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"end": 1019.5, "word": " بتساوي", "probability": 0.942626953125}, {"start": 1019.5, "end": 1020.0, "word": " إبسلون", "probability": 0.94765625}, {"start": 1020.0, "end": 1020.18, "word": " على", "probability": 0.7041015625}, {"start": 1020.18, "end": 1020.82, "word": " اتناشر", "probability": 0.791845703125}, {"start": 1020.82, "end": 1021.14, "word": " N", "probability": 0.371337890625}, {"start": 1021.14, "end": 1021.36, "word": " في", "probability": 0.755859375}, {"start": 1021.36, "end": 1021.74, "word": " مين", "probability": 0.6903076171875}, {"start": 1021.74, "end": 1021.94, "word": " في", "probability": 0.8623046875}, {"start": 1021.94, "end": 1022.18, "word": " M", "probability": 0.962890625}, {"start": 1022.18, "end": 1022.86, "word": " N", "probability": 0.38623046875}, {"start": 1022.86, "end": 1023.22, "word": " مين", "probability": 0.8681640625}, {"start": 1023.22, "end": 1024.1, "word": " هذه،", "probability": 0.621337890625}, {"start": 1024.1, "end": 1024.38, "word": " N", "probability": 0.796875}, {"start": 1024.38, "end": 1024.6, "word": " اللي", "probability": 0.980712890625}, {"start": 1024.6, "end": 1024.94, "word": " ظهرت", "probability": 0.942138671875}, {"start": 1024.94, "end": 1025.06, "word": " في", "probability": 0.95849609375}, {"start": 1025.06, "end": 1025.14, "word": " ال", "probability": 0.9794921875}, {"start": 1025.14, "end": 1025.5, "word": " partition", "probability": 0.36767578125}, {"start": 1025.5, "end": 1025.98, "word": " هنا", "probability": 0.896484375}, {"start": 1025.98, "end": 1026.56, "word": " اللي", "probability": 0.893798828125}, {"start": 1026.56, "end": 1026.82, "word": " هو", "probability": 0.9931640625}, {"start": 1026.82, "end": 1027.38, "word": " عدد", "probability": 0.9890950520833334}, {"start": 1027.38, "end": 1028.06, "word": " عناصر", "probability": 0.9930013020833334}, {"start": 1028.06, "end": 1028.22, "word": " ال", "probability": 0.962890625}, {"start": 1028.22, "end": 1028.66, "word": " partition", "probability": 0.7490234375}], "temperature": 1.0}, {"id": 42, "seek": 103875, "start": 1029.15, "end": 1038.75, "text": "اللي جزأني الفترة هي N زائد 1 هذا مين ال partition اللي لجيته في الريمان من خلال الintegrability للأف", "tokens": [6027, 20292, 10874, 11622, 10721, 22653, 27188, 2655, 25720, 39896, 426, 30767, 16373, 3215, 502, 23758, 3714, 9957, 2423, 24808, 13672, 1829, 5296, 7435, 36081, 3224, 8978, 2423, 16572, 2304, 7649, 9154, 16490, 1211, 6027, 2423, 31131, 2310, 24976, 10721, 5172], "avg_logprob": -0.30450149590060827, "compression_ratio": 1.2403100775193798, "no_speech_prob": 4.76837158203125e-07, "words": [{"start": 1029.15, "end": 1029.75, "word": "اللي", "probability": 0.79638671875}, {"start": 1029.75, "end": 1030.29, "word": " جزأني", "probability": 0.64495849609375}, {"start": 1030.29, "end": 1030.79, "word": " الفترة", "probability": 0.9241536458333334}, {"start": 1030.79, "end": 1031.07, "word": " هي", "probability": 0.77685546875}, {"start": 1031.07, "end": 1031.37, "word": " N", "probability": 0.365234375}, {"start": 1031.37, "end": 1031.67, "word": " زائد", "probability": 0.6756591796875}, {"start": 1031.67, "end": 1031.91, "word": " 1", "probability": 0.74658203125}, {"start": 1031.91, "end": 1032.43, "word": " هذا", "probability": 0.490966796875}, {"start": 1032.43, "end": 1032.91, "word": " مين", "probability": 0.6427001953125}, {"start": 1032.91, "end": 1033.61, "word": " ال", "probability": 0.927734375}, {"start": 1033.61, "end": 1034.15, "word": " partition", "probability": 0.3544921875}, {"start": 1034.15, "end": 1034.49, "word": " اللي", "probability": 0.917724609375}, {"start": 1034.49, "end": 1035.05, "word": " لجيته", "probability": 0.8150634765625}, {"start": 1035.05, "end": 1035.15, "word": " في", "probability": 0.85888671875}, {"start": 1035.15, "end": 1035.75, "word": " الريمان", "probability": 0.9080810546875}, {"start": 1035.75, "end": 1035.93, "word": " من", "probability": 0.95556640625}, {"start": 1035.93, "end": 1036.77, "word": " خلال", "probability": 0.9697265625}, {"start": 1036.77, "end": 1037.75, "word": " الintegrability", "probability": 0.667236328125}, {"start": 1037.75, "end": 1038.75, "word": " للأف", "probability": 0.61181640625}], "temperature": 1.0}, {"id": 43, "seek": 106141, "start": 1039.31, "end": 1061.41, "text": "إذاً where الـ N زائد واحد is the number of parts in B إبسلون يعني الـ Delta بتساوي إبسلون على 12 في N الـ N ارتبطت بال partition اللي لجيته والـ M هي عبارة عن ال supremum لكل الدالة على كل الفترة المذكورة نيجي الآن", "tokens": [28814, 15730, 14111, 689, 2423, 39184, 426, 30767, 16373, 3215, 36764, 24401, 307, 264, 1230, 295, 3166, 294, 363, 11933, 3555, 3794, 1211, 11536, 37495, 22653, 2423, 39184, 18183, 39894, 3794, 995, 45865, 11933, 3555, 3794, 1211, 11536, 15844, 2272, 8978, 426, 2423, 39184, 426, 1975, 43500, 3555, 9566, 2655, 20666, 24808, 13672, 1829, 5296, 7435, 36081, 3224, 16070, 39184, 376, 39896, 6225, 3555, 9640, 3660, 18871, 2423, 23710, 449, 5296, 28820, 32748, 6027, 3660, 15844, 28242, 27188, 2655, 25720, 9673, 8848, 4117, 13063, 3660, 8717, 1829, 7435, 1829, 6024, 48506], "avg_logprob": -0.2308084221313829, "compression_ratio": 1.502262443438914, "no_speech_prob": 2.0265579223632812e-06, "words": [{"start": 1039.31, "end": 1039.79, "word": "إذاً", "probability": 0.5068359375}, {"start": 1039.79, "end": 1040.17, "word": " where", "probability": 0.5771484375}, {"start": 1040.17, "end": 1040.89, "word": " الـ", "probability": 0.672607421875}, {"start": 1040.89, "end": 1041.01, "word": " N", "probability": 0.304443359375}, {"start": 1041.01, "end": 1041.33, "word": " زائد", "probability": 0.73681640625}, {"start": 1041.33, "end": 1041.79, "word": " واحد", "probability": 0.96240234375}, {"start": 1041.79, "end": 1042.11, "word": " is", "probability": 0.7353515625}, {"start": 1042.11, "end": 1042.33, "word": " the", "probability": 0.83837890625}, {"start": 1042.33, "end": 1042.77, "word": " number", "probability": 0.96923828125}, {"start": 1042.77, "end": 1043.25, "word": " of", "probability": 0.974609375}, {"start": 1043.25, "end": 1043.69, "word": " parts", "probability": 0.8955078125}, {"start": 1043.69, "end": 1044.01, "word": " in", "probability": 0.8955078125}, {"start": 1044.01, "end": 1044.37, "word": " B", "probability": 0.9033203125}, {"start": 1044.37, "end": 1045.61, "word": " إبسلون", "probability": 0.815478515625}, {"start": 1045.61, "end": 1046.13, "word": " يعني", "probability": 0.795166015625}, {"start": 1046.13, "end": 1046.37, "word": " الـ", "probability": 0.649658203125}, {"start": 1046.37, "end": 1046.59, "word": " Delta", "probability": 0.55029296875}, {"start": 1046.59, "end": 1047.09, "word": " بتساوي", "probability": 0.8348388671875}, {"start": 1047.09, "end": 1047.69, "word": " إبسلون", "probability": 0.95068359375}, {"start": 1047.69, "end": 1048.29, "word": " على", "probability": 0.73193359375}, {"start": 1048.29, "end": 1048.77, "word": " 12", "probability": 0.51123046875}, {"start": 1048.77, "end": 1048.95, "word": " في", "probability": 0.88671875}, {"start": 1048.95, "end": 1049.19, "word": " N", "probability": 0.84814453125}, {"start": 1049.19, "end": 1049.43, "word": " الـ", "probability": 0.599365234375}, {"start": 1049.43, "end": 1049.57, "word": " N", "probability": 0.9384765625}, {"start": 1049.57, "end": 1050.99, "word": " ارتبطت", "probability": 0.89228515625}, {"start": 1050.99, "end": 1051.11, "word": " بال", "probability": 0.96923828125}, {"start": 1051.11, "end": 1051.51, "word": " partition", "probability": 0.33154296875}, {"start": 1051.51, "end": 1051.79, "word": " اللي", "probability": 0.965576171875}, {"start": 1051.79, "end": 1052.35, "word": " لجيته", "probability": 0.7774658203125}, {"start": 1052.35, "end": 1052.97, "word": " والـ", "probability": 0.6015625}, {"start": 1052.97, "end": 1053.13, "word": " M", "probability": 0.95751953125}, {"start": 1053.13, "end": 1053.37, "word": " هي", "probability": 0.94091796875}, {"start": 1053.37, "end": 1053.69, "word": " عبارة", "probability": 0.99462890625}, {"start": 1053.69, "end": 1053.89, "word": " عن", "probability": 0.99755859375}, {"start": 1053.89, "end": 1054.07, "word": " ال", "probability": 0.80322265625}, {"start": 1054.07, "end": 1055.03, "word": " supremum", "probability": 0.57965087890625}, {"start": 1055.03, "end": 1055.79, "word": " لكل", "probability": 0.924560546875}, {"start": 1055.79, "end": 1056.75, "word": " الدالة", "probability": 0.9296875}, {"start": 1056.75, "end": 1058.39, "word": " على", "probability": 0.48486328125}, {"start": 1058.39, "end": 1058.69, "word": " كل", "probability": 0.876953125}, {"start": 1058.69, "end": 1059.25, "word": " الفترة", "probability": 0.9900716145833334}, {"start": 1059.25, "end": 1060.35, "word": " المذكورة", "probability": 0.9873046875}, {"start": 1060.35, "end": 1061.15, "word": " نيجي", "probability": 0.8232421875}, {"start": 1061.15, "end": 1061.41, "word": " الآن", "probability": 0.785888671875}], "temperature": 1.0}, {"id": 44, "seek": 108355, "start": 1066.35, "end": 1083.55, "text": "Now let Q بيساوي Y not Y واحد و Y اتنين لعند Y M مش N، Y M ماشي بـany partition of I with ال absolute value للـQ أو ال norm للـQ أصغر من Delta", "tokens": [13267, 718, 1249, 4724, 1829, 3794, 995, 45865, 398, 406, 398, 36764, 24401, 4032, 398, 1975, 2655, 1863, 9957, 5296, 3615, 41260, 398, 376, 37893, 426, 12399, 398, 376, 3714, 33599, 1829, 4724, 39184, 1325, 24808, 295, 286, 365, 2423, 8236, 2158, 24976, 39184, 48, 34051, 2423, 2026, 24976, 39184, 48, 5551, 9381, 17082, 2288, 9154, 18183], "avg_logprob": -0.4108297557666384, "compression_ratio": 1.18125, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1066.3500000000001, "end": 1067.19, "word": "Now", "probability": 0.396484375}, {"start": 1067.19, "end": 1068.03, "word": " let", "probability": 0.28076171875}, {"start": 1068.03, "end": 1068.51, "word": " Q", "probability": 0.60400390625}, {"start": 1068.51, "end": 1069.59, "word": " بيساوي", "probability": 0.53466796875}, {"start": 1069.59, "end": 1069.87, "word": " Y", "probability": 0.69580078125}, {"start": 1069.87, "end": 1070.15, "word": " not", "probability": 0.142822265625}, {"start": 1070.15, "end": 1070.41, "word": " Y", "probability": 0.5400390625}, {"start": 1070.41, "end": 1070.79, "word": " واحد", "probability": 0.727783203125}, {"start": 1070.79, "end": 1070.91, "word": " و", "probability": 0.72119140625}, {"start": 1070.91, "end": 1071.05, "word": " Y", "probability": 0.53759765625}, {"start": 1071.05, "end": 1071.59, "word": " اتنين", "probability": 0.9244384765625}, {"start": 1071.59, "end": 1072.49, "word": " لعند", "probability": 0.9142252604166666}, {"start": 1072.49, "end": 1073.13, "word": " Y", "probability": 0.90869140625}, {"start": 1073.13, "end": 1073.75, "word": " M", "probability": 0.464599609375}, {"start": 1073.75, "end": 1074.17, "word": " مش", "probability": 0.796875}, {"start": 1074.17, "end": 1074.89, "word": " N،", "probability": 0.17547607421875}, {"start": 1074.89, "end": 1075.21, "word": " Y", "probability": 0.75048828125}, {"start": 1075.21, "end": 1075.67, "word": " M", "probability": 0.88916015625}, {"start": 1075.67, "end": 1076.35, "word": " ماشي", "probability": 0.7566731770833334}, {"start": 1076.35, "end": 1078.09, "word": " بـany", "probability": 0.490234375}, {"start": 1078.09, "end": 1078.63, "word": " partition", "probability": 0.94677734375}, {"start": 1078.63, "end": 1078.95, "word": " of", "probability": 0.98046875}, {"start": 1078.95, "end": 1079.27, "word": " I", "probability": 0.986328125}, {"start": 1079.27, "end": 1079.69, "word": " with", "probability": 0.93798828125}, {"start": 1079.69, "end": 1079.89, "word": " ال", "probability": 0.6962890625}, {"start": 1079.89, "end": 1080.25, "word": " absolute", "probability": 0.703125}, {"start": 1080.25, "end": 1080.75, "word": " value", "probability": 0.9873046875}, {"start": 1080.75, "end": 1081.31, "word": " للـQ", "probability": 0.631103515625}, {"start": 1081.31, "end": 1081.89, "word": " أو", "probability": 0.87548828125}, {"start": 1081.89, "end": 1082.01, "word": " ال", "probability": 0.64599609375}, {"start": 1082.01, "end": 1082.25, "word": " norm", "probability": 0.708984375}, {"start": 1082.25, "end": 1082.69, "word": " للـQ", "probability": 0.8619791666666666}, {"start": 1082.69, "end": 1083.07, "word": " أصغر", "probability": 0.9713134765625}, {"start": 1083.07, "end": 1083.23, "word": " من", "probability": 0.99755859375}, {"start": 1083.23, "end": 1083.55, "word": " Delta", "probability": 0.392333984375}], "temperature": 1.0}, {"id": 45, "seek": 111164, "start": 1084.42, "end": 1111.64, "text": "أيش يا جماعة قاعد أنا أحاول أصل للي بديها؟ أيش غرضي؟ إن لكل epsilon أكبر من 0 بدي ألاقي delta بحيث أنه أي partition أصغر من delta norm يعطيني الفرق بين رمان صمه وال integration أصغر من epsilon وكأنه الآن بدأت أحط أيدي على الجرح وأصل أقول let Q بيساوي Y0 Y1 YM بأي partition", "tokens": [10721, 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{"start": 3123.97, "end": 3124.13, "word": " من", "probability": 0.9794921875}, {"start": 3124.13, "end": 3124.41, "word": " دلتا", "probability": 0.8663330078125}, {"start": 3124.41, "end": 3124.83, "word": " أصلا", "probability": 0.87353515625}, {"start": 3124.83, "end": 3125.15, "word": " احنا", "probability": 0.7970377604166666}, {"start": 3125.15, "end": 3125.43, "word": " بدنا", "probability": 0.93408203125}, {"start": 3125.43, "end": 3125.79, "word": " نصل", "probability": 0.936767578125}, {"start": 3125.79, "end": 3126.37, "word": " لإنه", "probability": 0.8907470703125}], "temperature": 1.0}, {"id": 128, "seek": 315406, "start": 3126.7, "end": 3154.06, "text": "المسافة بين هذولة اللي هو أصغر من إبسلون وعلى طول منها بنستنتج هذه فكيف وصلنا بإننا قلنا اللي هو ال integration هذه في هذه الفترة والفترة هذه جزء من هذه وهذه قلنا هذه طولها على الأكثر بساوي إبسلون عشان هيك صارت المسافة بين هذه وهذا أصغر من إبسلون وهو المطلوب طيب نيجي الآن ده اللي هي النظرية اللي بعدها theorem", 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3150.06, "end": 3150.74, "word": " بعدها", "probability": 0.80908203125}, {"start": 3150.74, "end": 3154.06, "word": " theorem", "probability": 0.7744140625}], "temperature": 1.0}, {"id": 129, "seek": 316507, "start": 3155.67, "end": 3165.07, "text": "لت I بتساوي A وB و لت F من I لعند R بيكون فنكشف", "tokens": [1211, 2655, 286, 39894, 3794, 995, 45865, 316, 4032, 33, 4032, 5296, 2655, 479, 9154, 286, 5296, 3615, 41260, 497, 4724, 1829, 30544, 6156, 1863, 4117, 8592, 5172], "avg_logprob": -0.5035021551724138, "compression_ratio": 1.0, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 3155.67, "end": 3156.11, "word": "لت", "probability": 0.53045654296875}, {"start": 3156.11, "end": 3156.33, "word": " I", "probability": 0.60693359375}, {"start": 3156.33, "end": 3156.97, "word": " بتساوي", "probability": 0.7498779296875}, {"start": 3156.97, "end": 3157.15, "word": " A", "probability": 0.8037109375}, {"start": 3157.15, "end": 3157.53, "word": " وB", "probability": 0.8173828125}, 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"word": " ابسلون", "probability": 0.9326171875}], "temperature": 1.0}, {"id": 140, "seek": 340292, "start": 3396.48, "end": 3402.92, "text": "أي بارتشن بي ابسلون بحيث أن أي بي بتحتول بي ابسلون", "tokens": [10721, 1829, 4724, 9640, 2655, 8592, 1863, 4724, 1829, 48127, 3794, 1211, 11536, 4724, 5016, 1829, 12984, 14739, 36632, 4724, 1829, 39894, 33753, 12610, 4724, 1829, 48127, 3794, 1211, 11536], "avg_logprob": -0.41229838325131324, "compression_ratio": 1.3846153846153846, "no_speech_prob": 4.827976226806641e-06, "words": [{"start": 3396.48, "end": 3397.52, "word": "أي", "probability": 0.3087158203125}, {"start": 3397.52, "end": 3398.56, "word": " بارتشن", "probability": 0.604052734375}, {"start": 3398.56, "end": 3398.76, "word": " بي", "probability": 0.814697265625}, {"start": 3398.76, "end": 3399.28, "word": " ابسلون", "probability": 0.80401611328125}, {"start": 3399.28, "end": 3400.62, "word": " بحيث", "probability": 0.80511474609375}, {"start": 3400.62, "end": 3400.74, "word": " أن", 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