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partition of I بدي يكون ال lower اللي هو sum لأي partition B و function F أصغر أو يساوي ال upper sum لنفس ال partition و لنفس اللي هي ال function F بعد هي طبعا خطينا خطوة أخرى", "tokens": [6027, 148, 48506, 5551, 9778, 3215, 8315, 5551, 12610, 32767, 11703, 3660, 9673, 25720, 9673, 46958, 10632, 4032, 4587, 1211, 8315, 11933, 15730, 25961, 2655, 479, 9154, 286, 5296, 49, 37498, 4032, 363, 604, 24808, 295, 286, 4724, 16254, 7251, 30544, 2423, 3126, 13672, 1829, 31439, 2408, 5296, 10721, 1829, 24808, 363, 4032, 2445, 479, 5551, 9381, 17082, 2288, 34051, 7251, 3794, 995, 45865, 2423, 6597, 2408, 5296, 1863, 36178, 2423, 24808, 4032, 5296, 1863, 36178, 13672, 1829, 39896, 2423, 2445, 479, 39182, 39896, 23032, 3555, 3615, 995, 16490, 9566, 1829, 8315, 16490, 9566, 2407, 3660, 5551, 34740, 7578], "avg_logprob": -0.2101562462747097, "compression_ratio": 1.6457399103139014, "no_speech_prob": 8.344650268554688e-07, "words": [{"start": 91.05, "end": 91.61, "word": "الآن", "probability": 0.6083984375}, {"start": 91.61, "end": 92.15, "word": " أخدنا", "probability": 0.881103515625}, {"start": 92.15, "end": 92.49, "word": " أول", "probability": 0.976318359375}, {"start": 92.49, "end": 93.09, "word": " لمّة", "probability": 0.71630859375}, {"start": 93.09, "end": 94.11, "word": " المرة", "probability": 0.947021484375}, {"start": 94.11, "end": 94.75, "word": " الماضية", "probability": 0.9939778645833334}, {"start": 94.75, "end": 95.27, "word": " وقلنا", "probability": 0.8489990234375}, {"start": 95.27, "end": 95.45, "word": " إذا", "probability": 0.893798828125}, {"start": 95.45, "end": 95.77, "word": " كانت", "probability": 0.8896484375}, {"start": 95.77, "end": 95.93, "word": " F", "probability": 0.477783203125}, {"start": 95.93, "end": 96.07, "word": " من", "probability": 0.95947265625}, {"start": 96.07, "end": 96.25, "word": " I", "probability": 0.97705078125}, {"start": 96.25, "end": 96.57, "word": " لR", "probability": 0.6402587890625}, {"start": 96.57, "end": 97.17, "word": " bounded", "probability": 0.71826171875}, {"start": 97.17, "end": 97.65, "word": " و", "probability": 0.76025390625}, {"start": 97.65, "end": 97.85, "word": " B", "probability": 0.19482421875}, {"start": 97.85, "end": 98.19, "word": " any", "probability": 0.52490234375}, {"start": 98.19, "end": 98.63, "word": " partition", "probability": 0.9208984375}, {"start": 98.63, "end": 98.93, "word": " of", "probability": 0.97119140625}, {"start": 98.93, "end": 99.27, "word": " I", "probability": 0.98876953125}, {"start": 99.27, "end": 99.55, "word": " بدي", "probability": 0.5367431640625}, {"start": 99.55, "end": 99.87, "word": " يكون", "probability": 0.6761474609375}, {"start": 99.87, "end": 100.15, "word": " ال", "probability": 0.93359375}, {"start": 100.15, "end": 100.65, "word": " lower", "probability": 0.6025390625}, {"start": 100.65, "end": 101.31, "word": " اللي", "probability": 0.854248046875}, {"start": 101.31, "end": 101.59, "word": " هو", "probability": 0.98046875}, {"start": 101.59, "end": 102.05, "word": " sum", "probability": 0.81689453125}, {"start": 102.05, "end": 103.23, "word": " لأي", "probability": 0.8489583333333334}, {"start": 103.23, "end": 104.33, "word": " partition", "probability": 0.6484375}, {"start": 104.33, "end": 104.95, "word": " B", "probability": 0.70166015625}, {"start": 104.95, "end": 105.31, "word": " و", "probability": 0.9833984375}, {"start": 105.31, "end": 105.75, "word": " function", "probability": 0.490234375}, {"start": 105.75, "end": 106.31, "word": " F", "probability": 0.97509765625}, {"start": 106.31, "end": 107.07, "word": " أصغر", "probability": 0.9805908203125}, {"start": 107.07, "end": 107.19, "word": " أو", "probability": 0.869140625}, {"start": 107.19, "end": 107.47, "word": " يساوي", "probability": 0.6431884765625}, {"start": 107.47, "end": 107.59, "word": " ال", "probability": 0.8681640625}, {"start": 107.59, "end": 107.81, "word": " upper", "probability": 0.59716796875}, {"start": 107.81, "end": 108.19, "word": " sum", "probability": 0.921875}, {"start": 108.19, "end": 108.69, "word": " لنفس", "probability": 0.9850260416666666}, {"start": 108.69, "end": 108.83, "word": " ال", "probability": 0.9609375}, {"start": 108.83, "end": 109.29, "word": " partition", "probability": 0.87548828125}, {"start": 109.29, "end": 109.99, "word": " و", "probability": 0.83935546875}, {"start": 109.99, "end": 110.53, "word": " لنفس", "probability": 0.9345703125}, {"start": 110.53, "end": 110.79, "word": " اللي", "probability": 0.7308349609375}, {"start": 110.79, "end": 111.19, "word": " هي", "probability": 0.93408203125}, {"start": 111.19, "end": 111.45, "word": " ال", "probability": 0.943359375}, {"start": 111.45, "end": 111.85, "word": " function", "probability": 0.95654296875}, {"start": 111.85, "end": 112.47, "word": " F", "probability": 0.9755859375}, {"start": 112.47, "end": 113.35, "word": " بعد", "probability": 0.9033203125}, {"start": 113.35, "end": 113.57, "word": " هي", "probability": 0.95556640625}, {"start": 113.57, "end": 114.03, "word": " طبعا", "probability": 0.8714599609375}, {"start": 114.03, "end": 115.03, "word": " خطينا", "probability": 0.894287109375}, {"start": 115.03, "end": 115.43, "word": " خطوة", "probability": 0.991455078125}, {"start": 115.43, "end": 115.95, "word": " أخرى", "probability": 0.9890950520833334}], "temperature": 1.0}, {"id": 6, "seek": 13141, "start": 116.45, "end": 131.41, "text": "و جينا عرفنا اللي هو شو معناته انها تكون اللي هو ال partition Q refinement لل partition B قلنا Q اللي هو تحسين ل B إذا كانت B بي عبارة عن مجموعة جزئية من Q", "tokens": [2407, 10874, 1829, 8315, 6225, 28480, 8315, 13672, 1829, 31439, 13412, 2407, 20449, 8315, 47395, 16472, 11296, 6055, 30544, 13672, 1829, 31439, 2423, 24808, 1249, 1895, 30229, 24976, 24808, 363, 12174, 1211, 8315, 1249, 13672, 1829, 31439, 6055, 5016, 3794, 9957, 5296, 363, 11933, 15730, 25961, 2655, 363, 4724, 1829, 6225, 3555, 9640, 3660, 18871, 3714, 7435, 2304, 2407, 27884, 10874, 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"word": " هو", "probability": 0.9638671875}, {"start": 120.89, "end": 121.31, "word": " ال", "probability": 0.6318359375}, {"start": 121.31, "end": 121.89, "word": " partition", "probability": 0.386474609375}, {"start": 121.89, "end": 122.35, "word": " Q", "probability": 0.1663818359375}, {"start": 122.35, "end": 123.11, "word": " refinement", "probability": 0.63232421875}, {"start": 123.11, "end": 123.39, "word": " لل", "probability": 0.720703125}, {"start": 123.39, "end": 123.85, "word": " partition", "probability": 0.70263671875}, {"start": 123.85, "end": 124.21, "word": " B", "probability": 0.8115234375}, {"start": 124.21, "end": 125.07, "word": " قلنا", "probability": 0.7986653645833334}, {"start": 125.07, "end": 125.51, "word": " Q", "probability": 0.373046875}, {"start": 125.51, "end": 125.81, "word": " اللي", "probability": 0.96044921875}, {"start": 125.81, "end": 125.95, "word": " هو", "probability": 0.96240234375}, {"start": 125.95, "end": 126.55, "word": " تحسين", "probability": 0.9896240234375}, {"start": 126.55, "end": 126.73, "word": " ل", "probability": 0.84423828125}, {"start": 126.73, "end": 127.01, "word": " B", "probability": 0.5771484375}, {"start": 127.01, "end": 127.85, "word": " إذا", "probability": 0.8515625}, {"start": 127.85, "end": 128.31, "word": " كانت", "probability": 0.9716796875}, {"start": 128.31, "end": 128.61, "word": " B", "probability": 0.7841796875}, {"start": 128.61, "end": 128.93, "word": " بي", "probability": 0.631591796875}, {"start": 128.93, "end": 129.35, "word": " عبارة", "probability": 0.9488525390625}, {"start": 129.35, "end": 129.49, "word": " عن", "probability": 0.98876953125}, {"start": 129.49, "end": 130.01, "word": " مجموعة", "probability": 0.96728515625}, {"start": 130.01, "end": 130.67, "word": " جزئية", "probability": 0.9501953125}, {"start": 130.67, "end": 131.13, "word": " من", "probability": 0.99267578125}, {"start": 131.13, "end": 131.41, "word": " Q", "probability": 0.806640625}], "temperature": 1.0}, {"id": 7, "seek": 14768, "start": 131.66, "end": 147.68, "text": "و بناء عليه اللي هو قلنا ان اي اللي هو sub interval xk-1xk من ال partition B يمكن كتابتها على صورة union of sub intervals من اللي هو التحسين اللي هو EQ", "tokens": [2407, 44945, 16606, 47356, 13672, 1829, 31439, 12174, 1211, 8315, 16472, 1975, 1829, 13672, 1829, 31439, 1422, 15035, 2031, 74, 12, 16, 87, 74, 9154, 2423, 24808, 363, 7251, 43020, 9122, 2655, 16758, 2655, 11296, 15844, 20328, 13063, 3660, 11671, 295, 1422, 26651, 9154, 13672, 1829, 31439, 16712, 5016, 3794, 9957, 13672, 1829, 31439, 33580], "avg_logprob": -0.23353794323546545, "compression_ratio": 1.457516339869281, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 131.66, "end": 132.0, "word": "و", "probability": 0.54638671875}, {"start": 132.0, "end": 132.4, "word": " بناء", "probability": 0.884521484375}, {"start": 132.4, "end": 132.98, "word": " عليه", "probability": 0.479248046875}, {"start": 132.98, "end": 133.82, "word": " اللي", "probability": 0.8271484375}, {"start": 133.82, "end": 133.94, "word": " هو", "probability": 0.8984375}, {"start": 133.94, "end": 134.32, "word": " قلنا", "probability": 0.8639322916666666}, {"start": 134.32, "end": 134.52, "word": " ان", "probability": 0.41845703125}, {"start": 134.52, "end": 135.08, "word": " اي", "probability": 0.6907958984375}, {"start": 135.08, "end": 135.4, "word": " اللي", "probability": 0.85595703125}, {"start": 135.4, "end": 135.68, "word": " هو", "probability": 0.96044921875}, {"start": 135.68, "end": 136.18, "word": " sub", "probability": 0.9130859375}, {"start": 136.18, "end": 136.98, "word": " interval", "probability": 0.60400390625}, {"start": 136.98, "end": 137.88, "word": " xk", "probability": 0.4771728515625}, {"start": 137.88, "end": 139.18, "word": "-1xk", "probability": 0.644805908203125}, {"start": 139.18, "end": 139.3, "word": " من", "probability": 0.94970703125}, {"start": 139.3, "end": 139.44, "word": " ال", "probability": 0.86572265625}, {"start": 139.44, "end": 139.86, "word": " partition", "probability": 0.5791015625}, {"start": 139.86, "end": 140.34, "word": " B", "probability": 0.59423828125}, {"start": 140.34, "end": 141.14, "word": " يمكن", "probability": 0.968017578125}, {"start": 141.14, "end": 141.7, "word": " كتابتها", "probability": 0.96669921875}, {"start": 141.7, "end": 141.9, "word": " على", "probability": 0.9033203125}, {"start": 141.9, "end": 142.3, "word": " صورة", "probability": 0.9835611979166666}, {"start": 142.3, "end": 142.74, "word": " union", "probability": 0.5654296875}, {"start": 142.74, "end": 143.22, "word": " of", "probability": 0.96240234375}, {"start": 143.22, "end": 143.52, "word": " sub", "probability": 0.9697265625}, {"start": 143.52, "end": 144.2, "word": " intervals", "probability": 0.81640625}, {"start": 144.2, "end": 144.48, "word": " من", "probability": 0.90283203125}, {"start": 144.48, "end": 145.08, "word": " اللي", "probability": 0.7861328125}, {"start": 145.08, "end": 145.58, "word": " هو", "probability": 0.86865234375}, {"start": 145.58, "end": 146.64, "word": " التحسين", "probability": 0.9815673828125}, {"start": 146.64, "end": 146.92, "word": " اللي", "probability": 0.76708984375}, {"start": 146.92, "end": 147.32, "word": " هو", "probability": 0.97900390625}, {"start": 147.32, "end": 147.68, "word": " EQ", "probability": 0.1844482421875}], "temperature": 1.0}, {"id": 8, "seek": 16410, "start": 151.06, "end": 164.1, "text": "الان جينا اللي هو بناء على هذا التعريف جينا قولنا لو كانت F is من I لعند R is bounded و B is any partition of I و Q refinement لل B", "tokens": [6027, 7649, 10874, 1829, 8315, 13672, 1829, 31439, 44945, 16606, 15844, 23758, 16712, 3615, 16572, 5172, 10874, 1829, 8315, 12174, 12610, 8315, 45164, 25961, 2655, 479, 307, 9154, 286, 5296, 3615, 41260, 497, 307, 37498, 4032, 363, 307, 604, 24808, 295, 286, 4032, 1249, 1895, 30229, 24976, 363], "avg_logprob": -0.2375637706445188, "compression_ratio": 1.2466666666666666, "no_speech_prob": 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0.92333984375}, {"start": 156.88, "end": 157.18, "word": " F", "probability": 0.398193359375}, {"start": 157.18, "end": 157.56, "word": " is", "probability": 0.460693359375}, {"start": 157.56, "end": 157.82, "word": " من", "probability": 0.97216796875}, {"start": 157.82, "end": 158.02, "word": " I", "probability": 0.9580078125}, {"start": 158.02, "end": 158.38, "word": " لعند", "probability": 0.81396484375}, {"start": 158.38, "end": 158.6, "word": " R", "probability": 0.9228515625}, {"start": 158.6, "end": 158.78, "word": " is", "probability": 0.90625}, {"start": 158.78, "end": 159.3, "word": " bounded", "probability": 0.896484375}, {"start": 159.3, "end": 159.86, "word": " و", "probability": 0.85791015625}, {"start": 159.86, "end": 160.04, "word": " B", "probability": 0.52099609375}, {"start": 160.04, "end": 160.28, "word": " is", "probability": 0.9658203125}, {"start": 160.28, "end": 160.48, "word": " any", "probability": 0.2763671875}, {"start": 160.48, "end": 160.94, "word": " partition", "probability": 0.92041015625}, {"start": 160.94, "end": 161.72, "word": " of", "probability": 0.974609375}, {"start": 161.72, "end": 162.14, "word": " I", "probability": 0.9912109375}, {"start": 162.14, "end": 162.62, "word": " و", "probability": 0.958984375}, {"start": 162.62, "end": 162.88, "word": " Q", "probability": 0.732421875}, {"start": 162.88, "end": 163.58, "word": " refinement", "probability": 0.7333984375}, {"start": 163.58, "end": 163.82, "word": " لل", "probability": 0.51220703125}, {"start": 163.82, "end": 164.1, "word": " B", "probability": 0.414306640625}], "temperature": 1.0}, {"id": 9, "seek": 19056, "start": 164.68, "end": 190.56, "text": "مدام اللي هو Q-refinement إذا ال lower sum هيعلى و ال upper sum هينزل على أساس انه اللي هو في النهاية يلتقي ال upper مع ال lower و نصل لاللي هو ال integrability أو معنى ال integrability كما سنرى لاحقا على الأقل في اللي هو يكون واضح من خلال الرسم في اللي هي الدوال الموجبة كما ذكرنا سابقا", "tokens": [2304, 3215, 10943, 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واضح ان الدالة هذه is a bounded function الان بدأ أثبت لكم ان هذا الدالة is not integrable on this interval is not integrable on this interval الان علشان أصل اللي هو اللي هي ان هذا الدالة غير قابلة تكامل بالنسبة لتكامل بالنسبة لتكامل الريمان بدي اخد الان B", "tokens": [6027, 20292, 43242, 497, 4032, 46958, 5016, 16472, 32748, 6027, 3660, 29538, 307, 257, 37498, 2445, 2423, 7649, 47525, 10721, 5551, 12984, 3555, 2655, 5296, 24793, 16472, 23758, 32748, 6027, 3660, 307, 406, 16200, 424, 638, 322, 341, 15035, 307, 406, 16200, 424, 638, 322, 341, 15035, 2423, 7649, 11203, 8592, 7649, 5551, 36520, 13672, 1829, 31439, 13672, 1829, 39896, 16472, 23758, 32748, 6027, 3660, 32771, 13546, 12174, 16758, 37977, 6055, 4117, 10943, 1211, 20666, 1863, 35457, 3660, 5296, 2655, 4117, 10943, 1211, 20666, 1863, 35457, 3660, 5296, 2655, 4117, 10943, 1211, 2423, 16572, 2304, 7649, 4724, 16254, 1975, 9778, 3215, 2423, 7649, 363], "avg_logprob": -0.25803570974440804, "compression_ratio": 1.975609756097561, 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partitions اللي هو B of I هيكون ال .. ال Supremum اللي هين صفر لإن كل اللي هين أصلا إشق بتنطلع .. تنطلع بساوي صفر إذا هذا إيش هيساوي يا شباب؟ هو يساوي Zero", "tokens": [10721, 2407, 2423, 39184, 9141, 2579, 449, 2423, 39184, 9141, 2579, 449, 5296, 28820, 2423, 39184, 441, 295, 363, 4032, 479, 9653, 300, 363, 4478, 294, 264, 992, 295, 439, 644, 2451, 13672, 1829, 31439, 363, 295, 286, 39896, 30544, 2423, 4386, 2423, 9141, 2579, 449, 13672, 1829, 8032, 9957, 20328, 5172, 2288, 5296, 28814, 1863, 28242, 13672, 1829, 8032, 9957, 5551, 9381, 15040, 11933, 8592, 4587, 39894, 1863, 9566, 1211, 3615, 4386, 6055, 1863, 9566, 1211, 3615, 4724, 3794, 995, 45865, 20328, 5172, 2288, 11933, 15730, 23758, 11933, 1829, 8592, 39896, 3794, 995, 45865, 35186, 13412, 3555, 16758, 22807, 31439, 7251, 3794, 995, 45865, 17182], "avg_logprob": -0.271466108126061, "compression_ratio": 1.6893203883495145, "no_speech_prob": 2.9802322387695312e-06, "words": [{"start": 658.53, "end": 659.15, "word": "أو", 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"tokens": [6027, 7649, 8717, 1829, 7435, 1829, 5296, 6027, 20292, 31439, 46691, 3714, 16095, 3660, 13672, 1829, 1975, 5016, 8315, 44945, 38251, 1829, 11296, 13672, 1829, 39896, 6225, 3555, 9640, 3660, 18871, 6222, 46691, 337, 16200, 5305, 1140], "avg_logprob": -0.28556742087790843, "compression_ratio": 1.2820512820512822, "no_speech_prob": 0.0, "words": [{"start": 879.0, "end": 879.52, "word": "الان", "probability": 0.708984375}, {"start": 879.52, "end": 880.14, "word": " نيجي", "probability": 0.82025146484375}, {"start": 880.14, "end": 880.86, "word": " لاللي", "probability": 0.530029296875}, {"start": 880.86, "end": 881.4, "word": " هو", "probability": 0.91650390625}, {"start": 881.4, "end": 883.04, "word": " criterion", "probability": 0.85302734375}, {"start": 883.04, "end": 884.36, "word": " مهمة", "probability": 0.94482421875}, {"start": 884.36, "end": 884.78, "word": " اللي", "probability": 0.896484375}, {"start": 884.78, "end": 885.6, "word": " احنا", "probability": 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طرق أخرى نحاول اللي هو نوسع اللي هي", "tokens": [10721, 5016, 8315, 23032, 3555, 3615, 995, 1975, 2655, 24401, 12984, 8315, 18871, 2423, 39184, 4080, 491, 5681, 1146, 5305, 1140, 9122, 33911, 8717, 12984, 3555, 2655, 14739, 3224, 4080, 491, 5681, 1146, 424, 638, 18871, 23032, 16572, 4587, 16712, 3615, 16572, 5172, 23032, 3555, 3615, 995, 6024, 48506, 37893, 11778, 47302, 15042, 47525, 8315, 8717, 12984, 3555, 2655, 18871, 23032, 16572, 4587, 16712, 3615, 16572, 5172, 11933, 15730, 47525, 8315, 13672, 1829, 31439, 23032, 2288, 4587, 5551, 34740, 7578, 8717, 5016, 995, 12610, 13672, 1829, 31439, 8717, 41779, 3615, 13672, 1829, 39896], "avg_logprob": -0.13264628277814133, "compression_ratio": 1.7714285714285714, "no_speech_prob": 1.7881393432617188e-06, "words": [{"start": 896.63, "end": 897.29, "word": "أحنا", "probability": 0.744140625}, {"start": 897.29, "end": 897.77, "word": " طبعا", "probability": 0.943603515625}, {"start": 897.77, "end": 898.97, "word": " اتحدثنا", "probability": 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there exists P إبسلون a partition of I such that ال P ال U ال P إبسلون", "tokens": [6027, 20292, 39896, 5296, 28820, 11933, 3555, 3794, 1211, 11536, 5551, 4117, 26890, 9154, 1958, 456, 8198, 257, 24808, 430, 11933, 3555, 3794, 1211, 11536, 23758, 2423, 430, 13672, 1829, 31439, 2423, 24808, 7251, 34268, 2304, 3215, 6225, 45340, 25528, 15844, 11933, 3555, 3794, 1211, 11536, 5296, 28820, 11933, 3555, 3794, 1211, 11536, 20666, 43761, 11778, 1829, 24808, 430, 11933, 3555, 3794, 1211, 11536, 5296, 2304, 9957, 2423, 24808, 23032, 3555, 3615, 995, 24976, 15035, 13672, 1829, 43242, 8315, 13672, 1829, 39896, 497, 456, 8198, 430, 11933, 3555, 3794, 1211, 11536, 257, 24808, 295, 286, 1270, 300, 2423, 430, 2423, 624, 2423, 430, 11933, 3555, 3794, 1211, 11536], "avg_logprob": -0.18133601136163835, "compression_ratio": 2.0656565656565657, "no_speech_prob": 3.0994415283203125e-05, "words": [{"start": 1014.76, "end": 1015.14, "word": "اللي", "probability": 0.7353515625}, {"start": 1015.14, "end": 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integrable أكيد لكل إبسلون هلجي بي إبسلون بحيث أن هذا يتحقق خلونا نيجي الآن نبرهم و نشوف كيف بدنا نبرهم نظريتنا", "tokens": [2407, 6027, 39184, 479, 8717, 995, 4587, 9381, 2423, 39184, 441, 4724, 1829, 11933, 3555, 3794, 1211, 11536, 4032, 479, 7251, 30544, 5551, 9381, 17082, 2288, 9154, 3714, 9957, 9154, 11933, 3555, 3794, 1211, 11536, 6024, 48506, 11933, 15730, 25961, 5296, 7435, 1829, 8315, 5296, 28820, 11933, 3555, 3794, 1211, 11536, 5296, 7435, 1829, 8315, 4724, 1829, 11933, 3555, 3794, 1211, 11536, 4724, 5016, 1829, 12984, 23758, 7251, 2655, 5016, 4587, 4587, 20449, 8315, 47395, 479, 307, 16200, 424, 638, 293, 2615, 736, 498, 479, 307, 16200, 424, 638, 5551, 4117, 25708, 5296, 28820, 11933, 3555, 3794, 1211, 11536, 8032, 1211, 7435, 1829, 4724, 1829, 11933, 3555, 3794, 1211, 11536, 4724, 5016, 1829, 12984, 14739, 23758, 7251, 2655, 5016, 4587, 4587, 16490, 1211, 2407, 8315, 8717, 1829, 7435, 1829, 6024, 48506, 8717, 26890, 16095, 4032, 8717, 8592, 38688, 9122, 33911, 47525, 8315, 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"start": 1069.54, "end": 1096.8, "text": "الان بدنا نفترض ان F اي شمالها is integrable ونصل منها للي عيدي اللي هي ال partition اللي مذكور مدام F is integrable اذا كانت ..الان بنقول suppose that F is integrable مدام integrable يا شباب", "tokens": [6027, 7649, 47525, 8315, 8717, 5172, 2655, 43042, 16472, 479, 1975, 1829, 13412, 2304, 6027, 11296, 307, 16200, 424, 638, 4032, 1863, 36520, 9154, 11296, 5296, 20292, 6225, 1829, 16254, 13672, 1829, 39896, 2423, 24808, 13672, 1829, 3714, 8848, 4117, 13063, 3714, 3215, 10943, 479, 307, 16200, 424, 638, 1975, 15730, 25961, 2655, 4386, 6027, 7649, 44945, 39648, 7297, 300, 479, 307, 16200, 424, 638, 3714, 3215, 10943, 3572, 712, 35186, 13412, 3555, 16758], "avg_logprob": -0.2714583396911621, "compression_ratio": 1.5862068965517242, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1069.54, "end": 1070.02, "word": "الان", "probability": 0.7315673828125}, {"start": 1070.02, "end": 1070.9, "word": " بدنا", "probability": 0.8486328125}, 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of F هو إيش يا شباب؟ هو عبارة عن الـ infimum للـ L of B و F such that B element in B of I، مظبوط؟ إذا الـ U of F عبارة عن infimum يعني هو عبارة عن greatest lower bound", "tokens": [3615, 1863, 16254, 2423, 39184, 624, 295, 479, 31439, 11933, 1829, 8592, 35186, 13412, 3555, 16758, 22807, 31439, 6225, 3555, 9640, 3660, 18871, 2423, 39184, 1536, 332, 449, 24976, 39184, 441, 295, 363, 4032, 479, 1270, 300, 363, 4478, 294, 363, 295, 286, 12399, 3714, 19913, 3555, 2407, 9566, 22807, 11933, 15730, 2423, 39184, 624, 295, 479, 6225, 3555, 9640, 3660, 18871, 1536, 332, 449, 37495, 22653, 31439, 6225, 3555, 9640, 3660, 18871, 6636, 3126, 5472], "avg_logprob": -0.15858360931470797, "compression_ratio": 1.455621301775148, "no_speech_prob": 0.0, "words": [{"start": 1125.19, "end": 1125.73, "word": "عندي", "probability": 0.767578125}, {"start": 1125.73, "end": 1126.01, "word": " الـ", "probability": 0.83349609375}, {"start": 1126.01, "end": 1126.13, "word": " U", "probability": 0.56787109375}, 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1258.54, "text": "ماشي الحال الان ايش معناه انه هذا infimum معناته هذا هو عبارة عن ال greatest lower bound مدام ال greatest lower bound اذا ال lower bound هذا", "tokens": [2304, 33599, 1829, 21542, 6027, 2423, 7649, 1975, 1829, 8592, 20449, 8315, 3224, 16472, 3224, 23758, 1536, 332, 449, 20449, 8315, 47395, 23758, 31439, 6225, 3555, 9640, 3660, 18871, 2423, 6636, 3126, 5472, 3714, 3215, 10943, 2423, 6636, 3126, 5472, 1975, 15730, 2423, 3126, 5472, 23758], "avg_logprob": -0.3124999911227125, "compression_ratio": 1.558139534883721, "no_speech_prob": 9.953975677490234e-06, "words": [{"start": 1243.72, "end": 1244.04, "word": "ماشي", "probability": 0.8440755208333334}, {"start": 1244.04, "end": 1244.4, "word": " الحال", "probability": 0.959716796875}, {"start": 1244.4, "end": 1245.38, "word": " الان", "probability": 0.581298828125}, {"start": 1245.38, "end": 1245.74, "word": " ايش", "probability": 0.7503255208333334}, {"start": 1245.74, "end": 1246.38, "word": " معناه", "probability": 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مثلا بالذنب يابسون على اتنين الـ game بتعرفوا ليش يابسون على اتنين يعني لو ضفتله أي رقم بيبطل Lower Bound إيش معناته بيبطل Lower Bound يعني هيصير هذا أكبر من ال UB 1 of F for some B وحدها", "tokens": [10721, 2407, 2423, 39184, 3769, 377, 25523, 363, 554, 45164, 48812, 5172, 2655, 43761, 36632, 12602, 4587, 2304, 7251, 16758, 3794, 11536, 15844, 1975, 2655, 1863, 9957, 50113, 15040, 20666, 8848, 1863, 3555, 7251, 16758, 3794, 11536, 15844, 1975, 2655, 1863, 9957, 2423, 39184, 1216, 39894, 3615, 28480, 14407, 32239, 8592, 7251, 16758, 3794, 11536, 15844, 1975, 2655, 1863, 9957, 37495, 22653, 45164, 48812, 5172, 2655, 43761, 36632, 12602, 4587, 2304, 4724, 1829, 3555, 9566, 1211, 25523, 363, 554, 11933, 1829, 8592, 20449, 8315, 47395, 4724, 1829, 3555, 9566, 1211, 25523, 363, 554, 37495, 22653, 39896, 9381, 13546, 23758, 5551, 4117, 26890, 9154, 2423, 624, 33, 502, 295, 479, 337, 512, 363, 4032, 24401, 11296], "avg_logprob": -0.23343210590296778, "compression_ratio": 1.875, 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لأن الـBy يا جماعة عبارة عن refinement للـB2 والlower لما يصير فيه تحسين بكبر، بروح نحو اتجاه نيل اللي هو المنحنة التالية مساحة تحت المنحنة الكلية لأن أيضا لو جيت قولة الـU of F", "tokens": [6027, 20292, 31439, 5551, 4117, 25708, 5551, 9381, 17082, 2288, 34051, 7251, 3794, 995, 45865, 441, 295, 3146, 12174, 10859, 4587, 6808, 5172, 12399, 32239, 8592, 22807, 5296, 33456, 2423, 39184, 33, 88, 35186, 10874, 15042, 27884, 6225, 3555, 9640, 3660, 18871, 1895, 30229, 24976, 39184, 33, 17, 16070, 34598, 5296, 15042, 7251, 9381, 13546, 8978, 3224, 6055, 5016, 3794, 9957, 4724, 4117, 26890, 12399, 4724, 32887, 5016, 8717, 5016, 2407, 1975, 2655, 7435, 40294, 8717, 26895, 13672, 1829, 31439, 9673, 1863, 5016, 1863, 3660, 16712, 6027, 10632, 47524, 39319, 3660, 6055, 33753, 9673, 1863, 5016, 1863, 3660, 33251, 1211, 10632, 5296, 33456, 36632, 11242, 995, 45164, 10874, 36081, 12174, 12610, 3660, 2423, 39184, 52, 295, 479], "avg_logprob": -0.2223252161579617, "compression_ratio": 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U بي واحد و F", "tokens": [11622, 18513, 11933, 3555, 3794, 1211, 11536, 15844, 1975, 2655, 1863, 9957, 8032, 2655, 15040, 38436, 11296, 5551, 4117, 26890, 9154, 2423, 624, 4724, 1829, 36764, 24401, 4032, 479], "avg_logprob": -0.3830729047457377, "compression_ratio": 1.119047619047619, "no_speech_prob": 3.337860107421875e-06, "words": [{"start": 1455.4, "end": 1455.9, "word": "زاد", "probability": 0.600341796875}, {"start": 1455.9, "end": 1456.38, "word": " إبسلون", "probability": 0.71796875}, {"start": 1456.38, "end": 1456.54, "word": " على", "probability": 0.69189453125}, {"start": 1456.54, "end": 1456.86, "word": " اتنين", "probability": 0.81903076171875}, {"start": 1456.86, "end": 1457.84, "word": " هتلاقيها", "probability": 0.869140625}, {"start": 1457.84, "end": 1459.86, "word": " أكبر", "probability": 0.7158610026041666}, {"start": 1459.86, "end": 1460.12, "word": " من", "probability": 0.91943359375}, {"start": 1460.12, "end": 1460.32, "word": " ال", "probability": 0.57080078125}, {"start": 1460.32, "end": 1460.66, "word": " U", "probability": 0.58544921875}, {"start": 1460.66, "end": 1464.4, "word": " بي", "probability": 0.461181640625}, {"start": 1464.4, "end": 1465.0, "word": " واحد", "probability": 0.85986328125}, {"start": 1465.0, "end": 1466.28, "word": " و", "probability": 0.8388671875}, {"start": 1466.28, "end": 1466.64, "word": " F", "probability": 0.63232421875}], "temperature": 1.0}, {"id": 66, "seek": 149167, "start": 1467.51, "end": 1491.67, "text": "وأكيد عندي الـ U of F زائد إبسلون عدنان أكبر من الـ U B1 of F هيكون هذا أكبر أو يساوي الـ U B epsilon of F لأن الـ B epsilon refinement لمين برضه؟ للـ B1 بزام refinement إذن اللي هو التحسين بيزغر القبر وبروح ناحية اللي هو المنحنة إذن الآن من الـ tip 2 هذولة", "tokens": [2407, 10721, 4117, 25708, 43242, 1829, 2423, 39184, 624, 295, 479, 30767, 16373, 3215, 11933, 3555, 3794, 1211, 11536, 6225, 3215, 1863, 7649, 5551, 4117, 26890, 9154, 2423, 39184, 624, 363, 16, 295, 479, 39896, 30544, 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"probability": 0.87197265625}, {"start": 1597.55, "end": 1598.11, "word": " بي", "probability": 0.757568359375}, {"start": 1598.11, "end": 1598.35, "word": " واحد", "probability": 0.95947265625}, {"start": 1598.35, "end": 1598.77, "word": " اتحاد", "probability": 0.89111328125}, {"start": 1598.77, "end": 1598.95, "word": " بي", "probability": 0.919921875}, {"start": 1598.95, "end": 1599.19, "word": " اتنين", "probability": 0.911376953125}, {"start": 1599.19, "end": 1599.41, "word": " حيث", "probability": 0.8756510416666666}, {"start": 1599.41, "end": 1599.61, "word": " بي", "probability": 0.829345703125}, {"start": 1599.61, "end": 1599.83, "word": " واحد", "probability": 0.975830078125}, {"start": 1599.83, "end": 1599.97, "word": " اللي", "probability": 0.994384765625}, {"start": 1599.97, "end": 1600.35, "word": " لجيناه", "probability": 0.84716796875}, {"start": 1600.35, "end": 1600.63, "word": " هان", "probability": 0.60546875}, {"start": 1600.63, "end": 1601.05, "word": " وال", "probability": 0.4052734375}, {"start": 1601.05, "end": 1601.25, "word": " بي", "probability": 0.677490234375}, {"start": 1601.25, "end": 1601.49, "word": " اتنين", "probability": 0.948974609375}, {"start": 1601.49, "end": 1601.65, "word": " اللي", "probability": 0.99560546875}, {"start": 1601.65, "end": 1602.11, "word": " لجيناه", "probability": 0.97880859375}, {"start": 1602.11, "end": 1602.41, "word": " هان", "probability": 0.952880859375}], "temperature": 1.0}, {"id": 71, "seek": 161986, "start": 1602.62, "end": 1619.86, "text": "such that U P Y of F نقص L P Y of F أصغر من اللي هو Epsilon وهو المطلوب أي سؤال؟ طيب، ماشي يا شباب، الآن خلصنا الجزء الأول من النظرية", "tokens": [39974, 300, 624, 430, 398, 295, 479, 8717, 4587, 9381, 441, 430, 398, 295, 479, 5551, 9381, 17082, 2288, 9154, 13672, 1829, 31439, 462, 16592, 37037, 2407, 9673, 9566, 1211, 37746, 36632, 8608, 33604, 6027, 22807, 23032, 1829, 3555, 12399, 3714, 33599, 1829, 35186, 13412, 3555, 16758, 12399, 6024, 48506, 16490, 1211, 9381, 8315, 25724, 11622, 38207, 16247, 12610, 9154, 28239, 19913, 2288, 10632], "avg_logprob": -0.25048076923076923, "compression_ratio": 1.3164556962025316, "no_speech_prob": 1.3887882232666016e-05, "words": [{"start": 1602.62, "end": 1603.24, "word": "such", "probability": 0.603515625}, {"start": 1603.24, "end": 1603.72, "word": " that", "probability": 0.95654296875}, {"start": 1603.72, "end": 1604.12, "word": " U", "probability": 0.2481689453125}, {"start": 1604.12, "end": 1604.3, "word": " P", "probability": 0.2509765625}, {"start": 1604.3, "end": 1604.62, "word": " Y", "probability": 0.5654296875}, {"start": 1604.62, "end": 1604.86, "word": " of", "probability": 0.215576171875}, {"start": 1604.86, "end": 1605.12, "word": " F", "probability": 0.9775390625}, {"start": 1605.12, "end": 1605.54, "word": " نقص", "probability": 0.7513834635416666}, {"start": 1605.54, "end": 1605.72, "word": " L", "probability": 0.150146484375}, {"start": 1605.72, "end": 1605.84, "word": " P", "probability": 0.95166015625}, {"start": 1605.84, "end": 1606.16, "word": " Y", "probability": 0.8681640625}, {"start": 1606.16, "end": 1606.28, "word": " of", "probability": 0.470458984375}, {"start": 1606.28, "end": 1606.5, "word": " F", "probability": 0.99658203125}, {"start": 1606.5, "end": 1607.1, "word": " أصغر", "probability": 0.95556640625}, {"start": 1607.1, "end": 1607.62, "word": " من", "probability": 0.97216796875}, {"start": 1607.62, "end": 1607.82, "word": " اللي", "probability": 0.62060546875}, {"start": 1607.82, "end": 1608.16, "word": " هو", "probability": 0.95947265625}, {"start": 1608.16, "end": 1609.12, "word": " Epsilon", "probability": 0.598388671875}, {"start": 1609.12, "end": 1609.96, "word": " وهو", "probability": 0.760498046875}, {"start": 1609.96, "end": 1611.3, "word": " المطلوب", "probability": 0.9892578125}, {"start": 1611.3, "end": 1612.48, "word": " أي", "probability": 0.5947265625}, {"start": 1612.48, "end": 1614.04, "word": " سؤال؟", "probability": 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انه suppose that star holds اللي هي star ليه هذه نفترض ان لكل epsilon أكبر من 0 there exists B of epsilon such that U B Epsilon و F نقصها دي أصغر من Epsilon و بدنا نصل من خلالها لإيش لأن ال F is integrable فنشوف", "tokens": [10721, 12984, 3555, 2655, 8315, 13672, 1829, 47525, 8315, 35186, 16472, 3224, 13672, 1829, 31439, 29538, 18863, 15040, 28671, 20328, 5016, 1829, 5016, 3660, 5296, 33456, 8315, 8717, 5172, 2655, 43042, 16472, 3224, 7297, 300, 3543, 9190, 13672, 1829, 39896, 3543, 32239, 3224, 29538, 8717, 5172, 2655, 43042, 16472, 5296, 28820, 17889, 5551, 4117, 26890, 9154, 1958, 456, 8198, 363, 295, 17889, 1270, 300, 624, 363, 462, 16592, 4032, 479, 8717, 4587, 9381, 11296, 11778, 1829, 5551, 9381, 17082, 2288, 9154, 462, 16592, 4032, 47525, 8315, 8717, 36520, 9154, 16490, 1211, 6027, 11296, 5296, 28814, 1829, 8592, 5296, 33456, 2423, 479, 307, 16200, 424, 638, 6156, 1863, 8592, 38688], "avg_logprob": -0.2977272862737829, "compression_ratio": 1.6514522821576763, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 1622.18, "end": 1622.88, "word": "أثبتنا", "probability": 0.840576171875}, {"start": 1622.88, "end": 1623.1, "word": " اللي", "probability": 0.627197265625}, {"start": 1623.1, "end": 1623.46, "word": " بدنا", "probability": 0.9169921875}, {"start": 1623.46, "end": 1623.72, "word": " يا", "probability": 0.194091796875}, {"start": 1623.72, "end": 1624.16, "word": " انه", "probability": 0.4786376953125}, {"start": 1624.16, "end": 1624.42, "word": " اللي", "probability": 0.71923828125}, {"start": 1624.42, "end": 1624.6, "word": " هو", "probability": 0.94970703125}, {"start": 1624.6, "end": 1624.8, "word": " هذه", "probability": 0.63671875}, {"start": 1624.8, "end": 1625.16, "word": " العلاقة", "probability": 0.9578450520833334}, {"start": 1625.16, "end": 1626.08, "word": " صحيحة", "probability": 0.901171875}, {"start": 1626.08, "end": 1626.6, "word": " لأننا", "probability": 0.590576171875}, {"start": 1626.6, "end": 1627.1, "word": " نفترض", "probability": 0.9346923828125}, {"start": 1627.1, "end": 1627.62, "word": " انه", "probability": 0.4951171875}, {"start": 1627.62, "end": 1628.4, "word": " suppose", "probability": 0.6474609375}, {"start": 1628.4, "end": 1628.86, "word": " that", "probability": 0.8828125}, {"start": 1628.86, "end": 1629.3, "word": " star", "probability": 0.50830078125}, {"start": 1629.3, "end": 1629.76, "word": " holds", "probability": 0.82373046875}, {"start": 1629.76, "end": 1629.96, "word": " اللي", "probability": 0.95361328125}, {"start": 1629.96, "end": 1630.12, "word": " هي", "probability": 0.8671875}, {"start": 1630.12, "end": 1630.4, "word": " star", "probability": 0.410400390625}, {"start": 1630.4, "end": 1630.72, "word": " ليه", "probability": 0.611328125}, {"start": 1630.72, "end": 1631.02, "word": " هذه", "probability": 0.607421875}, {"start": 1631.02, "end": 1631.9, "word": " نفترض", "probability": 0.9337158203125}, {"start": 1631.9, "end": 1632.04, "word": " ان", "probability": 0.69189453125}, {"start": 1632.04, "end": 1632.38, "word": " لكل", "probability": 0.869384765625}, {"start": 1632.38, "end": 1632.82, "word": " epsilon", "probability": 0.1429443359375}, {"start": 1632.82, "end": 1633.12, "word": " أكبر", "probability": 0.9319661458333334}, {"start": 1633.12, "end": 1633.24, "word": " من", "probability": 0.88818359375}, {"start": 1633.24, "end": 1633.44, "word": " 0", "probability": 0.499267578125}, {"start": 1633.44, "end": 1633.66, "word": " there", "probability": 0.74462890625}, {"start": 1633.66, "end": 1633.96, "word": " exists", "probability": 0.6494140625}, {"start": 1633.96, "end": 1634.16, "word": " B", "probability": 0.363037109375}, {"start": 1634.16, "end": 1634.36, "word": " of", "probability": 0.8115234375}, {"start": 1634.36, "end": 1634.8, "word": " epsilon", "probability": 0.86328125}, {"start": 1634.8, "end": 1635.38, "word": " such", "probability": 0.88818359375}, {"start": 1635.38, "end": 1635.74, "word": " that", "probability": 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ال limit هذا بيساوي سفر then f is integrable and ال limit لل integration بيساوي ال integration بيساوي ال limit ال أسف ال limit لل lower p and f بيساوي ال limit لل upper p and f اللي هو بيساوي قيمة ال integration حتى ال converse جماعة اللي هو", "tokens": [1211, 33456, 45164, 6156, 43042, 8315, 4724, 1829, 14739, 14739, 4478, 6022, 307, 257, 8310, 295, 644, 2451, 295, 286, 4724, 5016, 1829, 12984, 14739, 2423, 4948, 23758, 4724, 1829, 3794, 995, 45865, 8608, 5172, 2288, 550, 283, 307, 16200, 424, 638, 293, 2423, 4948, 24976, 10980, 4724, 1829, 3794, 995, 45865, 2423, 10980, 4724, 1829, 3794, 995, 45865, 2423, 4948, 2423, 5551, 3794, 5172, 2423, 4948, 24976, 3126, 280, 293, 283, 4724, 1829, 3794, 995, 45865, 2423, 4948, 24976, 6597, 280, 293, 283, 13672, 1829, 31439, 4724, 1829, 3794, 995, 45865, 12174, 32640, 3660, 2423, 10980, 11331, 49975, 2423, 416, 4308, 10874, 15042, 27884, 13672, 1829, 31439], "avg_logprob": -0.30877293906080616, "compression_ratio": 1.9631336405529953, 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"probability": 0.69580078125}, {"start": 1924.48, "end": 1924.7, "word": " limit", "probability": 0.98583984375}, {"start": 1924.7, "end": 1924.9, "word": " لل", "probability": 0.96826171875}, {"start": 1924.9, "end": 1925.18, "word": " upper", "probability": 0.78955078125}, {"start": 1925.18, "end": 1925.42, "word": " p", "probability": 0.81787109375}, {"start": 1925.42, "end": 1925.62, "word": " and", "probability": 0.94482421875}, {"start": 1925.62, "end": 1925.86, "word": " f", "probability": 0.9755859375}, {"start": 1925.86, "end": 1926.0, "word": " اللي", "probability": 0.927734375}, {"start": 1926.0, "end": 1926.1, "word": " هو", "probability": 0.90869140625}, {"start": 1926.1, "end": 1926.4, "word": " بيساوي", "probability": 0.97470703125}, {"start": 1926.4, "end": 1926.88, "word": " قيمة", "probability": 0.9860026041666666}, {"start": 1926.88, "end": 1927.02, "word": " ال", "probability": 0.98583984375}, {"start": 1927.02, "end": 1927.56, "word": " integration", "probability": 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"probability": 0.752685546875}, {"start": 1933.6, "end": 1933.82, "word": " كان", "probability": 0.94921875}, {"start": 1933.82, "end": 1933.96, "word": " ..", "probability": 0.13916015625}, {"start": 1933.96, "end": 1934.08, "word": " اللي", "probability": 0.917724609375}, {"start": 1934.08, "end": 1934.2, "word": " هي", "probability": 0.64794921875}, {"start": 1934.2, "end": 1934.56, "word": " كانت", "probability": 0.953369140625}, {"start": 1934.56, "end": 1934.7, "word": " F", "probability": 0.71875}, {"start": 1934.7, "end": 1935.2, "word": " أندولي", "probability": 0.4805145263671875}, {"start": 1935.2, "end": 1935.52, "word": " F", "probability": 0.951171875}, {"start": 1935.52, "end": 1936.46, "word": " لأن", "probability": 0.85400390625}, {"start": 1936.46, "end": 1936.82, "word": " لو", "probability": 0.9892578125}, {"start": 1936.82, "end": 1937.3, "word": " كانت", "probability": 0.98388671875}, {"start": 1937.3, "end": 1937.56, "word": " F", "probability": 0.92919921875}, 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"probability": 0.75927734375}, {"start": 1949.58, "end": 1949.76, "word": " اللي", "probability": 0.985595703125}, {"start": 1949.76, "end": 1949.96, "word": " هو", "probability": 0.99462890625}, {"start": 1949.96, "end": 1950.5, "word": " برهان", "probability": 0.9271240234375}, {"start": 1950.5, "end": 1950.96, "word": " إيجاد", "probability": 0.9779052734375}, {"start": 1950.96, "end": 1951.28, "word": " الـ", "probability": 0.6883544921875}, {"start": 1951.28, "end": 1951.38, "word": " B", "probability": 0.252685546875}, {"start": 1951.38, "end": 1952.06, "word": " epsilon", "probability": 0.165771484375}, {"start": 1952.06, "end": 1952.74, "word": " ولكن", "probability": 0.84375}, {"start": 1952.74, "end": 1952.92, "word": " هنا", "probability": 0.7412109375}, {"start": 1952.92, "end": 1953.38, "word": " بنجد", "probability": 0.7364908854166666}], "temperature": 1.0}, {"id": 85, "seek": 197478, "start": 1953.78, "end": 1974.78, "text": "اللي هو الـ Epsilon بساوية واحدة لان فبنلاقي اللي هو ال sequence هذه في ال corollary .. في من مشابه .. شيء مشابه في برهان النظرية الأولى اللي قبل بشوية و ياريت تجربوها عندكم خلينا ناخد اللي .. اللي موجود حاليا اللي هو الاتجاه هذا ان لو لجينا sequence of partitions", "tokens": [6027, 20292, 31439, 2423, 39184, 462, 16592, 4724, 3794, 995, 2407, 10632, 36764, 24401, 3660, 5296, 7649, 6156, 3555, 1863, 15040, 38436, 13672, 1829, 31439, 2423, 8310, 29538, 8978, 2423, 1181, 1833, 822, 4386, 8978, 9154, 37893, 16758, 3224, 4386, 44049, 38207, 37893, 16758, 3224, 8978, 4724, 2288, 3224, 7649, 28239, 19913, 2288, 10632, 16247, 12610, 7578, 13672, 1829, 12174, 36150, 4724, 8592, 2407, 10632, 4032, 7251, 9640, 36081, 6055, 7435, 25513, 2407, 11296, 43242, 24793, 16490, 20292, 8315, 8717, 47283, 3215, 13672, 1829, 4386, 13672, 1829, 3714, 29245, 23328, 11331, 6027, 25528, 13672, 1829, 31439, 2423, 9307, 7435, 40294, 23758, 16472, 45164, 5296, 7435, 1829, 8315, 8310, 295, 644, 2451], "avg_logprob": -0.27525111261223045, "compression_ratio": 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"end": 1957.66, "word": " sequence", "probability": 0.611328125}, {"start": 1957.66, "end": 1958.24, "word": " هذه", "probability": 0.481201171875}, {"start": 1958.24, "end": 1958.92, "word": " في", "probability": 0.6611328125}, {"start": 1958.92, "end": 1959.14, "word": " ال", "probability": 0.677734375}, {"start": 1959.14, "end": 1959.72, "word": " corollary", "probability": 0.6469930013020834}, {"start": 1959.72, "end": 1959.82, "word": " ..", "probability": 0.4609375}, {"start": 1959.82, "end": 1959.96, "word": " في", "probability": 0.75244140625}, {"start": 1959.96, "end": 1960.36, "word": " من", "probability": 0.69287109375}, {"start": 1960.36, "end": 1961.8, "word": " مشابه", "probability": 0.6602376302083334}, {"start": 1961.8, "end": 1961.8, "word": " ..", "probability": 0.7939453125}, {"start": 1961.8, "end": 1962.38, "word": " شيء", "probability": 0.666015625}, {"start": 1962.38, "end": 1962.9, "word": " مشابه", "probability": 0.98876953125}, {"start": 1962.9, "end": 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"word": " ناخد", "probability": 0.9523111979166666}, {"start": 1968.6, "end": 1968.8, "word": " اللي", "probability": 0.968994140625}, {"start": 1968.8, "end": 1968.8, "word": " ..", "probability": 0.39990234375}, {"start": 1968.8, "end": 1968.96, "word": " اللي", "probability": 0.994384765625}, {"start": 1968.96, "end": 1969.36, "word": " موجود", "probability": 0.9890950520833334}, {"start": 1969.36, "end": 1969.88, "word": " حاليا", "probability": 0.70849609375}, {"start": 1969.88, "end": 1970.9, "word": " اللي", "probability": 0.6544189453125}, {"start": 1970.9, "end": 1971.12, "word": " هو", "probability": 0.91064453125}, {"start": 1971.12, "end": 1971.8, "word": " الاتجاه", "probability": 0.9072265625}, {"start": 1971.8, "end": 1972.02, "word": " هذا", "probability": 0.95654296875}, {"start": 1972.02, "end": 1972.16, "word": " ان", "probability": 0.27392578125}, {"start": 1972.16, "end": 1972.34, "word": " لو", "probability": 0.703125}, {"start": 1972.34, "end": 1972.88, "word": " 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2578.01, "word": " ال", "probability": 0.46240234375}, {"start": 2578.01, "end": 2578.21, "word": " lower", "probability": 0.83935546875}, {"start": 2578.21, "end": 2578.51, "word": " sum", "probability": 0.978515625}, {"start": 2578.51, "end": 2578.61, "word": " و", "probability": 0.8349609375}, {"start": 2578.61, "end": 2578.89, "word": " بعدين", "probability": 0.93798828125}, {"start": 2578.89, "end": 2579.15, "word": " جيبنا", "probability": 0.990234375}, {"start": 2579.15, "end": 2579.25, "word": " ال", "probability": 0.9228515625}, {"start": 2579.25, "end": 2579.49, "word": " upper", "probability": 0.90087890625}, {"start": 2579.49, "end": 2581.87, "word": " integral", "probability": 0.4345703125}, {"start": 2581.87, "end": 2582.17, "word": " و", "probability": 0.97509765625}, {"start": 2582.17, "end": 2582.25, "word": " ال", "probability": 0.44921875}, {"start": 2582.25, "end": 2582.43, "word": " lower", "probability": 0.90625}, {"start": 2582.43, "end": 2582.93, "word": " 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عبارة عن Any Partition اللي هو بالطريقة اللي أمامي يعني حسب N بيصير بختلف ال Partition أما إيش فكرة ال Partition زي ما قلنا المرة الفائتة من 0 لعند 1 جزأناها إلى أجزاء متساوية إلى N من الأجزاء المتساوية", "tokens": [27842, 2423, 39184, 24755, 781, 13672, 1829, 5551, 12984, 3555, 2655, 8315, 8978, 3224, 16472, 11296, 5681, 1146, 424, 20666, 3555, 14407, 3794, 9566, 3660, 13672, 1829, 39896, 16712, 3615, 16572, 5172, 5551, 9778, 3215, 8315, 430, 426, 13672, 1829, 31439, 17182, 36764, 24401, 15844, 426, 4032, 5718, 104, 1863, 9957, 15844, 426, 4032, 7649, 8717, 4587, 9381, 36764, 24401, 15844, 426, 5296, 3615, 41260, 2423, 14407, 24401, 5551, 9778, 3215, 8315, 13672, 1829, 31439, 6225, 3555, 9640, 3660, 18871, 2639, 4100, 849, 13672, 1829, 31439, 20666, 9566, 16572, 28671, 13672, 1829, 5551, 2304, 10943, 1829, 37495, 22653, 11331, 35457, 426, 4724, 1829, 9381, 13546, 4724, 46456, 46538, 2423, 4100, 849, 5551, 15042, 11933, 1829, 8592, 6156, 4117, 25720, 2423, 4100, 849, 30767, 1829, 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integration ايش هيكون قيمة ال limit limit u, b, n, g هيقدر الغرض و limit l of n of g هيقدر الغرض ليش لأن limit هذا اصلا هيطلع لك limit ال u, b, n و g", "tokens": [6027, 7649, 4724, 4587, 32640, 3660, 2423, 10980, 1975, 1829, 8592, 39896, 30544, 12174, 32640, 3660, 2423, 4948, 4948, 344, 11, 272, 11, 297, 11, 290, 39896, 28543, 2288, 6024, 118, 43042, 4032, 4948, 287, 295, 297, 295, 290, 39896, 28543, 2288, 6024, 118, 43042, 32239, 8592, 5296, 33456, 4948, 23758, 1975, 9381, 15040, 39896, 9566, 1211, 3615, 5296, 4117, 4948, 2423, 344, 11, 272, 11, 297, 4032, 290], "avg_logprob": -0.3066964362348829, "compression_ratio": 1.6, "no_speech_prob": 0.0, "words": [{"start": 2775.6000000000004, "end": 2776.2000000000003, "word": "الان", "probability": 0.715576171875}, {"start": 2776.2000000000003, "end": 2776.8, "word": " بقيمة", "probability": 0.675537109375}, {"start": 2776.8, "end": 2776.88, "word": " ال", "probability": 0.89892578125}, {"start": 2776.88, "end": 2777.38, "word": " 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2904.64, "word": " عبارة", "probability": 0.9227294921875}, {"start": 2904.64, "end": 2905.02, "word": " عن", "probability": 0.98876953125}, {"start": 2905.02, "end": 2906.12, "word": " integrable", "probability": 0.7100830078125}, {"start": 2906.12, "end": 2906.98, "word": " functions", "probability": 0.84912109375}, {"start": 2906.98, "end": 2907.64, "word": " اذا", "probability": 0.681884765625}, {"start": 2907.64, "end": 2908.2, "word": " اول", "probability": 0.785400390625}, {"start": 2908.2, "end": 2908.8, "word": " اعلان", "probability": 0.9150390625}, {"start": 2908.8, "end": 2909.38, "word": " الان", "probability": 0.6268310546875}, {"start": 2909.38, "end": 2910.5, "word": " اللي", "probability": 0.949951171875}, {"start": 2910.5, "end": 2910.84, "word": " هو", "probability": 0.94775390625}, {"start": 2910.84, "end": 2912.0, "word": " any", "probability": 0.428955078125}, {"start": 2912.0, "end": 2912.62, "word": " monotone", "probability": 0.88916015625}, {"start": 2912.62, "end": 2913.32, "word": " function", "probability": 0.96337890625}], "temperature": 1.0}, {"id": 126, "seek": 292529, "start": 2914.67, "end": 2925.29, "text": "on a closed bounded interval is integrable وهذا اللي هو عنواننا integrability of monotone functions", "tokens": [266, 257, 5395, 37498, 15035, 307, 16200, 424, 638, 37037, 15730, 13672, 1829, 31439, 18871, 2407, 7649, 8315, 3572, 2310, 295, 1108, 310, 546, 6828], "avg_logprob": -0.3587740258528636, "compression_ratio": 1.1262135922330097, "no_speech_prob": 2.384185791015625e-07, "words": [{"start": 2914.67, "end": 2915.09, "word": "on", "probability": 0.02874755859375}, {"start": 2915.09, "end": 2915.73, "word": " a", "probability": 0.97216796875}, {"start": 2915.73, "end": 2916.29, "word": " closed", "probability": 0.75439453125}, {"start": 2916.29, "end": 2916.81, "word": " bounded", "probability": 0.890625}, {"start": 2916.81, "end": 2917.77, "word": " interval", "probability": 0.95751953125}, {"start": 2917.77, "end": 2918.83, "word": " is", "probability": 0.83251953125}, {"start": 2918.83, "end": 2920.13, "word": " integrable", "probability": 0.7224934895833334}, {"start": 2920.13, "end": 2920.71, "word": " وهذا", "probability": 0.6890869140625}, {"start": 2920.71, "end": 2920.85, "word": " اللي", "probability": 0.818603515625}, {"start": 2920.85, "end": 2921.09, "word": " هو", "probability": 0.98046875}, {"start": 2921.09, "end": 2921.83, "word": " عنواننا", "probability": 0.83203125}, {"start": 2921.83, "end": 2923.27, "word": " integrability", "probability": 0.55914306640625}, {"start": 2923.27, "end": 2923.57, "word": " of", "probability": 0.9560546875}, {"start": 2923.57, "end": 2924.49, "word": " monotone", "probability": 0.9488932291666666}, {"start": 2924.49, "end": 2925.29, "word": " functions", "probability": 0.833984375}], "temperature": 1.0}, {"id": 127, "seek": 294413, "start": 2926.29, "end": 2944.13, "text": "لت I بتساوي A و B و لت F من I لR بيكون مونوتون فانكشن on I ثم F أشمالها is integrable on I نفترض أن F انتقل هو مونوتور نصل إليها integrable نفترض أن F مثلا increasing", "tokens": [1211, 2655, 286, 39894, 3794, 995, 45865, 316, 4032, 363, 4032, 5296, 2655, 479, 9154, 286, 5296, 49, 4724, 1829, 30544, 3714, 11536, 35473, 11536, 6156, 7649, 4117, 8592, 1863, 322, 286, 38637, 2304, 479, 5551, 8592, 2304, 6027, 11296, 307, 16200, 424, 638, 322, 286, 8717, 5172, 2655, 43042, 14739, 479, 16472, 2655, 4587, 1211, 31439, 3714, 11536, 35473, 13063, 8717, 36520, 11933, 20292, 11296, 16200, 424, 638, 8717, 5172, 2655, 43042, 14739, 479, 50113, 15040, 5662], "avg_logprob": -0.4005142382428616, "compression_ratio": 1.4850299401197604, "no_speech_prob": 3.0994415283203125e-06, "words": [{"start": 2926.29, "end": 2926.75, "word": "لت", "probability": 0.4788055419921875}, {"start": 2926.75, "end": 2927.09, "word": " I", "probability": 0.62939453125}, {"start": 2927.09, "end": 2927.99, "word": " بتساوي", "probability": 0.669525146484375}, {"start": 2927.99, "end": 2928.17, 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وsimilarly وفعلا similarly لو كانت f is decreasing هتكون برضه is integrable خلّينا مع بعض شباب نفترض suppose that f is increasing يعني الدالة على الفترة هي a وb مثلا", "tokens": [2407, 1863, 36520, 36145, 11296, 16200, 424, 638, 4032, 30937, 2202, 356, 4032, 5172, 3615, 15040, 14138, 45164, 25961, 2655, 283, 307, 23223, 8032, 2655, 30544, 4724, 43042, 3224, 307, 16200, 424, 638, 16490, 1211, 11703, 1829, 8315, 20449, 45030, 11242, 13412, 3555, 16758, 8717, 5172, 2655, 43042, 7297, 300, 283, 307, 5662, 37495, 22653, 32748, 6027, 3660, 15844, 27188, 2655, 25720, 39896, 257, 4032, 65, 50113, 15040], "avg_logprob": -0.25226449102595233, "compression_ratio": 1.4184782608695652, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2945.06, "end": 2945.64, "word": "ونصل", "probability": 0.5909830729166666}, {"start": 2945.64, "end": 2946.34, "word": " إنها", "probability": 0.713134765625}, {"start": 2946.34, "end": 2947.7, "word": " integrable", "probability": 0.690673828125}, 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0.8484700520833334}, {"start": 2956.3, "end": 2956.64, "word": " خلّينا", "probability": 0.7337890625}, {"start": 2956.64, "end": 2956.76, "word": " مع", "probability": 0.99169921875}, {"start": 2956.76, "end": 2957.04, "word": " بعض", "probability": 0.9970703125}, {"start": 2957.04, "end": 2957.46, "word": " شباب", "probability": 0.8163248697916666}, {"start": 2957.46, "end": 2959.92, "word": " نفترض", "probability": 0.824462890625}, {"start": 2959.92, "end": 2961.5, "word": " suppose", "probability": 0.4501953125}, {"start": 2961.5, "end": 2964.26, "word": " that", "probability": 0.92431640625}, {"start": 2964.26, "end": 2966.06, "word": " f", "probability": 0.85205078125}, {"start": 2966.06, "end": 2967.08, "word": " is", "probability": 0.9638671875}, {"start": 2967.08, "end": 2969.02, "word": " increasing", "probability": 0.9658203125}, {"start": 2969.02, "end": 2969.9, "word": " يعني", "probability": 0.956298828125}, {"start": 2969.9, "end": 2970.4, "word": " الدالة", 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"word": " هيك", "probability": 0.6492919921875}, {"start": 3447.03, "end": 3447.33, "word": " تصبح", "probability": 0.8414713541666666}, {"start": 3447.33, "end": 3448.07, "word": " أشمالها", "probability": 0.93193359375}, {"start": 3448.07, "end": 3448.91, "word": " نازلة", "probability": 0.6817220052083334}, {"start": 3448.91, "end": 3449.35, "word": " نزول", "probability": 0.85107421875}, {"start": 3449.35, "end": 3450.07, "word": " الدالة", "probability": 0.9638671875}, {"start": 3450.07, "end": 3450.95, "word": " فبصير", "probability": 0.73687744140625}, {"start": 3450.95, "end": 3451.61, "word": " عندك", "probability": 0.906005859375}, {"start": 3451.61, "end": 3452.17, "word": " اللي", "probability": 0.888916015625}, {"start": 3452.17, "end": 3452.49, "word": " هو", "probability": 0.98974609375}, {"start": 3452.49, "end": 3452.77, "word": " ال", "probability": 0.83544921875}, {"start": 3452.77, "end": 3453.25, "word": " maximum", "probability": 0.9638671875}, {"start": 3453.25, 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" البرهان", "probability": 0.9169921875}, {"start": 3465.2, "end": 3465.58, "word": " بنفس", "probability": 0.98876953125}, {"start": 3465.58, "end": 3466.22, "word": " الطريقة،", "probability": 0.8271484375}, {"start": 3466.22, "end": 3466.76, "word": " هيطلع", "probability": 0.86114501953125}, {"start": 3466.76, "end": 3467.44, "word": " عندكم", "probability": 0.958251953125}, {"start": 3467.44, "end": 3468.7, "word": " البرهان", "probability": 0.9713134765625}, {"start": 3468.7, "end": 3469.3, "word": " automatic", "probability": 0.361328125}, {"start": 3469.3, "end": 3470.0, "word": " وبشكل", "probability": 0.9265950520833334}, {"start": 3470.0, "end": 3470.44, "word": " سهل", "probability": 0.9943033854166666}, {"start": 3470.44, "end": 3471.06, "word": " وبشكل", "probability": 0.935546875}, {"start": 3471.06, "end": 3472.04, "word": " سلس،", "probability": 0.84130859375}, {"start": 3472.04, "end": 3472.5, "word": " similar", "probability": 0.791015625}, {"start": 3472.5, "end": 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"word": " إذا", "probability": 0.611083984375}, {"start": 3500.14, "end": 3500.42, "word": " صار", "probability": 0.93212890625}, {"start": 3500.42, "end": 3500.56, "word": " في", "probability": 0.7041015625}, {"start": 3500.56, "end": 3500.78, "word": " عنا", "probability": 0.6578369140625}, {"start": 3500.78, "end": 3501.48, "word": " عائلة", "probability": 0.9933268229166666}, {"start": 3501.48, "end": 3502.5, "word": " كاملة", "probability": 0.9931640625}, {"start": 3502.5, "end": 3502.7, "word": " من", "probability": 0.99365234375}, {"start": 3502.7, "end": 3503.34, "word": " الدوال", "probability": 0.93212890625}, {"start": 3503.34, "end": 3504.14, "word": " القابلة", "probability": 0.9798177083333334}, {"start": 3504.14, "end": 3505.04, "word": " للتكامل", "probability": 0.96845703125}, {"start": 3505.04, "end": 3506.06, "word": " بواسط", "probability": 0.9505615234375}, {"start": 3506.06, "end": 3506.92, "word": " التكامل", "probability": 0.9677734375}, {"start": 3506.92, 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