اتكملت بالثلاث نقاط وخلصنا وبهيك انت
+
+766
+01:09:51,370 --> 01:09:55,950
+بترسم على أو بتقدر تحصل على ال minimum spanning
+
+767
+01:09:55,950 --> 01:09:56,810
+tree
+
+768
+01:10:02,620 --> 01:10:07,480
+الأسماء لـ Algorithm لرسم التتعامل أو الوصول للـ
+
+769
+01:10:07,480 --> 01:10:11,360
+Tree خلاص بس انت بدك تعرف الأسماء مش اكتر من هيك
+
+770
+01:10:11,360 --> 01:10:17,000
+تمويها بدك تعرف ان في عندك two algorithms كمان من
+
+771
+01:10:17,000 --> 01:10:20,100
+أجل الوصول ل ال minimum spanning trees هيهم
+
+772
+01:10:20,100 --> 01:10:24,040
+crosscan و prim algorithms لكن الطريقة اللي انا ..
+
+773
+01:10:24,040 --> 01:10:26,720
+لو قلتلك هتل ال minimum spanning tree اشغل
+
+774
+01:10:26,720 --> 01:10:31,670
+بالطريقة اللي اناقلتلك عنها ..طيب وبهيك الشباب مع
+
+775
+01:10:31,670 --> 01:10:35,230
+ال crosscut algorithm نكون انتهينا من ال chapter
+
+776
+01:10:35,230 --> 01:10:40,190
+الأخير في المساق للفصل هذا هو فعليا انا ال .. هذا
+
+777
+01:10:40,190 --> 01:10:43,990
+المفروض ال three في ال chapter سبعة فاحنا فعليا
+
+778
+01:10:43,990 --> 01:10:46,030
+طلعنا من الستة و روحنا على سبعة و جيبنا اللي
+
+779
+01:10:46,030 --> 01:10:49,950
+بدنايا وبهيك نكون خلصنا الفصل بالكامل ان شاء الله
+
+780
+01:10:49,950 --> 01:10:54,530
+تعالى اذا في حد عنده اي سؤال احنا جاهزين في المكتب
+
+781
+01:10:54,530 --> 01:10:56,310
+باستماعه خلال الأسبوع اللي جاي ان شاء الله جابيه
+
+782
+01:10:56,310 --> 01:11:01,720
+لاياشيقبل الامتحان تحضر نفسك تدراجع ماتجينيش ان
+
+783
+01:11:01,720 --> 01:11:05,880
+اشرحلك المادة من الصفر لازم أشوفك فعلا انت بذالك
+
+784
+01:11:05,880 --> 01:11:10,080
+جهود و جايين ان انا اعيش ان فاهمك الشغل اللي انت
+
+785
+01:11:10,080 --> 01:11:13,160
+ماقدرتش توصل لها و ان شاء الله هنكون بانتظارك بإذن
+
+786
+01:11:13,160 --> 01:11:16,280
+الله تبارك وتعالى بس الحال هيك بكون نهينا محاضرتنا
+
+787
+01:11:16,280 --> 01:11:19,000
+و نهينا الفصل سبحانك اللهم وبحمدك نشهد ولا إله إلا
+
+788
+01:11:19,000 --> 01:11:21,820
+أنت و نستغفرك و أتوب إليك و سامحونا إذا ان احنا
+
+789
+01:11:21,820 --> 01:11:25,700
+عايش .. إذا ناكل محاضرة هكذا الله يعطي كل عافية إن
+
+790
+01:11:25,700 --> 01:11:25,800
+شاء الله
+