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+{"segments": [{"id": 1, "seek": 3311, "start": 19.74, "end": 33.12, "text": "بسم الله الرحمن الرحيم، هنواصل مع الـdenominable sets وطبعا ال section خمسة تلاتة هو مكمل لsection خمسة اتنين بيتحدث عن اللي هو examples and probabilities of denominable sets", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 12399, 8032, 1863, 2407, 33546, 1211, 20449, 2423, 39184, 1556, 6981, 712, 6352, 4032, 9566, 3555, 3615, 995, 2423, 3541, 16490, 2304, 3794, 3660, 6055, 1211, 9307, 3660, 31439, 3714, 24793, 1211, 5296, 11963, 16490, 2304, 3794, 3660, 1975, 2655, 1863, 9957, 4724, 36081, 24401, 12984, 18871, 13672, 1829, 31439, 5110, 293, 33783, 295, 1441, 6981, 712, 6352], "avg_logprob": -0.21449907715706265, "compression_ratio": 1.494047619047619, "no_speech_prob": 0.0, "words": [{"start": 19.74, "end": 20.04, "word": "بسم", "probability": 0.8984375}, {"start": 20.04, "end": 20.22, "word": " الله", "probability": 0.970703125}, {"start": 20.22, "end": 20.62, "word": " الرحمن", 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union B is denomable نشوف البراحة", "tokens": [5172, 6027, 3615, 1863, 2407, 7649, 264, 11671, 295, 732, 1441, 298, 712, 6352, 307, 1441, 298, 712, 11331, 49975, 45164, 6055, 5172, 1863, 3615, 11296, 9122, 2304, 7649, 1441, 298, 712, 39894, 10943, 11296, 1441, 298, 712, 6156, 3615, 8315, 8717, 19913, 2288, 10632, 498, 316, 293, 363, 366, 1441, 298, 712, 6352, 550, 316, 11671, 363, 307, 1441, 298, 712, 8717, 8592, 38688, 29739, 23557, 5016, 3660], "avg_logprob": -0.21785714966910227, "compression_ratio": 1.4935064935064934, "no_speech_prob": 0.0, "words": [{"start": 105.69, "end": 106.39, "word": "فالعنوان", "probability": 0.8196207682291666}, {"start": 106.39, "end": 106.55, "word": " the", "probability": 0.180419921875}, {"start": 106.55, "end": 107.09, "word": " union", "probability": 0.95556640625}, {"start": 107.09, "end": 107.53, "word": " of", "probability": 0.978515625}, {"start": 107.53, "end": 107.89, "word": " two", "probability": 0.92919921875}, {"start": 107.89, "end": 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"end": 114.95, "word": " نظرية", "probability": 0.9649658203125}, {"start": 114.95, "end": 115.67, "word": " if", "probability": 0.837890625}, {"start": 115.67, "end": 115.99, "word": " A", "probability": 0.5859375}, {"start": 115.99, "end": 116.25, "word": " and", "probability": 0.814453125}, {"start": 116.25, "end": 116.49, "word": " B", "probability": 0.99169921875}, {"start": 116.49, "end": 116.71, "word": " are", "probability": 0.95703125}, {"start": 116.71, "end": 117.29, "word": " denomable", "probability": 0.93408203125}, {"start": 117.29, "end": 117.69, "word": " sets", "probability": 0.8876953125}, {"start": 117.69, "end": 118.39, "word": " then", "probability": 0.7314453125}, {"start": 118.39, "end": 118.79, "word": " A", "probability": 0.951171875}, {"start": 118.79, "end": 119.23, "word": " union", "probability": 0.85107421875}, {"start": 119.23, "end": 119.67, "word": " B", "probability": 0.9931640625}, {"start": 119.67, "end": 120.23, "word": " is", "probability": 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"probability": 0.1981201171875}, {"start": 136.32, "end": 137.6, "word": " طبعا", "probability": 0.951171875}, {"start": 137.6, "end": 137.9, "word": " جملة", "probability": 0.9342447916666666}, {"start": 137.9, "end": 138.52, "word": " شرطية", "probability": 0.992919921875}, {"start": 138.52, "end": 139.86, "word": " فنبدأ", "probability": 0.953369140625}, {"start": 139.86, "end": 139.94, "word": " ان", "probability": 0.478515625}, {"start": 139.94, "end": 140.24, "word": " الشرط", "probability": 0.9609375}, {"start": 140.24, "end": 141.3, "word": " صحيح", "probability": 0.9981689453125}, {"start": 141.3, "end": 142.18, "word": " assume", "probability": 0.66650390625}, {"start": 142.18, "end": 144.16, "word": " ال", "probability": 0.8505859375}, {"start": 144.16, "end": 144.48, "word": " A", "probability": 0.2393798828125}, {"start": 144.48, "end": 145.32, "word": " is", "probability": 0.896484375}, {"start": 145.32, "end": 145.9, "word": " denominable", "probability": 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"end": 151.04, "word": " and", "probability": 0.94580078125}], "temperature": 1.0}, {"id": 7, "seek": 17901, "start": 151.65, "end": 179.01, "text": "الـ B is denomable مطلوب نثبت أن الاتحاد is denomable بدنا نثبت أن الـ A union B is denomable we want to prove A union B is denomable تمام مرة علينا نظريات", "tokens": [6027, 39184, 363, 307, 1441, 298, 712, 3714, 9566, 1211, 37746, 8717, 12984, 3555, 2655, 14739, 2423, 9307, 5016, 18513, 307, 1441, 298, 712, 47525, 8315, 8717, 12984, 3555, 2655, 14739, 2423, 39184, 316, 11671, 363, 307, 1441, 298, 712, 321, 528, 281, 7081, 316, 11671, 363, 307, 1441, 298, 712, 46811, 10943, 3714, 25720, 11203, 9957, 995, 8717, 19913, 16572, 9307], "avg_logprob": -0.24404762093982998, "compression_ratio": 1.544776119402985, "no_speech_prob": 0.0, "words": [{"start": 151.65, "end": 152.01, "word": "الـ", "probability": 0.702880859375}, {"start": 152.01, "end": 152.29, "word": " B", "probability": 0.56591796875}, {"start": 152.29, "end": 152.97, "word": " 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"probability": 0.8583984375}, {"start": 160.13, "end": 160.39, "word": " union", "probability": 0.55908203125}, {"start": 160.39, "end": 160.73, "word": " B", "probability": 0.986328125}, {"start": 160.73, "end": 161.37, "word": " is", "probability": 0.83837890625}, {"start": 161.37, "end": 161.93, "word": " denomable", "probability": 0.9537760416666666}, {"start": 161.93, "end": 163.87, "word": " we", "probability": 0.2381591796875}, {"start": 163.87, "end": 164.47, "word": " want", "probability": 0.9306640625}, {"start": 164.47, "end": 166.39, "word": " to", "probability": 0.935546875}, {"start": 166.39, "end": 167.03, "word": " prove", "probability": 0.95068359375}, {"start": 167.03, "end": 169.19, "word": " A", "probability": 0.8330078125}, {"start": 169.19, "end": 169.71, "word": " union", "probability": 0.95751953125}, {"start": 169.71, "end": 170.31, "word": " B", "probability": 0.9951171875}, {"start": 170.31, "end": 171.19, "word": " is", "probability": 0.9638671875}, {"start": 171.19, "end": 171.81, "word": " denomable", "probability": 0.9646809895833334}, {"start": 171.81, "end": 175.17, "word": " تمام", "probability": 0.841064453125}, {"start": 175.17, "end": 177.95, "word": " مرة", "probability": 0.63720703125}, {"start": 177.95, "end": 178.23, "word": " علينا", "probability": 0.8141276041666666}, {"start": 178.23, "end": 179.01, "word": " نظريات", "probability": 0.9698486328125}], "temperature": 1.0}, {"id": 8, "seek": 19411, "start": 179.73, "end": 194.11, "text": "بتقول لو مجموعتين متكافئتين او مجموعة X تكافئ Y قلنا و W تكافئ V فالاتحاد يكافئ الاتحاد تحت بعض الشروط صح فهل ممكن استخدم الفكرة هذه هنا ولا لأ؟", "tokens": [3555, 2655, 39648, 45164, 3714, 7435, 2304, 45367, 2655, 9957, 44650, 4117, 31845, 19986, 2655, 9957, 1975, 2407, 3714, 7435, 2304, 45367, 3660, 1783, 6055, 4117, 31845, 19986, 398, 12174, 1211, 8315, 4032, 343, 6055, 4117, 31845, 19986, 691, 6156, 6027, 9307, 5016, 18513, 7251, 4117, 31845, 19986, 2423, 9307, 5016, 18513, 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214.92, "word": " التانية", "probability": 0.9744466145833334}, {"start": 214.92, "end": 215.1, "word": " في", "probability": 0.98095703125}, {"start": 215.1, "end": 215.26, "word": " في", "probability": 0.65478515625}, {"start": 215.26, "end": 215.76, "word": " الاتحاد", "probability": 0.9190673828125}, {"start": 215.76, "end": 216.08, "word": " وكفي", "probability": 0.5281575520833334}, {"start": 216.08, "end": 216.72, "word": " الاتحاد", "probability": 0.9610595703125}, {"start": 216.72, "end": 217.38, "word": " ممكن", "probability": 0.973388671875}, {"start": 217.38, "end": 217.86, "word": " نستخدم", "probability": 0.9798583984375}, {"start": 217.86, "end": 218.02, "word": " هذا", "probability": 0.84423828125}, {"start": 218.02, "end": 218.32, "word": " الكلام", "probability": 0.9606119791666666}, {"start": 218.32, "end": 218.64, "word": " هنا", "probability": 0.9892578125}, {"start": 218.64, "end": 219.58, "word": " ممكن", "probability": 0.720947265625}, {"start": 219.58, "end": 219.92, "word": " ليش", "probability": 0.875244140625}, {"start": 219.92, "end": 220.16, "word": " لأ", "probability": 0.915771484375}, {"start": 220.16, "end": 220.58, "word": " بس", "probability": 0.929443359375}, {"start": 220.58, "end": 220.72, "word": " بنا", "probability": 0.3714599609375}, {"start": 220.72, "end": 221.02, "word": " ناخد", "probability": 0.8258463541666666}, {"start": 221.02, "end": 221.52, "word": " احتمالات", "probability": 0.896875}, {"start": 221.52, "end": 221.8, "word": " هذه", "probability": 0.80419921875}, {"start": 221.8, "end": 222.76, "word": " فالان", "probability": 0.92041015625}, {"start": 222.76, "end": 223.16, "word": " ال", "probability": 0.93359375}, {"start": 223.16, "end": 223.28, "word": " A", "probability": 0.81396484375}, {"start": 223.28, "end": 223.46, "word": " و", "probability": 0.84130859375}, {"start": 223.46, "end": 223.54, "word": " ال", "probability": 0.7607421875}, {"start": 223.54, "end": 223.82, "word": " B", "probability": 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"word": " أشتغل", "probability": 0.94521484375}, {"start": 230.26, "end": 230.36, "word": " على", "probability": 0.9306640625}, {"start": 230.36, "end": 230.5, "word": " هذا", "probability": 0.96533203125}, {"start": 230.5, "end": 230.9, "word": " الموضوع", "probability": 0.998779296875}, {"start": 230.9, "end": 231.34, "word": " فانا", "probability": 0.7840169270833334}, {"start": 231.34, "end": 231.62, "word": " أخد", "probability": 0.83203125}, {"start": 231.62, "end": 231.8, "word": " هذه", "probability": 0.83544921875}, {"start": 231.8, "end": 233.26, "word": " الحالة", "probability": 0.9899088541666666}, {"start": 233.26, "end": 234.0, "word": " case", "probability": 0.66015625}, {"start": 234.0, "end": 236.5, "word": " one", "probability": 0.54443359375}, {"start": 236.5, "end": 239.0, "word": " a", "probability": 0.4150390625}, {"start": 239.0, "end": 240.2, "word": " تقاطع", "probability": 0.9632568359375}, {"start": 240.2, "end": 240.38, "word": " ال", "probability": 0.92578125}, {"start": 240.38, "end": 240.68, "word": " b", "probability": 0.451904296875}, {"start": 240.68, "end": 241.74, "word": " يساوي", "probability": 0.9468994140625}, {"start": 241.74, "end": 241.98, "word": " في", "probability": 0.83740234375}], "temperature": 1.0}, {"id": 11, "seek": 25656, "start": 244.1, "end": 256.56, "text": "فإذا هنا ممكن اتحدث عن اتحاد بدون مشاكل طيب بينفع اقول ما زال ال A تكافئ ال N و ال B تكافئ ال N إذا A Union B يكافئ N اتحاد ال N", "tokens": [5172, 28814, 15730, 34105, 3714, 43020, 1975, 2655, 24401, 12984, 18871, 1975, 2655, 5016, 18513, 47525, 11536, 37893, 995, 28820, 23032, 1829, 3555, 4724, 9957, 5172, 3615, 1975, 39648, 19446, 30767, 6027, 2423, 316, 6055, 4117, 31845, 19986, 2423, 426, 4032, 2423, 363, 6055, 4117, 31845, 19986, 2423, 426, 11933, 15730, 316, 8133, 363, 7251, 4117, 31845, 19986, 426, 1975, 2655, 5016, 18513, 2423, 426], "avg_logprob": -0.22798295838363242, "compression_ratio": 1.5514705882352942, "no_speech_prob": 0.0, 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فعملت حالتين جسمتها نصين لأن مافيش عندي برهان لجميع الحالات مع بعض فبضطر أعملها حالات متعددة كل حالة بقدر أعليجها بطريقة مختلفة", "tokens": [1211, 10721, 11933, 5016, 8315, 11778, 1829, 9154, 23032, 2288, 4587, 13672, 1829, 31439, 2423, 26890, 3224, 7649, 538, 3331, 5551, 5016, 1829, 7649, 995, 41850, 8978, 18871, 16254, 9673, 3615, 9566, 1829, 9307, 28242, 11296, 4724, 8592, 28820, 11296, 18863, 10943, 4724, 28543, 2288, 8592, 5551, 25957, 1211, 11296, 3714, 25720, 36764, 24401, 3660, 41850, 28242, 9673, 30241, 20498, 9307, 18871, 2423, 39184, 32, 4032, 2423, 39184, 33, 36145, 16095, 11778, 1829, 8717, 29973, 14407, 1975, 8592, 2655, 47432, 2407, 5016, 16095, 37893, 20449, 32887, 5172, 23032, 3555, 8032, 1211, 4724, 28543, 2288, 5551, 8592, 2655, 17082, 1211, 31767, 13063, 3660, 18863, 10943, 3660, 3714, 25720, 36764, 24401, 3660, 37893, 10874, 18513, 3660, 6156, 25957, 1211, 2655, 11331, 6027, 2655, 9957, 10874, 38251, 2655, 11296, 8717, 9381, 9957, 5296, 33456, 19446, 41185, 8592, 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65903, "start": 648.99, "end": 659.03, "text": "نمشي كمان طيب الاتحاد ديناميرابول ديناميرابول طب تلاتة ديناميرابول اتحادهم ديناميرابول وعشرة ديناميرابول اتحادهم ديناميرابول نتيجة", "tokens": [1863, 2304, 8592, 1829, 9122, 2304, 7649, 23032, 1829, 3555, 2423, 9307, 5016, 18513, 11778, 9957, 10943, 13546, 16758, 12610, 11778, 9957, 10943, 13546, 16758, 12610, 23032, 3555, 6055, 1211, 9307, 3660, 11778, 9957, 10943, 13546, 16758, 12610, 1975, 2655, 5016, 18513, 16095, 11778, 9957, 10943, 13546, 16758, 12610, 4032, 3615, 8592, 25720, 11778, 9957, 10943, 13546, 16758, 12610, 1975, 2655, 5016, 18513, 16095, 11778, 9957, 10943, 13546, 16758, 12610, 8717, 31371, 7435, 3660], "avg_logprob": -0.24375000357627868, "compression_ratio": 2.5520833333333335, "no_speech_prob": 0.0, "words": [{"start": 648.99, "end": 649.51, "word": "نمشي", "probability": 0.68988037109375}, {"start": 649.51, "end": 649.89, "word": " كمان", "probability": 0.8375651041666666}, {"start": 649.89, "end": 650.91, "word": " طيب", "probability": 0.6432698567708334}, {"start": 650.91, "end": 651.83, "word": " الاتحاد", "probability": 0.7215118408203125}, {"start": 651.83, "end": 652.33, "word": " ديناميرابول", "probability": 0.57586669921875}, {"start": 652.33, "end": 652.91, "word": " ديناميرابول", "probability": 0.884033203125}, {"start": 652.91, "end": 653.15, "word": " طب", "probability": 0.5462646484375}, {"start": 653.15, "end": 653.57, "word": " تلاتة", "probability": 0.895751953125}, {"start": 653.57, "end": 653.97, "word": " ديناميرابول", "probability": 0.9454752604166666}, {"start": 653.97, "end": 654.61, "word": " اتحادهم", "probability": 0.9435546875}, {"start": 654.61, "end": 655.83, "word": " ديناميرابول", "probability": 0.9654947916666666}, {"start": 655.83, "end": 656.81, "word": " وعشرة", "probability": 0.715576171875}, {"start": 656.81, "end": 657.29, "word": " ديناميرابول", "probability": 0.9728190104166666}, {"start": 657.29, "end": 657.73, "word": " اتحادهم", "probability": 0.9861328125}, {"start": 657.73, "end": 658.25, "word": " ديناميرابول", "probability": 0.97705078125}, {"start": 658.25, "end": 659.03, "word": " نتيجة", "probability": 0.934814453125}], "temperature": 1.0}, {"id": 29, "seek": 68653, "start": 659.59, "end": 686.53, "text": "بقول ليه؟ finite union يعني عدد محدود عشرة، خمسة، مية، ألف of denumerable sets is denumerable تعميم للنظرية النتيجة بشكل نص واضح وصريح let A1, A2, AN be denumerable sets عندنا مجموعة من المجموعات القابلة للعدد then the union J من 1 ل N AJ is denumerable عملية تعميم", "tokens": [3555, 39648, 32239, 3224, 22807, 19362, 11671, 37495, 22653, 6225, 3215, 3215, 3714, 24401, 23328, 6225, 8592, 25720, 12399, 16490, 2304, 3794, 3660, 12399, 3714, 10632, 12399, 5551, 46538, 295, 1441, 15583, 712, 6352, 307, 1441, 15583, 712, 37279, 2304, 32640, 24976, 1863, 19913, 2288, 10632, 28239, 31371, 7435, 3660, 4724, 8592, 28820, 8717, 9381, 4032, 46958, 5016, 4032, 9381, 16572, 5016, 718, 316, 16, 11, 316, 17, 11, 316, 45, 312, 1441, 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"probability": 0.94130859375}, {"start": 677.25, "end": 677.43, "word": " من", "probability": 0.9931640625}, {"start": 677.43, "end": 678.25, "word": " المجموعات", "probability": 0.9642578125}, {"start": 678.25, "end": 679.13, "word": " القابلة", "probability": 0.9384765625}, {"start": 679.13, "end": 679.85, "word": " للعدد", "probability": 0.748046875}, {"start": 679.85, "end": 680.17, "word": " then", "probability": 0.82373046875}, {"start": 680.17, "end": 680.41, "word": " the", "probability": 0.8583984375}, {"start": 680.41, "end": 680.83, "word": " union", "probability": 0.9541015625}, {"start": 680.83, "end": 681.47, "word": " J", "probability": 0.587890625}, {"start": 681.47, "end": 681.69, "word": " من", "probability": 0.978515625}, {"start": 681.69, "end": 682.01, "word": " 1", "probability": 0.642578125}, {"start": 682.01, "end": 682.23, "word": " ل", "probability": 0.904296875}, {"start": 682.23, "end": 682.47, "word": " N", "probability": 0.5771484375}, {"start": 682.47, "end": 682.87, "word": " AJ", "probability": 0.2783203125}, {"start": 682.87, "end": 683.21, "word": " is", "probability": 0.9482421875}, {"start": 683.21, "end": 683.71, "word": " denumerable", "probability": 0.9422200520833334}, {"start": 683.71, "end": 686.07, "word": " عملية", "probability": 0.94482421875}, {"start": 686.07, "end": 686.53, "word": " تعميم", "probability": 0.8285319010416666}], "temperature": 1.0}, {"id": 30, "seek": 71575, "start": 688.55, "end": 715.75, "text": "البرهان بال induction هتركه exercise أن ال statement for all n أكبر ات ساوى 2، ليش؟ لأن اتحاده، لأن اتحاده يشتغل على أكتر من عنصره، أجل من عنصره يعني، صحيح طبعا الجملة إذا كانت a واحد ل a undenumerable فالاتحاد denumerable طبعا b of two is true ليش؟ نظرية، بعدين induction و induction hypothesis وخلصت، فده exercise", "tokens": [6027, 26890, 3224, 7649, 20666, 33371, 8032, 2655, 31747, 3224, 5380, 14739, 2423, 5629, 337, 439, 297, 5551, 4117, 26890, 1975, 2655, 8608, 995, 2407, 7578, 568, 12399, 32239, 8592, 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"probability": 0.67193603515625}, {"start": 706.43, "end": 707.25, "word": " فالاتحاد", "probability": 0.95888671875}, {"start": 707.25, "end": 707.69, "word": " denumerable", "probability": 0.6520182291666666}, {"start": 707.69, "end": 708.27, "word": " طبعا", "probability": 0.87158203125}, {"start": 708.27, "end": 708.89, "word": " b", "probability": 0.2181396484375}, {"start": 708.89, "end": 709.05, "word": " of", "probability": 0.92822265625}, {"start": 709.05, "end": 709.23, "word": " two", "probability": 0.6572265625}, {"start": 709.23, "end": 709.39, "word": " is", "probability": 0.9091796875}, {"start": 709.39, "end": 709.67, "word": " true", "probability": 0.984375}, {"start": 709.67, "end": 710.25, "word": " ليش؟", "probability": 0.8084309895833334}, {"start": 710.25, "end": 711.03, "word": " نظرية،", "probability": 0.92607421875}, {"start": 711.03, "end": 711.73, "word": " بعدين", "probability": 0.6103515625}, {"start": 711.73, "end": 712.29, "word": " induction", 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92241, "start": 897.71, "end": 922.41, "text": "فده بس مثال والسرجاع وفكرة جديدة وكيف نشتغل مع الـdenimrable نرجع لفكرتنا الرئيسية اللي حكينا فيها من أول المحاضرة احنا بدأنا من الـdenimrable بدأنا نكبر فيها دفنالها عنصر دفنالها finite set بعدين دفنالها الـdenimrable تم الـdenimrable طب لو ضربنا عملنا Cartesian product طبعا الـCartesian product مين أكبر الاتحاد ولا الـCartesian؟", "tokens": [5172, 3215, 3224, 4724, 3794, 50113, 6027, 16070, 3794, 47341, 45761, 4032, 5172, 4117, 25720, 10874, 16254, 41891, 4032, 4117, 33911, 8717, 8592, 2655, 17082, 1211, 20449, 2423, 39184, 1556, 332, 424, 638, 8717, 47341, 3615, 5296, 5172, 4117, 43500, 8315, 34892, 19986, 1829, 3794, 10632, 13672, 1829, 11331, 4117, 1829, 8315, 8978, 11296, 9154, 5551, 12610, 9673, 5016, 46958, 25720, 1975, 5016, 8315, 47525, 10721, 8315, 9154, 2423, 39184, 1556, 332, 424, 638, 47525, 10721, 8315, 8717, 4117, 26890, 8978, 11296, 11778, 5172, 1863, 6027, 11296, 18871, 9381, 2288, 11778, 5172, 1863, 6027, 11296, 19362, 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"text": "يعني لو أخدنا كل الأزواج المرتبة من الـnatural numbers بتامها المجموعة denominable قابلة للعدد نظرية 15 approve الآن طبعا بدي أثبت إنها denominable يا بدى أستخدم النظريات إذا قدرت يا بدى أجيب bijection بينها وبين الان", "tokens": [40228, 22653, 45164, 5551, 9778, 3215, 8315, 28242, 16247, 11622, 2407, 26108, 9673, 43500, 49401, 9154, 2423, 39184, 16296, 3547, 39894, 10943, 11296, 9673, 7435, 2304, 2407, 27884, 1441, 6981, 712, 12174, 16758, 37977, 24976, 22488, 3215, 8717, 19913, 2288, 10632, 2119, 18827, 6024, 48506, 23032, 3555, 3615, 995, 4724, 16254, 5551, 12984, 3555, 2655, 36145, 11296, 1441, 6981, 712, 35186, 47525, 7578, 5551, 14851, 9778, 40448, 28239, 19913, 16572, 9307, 11933, 15730, 12174, 3215, 43500, 35186, 47525, 7578, 5551, 7435, 1829, 3555, 3228, 1020, 313, 49374, 11296, 46599, 9957, 2423, 7649], "avg_logprob": -0.22899865014578707, "compression_ratio": 1.547085201793722, "no_speech_prob": 0.0, "words": [{"start": 952.44, "end": 952.8, "word": "يعني", 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subset", "probability": 0.94873046875}, {"start": 1556.89, "end": 1557.15, "word": " من", "probability": 0.99560546875}, {"start": 1557.15, "end": 1557.31, "word": " ال", "probability": 0.85986328125}, {"start": 1557.31, "end": 1557.51, "word": " end", "probability": 0.126220703125}, {"start": 1557.51, "end": 1557.75, "word": " وهذه", "probability": 0.7740071614583334}, {"start": 1557.75, "end": 1558.47, "word": " تكافئها", "probability": 0.991796875}, {"start": 1558.47, "end": 1559.45, "word": " فهي", "probability": 0.6263834635416666}, {"start": 1559.45, "end": 1559.61, "word": " على", "probability": 0.97021484375}, {"start": 1559.61, "end": 1559.87, "word": " طول", "probability": 0.9931640625}, {"start": 1559.87, "end": 1560.43, "word": " denominable", "probability": 0.9197591145833334}, {"start": 1560.43, "end": 1561.23, "word": " كيف", "probability": 0.759033203125}, {"start": 1561.23, "end": 1561.43, "word": " بدنا", "probability": 0.749267578125}, {"start": 1561.43, "end": 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"compression_ratio": 1.4, "no_speech_prob": 0.0, "words": [{"start": 1569.6100000000001, "end": 1570.73, "word": "N", "probability": 0.3291015625}, {"start": 1570.73, "end": 1571.85, "word": " cross", "probability": 0.3232421875}, {"start": 1571.85, "end": 1572.13, "word": " الـ", "probability": 0.69970703125}, {"start": 1572.13, "end": 1572.37, "word": " N", "probability": 0.8017578125}, {"start": 1572.37, "end": 1573.49, "word": " is", "probability": 0.87158203125}, {"start": 1573.49, "end": 1574.19, "word": " infinite", "probability": 0.8984375}, {"start": 1574.19, "end": 1578.69, "word": " we", "probability": 0.10931396484375}, {"start": 1578.69, "end": 1580.53, "word": " have", "probability": 0.96728515625}, {"start": 1580.53, "end": 1581.35, "word": " F", "probability": 0.7783203125}, {"start": 1581.35, "end": 1582.05, "word": " of", "probability": 0.50634765625}, {"start": 1582.05, "end": 1582.23, "word": " N", "probability": 0.9072265625}, {"start": 1582.23, "end": 1582.61, "word": " cross", "probability": 0.90869140625}, {"start": 1582.61, "end": 1582.85, "word": " ال", "probability": 0.84765625}, {"start": 1582.85, "end": 1583.13, "word": " N", "probability": 0.8671875}, {"start": 1583.13, "end": 1584.51, "word": " is", "probability": 0.94140625}, {"start": 1584.51, "end": 1585.19, "word": " infinite", "probability": 0.9189453125}, {"start": 1585.19, "end": 1588.33, "word": " وهذا", "probability": 0.88037109375}, {"start": 1588.33, "end": 1588.87, "word": " يؤدي", "probability": 0.892578125}, {"start": 1588.87, "end": 1589.79, "word": " أن", "probability": 0.26318359375}, {"start": 1589.79, "end": 1590.25, "word": " F", "probability": 0.84228515625}, {"start": 1590.25, "end": 1590.55, "word": " of", "probability": 0.87890625}, {"start": 1590.55, "end": 1590.89, "word": " N", "probability": 0.9736328125}, {"start": 1590.89, "end": 1591.23, "word": " cross", "probability": 0.93603515625}, {"start": 1591.23, "end": 1591.47, "word": " ال", "probability": 0.953125}, {"start": 1591.47, "end": 1591.77, "word": " N", "probability": 0.98046875}, {"start": 1591.77, "end": 1592.89, "word": " is", "probability": 0.94482421875}, {"start": 1592.89, "end": 1593.45, "word": " innumerable", "probability": 0.78076171875}], "temperature": 1.0}, {"id": 66, "seek": 162539, "start": 1598.43, "end": 1625.39, "text": "هذه نظرية نظرية جداش infinite subset of denumerable set is denumerable نظرية خمسة تمانية صحيح خلاص مع ذلك عملية equivalence relation therefore n x n is denumerable", "tokens": [3224, 24192, 8717, 19913, 2288, 10632, 8717, 19913, 2288, 10632, 10874, 3215, 33599, 13785, 25993, 295, 1441, 15583, 712, 992, 307, 1441, 15583, 712, 8717, 19913, 2288, 10632, 16490, 2304, 3794, 3660, 46811, 7649, 10632, 20328, 5016, 1829, 5016, 16490, 1211, 33546, 20449, 29910, 23275, 6225, 42213, 10632, 9052, 655, 9721, 4412, 297, 2031, 297, 307, 1441, 15583, 712], "avg_logprob": -0.288802078862985, "compression_ratio": 1.4489795918367347, "no_speech_prob": 0.0, "words": [{"start": 1598.43, "end": 1598.77, "word": "هذه", "probability": 0.853759765625}, {"start": 1598.77, "end": 1599.29, "word": " نظرية", "probability": 0.9732666015625}, {"start": 1599.29, "end": 1600.59, "word": " نظرية", "probability": 0.84283447265625}, {"start": 1600.59, "end": 1601.15, "word": " جداش", "probability": 0.5769856770833334}, {"start": 1601.15, "end": 1603.27, "word": " infinite", "probability": 0.58447265625}, {"start": 1603.27, "end": 1603.87, "word": " subset", "probability": 0.91259765625}, {"start": 1603.87, "end": 1604.03, "word": " of", "probability": 0.9599609375}, {"start": 1604.03, "end": 1604.57, "word": " denumerable", "probability": 0.600830078125}, {"start": 1604.57, "end": 1604.83, "word": " set", "probability": 0.9267578125}, {"start": 1604.83, "end": 1605.17, "word": " is", "probability": 0.91064453125}, {"start": 1605.17, "end": 1606.01, "word": " denumerable", "probability": 0.9072265625}, {"start": 1606.01, "end": 1607.01, "word": " نظرية", "probability": 0.9559326171875}, {"start": 1607.01, "end": 1607.79, "word": " خمسة", "probability": 0.9044189453125}, {"start": 1607.79, "end": 1611.85, "word": " تمانية", "probability": 0.7997233072916666}, {"start": 1611.85, "end": 1612.73, "word": " صحيح", "probability": 0.76141357421875}, {"start": 1612.73, "end": 1615.31, "word": " خلاص", "probability": 0.7452799479166666}, {"start": 1615.31, "end": 1615.65, "word": " مع", "probability": 0.09405517578125}, {"start": 1615.65, "end": 1615.89, "word": " ذلك", "probability": 0.869140625}, {"start": 1615.89, "end": 1616.37, "word": " عملية", "probability": 0.9244791666666666}, {"start": 1616.37, "end": 1617.47, "word": " equivalence", "probability": 0.6571044921875}, {"start": 1617.47, "end": 1618.35, "word": " relation", "probability": 0.98974609375}, {"start": 1618.35, "end": 1620.25, "word": " therefore", "probability": 0.58642578125}, {"start": 1620.25, "end": 1622.65, "word": " n", "probability": 0.258056640625}, {"start": 1622.65, "end": 1622.99, "word": " x", "probability": 0.26953125}, {"start": 1622.99, "end": 1623.55, "word": " n", "probability": 0.95751953125}, {"start": 1623.55, "end": 1624.87, "word": " is", "probability": 0.9072265625}, {"start": 1624.87, "end": 1625.39, "word": " denumerable", "probability": 0.9547526041666666}], "temperature": 1.0}, {"id": 67, "seek": 165696, "start": 1629.36, "end": 1656.96, "text": "ليش؟ لأن علاقة التكافئة في واحدة شمالها equivalence relation وبشكل خاص شمالها transitive is transitive فاحنا ليش أثبتنا أن cross الان تكافئ هذه المجموعة و هذه المجموعة تكافئ الان فإذا الأولى تكافئ التالتة وهو المطلوب فهنا ماقدرناش نوصل مباشرة لكن وصلنا بهذه الطريقة غير المباشرة", "tokens": [20292, 8592, 22807, 5296, 33456, 11203, 995, 28671, 16712, 4117, 31845, 19986, 3660, 8978, 36764, 24401, 3660, 13412, 2304, 6027, 11296, 9052, 655, 9721, 46599, 8592, 28820, 16490, 33546, 13412, 2304, 6027, 11296, 1145, 2187, 307, 1145, 2187, 6156, 39319, 8315, 32239, 8592, 5551, 12984, 3555, 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"word": " في", "probability": 0.425048828125}, {"start": 1632.18, "end": 1632.3, "word": " واحدة", "probability": 0.6028645833333334}, {"start": 1632.3, "end": 1632.74, "word": " شمالها", "probability": 0.8724365234375}, {"start": 1632.74, "end": 1633.78, "word": " equivalence", "probability": 0.736572265625}, {"start": 1633.78, "end": 1634.22, "word": " relation", "probability": 0.98779296875}, {"start": 1634.22, "end": 1634.86, "word": " وبشكل", "probability": 0.8942057291666666}, {"start": 1634.86, "end": 1635.16, "word": " خاص", "probability": 0.97314453125}, {"start": 1635.16, "end": 1635.64, "word": " شمالها", "probability": 0.8778076171875}, {"start": 1635.64, "end": 1636.6, "word": " transitive", "probability": 0.87548828125}, {"start": 1636.6, "end": 1637.48, "word": " is", "probability": 0.3984375}, {"start": 1637.48, "end": 1640.82, "word": " transitive", "probability": 0.761962890625}, {"start": 1640.82, "end": 1643.1, "word": " فاحنا", "probability": 0.6236165364583334}, {"start": 1643.1, "end": 1643.24, "word": " ليش", "probability": 0.7109375}, {"start": 1643.24, "end": 1643.76, "word": " أثبتنا", "probability": 0.9330078125}, {"start": 1643.76, "end": 1643.98, "word": " أن", "probability": 0.435302734375}, {"start": 1643.98, "end": 1644.24, "word": " cross", "probability": 0.5927734375}, {"start": 1644.24, "end": 1644.54, "word": " الان", "probability": 0.62744140625}, {"start": 1644.54, "end": 1645.02, "word": " تكافئ", "probability": 0.99365234375}, {"start": 1645.02, "end": 1645.44, "word": " هذه", "probability": 0.89501953125}, {"start": 1645.44, "end": 1646.62, "word": " المجموعة", "probability": 0.9353515625}, {"start": 1646.62, "end": 1646.76, "word": " و", "probability": 0.67626953125}, {"start": 1646.76, "end": 1646.88, "word": " هذه", "probability": 0.458984375}, {"start": 1646.88, "end": 1647.34, "word": " المجموعة", "probability": 0.94453125}, {"start": 1647.34, "end": 1647.88, "word": " تكافئ", "probability": 0.9962158203125}, {"start": 1647.88, "end": 1648.22, "word": " الان", "probability": 0.946044921875}, {"start": 1648.22, "end": 1648.74, "word": " فإذا", "probability": 0.748046875}, {"start": 1648.74, "end": 1649.08, "word": " الأولى", "probability": 0.9378255208333334}, {"start": 1649.08, "end": 1649.48, "word": " تكافئ", "probability": 0.995849609375}, {"start": 1649.48, "end": 1650.4, "word": " التالتة", "probability": 0.8760986328125}, {"start": 1650.4, "end": 1650.76, "word": " وهو", "probability": 0.7509765625}, {"start": 1650.76, "end": 1651.26, "word": " المطلوب", "probability": 0.990234375}, {"start": 1651.26, "end": 1652.36, "word": " فهنا", "probability": 0.94921875}, {"start": 1652.36, "end": 1652.92, "word": " ماقدرناش", "probability": 0.7876953125}, {"start": 1652.92, "end": 1653.18, "word": " نوصل", "probability": 0.978515625}, {"start": 1653.18, "end": 1653.86, "word": " مباشرة", "probability": 0.9820556640625}, {"start": 1653.86, "end": 1654.44, "word": " لكن", "probability": 0.88330078125}, {"start": 1654.44, "end": 1654.94, "word": " وصلنا", "probability": 0.8346354166666666}, {"start": 1654.94, "end": 1655.3, "word": " بهذه", "probability": 0.963623046875}, {"start": 1655.3, "end": 1655.8, "word": " الطريقة", "probability": 0.990234375}, {"start": 1655.8, "end": 1656.34, "word": " غير", "probability": 0.995361328125}, {"start": 1656.34, "end": 1656.96, "word": " المباشرة", "probability": 0.9925537109375}], "temperature": 1.0}, {"id": 68, "seek": 167005, "start": 1659.99, "end": 1670.05, "text": "هذه واحدة التركيات التي نجعلها أحياناً عندما الأمور لا تصبح مجموعة كبيرة ولا نستطيع إجابة بشكل مباشر", "tokens": [3224, 24192, 36764, 24401, 3660, 16712, 31747, 1829, 9307, 38392, 8717, 7435, 30241, 11296, 5551, 5016, 1829, 7649, 995, 14111, 43242, 15042, 16247, 2304, 13063, 20193, 6055, 9381, 49628, 3714, 7435, 2304, 2407, 27884, 9122, 3555, 48923, 49429, 8717, 14851, 9566, 40228, 11933, 7435, 16758, 3660, 4724, 8592, 28820, 3714, 3555, 33599, 2288], "avg_logprob": 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"probability": 0.768505859375}, {"start": 1666.55, "end": 1667.01, "word": " كبيرة", "probability": 0.9685872395833334}, {"start": 1667.01, "end": 1667.55, "word": " ولا", "probability": 0.20849609375}, {"start": 1667.55, "end": 1667.91, "word": " نستطيع", "probability": 0.888427734375}, {"start": 1667.91, "end": 1668.43, "word": " إجابة", "probability": 0.5142822265625}, {"start": 1668.43, "end": 1669.55, "word": " بشكل", "probability": 0.9187825520833334}, {"start": 1669.55, "end": 1670.05, "word": " مباشر", "probability": 0.9835205078125}], "temperature": 1.0}, {"id": 69, "seek": 170773, "start": 1679.53, "end": 1707.73, "text": "مزيد من التوسع دائما حاضر فزي ما احنا شايفين احنا كل ما لقوا بدينا يعني المم��ن الفكرة اللي ماشيين فيها جاعدين بنكبر كل ما قاش وانا نوصل هل هتوجه مرحلة ونبطل denim rubble بنشوف بنكبر denim rubble بنكبر denim rubble بدنا نشوف وقت إيش الكلب بده يطف ويتبطل المجموعة denim rubble لمّا جداش نكبرها جداش نضفلها فعنا نتيجة خمسة خمسة", "tokens": [2304, 11622, 25708, 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{"start": 1706.45, "end": 1706.93, "word": " نتيجة", "probability": 0.995849609375}, {"start": 1706.93, "end": 1707.33, "word": " خمسة", "probability": 0.77734375}, {"start": 1707.33, "end": 1707.73, "word": " خمسة", "probability": 0.9693603515625}], "temperature": 1.0}, {"id": 70, "seek": 172182, "start": 1708.86, "end": 1721.82, "text": "Infinite union of disjoint denumerable sets is denumerable كان في عندنا نتيجة نتيجة اللي هو finite union", "tokens": [4575, 5194, 642, 11671, 295, 717, 48613, 1441, 15583, 712, 6352, 307, 1441, 15583, 712, 25961, 8978, 43242, 8315, 8717, 31371, 7435, 3660, 8717, 31371, 7435, 3660, 13672, 1829, 31439, 19362, 11671], "avg_logprob": -0.37642045454545453, "compression_ratio": 1.2745098039215685, "no_speech_prob": 0.0, "words": [{"start": 1708.86, "end": 1709.62, "word": "Infinite", "probability": 0.7107747395833334}, {"start": 1709.62, "end": 1710.1, "word": " union", "probability": 0.70361328125}, {"start": 1710.1, "end": 1710.42, "word": " of", 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1747.64, "end": 1771.2, "text": "نشوف البرهان و الفكرة تبعها البرهان و إيش بدنا نشتغل معاها for each k تنتمي لأن لأي عدد طبيعي let a sub k be a denominable set satisfying a j تقاطع a k تساوي five for all j لا تساوي k نحاول نفهم هذا الكلام", "tokens": [1863, 8592, 38688, 2423, 26890, 3224, 7649, 4032, 27188, 4117, 25720, 6055, 3555, 3615, 11296, 2423, 26890, 3224, 7649, 4032, 11933, 1829, 8592, 47525, 8315, 8717, 8592, 2655, 17082, 1211, 20449, 995, 11296, 337, 1184, 350, 6055, 29399, 2304, 1829, 5296, 33456, 5296, 10721, 1829, 6225, 3215, 3215, 23032, 21292, 3615, 1829, 718, 257, 1422, 350, 312, 257, 1441, 6981, 712, 992, 18348, 257, 361, 6055, 4587, 41193, 3615, 257, 350, 6055, 3794, 995, 45865, 1732, 337, 439, 361, 20193, 6055, 3794, 995, 45865, 350, 8717, 5016, 995, 12610, 8717, 5172, 16095, 23758, 2423, 28820, 10943], "avg_logprob": -0.23179767549652414, "compression_ratio": 1.5049019607843137, "no_speech_prob": 0.0, "words": [{"start": 1747.64, "end": 1748.26, "word": "نشوف", 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{"start": 2668.27, "end": 2668.59, "word": " Q", "probability": 0.9033203125}, {"start": 2668.59, "end": 2668.81, "word": " Plus", "probability": 0.8759765625}, {"start": 2668.81, "end": 2669.17, "word": " شمالها", "probability": 0.725341796875}, {"start": 2669.17, "end": 2669.41, "word": " أكبر", "probability": 0.9601236979166666}, {"start": 2669.41, "end": 2669.57, "word": " من", "probability": 0.99267578125}, {"start": 2669.57, "end": 2669.73, "word": " الـ", "probability": 0.771484375}, {"start": 2669.73, "end": 2669.89, "word": " N", "probability": 0.8779296875}, {"start": 2669.89, "end": 2670.43, "word": " Infinite", "probability": 0.72705078125}, {"start": 2670.43, "end": 2671.05, "word": " أه", "probability": 0.7646484375}, {"start": 2671.05, "end": 2671.79, "word": " فالأن", "probability": 0.7744140625}, {"start": 2671.79, "end": 2672.79, "word": " ال", "probability": 0.59814453125}, {"start": 2672.79, "end": 2673.13, "word": " subset", "probability": 0.84521484375}, {"start": 2673.13, "end": 2673.81, "word": " and", "probability": 0.6455078125}, {"start": 2673.81, "end": 2675.49, "word": " F", "probability": 0.73046875}, {"start": 2675.49, "end": 2675.67, "word": " of", "probability": 0.6953125}, {"start": 2675.67, "end": 2675.97, "word": " Q", "probability": 0.92236328125}, {"start": 2675.97, "end": 2676.59, "word": " Plus", "probability": 0.845703125}, {"start": 2676.59, "end": 2678.89, "word": " is", "probability": 0.91552734375}, {"start": 2678.89, "end": 2679.41, "word": " Infinite", "probability": 0.76318359375}], "temperature": 1.0}, {"id": 106, "seek": 270982, "start": 2681.62, "end": 2709.82, "text": "implies F of Q plus is denumerable وبالتالي Q plus is denumerable والباقي زي ما حكينا طبعا Q minus تكافئ Q plus Q minus", "tokens": [332, 564, 530, 479, 295, 1249, 1804, 307, 1441, 15583, 712, 46599, 6027, 2655, 6027, 1829, 1249, 1804, 307, 1441, 15583, 712, 4032, 6027, 3555, 995, 38436, 30767, 1829, 19446, 11331, 4117, 1829, 8315, 23032, 3555, 3615, 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