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+{"segments": [{"id": 1, "seek": 4630, "start": 21.6, "end": 46.3, "text": "ال .. في المحاضرة السابقة بدأنا التعرف على cushy sequences فأخدنا تعريف ال cushy sequence و أثبتنا أنه كل convergence sequence is cushy و أعتقد كمان أثبتنا أنه كل cushy sequence is bounded صحيح؟", "tokens": [6027, 4386, 8978, 9673, 5016, 46958, 25720, 21136, 16758, 28671, 47525, 10721, 8315, 16712, 3615, 28480, 15844, 18422, 88, 22978, 6156, 10721, 9778, 3215, 8315, 37279, 16572, 5172, 2423, 18422, 88, 8310, 4032, 5551, 12984, 3555, 2655, 8315, 14739, 3224, 28242, 32181, 8310, 307, 18422, 88, 4032, 5551, 34268, 28543, 9122, 2304, 7649, 5551, 12984, 3555, 2655, 8315, 14739, 3224, 28242, 18422, 88, 8310, 307, 37498, 20328, 5016, 1829, 5016, 22807], "avg_logprob": -0.11143662966787815, "compression_ratio": 1.6449704142011834, "no_speech_prob": 0.0, "words": [{"start": 21.6, "end": 21.98, "word": "ال", "probability": 0.935546875}, {"start": 21.98, "end": 22.76, "word": " ..", "probability": 0.77978515625}, 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"probability": 0.98681640625}], "temperature": 1.0}, {"id": 6, "seek": 18815, "start": 160.29, "end": 188.15, "text": "is bounded اليوم هنثبت نظرية مهمة نظرية اتنين تلاتة وعشرين وهذه النظرية هي كوشي كوشي criterion", "tokens": [271, 37498, 45595, 20498, 8032, 1863, 12984, 3555, 2655, 8717, 19913, 2288, 10632, 3714, 16095, 3660, 8717, 19913, 2288, 10632, 1975, 2655, 1863, 9957, 6055, 1211, 9307, 3660, 4032, 3615, 46309, 9957, 37037, 24192, 28239, 19913, 2288, 10632, 39896, 9122, 2407, 8592, 1829, 9122, 2407, 8592, 1829, 46691], "avg_logprob": -0.2256058624812535, "compression_ratio": 1.3963963963963963, "no_speech_prob": 0.0, "words": [{"start": 160.29, "end": 160.79, "word": "is", "probability": 0.7607421875}, {"start": 160.79, "end": 161.43, "word": " bounded", "probability": 0.95263671875}, {"start": 161.43, "end": 169.63, "word": " اليوم", "probability": 0.91650390625}, {"start": 169.63, "end": 170.49, "word": " هنثبت", "probability": 0.90009765625}, {"start": 170.49, "end": 171.51, 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"seek": 21670, "start": 191.82, "end": 216.7, "text": "أو معيار كوشي معيار كوشي للتقارب النظرية بتنص على أن a sequence x in contained in R is convergent", "tokens": [10721, 2407, 20449, 1829, 9640, 9122, 2407, 8592, 1829, 20449, 1829, 9640, 9122, 2407, 8592, 1829, 24976, 2655, 4587, 9640, 3555, 28239, 19913, 2288, 10632, 39894, 1863, 9381, 15844, 14739, 257, 8310, 2031, 294, 16212, 294, 497, 307, 9652, 6930], "avg_logprob": -0.15377286003857124, "compression_ratio": 1.2280701754385965, "no_speech_prob": 0.0, "words": [{"start": 191.82, "end": 192.3, "word": "أو", "probability": 0.874267578125}, {"start": 192.3, "end": 193.02, "word": " معيار", "probability": 0.97119140625}, {"start": 193.02, "end": 193.66, "word": " كوشي", "probability": 0.9071044921875}, {"start": 193.66, "end": 198.68, "word": " معيار", "probability": 0.951171875}, {"start": 198.68, "end": 199.28, "word": " كوشي", "probability": 0.9801025390625}, {"start": 199.28, "end": 200.68, "word": " للتقارب", "probability": 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Bolzano-Weierstrass theorem", "tokens": [28814, 15730, 538, 32767, 49401, 11933, 2655, 1863, 9957, 4032, 6225, 46309, 9957, 2423, 8310, 2031, 294, 307, 37498, 4724, 14851, 9778, 3215, 10943, 14331, 89, 3730, 12, 4360, 811, 9733, 640, 20904], "avg_logprob": -0.40119486083002653, "compression_ratio": 0.9747899159663865, "no_speech_prob": 0.0, "words": [{"start": 336.76, "end": 337.16, "word": "إذا", "probability": 0.4952392578125}, {"start": 337.16, "end": 337.5, "word": " by", "probability": 0.266845703125}, {"start": 337.5, "end": 338.02, "word": " لمبة", "probability": 0.63671875}, {"start": 338.02, "end": 339.12, "word": " إتنين", "probability": 0.7867431640625}, {"start": 339.12, "end": 339.24, "word": " و", "probability": 0.82421875}, {"start": 339.24, "end": 339.8, "word": " عشرين", "probability": 0.8592122395833334}, {"start": 339.8, "end": 341.18, "word": " ال", "probability": 0.6416015625}, {"start": 341.18, "end": 341.72, "word": " sequence", "probability": 0.71923828125}, 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612.7, "end": 636.5, "text": "إذا يوجد كابتل K اللي هو واحد عدد طبيعي وهذا واحد من مؤشرات ال subsequence ممكن أختاره هذا كابتل K أكبر من أو ساوي كابتل N بحيث أن ال absolute value ل X", "tokens": [28814, 15730, 7251, 29245, 3215, 9122, 16758, 2655, 1211, 591, 13672, 1829, 31439, 36764, 24401, 6225, 3215, 3215, 23032, 21292, 3615, 1829, 37037, 15730, 36764, 24401, 9154, 3714, 33604, 46309, 9307, 2423, 13924, 655, 3714, 43020, 5551, 46456, 9640, 3224, 23758, 9122, 16758, 2655, 1211, 591, 5551, 4117, 26890, 9154, 34051, 8608, 995, 45865, 9122, 16758, 2655, 1211, 426, 4724, 5016, 1829, 12984, 14739, 2423, 8236, 2158, 5296, 1783], "avg_logprob": -0.22879463604518346, "compression_ratio": 1.4523809523809523, "no_speech_prob": 0.0, "words": [{"start": 612.7, "end": 613.02, "word": "إذا", "probability": 0.370025634765625}, {"start": 613.02, "end": 613.54, "word": " يوجد", "probability": 0.8839518229166666}, {"start": 613.54, "end": 614.0, "word": " كابتل", "probability": 0.69451904296875}, 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792.98, "end": 793.42, "word": " اتنين", "probability": 0.8677978515625}, {"start": 793.42, "end": 794.0, "word": " و", "probability": 0.450927734375}, {"start": 794.0, "end": 794.22, "word": " الـ", "probability": 0.7298583984375}, {"start": 794.22, "end": 794.4, "word": " N", "probability": 0.87353515625}, {"start": 794.4, "end": 794.9, "word": " هذه", "probability": 0.8525390625}, {"start": 794.9, "end": 796.06, "word": " لازم", "probability": 0.9920247395833334}, {"start": 796.06, "end": 796.64, "word": " تكون", "probability": 0.990234375}, {"start": 796.64, "end": 797.26, "word": " أكبر", "probability": 0.9710286458333334}, {"start": 797.26, "end": 797.5, "word": " من", "probability": 0.99609375}, {"start": 797.5, "end": 797.74, "word": " أو", "probability": 0.99169921875}, {"start": 797.74, "end": 798.26, "word": " ساوي", "probability": 0.9609375}, {"start": 798.26, "end": 798.68, "word": " M،", "probability": 0.651123046875}, {"start": 798.68, "end": 798.86, "word": " إذن", "probability": 0.7415364583333334}, {"start": 798.86, "end": 799.1, "word": " هذا", "probability": 0.91943359375}, {"start": 799.1, "end": 799.6, "word": " صحيح", "probability": 0.99755859375}, {"start": 799.6, "end": 800.18, "word": " لكل", "probability": 0.980224609375}, {"start": 800.18, "end": 800.66, "word": " small", "probability": 0.763671875}, {"start": 800.66, "end": 801.1, "word": " M", "probability": 0.44482421875}, {"start": 801.1, "end": 802.34, "word": " أكبر", "probability": 0.9820963541666666}, {"start": 802.34, "end": 802.58, "word": " من", "probability": 0.99658203125}, {"start": 802.58, "end": 802.78, "word": " أو", "probability": 0.994140625}, {"start": 802.78, "end": 803.42, "word": " ساوي", "probability": 0.9705403645833334}, {"start": 803.42, "end": 804.02, "word": " كابتال", "probability": 0.83087158203125}, {"start": 804.02, "end": 804.26, "word": " M", "probability": 0.7490234375}], "temperature": 1.0}, {"id": 29, "seek": 82405, "start": 809.67, "end": 824.05, "text": "تمام hence by double star الآن من double star and triple star", "tokens": [39237, 10943, 16678, 538, 3834, 3543, 6024, 48506, 9154, 3834, 3543, 293, 15508, 3543], "avg_logprob": -0.26666667858759563, "compression_ratio": 1.1451612903225807, "no_speech_prob": 0.0, "words": [{"start": 809.6700000000001, "end": 811.07, "word": "تمام", "probability": 0.73974609375}, {"start": 811.07, "end": 812.47, "word": " hence", "probability": 0.350830078125}, {"start": 812.47, "end": 815.67, "word": " by", "probability": 0.9033203125}, {"start": 815.67, "end": 816.49, "word": " double", "probability": 0.8359375}, {"start": 816.49, "end": 817.09, "word": " star", "probability": 0.94580078125}, {"start": 817.09, "end": 817.65, "word": " الآن", "probability": 0.58349609375}, {"start": 817.65, "end": 817.97, "word": " من", "probability": 0.98486328125}, {"start": 817.97, "end": 818.35, "word": " double", "probability": 0.93017578125}, {"start": 818.35, "end": 818.99, "word": " star", "probability": 0.93310546875}, {"start": 818.99, "end": 820.69, "word": " and", "probability": 0.9541015625}, {"start": 820.69, "end": 822.85, "word": " triple", "probability": 0.9521484375}, {"start": 822.85, "end": 824.05, "word": " star", "probability": 0.96337890625}], "temperature": 1.0}, {"id": 30, "seek": 85853, "start": 828.93, "end": 858.53, "text": "لدينا we have لو كان n أكبر من أو ساوي capital N فهذا بيقدي أنه absolute xn minus x star طبعا هنا هترح x capital K و هرجعها", "tokens": [1211, 16254, 8315, 321, 362, 45164, 25961, 297, 5551, 4117, 26890, 9154, 34051, 8608, 995, 45865, 4238, 426, 6156, 3224, 15730, 4724, 1829, 4587, 16254, 14739, 3224, 8236, 2031, 77, 3175, 2031, 3543, 23032, 3555, 3615, 995, 34105, 8032, 2655, 2288, 5016, 2031, 4238, 591, 4032, 8032, 47341, 3615, 11296], "avg_logprob": -0.21706495214911067, "compression_ratio": 1.1904761904761905, "no_speech_prob": 0.0, "words": [{"start": 828.93, "end": 829.87, "word": "لدينا", "probability": 0.896484375}, {"start": 829.87, "end": 830.23, "word": " we", "probability": 0.2354736328125}, {"start": 830.23, "end": 831.31, "word": " have", "probability": 0.970703125}, {"start": 831.31, "end": 833.23, "word": " لو", "probability": 0.83740234375}, {"start": 833.23, "end": 833.87, "word": " كان", "probability": 0.98974609375}, {"start": 833.87, "end": 834.39, "word": " n", "probability": 0.5517578125}, {"start": 834.39, "end": 835.31, "word": " أكبر", "probability": 0.9386393229166666}, {"start": 835.31, "end": 835.53, "word": " من", "probability": 0.89990234375}, {"start": 835.53, "end": 835.75, "word": " أو", "probability": 0.97998046875}, {"start": 835.75, "end": 836.33, "word": " ساوي", "probability": 0.9410807291666666}, {"start": 836.33, "end": 836.87, "word": " capital", "probability": 0.50537109375}, {"start": 836.87, "end": 837.27, "word": " N", "probability": 0.67333984375}, {"start": 837.27, "end": 839.03, "word": " فهذا", "probability": 0.98046875}, {"start": 839.03, "end": 839.71, "word": " بيقدي", "probability": 0.70599365234375}, {"start": 839.71, "end": 840.33, "word": " أنه", "probability": 0.43798828125}, {"start": 840.33, "end": 841.01, "word": " absolute", "probability": 0.88720703125}, {"start": 841.01, "end": 843.27, "word": " xn", "probability": 0.657470703125}, {"start": 843.27, "end": 843.99, "word": " minus", "probability": 0.78125}, {"start": 843.99, "end": 844.47, "word": " x", "probability": 0.99267578125}, {"start": 844.47, "end": 845.15, "word": " star", "probability": 0.33056640625}, {"start": 845.15, "end": 851.33, "word": " طبعا", "probability": 0.9764404296875}, {"start": 851.33, "end": 851.65, "word": " هنا", "probability": 0.94775390625}, {"start": 851.65, "end": 853.55, "word": " هترح", "probability": 0.8350830078125}, {"start": 853.55, "end": 855.67, "word": " x", "probability": 0.8837890625}, {"start": 855.67, "end": 856.21, "word": " capital", "probability": 0.73583984375}, {"start": 856.21, "end": 856.71, "word": " K", "probability": 0.74853515625}, {"start": 856.71, "end": 857.71, "word": " و", "probability": 0.6435546875}, {"start": 857.71, "end": 858.53, "word": " هرجعها", "probability": 0.90771484375}], "temperature": 1.0}, {"id": 31, "seek": 88163, "start": 868.69, "end": 881.63, "text": "إذا I subtracted XK and get it back باخد هدوع الأثنين مع بعض و التحدين هدوع مع بعض", "tokens": [28814, 15730, 286, 16390, 292, 1783, 42, 293, 483, 309, 646, 4724, 47283, 3215, 8032, 3215, 2407, 3615, 16247, 12984, 1863, 9957, 20449, 45030, 11242, 4032, 16712, 5016, 16254, 1863, 8032, 3215, 2407, 3615, 20449, 45030, 11242], "avg_logprob": -0.32298521070103897, "compression_ratio": 1.1844660194174756, "no_speech_prob": 0.0, "words": [{"start": 868.69, "end": 869.07, "word": "إذا", "probability": 0.5443115234375}, {"start": 869.07, "end": 870.33, "word": " I", "probability": 0.279052734375}, {"start": 870.33, "end": 871.95, "word": " subtracted", "probability": 0.749755859375}, {"start": 871.95, "end": 873.45, "word": " XK", "probability": 0.615478515625}, {"start": 873.45, "end": 874.03, "word": " and", "probability": 0.92626953125}, {"start": 874.03, "end": 875.99, "word": " get", "probability": 0.697265625}, {"start": 875.99, "end": 876.15, "word": " it", "probability": 0.96484375}, {"start": 876.15, "end": 876.59, "word": " back", "probability": 0.91748046875}, {"start": 876.59, "end": 878.43, "word": " باخد", "probability": 0.8702799479166666}, {"start": 878.43, "end": 878.73, "word": " هدوع", "probability": 0.70684814453125}, {"start": 878.73, "end": 879.23, "word": " الأثنين", "probability": 0.76739501953125}, {"start": 879.23, "end": 879.45, "word": " مع", "probability": 0.98388671875}, {"start": 879.45, "end": 879.91, "word": " بعض", "probability": 0.9873046875}, {"start": 879.91, "end": 880.05, "word": " و", "probability": 0.6181640625}, {"start": 880.05, "end": 880.65, "word": " التحدين", "probability": 0.66290283203125}, {"start": 880.65, "end": 880.91, "word": " هدوع", "probability": 0.9063720703125}, {"start": 880.91, "end": 881.15, "word": " مع", "probability": 0.7568359375}, {"start": 881.15, "end": 881.63, "word": " بعض", "probability": 0.9951171875}], "temperature": 1.0}, {"id": 32, "seek": 91116, "start": 882.98, "end": 911.16, "text": "الـ absolute value بالترانجل inequality بالترانجل الانيقواليتي هذا أصغر من أسابع absolute الحد الأول اللي هو xn minus xk زائد absolute الحد التاني اللي هو xk minus x star الآن باستخدام triple star", "tokens": [6027, 39184, 8236, 2158, 20666, 2655, 2288, 7649, 7435, 1211, 16970, 20666, 2655, 2288, 7649, 7435, 1211, 2423, 7649, 1829, 4587, 2407, 6027, 1829, 31371, 23758, 5551, 9381, 17082, 2288, 9154, 5551, 3794, 16758, 3615, 8236, 21542, 3215, 16247, 12610, 13672, 1829, 31439, 2031, 77, 3175, 2031, 74, 30767, 16373, 3215, 8236, 21542, 3215, 16712, 7649, 1829, 13672, 1829, 31439, 2031, 74, 3175, 2031, 3543, 6024, 48506, 4724, 995, 14851, 9778, 3215, 10943, 15508, 3543], "avg_logprob": -0.30921052553151784, "compression_ratio": 1.6384180790960452, "no_speech_prob": 0.0, "words": [{"start": 882.98, "end": 883.28, "word": "الـ", "probability": 0.605224609375}, {"start": 883.28, "end": 883.64, "word": " absolute", "probability": 0.5986328125}, {"start": 883.64, "end": 884.16, "word": " value", "probability": 0.98779296875}, {"start": 884.16, "end": 885.02, "word": " بالترانجل", "probability": 0.65740966796875}, {"start": 885.02, "end": 885.52, "word": " inequality", "probability": 0.5302734375}, {"start": 885.52, "end": 888.2, "word": " بالترانجل", "probability": 0.9303385416666666}, {"start": 888.2, "end": 889.1, "word": " الانيقواليتي", "probability": 0.693603515625}, {"start": 889.1, "end": 889.74, "word": " هذا", "probability": 0.7080078125}, {"start": 889.74, "end": 890.18, "word": " أصغر", "probability": 0.7962646484375}, {"start": 890.18, "end": 890.32, "word": " من", "probability": 0.501953125}, {"start": 890.32, "end": 890.84, "word": " أسابع", "probability": 0.46136474609375}, {"start": 890.84, "end": 891.7, "word": " absolute", "probability": 0.1199951171875}, {"start": 891.7, "end": 892.96, "word": " الحد", "probability": 0.9609375}, {"start": 892.96, "end": 893.38, "word": " الأول", "probability": 0.970458984375}, {"start": 893.38, "end": 893.56, "word": " اللي", "probability": 0.73974609375}, {"start": 893.56, "end": 893.78, "word": " هو", "probability": 0.9814453125}, {"start": 893.78, "end": 894.38, "word": " xn", "probability": 0.59033203125}, {"start": 894.38, "end": 894.94, "word": " minus", "probability": 0.280029296875}, {"start": 894.94, "end": 896.76, "word": " xk", "probability": 0.891845703125}, {"start": 896.76, "end": 897.54, "word": " زائد", "probability": 0.7041829427083334}, {"start": 897.54, "end": 898.1, "word": " absolute", "probability": 0.85400390625}, {"start": 898.1, "end": 898.72, "word": " الحد", "probability": 0.980712890625}, {"start": 898.72, "end": 899.22, "word": " التاني", "probability": 0.9677734375}, {"start": 899.22, "end": 899.4, "word": " اللي", "probability": 0.974365234375}, {"start": 899.4, "end": 899.62, "word": " هو", "probability": 0.986328125}, {"start": 899.62, "end": 901.4, "word": " xk", "probability": 0.969482421875}, {"start": 901.4, "end": 902.22, "word": " minus", "probability": 0.98974609375}, {"start": 902.22, "end": 902.66, "word": " x", "probability": 0.99462890625}, {"start": 902.66, "end": 903.22, "word": " star", "probability": 0.1741943359375}, {"start": 903.22, "end": 908.5, "word": " الآن", "probability": 0.6878662109375}, {"start": 908.5, "end": 909.3, "word": " باستخدام", "probability": 0.9916178385416666}, {"start": 909.3, "end": 909.78, "word": " triple", "probability": 0.4912109375}, {"start": 909.78, "end": 911.16, "word": " star", "probability": 0.919921875}], "temperature": 1.0}, {"id": 33, "seek": 93767, "start": 912.65, "end": 937.67, "text": "من المتباينة هذه هاي عندي انا x اول شي ال n small n أكبر من أو ساوي capital N هاي small n أكبر من أو ساوي capital N وبالتالي ال absolute value هذه أصغر من epsilon على اتنين زاد و من double star من double star", "tokens": [27842, 9673, 2655, 3555, 995, 9957, 3660, 29538, 8032, 47302, 18871, 16254, 1975, 8315, 2031, 1975, 12610, 44049, 2423, 297, 1359, 297, 5551, 4117, 26890, 9154, 34051, 8608, 995, 45865, 4238, 426, 8032, 47302, 1359, 297, 5551, 4117, 26890, 9154, 34051, 8608, 995, 45865, 4238, 426, 46599, 6027, 2655, 6027, 1829, 2423, 8236, 2158, 29538, 5551, 9381, 17082, 2288, 9154, 17889, 15844, 1975, 2655, 1863, 9957, 30767, 18513, 4032, 9154, 3834, 3543, 9154, 3834, 3543], "avg_logprob": -0.23087993460266212, "compression_ratio": 1.7298850574712643, "no_speech_prob": 0.0, "words": [{"start": 912.65, "end": 912.95, "word": "من", "probability": 0.88623046875}, {"start": 912.95, "end": 913.79, "word": " المتباينة", "probability": 0.9475911458333334}, {"start": 913.79, "end": 914.23, "word": " هذه", "probability": 0.81884765625}, {"start": 914.23, "end": 916.09, "word": " هاي", "probability": 0.466552734375}, {"start": 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"probability": 0.7247721354166666}, {"start": 922.39, "end": 922.77, "word": " capital", "probability": 0.71826171875}, {"start": 922.77, "end": 923.17, "word": " N", "probability": 0.71923828125}, {"start": 923.17, "end": 924.35, "word": " هاي", "probability": 0.76611328125}, {"start": 924.35, "end": 924.77, "word": " small", "probability": 0.9052734375}, {"start": 924.77, "end": 925.13, "word": " n", "probability": 0.95068359375}, {"start": 925.13, "end": 925.69, "word": " أكبر", "probability": 0.9542643229166666}, {"start": 925.69, "end": 925.83, "word": " من", "probability": 0.99365234375}, {"start": 925.83, "end": 926.01, "word": " أو", "probability": 0.97509765625}, {"start": 926.01, "end": 926.29, "word": " ساوي", "probability": 0.9775390625}, {"start": 926.29, "end": 926.69, "word": " capital", "probability": 0.8525390625}, {"start": 926.69, "end": 927.07, "word": " N", "probability": 0.97119140625}, {"start": 927.07, "end": 928.43, "word": " وبالتالي", "probability": 0.900390625}, {"start": 928.43, "end": 928.59, "word": " ال", "probability": 0.95458984375}, {"start": 928.59, "end": 928.95, "word": " absolute", "probability": 0.9208984375}, {"start": 928.95, "end": 929.51, "word": " value", "probability": 0.9970703125}, {"start": 929.51, "end": 929.87, "word": " هذه", "probability": 0.6064453125}, {"start": 929.87, "end": 930.51, "word": " أصغر", "probability": 0.964599609375}, {"start": 930.51, "end": 931.93, "word": " من", "probability": 0.9765625}, {"start": 931.93, "end": 932.29, "word": " epsilon", "probability": 0.68212890625}, {"start": 932.29, "end": 932.57, "word": " على", "probability": 0.271728515625}, {"start": 932.57, "end": 933.01, "word": " اتنين", "probability": 0.882080078125}, {"start": 933.01, "end": 933.77, "word": " زاد", "probability": 0.740966796875}, {"start": 933.77, "end": 934.87, "word": " و", "probability": 0.96240234375}, {"start": 934.87, "end": 935.19, "word": " من", "probability": 0.6748046875}, {"start": 935.19, "end": 935.61, "word": " double", "probability": 0.82373046875}, {"start": 935.61, "end": 936.23, "word": " star", "probability": 0.560546875}, {"start": 936.23, "end": 936.79, "word": " من", "probability": 0.80126953125}, {"start": 936.79, "end": 937.15, "word": " double", "probability": 0.9287109375}, {"start": 937.15, "end": 937.67, "word": " star", "probability": 0.9658203125}], "temperature": 1.0}, {"id": 34, "seek": 96000, "start": 939.8, "end": 960.0, "text": "هي عندي absolute x K minus x star أصغر من إبسمن على اتنين المجموع بتطلع إبسمن since إبسمن أكبر من السفر was arbitrarily", "tokens": [3224, 1829, 18871, 16254, 8236, 2031, 591, 3175, 2031, 3543, 5551, 9381, 17082, 2288, 9154, 11933, 3555, 3794, 27842, 15844, 1975, 2655, 1863, 9957, 9673, 7435, 2304, 45367, 39894, 9566, 1211, 3615, 11933, 3555, 3794, 27842, 1670, 11933, 3555, 3794, 27842, 5551, 4117, 26890, 9154, 21136, 5172, 2288, 390, 19071, 3289], "avg_logprob": -0.2656250097430669, "compression_ratio": 1.2733812949640289, "no_speech_prob": 0.0, "words": [{"start": 939.8, "end": 940.12, "word": "هي", "probability": 0.59423828125}, {"start": 940.12, "end": 940.5, "word": " عندي", "probability": 0.7083740234375}, {"start": 940.5, "end": 941.2, "word": " absolute", "probability": 0.744140625}, {"start": 941.2, "end": 941.8, "word": " x", "probability": 0.68017578125}, {"start": 941.8, "end": 942.36, "word": " K", "probability": 0.23974609375}, {"start": 942.36, "end": 942.98, "word": " minus", "probability": 0.4580078125}, {"start": 942.98, "end": 943.44, "word": " x", "probability": 0.87451171875}, {"start": 943.44, "end": 943.98, "word": " star", "probability": 0.43017578125}, {"start": 943.98, "end": 945.7, "word": " أصغر", "probability": 0.940673828125}, {"start": 945.7, "end": 945.88, "word": " من", "probability": 0.99267578125}, {"start": 945.88, "end": 946.22, "word": " إبسمن", "probability": 0.77789306640625}, {"start": 946.22, "end": 946.44, "word": " على", "probability": 0.376708984375}, {"start": 946.44, "end": 946.76, "word": " اتنين", "probability": 0.8538818359375}, {"start": 946.76, "end": 947.24, "word": " المجموع", "probability": 0.846923828125}, {"start": 947.24, "end": 947.64, "word": " بتطلع", "probability": 0.826416015625}, {"start": 947.64, "end": 948.66, "word": " إبسمن", "probability": 0.80926513671875}, {"start": 948.66, "end": 953.46, "word": " since", "probability": 0.3876953125}, {"start": 953.46, "end": 955.56, "word": " إبسمن", "probability": 0.879638671875}, {"start": 955.56, "end": 956.02, "word": " أكبر", "probability": 0.96533203125}, {"start": 956.02, "end": 956.24, "word": " من", "probability": 0.9951171875}, {"start": 956.24, "end": 956.82, "word": " السفر", "probability": 0.87451171875}, {"start": 956.82, "end": 957.44, "word": " was", "probability": 0.9541015625}, {"start": 957.44, "end": 960.0, "word": " arbitrarily", "probability": 0.691162109375}], "temperature": 1.0}, {"id": 35, "seek": 98789, "start": 963.85, "end": 987.89, "text": "نحن لدينا من مفهوم الـ convergence أنه هيك منكون أثبتنا أنه limit xn as n tends to infinity equals x star وهذا بكمل برهان ال claim و النظرية تمام؟ هاي لاحظوا أن احنا", "tokens": [1863, 5016, 1863, 5296, 16254, 8315, 9154, 3714, 5172, 3224, 20498, 2423, 39184, 32181, 14739, 3224, 39896, 4117, 9154, 30544, 5551, 12984, 3555, 2655, 8315, 14739, 3224, 4948, 2031, 77, 382, 297, 12258, 281, 13202, 6915, 2031, 3543, 37037, 15730, 4724, 24793, 1211, 4724, 2288, 3224, 7649, 2423, 3932, 4032, 28239, 19913, 2288, 10632, 46811, 10943, 22807, 8032, 47302, 20193, 5016, 19913, 14407, 14739, 1975, 5016, 8315], "avg_logprob": -0.4177389780388159, "compression_ratio": 1.3591160220994476, "no_speech_prob": 0.0, "words": [{"start": 963.85, "end": 964.29, "word": "نحن", "probability": 0.50927734375}, {"start": 964.29, "end": 965.47, "word": " لدينا", "probability": 0.7731119791666666}, {"start": 965.47, "end": 965.99, "word": " من", "probability": 0.87646484375}, {"start": 965.99, "end": 966.65, "word": " مفهوم", "probability": 0.531707763671875}, {"start": 966.65, "end": 966.89, "word": " الـ", "probability": 0.36285400390625}, {"start": 966.89, "end": 967.65, "word": " convergence", "probability": 0.59521484375}, {"start": 967.65, "end": 969.29, "word": " أنه", "probability": 0.5533447265625}, {"start": 969.29, "end": 969.53, "word": " هيك", "probability": 0.464111328125}, {"start": 969.53, "end": 969.87, "word": " منكون", "probability": 0.78564453125}, {"start": 969.87, "end": 970.57, "word": " أثبتنا", "probability": 0.95244140625}, {"start": 970.57, "end": 971.11, "word": " أنه", "probability": 0.449462890625}, {"start": 971.11, "end": 971.45, "word": " limit", "probability": 0.60107421875}, {"start": 971.45, "end": 973.49, "word": " xn", "probability": 0.4443359375}, {"start": 973.49, "end": 974.31, "word": " as", "probability": 0.53515625}, {"start": 974.31, "end": 974.85, "word": " n", "probability": 0.814453125}, {"start": 974.85, "end": 975.19, "word": " tends", "probability": 0.488037109375}, {"start": 975.19, "end": 975.37, "word": " to", "probability": 0.83544921875}, {"start": 975.37, "end": 975.95, "word": " infinity", "probability": 0.8974609375}, {"start": 975.95, "end": 976.69, "word": " equals", "probability": 0.830078125}, {"start": 976.69, "end": 977.15, "word": " x", "probability": 0.9609375}, {"start": 977.15, "end": 977.69, "word": " star", "probability": 0.10491943359375}, {"start": 977.69, "end": 980.63, "word": " وهذا", "probability": 0.837646484375}, {"start": 980.63, "end": 981.23, "word": " بكمل", "probability": 0.8505859375}, {"start": 981.23, "end": 981.85, "word": " برهان", "probability": 0.924072265625}, {"start": 981.85, "end": 982.73, "word": " ال", "probability": 0.81787109375}, {"start": 982.73, "end": 983.17, "word": " claim", "probability": 0.51416015625}, {"start": 983.17, "end": 983.41, "word": " و", "probability": 0.55517578125}, {"start": 983.41, "end": 984.67, "word": " النظرية", "probability": 0.9525146484375}, {"start": 984.67, "end": 986.79, "word": " تمام؟", "probability": 0.6493326822916666}, {"start": 986.79, "end": 987.09, "word": " هاي", "probability": 0.4625244140625}, {"start": 987.09, "end": 987.51, "word": " لاحظوا", "probability": 0.82470703125}, {"start": 987.51, "end": 987.61, "word": " أن", "probability": 0.73046875}, {"start": 987.61, "end": 987.89, "word": " احنا", "probability": 0.8435872395833334}], "temperature": 1.0}, {"id": 36, "seek": 100766, "start": 988.84, "end": 1007.66, "text": "بنثبت أننا ندعي أن الـSequence Xn هي الـConversion لـX الصار حسب تعريف epsilon capital N للـLimits بدأنا بـepsilon given عشوائية عدد موجب أثبتنا هي يوجد capital N يعتمد على epsilon أشرر number", "tokens": [3555, 1863, 12984, 3555, 2655, 14739, 8315, 8717, 3215, 3615, 1829, 14739, 2423, 39184, 10637, 358, 655, 1783, 77, 39896, 2423, 39184, 9838, 29153, 5296, 39184, 55, 31767, 9640, 11331, 35457, 37279, 16572, 5172, 17889, 4238, 426, 24976, 39184, 43, 332, 1208, 47525, 10721, 8315, 4724, 39184, 10653, 15754, 2212, 6225, 8592, 2407, 16373, 10632, 6225, 3215, 3215, 3714, 29245, 3555, 5551, 12984, 3555, 2655, 8315, 39896, 7251, 29245, 3215, 4238, 426, 7251, 34268, 2304, 3215, 15844, 17889, 5551, 46309, 2288, 1230], "avg_logprob": -0.4510542283575219, "compression_ratio": 1.4111675126903553, "no_speech_prob": 0.0, "words": [{"start": 988.84, "end": 989.7, "word": "بنثبت", "probability": 0.647705078125}, {"start": 989.7, "end": 990.46, "word": " أننا", "probability": 0.28179931640625}, {"start": 990.46, "end": 991.4, "word": " ندعي", "probability": 0.8427734375}, {"start": 991.4, "end": 991.58, "word": " أن", "probability": 0.60595703125}, {"start": 991.58, "end": 992.16, "word": " الـSequence", "probability": 0.6713134765625}, {"start": 992.16, "end": 992.54, "word": " Xn", "probability": 0.3719482421875}, {"start": 992.54, "end": 992.72, "word": " هي", "probability": 0.099365234375}, {"start": 992.72, "end": 992.98, "word": " الـConversion", "probability": 0.505615234375}, {"start": 992.98, "end": 993.28, "word": " لـX", "probability": 0.5950520833333334}, {"start": 993.28, "end": 993.72, "word": " الصار", "probability": 0.516357421875}, {"start": 993.72, "end": 994.82, "word": " حسب", "probability": 0.810302734375}, {"start": 994.82, "end": 995.26, "word": " تعريف", "probability": 0.8606770833333334}, {"start": 995.26, "end": 995.66, "word": " epsilon", "probability": 0.1988525390625}, {"start": 995.66, "end": 996.06, "word": " capital", "probability": 0.2449951171875}, {"start": 996.06, "end": 996.36, "word": " N", "probability": 0.89208984375}, {"start": 996.36, "end": 997.06, "word": " للـLimits", "probability": 0.751611328125}, {"start": 997.06, "end": 998.5, "word": " بدأنا", "probability": 0.7568359375}, {"start": 998.5, "end": 999.06, "word": " بـepsilon", "probability": 0.7489013671875}, {"start": 999.06, "end": 999.46, "word": " given", "probability": 0.48388671875}, {"start": 999.46, "end": 1000.36, "word": " عشوائية", "probability": 0.97529296875}, {"start": 1000.36, "end": 1000.86, "word": " عدد", "probability": 0.8904622395833334}, {"start": 1000.86, "end": 1001.36, "word": " موجب", "probability": 0.859375}, {"start": 1001.36, "end": 1003.4, "word": " أثبتنا", "probability": 0.9666015625}, {"start": 1003.4, "end": 1003.66, "word": " هي", "probability": 0.525390625}, {"start": 1003.66, "end": 1004.44, "word": " يوجد", "probability": 0.84765625}, {"start": 1004.44, "end": 1005.16, "word": " capital", "probability": 0.5029296875}, {"start": 1005.16, "end": 1005.6, "word": " N", "probability": 0.943359375}, {"start": 1005.6, "end": 1006.2, "word": " يعتمد", "probability": 0.9130859375}, {"start": 1006.2, "end": 1006.36, "word": " على", "probability": 0.82080078125}, {"start": 1006.36, "end": 1006.82, "word": " epsilon", "probability": 0.79296875}, {"start": 1006.82, "end": 1007.34, "word": " أشرر", "probability": 0.4326985677083333}, {"start": 1007.34, "end": 1007.66, "word": " number", "probability": 0.384521484375}], "temperature": 1.0}, {"id": 37, "seek": 102508, "start": 1008.38, "end": 1025.08, "text": "بحيث انه لكل N أكبر من او ساوي capital N طلع absolute xn minus x star less than epsilon لما ان هذا الكلام صحيح لكل epsilon", "tokens": [49628, 1829, 12984, 16472, 3224, 5296, 28820, 426, 5551, 4117, 26890, 9154, 1975, 2407, 8608, 995, 45865, 4238, 426, 23032, 1211, 3615, 8236, 2031, 77, 3175, 2031, 3543, 1570, 813, 17889, 5296, 15042, 16472, 23758, 2423, 28820, 10943, 20328, 5016, 1829, 5016, 5296, 28820, 17889], "avg_logprob": -0.29228941253993823, "compression_ratio": 1.2444444444444445, "no_speech_prob": 0.0, "words": [{"start": 1008.38, "end": 1009.08, "word": "بحيث", "probability": 0.83544921875}, {"start": 1009.08, "end": 1009.52, "word": " انه", "probability": 0.6846923828125}, {"start": 1009.52, "end": 1010.08, "word": " لكل", "probability": 0.978515625}, {"start": 1010.08, "end": 1010.4, "word": " N", "probability": 0.50732421875}, {"start": 1010.4, 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1018.84, "word": " less", "probability": 0.93408203125}, {"start": 1018.84, "end": 1019.4, "word": " than", "probability": 0.931640625}, {"start": 1019.4, "end": 1020.0, "word": " epsilon", "probability": 0.72900390625}, {"start": 1020.0, "end": 1022.92, "word": " لما", "probability": 0.58154296875}, {"start": 1022.92, "end": 1023.04, "word": " ان", "probability": 0.6474609375}, {"start": 1023.04, "end": 1023.24, "word": " هذا", "probability": 0.81103515625}, {"start": 1023.24, "end": 1023.64, "word": " الكلام", "probability": 0.9469401041666666}, {"start": 1023.64, "end": 1024.1, "word": " صحيح", "probability": 0.997314453125}, {"start": 1024.1, "end": 1024.6, "word": " لكل", "probability": 0.949462890625}, {"start": 1024.6, "end": 1025.08, "word": " epsilon", "probability": 0.5625}], "temperature": 1.0}, {"id": 38, "seek": 104396, "start": 1026.56, "end": 1043.96, "text": "إذا by definition limit xn ساوي x أسطورة، إذا ال sequence convergent إذا هذا بيكمل البرهان إن لو كانت ال 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باستخدام التعريف مباشرة و ليس باستخدام اللي هو koshi criterion", "tokens": [8297, 5551, 34268, 28543, 14739, 2423, 26890, 3224, 7649, 4032, 46958, 5016, 37495, 22653, 45164, 12174, 2288, 10721, 47395, 39894, 15042, 3615, 3224, 8032, 2655, 7435, 3215, 14739, 3224, 37495, 22653, 8608, 3224, 1211, 4032, 4724, 3794, 1829, 9566, 23032, 1829, 3555, 8717, 47283, 3215, 5551, 2304, 12984, 37977, 15844, 9122, 33911, 8717, 14851, 9778, 40448, 37279, 16572, 5172, 2423, 350, 17392, 8310, 8978, 11933, 12984, 3555, 9307, 14739, 3224, 2212, 8310, 307, 350, 17392, 4724, 995, 14851, 9778, 3215, 10943, 16712, 3615, 16572, 5172, 3714, 3555, 33599, 25720, 4032, 32239, 3794, 4724, 995, 14851, 9778, 3215, 10943, 13672, 1829, 31439, 350, 17392, 46691], "avg_logprob": -0.13370536168416342, "compression_ratio": 1.6216216216216217, "no_speech_prob": 0.0, "words": [{"start": 1139.89, "end": 1140.37, "word": "Okay", "probability": 0.8291015625}, {"start": 1140.37, "end": 1140.83, "word": " أعتقد", "probability": 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في", "probability": 0.92236328125}, {"start": 1156.35, "end": 1156.95, "word": " إثبات", "probability": 0.86700439453125}, {"start": 1156.95, "end": 1157.43, "word": " أنه", "probability": 0.6025390625}, {"start": 1157.43, "end": 1157.75, "word": " given", "probability": 0.908203125}, {"start": 1157.75, "end": 1159.37, "word": " sequence", "probability": 0.97998046875}, {"start": 1159.37, "end": 1159.79, "word": " is", "probability": 0.96728515625}, {"start": 1159.79, "end": 1160.25, "word": " koshi", "probability": 0.763671875}, {"start": 1160.25, "end": 1162.21, "word": " باستخدام", "probability": 0.9765625}, {"start": 1162.21, "end": 1162.73, "word": " التعريف", "probability": 0.9949951171875}, {"start": 1162.73, "end": 1163.45, "word": " مباشرة", "probability": 0.9935302734375}, {"start": 1163.45, "end": 1165.73, "word": " و", "probability": 0.98486328125}, {"start": 1165.73, "end": 1166.13, "word": " ليس", "probability": 0.79931640625}, {"start": 1166.13, "end": 1166.91, "word": " باستخدام", "probability": 0.9942220052083334}, {"start": 1166.91, "end": 1167.25, "word": " اللي", "probability": 0.946044921875}, {"start": 1167.25, "end": 1167.51, "word": " هو", "probability": 0.9892578125}, {"start": 1167.51, "end": 1167.89, "word": " koshi", "probability": 0.828125}, {"start": 1167.89, "end": 1168.41, "word": " criterion", "probability": 0.97509765625}], "temperature": 1.0}, {"id": 43, "seek": 120025, "start": 1171.95, "end": 1200.25, "text": "إذا ناخد هنا بعض الأمثلة examples الأمثلة دي أنا أعطيها الرقم 224 أول مثال show", "tokens": [28814, 15730, 8717, 47283, 3215, 34105, 45030, 11242, 16247, 2304, 12984, 37977, 5110, 16247, 2304, 12984, 37977, 11778, 1829, 41850, 5551, 3615, 9566, 1829, 11296, 34892, 4587, 2304, 5853, 19, 5551, 12610, 50113, 6027, 855], "avg_logprob": -0.15603297907445166, "compression_ratio": 1.1944444444444444, "no_speech_prob": 0.0, "words": [{"start": 1171.95, "end": 1172.29, "word": "إذا", "probability": 0.710693359375}, {"start": 1172.29, 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1246.61, "word": " Cauchy", "probability": 0.8922526041666666}, {"start": 1246.61, "end": 1247.15, "word": " sequence", "probability": 0.83447265625}, {"start": 1247.15, "end": 1250.45, "word": " فنشوف", "probability": 0.947509765625}, {"start": 1250.45, "end": 1250.65, "word": " مع", "probability": 0.99658203125}, {"start": 1250.65, "end": 1251.15, "word": " بعض", "probability": 0.987548828125}, {"start": 1251.15, "end": 1256.21, "word": " طبعا", "probability": 0.9619140625}, {"start": 1256.21, "end": 1257.57, "word": " البرهان", "probability": 0.9344482421875}], "temperature": 1.0}, {"id": 46, "seek": 128767, "start": 1258.87, "end": 1287.67, "text": "باستخدام التعريف هنبدأ بأبسلون أكبر من السفر ونرد عليها بcapital N بتخلي ال implication هي دي تتحقق بالظبط زي .. يعني قريب يعني بالظبط زي ما عملنا في اثبات ان ال sequence is convergent و هنستخدم الarchimedean property نشوف مع بعض let", "tokens": [3555, 995, 14851, 9778, 3215, 10943, 16712, 3615, 16572, 5172, 8032, 1863, 44510, 10721, 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"probability": 0.6169026692708334}, {"start": 1261.71, "end": 1262.01, "word": " أكبر", "probability": 0.966796875}, {"start": 1262.01, "end": 1262.23, "word": " من", "probability": 0.974609375}, {"start": 1262.23, "end": 1262.75, "word": " السفر", "probability": 0.7836100260416666}, {"start": 1262.75, "end": 1264.15, "word": " ونرد", "probability": 0.813720703125}, {"start": 1264.15, "end": 1264.63, "word": " عليها", "probability": 0.9853515625}, {"start": 1264.63, "end": 1265.27, "word": " بcapital", "probability": 0.6790364583333334}, {"start": 1265.27, "end": 1265.57, "word": " N", "probability": 0.712890625}, {"start": 1265.57, "end": 1266.97, "word": " بتخلي", "probability": 0.7236328125}, {"start": 1266.97, "end": 1267.07, "word": " ال", "probability": 0.96142578125}, {"start": 1267.07, "end": 1267.51, "word": " implication", "probability": 0.82861328125}, {"start": 1267.51, "end": 1267.79, "word": " هي", "probability": 0.400634765625}, {"start": 1267.79, "end": 1267.95, "word": " دي", "probability": 0.599365234375}, {"start": 1267.95, "end": 1268.57, "word": " تتحقق", "probability": 0.97587890625}, {"start": 1268.57, "end": 1269.11, "word": " بالظبط", "probability": 0.84478759765625}, {"start": 1269.11, "end": 1269.35, "word": " زي", "probability": 0.81396484375}, {"start": 1269.35, "end": 1269.39, "word": " ..", "probability": 0.312255859375}, {"start": 1269.39, "end": 1269.59, "word": " يعني", "probability": 0.874267578125}, {"start": 1269.59, "end": 1270.09, "word": " قريب", "probability": 0.9822591145833334}, {"start": 1270.09, "end": 1271.33, "word": " يعني", "probability": 0.6920166015625}, {"start": 1271.33, "end": 1272.05, "word": " بالظبط", "probability": 0.994873046875}, {"start": 1272.05, "end": 1273.89, "word": " زي", "probability": 0.95068359375}, {"start": 1273.89, "end": 1274.07, "word": " ما", "probability": 0.97216796875}, {"start": 1274.07, "end": 1274.61, "word": " عملنا", "probability": 0.9602864583333334}, {"start": 1274.61, "end": 1274.95, "word": " في", "probability": 0.9248046875}, {"start": 1274.95, "end": 1275.41, "word": " اثبات", "probability": 0.8251953125}, {"start": 1275.41, "end": 1275.57, "word": " ان", "probability": 0.45654296875}, {"start": 1275.57, "end": 1275.73, "word": " ال", "probability": 0.9599609375}, {"start": 1275.73, "end": 1276.05, "word": " sequence", "probability": 0.935546875}, {"start": 1276.05, "end": 1276.79, "word": " is", "probability": 0.94287109375}, {"start": 1276.79, "end": 1277.55, "word": " convergent", "probability": 0.930419921875}, {"start": 1277.55, "end": 1278.37, "word": " و", "probability": 0.6298828125}, {"start": 1278.37, "end": 1279.05, "word": " هنستخدم", "probability": 0.9044921875}, {"start": 1279.05, "end": 1280.05, "word": " الarchimedean", "probability": 0.759326171875}, {"start": 1280.05, "end": 1280.75, "word": " property", "probability": 0.9697265625}, {"start": 1280.75, "end": 1282.27, "word": " نشوف", "probability": 0.8445638020833334}, {"start": 1282.27, "end": 1282.47, "word": " مع", "probability": 0.99609375}, {"start": 1282.47, "end": 1283.31, "word": " بعض", "probability": 0.994384765625}, {"start": 1283.31, "end": 1287.67, "word": " let", "probability": 0.84521484375}], "temperature": 1.0}, {"id": 47, "seek": 130001, "start": 1289.57, "end": 1300.01, "text": "بالمناسبة .. بالمناسبة يعني احنا كيف نحدد ال capital N for any given epsilon؟", "tokens": [3555, 45340, 8315, 35457, 3660, 4386, 20666, 2304, 8315, 35457, 3660, 37495, 22653, 1975, 5016, 8315, 9122, 33911, 8717, 24401, 3215, 2423, 4238, 426, 337, 604, 2212, 17889, 22807], "avg_logprob": -0.1499999940395355, "compression_ratio": 1.118811881188119, "no_speech_prob": 0.0, "words": [{"start": 1289.57, "end": 1290.51, "word": "بالمناسبة", "probability": 0.9466796875}, {"start": 1290.51, "end": 1290.53, "word": " ..", "probability": 0.459716796875}, {"start": 1290.53, "end": 1291.21, "word": " بالمناسبة", "probability": 0.94140625}, {"start": 1291.21, "end": 1291.39, 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xn minus xm لو في عندي epsilon given epsilon موجة given فمن الآخر أنا عايز أثبت أنه هذا أصغر من إمسنان، مظبوط؟ طب ما هذا عبارة عن absolute واحد على n minus واحد على m وهذا أصغر من أو ساوي absolute واحد على n زائد absolute واحد على m", "tokens": [10721, 8315, 37495, 22653, 39896, 18871, 16254, 8236, 2031, 77, 3175, 2031, 76, 45164, 8978, 18871, 16254, 17889, 2212, 17889, 3714, 29245, 3660, 2212, 6156, 27842, 6024, 95, 34740, 41850, 6225, 47302, 11622, 5551, 12984, 3555, 2655, 14739, 3224, 23758, 5551, 9381, 17082, 2288, 9154, 11933, 2304, 3794, 1863, 7649, 12399, 3714, 19913, 3555, 2407, 9566, 22807, 23032, 3555, 19446, 23758, 6225, 3555, 9640, 3660, 18871, 8236, 36764, 24401, 15844, 297, 3175, 36764, 24401, 15844, 275, 37037, 15730, 5551, 9381, 17082, 2288, 9154, 34051, 8608, 995, 45865, 8236, 36764, 24401, 15844, 297, 30767, 16373, 3215, 8236, 36764, 24401, 15844, 275], "avg_logprob": -0.26794553983329544, "compression_ratio": 1.8701923076923077, "no_speech_prob": 0.0, "words": 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{"start": 1327.31, "end": 1327.79, "word": " minus", "probability": 0.98193359375}, {"start": 1327.79, "end": 1328.23, "word": " واحد", "probability": 0.97509765625}, {"start": 1328.23, "end": 1328.49, "word": " على", "probability": 0.87548828125}, {"start": 1328.49, "end": 1328.89, "word": " m", "probability": 0.6279296875}, {"start": 1328.89, "end": 1331.53, "word": " وهذا", "probability": 0.775390625}, {"start": 1331.53, "end": 1332.03, "word": " أصغر", "probability": 0.9906005859375}, {"start": 1332.03, "end": 1332.17, "word": " من", "probability": 0.9736328125}, {"start": 1332.17, "end": 1332.31, "word": " أو", "probability": 0.55126953125}, {"start": 1332.31, "end": 1332.89, "word": " ساوي", "probability": 0.8175455729166666}, {"start": 1332.89, "end": 1333.43, "word": " absolute", "probability": 0.900390625}, {"start": 1333.43, "end": 1334.23, "word": " واحد", "probability": 0.991943359375}, {"start": 1334.23, "end": 1334.45, "word": " على", "probability": 0.91552734375}, 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ل M، مظبوط؟ إذاً هذا هيصير أصغر من أو يساوي 1 على capital N وهذا أصغر من 1 على capital N بساوي 2 على capital M الآن بدي أخلي هذا، متى بيكون هذا أصغر من epsilon؟", "tokens": [28814, 15730, 25961, 2655, 297, 5551, 4117, 26890, 9154, 34051, 7251, 3794, 995, 45865, 4238, 426, 6156, 16, 15844, 297, 8032, 2655, 9381, 13546, 5551, 9381, 17082, 2288, 9154, 34051, 7251, 3794, 995, 45865, 502, 15844, 4238, 426, 4032, 4117, 8848, 23275, 20666, 1863, 35457, 3660, 5296, 376, 12399, 3714, 19913, 3555, 2407, 9566, 22807, 11933, 15730, 14111, 23758, 8032, 1829, 9381, 13546, 5551, 9381, 17082, 2288, 9154, 34051, 7251, 3794, 995, 45865, 502, 15844, 4238, 426, 37037, 15730, 5551, 9381, 17082, 2288, 9154, 502, 15844, 4238, 426, 4724, 3794, 995, 45865, 568, 15844, 4238, 376, 6024, 48506, 4724, 16254, 5551, 9778, 20292, 23758, 12399, 44650, 7578, 4724, 1829, 30544, 23758, 5551, 9381, 17082, 2288, 9154, 17889, 22807], "avg_logprob": -0.18448003625669399, "compression_ratio": 2.076530612244898, 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"probability": 0.76611328125}, {"start": 1462.18, "end": 1462.38, "word": " ع", "probability": 0.94775390625}, {"start": 1462.38, "end": 1462.7, "word": " اتنين", "probability": 0.9276123046875}, {"start": 1462.7, "end": 1463.16, "word": " عشان", "probability": 0.9619140625}, {"start": 1463.16, "end": 1463.64, "word": " يطلع", "probability": 0.9766845703125}, {"start": 1463.64, "end": 1464.06, "word": " هذا", "probability": 0.95556640625}, {"start": 1464.06, "end": 1465.26, "word": " أصغر", "probability": 0.968994140625}, {"start": 1465.26, "end": 1465.48, "word": " من", "probability": 0.99462890625}, {"start": 1465.48, "end": 1465.92, "word": " epsilon", "probability": 0.869140625}, {"start": 1465.92, "end": 1466.52, "word": " شوفتوا", "probability": 0.843994140625}, {"start": 1466.52, "end": 1466.8, "word": " كيف", "probability": 0.986328125}, {"start": 1466.8, "end": 1467.48, "word": " منطلق", "probability": 0.8106689453125}, {"start": 1467.48, "end": 1467.74, "word": " ال", "probability": 0.79150390625}, {"start": 1467.74, "end": 1468.08, "word": " capital", "probability": 0.79296875}, {"start": 1468.08, "end": 1468.46, "word": " N", "probability": 0.955078125}, {"start": 1468.46, "end": 1469.54, "word": " و", "probability": 0.346923828125}, {"start": 1469.54, "end": 1469.66, "word": " ال", "probability": 0.88916015625}, {"start": 1469.66, "end": 1470.32, "word": " Archimedean", "probability": 0.735107421875}, {"start": 1470.32, "end": 1470.84, "word": " property", "probability": 0.88330078125}, {"start": 1470.84, "end": 1471.24, "word": " طبعا", "probability": 0.9610595703125}, {"start": 1471.24, "end": 1471.96, "word": " تضمنلي", "probability": 0.80987548828125}, {"start": 1471.96, "end": 1472.68, "word": " وجود", "probability": 0.98583984375}, {"start": 1472.68, "end": 1473.74, "word": " مثل", "probability": 0.98779296875}, {"start": 1473.74, "end": 1474.52, "word": " هالعدد", "probability": 0.75433349609375}, {"start": 1474.52, "end": 1475.04, "word": " capital", "probability": 0.8447265625}, {"start": 1475.04, "end": 1475.36, "word": " N", "probability": 0.96875}], "temperature": 1.0}, {"id": 54, "seek": 150411, "start": 1476.83, "end": 1504.11, "text": "تمام؟ إذا باجي بقول هنا let epsilon الكلام هذا طبعا بعمله في الهامش بعدين باجي برتبه بقول let epsilon أكبر من السفر be given إذا it choose by Archimedean property", "tokens": [2655, 15042, 2304, 22807, 11933, 15730, 4724, 26108, 1829, 4724, 39648, 34105, 718, 17889, 2423, 28820, 10943, 23758, 23032, 3555, 3615, 995, 4724, 25957, 43761, 8978, 2423, 3224, 10943, 8592, 39182, 9957, 4724, 26108, 1829, 4724, 43500, 3555, 3224, 4724, 39648, 718, 17889, 5551, 4117, 26890, 9154, 21136, 5172, 2288, 312, 2212, 11933, 15730, 309, 2826, 538, 10984, 332, 4858, 282, 4707], "avg_logprob": -0.19680060186083354, "compression_ratio": 1.4226190476190477, "no_speech_prob": 0.0, "words": [{"start": 1476.83, "end": 1477.85, "word": "تمام؟", "probability": 0.55889892578125}, {"start": 1477.85, "end": 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"end": 1572.24, "word": " واحد", "probability": 0.967041015625}, {"start": 1572.24, "end": 1572.48, "word": " على", "probability": 0.90869140625}, {"start": 1572.48, "end": 1572.88, "word": " M", "probability": 0.49560546875}, {"start": 1572.88, "end": 1574.16, "word": " minus", "probability": 0.72314453125}, {"start": 1574.16, "end": 1574.94, "word": " واحد", "probability": 0.965087890625}, {"start": 1574.94, "end": 1575.12, "word": " على", "probability": 0.90380859375}, {"start": 1575.12, "end": 1575.58, "word": " M", "probability": 0.826171875}, {"start": 1575.58, "end": 1577.1, "word": " طبعا", "probability": 0.9405517578125}, {"start": 1577.1, "end": 1577.42, "word": " هذه", "probability": 0.393798828125}, {"start": 1577.42, "end": 1578.26, "word": " XM", "probability": 0.625244140625}, {"start": 1578.26, "end": 1580.58, "word": " وهذه", "probability": 0.875732421875}, {"start": 1580.58, "end": 1582.7, "word": " XM", "probability": 0.943359375}, {"start": 1582.7, "end": 1584.58, 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60, "seek": 167131, "start": 1642.37, "end": 1671.31, "text": "إذا by definition بما أن هذا صحيح لكل epsilon since epsilon أكبر من الصفر was arbitrary by definition of Cauchy sequence ال sequence xn is اللي هي واحد على n اللي الحد ��لعام تبعها واحد على n", "tokens": [28814, 15730, 538, 7123, 4724, 15042, 14739, 23758, 20328, 5016, 1829, 5016, 5296, 28820, 17889, 1670, 17889, 5551, 4117, 26890, 9154, 31767, 5172, 2288, 390, 23211, 538, 7123, 295, 7544, 625, 88, 8310, 2423, 8310, 2031, 77, 307, 13672, 1829, 39896, 36764, 24401, 15844, 297, 13672, 1829, 21542, 3215, 18863, 10943, 6055, 3555, 3615, 11296, 36764, 24401, 15844, 297], "avg_logprob": -0.28020832389593125, "compression_ratio": 1.505813953488372, "no_speech_prob": 0.0, "words": [{"start": 1642.37, "end": 1642.83, "word": "إذا", "probability": 0.5155029296875}, {"start": 1642.83, "end": 1643.45, "word": " by", "probability": 0.61083984375}, {"start": 1643.45, "end": 1644.11, "word": " definition", "probability": 0.93896484375}, 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{"start": 1653.25, "end": 1654.07, "word": " arbitrary", "probability": 0.83740234375}, {"start": 1654.07, "end": 1659.99, "word": " by", "probability": 0.89111328125}, {"start": 1659.99, "end": 1660.67, "word": " definition", "probability": 0.87890625}, {"start": 1660.67, "end": 1661.17, "word": " of", "probability": 0.9697265625}, {"start": 1661.17, "end": 1661.59, "word": " Cauchy", "probability": 0.869140625}, {"start": 1661.59, "end": 1662.25, "word": " sequence", "probability": 0.8857421875}, {"start": 1662.25, "end": 1663.51, "word": " ال", "probability": 0.491455078125}, {"start": 1663.51, "end": 1663.99, "word": " sequence", "probability": 0.90087890625}, {"start": 1663.99, "end": 1664.99, "word": " xn", "probability": 0.519775390625}, {"start": 1664.99, "end": 1665.83, "word": " is", "probability": 0.362060546875}, {"start": 1665.83, "end": 1666.05, "word": " اللي", "probability": 0.68994140625}, {"start": 1666.05, "end": 1666.31, "word": " هي", "probability": 0.921875}, {"start": 1666.31, "end": 1666.75, "word": " واحد", "probability": 0.963134765625}, {"start": 1666.75, "end": 1666.95, "word": " على", "probability": 0.70849609375}, {"start": 1666.95, "end": 1667.31, "word": " n", "probability": 0.415283203125}, {"start": 1667.31, "end": 1668.91, "word": " اللي", "probability": 0.833251953125}, {"start": 1668.91, "end": 1669.33, "word": " الحد", "probability": 0.9091796875}, {"start": 1669.33, "end": 1669.63, "word": " العام", "probability": 0.6649169921875}, {"start": 1669.63, "end": 1670.29, "word": " تبعها", "probability": 0.8441162109375}, {"start": 1670.29, "end": 1670.83, "word": " واحد", "probability": 0.96044921875}, {"start": 1670.83, "end": 1670.99, "word": " على", "probability": 0.796875}, {"start": 1670.99, "end": 1671.31, "word": " n", "probability": 0.611328125}], "temperature": 1.0}, {"id": 61, "seek": 169901, "start": 1672.61, "end": 1699.01, "text": "is Cauchy تمام هنا أثبتنا إن ال sequence Cauchy مباشرة باستخدام التعريف طبعا في برهان تاني ممكن نستخدم Cauchy criterion احنا ممكن نثبت إن ال sequence هذي convergent", "tokens": [271, 7544, 625, 88, 46811, 10943, 34105, 5551, 12984, 3555, 2655, 8315, 36145, 2423, 8310, 7544, 625, 88, 3714, 3555, 33599, 25720, 4724, 995, 14851, 9778, 3215, 10943, 16712, 3615, 16572, 5172, 23032, 3555, 3615, 995, 8978, 4724, 2288, 3224, 7649, 6055, 7649, 1829, 3714, 43020, 8717, 14851, 9778, 40448, 7544, 625, 88, 46691, 1975, 5016, 8315, 3714, 43020, 8717, 12984, 3555, 2655, 36145, 2423, 8310, 8032, 8848, 1829, 9652, 6930], "avg_logprob": -0.15896267050670254, "compression_ratio": 1.4819277108433735, "no_speech_prob": 0.0, "words": [{"start": 1672.61, "end": 1673.17, "word": "is", "probability": 0.44580078125}, {"start": 1673.17, "end": 1673.85, "word": " Cauchy", "probability": 0.7613932291666666}, {"start": 1673.85, "end": 1677.61, "word": " تمام", "probability": 0.6146240234375}, {"start": 1677.61, "end": 1680.03, "word": " هنا", "probability": 0.348876953125}, {"start": 1680.03, "end": 1680.61, "word": " أثبتنا", "probability": 0.97685546875}, {"start": 1680.61, "end": 1680.85, "word": " إن", "probability": 0.458740234375}, {"start": 1680.85, "end": 1680.97, "word": " ال", "probability": 0.68359375}, {"start": 1680.97, "end": 1681.29, "word": " sequence", "probability": 0.603515625}, {"start": 1681.29, "end": 1682.05, "word": " Cauchy", "probability": 0.8702799479166666}, {"start": 1682.05, "end": 1683.41, "word": " مباشرة", "probability": 0.974853515625}, {"start": 1683.41, "end": 1684.23, "word": " باستخدام", "probability": 0.976318359375}, {"start": 1684.23, "end": 1684.97, "word": " التعريف", "probability": 0.97802734375}, {"start": 1684.97, "end": 1687.01, "word": " طبعا", "probability": 0.972900390625}, {"start": 1687.01, "end": 1687.47, "word": " في", "probability": 0.515625}, {"start": 1687.47, "end": 1688.13, "word": " برهان", "probability": 0.95458984375}, {"start": 1688.13, "end": 1688.91, "word": " تاني", "probability": 0.9759114583333334}, {"start": 1688.91, "end": 1690.91, "word": " ممكن", "probability": 0.9716796875}, {"start": 1690.91, "end": 1691.53, "word": " نستخدم", "probability": 0.9906005859375}, {"start": 1691.53, "end": 1692.05, "word": " Cauchy", "probability": 0.9373372395833334}, {"start": 1692.05, "end": 1692.79, "word": " criterion", "probability": 0.91357421875}, {"start": 1692.79, "end": 1695.79, "word": " احنا", "probability": 0.8611653645833334}, {"start": 1695.79, "end": 1696.45, "word": " ممكن", "probability": 0.992919921875}, {"start": 1696.45, "end": 1697.07, "word": " نثبت", "probability": 0.99658203125}, {"start": 1697.07, "end": 1697.29, "word": " إن", "probability": 0.732421875}, {"start": 1697.29, "end": 1697.43, "word": " ال", "probability": 0.96630859375}, {"start": 1697.43, "end": 1697.87, "word": " sequence", "probability": 0.96923828125}, {"start": 1697.87, "end": 1698.29, "word": " هذي", "probability": 0.6671549479166666}, {"start": 1698.29, "end": 1699.01, "word": " convergent", "probability": 0.73681640625}], "temperature": 1.0}, {"id": 62, "seek": 172640, "start": 1699.88, "end": 1726.4, "text": "و أثبتنا هذا الكلام جبليك صح؟ و حسب cushy criterion بما أنه ال sequence convergent then it is cushy صح؟ هذا برهان تاني لكن إذا كنا لكم برهنيها directly يعني استخدم التعريف لازم البرهان هذا هو اللي إيه تكتبوه واضح تمام؟ في أي استفسار؟", "tokens": [2407, 5551, 12984, 3555, 2655, 8315, 23758, 2423, 28820, 10943, 10874, 3555, 20292, 4117, 20328, 5016, 22807, 4032, 11331, 35457, 18422, 88, 46691, 4724, 15042, 14739, 3224, 2423, 8310, 9652, 6930, 550, 309, 307, 18422, 88, 20328, 5016, 22807, 23758, 4724, 2288, 3224, 7649, 6055, 7649, 1829, 44381, 11933, 15730, 9122, 8315, 5296, 24793, 4724, 2288, 3224, 22653, 11296, 3838, 37495, 22653, 44713, 9778, 40448, 16712, 3615, 16572, 5172, 5296, 31377, 2304, 2423, 26890, 3224, 7649, 23758, 31439, 13672, 1829, 11933, 1829, 3224, 6055, 4117, 2655, 3555, 2407, 3224, 4032, 46958, 5016, 46811, 10943, 22807, 8978, 36632, 44713, 36178, 9640, 22807], "avg_logprob": -0.19071691118034662, "compression_ratio": 1.6017316017316017, "no_speech_prob": 0.0, "words": [{"start": 1699.88, "end": 1700.14, "word": "و", "probability": 0.984375}, {"start": 1700.14, "end": 1700.6, "word": " أثبتنا", "probability": 0.93330078125}, {"start": 1700.6, "end": 1700.8, "word": " هذا", "probability": 0.9775390625}, {"start": 1700.8, "end": 1701.16, "word": " الكلام", "probability": 0.97216796875}, {"start": 1701.16, "end": 1701.82, "word": " جبليك", "probability": 0.52154541015625}, {"start": 1701.82, "end": 1702.82, "word": " صح؟", "probability": 0.7996419270833334}, {"start": 1702.82, "end": 1703.92, "word": " و", "probability": 0.9345703125}, {"start": 1703.92, "end": 1704.62, "word": " حسب", "probability": 0.843505859375}, {"start": 1704.62, "end": 1705.06, "word": " cushy", "probability": 0.552642822265625}, {"start": 1705.06, "end": 1705.74, "word": " criterion", "probability": 0.9873046875}, {"start": 1705.74, "end": 1707.16, "word": " بما", "probability": 0.8740234375}, {"start": 1707.16, "end": 1707.4, "word": " أنه", "probability": 0.69580078125}, {"start": 1707.4, "end": 1707.46, "word": " ال", "probability": 0.451904296875}, {"start": 1707.46, "end": 1707.72, "word": " sequence", "probability": 0.97607421875}, {"start": 1707.72, "end": 1708.64, "word": " convergent", "probability": 0.79541015625}, {"start": 1708.64, "end": 1709.02, "word": " then", "probability": 0.65576171875}, {"start": 1709.02, "end": 1709.32, "word": " it", "probability": 0.97314453125}, {"start": 1709.32, "end": 1709.62, "word": " is", "probability": 0.9599609375}, {"start": 1709.62, "end": 1710.16, "word": " cushy", "probability": 0.801513671875}, {"start": 1710.16, "end": 1711.16, "word": " صح؟", "probability": 0.9236653645833334}, {"start": 1711.16, "end": 1711.4, "word": " هذا", "probability": 0.8876953125}, {"start": 1711.4, "end": 1711.8, "word": " برهان", "probability": 0.9493408203125}, {"start": 1711.8, "end": 1712.16, "word": " تاني", "probability": 0.9658203125}, {"start": 1712.16, "end": 1712.4, "word": " لكن", "probability": 0.55029296875}, {"start": 1712.4, "end": 1712.56, "word": " إذا", "probability": 0.859375}, {"start": 1712.56, "end": 1712.76, "word": " كنا", "probability": 0.607666015625}, {"start": 1712.76, "end": 1713.1, "word": " لكم", "probability": 0.741455078125}, {"start": 1713.1, "end": 1714.74, "word": " برهنيها", "probability": 0.799951171875}, {"start": 1714.74, "end": 1715.34, "word": " directly", "probability": 0.9697265625}, {"start": 1715.34, "end": 1715.72, "word": " يعني", "probability": 0.966064453125}, {"start": 1715.72, "end": 1716.16, "word": " استخدم", "probability": 0.92333984375}, {"start": 1716.16, "end": 1716.92, "word": " التعريف", "probability": 0.9747314453125}, {"start": 1716.92, "end": 1718.26, "word": " لازم", "probability": 0.9679361979166666}, {"start": 1718.26, "end": 1718.8, "word": " البرهان", "probability": 0.86651611328125}, {"start": 1718.8, "end": 1719.16, "word": " هذا", "probability": 0.91943359375}, {"start": 1719.16, "end": 1719.42, "word": " هو", "probability": 0.99609375}, {"start": 1719.42, "end": 1719.7, "word": " اللي", "probability": 0.9814453125}, {"start": 1719.7, "end": 1720.46, "word": " إيه", "probability": 0.8179524739583334}, {"start": 1720.46, "end": 1721.42, "word": " تكتبوه", "probability": 0.976806640625}, {"start": 1721.42, "end": 1722.16, "word": " واضح", "probability": 0.9664713541666666}, {"start": 1722.16, "end": 1723.9, "word": " تمام؟", "probability": 0.789794921875}, {"start": 1723.9, "end": 1725.46, "word": " في", "probability": 0.94091796875}, {"start": 1725.46, "end": 1725.6, "word": " أي", "probability": 0.8017578125}, {"start": 1725.6, "end": 1726.4, "word": " استفسار؟", "probability": 0.81695556640625}], "temperature": 1.0}, {"id": 63, "seek": 173170, "start": 1730.06, "end": 1731.7, "text": "ناخد مثال تاني", "tokens": [1863, 47283, 3215, 50113, 6027, 6055, 7649, 1829], "avg_logprob": -0.0759548611111111, "compression_ratio": 0.7647058823529411, "no_speech_prob": 0.0, "words": [{"start": 1730.06, "end": 1730.64, "word": "ناخد", "probability": 0.96728515625}, {"start": 1730.64, "end": 1731.1, "word": " مثال", "probability": 0.97021484375}, {"start": 1731.1, "end": 1731.7, "word": " تاني", "probability": 0.8798828125}], "temperature": 1.0}, {"id": 64, "seek": 177871, "start": 1758.73, "end": 1778.71, "text": "مثال تقم اتنين consider .. consider ال sequence defined inductively", "tokens": [2304, 12984, 6027, 6055, 4587, 2304, 1975, 2655, 1863, 9957, 1949, 4386, 1949, 2423, 8310, 7642, 31612, 3413], "avg_logprob": -0.3055098746952258, "compression_ratio": 1.0384615384615385, "no_speech_prob": 0.0, "words": [{"start": 1758.73, "end": 1759.59, "word": "مثال", "probability": 0.7496744791666666}, {"start": 1759.59, "end": 1760.99, "word": " تقم", "probability": 0.6710611979166666}, {"start": 1760.99, "end": 1761.55, "word": " اتنين", "probability": 0.8878173828125}, {"start": 1761.55, "end": 1764.09, "word": " consider", "probability": 0.73388671875}, {"start": 1764.09, "end": 1764.45, "word": " ..", "probability": 0.271484375}, {"start": 1764.45, "end": 1767.75, "word": " consider", "probability": 0.9033203125}, {"start": 1767.75, "end": 1768.53, "word": " ال", "probability": 0.88720703125}, {"start": 1768.53, "end": 1769.15, "word": " sequence", "probability": 0.8642578125}, {"start": 1769.15, "end": 1776.37, "word": " defined", "probability": 0.92138671875}, {"start": 1776.37, "end": 1778.71, "word": " inductively", "probability": 0.880859375}], "temperature": 1.0}, {"id": 65, "seek": 181525, "start": 1788.75, "end": 1815.25, "text": "إذا في عندي sequence معرفة بطريقة استقرائية كالتالي كما هي ليه هناخد x1 بساوي واحد و x2 بساوي اتنين طب و xn-n أكبر من أو ساوي تلاتة هناخده بساوي نص في", "tokens": [28814, 15730, 8978, 18871, 16254, 8310, 20449, 28480, 3660, 4724, 9566, 16572, 28671, 44713, 4587, 2288, 16373, 10632, 9122, 6027, 2655, 6027, 1829, 9122, 15042, 39896, 32239, 3224, 8032, 1863, 47283, 3215, 2031, 16, 4724, 3794, 995, 45865, 36764, 24401, 4032, 2031, 17, 4724, 3794, 995, 45865, 1975, 2655, 1863, 9957, 23032, 3555, 4032, 2031, 77, 12, 77, 5551, 4117, 26890, 9154, 34051, 8608, 995, 45865, 6055, 1211, 9307, 3660, 8032, 1863, 47283, 3215, 3224, 4724, 3794, 995, 45865, 8717, 9381, 8978], "avg_logprob": -0.1864646109471838, "compression_ratio": 1.548780487804878, "no_speech_prob": 0.0, "words": [{"start": 1788.75, "end": 1789.11, "word": "إذا", "probability": 0.4149169921875}, {"start": 1789.11, "end": 1789.69, "word": " في", "probability": 0.3603515625}, {"start": 1789.69, "end": 1790.01, "word": " عندي", "probability": 0.7391357421875}, {"start": 1790.01, "end": 1790.49, "word": " sequence", "probability": 0.7763671875}, {"start": 1790.49, "end": 1791.23, "word": " معرفة", "probability": 0.900390625}, {"start": 1791.23, "end": 1791.87, "word": " بطريقة", "probability": 0.9862060546875}, {"start": 1791.87, "end": 1792.77, "word": " استقرائية", "probability": 0.97099609375}, {"start": 1792.77, "end": 1793.55, "word": " كالتالي", "probability": 0.8935546875}, {"start": 1793.55, "end": 1794.21, "word": " كما", "probability": 0.853759765625}, {"start": 1794.21, "end": 1794.33, "word": " هي", "probability": 0.5263671875}, {"start": 1794.33, "end": 1794.91, "word": " ليه", "probability": 0.883544921875}, {"start": 1794.91, "end": 1796.39, "word": " هناخد", "probability": 0.8155517578125}, {"start": 1796.39, "end": 1797.01, "word": " x1", "probability": 0.629638671875}, {"start": 1797.01, "end": 1797.93, "word": " بساوي", "probability": 0.7864990234375}, {"start": 1797.93, "end": 1798.53, "word": " واحد", "probability": 0.927734375}, {"start": 1798.53, "end": 1800.81, "word": " و", "probability": 0.89990234375}, {"start": 1800.81, "end": 1801.75, "word": " x2", "probability": 0.8232421875}, {"start": 1801.75, "end": 1803.07, "word": " بساوي", "probability": 0.9493408203125}, {"start": 1803.07, "end": 1804.71, "word": " اتنين", "probability": 0.9737548828125}, {"start": 1804.71, "end": 1805.19, "word": " طب", "probability": 0.895263671875}, {"start": 1805.19, "end": 1805.31, "word": " و", "probability": 0.6015625}, {"start": 1805.31, "end": 1806.13, "word": " xn", "probability": 0.90283203125}, {"start": 1806.13, "end": 1808.47, "word": "-n", "probability": 0.4296875}, {"start": 1808.47, "end": 1808.95, "word": " أكبر", "probability": 0.9265950520833334}, {"start": 1808.95, "end": 1809.15, "word": " من", "probability": 0.95703125}, {"start": 1809.15, "end": 1809.33, "word": " أو", "probability": 0.548828125}, {"start": 1809.33, "end": 1809.69, "word": " ساوي", "probability": 0.8251953125}, {"start": 1809.69, "end": 1810.39, "word": " تلاتة", "probability": 0.944091796875}, {"start": 1810.39, "end": 1812.01, "word": " هناخده", "probability": 0.944140625}, {"start": 1812.01, "end": 1812.71, "word": " بساوي", "probability": 0.9678955078125}, {"start": 1812.71, "end": 1813.25, "word": " نص", "probability": 0.9921875}, {"start": 1813.25, "end": 1815.25, "word": " في", "probability": 0.93505859375}], "temperature": 1.0}, {"id": 66, "seek": 184450, "start": 1815.68, "end": 1844.5, "text": "xn سالب اتنين زائد xn negative one طبعا هذا لكل n أدب طبيعي أكبر من أو ساوى تلاتة اذا هنا في اندي سيكوانس معرفة بطريقة استقرائية اول حدين اللي هم قيم معينة الحد التالت وانت طالع معرف بدلالة الحد اللي حدين اللي جابله مباشرة", "tokens": [87, 77, 8608, 6027, 3555, 1975, 2655, 1863, 9957, 30767, 16373, 3215, 2031, 77, 3671, 472, 23032, 3555, 3615, 995, 23758, 5296, 28820, 297, 5551, 3215, 3555, 23032, 21292, 3615, 1829, 5551, 4117, 26890, 9154, 34051, 8608, 995, 2407, 7578, 6055, 1211, 9307, 3660, 1975, 15730, 34105, 8978, 16472, 16254, 8608, 1829, 4117, 2407, 7649, 3794, 20449, 28480, 3660, 4724, 9566, 16572, 28671, 44713, 4587, 2288, 16373, 10632, 1975, 12610, 11331, 3215, 9957, 13672, 1829, 8032, 2304, 12174, 32640, 20449, 9957, 3660, 21542, 3215, 16712, 6027, 2655, 4032, 7649, 2655, 23032, 6027, 3615, 20449, 28480, 4724, 3215, 1211, 6027, 3660, 21542, 3215, 13672, 1829, 11331, 3215, 9957, 13672, 1829, 10874, 16758, 43761, 3714, 3555, 33599, 25720], "avg_logprob": -0.23424144891592172, "compression_ratio": 1.742081447963801, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1815.68, "end": 1817.26, "word": "xn", "probability": 0.3876953125}, {"start": 1817.26, "end": 1818.02, "word": " سالب", "probability": 0.5388081868489584}, {"start": 1818.02, "end": 1818.82, "word": " اتنين", "probability": 0.9366455078125}, {"start": 1818.82, "end": 1820.36, "word": " زائد", "probability": 0.5478922526041666}, {"start": 1820.36, "end": 1821.48, "word": " xn", "probability": 0.8603515625}, {"start": 1821.48, "end": 1822.02, "word": " negative", "probability": 0.7353515625}, {"start": 1822.02, "end": 1822.6, "word": " one", "probability": 0.95703125}, {"start": 1822.6, "end": 1824.1, "word": " طبعا", "probability": 0.85040283203125}, {"start": 1824.1, "end": 1824.34, "word": " هذا", 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0.55810546875}, {"start": 1830.74, "end": 1831.0, "word": " اندي", "probability": 0.4024658203125}, {"start": 1831.0, "end": 1831.58, "word": " سيكوانس", "probability": 0.827392578125}, {"start": 1831.58, "end": 1832.18, "word": " معرفة", "probability": 0.8761393229166666}, {"start": 1832.18, "end": 1832.66, "word": " بطريقة", "probability": 0.977783203125}, {"start": 1832.66, "end": 1833.58, "word": " استقرائية", "probability": 0.95859375}, {"start": 1833.58, "end": 1834.5, "word": " اول", "probability": 0.771240234375}, {"start": 1834.5, "end": 1834.98, "word": " حدين", "probability": 0.9518229166666666}, {"start": 1834.98, "end": 1835.16, "word": " اللي", "probability": 0.71337890625}, {"start": 1835.16, "end": 1835.32, "word": " هم", "probability": 0.6529541015625}, {"start": 1835.32, "end": 1835.66, "word": " قيم", "probability": 0.97314453125}, {"start": 1835.66, "end": 1836.5, "word": " معينة", "probability": 0.9905598958333334}, {"start": 1836.5, "end": 1837.38, "word": " الحد", "probability": 0.902099609375}, {"start": 1837.38, "end": 1837.92, "word": " التالت", "probability": 0.9871419270833334}, {"start": 1837.92, "end": 1838.2, "word": " وانت", "probability": 0.8356119791666666}, {"start": 1838.2, "end": 1838.66, "word": " طالع", "probability": 0.9158528645833334}, {"start": 1838.66, "end": 1840.02, "word": " معرف", "probability": 0.94091796875}, {"start": 1840.02, "end": 1841.2, "word": " بدلالة", "probability": 0.80205078125}, {"start": 1841.2, "end": 1841.78, "word": " الحد", "probability": 0.956787109375}, {"start": 1841.78, "end": 1842.74, "word": " اللي", "probability": 0.665771484375}, {"start": 1842.74, "end": 1843.34, "word": " حدين", "probability": 0.8517252604166666}, {"start": 1843.34, "end": 1843.54, "word": " اللي", "probability": 0.98095703125}, {"start": 1843.54, "end": 1843.9, "word": " جابله", "probability": 0.8738606770833334}, {"start": 1843.9, "end": 1844.5, "word": " مباشرة", "probability": 0.9923095703125}], "temperature": 1.0}, {"id": 67, "seek": 187222, "start": 1846.38, "end": 1872.22, "text": "هذا طبعا بيعطينا sequence المطلوب عايزين نثبت show ان ال sequence x in is convergent و converges to the number 5 over 3 البرهان", "tokens": [3224, 15730, 23032, 3555, 3615, 995, 4724, 40228, 9566, 1829, 8315, 8310, 9673, 9566, 1211, 37746, 6225, 47302, 11622, 9957, 8717, 12984, 3555, 2655, 855, 16472, 2423, 8310, 2031, 294, 307, 9652, 6930, 4032, 9652, 2880, 281, 264, 1230, 1025, 670, 805, 2423, 26890, 3224, 7649], "avg_logprob": -0.185505322319396, "compression_ratio": 1.297709923664122, "no_speech_prob": 0.0, "words": [{"start": 1846.38, "end": 1846.72, "word": "هذا", "probability": 0.82470703125}, {"start": 1846.72, "end": 1847.0, "word": " طبعا", "probability": 0.927490234375}, {"start": 1847.0, "end": 1847.52, "word": " بيعطينا", "probability": 0.80322265625}, {"start": 1847.52, "end": 1847.86, "word": " sequence", "probability": 0.487548828125}, {"start": 1847.86, "end": 1848.76, "word": " المطلوب", "probability": 0.9652099609375}, {"start": 1848.76, "end": 1849.78, "word": " عايزين", "probability": 0.8895263671875}, {"start": 1849.78, "end": 1850.34, "word": " نثبت", "probability": 0.9884033203125}, {"start": 1850.34, "end": 1850.8, "word": " show", "probability": 0.84033203125}, {"start": 1850.8, "end": 1852.44, "word": " ان", "probability": 0.50634765625}, {"start": 1852.44, "end": 1852.64, "word": " ال", "probability": 0.595703125}, {"start": 1852.64, "end": 1853.2, "word": " sequence", "probability": 0.91748046875}, {"start": 1853.2, "end": 1853.72, "word": " x", "probability": 0.7421875}, {"start": 1853.72, "end": 1854.2, "word": " in", "probability": 0.3115234375}, {"start": 1854.2, "end": 1855.7, "word": " is", "probability": 0.8642578125}, {"start": 1855.7, "end": 1856.9, "word": " convergent", "probability": 0.9287109375}, {"start": 1856.9, "end": 1858.72, "word": " و", "probability": 0.8564453125}, {"start": 1858.72, "end": 1859.78, "word": " converges", "probability": 0.803466796875}, {"start": 1859.78, "end": 1860.22, "word": " to", "probability": 0.96923828125}, {"start": 1860.22, "end": 1862.38, "word": " the", "probability": 0.63720703125}, {"start": 1862.38, "end": 1862.86, "word": " number", "probability": 0.96630859375}, {"start": 1862.86, "end": 1863.64, "word": " 5", "probability": 0.5078125}, {"start": 1863.64, "end": 1864.02, "word": " over", "probability": 0.72802734375}, {"start": 1864.02, "end": 1865.16, "word": " 3", "probability": 0.97998046875}, {"start": 1865.16, "end": 1872.22, "word": " البرهان", "probability": 0.8778076171875}], "temperature": 1.0}, {"id": 68, "seek": 190654, "start": 1877.02, "end": 1906.54, "text": "هنثبت we first show that sequence xn converges by showing بإثبات أنه", "tokens": [3224, 1863, 12984, 3555, 2655, 321, 700, 855, 300, 8310, 2031, 77, 9652, 2880, 538, 4099, 4724, 28814, 12984, 3555, 9307, 14739, 3224], "avg_logprob": -0.3629557229578495, "compression_ratio": 1.0, "no_speech_prob": 0.0, "words": [{"start": 1877.02, "end": 1878.06, "word": "هنثبت", "probability": 0.825537109375}, {"start": 1878.06, "end": 1879.38, "word": " we", "probability": 0.0870361328125}, {"start": 1879.38, "end": 1880.38, "word": " first", "probability": 0.91552734375}, {"start": 1880.38, "end": 1884.0, "word": " show", "probability": 0.34326171875}, {"start": 1884.0, "end": 1886.88, "word": " that", "probability": 0.8603515625}, {"start": 1886.88, "end": 1888.68, "word": " sequence", "probability": 0.73583984375}, {"start": 1888.68, "end": 1889.36, "word": " xn", "probability": 0.545654296875}, {"start": 1889.36, "end": 1890.34, "word": " converges", "probability": 0.92041015625}, {"start": 1890.34, "end": 1897.7, "word": " by", "probability": 0.57666015625}, {"start": 1897.7, "end": 1901.7, "word": " showing", "probability": 0.892578125}, {"start": 1901.7, "end": 1904.4, "word": " بإثبات", "probability": 0.88544921875}, {"start": 1904.4, "end": 1906.54, "word": " أنه", "probability": 0.768798828125}], "temperature": 1.0}, {"id": 69, "seek": 194105, "start": 1911.51, "end": 1941.05, "text": "إنها كوشي thanks to koshi criterion طبعا هذا بفضل معيار كوشي أو كوشي criterion هنثبت الأول أن ال sequence هي to convergent", "tokens": [28814, 1863, 11296, 9122, 2407, 8592, 1829, 3231, 281, 350, 17392, 46691, 23032, 3555, 3615, 995, 23758, 4724, 5172, 11242, 1211, 20449, 1829, 9640, 9122, 2407, 8592, 1829, 34051, 9122, 2407, 8592, 1829, 46691, 8032, 1863, 12984, 3555, 2655, 16247, 12610, 14739, 2423, 8310, 39896, 281, 9652, 6930], "avg_logprob": -0.2552614893232073, "compression_ratio": 1.303030303030303, "no_speech_prob": 0.0, "words": [{"start": 1911.51, "end": 1912.01, "word": "إنها", "probability": 0.729248046875}, {"start": 1912.01, "end": 1912.57, "word": " كوشي", "probability": 0.81475830078125}, {"start": 1912.57, "end": 1920.17, "word": " thanks", "probability": 0.6484375}, {"start": 1920.17, "end": 1922.13, "word": " to", "probability": 0.95263671875}, {"start": 1922.13, "end": 1923.07, "word": " koshi", "probability": 0.59619140625}, {"start": 1923.07, "end": 1927.61, "word": " criterion", "probability": 0.923828125}, {"start": 1927.61, "end": 1929.73, "word": " طبعا", "probability": 0.96826171875}, {"start": 1929.73, "end": 1930.05, "word": " هذا", "probability": 0.6845703125}, {"start": 1930.05, "end": 1931.43, "word": " بفضل", "probability": 0.9949951171875}, {"start": 1931.43, "end": 1932.95, "word": " معيار", "probability": 0.8262532552083334}, {"start": 1932.95, "end": 1933.43, "word": " كوشي", "probability": 0.897705078125}, {"start": 1933.43, "end": 1933.57, "word": " أو", "probability": 0.6923828125}, {"start": 1933.57, "end": 1933.87, "word": " كوشي", "probability": 0.83880615234375}, {"start": 1933.87, "end": 1934.29, "word": " criterion", "probability": 0.8671875}, {"start": 1934.29, "end": 1937.39, "word": " هنثبت", "probability": 0.870361328125}, {"start": 1937.39, "end": 1938.35, "word": " الأول", "probability": 0.9267578125}, {"start": 1938.35, "end": 1938.61, "word": " أن", "probability": 0.56787109375}, {"start": 1938.61, "end": 1939.41, "word": " ال", "probability": 0.45849609375}, {"start": 1939.41, "end": 1939.73, "word": " sequence", "probability": 0.884765625}, {"start": 1939.73, "end": 1940.09, "word": " هي", "probability": 0.6591796875}, {"start": 1940.09, "end": 1940.19, "word": " to", "probability": 0.303466796875}, {"start": 1940.19, "end": 1941.05, "word": " convergent", "probability": 0.7384033203125}], "temperature": 1.0}, {"id": 70, "seek": 196681, "start": 1942.35, "end": 1966.81, "text": "بإثبات إنه كوشي وهذا طبعا حسب كوشي criterion إذا أثبتنا إن ال sequence كوشي بتكون convergent تمام فنشوف كيف ممكن نثبت الكلام هذا فأول شيء بدي أثبت إن ال sequence bounded إذن هنا الإدعاء الأول أو claim number one", "tokens": [3555, 28814, 12984, 3555, 9307, 36145, 3224, 9122, 2407, 8592, 1829, 37037, 15730, 23032, 3555, 3615, 995, 11331, 35457, 9122, 2407, 8592, 1829, 46691, 11933, 15730, 5551, 12984, 3555, 2655, 8315, 36145, 2423, 8310, 9122, 2407, 8592, 1829, 39894, 30544, 9652, 6930, 46811, 10943, 6156, 1863, 8592, 38688, 9122, 33911, 3714, 43020, 8717, 12984, 3555, 2655, 2423, 28820, 10943, 23758, 6156, 10721, 12610, 44049, 38207, 4724, 16254, 5551, 12984, 3555, 2655, 36145, 2423, 8310, 37498, 11933, 8848, 1863, 34105, 33688, 3215, 3615, 16606, 16247, 12610, 34051, 3932, 1230, 472], "avg_logprob": -0.20208332935969034, "compression_ratio": 1.64, "no_speech_prob": 0.0, "words": [{"start": 1942.3500000000001, "end": 1943.15, "word": "بإثبات", "probability": 0.801171875}, {"start": 1943.15, "end": 1943.51, "word": " إنه", "probability": 0.3570556640625}, {"start": 1943.51, "end": 1944.55, "word": " كوشي", "probability": 0.81964111328125}, {"start": 1944.55, "end": 1946.57, "word": " وهذا", "probability": 0.828125}, {"start": 1946.57, "end": 1946.91, "word": " طبعا", "probability": 0.85516357421875}, {"start": 1946.91, "end": 1947.29, "word": " حسب", "probability": 0.9150390625}, {"start": 1947.29, "end": 1947.63, "word": " كوشي", "probability": 0.794403076171875}, {"start": 1947.63, "end": 1948.09, "word": " criterion", "probability": 0.9296875}, {"start": 1948.09, "end": 1948.35, "word": " إذا", "probability": 0.84814453125}, {"start": 1948.35, "end": 1948.77, "word": " أثبتنا", "probability": 0.966015625}, {"start": 1948.77, "end": 1948.89, "word": " إن", "probability": 0.68115234375}, {"start": 1948.89, "end": 1948.97, "word": " ال", "probability": 0.5751953125}, {"start": 1948.97, "end": 1949.31, "word": " sequence", "probability": 0.60791015625}, {"start": 1949.31, "end": 1949.69, "word": " كوشي", "probability": 0.94189453125}, {"start": 1949.69, "end": 1950.17, "word": " بتكون", "probability": 0.777099609375}, {"start": 1950.17, "end": 1951.43, "word": " convergent", "probability": 0.808837890625}, {"start": 1951.43, "end": 1952.17, "word": " تمام", "probability": 0.6429443359375}, {"start": 1952.17, "end": 1954.93, "word": " فنشوف", "probability": 0.8193359375}, {"start": 1954.93, "end": 1955.31, "word": " كيف", "probability": 0.9697265625}, {"start": 1955.31, "end": 1955.73, "word": " ممكن", "probability": 0.939208984375}, {"start": 1955.73, "end": 1956.37, "word": " نثبت", "probability": 0.971435546875}, {"start": 1956.37, "end": 1956.89, "word": " الكلام", "probability": 0.95654296875}, {"start": 1956.89, "end": 1957.29, "word": " هذا", "probability": 0.94140625}, {"start": 1957.29, "end": 1958.71, "word": " فأول", "probability": 0.9322916666666666}, {"start": 1958.71, "end": 1959.07, "word": " شيء", "probability": 0.767333984375}, {"start": 1959.07, "end": 1959.27, "word": " بدي", "probability": 0.5406494140625}, {"start": 1959.27, "end": 1959.61, "word": " أثبت", "probability": 0.9930419921875}, {"start": 1959.61, "end": 1959.73, "word": " إن", "probability": 0.8818359375}, {"start": 1959.73, "end": 1959.83, "word": " ال", "probability": 0.9638671875}, {"start": 1959.83, "end": 1960.15, "word": " sequence", "probability": 0.9794921875}, {"start": 1960.15, "end": 1960.89, "word": " bounded", "probability": 0.86083984375}, {"start": 1960.89, "end": 1961.25, "word": " إذن", "probability": 0.6417643229166666}, {"start": 1961.25, "end": 1961.49, "word": " هنا", "probability": 0.982421875}, {"start": 1961.49, "end": 1964.75, "word": " الإدعاء", "probability": 0.92431640625}, {"start": 1964.75, "end": 1965.27, "word": " الأول", "probability": 0.992919921875}, {"start": 1965.27, "end": 1965.55, "word": " أو", "probability": 0.86865234375}, {"start": 1965.55, "end": 1965.95, "word": " claim", "probability": 0.81787109375}, {"start": 1965.95, "end": 1966.35, "word": " number", "probability": 0.9560546875}, {"start": 1966.35, "end": 1966.81, "word": " one", "probability": 0.92919921875}], "temperature": 1.0}, {"id": 71, "seek": 199431, "start": 1968.71, "end": 1994.31, "text": "السيكونس xn الحد العام تبعها أكبر من أو ساوي الواحد أصغر من أو ساوي اتنين لكل n في n لبرهان ذلك to see this use induction", "tokens": [6027, 3794, 1829, 4117, 11536, 3794, 2031, 77, 21542, 3215, 18863, 10943, 6055, 3555, 3615, 11296, 5551, 4117, 26890, 9154, 34051, 8608, 995, 45865, 2423, 14407, 24401, 5551, 9381, 17082, 2288, 9154, 34051, 8608, 995, 45865, 1975, 2655, 1863, 9957, 5296, 28820, 297, 8978, 297, 5296, 26890, 3224, 7649, 29910, 23275, 281, 536, 341, 764, 33371], "avg_logprob": -0.2128563638319049, "compression_ratio": 1.4014598540145986, "no_speech_prob": 0.0, "words": [{"start": 1968.71, "end": 1969.73, "word": "السيكونس", "probability": 0.6082967122395834}, {"start": 1969.73, "end": 1970.75, "word": " xn", "probability": 0.419677734375}, {"start": 1970.75, "end": 1971.37, "word": " الحد", "probability": 0.81005859375}, {"start": 1971.37, "end": 1971.71, "word": " العام", "probability": 0.970703125}, {"start": 1971.71, "end": 1972.31, "word": " تبعها", "probability": 0.840087890625}, {"start": 1972.31, "end": 1973.67, "word": " أكبر", "probability": 0.89794921875}, {"start": 1973.67, "end": 1973.85, "word": " من", "probability": 0.81982421875}, {"start": 1973.85, "end": 1974.03, "word": " أو", "probability": 0.91748046875}, {"start": 1974.03, "end": 1974.45, "word": " ساوي", "probability": 0.7049153645833334}, {"start": 1974.45, "end": 1975.01, "word": " الواحد", "probability": 0.9122721354166666}, {"start": 1975.01, "end": 1975.51, "word": " أصغر", "probability": 0.9034423828125}, {"start": 1975.51, "end": 1975.67, "word": " من", "probability": 0.98974609375}, {"start": 1975.67, "end": 1975.85, "word": " أو", "probability": 0.94580078125}, {"start": 1975.85, "end": 1976.23, "word": " ساوي", "probability": 0.9591471354166666}, {"start": 1976.23, "end": 1976.89, "word": " اتنين", "probability": 0.871826171875}, {"start": 1976.89, "end": 1978.37, "word": " لكل", "probability": 0.970947265625}, {"start": 1978.37, "end": 1978.79, "word": " n", "probability": 0.6259765625}, {"start": 1978.79, "end": 1979.09, "word": " في", "probability": 0.96240234375}, {"start": 1979.09, "end": 1979.55, "word": " n", "probability": 0.86328125}, {"start": 1979.55, "end": 1985.05, "word": " لبرهان", "probability": 0.8685302734375}, {"start": 1985.05, "end": 1985.57, "word": " ذلك", "probability": 0.99169921875}, {"start": 1985.57, "end": 1985.83, "word": " to", "probability": 0.763671875}, {"start": 1985.83, "end": 1986.15, "word": " see", "probability": 0.9208984375}, {"start": 1986.15, "end": 1987.19, "word": " this", "probability": 0.96337890625}, {"start": 1987.19, "end": 1991.81, "word": " use", "probability": 0.78125}, {"start": 1991.81, "end": 1994.31, "word": " induction", "probability": 0.96826171875}], "temperature": 1.0}, {"id": 72, "seek": 202895, "start": 1999.65, "end": 2028.95, "text": "on n so I will leave it for you to prove claim one by induction on n فالحالة لو بنشوف بقرا ال statement هذا when n equals one هذا معناه ان المتباين هذه هتكون x one أكبر من أو ساوى الواحد أصغر من أو ساوى اتنين وهذا true", "tokens": [266, 297, 370, 286, 486, 1856, 309, 337, 291, 281, 7081, 3932, 472, 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