diff --git "a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/a-utq7LmSIM_raw.json" "b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/a-utq7LmSIM_raw.json"
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+++ "b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/a-utq7LmSIM_raw.json"
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+{"segments": [{"id": 1, "seek": 5042, "start": 21.06, "end": 50.42, "text": "اليوم ان شاء الله هنحاول نحل امتحان نصفي سابق كمراجعة للامتحان النصفي الأول اللي هناخده ان شاء الله غدا اول سؤال في الامتحان هذا عبارة عن سؤال true or false اذا العبارة صح فبنعلم عليها صح او true واذا خطأ بنعلم عليها خطأ فأول عبارة", "tokens": [6027, 1829, 20498, 16472, 13412, 16606, 21984, 8032, 1863, 5016, 995, 12610, 8717, 5016, 1211, 1975, 2304, 2655, 5016, 7649, 8717, 9381, 41185, 8608, 16758, 4587, 9122, 2304, 2288, 26108, 27884, 24976, 10943, 2655, 5016, 7649, 28239, 9381, 41185, 16247, 12610, 13672, 1829, 8032, 1863, 47283, 3215, 3224, 16472, 13412, 16606, 21984, 32771, 28259, 1975, 12610, 8608, 33604, 6027, 8978, 2423, 10943, 2655, 5016, 7649, 23758, 6225, 3555, 9640, 3660, 18871, 8608, 33604, 6027, 2074, 420, 7908, 1975, 15730, 18863, 3555, 9640, 3660, 20328, 5016, 6156, 3555, 1863, 3615, 19528, 25894, 11296, 20328, 5016, 1975, 2407, 2074, 4032, 45636, 995, 16490, 9566, 10721, 44945, 3615, 19528, 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"tokens": [5172, 6027, 8310, 29538, 9652, 6930, 8032, 1211, 23758, 20328, 5016, 1829, 5016, 49429, 16490, 9566, 10721, 23758, 2074, 4032, 45164, 47525, 8315, 8717, 26890, 3224, 1863, 2423, 28820, 10943, 23758, 4032, 20666, 2304, 8315, 35457, 3660, 2423, 8310, 29538, 41881, 5296, 9381, 5172, 2288, 41881, 4032, 2423, 4948, 6055, 3555, 34268, 11296, 20328, 5172, 2288], "avg_logprob": -0.19462719716523824, "compression_ratio": 1.6, "no_speech_prob": 0.0, "words": [{"start": 282.57, "end": 283.09, "word": "فال", "probability": 0.5601806640625}, {"start": 283.09, "end": 283.55, "word": " sequence", "probability": 0.5400390625}, {"start": 283.55, "end": 283.91, "word": " هذه", "probability": 0.5732421875}, {"start": 283.91, "end": 284.73, "word": " convergent", "probability": 0.6905517578125}, {"start": 284.73, "end": 285.25, "word": " هل", "probability": 0.75146484375}, {"start": 285.25, "end": 285.53, "word": " هذا", "probability": 0.94384765625}, {"start": 285.53, "end": 286.05, "word": " صحيح", "probability": 0.9951171875}, {"start": 286.05, "end": 286.31, "word": " ولا", "probability": 0.82177734375}, {"start": 286.31, "end": 287.33, "word": " خطأ", "probability": 0.9664713541666666}, {"start": 287.33, "end": 290.29, "word": " هذا", "probability": 0.357177734375}, {"start": 290.29, "end": 290.83, "word": " true", "probability": 0.927734375}, {"start": 290.83, "end": 294.79, "word": " و", "probability": 0.60888671875}, {"start": 294.79, "end": 294.95, "word": " لو", "probability": 0.8427734375}, {"start": 294.95, "end": 295.27, "word": " بدنا", "probability": 0.98291015625}, {"start": 295.27, "end": 295.83, "word": " نبرهن", "probability": 0.9649658203125}, {"start": 295.83, "end": 296.33, "word": " الكلام", "probability": 0.958984375}, {"start": 296.33, "end": 296.89, "word": " هذا", "probability": 0.96142578125}, {"start": 296.89, "end": 298.87, "word": " و", "probability": 0.3701171875}, {"start": 298.87, "end": 299.59, "word": " بالمناسبة", "probability": 0.98046875}, {"start": 299.59, "end": 299.75, "word": " ال", "probability": 0.9150390625}, {"start": 299.75, "end": 300.05, "word": " sequence", "probability": 0.98828125}, {"start": 300.05, "end": 300.49, "word": " هذه", "probability": 0.884765625}, {"start": 300.49, "end": 301.31, "word": " converge", "probability": 0.876953125}, {"start": 301.31, "end": 302.01, "word": " لصفر", "probability": 0.76593017578125}, {"start": 302.01, "end": 304.53, "word": " converge", "probability": 0.65380859375}, {"start": 304.53, "end": 304.75, "word": " و", "probability": 0.8525390625}, {"start": 304.75, "end": 304.93, "word": " ال", "probability": 0.66162109375}, {"start": 304.93, "end": 305.21, "word": " limit", "probability": 0.97021484375}, {"start": 305.21, "end": 305.87, "word": " تبعتها", "probability": 0.9056396484375}, {"start": 305.87, "end": 306.41, "word": " صفر", "probability": 0.9443359375}], "temperature": 1.0}, {"id": 11, "seek": 32832, "start": 307.9, "end": 328.32, "text": "ليه؟ لأنه هاي المسافة بين ال inf term لحد انه ليه؟ سالب واحد أس ان على n سالب سفر ايش هاد بالساوي؟ بتساوي", "tokens": [20292, 3224, 22807, 5296, 33456, 3224, 8032, 47302, 9673, 3794, 31845, 3660, 49374, 2423, 1536, 1433, 5296, 24401, 16472, 3224, 32239, 3224, 22807, 8608, 6027, 3555, 36764, 24401, 5551, 3794, 16472, 15844, 297, 8608, 6027, 3555, 8608, 5172, 2288, 1975, 1829, 8592, 8032, 18513, 20666, 3794, 995, 45865, 22807, 39894, 3794, 995, 45865], "avg_logprob": -0.3776041528692952, "compression_ratio": 1.4516129032258065, "no_speech_prob": 0.0, "words": [{"start": 307.90000000000003, "end": 309.1, "word": "ليه؟", "probability": 0.6089680989583334}, {"start": 309.1, "end": 309.7, "word": " لأنه", "probability": 0.6307373046875}, {"start": 309.7, "end": 310.34, "word": " هاي", "probability": 0.5247802734375}, {"start": 310.34, "end": 311.06, "word": " المسافة", "probability": 0.9866943359375}, {"start": 311.06, "end": 311.44, "word": " بين", "probability": 0.95556640625}, {"start": 311.44, "end": 312.02, "word": " ال", "probability": 0.96826171875}, {"start": 312.02, "end": 312.34, "word": " inf", "probability": 0.08929443359375}, {"start": 312.34, "end": 312.96, "word": " term", "probability": 0.9365234375}, {"start": 312.96, "end": 313.64, "word": " لحد", "probability": 0.737548828125}, {"start": 313.64, "end": 313.98, "word": " انه", "probability": 0.72705078125}, {"start": 313.98, "end": 314.94, "word": " ليه؟", "probability": 0.664306640625}, {"start": 314.94, "end": 315.48, "word": " سالب", "probability": 0.8170572916666666}, {"start": 315.48, "end": 315.9, "word": " واحد", "probability": 0.9677734375}, {"start": 315.9, "end": 316.24, "word": " أس", "probability": 0.466552734375}, {"start": 316.24, "end": 316.62, "word": " ان", "probability": 0.469970703125}, {"start": 316.62, "end": 317.04, "word": " على", "probability": 0.45947265625}, {"start": 317.04, "end": 319.14, "word": " n", "probability": 0.2313232421875}, {"start": 319.14, "end": 319.94, "word": " سالب", "probability": 0.9637044270833334}, {"start": 319.94, "end": 320.44, "word": " سفر", "probability": 0.9129231770833334}, {"start": 320.44, "end": 323.62, "word": " ايش", "probability": 0.6831868489583334}, {"start": 323.62, "end": 323.82, "word": " هاد", "probability": 0.470947265625}, {"start": 323.82, "end": 327.52, "word": " بالساوي؟", "probability": 0.82333984375}, {"start": 327.52, "end": 328.32, "word": " بتساوي", "probability": 0.965576171875}], "temperature": 1.0}, {"id": 12, "seek": 36675, "start": 337.95, "end": 366.75, "text": "بتساوي واحد على ان صح؟ نصبوت؟ وهذا أصغر من اذا كان واحد ضرب واحد على ان هذا عدد موجب واحد على ان تقول للسفر إذن حسب نظرية سابقة رقمها كان في النقص اتنين اربعة", "tokens": [3555, 2655, 3794, 995, 45865, 36764, 24401, 15844, 16472, 20328, 5016, 22807, 8717, 9381, 3555, 35473, 22807, 37037, 15730, 5551, 9381, 17082, 2288, 9154, 1975, 15730, 25961, 36764, 24401, 48812, 25513, 36764, 24401, 15844, 16472, 23758, 6225, 3215, 3215, 3714, 29245, 3555, 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0.82373046875}, {"start": 344.87, "end": 345.01, "word": " من", "probability": 0.67626953125}, {"start": 345.01, "end": 345.19, "word": " اذا", "probability": 0.694580078125}, {"start": 345.19, "end": 345.59, "word": " كان", "probability": 0.352294921875}, {"start": 345.59, "end": 346.09, "word": " واحد", "probability": 0.84033203125}, {"start": 346.09, "end": 346.55, "word": " ضرب", "probability": 0.833251953125}, {"start": 346.55, "end": 347.05, "word": " واحد", "probability": 0.978515625}, {"start": 347.05, "end": 347.27, "word": " على", "probability": 0.8740234375}, {"start": 347.27, "end": 347.53, "word": " ان", "probability": 0.81640625}, {"start": 347.53, "end": 349.57, "word": " هذا", "probability": 0.75732421875}, {"start": 349.57, "end": 350.11, "word": " عدد", "probability": 0.984375}, {"start": 350.11, "end": 350.69, "word": " موجب", "probability": 0.9894205729166666}, {"start": 350.69, "end": 352.97, "word": " واح��", "probability": 0.945556640625}, {"start": 352.97, "end": 353.17, "word": " على", "probability": 0.8681640625}, {"start": 353.17, "end": 353.63, "word": " ان", "probability": 0.88037109375}, {"start": 353.63, "end": 354.41, "word": " تقول", "probability": 0.876708984375}, {"start": 354.41, "end": 356.77, "word": " للسفر", "probability": 0.6934814453125}, {"start": 356.77, "end": 359.09, "word": " إذن", "probability": 0.5478922526041666}, {"start": 359.09, "end": 360.75, "word": " حسب", "probability": 0.953369140625}, {"start": 360.75, "end": 361.31, "word": " نظرية", "probability": 0.9681396484375}, {"start": 361.31, "end": 362.05, "word": " سابقة", "probability": 0.9817708333333334}, {"start": 362.05, "end": 365.09, "word": " رقمها", "probability": 0.922607421875}, {"start": 365.09, "end": 365.31, "word": " كان", "probability": 0.97998046875}, {"start": 365.31, "end": 365.45, "word": " في", "probability": 0.943359375}, {"start": 365.45, "end": 365.85, "word": " النقص", "probability": 0.6223958333333334}, {"start": 365.85, "end": 366.23, "word": " اتنين", "probability": 0.941162109375}, {"start": 366.23, "end": 366.75, "word": " اربعة", "probability": 0.8953450520833334}], "temperature": 1.0}, {"id": 13, "seek": 39165, "start": 369.05, "end": 391.65, "text": "بطلع limit xn بساوي سفر limit سالب واحد بس n على n لما n تقوى ل infinity بساوي سفر إذا ال sequence هذي convergent إذا العبارة هذه true طيب عبارة تانية", "tokens": [3555, 9566, 1211, 3615, 4948, 2031, 77, 4724, 3794, 995, 45865, 8608, 5172, 2288, 4948, 8608, 6027, 3555, 36764, 24401, 4724, 3794, 297, 15844, 297, 5296, 15042, 297, 6055, 4587, 2407, 7578, 5296, 13202, 4724, 3794, 995, 45865, 8608, 5172, 2288, 11933, 15730, 2423, 8310, 8032, 8848, 1829, 9652, 6930, 11933, 15730, 18863, 3555, 9640, 3660, 29538, 2074, 23032, 1829, 3555, 6225, 3555, 9640, 3660, 6055, 7649, 10632], "avg_logprob": -0.30729167703269183, "compression_ratio": 1.4610389610389611, "no_speech_prob": 0.0, "words": [{"start": 369.05, "end": 369.91, "word": "بطلع", "probability": 0.6873779296875}, {"start": 369.91, "end": 370.19, "word": " limit", "probability": 0.81103515625}, {"start": 370.19, "end": 370.77, "word": " xn", "probability": 0.5648193359375}, {"start": 370.77, "end": 371.25, "word": " بساوي", "probability": 0.600128173828125}, {"start": 371.25, "end": 371.61, "word": " سفر", "probability": 0.8406575520833334}, {"start": 371.61, "end": 372.07, "word": " limit", "probability": 0.7158203125}, {"start": 372.07, "end": 375.19, "word": " سالب", "probability": 0.7190755208333334}, {"start": 375.19, "end": 375.69, "word": " واحد", "probability": 0.955322265625}, {"start": 375.69, "end": 376.07, "word": " بس", "probability": 0.4547119140625}, {"start": 376.07, "end": 376.39, "word": " n", "probability": 0.330810546875}, {"start": 376.39, "end": 376.61, "word": " على", "probability": 0.65625}, {"start": 376.61, "end": 377.09, "word": " n", "probability": 0.89599609375}, {"start": 377.09, "end": 378.31, "word": " لما", "probability": 0.874755859375}, {"start": 378.31, "end": 378.63, "word": " n", "probability": 0.58056640625}, {"start": 378.63, "end": 378.91, "word": " تقوى", "probability": 0.689697265625}, {"start": 378.91, "end": 379.05, "word": " ل", "probability": 0.79052734375}, {"start": 379.05, "end": 379.59, "word": " infinity", "probability": 0.59228515625}, {"start": 379.59, "end": 380.27, "word": " بساوي", "probability": 0.9530029296875}, {"start": 380.27, "end": 380.75, "word": " سفر", "probability": 0.98779296875}, {"start": 380.75, "end": 385.23, "word": " إذا", "probability": 0.5269775390625}, {"start": 385.23, "end": 385.39, "word": " ال", "probability": 0.90478515625}, {"start": 385.39, "end": 385.65, "word": " sequence", "probability": 0.95263671875}, {"start": 385.65, "end": 386.11, "word": " هذي", "probability": 0.5267740885416666}, {"start": 386.11, "end": 386.73, "word": " convergent", "probability": 0.5574951171875}, {"start": 386.73, "end": 387.39, "word": " إذا", "probability": 0.7666015625}, {"start": 387.39, "end": 387.83, "word": " العبارة", "probability": 0.8741455078125}, {"start": 387.83, "end": 388.23, "word": " هذه", "probability": 0.517578125}, {"start": 388.23, "end": 388.65, "word": " true", "probability": 0.97705078125}, {"start": 388.65, "end": 390.17, "word": " طيب", "probability": 0.9521484375}, {"start": 390.17, "end": 391.15, "word": " عبارة", "probability": 0.889404296875}, {"start": 391.15, "end": 391.65, "word": " تانية", "probability": 0.986328125}], "temperature": 1.0}, {"id": 14, "seek": 42528, "start": 405.94, "end": 425.28, "text": "product of two divergent sequences is divergent هل هذا true ولا false؟", "tokens": [33244, 295, 732, 18558, 6930, 22978, 307, 18558, 6930, 8032, 1211, 23758, 2074, 49429, 7908, 22807], "avg_logprob": -0.3125, "compression_ratio": 1.0394736842105263, "no_speech_prob": 0.0, "words": [{"start": 405.94000000000005, "end": 407.34000000000003, "word": "product", "probability": 0.260009765625}, {"start": 407.34000000000003, "end": 408.74, "word": " of", "probability": 0.93212890625}, {"start": 408.74, "end": 409.2, "word": " two", "probability": 0.912109375}, {"start": 409.2, "end": 410.34, "word": " divergent", "probability": 0.83154296875}, {"start": 410.34, "end": 415.32, "word": " sequences", "probability": 0.6806640625}, {"start": 415.32, "end": 416.98, "word": " is", "probability": 0.8828125}, {"start": 416.98, "end": 418.38, "word": " divergent", "probability": 0.918212890625}, {"start": 418.38, "end": 423.7, "word": " هل", "probability": 0.5965576171875}, {"start": 423.7, "end": 424.0, "word": " هذا", "probability": 0.9169921875}, {"start": 424.0, "end": 424.34, "word": " true", "probability": 0.91162109375}, {"start": 424.34, "end": 424.6, "word": " ولا", "probability": 0.728515625}, {"start": 424.6, "end": 425.28, "word": " false؟", "probability": 0.836181640625}], "temperature": 1.0}, {"id": 15, "seek": 44853, "start": 428.09, "end": 448.53, "text": "العبارة هادف false طب لما قلنا لكوا جيبوا counter example ممكن تجيب سالب واحد اثنان وكمان ال sequence التانية تكون سالب واحد اثنان او ممكن تكون سالب واحد اثنان زائد واحد نفس الشغل بتطلع convergent ال product", "tokens": [6027, 3615, 3555, 9640, 3660, 8032, 18513, 5172, 7908, 23032, 3555, 5296, 15042, 12174, 1211, 8315, 5296, 4117, 14407, 10874, 1829, 3555, 14407, 5682, 1365, 3714, 43020, 6055, 7435, 1829, 3555, 8608, 6027, 3555, 36764, 24401, 1975, 12984, 1863, 7649, 4032, 24793, 7649, 2423, 8310, 16712, 7649, 10632, 6055, 30544, 8608, 6027, 3555, 36764, 24401, 1975, 12984, 1863, 7649, 1975, 2407, 3714, 43020, 6055, 30544, 8608, 6027, 3555, 36764, 24401, 1975, 12984, 1863, 7649, 30767, 16373, 3215, 36764, 24401, 8717, 36178, 25124, 17082, 1211, 39894, 9566, 1211, 3615, 9652, 6930, 2423, 1674], "avg_logprob": -0.27116935099324874, "compression_ratio": 1.7486910994764397, "no_speech_prob": 0.0, "words": [{"start": 428.09000000000003, "end": 428.81, "word": "العبارة", "probability": 0.88515625}, {"start": 428.81, "end": 429.17, "word": " هادف", "probability": 0.5633951822916666}, {"start": 429.17, "end": 429.45, "word": " false", "probability": 0.247314453125}, {"start": 429.45, "end": 429.67, "word": " طب", "probability": 0.621337890625}, {"start": 429.67, "end": 429.83, "word": " لما", "probability": 0.7841796875}, {"start": 429.83, "end": 430.05, "word": " قلنا", "probability": 0.8557942708333334}, {"start": 430.05, "end": 430.29, "word": " لكوا", "probability": 0.5581868489583334}, {"start": 430.29, "end": 430.65, "word": " جيبوا", "probability": 0.934326171875}, {"start": 430.65, "end": 430.99, "word": " counter", "probability": 0.82470703125}, {"start": 430.99, "end": 431.71, "word": " example", "probability": 0.93359375}, {"start": 431.71, "end": 433.23, "word": " ممكن", "probability": 0.8603515625}, {"start": 433.23, "end": 433.67, "word": " تجيب", "probability": 0.97265625}, {"start": 433.67, "end": 434.03, "word": " سالب", "probability": 0.4417317708333333}, {"start": 434.03, "end": 434.39, "word": " واحد", "probability": 0.979736328125}, {"start": 434.39, "end": 435.07, "word": " اثنان", "probability": 0.50323486328125}, {"start": 435.07, "end": 437.19, "word": " وكمان", "probability": 0.8601888020833334}, {"start": 437.19, "end": 437.31, "word": " ال", "probability": 0.8857421875}, {"start": 437.31, "end": 437.67, "word": " sequence", "probability": 0.890625}, {"start": 437.67, "end": 438.01, "word": " التانية", "probability": 0.86865234375}, {"start": 438.01, "end": 438.25, "word": " تكون", "probability": 0.957763671875}, {"start": 438.25, "end": 438.55, "word": " سالب", "probability": 0.91650390625}, {"start": 438.55, "end": 438.85, "word": " واحد", "probability": 0.9921875}, {"start": 438.85, "end": 439.45, "word": " اثنان", "probability": 0.909912109375}, {"start": 439.45, "end": 443.29, "word": " او", "probability": 0.917236328125}, {"start": 443.29, "end": 443.51, "word": " ممكن", "probability": 0.954833984375}, {"start": 443.51, "end": 443.75, "word": " تكون", "probability": 0.9931640625}, {"start": 443.75, "end": 444.05, "word": " سالب", "probability": 0.89208984375}, {"start": 444.05, "end": 444.31, "word": " واحد", "probability": 0.994873046875}, {"start": 444.31, "end": 444.71, "word": " اثنان", "probability": 0.9189453125}, {"start": 444.71, "end": 444.95, "word": " زائد", "probability": 0.745361328125}, {"start": 444.95, "end": 445.77, "word": " واحد", "probability": 0.86767578125}, {"start": 445.77, "end": 446.47, "word": " نفس", "probability": 0.939697265625}, {"start": 446.47, "end": 446.83, "word": " الشغل", "probability": 0.8821614583333334}, {"start": 446.83, "end": 447.21, "word": " بتطلع", "probability": 0.72735595703125}, {"start": 447.21, "end": 447.85, "word": " convergent", "probability": 0.533935546875}, {"start": 447.85, "end": 448.19, "word": " ال", "probability": 0.3564453125}, {"start": 448.19, "end": 448.53, "word": " product", "probability": 0.95849609375}], "temperature": 1.0}, {"id": 16, "seek": 47945, "start": 450.65, "end": 479.45, "text": "هذه الـ divergent وهذه الـ divergent لكن X in في Y in هساوي ال sequence سلب واحد واست اتنين in لما نضربهم في بعض فهذا بيعطيني ال sequence ثابت واحد وهذه converge لواحد اذا هذه في عندي example of two divergent sequences لكن حصل ضربهم بيطلع", "tokens": [3224, 24192, 2423, 39184, 18558, 6930, 37037, 24192, 2423, 39184, 18558, 6930, 44381, 1783, 294, 8978, 398, 294, 8032, 3794, 995, 45865, 2423, 8310, 8608, 46152, 36764, 24401, 4032, 32277, 2655, 1975, 2655, 1863, 9957, 294, 5296, 15042, 8717, 11242, 25513, 16095, 8978, 45030, 11242, 6156, 3224, 15730, 4724, 1829, 3615, 9566, 1829, 22653, 2423, 8310, 38637, 16758, 2655, 36764, 24401, 37037, 24192, 41881, 5296, 14407, 24401, 1975, 15730, 29538, 8978, 18871, 16254, 1365, 295, 732, 18558, 6930, 22978, 44381, 11331, 36520, 48812, 25513, 16095, 4724, 1829, 9566, 1211, 3615], "avg_logprob": -0.39217031919039214, "compression_ratio": 1.729064039408867, "no_speech_prob": 0.0, "words": [{"start": 450.65, "end": 451.19, "word": "هذه", "probability": 0.4556884765625}, {"start": 451.19, "end": 451.31, "word": " الـ", "probability": 0.20526123046875}, {"start": 451.31, "end": 452.05, "word": " divergent", "probability": 0.60687255859375}, {"start": 452.05, "end": 452.39, "word": " وهذه", "probability": 0.516357421875}, {"start": 452.39, "end": 452.51, "word": " الـ", "probability": 0.826171875}, {"start": 452.51, "end": 453.21, "word": " divergent", "probability": 0.771728515625}, {"start": 453.21, "end": 453.65, "word": " لكن", "probability": 0.70068359375}, {"start": 453.65, "end": 455.17, "word": " X", "probability": 0.2371826171875}, {"start": 455.17, "end": 455.47, "word": " in", "probability": 0.25146484375}, {"start": 455.47, "end": 455.69, "word": " في", "probability": 0.89501953125}, {"start": 455.69, "end": 456.11, "word": " Y", "probability": 0.876953125}, {"start": 456.11, "end": 456.51, "word": " in", "probability": 0.92822265625}, {"start": 456.51, "end": 457.39, "word": " هساوي", "probability": 0.625732421875}, {"start": 457.39, "end": 457.61, "word": " ال", "probability": 0.599609375}, {"start": 457.61, "end": 458.21, "word": " sequence", "probability": 0.76953125}, {"start": 458.21, "end": 459.99, "word": " سلب", "probability": 0.460693359375}, {"start": 459.99, "end": 460.35, "word": " واحد", "probability": 0.950439453125}, {"start": 460.35, "end": 460.63, "word": " واست", "probability": 0.3516438802083333}, {"start": 460.63, "end": 461.03, "word": " اتنين", "probability": 0.9036865234375}, {"start": 461.03, "end": 461.39, "word": " in", "probability": 0.81103515625}, {"start": 461.39, "end": 464.65, "word": " لما", "probability": 0.865478515625}, {"start": 464.65, "end": 465.13, "word": " نضربهم", "probability": 0.923828125}, {"start": 465.13, "end": 465.31, "word": " في", "probability": 0.8896484375}, {"start": 465.31, "end": 465.67, "word": " بعض", "probability": 0.992431640625}, {"start": 465.67, "end": 467.13, "word": " فهذا", "probability": 0.791015625}, {"start": 467.13, "end": 467.71, "word": " بيعطيني", "probability": 0.767333984375}, {"start": 467.71, "end": 467.91, "word": " ال", "probability": 0.9013671875}, {"start": 467.91, "end": 468.35, "word": " sequence", "probability": 0.96435546875}, {"start": 468.35, "end": 468.83, "word": " ثابت", "probability": 0.9873046875}, {"start": 468.83, "end": 469.37, "word": " واحد", "probability": 0.96337890625}, {"start": 469.37, "end": 470.29, "word": " وهذه", "probability": 0.80224609375}, {"start": 470.29, "end": 470.91, "word": " converge", "probability": 0.07000732421875}, {"start": 470.91, "end": 471.49, "word": " لواحد", "probability": 0.81591796875}, {"start": 471.49, "end": 473.53, "word": " اذا", "probability": 0.6136474609375}, {"start": 473.53, "end": 473.83, "word": " هذه", "probability": 0.361083984375}, {"start": 473.83, "end": 473.99, "word": " في", "probability": 0.5361328125}, {"start": 473.99, "end": 474.39, "word": " عندي", "probability": 0.8232421875}, {"start": 474.39, "end": 475.23, "word": " example", "probability": 0.73974609375}, {"start": 475.23, "end": 475.51, "word": " of", "probability": 0.9169921875}, {"start": 475.51, "end": 475.73, "word": " two", "probability": 0.931640625}, {"start": 475.73, "end": 476.35, "word": " divergent", "probability": 0.7841796875}, {"start": 476.35, "end": 477.11, "word": " sequences", "probability": 0.951171875}, {"start": 477.11, "end": 477.99, "word": " لكن", "probability": 0.90869140625}, {"start": 477.99, "end": 478.41, "word": " حصل", "probability": 0.818115234375}, {"start": 478.41, "end": 478.93, "word": " ضربهم", "probability": 0.97998046875}, {"start": 478.93, "end": 479.45, "word": " بيطلع", "probability": 0.786083984375}], "temperature": 1.0}, {"id": 17, "seek": 50851, "start": 480.21, "end": 508.51, "text": "convergent وليس divergent طيب لو كانت S bounded S bounded subset of R وS0 subset من S هل هذا بيقدّي ان انفمم", "tokens": [1671, 331, 6930, 4032, 20292, 3794, 18558, 6930, 23032, 1829, 3555, 45164, 25961, 2655, 318, 37498, 318, 37498, 25993, 295, 497, 4032, 50, 15, 25993, 9154, 318, 8032, 1211, 23758, 4724, 1829, 28543, 11703, 1829, 16472, 16472, 5172, 2304, 2304], "avg_logprob": -0.28315549943505264, "compression_ratio": 1.1932773109243697, "no_speech_prob": 0.0, "words": [{"start": 480.21, "end": 481.09, "word": "convergent", "probability": 0.8377278645833334}, {"start": 481.09, "end": 481.69, "word": " وليس", "probability": 0.83447265625}, {"start": 481.69, "end": 482.69, "word": " divergent", "probability": 0.6734619140625}, {"start": 482.69, "end": 486.23, "word": " طيب", "probability": 0.8849283854166666}, {"start": 486.23, "end": 486.97, "word": " لو", "probability": 0.8583984375}, {"start": 486.97, "end": 488.89, "word": " كانت", "probability": 0.9833984375}, {"start": 488.89, "end": 489.73, "word": " S", "probability": 0.70947265625}, {"start": 489.73, "end": 490.47, "word": " bounded", "probability": 0.9404296875}, {"start": 490.47, "end": 492.69, "word": " S", "probability": 0.436767578125}, {"start": 492.69, "end": 493.59, "word": " bounded", "probability": 0.9619140625}, {"start": 493.59, "end": 496.15, "word": " subset", "probability": 0.87646484375}, {"start": 496.15, "end": 496.97, "word": " of", "probability": 0.974609375}, {"start": 496.97, "end": 497.69, "word": " R", "probability": 0.9560546875}, {"start": 497.69, "end": 501.47, "word": " وS0", "probability": 0.531494140625}, {"start": 501.47, "end": 502.03, "word": " subset", "probability": 0.9072265625}, {"start": 502.03, "end": 502.45, "word": " من", "probability": 0.9921875}, {"start": 502.45, "end": 502.91, "word": " S", "probability": 0.9853515625}, {"start": 502.91, "end": 504.87, "word": " هل", "probability": 0.864501953125}, {"start": 504.87, "end": 505.17, "word": " هذا", "probability": 0.91845703125}, {"start": 505.17, "end": 505.79, "word": " بيقدّي", "probability": 0.6695068359375}, {"start": 505.79, "end": 506.07, "word": " ان", "probability": 0.73876953125}, {"start": 506.07, "end": 508.51, "word": " انفمم", "probability": 0.686279296875}], "temperature": 1.0}, {"id": 18, "seek": 53482, "start": 509.76, "end": 534.82, "text": "S0 subset أصغر من أو يساوي انفمه من ال S هل هذه العبارة صحيحة؟ أيه رأيكم؟ العبارة هذه false", "tokens": [50, 15, 25993, 5551, 9381, 17082, 2288, 9154, 34051, 7251, 3794, 995, 45865, 16472, 5172, 2304, 3224, 9154, 2423, 318, 8032, 1211, 29538, 18863, 3555, 9640, 3660, 20328, 5016, 1829, 5016, 3660, 22807, 36632, 3224, 12602, 10721, 1829, 24793, 22807, 18863, 3555, 9640, 3660, 29538, 7908], "avg_logprob": -0.20728058764275084, "compression_ratio": 1.25, "no_speech_prob": 0.0, "words": [{"start": 509.76, "end": 510.88, "word": "S0", "probability": 0.681884765625}, {"start": 510.88, "end": 511.76, "word": " subset", "probability": 0.7216796875}, {"start": 511.76, "end": 513.64, "word": " أصغر", "probability": 0.9100341796875}, {"start": 513.64, "end": 513.94, "word": " من", "probability": 0.9736328125}, {"start": 513.94, "end": 514.22, "word": " أو", "probability": 0.91162109375}, {"start": 514.22, "end": 514.9, "word": " يساوي", "probability": 0.83941650390625}, {"start": 514.9, "end": 517.34, "word": " انفمه", "probability": 0.56390380859375}, {"start": 517.34, "end": 517.48, "word": " من", "probability": 0.91259765625}, {"start": 517.48, "end": 517.66, "word": " ال", "probability": 0.791015625}, {"start": 517.66, "end": 518.08, "word": " S", "probability": 0.62548828125}, {"start": 518.08, "end": 522.48, "word": " هل", "probability": 0.919921875}, {"start": 522.48, "end": 522.7, "word": " هذه", "probability": 0.87451171875}, {"start": 522.7, "end": 523.2, "word": " العبارة", "probability": 0.9442138671875}, {"start": 523.2, "end": 526.1, "word": " صحيحة؟", "probability": 0.8980305989583334}, {"start": 526.1, "end": 531.02, "word": " أيه", "probability": 0.6510009765625}, {"start": 531.02, "end": 531.58, "word": " رأيكم؟", "probability": 0.91943359375}, {"start": 531.58, "end": 533.98, "word": " العبارة", "probability": 0.927734375}, {"start": 533.98, "end": 534.34, "word": " هذه", "probability": 0.830078125}, {"start": 534.34, "end": 534.82, "word": " false", "probability": 0.7197265625}], "temperature": 1.0}, {"id": 19, "seek": 55732, "start": 536.54, "end": 557.32, "text": "لما مجموعة تصغر ال inform تباعها بيكبر، لكن اللي بيكون صح أنه ال supremum لو أخدت ال supremum للمجموعة الجزئية S0 فهذا بيطلع أصغر من أو ساوي ال supremum للمجموع S، هذه العبارة true", "tokens": [1211, 15042, 3714, 7435, 2304, 2407, 27884, 6055, 9381, 17082, 2288, 2423, 1356, 6055, 3555, 45761, 11296, 4724, 1829, 4117, 26890, 12399, 44381, 13672, 1829, 4724, 1829, 30544, 20328, 5016, 14739, 3224, 2423, 23710, 449, 45164, 5551, 9778, 3215, 2655, 2423, 23710, 449, 5296, 19528, 7435, 2304, 45367, 3660, 25724, 11622, 19986, 10632, 318, 15, 6156, 3224, 15730, 4724, 1829, 9566, 1211, 3615, 5551, 9381, 17082, 2288, 9154, 34051, 8608, 995, 45865, 2423, 23710, 449, 5296, 19528, 7435, 2304, 45367, 318, 12399, 29538, 18863, 3555, 9640, 3660, 2074], "avg_logprob": -0.24859551901227972, "compression_ratio": 1.6571428571428573, "no_speech_prob": 0.0, "words": [{"start": 536.54, "end": 537.08, "word": "لما", "probability": 0.7100830078125}, {"start": 537.08, "end": 538.1, "word": " مجموعة", "probability": 0.82216796875}, {"start": 538.1, "end": 538.74, "word": " تصغر", "probability": 0.9644775390625}, {"start": 538.74, "end": 538.92, "word": " ال", "probability": 0.912109375}, {"start": 538.92, "end": 539.32, "word": " inform", "probability": 0.11175537109375}, {"start": 539.32, "end": 540.02, "word": " تباعها", "probability": 0.876220703125}, {"start": 540.02, "end": 541.4, "word": " بيكبر،", "probability": 0.7787109375}, {"start": 541.4, "end": 542.92, "word": " لكن", "probability": 0.9736328125}, {"start": 542.92, "end": 544.54, "word": " اللي", "probability": 0.841552734375}, {"start": 544.54, "end": 544.98, "word": " بيكون", "probability": 0.9650065104166666}, {"start": 544.98, "end": 545.44, "word": " صح", "probability": 0.993896484375}, {"start": 545.44, "end": 546.08, "word": " أنه", "probability": 0.35626220703125}, {"start": 546.08, "end": 546.2, "word": " ال", "probability": 0.5810546875}, {"start": 546.2, "end": 546.94, "word": " supremum", "probability": 0.32171630859375}, {"start": 546.94, "end": 547.94, "word": " لو", "probability": 0.8017578125}, {"start": 547.94, "end": 548.38, "word": " أخدت", "probability": 0.7921142578125}, {"start": 548.38, "end": 548.54, "word": " ال", "probability": 0.87646484375}, {"start": 548.54, "end": 549.0, "word": " supremum", "probability": 0.871826171875}, {"start": 549.0, "end": 549.7, "word": " للمجموعة", "probability": 0.863525390625}, {"start": 549.7, "end": 550.16, "word": " الجزئية", "probability": 0.8603515625}, {"start": 550.16, "end": 550.82, "word": " S0", "probability": 0.797119140625}, {"start": 550.82, "end": 551.84, "word": " فهذا", "probability": 0.9054361979166666}, {"start": 551.84, "end": 552.6, "word": " بيطلع", "probability": 0.87900390625}, {"start": 552.6, "end": 553.08, "word": " أصغر", "probability": 0.9700927734375}, {"start": 553.08, "end": 553.22, "word": " من", "probability": 0.9345703125}, {"start": 553.22, "end": 553.4, "word": " أو", "probability": 0.81884765625}, {"start": 553.4, "end": 553.9, "word": " ساوي", "probability": 0.9163411458333334}, {"start": 553.9, "end": 554.08, "word": " ال", "probability": 0.84375}, {"start": 554.08, "end": 555.22, "word": " supremum", "probability": 0.894775390625}, {"start": 555.22, "end": 555.94, "word": " للمجموع", "probability": 0.89501953125}, {"start": 555.94, "end": 556.26, "word": " S،", "probability": 0.7314453125}, {"start": 556.26, "end": 556.48, "word": " هذه", "probability": 0.626953125}, {"start": 556.48, "end": 557.04, "word": " العبارة", "probability": 0.781890869140625}, {"start": 557.04, "end": 557.32, "word": " true", "probability": 0.8291015625}], "temperature": 1.0}, {"id": 20, "seek": 57811, "start": 560.87, "end": 578.11, "text": "ال supremum لما المجموعه تكبر بيكبر لكن ال infimum لما المجموعه تكبر بيصغر عكس بعض طيب", "tokens": [6027, 23710, 449, 5296, 15042, 9673, 7435, 2304, 45367, 3224, 6055, 4117, 26890, 4724, 1829, 4117, 26890, 44381, 2423, 1536, 332, 449, 5296, 15042, 9673, 7435, 2304, 45367, 3224, 6055, 4117, 26890, 4724, 1829, 9381, 17082, 2288, 6225, 4117, 3794, 45030, 11242, 23032, 1829, 3555], "avg_logprob": -0.16635529696941376, "compression_ratio": 1.5106382978723405, "no_speech_prob": 0.0, "words": [{"start": 560.87, "end": 561.19, "word": "ال", "probability": 0.89697265625}, {"start": 561.19, "end": 561.93, "word": " supremum", "probability": 0.5238037109375}, {"start": 561.93, "end": 562.79, "word": " لما", "probability": 0.939453125}, {"start": 562.79, "end": 563.31, "word": " المجموعه", "probability": 0.831884765625}, {"start": 563.31, "end": 563.73, "word": " تكبر", "probability": 0.9637044270833334}, {"start": 563.73, "end": 564.21, "word": " بيكبر", "probability": 0.892333984375}, {"start": 564.21, "end": 564.57, "word": " لكن", "probability": 0.72412109375}, {"start": 564.57, "end": 565.17, "word": " ال", "probability": 0.90673828125}, {"start": 565.17, "end": 565.71, "word": " infimum", "probability": 0.5775553385416666}, {"start": 565.71, "end": 565.93, "word": " لما", "probability": 0.983642578125}, {"start": 565.93, "end": 566.35, "word": " المجموعه", "probability": 0.9859375}, {"start": 566.35, "end": 566.79, "word": " تكبر", "probability": 0.9754231770833334}, {"start": 566.79, "end": 567.51, "word": " بيصغر", "probability": 0.9685546875}, {"start": 567.51, "end": 568.81, "word": " عكس", "probability": 0.92138671875}, {"start": 568.81, "end": 569.21, "word": " بعض", "probability": 0.9951171875}, {"start": 569.21, "end": 578.11, "word": " طيب", "probability": 0.9544270833333334}], "temperature": 1.0}, {"id": 21, "seek": 61174, "start": 583.2, "end": 611.74, "text": "لو كانت x in sequence of positive real numbers و limit x in plus one over x in بساوي واحد فهذا بيقدي ان ال sequence x in diverges هل هذه العبارة صح ولا خطأ؟", "tokens": [1211, 2407, 25961, 2655, 2031, 294, 8310, 295, 3353, 957, 3547, 4032, 4948, 2031, 294, 1804, 472, 670, 2031, 294, 4724, 3794, 995, 45865, 36764, 24401, 6156, 3224, 15730, 4724, 1829, 4587, 16254, 16472, 2423, 8310, 2031, 294, 18558, 2880, 8032, 1211, 29538, 18863, 3555, 9640, 3660, 20328, 5016, 49429, 16490, 9566, 10721, 22807], "avg_logprob": -0.17571022998202931, "compression_ratio": 1.2875, "no_speech_prob": 0.0, "words": [{"start": 583.2, "end": 583.58, "word": "لو", "probability": 0.855712890625}, {"start": 583.58, "end": 584.16, "word": " كانت", "probability": 0.974853515625}, {"start": 584.16, "end": 584.52, "word": " x", "probability": 0.5390625}, {"start": 584.52, "end": 585.0, "word": " in", "probability": 0.353515625}, {"start": 585.0, "end": 586.68, "word": " sequence", "probability": 0.76220703125}, {"start": 586.68, "end": 587.38, "word": " of", "probability": 0.96533203125}, {"start": 587.38, "end": 587.86, "word": " positive", "probability": 0.90380859375}, {"start": 587.86, "end": 588.24, "word": " real", "probability": 0.958984375}, {"start": 588.24, "end": 588.82, "word": " numbers", "probability": 0.87109375}, {"start": 588.82, "end": 590.1, "word": " و", "probability": 0.7646484375}, {"start": 590.1, "end": 590.74, "word": " limit", "probability": 0.89306640625}, {"start": 590.74, "end": 592.86, "word": " x", "probability": 0.865234375}, {"start": 592.86, "end": 593.38, "word": " in", "probability": 0.9052734375}, {"start": 593.38, "end": 593.92, "word": " plus", "probability": 0.85693359375}, {"start": 593.92, "end": 594.52, "word": " one", "probability": 0.90185546875}, {"start": 594.52, "end": 595.16, "word": " over", "probability": 0.9130859375}, {"start": 595.16, "end": 595.72, "word": " x", "probability": 0.990234375}, {"start": 595.72, "end": 596.5, "word": " in", "probability": 0.9111328125}, {"start": 596.5, "end": 597.8, "word": " بساوي", "probability": 0.8458251953125}, {"start": 597.8, "end": 598.42, "word": " واحد", "probability": 0.975830078125}, {"start": 598.42, "end": 602.06, "word": " فهذا", "probability": 0.9503580729166666}, {"start": 602.06, "end": 602.62, "word": " بيقدي", "probability": 0.63690185546875}, {"start": 602.62, "end": 602.98, "word": " ان", "probability": 0.66015625}, {"start": 602.98, "end": 603.36, "word": " ال", "probability": 0.623046875}, {"start": 603.36, "end": 603.96, "word": " sequence", "probability": 0.98291015625}, {"start": 603.96, "end": 604.42, "word": " x", "probability": 0.916015625}, {"start": 604.42, "end": 605.02, "word": " in", "probability": 0.9453125}, {"start": 605.02, "end": 608.18, "word": " diverges", "probability": 0.7225341796875}, {"start": 608.18, "end": 609.92, "word": " هل", "probability": 0.87353515625}, {"start": 609.92, "end": 610.14, "word": " هذه", "probability": 0.8154296875}, {"start": 610.14, "end": 610.62, "word": " العبارة", "probability": 0.9136962890625}, {"start": 610.62, "end": 610.92, "word": " صح", "probability": 0.997314453125}, {"start": 610.92, "end": 611.12, "word": " ولا", "probability": 0.943359375}, {"start": 611.12, "end": 611.74, "word": " خطأ؟", "probability": 0.9351806640625}], "temperature": 1.0}, {"id": 22, "seek": 63835, "start": 612.75, "end": 638.35, "text": "العبارة هذه خطأ لأنه احنا فينا في تمرين سبتاشر في section تلاتة اتنين بقول اذا كانت ال sequence .. اذا كان ال limit ratio هذا بساوي واحد فال sequence ممكن تكون convergent او divergent وفي السؤال هذا اعطينا مثلين واحد ل sequence convergent", "tokens": [6027, 3615, 3555, 9640, 3660, 29538, 16490, 9566, 10721, 5296, 33456, 3224, 1975, 5016, 8315, 8978, 8315, 8978, 6055, 29973, 9957, 8608, 3555, 2655, 33599, 2288, 8978, 3541, 6055, 1211, 9307, 3660, 1975, 2655, 1863, 9957, 4724, 39648, 1975, 15730, 25961, 2655, 2423, 8310, 4386, 1975, 15730, 25961, 2423, 4948, 8509, 23758, 4724, 3794, 995, 45865, 36764, 24401, 6156, 6027, 8310, 3714, 43020, 6055, 30544, 9652, 6930, 1975, 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{"start": 620.69, "end": 620.91, "word": " في", "probability": 0.7373046875}, {"start": 620.91, "end": 621.29, "word": " section", "probability": 0.60791015625}, {"start": 621.29, "end": 621.83, "word": " تلاتة", "probability": 0.81884765625}, {"start": 621.83, "end": 622.23, "word": " اتنين", "probability": 0.9705810546875}, {"start": 622.23, "end": 623.77, "word": " بقول", "probability": 0.812744140625}, {"start": 623.77, "end": 624.07, "word": " اذا", "probability": 0.775146484375}, {"start": 624.07, "end": 624.55, "word": " كانت", "probability": 0.9296875}, {"start": 624.55, "end": 624.69, "word": " ال", "probability": 0.91015625}, {"start": 624.69, "end": 625.29, "word": " sequence", "probability": 0.83251953125}, {"start": 625.29, "end": 625.57, "word": " ..", "probability": 0.223388671875}, {"start": 625.57, "end": 625.71, "word": " اذا", "probability": 0.899169921875}, {"start": 625.71, "end": 625.93, "word": " كان", "probability": 0.9931640625}, {"start": 625.93, "end": 626.03, "word": " ال", "probability": 0.41650390625}, {"start": 626.03, "end": 626.23, "word": " limit", "probability": 0.91845703125}, {"start": 626.23, "end": 626.67, "word": " ratio", "probability": 0.316162109375}, {"start": 626.67, "end": 626.87, "word": " هذا", "probability": 0.5595703125}, {"start": 626.87, "end": 627.27, "word": " بساوي", "probability": 0.68963623046875}, {"start": 627.27, "end": 627.75, "word": " واحد", "probability": 0.9873046875}, {"start": 627.75, "end": 628.61, "word": " فال", "probability": 0.90380859375}, {"start": 628.61, "end": 628.89, "word": " sequence", "probability": 0.98193359375}, {"start": 628.89, "end": 629.29, "word": " ممكن", "probability": 0.9833984375}, {"start": 629.29, "end": 629.63, "word": " تكون", "probability": 0.970947265625}, {"start": 629.63, "end": 630.35, "word": " convergent", "probability": 0.88232421875}, {"start": 630.35, "end": 630.55, "word": " او", "probability": 0.8671875}, {"start": 630.55, "end": 631.29, "word": " divergent", "probability": 0.837158203125}, {"start": 631.29, "end": 631.99, "word": " وفي", "probability": 0.779296875}, {"start": 631.99, "end": 632.41, "word": " السؤال", "probability": 0.9949544270833334}, {"start": 632.41, "end": 632.77, "word": " هذا", "probability": 0.95263671875}, {"start": 632.77, "end": 633.89, "word": " اعطينا", "probability": 0.8900390625}, {"start": 633.89, "end": 634.57, "word": " مثلين", "probability": 0.95068359375}, {"start": 634.57, "end": 636.29, "word": " واحد", "probability": 0.924072265625}, {"start": 636.29, "end": 636.81, "word": " ل", "probability": 0.9287109375}, {"start": 636.81, "end": 637.27, "word": " sequence", "probability": 0.9443359375}, {"start": 637.27, "end": 638.35, "word": " convergent", "probability": 0.95947265625}], "temperature": 1.0}, {"id": 23, "seek": 66834, "start": 639.76, "end": 668.34, "text": "ال ratio limit ال ratio تبعها بيساوي واحد لكنها convergent ومثال تاني ل sequence limit ال ratio تبعها أيضا بيساوي واحد لكنها divergent إذا لو كان limit ال ratio بيساوي واحد فال sequence إما converge أو divergent مالضايش نجزم إنها convergent أو نجزم إنها divergent okay إذا العبارة هذه خطأ أو false إذا العبارة هذه false", "tokens": [6027, 8509, 4948, 2423, 8509, 6055, 3555, 3615, 11296, 4724, 1829, 3794, 995, 45865, 36764, 24401, 44381, 11296, 9652, 6930, 4032, 2304, 12984, 6027, 6055, 7649, 1829, 5296, 8310, 4948, 2423, 8509, 6055, 3555, 3615, 11296, 36632, 11242, 995, 4724, 1829, 3794, 995, 45865, 36764, 24401, 44381, 11296, 18558, 6930, 11933, 15730, 45164, 25961, 4948, 2423, 8509, 4724, 1829, 3794, 995, 45865, 36764, 24401, 6156, 6027, 8310, 11933, 15042, 41881, 34051, 18558, 6930, 3714, 6027, 11242, 47302, 8592, 8717, 7435, 11622, 2304, 36145, 11296, 9652, 6930, 34051, 8717, 7435, 11622, 2304, 36145, 11296, 18558, 6930, 1392, 11933, 15730, 18863, 3555, 9640, 3660, 29538, 16490, 9566, 10721, 34051, 7908, 11933, 15730, 18863, 3555, 9640, 3660, 29538, 7908], "avg_logprob": -0.21941774217491475, "compression_ratio": 2.2807881773399017, "no_speech_prob": 0.0, "words": [{"start": 639.76, "end": 640.06, "word": "ال", "probability": 0.35498046875}, {"start": 640.06, "end": 640.52, "word": " ratio", "probability": 0.257080078125}, {"start": 640.52, "end": 640.96, "word": " limit", "probability": 0.50439453125}, {"start": 640.96, "end": 641.24, "word": " ال", "probability": 0.63232421875}, {"start": 641.24, "end": 641.5, "word": " ratio", "probability": 0.98876953125}, {"start": 641.5, "end": 641.88, "word": " تبعها", "probability": 0.8426513671875}, {"start": 641.88, "end": 642.28, "word": " بيساوي", "probability": 0.6823974609375}, {"start": 642.28, "end": 642.7, "word": " واحد", "probability": 0.955078125}, {"start": 642.7, "end": 643.24, "word": " لكنها", "probability": 0.874755859375}, {"start": 643.24, "end": 644.02, "word": " convergent", "probability": 0.855224609375}, {"start": 644.02, "end": 645.1, "word": " ومثال", "probability": 0.806640625}, {"start": 645.1, "end": 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"probability": 0.763916015625}, {"start": 652.6, "end": 652.84, "word": " لو", "probability": 0.9912109375}, {"start": 652.84, "end": 653.06, "word": " كان", "probability": 0.9873046875}, {"start": 653.06, "end": 653.28, "word": " limit", "probability": 0.9111328125}, {"start": 653.28, "end": 653.46, "word": " ال", "probability": 0.97900390625}, {"start": 653.46, "end": 653.7, "word": " ratio", "probability": 0.99609375}, {"start": 653.7, "end": 654.08, "word": " بيساوي", "probability": 0.98505859375}, {"start": 654.08, "end": 654.4, "word": " واحد", "probability": 0.993408203125}, {"start": 654.4, "end": 654.64, "word": " فال", "probability": 0.4534912109375}, {"start": 654.64, "end": 654.98, "word": " sequence", "probability": 0.97021484375}, {"start": 654.98, "end": 655.28, "word": " إما", "probability": 0.7822265625}, {"start": 655.28, "end": 655.9, "word": " converge", "probability": 0.90625}, {"start": 655.9, "end": 656.38, "word": " أو", "probability": 0.6884765625}, {"start": 656.38, "end": 657.1, "word": " divergent", "probability": 0.797607421875}, {"start": 657.1, "end": 658.06, "word": " مالضايش", "probability": 0.526171875}, {"start": 658.06, "end": 658.46, "word": " نجزم", "probability": 0.7840576171875}, {"start": 658.46, "end": 658.68, "word": " إنها", "probability": 0.6900634765625}, {"start": 658.68, "end": 659.46, "word": " convergent", "probability": 0.904541015625}, {"start": 659.46, "end": 659.9, "word": " أو", "probability": 0.93896484375}, {"start": 659.9, "end": 661.0, "word": " نجزم", "probability": 0.9857177734375}, {"start": 661.0, "end": 661.4, "word": " إنها", "probability": 0.948974609375}, {"start": 661.4, "end": 662.14, "word": " divergent", "probability": 0.89501953125}, {"start": 662.14, "end": 662.58, "word": " okay", "probability": 0.642578125}, {"start": 662.58, "end": 663.42, "word": " إذا", "probability": 0.7392578125}, {"start": 663.42, "end": 663.86, "word": " العبارة", "probability": 0.917724609375}, {"start": 663.86, "end": 664.12, "word": " هذه", "probability": 0.7744140625}, {"start": 664.12, "end": 664.66, "word": " خطأ", "probability": 0.9319661458333334}, {"start": 664.66, "end": 665.52, "word": " أو", "probability": 0.86572265625}, {"start": 665.52, "end": 666.1, "word": " false", "probability": 0.87109375}, {"start": 666.1, "end": 667.02, "word": " إذا", "probability": 0.766357421875}, {"start": 667.02, "end": 667.6, "word": " العبارة", "probability": 0.9921875}, {"start": 667.6, "end": 667.86, "word": " هذه", "probability": 0.927734375}, {"start": 667.86, "end": 668.34, "word": " false", "probability": 0.9052734375}], "temperature": 1.0}, {"id": 24, "seek": 68833, "start": 670.83, "end": 688.33, "text": "لو بدلت divergent بconvergent برضه false الصح انها may converge or may diverge طيب العبارة الأخيرة تسعة", "tokens": [1211, 2407, 47525, 1211, 2655, 18558, 6930, 4724, 1671, 331, 6930, 4724, 43042, 3224, 7908, 31767, 5016, 16472, 11296, 815, 41881, 420, 815, 18558, 432, 23032, 1829, 3555, 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"text": "إذن هذا برهان الجزء التاني من السؤال الأول في عند هنا السؤال التاني question 2 الفرع a show S&T", "tokens": [28814, 8848, 1863, 23758, 4724, 2288, 3224, 7649, 25724, 11622, 38207, 16712, 7649, 1829, 9154, 21136, 33604, 6027, 16247, 12610, 8978, 43242, 34105, 21136, 33604, 6027, 16712, 7649, 1829, 1168, 568, 27188, 2288, 3615, 257, 855, 318, 5, 51], "avg_logprob": -0.28437499031424524, "compression_ratio": 1.3478260869565217, "no_speech_prob": 0.0, "words": [{"start": 973.89, "end": 974.25, "word": "إذن", "probability": 0.4686279296875}, {"start": 974.25, "end": 974.49, "word": " هذا", "probability": 0.92724609375}, {"start": 974.49, "end": 975.07, "word": " برهان", "probability": 0.8612060546875}, {"start": 975.07, "end": 975.61, "word": " الجزء", "probability": 0.876953125}, {"start": 975.61, "end": 976.45, "word": " التاني", "probability": 0.9241536458333334}, {"start": 976.45, "end": 976.91, "word": " من", "probability": 0.98974609375}, {"start": 976.91, "end": 977.65, 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"end": 1138.21, "word": " صح", "probability": 0.7183837890625}, {"start": 1138.21, "end": 1139.85, "word": " فلبرهان", "probability": 0.7212890625}, {"start": 1139.85, "end": 1140.81, "word": " ذلك", "probability": 0.99462890625}, {"start": 1140.81, "end": 1142.41, "word": " assume", "probability": 0.43896484375}, {"start": 1142.41, "end": 1144.23, "word": " بنعمل", "probability": 0.8865559895833334}, {"start": 1144.23, "end": 1144.59, "word": " برهان", "probability": 0.9871826171875}, {"start": 1144.59, "end": 1145.49, "word": " بالتناقض", "probability": 0.9791015625}, {"start": 1145.49, "end": 1146.99, "word": " on", "probability": 0.9033203125}, {"start": 1146.99, "end": 1147.71, "word": " contrary", "probability": 0.7939453125}], "temperature": 1.0}, {"id": 41, "seek": 117068, "start": 1149.52, "end": 1170.68, "text": "أفرضه على النقيد أن w أكبر من سفر then by Archimedean property .. by Archimedean property لأي عدد موجب زي هذا", "tokens": [10721, 5172, 43042, 3224, 15844, 28239, 38436, 3215, 14739, 261, 5551, 4117, 26890, 9154, 8608, 5172, 2288, 550, 538, 10984, 332, 4858, 282, 4707, 4386, 538, 10984, 332, 4858, 282, 4707, 5296, 10721, 1829, 6225, 3215, 3215, 3714, 29245, 3555, 30767, 1829, 23758], "avg_logprob": -0.2757457427003167, "compression_ratio": 1.2016129032258065, "no_speech_prob": 0.0, "words": [{"start": 1149.52, "end": 1150.12, "word": "أفرضه", "probability": 0.6683349609375}, {"start": 1150.12, "end": 1150.26, "word": " على", "probability": 0.90478515625}, {"start": 1150.26, "end": 1150.94, "word": " النقيد", "probability": 0.8466796875}, {"start": 1150.94, "end": 1151.28, "word": " أن", "probability": 0.189453125}, {"start": 1151.28, "end": 1151.88, "word": " w", "probability": 0.3017578125}, {"start": 1151.88, "end": 1153.66, "word": " أكبر", "probability": 0.87939453125}, {"start": 1153.66, "end": 1153.92, "word": " من", "probability": 0.99365234375}, {"start": 1153.92, "end": 1154.76, "word": " سفر", "probability": 0.8133138020833334}, 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"probability": 0.6461181640625}, {"start": 1194.21, "end": 1194.73, "word": " تربية", "probability": 0.9599609375}, {"start": 1194.73, "end": 1195.47, "word": " بالتأكيد", "probability": 0.96474609375}, {"start": 1195.47, "end": 1195.79, "word": " عدد", "probability": 0.994140625}, {"start": 1195.79, "end": 1196.25, "word": " موجب", "probability": 0.994140625}], "temperature": 1.0}, {"id": 43, "seek": 122224, "start": 1196.96, "end": 1222.24, "text": "فانا بطبّق الـ Archimedean property مش على w وعلى w تربية العدد الموجب w square فبقدر ألاقي by Archimedean property natural number n0 مقلوب وأصغر من w تربية طبعا هذا بيقدّي أن واحد على جذر n0 أصغر من w ومن ال", "tokens": [5172, 7649, 995, 4724, 9566, 3555, 11703, 4587, 2423, 39184, 10984, 332, 4858, 282, 4707, 37893, 15844, 261, 4032, 3615, 23942, 261, 6055, 25513, 10632, 18863, 3215, 3215, 9673, 29245, 3555, 261, 3732, 6156, 3555, 28543, 2288, 5551, 15040, 38436, 538, 10984, 332, 4858, 282, 4707, 3303, 1230, 297, 15, 3714, 4587, 1211, 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" w", "probability": 0.450439453125}, {"start": 1199.94, "end": 1200.22, "word": " وعلى", "probability": 0.6293131510416666}, {"start": 1200.22, "end": 1200.54, "word": " w", "probability": 0.7626953125}, {"start": 1200.54, "end": 1201.02, "word": " تربية", "probability": 0.8199869791666666}, {"start": 1201.02, "end": 1201.36, "word": " العدد", "probability": 0.8310546875}, {"start": 1201.36, "end": 1201.8, "word": " الموجب", "probability": 0.9519856770833334}, {"start": 1201.8, "end": 1202.18, "word": " w", "probability": 0.51611328125}, {"start": 1202.18, "end": 1202.84, "word": " square", "probability": 0.351806640625}, {"start": 1202.84, "end": 1204.68, "word": " فبقدر", "probability": 0.8797607421875}, {"start": 1204.68, "end": 1205.12, "word": " ألاقي", "probability": 0.74072265625}, {"start": 1205.12, "end": 1205.36, "word": " by", "probability": 0.56396484375}, {"start": 1205.36, "end": 1206.06, "word": " Archimedean", "probability": 0.9556884765625}, {"start": 1206.06, "end": 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"end": 1214.02, "word": " أن", "probability": 0.440185546875}, {"start": 1214.02, "end": 1214.86, "word": " واحد", "probability": 0.89697265625}, {"start": 1214.86, "end": 1215.22, "word": " على", "probability": 0.88916015625}, {"start": 1215.22, "end": 1215.9, "word": " جذر", "probability": 0.75537109375}, {"start": 1215.9, "end": 1218.08, "word": " n0", "probability": 0.811767578125}, {"start": 1218.08, "end": 1218.68, "word": " أصغر", "probability": 0.9739990234375}, {"start": 1218.68, "end": 1218.92, "word": " من", "probability": 0.99462890625}, {"start": 1218.92, "end": 1219.36, "word": " w", "probability": 0.8798828125}, {"start": 1219.36, "end": 1221.94, "word": " ومن", "probability": 0.90966796875}, {"start": 1221.94, "end": 1222.24, "word": " ال", "probability": 0.90869140625}], "temperature": 1.0}, {"id": 44, "seek": 125032, "start": 1226.3, "end": 1250.32, "text": "من الفرض الـ W هذا lower bound للست S وبالتالي هذا أصغر من أو سوى واحد على الجدر التربيهي ل N0 لأن هذا ينتمي ل S، هذا عنصر في S، صح؟ واحنا فرضين أن الـ W أشمل lower bound", "tokens": [27842, 27188, 43042, 2423, 39184, 343, 23758, 3126, 5472, 24976, 14851, 318, 46599, 6027, 2655, 6027, 1829, 23758, 5551, 9381, 17082, 2288, 9154, 34051, 8608, 2407, 7578, 36764, 24401, 15844, 25724, 3215, 2288, 16712, 2288, 21292, 3224, 1829, 5296, 426, 15, 5296, 33456, 23758, 7251, 29399, 2304, 1829, 5296, 318, 12399, 23758, 18871, 9381, 2288, 8978, 318, 12399, 20328, 5016, 22807, 4032, 39319, 8315, 6156, 43042, 9957, 14739, 2423, 39184, 343, 5551, 8592, 42213, 2295, 260, 5472], "avg_logprob": -0.27243590660584277, "compression_ratio": 1.5449438202247192, "no_speech_prob": 0.0, "words": [{"start": 1226.3, "end": 1226.66, "word": "من", "probability": 0.6181640625}, {"start": 1226.66, "end": 1227.26, "word": " الفرض", "probability": 0.95556640625}, {"start": 1227.26, "end": 1228.1, "word": " الـ", "probability": 0.627197265625}, {"start": 1228.1, "end": 1228.44, "word": " W", "probability": 0.33837890625}, 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في المجموع S إذا ال W كونه lower bound ل S أصغر من أو ساوي واحد على square root ل N0 فطبعا هذا بيدي ان واحد على square root ل N0 أصغر من واحد على square root ل N0 وهذا مدينة تناقض", "tokens": [1211, 19528, 7435, 2304, 45367, 318, 37037, 15730, 1867, 8978, 9673, 7435, 2304, 45367, 318, 11933, 15730, 2423, 343, 9122, 11536, 3224, 3126, 5472, 5296, 318, 5551, 9381, 17082, 2288, 9154, 34051, 8608, 995, 45865, 36764, 24401, 15844, 3732, 5593, 5296, 426, 15, 6156, 9566, 3555, 3615, 995, 23758, 4724, 25708, 1829, 16472, 36764, 24401, 15844, 3732, 5593, 5296, 426, 15, 5551, 9381, 17082, 2288, 9154, 36764, 24401, 15844, 3732, 5593, 5296, 426, 15, 37037, 15730, 3714, 3215, 9957, 3660, 6055, 8315, 4587, 11242], "avg_logprob": -0.18382353502161364, "compression_ratio": 1.739884393063584, "no_speech_prob": 0.0, "words": [{"start": 1251.23, "end": 1252.01, "word": "للمجموع", "probability": 0.818701171875}, {"start": 1252.01, "end": 1252.41, "word": " S", "probability": 0.7802734375}, {"start": 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"word": " على", "probability": 0.89111328125}, {"start": 1268.69, "end": 1269.15, "word": " square", "probability": 0.89013671875}, {"start": 1269.15, "end": 1269.69, "word": " root", "probability": 0.92724609375}, {"start": 1269.69, "end": 1271.05, "word": " ل", "probability": 0.974609375}, {"start": 1271.05, "end": 1272.45, "word": " N0", "probability": 0.9765625}, {"start": 1272.45, "end": 1273.97, "word": " وهذا", "probability": 0.8994140625}, {"start": 1273.97, "end": 1274.45, "word": " مدينة", "probability": 0.71478271484375}, {"start": 1274.45, "end": 1275.01, "word": " تناقض", "probability": 0.82275390625}], "temperature": 1.0}, {"id": 46, "seek": 130575, "start": 1276.61, "end": 1305.75, "text": "كيف عدد بيطلع أصغر من نفسه هذا تناقض لأن هذا التناقض بيقول لإن ال assumption تبعنا ان ال W أكبر من السفر خطأ وبالتالي ال W لازم يكون أصغر بدل ما هو أكبر من السفر يطلع أصغر من أو يساوي سفر وبالتالي ال W السفر هو أكبر lower bound okay إذا هذا بيكمل البرهان تمام", "tokens": [4117, 33911, 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"end": 1442.29, "word": " ألاقي", "probability": 0.8323567708333334}, {"start": 1442.29, "end": 1442.69, "word": " عدد", "probability": 0.9930013020833334}, {"start": 1442.69, "end": 1443.13, "word": " طبيعي", "probability": 0.95458984375}, {"start": 1443.13, "end": 1443.55, "word": " capital", "probability": 0.677734375}, {"start": 1443.55, "end": 1443.75, "word": " N", "probability": 0.87548828125}, {"start": 1443.75, "end": 1444.19, "word": " مقلوب", "probability": 0.935791015625}, {"start": 1444.19, "end": 1444.53, "word": " وأصغر", "probability": 0.863037109375}, {"start": 1444.53, "end": 1444.67, "word": " من", "probability": 0.99169921875}, {"start": 1444.67, "end": 1444.93, "word": " epsilon", "probability": 0.85498046875}, {"start": 1444.93, "end": 1445.47, "word": " تربية", "probability": 0.9837239583333334}, {"start": 1445.47, "end": 1447.55, "word": " ناشي", "probability": 0.7849934895833334}], "temperature": 1.0}, {"id": 51, "seek": 147676, "start": 1448.92, "end": 1476.76, "text": "بدا هنا given epsilon أكبر من السفر use الarchimedean property to choose n عدد طبيعي بحيث أن واحد على n أصغر من epsilon", "tokens": [3555, 28259, 34105, 2212, 17889, 5551, 4117, 26890, 9154, 21136, 5172, 2288, 764, 2423, 1178, 332, 4858, 282, 4707, 281, 2826, 297, 6225, 3215, 3215, 23032, 21292, 3615, 1829, 4724, 5016, 1829, 12984, 14739, 36764, 24401, 15844, 297, 5551, 9381, 17082, 2288, 9154, 17889], "avg_logprob": -0.3484374973509047, "compression_ratio": 1.1785714285714286, "no_speech_prob": 0.0, "words": [{"start": 1448.92, "end": 1449.7, "word": "بدا", "probability": 0.21490478515625}, {"start": 1449.7, "end": 1450.02, "word": " هنا", "probability": 0.87939453125}, {"start": 1450.02, "end": 1451.72, "word": " given", "probability": 0.517578125}, {"start": 1451.72, "end": 1455.32, "word": " epsilon", "probability": 0.249755859375}, {"start": 1455.32, "end": 1455.8, "word": " أكبر", "probability": 0.9171549479166666}, {"start": 1455.8, "end": 1456.0, "word": " من", "probability": 0.982421875}, {"start": 1456.0, "end": 1456.56, "word": " السفر", "probability": 0.8181966145833334}, {"start": 1456.56, "end": 1458.1, "word": " use", "probability": 0.57080078125}, {"start": 1458.1, "end": 1460.84, "word": " الarchimedean", "probability": 0.661492919921875}, {"start": 1460.84, "end": 1463.48, "word": " property", "probability": 0.97314453125}, {"start": 1463.48, "end": 1466.22, "word": " to", "probability": 0.87939453125}, {"start": 1466.22, "end": 1467.32, "word": " choose", "probability": 0.95654296875}, {"start": 1467.32, "end": 1469.88, "word": " n", "probability": 0.67724609375}, {"start": 1469.88, "end": 1470.4, "word": " عدد", "probability": 0.9820963541666666}, {"start": 1470.4, "end": 1471.28, "word": " طبيعي", "probability": 0.96630859375}, {"start": 1471.28, "end": 1473.3, "word": " بحيث", "probability": 0.9539794921875}, {"start": 1473.3, "end": 1473.5, "word": " أن", "probability": 0.365966796875}, {"start": 1473.5, "end": 1474.06, "word": " واحد", "probability": 0.936279296875}, {"start": 1474.06, "end": 1474.32, "word": " على", "probability": 0.71240234375}, {"start": 1474.32, "end": 1474.8, "word": " n", "probability": 0.4326171875}, {"start": 1474.8, "end": 1476.04, "word": " أصغر", "probability": 0.9859619140625}, {"start": 1476.04, "end": 1476.26, "word": " من", "probability": 0.99267578125}, {"start": 1476.26, "end": 1476.76, "word": " epsilon", "probability": 0.84228515625}], "temperature": 1.0}, {"id": 52, "seek": 150019, "start": 1479.75, "end": 1500.19, "text": "الان لو خدت small n أكبر من أو ساوي capital N فهذا بيقدي أن واحد على small n أصغر لو ساوي واحد على capital N", "tokens": [6027, 7649, 45164, 16490, 3215, 2655, 1359, 297, 5551, 4117, 26890, 9154, 34051, 8608, 995, 45865, 4238, 426, 6156, 3224, 15730, 4724, 1829, 4587, 16254, 14739, 36764, 24401, 15844, 1359, 297, 5551, 9381, 17082, 2288, 45164, 8608, 995, 45865, 36764, 24401, 15844, 4238, 426], "avg_logprob": -0.239062496026357, "compression_ratio": 1.3666666666666667, "no_speech_prob": 0.0, "words": [{"start": 1479.7499999999998, "end": 1480.6299999999999, "word": "الان", "probability": 0.3876953125}, {"start": 1480.6299999999999, "end": 1481.51, "word": " لو", "probability": 0.79443359375}, {"start": 1481.51, "end": 1481.97, "word": " خدت", "probability": 0.8058268229166666}, {"start": 1481.97, "end": 1482.43, "word": " small", "probability": 0.587890625}, {"start": 1482.43, "end": 1482.85, "word": " n", "probability": 0.68212890625}, {"start": 1482.85, "end": 1483.95, "word": " أكبر", "probability": 0.875}, {"start": 1483.95, "end": 1484.15, "word": " من", "probability": 0.841796875}, {"start": 1484.15, "end": 1484.31, "word": " أو", "probability": 0.72607421875}, {"start": 1484.31, "end": 1484.77, "word": " ساوي", "probability": 0.83349609375}, {"start": 1484.77, "end": 1485.21, "word": " capital", "probability": 0.59375}, {"start": 1485.21, "end": 1485.65, "word": " N", "probability": 0.81396484375}, {"start": 1485.65, "end": 1494.59, "word": " فهذا", "probability": 0.9583333333333334}, {"start": 1494.59, "end": 1495.21, "word": " بيقدي", "probability": 0.68408203125}, {"start": 1495.21, "end": 1496.37, "word": " أن", "probability": 0.409912109375}, {"start": 1496.37, "end": 1497.03, "word": " واحد", "probability": 0.841064453125}, {"start": 1497.03, "end": 1497.23, "word": " على", "probability": 0.7900390625}, {"start": 1497.23, "end": 1497.65, "word": " small", "probability": 0.9248046875}, {"start": 1497.65, "end": 1497.97, "word": " n", "probability": 0.833984375}, {"start": 1497.97, "end": 1498.43, "word": " أصغر", "probability": 0.9796142578125}, {"start": 1498.43, "end": 1498.65, "word": " لو", "probability": 0.822265625}, {"start": 1498.65, "end": 1498.97, "word": " ساوي", "probability": 0.93994140625}, {"start": 1498.97, "end": 1499.25, "word": " واحد", "probability": 0.986328125}, {"start": 1499.25, "end": 1499.41, "word": " على", "probability": 0.82177734375}, {"start": 1499.41, "end": 1499.81, "word": " capital", "probability": 0.73095703125}, {"start": 1499.81, "end": 1500.19, "word": " N", "probability": 0.97607421875}], "temperature": 1.0}, {"id": 53, "seek": 153425, "start": 1505.57, "end": 1534.25, "text": "بيقدي واحد على square root ل N أصغر من لو يساوي واحد على square root ل capital N وهذا بيقدي ان ال absolute value لواحد على square root ل N minus صفر بيساوي واحد على square root ل N وهذا أصغر من لو ي��اوي واحد على square root ل capital N وهذا من هنا", "tokens": [3555, 1829, 4587, 16254, 36764, 24401, 15844, 3732, 5593, 5296, 426, 5551, 9381, 17082, 2288, 9154, 45164, 7251, 3794, 995, 45865, 36764, 24401, 15844, 3732, 5593, 5296, 4238, 426, 37037, 15730, 4724, 1829, 4587, 16254, 16472, 2423, 8236, 2158, 5296, 14407, 24401, 15844, 3732, 5593, 5296, 426, 3175, 20328, 5172, 2288, 4724, 1829, 3794, 995, 45865, 36764, 24401, 15844, 3732, 5593, 5296, 426, 37037, 15730, 5551, 9381, 17082, 2288, 9154, 45164, 7251, 3794, 995, 45865, 36764, 24401, 15844, 3732, 5593, 5296, 4238, 426, 37037, 15730, 9154, 34105], "avg_logprob": -0.1738281227986921, "compression_ratio": 2.36, "no_speech_prob": 0.0, "words": [{"start": 1505.57, "end": 1506.21, "word": "بيقدي", "probability": 0.4837646484375}, {"start": 1506.21, "end": 1506.79, "word": " واحد", "probability": 0.79833984375}, {"start": 1506.79, "end": 1507.01, "word": " على", "probability": 0.65869140625}, {"start": 1507.01, "end": 1507.41, "word": " square", "probability": 0.79931640625}, {"start": 1507.41, "end": 1507.97, "word": " root", "probability": 0.90673828125}, {"start": 1507.97, "end": 1508.23, "word": " ل", "probability": 0.90869140625}, {"start": 1508.23, "end": 1508.51, "word": " N", "probability": 0.37646484375}, {"start": 1508.51, "end": 1509.01, "word": " أصغر", "probability": 0.9100341796875}, {"start": 1509.01, "end": 1509.13, "word": " من", "probability": 0.87158203125}, {"start": 1509.13, "end": 1509.27, "word": " لو", "probability": 0.38671875}, {"start": 1509.27, "end": 1509.57, "word": " يساوي", "probability": 0.7838134765625}, {"start": 1509.57, "end": 1510.07, "word": " واحد", "probability": 0.970947265625}, {"start": 1510.07, "end": 1511.25, "word": " على", "probability": 0.81396484375}, {"start": 1511.25, "end": 1511.65, "word": " square", "probability": 0.89990234375}, {"start": 1511.65, "end": 1512.03, "word": " root", "probability": 0.943359375}, {"start": 1512.03, "end": 1512.21, "word": " ل", "probability": 0.962890625}, {"start": 1512.21, "end": 1512.55, "word": " capital", "probability": 0.37744140625}, {"start": 1512.55, "end": 1512.87, "word": " N", "probability": 0.9560546875}, {"start": 1512.87, "end": 1515.31, "word": " وهذا", "probability": 0.847900390625}, {"start": 1515.31, "end": 1515.95, "word": " بيقدي", "probability": 0.8468017578125}, {"start": 1515.95, "end": 1516.31, "word": " ان", "probability": 0.49658203125}, {"start": 1516.31, "end": 1516.45, "word": " ال", "probability": 0.8681640625}, {"start": 1516.45, "end": 1516.89, "word": " absolute", "probability": 0.736328125}, {"start": 1516.89, "end": 1517.77, "word": " value", "probability": 0.99267578125}, {"start": 1517.77, "end": 1520.05, "word": " لواحد", "probability": 0.82666015625}, {"start": 1520.05, "end": 1520.31, "word": " على", "probability": 0.85498046875}, {"start": 1520.31, "end": 1520.81, "word": " square", "probability": 0.90966796875}, {"start": 1520.81, "end": 1521.33, "word": " root", "probability": 0.93408203125}, {"start": 1521.33, "end": 1521.59, "word": " ل", "probability": 0.9697265625}, {"start": 1521.59, "end": 1521.83, "word": " N", "probability": 0.89111328125}, {"start": 1521.83, "end": 1522.37, "word": " minus", "probability": 0.8349609375}, {"start": 1522.37, "end": 1523.65, "word": " صفر", "probability": 0.888671875}, {"start": 1523.65, "end": 1524.59, "word": " بيساوي", "probability": 0.8841796875}, {"start": 1524.59, "end": 1525.15, "word": " واحد", "probability": 0.9873046875}, {"start": 1525.15, "end": 1525.31, "word": " على", "probability": 0.86474609375}, {"start": 1525.31, "end": 1525.73, "word": " square", "probability": 0.9248046875}, {"start": 1525.73, "end": 1526.15, "word": " root", "probability": 0.93017578125}, {"start": 1526.15, "end": 1526.39, "word": " ل", "probability": 0.97705078125}, {"start": 1526.39, "end": 1526.63, "word": " N", "probability": 0.93359375}, {"start": 1526.63, "end": 1527.05, "word": " وهذا", "probability": 0.91357421875}, {"start": 1527.05, "end": 1527.51, "word": " أصغر", "probability": 0.9525146484375}, {"start": 1527.51, "end": 1527.65, "word": " من", "probability": 0.96923828125}, {"start": 1527.65, "end": 1527.79, "word": " لو", "probability": 0.98681640625}, {"start": 1527.79, "end": 1528.41, "word": " يساوي", "probability": 0.982666015625}, {"start": 1528.41, "end": 1529.61, "word": " واحد", "probability": 0.986572265625}, {"start": 1529.61, "end": 1529.77, "word": " على", "probability": 0.87646484375}, {"start": 1529.77, "end": 1530.17, "word": " square", "probability": 0.927734375}, {"start": 1530.17, "end": 1530.59, "word": " root", "probability": 0.92333984375}, {"start": 1530.59, "end": 1530.77, "word": " ل", "probability": 0.98681640625}, {"start": 1530.77, "end": 1531.17, "word": " capital", "probability": 0.72216796875}, {"start": 1531.17, "end": 1531.67, "word": " N", "probability": 0.99560546875}, {"start": 1531.67, "end": 1533.71, "word": " وهذا", "probability": 0.95654296875}, {"start": 1533.71, "end": 1533.93, "word": " من", "probability": 0.98046875}, {"start": 1533.93, "end": 1534.25, "word": " هنا", "probability": 0.99755859375}], "temperature": 1.0}, {"id": 54, "seek": 156390, "start": 1536.26, "end": 1563.9, "text": "لو سمينا الـ inequality هذه الـ star إذا by star واحد على square root ل N أصغر من epsilon إذا هاي نحققنا تعريف epsilon capital N للنهايات for any given epsilon أثبتنا إنه يوجد capital N عدد طبيعي وهذا العدد الطبيعي يعتمد على epsilon هاي مرتبط بepsilon", "tokens": [1211, 2407, 8608, 2304, 1829, 8315, 2423, 39184, 16970, 29538, 2423, 39184, 3543, 11933, 15730, 538, 3543, 36764, 24401, 15844, 3732, 5593, 5296, 426, 5551, 9381, 17082, 2288, 9154, 17889, 11933, 15730, 8032, 47302, 8717, 5016, 4587, 4587, 8315, 37279, 16572, 5172, 17889, 4238, 426, 24976, 1863, 11296, 1829, 9307, 337, 604, 2212, 17889, 5551, 12984, 3555, 2655, 8315, 36145, 3224, 7251, 29245, 3215, 4238, 426, 6225, 3215, 3215, 23032, 21292, 3615, 1829, 37037, 15730, 18863, 3215, 3215, 41950, 21292, 3615, 1829, 7251, 34268, 2304, 3215, 15844, 17889, 8032, 47302, 3714, 43500, 3555, 9566, 4724, 10653, 15754], "avg_logprob": -0.23007014925990785, "compression_ratio": 1.6133333333333333, "no_speech_prob": 0.0, "words": [{"start": 1536.26, "end": 1536.62, "word": "لو", "probability": 0.743408203125}, {"start": 1536.62, "end": 1537.06, "word": " سمينا", "probability": 0.79901123046875}, {"start": 1537.06, "end": 1537.18, "word": " الـ", "probability": 0.6502685546875}, {"start": 1537.18, "end": 1537.62, "word": " inequality", "probability": 0.7763671875}, {"start": 1537.62, "end": 1538.0, "word": " هذه", "probability": 0.242431640625}, {"start": 1538.0, "end": 1538.16, "word": " الـ", "probability": 0.745361328125}, {"start": 1538.16, "end": 1538.52, "word": " star", "probability": 0.595703125}, {"start": 1538.52, "end": 1539.66, "word": " إذا", "probability": 0.5701904296875}, {"start": 1539.66, "end": 1540.04, "word": " by", "probability": 0.495361328125}, {"start": 1540.04, "end": 1540.76, "word": " star", "probability": 0.71728515625}, {"start": 1540.76, "end": 1542.76, "word": " واحد", "probability": 0.76513671875}, {"start": 1542.76, "end": 1542.92, "word": " على", "probability": 0.71533203125}, {"start": 1542.92, "end": 1543.24, "word": " square", "probability": 0.7294921875}, {"start": 1543.24, "end": 1543.64, "word": " root", "probability": 0.92333984375}, {"start": 1543.64, "end": 1543.82, "word": " ل", "probability": 0.93017578125}, {"start": 1543.82, "end": 1544.02, "word": " N", "probability": 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0.8828125}, {"start": 1553.44, "end": 1553.7, "word": " any", "probability": 0.93310546875}, {"start": 1553.7, "end": 1554.04, "word": " given", "probability": 0.90576171875}, {"start": 1554.04, "end": 1554.54, "word": " epsilon", "probability": 0.95849609375}, {"start": 1554.54, "end": 1555.14, "word": " أثبتنا", "probability": 0.9875}, {"start": 1555.14, "end": 1555.42, "word": " إنه", "probability": 0.4730224609375}, {"start": 1555.42, "end": 1555.84, "word": " يوجد", "probability": 0.9847005208333334}, {"start": 1555.84, "end": 1556.28, "word": " capital", "probability": 0.74462890625}, {"start": 1556.28, "end": 1556.74, "word": " N", "probability": 0.96435546875}, {"start": 1556.74, "end": 1558.6, "word": " عدد", "probability": 0.7327473958333334}, {"start": 1558.6, "end": 1559.28, "word": " طبيعي", "probability": 0.982421875}, {"start": 1559.28, "end": 1560.38, "word": " وهذا", "probability": 0.811279296875}, {"start": 1560.38, "end": 1560.76, "word": " العدد", "probability": 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1587.83, "word": " على", "probability": 0.578125}, {"start": 1587.83, "end": 1588.23, "word": " square", "probability": 0.88671875}, {"start": 1588.23, "end": 1588.69, "word": " root", "probability": 0.91796875}, {"start": 1588.69, "end": 1588.91, "word": " ل", "probability": 0.9072265625}, {"start": 1588.91, "end": 1589.19, "word": " n", "probability": 0.39501953125}, {"start": 1589.19, "end": 1590.49, "word": " بساوي", "probability": 0.9053955078125}, {"start": 1590.49, "end": 1590.93, "word": " سفر", "probability": 0.97314453125}, {"start": 1590.93, "end": 1591.25, "word": " وهو", "probability": 0.764404296875}, {"start": 1591.25, "end": 1591.83, "word": " المطلوب", "probability": 0.9893798828125}, {"start": 1591.83, "end": 1593.29, "word": " طبعا", "probability": 0.8341064453125}], "temperature": 1.0}, {"id": 56, "seek": 162435, "start": 1597.55, "end": 1624.35, "text": "طبعاً في حال تاني أو في برهان تاني باستخدام الـ monotone convergence theorem إذا ال solution to use monotone convergence theorem ال sequence أنا عندي xn بساوي واحد على square root ل n", "tokens": [9566, 3555, 3615, 995, 14111, 8978, 11331, 6027, 6055, 7649, 1829, 34051, 8978, 4724, 2288, 3224, 7649, 6055, 7649, 1829, 4724, 995, 14851, 9778, 3215, 10943, 2423, 39184, 1108, 310, 546, 32181, 20904, 11933, 15730, 2423, 3827, 281, 764, 1108, 310, 546, 32181, 20904, 2423, 8310, 41850, 18871, 16254, 2031, 77, 4724, 3794, 995, 45865, 36764, 24401, 15844, 3732, 5593, 5296, 297], "avg_logprob": -0.26041666761277216, "compression_ratio": 1.503030303030303, "no_speech_prob": 0.0, "words": [{"start": 1597.55, "end": 1597.97, "word": "طبعاً", "probability": 0.756982421875}, {"start": 1597.97, "end": 1598.07, "word": " في", "probability": 0.77978515625}, {"start": 1598.07, "end": 1598.43, "word": " حال", "probability": 0.7939453125}, {"start": 1598.43, "end": 1599.07, "word": " تاني", "probability": 0.8639322916666666}, {"start": 1599.07, "end": 1599.61, "word": " أو", "probability": 0.49462890625}, {"start": 1599.61, "end": 1599.79, "word": " في", "probability": 0.84228515625}, {"start": 1599.79, "end": 1600.15, "word": " برهان", "probability": 0.8060302734375}, {"start": 1600.15, "end": 1600.73, "word": " تاني", "probability": 0.9918619791666666}, {"start": 1600.73, "end": 1602.23, "word": " باستخدام", "probability": 0.9806315104166666}, {"start": 1602.23, "end": 1602.93, "word": " الـ", "probability": 0.777099609375}, {"start": 1602.93, "end": 1603.41, "word": " monotone", "probability": 0.77392578125}, {"start": 1603.41, "end": 1604.15, "word": " convergence", "probability": 0.943359375}, {"start": 1604.15, "end": 1604.75, "word": " theorem", "probability": 0.8994140625}, {"start": 1604.75, "end": 1608.77, "word": " إذا", "probability": 0.506591796875}, {"start": 1608.77, "end": 1609.21, "word": " ال", "probability": 0.35400390625}, {"start": 1609.21, "end": 1610.15, "word": " solution", "probability": 0.9072265625}, {"start": 1610.15, "end": 1611.23, "word": " to", "probability": 0.28662109375}, {"start": 1611.23, "end": 1614.35, "word": " use", "probability": 0.87744140625}, {"start": 1614.35, "end": 1615.87, "word": " monotone", "probability": 0.9811197916666666}, {"start": 1615.87, "end": 1617.57, "word": " convergence", "probability": 0.9326171875}, {"start": 1617.57, "end": 1618.21, "word": " theorem", "probability": 0.82373046875}, {"start": 1618.21, "end": 1620.05, "word": " ال", "probability": 0.69091796875}, {"start": 1620.05, "end": 1620.51, "word": " sequence", "probability": 0.849609375}, {"start": 1620.51, "end": 1620.75, "word": " أنا", "probability": 0.564453125}, {"start": 1620.75, "end": 1621.09, "word": " عندي", "probability": 0.9287109375}, {"start": 1621.09, "end": 1621.81, "word": " xn", "probability": 0.42919921875}, {"start": 1621.81, "end": 1622.45, "word": " بساوي", "probability": 0.65203857421875}, {"start": 1622.45, "end": 1622.93, "word": " واحد", "probability": 0.888671875}, {"start": 1622.93, "end": 1623.15, "word": " على", "probability": 0.69189453125}, {"start": 1623.15, "end": 1623.49, "word": " square", "probability": 0.82421875}, {"start": 1623.49, "end": 1623.89, "word": " root", "probability": 0.91162109375}, {"start": 1623.89, "end": 1624.11, "word": " ل", "probability": 0.8701171875}, {"start": 1624.11, "end": 1624.35, "word": " n", "probability": 0.405029296875}], "temperature": 1.0}, {"id": 57, "seek": 164855, "start": 1629.01, "end": 1648.55, "text": "هذا أكبر من أو ساوي واحد على square root ل n زايد واحد اللي هو xn زايد واحد وبالتالي ال sequence is decreasing صح؟", "tokens": [3224, 15730, 5551, 4117, 26890, 9154, 34051, 8608, 995, 45865, 36764, 24401, 15844, 3732, 5593, 5296, 297, 30767, 995, 25708, 36764, 24401, 13672, 1829, 31439, 2031, 77, 30767, 995, 25708, 36764, 24401, 46599, 6027, 2655, 6027, 1829, 2423, 8310, 307, 23223, 20328, 5016, 22807], "avg_logprob": -0.1500868108537462, "compression_ratio": 1.323076923076923, "no_speech_prob": 0.0, "words": [{"start": 1629.0100000000002, "end": 1630.0700000000002, "word": "هذا", "probability": 0.893310546875}, {"start": 1630.0700000000002, "end": 1631.13, "word": " أكبر", "probability": 0.87109375}, {"start": 1631.13, "end": 1631.39, "word": " من", "probability": 0.98291015625}, {"start": 1631.39, "end": 1631.59, "word": " أو", "probability": 0.9501953125}, {"start": 1631.59, "end": 1632.11, "word": " ساوي", "probability": 0.7522786458333334}, {"start": 1632.11, "end": 1632.65, "word": " واحد", "probability": 0.944091796875}, {"start": 1632.65, "end": 1632.83, "word": " على", "probability": 0.70849609375}, {"start": 1632.83, "end": 1633.21, "word": " square", "probability": 0.73486328125}, {"start": 1633.21, "end": 1633.73, "word": " root", "probability": 0.91845703125}, {"start": 1633.73, "end": 1633.93, "word": " ل", "probability": 0.82177734375}, {"start": 1633.93, "end": 1634.15, "word": " n", "probability": 0.280517578125}, {"start": 1634.15, "end": 1634.59, "word": " زايد", "probability": 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"probability": 0.8836263020833334}], "temperature": 1.0}, {"id": 58, "seek": 167910, "start": 1649.8, "end": 1679.1, "text": "بعدين انا عندي absolute xn بساوي absolute واحد على جدر ال n أصغر من أو ساوي واحد لكل n لكل n فهذا بيقدي ان ال sequence xn is bounded اذا bounded و decrease in", "tokens": [3555, 22488, 9957, 1975, 8315, 18871, 16254, 8236, 2031, 77, 4724, 3794, 995, 45865, 8236, 36764, 24401, 15844, 10874, 3215, 2288, 2423, 297, 5551, 9381, 17082, 2288, 9154, 34051, 8608, 995, 45865, 36764, 24401, 5296, 28820, 297, 5296, 28820, 297, 6156, 3224, 15730, 4724, 1829, 4587, 16254, 16472, 2423, 8310, 2031, 77, 307, 37498, 1975, 15730, 37498, 4032, 11514, 294], "avg_logprob": -0.22989241314716027, "compression_ratio": 1.4675324675324675, "no_speech_prob": 0.0, "words": [{"start": 1649.8, "end": 1650.36, "word": "بعدين", "probability": 0.81298828125}, {"start": 1650.36, "end": 1650.48, "word": " انا", "probability": 0.5904541015625}, {"start": 1650.48, "end": 1650.78, "word": " عندي", "probability": 0.887451171875}, {"start": 1650.78, "end": 1651.24, "word": " absolute", "probability": 0.74853515625}, {"start": 1651.24, "end": 1652.22, "word": " xn", "probability": 0.4544677734375}, {"start": 1652.22, "end": 1652.9, "word": " بساوي", "probability": 0.78564453125}, {"start": 1652.9, "end": 1653.44, "word": " absolute", "probability": 0.71826171875}, {"start": 1653.44, "end": 1654.1, "word": " واحد", "probability": 0.938232421875}, {"start": 1654.1, "end": 1654.28, "word": " على", "probability": 0.67138671875}, {"start": 1654.28, "end": 1654.78, "word": " جدر", "probability": 0.8649088541666666}, {"start": 1654.78, "end": 1654.96, "word": " ال", "probability": 0.8935546875}, {"start": 1654.96, "end": 1655.26, "word": " n", "probability": 0.58837890625}, {"start": 1655.26, "end": 1656.8, "word": " أصغر", "probability": 0.8865966796875}, {"start": 1656.8, "end": 1656.98, "word": " من", "probability": 0.970703125}, {"start": 1656.98, "end": 1657.18, "word": " أو", "probability": 0.74072265625}, {"start": 1657.18, "end": 1657.68, "word": " ساوي", "probability": 0.93359375}, {"start": 1657.68, "end": 1658.3, "word": " واحد", "probability": 0.980224609375}, {"start": 1658.3, "end": 1660.74, "word": " لكل", "probability": 0.982666015625}, {"start": 1660.74, "end": 1661.08, "word": " n", "probability": 0.84228515625}, {"start": 1661.08, "end": 1667.12, "word": " لكل", "probability": 0.896240234375}, {"start": 1667.12, "end": 1667.54, "word": " n", "probability": 0.919921875}, {"start": 1667.54, "end": 1670.34, "word": " فهذا", "probability": 0.9306640625}, {"start": 1670.34, "end": 1670.86, "word": " بيقدي", "probability": 0.66094970703125}, {"start": 1670.86, "end": 1671.1, "word": " ان", "probability": 0.712890625}, {"start": 1671.1, "end": 1671.28, "word": " ال", "probability": 0.638671875}, {"start": 1671.28, "end": 1671.76, "word": " sequence", "probability": 0.9609375}, {"start": 1671.76, "end": 1672.74, "word": " xn", "probability": 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5296, 2031, 77, 11331, 1829, 12984, 297, 7251, 29399, 2304, 1829, 30731, 297, 6156, 10721, 12984, 3555, 2655, 8315, 14739, 2423, 7649, 5172, 2304, 10943, 4724, 3794, 995, 2407, 3660, 8608, 5172, 2288, 20666, 5172, 2288, 3615, 13672, 1829, 10874, 16758, 43761], "avg_logprob": -0.27581520875295, "compression_ratio": 1.3821656050955413, "no_speech_prob": 0.0, "words": [{"start": 1680.09, "end": 1680.43, "word": "إذا", "probability": 0.51727294921875}, {"start": 1680.43, "end": 1680.65, "word": " الـ", "probability": 0.686279296875}, {"start": 1680.65, "end": 1681.17, "word": " sequence", "probability": 0.732421875}, {"start": 1681.17, "end": 1682.49, "word": " xn", "probability": 0.4052734375}, {"start": 1682.49, "end": 1682.75, "word": " by", "probability": 0.57275390625}, {"start": 1682.75, "end": 1683.39, "word": " monotone", "probability": 0.8846028645833334}, {"start": 1683.39, "end": 1684.03, "word": " convergence", "probability": 0.9638671875}, {"start": 1684.03, "end": 1684.57, "word": " theorem", "probability": 0.9072265625}, {"start": 1684.57, "end": 1686.25, "word": " limit", "probability": 0.87890625}, {"start": 1686.25, "end": 1686.97, "word": " xn", "probability": 0.964599609375}, {"start": 1686.97, "end": 1687.69, "word": " بساوة", "probability": 0.624462890625}, {"start": 1687.69, "end": 1688.49, "word": " الانفمام", "probability": 0.65867919921875}, {"start": 1688.49, "end": 1691.31, "word": " ل", "probability": 0.9443359375}, {"start": 1691.31, "end": 1692.35, "word": " xn", "probability": 0.74658203125}, {"start": 1692.35, "end": 1692.89, "word": " حيث", "probability": 0.9827473958333334}, {"start": 1692.89, "end": 1693.19, "word": " n", "probability": 0.7314453125}, {"start": 1693.19, "end": 1694.01, "word": " ينتمي", "probability": 0.95654296875}, {"start": 1694.01, "end": 1694.23, "word": " إلى", "probability": 0.89990234375}, {"start": 1694.23, "end": 1694.59, "word": " n", "probability": 0.64453125}, {"start": 1694.59, "end": 1697.53, "word": " فأثبتنا", "probability": 0.7340494791666666}, {"start": 1697.53, "end": 1697.71, "word": " أن", "probability": 0.420166015625}, {"start": 1697.71, "end": 1698.33, "word": " الانفمام", "probability": 0.95625}, {"start": 1698.33, "end": 1698.85, "word": " بساوة", "probability": 0.941015625}, {"start": 1698.85, "end": 1699.25, "word": " سفر", "probability": 0.7820638020833334}, {"start": 1699.25, "end": 1701.47, "word": " بالفرع", "probability": 0.79779052734375}, {"start": 1701.47, "end": 1701.65, "word": " اللي", "probability": 0.93505859375}, {"start": 1701.65, "end": 1702.07, "word": " جابله", "probability": 0.8919270833333334}], "temperature": 1.0}, {"id": 60, "seek": 172640, "start": 1704.0, "end": 1726.4, "text": "فهذا برهان تاني لكن احنا ال .. ال monotone convergence الكلام مش داخله في الامتحان فممكن انكم يعني ال .. تستخدموا البرهان الأول يعني ممكن تستخدموا البرهان الأول يعني okay تمام طيب نكمل", "tokens": [5172, 3224, 15730, 4724, 2288, 3224, 7649, 6055, 7649, 1829, 44381, 1975, 5016, 8315, 2423, 4386, 2423, 1108, 310, 546, 32181, 2423, 28820, 10943, 37893, 11778, 47283, 43761, 8978, 2423, 10943, 2655, 5016, 7649, 6156, 2304, 43020, 16472, 24793, 37495, 22653, 2423, 4386, 6055, 14851, 9778, 40448, 14407, 2423, 26890, 3224, 7649, 16247, 12610, 37495, 22653, 3714, 43020, 6055, 14851, 9778, 40448, 14407, 2423, 26890, 3224, 7649, 16247, 12610, 37495, 22653, 1392, 46811, 10943, 23032, 1829, 3555, 8717, 24793, 1211], "avg_logprob": -0.16763117578294542, "compression_ratio": 1.8176470588235294, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1704.0, "end": 1704.36, "word": "فهذا", "probability": 0.8424479166666666}, {"start": 1704.36, "end": 1704.76, "word": " برهان", "probability": 0.957275390625}, {"start": 1704.76, "end": 1705.12, "word": " تاني", "probability": 0.9134114583333334}, {"start": 1705.12, "end": 1705.36, "word": " لكن", "probability": 0.68115234375}, {"start": 1705.36, "end": 1705.8, "word": " احنا", "probability": 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0.751220703125}, {"start": 1712.84, "end": 1713.3, "word": " يعني", "probability": 0.952880859375}, {"start": 1713.3, "end": 1713.76, "word": " ال", "probability": 0.89453125}, {"start": 1713.76, "end": 1714.86, "word": " ..", "probability": 0.8505859375}, {"start": 1714.86, "end": 1715.92, "word": " تستخدموا", "probability": 0.97861328125}, {"start": 1715.92, "end": 1716.42, "word": " البرهان", "probability": 0.9447021484375}, {"start": 1716.42, "end": 1716.8, "word": " الأول", "probability": 0.82421875}, {"start": 1716.8, "end": 1717.12, "word": " يعني", "probability": 0.760986328125}, {"start": 1717.12, "end": 1717.54, "word": " ممكن", "probability": 0.78857421875}, {"start": 1717.54, "end": 1718.12, "word": " تستخدموا", "probability": 0.94560546875}, {"start": 1718.12, "end": 1718.58, "word": " البرهان", "probability": 0.978515625}, {"start": 1718.58, "end": 1718.98, "word": " الأول", "probability": 0.964111328125}, {"start": 1718.98, "end": 1719.3, "word": " يعني", "probability": 0.861083984375}, {"start": 1719.3, "end": 1722.36, "word": " okay", "probability": 0.56591796875}, {"start": 1722.36, "end": 1722.92, "word": " تمام", "probability": 0.94580078125}, {"start": 1722.92, "end": 1725.66, "word": " طيب", "probability": 0.8828125}, {"start": 1725.66, "end": 1726.4, "word": " نكمل", "probability": 0.896484375}], "temperature": 1.0}, {"id": 61, "seek": 177410, "start": 1749.04, "end": 1774.1, "text": "find the supremum الجزء C بإنه نوجد ال supremum لواحد سالب واحد على الجدر ال N حيث N ينتمي ل N فهذا حسب exercise أخدنا supremum A زائد 6 بساوي A زائد supremum", "tokens": [35072, 264, 23710, 449, 25724, 11622, 38207, 383, 4724, 28814, 1863, 3224, 8717, 29245, 3215, 2423, 23710, 449, 5296, 14407, 24401, 8608, 6027, 3555, 36764, 24401, 15844, 25724, 3215, 2288, 2423, 426, 11331, 1829, 12984, 426, 7251, 29399, 2304, 1829, 5296, 426, 6156, 3224, 15730, 11331, 35457, 5380, 5551, 9778, 3215, 8315, 23710, 449, 316, 30767, 16373, 3215, 1386, 4724, 3794, 995, 45865, 316, 30767, 16373, 3215, 23710, 449], "avg_logprob": -0.25468750170298987, "compression_ratio": 1.4743589743589745, "no_speech_prob": 0.0, "words": [{"start": 1749.04, "end": 1750.0, "word": "find", "probability": 0.37939453125}, {"start": 1750.0, "end": 1750.3, "word": " the", "probability": 0.22900390625}, {"start": 1750.3, "end": 1750.92, "word": " supremum", "probability": 0.8798828125}, {"start": 1750.92, "end": 1752.02, "word": " الجزء", "probability": 0.85498046875}, {"start": 1752.02, "end": 1752.4, "word": " C", "probability": 0.521484375}, {"start": 1752.4, "end": 1753.9, "word": " بإنه", "probability": 0.54803466796875}, {"start": 1753.9, "end": 1754.2, "word": " نوجد", "probability": 0.9217122395833334}, {"start": 1754.2, "end": 1754.4, "word": " ال", "probability": 0.439208984375}, {"start": 1754.4, "end": 1755.54, "word": " supremum", "probability": 0.8408203125}, {"start": 1755.54, "end": 1756.64, "word": " لواحد", "probability": 0.628173828125}, {"start": 1756.64, "end": 1757.14, "word": " سالب", "probability": 0.84716796875}, {"start": 1757.14, "end": 1757.56, "word": " واحد", "probability": 0.978515625}, {"start": 1757.56, "end": 1757.76, "word": " على", "probability": 0.8837890625}, {"start": 1757.76, "end": 1758.24, "word": " الجدر", "probability": 0.9065755208333334}, {"start": 1758.24, "end": 1758.4, "word": " ال", "probability": 0.42626953125}, {"start": 1758.4, "end": 1758.7, "word": " N", "probability": 0.73193359375}, {"start": 1758.7, "end": 1759.28, "word": " حيث", "probability": 0.9700520833333334}, {"start": 1759.28, "end": 1759.6, "word": " N", "probability": 0.3291015625}, {"start": 1759.6, "end": 1760.28, "word": " ينتمي", "probability": 0.9725341796875}, {"start": 1760.28, "end": 1760.48, "word": " ل", "probability": 0.438232421875}, {"start": 1760.48, "end": 1760.8, "word": " N", "probability": 0.72900390625}, {"start": 1760.8, "end": 1763.78, "word": " فهذا", "probability": 0.9415690104166666}, {"start": 1763.78, "end": 1764.28, "word": " حسب", "probability": 0.98291015625}, {"start": 1764.28, "end": 1766.44, "word": " exercise", "probability": 0.75048828125}, {"start": 1766.44, "end": 1766.98, "word": " أخدنا", "probability": 0.938232421875}, {"start": 1766.98, "end": 1768.7, "word": " supremum", "probability": 0.748291015625}, {"start": 1768.7, "end": 1769.08, "word": " A", "probability": 0.59375}, {"start": 1769.08, "end": 1769.7, "word": " زائد", "probability": 0.8634440104166666}, {"start": 1769.7, "end": 1770.22, "word": " 6", "probability": 0.81787109375}, {"start": 1770.22, "end": 1772.2, "word": " بساوي", "probability": 0.8326416015625}, {"start": 1772.2, "end": 1772.62, "word": " A", "probability": 0.8466796875}, {"start": 1772.62, "end": 1773.32, "word": " زائد", "probability": 0.9568684895833334}, {"start": 1773.32, "end": 1774.1, "word": " supremum", "probability": 0.893310546875}], "temperature": 1.0}, {"id": 62, "seek": 179664, "start": 1776.02, "end": 1796.64, "text": "الست اللي هي عناصرها سالب واحد على جدر ال N هيف N ينتمي الى N ويساوي واحد الان supremum سالب ست بيساوي سالب ال infimum لعناصر الست", "tokens": [6027, 14851, 13672, 1829, 39896, 18871, 33546, 2288, 11296, 8608, 6027, 3555, 36764, 24401, 15844, 10874, 3215, 2288, 2423, 426, 39896, 5172, 426, 7251, 29399, 2304, 1829, 2423, 7578, 426, 4032, 1829, 3794, 995, 45865, 36764, 24401, 2423, 7649, 23710, 449, 8608, 6027, 3555, 8608, 2655, 4724, 1829, 3794, 995, 45865, 8608, 6027, 3555, 2423, 1536, 332, 449, 5296, 3615, 1863, 33546, 2288, 2423, 14851], "avg_logprob": -0.29521781386751117, "compression_ratio": 1.588235294117647, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1776.02, "end": 1776.64, "word": "الست", "probability": 0.734130859375}, {"start": 1776.64, "end": 1776.86, "word": " اللي", "probability": 0.55908203125}, {"start": 1776.86, "end": 1777.0, "word": " هي", "probability": 0.828125}, {"start": 1777.0, "end": 1777.58, "word": " عناصرها", "probability": 0.9691162109375}, {"start": 1777.58, "end": 1778.0, "word": " سالب", "probability": 0.8474934895833334}, {"start": 1778.0, "end": 1778.44, "word": " واحد", "probability": 0.982666015625}, {"start": 1778.44, "end": 1778.64, "word": " على", "probability": 0.76513671875}, {"start": 1778.64, "end": 1779.2, "word": " جدر", "probability": 0.7694498697916666}, {"start": 1779.2, "end": 1779.38, "word": " ال", "probability": 0.94091796875}, {"start": 1779.38, "end": 1779.7, "word": " N", "probability": 0.364501953125}, {"start": 1779.7, "end": 1781.02, "word": " هيف", "probability": 0.34503173828125}, {"start": 1781.02, "end": 1781.24, "word": " N", "probability": 0.380859375}, {"start": 1781.24, "end": 1781.92, "word": " ينتمي", "probability": 0.968505859375}, {"start": 1781.92, "end": 1782.24, "word": " الى", "probability": 0.596435546875}, {"start": 1782.24, "end": 1782.52, "word": " N", "probability": 0.626953125}, {"start": 1782.52, "end": 1785.22, "word": " ويساوي", "probability": 0.791796875}, {"start": 1785.22, "end": 1788.18, "word": " واحد", "probability": 0.961181640625}, {"start": 1788.18, "end": 1788.8, "word": " الان", "probability": 0.5023193359375}, {"start": 1788.8, "end": 1789.56, "word": " supremum", "probability": 0.6082763671875}, {"start": 1789.56, "end": 1790.12, "word": " سالب", "probability": 0.9562174479166666}, {"start": 1790.12, "end": 1790.56, "word": " ست", "probability": 0.8544921875}, {"start": 1790.56, "end": 1792.36, "word": " بيساوي", "probability": 0.827294921875}, {"start": 1792.36, "end": 1792.94, "word": " سالب", "probability": 0.9593098958333334}, {"start": 1792.94, "end": 1793.14, "word": " ال", "probability": 0.841796875}, {"start": 1793.14, "end": 1793.9, "word": " infimum", "probability": 0.7963053385416666}, {"start": 1793.9, "end": 1796.14, "word": " لعناصر", "probability": 0.8015625}, {"start": 1796.14, "end": 1796.64, "word": " الست", "probability": 0.75537109375}], "temperature": 1.0}, {"id": 63, "seek": 183057, "start": 1805.05, "end": 1830.57, "text": "و احنا لسه مثبتين ان ال inform هذا بساوي سفر اذا ال suprem للست هذي بطلع واحد طيب فرقة تانية show that اثبتي انه limit cosine n على n او على جدر ال n", "tokens": [2407, 1975, 5016, 8315, 5296, 3794, 3224, 3714, 12984, 3555, 2655, 9957, 16472, 2423, 1356, 23758, 4724, 3794, 995, 45865, 8608, 5172, 2288, 1975, 15730, 2423, 23710, 24976, 14851, 8032, 8848, 1829, 4724, 9566, 1211, 3615, 36764, 24401, 23032, 1829, 3555, 6156, 2288, 28671, 6055, 7649, 10632, 855, 300, 1975, 12984, 3555, 31371, 16472, 3224, 4948, 23565, 297, 15844, 297, 1975, 2407, 15844, 10874, 3215, 2288, 2423, 297], "avg_logprob": -0.2461503657741823, "compression_ratio": 1.4171779141104295, "no_speech_prob": 0.0, "words": [{"start": 1805.05, "end": 1805.31, "word": "و", "probability": 0.5537109375}, {"start": 1805.31, "end": 1805.57, "word": " احنا", "probability": 0.7749837239583334}, {"start": 1805.57, "end": 1805.87, "word": " لسه", "probability": 0.9192708333333334}, {"start": 1805.87, "end": 1806.51, "word": " مثبتين", "probability": 0.88857421875}, {"start": 1806.51, "end": 1806.67, "word": " ان", "probability": 0.89404296875}, {"start": 1806.67, "end": 1806.83, "word": " ال", "probability": 0.8984375}, {"start": 1806.83, "end": 1807.13, "word": " inform", "probability": 0.2303466796875}, {"start": 1807.13, "end": 1807.59, "word": " هذا", "probability": 0.79052734375}, {"start": 1807.59, "end": 1808.21, "word": " بساوي", "probability": 0.787841796875}, {"start": 1808.21, "end": 1808.75, "word": " سفر", "probability": 0.8240559895833334}, {"start": 1808.75, "end": 1809.91, "word": " اذا", "probability": 0.51788330078125}, {"start": 1809.91, "end": 1810.13, "word": " ال", "probability": 0.82177734375}, {"start": 1810.13, "end": 1810.45, "word": " suprem", "probability": 0.57470703125}, {"start": 1810.45, "end": 1811.11, "word": " للست", "probability": 0.755615234375}, {"start": 1811.11, "end": 1811.35, "word": " هذي", "probability": 0.5591634114583334}, {"start": 1811.35, "end": 1811.73, "word": " بطلع", "probability": 0.8756103515625}, {"start": 1811.73, "end": 1812.19, "word": " واحد", "probability": 0.987060546875}, {"start": 1812.19, "end": 1815.21, "word": " طيب", "probability": 0.9658203125}, {"start": 1815.21, "end": 1815.97, "word": " فرقة", "probability": 0.8746744791666666}, {"start": 1815.97, "end": 1816.51, "word": " تانية", "probability": 0.8479817708333334}, {"start": 1816.51, "end": 1817.07, "word": " show", "probability": 0.810546875}, {"start": 1817.07, "end": 1818.55, "word": " that", "probability": 0.92626953125}, {"start": 1818.55, "end": 1820.71, "word": " اثبتي", "probability": 0.87255859375}, {"start": 1820.71, "end": 1821.13, "word": " انه", "probability": 0.881103515625}, {"start": 1821.13, "end": 1821.55, "word": " limit", "probability": 0.9736328125}, {"start": 1821.55, "end": 1825.97, "word": " cosine", "probability": 0.650390625}, {"start": 1825.97, "end": 1827.61, "word": " n", "probability": 0.49951171875}, {"start": 1827.61, "end": 1827.91, "word": " على", "probability": 0.6904296875}, {"start": 1827.91, "end": 1828.45, "word": " n", "probability": 0.896484375}, {"start": 1828.45, "end": 1829.63, "word": " او", "probability": 0.896484375}, {"start": 1829.63, "end": 1829.81, "word": " على", "probability": 0.86572265625}, {"start": 1829.81, "end": 1830.21, "word": " جدر", "probability": 0.88671875}, {"start": 1830.21, "end": 1830.35, "word": " ال", "probability": 0.96142578125}, {"start": 1830.35, "end": 1830.57, "word": " n", "probability": 0.62353515625}], "temperature": 1.0}, {"id": 64, "seek": 185963, "start": 1832.47, "end": 1859.63, "text": "as n tends to infinity بساوي سفر proof أنا عندي cosine n أكبر من أو أصغر من أو ساوي واحد أكبر من أو ساوي سالب واحد لكل n في n وواحد", "tokens": [296, 297, 12258, 281, 13202, 4724, 3794, 995, 45865, 8608, 5172, 2288, 8177, 41850, 18871, 16254, 23565, 297, 5551, 4117, 26890, 9154, 34051, 5551, 9381, 17082, 2288, 9154, 34051, 8608, 995, 45865, 36764, 24401, 5551, 4117, 26890, 9154, 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عندي", "probability": 0.87353515625}, {"start": 1843.79, "end": 1844.81, "word": " cosine", "probability": 0.67138671875}, {"start": 1844.81, "end": 1846.13, "word": " n", "probability": 0.412841796875}, {"start": 1846.13, "end": 1847.35, "word": " أكبر", "probability": 0.9060872395833334}, {"start": 1847.35, "end": 1847.57, "word": " من", "probability": 0.93310546875}, {"start": 1847.57, "end": 1847.73, "word": " أو", "probability": 0.52490234375}, {"start": 1847.73, "end": 1848.27, "word": " أصغر", "probability": 0.9534912109375}, {"start": 1848.27, "end": 1848.45, "word": " من", "probability": 0.98779296875}, {"start": 1848.45, "end": 1848.61, "word": " أو", "probability": 0.83642578125}, {"start": 1848.61, "end": 1849.07, "word": " ساوي", "probability": 0.9366861979166666}, {"start": 1849.07, "end": 1849.53, "word": " واحد", "probability": 0.979248046875}, {"start": 1849.53, "end": 1850.01, "word": " أكبر", "probability": 0.9440104166666666}, {"start": 1850.01, "end": 1850.15, 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ال N أصغر لو سوى واحد على جدر ال N لكل N في N", "tokens": [3615, 23942, 10874, 3215, 2288, 2423, 426, 6225, 3215, 3215, 3714, 29245, 3555, 6156, 1211, 2407, 48812, 25513, 2655, 9673, 2655, 3555, 995, 9957, 3660, 29538, 8978, 36764, 24401, 15844, 10874, 3215, 2288, 2423, 426, 6156, 3555, 9566, 1211, 3615, 8608, 6027, 3555, 36764, 24401, 15844, 10874, 3215, 2288, 2423, 426, 5551, 9381, 17082, 2288, 45164, 8608, 2407, 7578, 23565, 426, 15844, 10874, 3215, 2288, 2423, 426, 5551, 9381, 17082, 2288, 45164, 8608, 2407, 7578, 36764, 24401, 15844, 10874, 3215, 2288, 2423, 426, 5296, 28820, 426, 8978, 426], "avg_logprob": -0.1254389018155216, "compression_ratio": 2.007142857142857, "no_speech_prob": 4.172325134277344e-07, "words": [{"start": 1861.53, "end": 1861.93, "word": "على", "probability": 0.734375}, {"start": 1861.93, "end": 1862.45, "word": " جدر", "probability": 0.9046223958333334}, {"start": 1862.45, "end": 1862.59, "word": " ال", "probability": 0.91796875}, {"start": 1862.59, "end": 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"end": 1874.41, "word": " N", "probability": 0.83544921875}, {"start": 1874.41, "end": 1875.65, "word": " على", "probability": 0.8818359375}, {"start": 1875.65, "end": 1876.11, "word": " جدر", "probability": 0.9977213541666666}, {"start": 1876.11, "end": 1876.29, "word": " ال", "probability": 0.96923828125}, {"start": 1876.29, "end": 1876.47, "word": " N", "probability": 0.94482421875}, {"start": 1876.47, "end": 1877.01, "word": " أصغر", "probability": 0.9765625}, {"start": 1877.01, "end": 1877.21, "word": " لو", "probability": 0.96923828125}, {"start": 1877.21, "end": 1877.65, "word": " سوى", "probability": 0.93115234375}, {"start": 1877.65, "end": 1878.13, "word": " واحد", "probability": 0.955322265625}, {"start": 1878.13, "end": 1878.37, "word": " على", "probability": 0.9189453125}, {"start": 1878.37, "end": 1878.77, "word": " جدر", "probability": 0.998046875}, {"start": 1878.77, "end": 1878.95, "word": " ال", "probability": 0.96630859375}, {"start": 1878.95, "end": 1880.15, "word": " N", "probability": 0.986328125}, {"start": 1880.15, "end": 1880.89, "word": " لكل", "probability": 0.972900390625}, {"start": 1880.89, "end": 1881.25, "word": " N", "probability": 0.8359375}, {"start": 1881.25, "end": 1881.45, "word": " في", "probability": 0.93359375}, {"start": 1881.45, "end": 1881.69, "word": " N", "probability": 0.7412109375}], "temperature": 1.0}, {"id": 66, "seek": 190791, "start": 1884.53, "end": 1907.91, "text": "طيب انا عند ال sequence لسه مثبتين احنا هنا في الفرع b ان ال sequence هذه ال limit تبعتها as n tends to infinity بساوة سفر و ال sequence هذه ال limit تبعتها سالب limit واحد على الجدر ال n و سالب واحد بسفر بطلع سفر as n tends to infinity اذا by squeeze theorem", "tokens": [9566, 1829, 3555, 1975, 8315, 43242, 2423, 8310, 5296, 3794, 3224, 50113, 3555, 2655, 9957, 1975, 5016, 8315, 34105, 8978, 27188, 2288, 3615, 272, 16472, 2423, 8310, 29538, 2423, 4948, 6055, 3555, 34268, 11296, 382, 297, 12258, 281, 13202, 4724, 3794, 995, 2407, 3660, 8608, 5172, 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{"start": 1895.97, "end": 1896.15, "word": " limit", "probability": 0.96728515625}, {"start": 1896.15, "end": 1896.71, "word": " تبعتها", "probability": 0.952880859375}, {"start": 1896.71, "end": 1897.37, "word": " سالب", "probability": 0.87841796875}, {"start": 1897.37, "end": 1897.87, "word": " limit", "probability": 0.984375}, {"start": 1897.87, "end": 1898.83, "word": " واحد", "probability": 0.952392578125}, {"start": 1898.83, "end": 1899.03, "word": " على", "probability": 0.6416015625}, {"start": 1899.03, "end": 1899.51, "word": " الجدر", "probability": 0.8527018229166666}, {"start": 1899.51, "end": 1899.65, "word": " ال", "probability": 0.76416015625}, {"start": 1899.65, "end": 1899.93, "word": " n", "probability": 0.281005859375}, {"start": 1899.93, "end": 1900.85, "word": " و", "probability": 0.787109375}, {"start": 1900.85, "end": 1901.43, "word": " سالب", "probability": 0.9425455729166666}, {"start": 1901.43, "end": 1901.75, "word": " واحد", "probability": 0.984619140625}, {"start": 1901.75, "end": 1902.15, "word": " بسفر", "probability": 0.80413818359375}, {"start": 1902.15, "end": 1902.55, "word": " بطلع", "probability": 0.8868408203125}, {"start": 1902.55, "end": 1902.91, "word": " سفر", "probability": 0.9763997395833334}, {"start": 1902.91, "end": 1903.31, "word": " as", "probability": 0.94091796875}, {"start": 1903.31, "end": 1903.69, "word": " n", "probability": 0.90234375}, {"start": 1903.69, "end": 1904.01, "word": " tends", "probability": 0.8056640625}, {"start": 1904.01, "end": 1904.63, "word": " to", "probability": 0.96923828125}, {"start": 1904.63, "end": 1905.09, "word": " infinity", "probability": 0.91259765625}, {"start": 1905.09, "end": 1906.51, "word": " اذا", "probability": 0.781982421875}, {"start": 1906.51, "end": 1906.83, "word": " by", "probability": 0.8212890625}, {"start": 1906.83, "end": 1907.43, "word": " squeeze", "probability": 0.405517578125}, {"start": 1907.43, "end": 1907.91, "word": " theorem", "probability": 0.90771484375}], "temperature": 1.0}, {"id": 67, "seek": 193607, "start": 1911.91, "end": 1936.07, "text": "بسكويز تيريم أو sandwich theorem بطلع limit ال sequence اللي لحد تبعها محصور في النص اللي هو cosine n على square root ل n as n times infinity بساوي 7 تمام؟ إذن هذا برهان الجزء دي", "tokens": [3555, 3794, 4117, 45865, 11622, 6055, 13546, 32640, 34051, 11141, 20904, 4724, 9566, 1211, 3615, 4948, 2423, 8310, 13672, 1829, 5296, 24401, 6055, 3555, 3615, 11296, 3714, 5016, 9381, 13063, 8978, 28239, 9381, 13672, 1829, 31439, 23565, 297, 15844, 3732, 5593, 5296, 297, 382, 297, 1413, 13202, 4724, 3794, 995, 45865, 1614, 46811, 10943, 22807, 11933, 8848, 1863, 23758, 4724, 2288, 3224, 7649, 25724, 11622, 38207, 11778, 1829], "avg_logprob": -0.38971918907718384, "compression_ratio": 1.2964824120603016, "no_speech_prob": 0.0, "words": [{"start": 1911.91, "end": 1912.89, "word": "بسكويز", "probability": 0.59267578125}, {"start": 1912.89, "end": 1913.45, "word": " تيريم", "probability": 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2102.13, "end": 2103.75, "word": " infimum", "probability": 0.7586263020833334}, {"start": 2103.75, "end": 2106.73, "word": " لواحد", "probability": 0.739501953125}, {"start": 2106.73, "end": 2106.93, "word": " على", "probability": 0.826171875}, {"start": 2106.93, "end": 2107.49, "word": " جذر", "probability": 0.6029459635416666}, {"start": 2107.49, "end": 2107.79, "word": " n", "probability": 0.4970703125}, {"start": 2107.79, "end": 2108.35, "word": " سالب", "probability": 0.6568196614583334}, {"start": 2108.35, "end": 2108.81, "word": " سفر", "probability": 0.8489583333333334}], "temperature": 1.0}, {"id": 74, "seek": 213637, "start": 2118.07, "end": 2136.37, "text": "هذا الان from أثبتنا أنه بساوي سبر إذا حسب by nested intervals theorem", "tokens": [3224, 15730, 2423, 7649, 490, 5551, 12984, 3555, 2655, 8315, 14739, 3224, 4724, 3794, 995, 45865, 8608, 3555, 2288, 11933, 15730, 11331, 35457, 538, 15646, 292, 26651, 20904], "avg_logprob": -0.5312500164426607, "compression_ratio": 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"end": 2132.45, "word": " intervals", "probability": 0.8759765625}, {"start": 2132.45, "end": 2136.37, "word": " theorem", "probability": 0.7890625}], "temperature": 1.0}, {"id": 75, "seek": 216878, "start": 2139.78, "end": 2168.78, "text": "الـ intersection has unique element has unique element يعني في التقاطع مافيش أنصر وحيد طب احنا قلنا ان السفر ينتمي لتقاطع وتقاطع في أنصر واحد لذا لازم يساوي السفر in a sense", "tokens": [6027, 39184, 15236, 575, 3845, 4478, 575, 3845, 4478, 37495, 22653, 8978, 16712, 4587, 41193, 3615, 19446, 41185, 8592, 14739, 9381, 2288, 4032, 5016, 25708, 23032, 3555, 1975, 5016, 8315, 12174, 1211, 8315, 16472, 21136, 5172, 2288, 7251, 29399, 2304, 1829, 5296, 2655, 4587, 41193, 3615, 4032, 2655, 4587, 41193, 3615, 8978, 14739, 9381, 2288, 36764, 24401, 5296, 15730, 5296, 31377, 2304, 7251, 3794, 995, 45865, 21136, 5172, 2288, 294, 257, 2020], "avg_logprob": -0.2765410991564189, "compression_ratio": 1.593939393939394, "no_speech_prob": 0.0, "words": [{"start": 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{"start": 2154.54, "end": 2155.26, "word": " أنصر", "probability": 0.7730305989583334}, {"start": 2155.26, "end": 2155.66, "word": " وحيد", "probability": 0.698974609375}, {"start": 2155.66, "end": 2156.62, "word": " طب", "probability": 0.857666015625}, {"start": 2156.62, "end": 2156.82, "word": " احنا", "probability": 0.8943684895833334}, {"start": 2156.82, "end": 2157.16, "word": " قلنا", "probability": 0.8525390625}, {"start": 2157.16, "end": 2157.34, "word": " ان", "probability": 0.51806640625}, {"start": 2157.34, "end": 2157.84, "word": " السفر", "probability": 0.8160807291666666}, {"start": 2157.84, "end": 2158.78, "word": " ينتمي", "probability": 0.974609375}, {"start": 2158.78, "end": 2160.6, "word": " لتقاطع", "probability": 0.8025146484375}, {"start": 2160.6, "end": 2161.74, "word": " وتقاطع", "probability": 0.7427734375}, {"start": 2161.74, "end": 2161.9, "word": " في", "probability": 0.81103515625}, {"start": 2161.9, "end": 2162.36, "word": " أنصر", "probability": 0.9728190104166666}, {"start": 2162.36, "end": 2162.86, "word": " واحد", "probability": 0.9853515625}, {"start": 2162.86, "end": 2163.18, "word": " لذا", "probability": 0.4593505859375}, {"start": 2163.18, "end": 2163.5, "word": " لازم", "probability": 0.9430338541666666}, {"start": 2163.5, "end": 2163.82, "word": " يساوي", "probability": 0.8492431640625}, {"start": 2163.82, "end": 2164.3, "word": " السفر", "probability": 0.9728190104166666}, {"start": 2164.3, "end": 2167.96, "word": " in", "probability": 0.1402587890625}, {"start": 2167.96, "end": 2168.06, "word": " a", "probability": 0.83056640625}, {"start": 2168.06, "end": 2168.78, "word": " sense", "probability": 0.89013671875}], "temperature": 1.0}, {"id": 76, "seek": 219361, "start": 2173.33, "end": 2193.61, "text": "بما أن السفر ينتمي للتقاطع يجب أن يكون التقاطع من N بساوي واحد infinity ل I N بساوي بس single tone سفر", "tokens": [3555, 15042, 14739, 21136, 5172, 2288, 7251, 29399, 2304, 1829, 24976, 2655, 4587, 41193, 3615, 7251, 7435, 3555, 14739, 7251, 30544, 16712, 4587, 41193, 3615, 9154, 426, 4724, 3794, 995, 45865, 36764, 24401, 13202, 5296, 286, 426, 4724, 3794, 995, 45865, 4724, 3794, 2167, 8027, 8608, 5172, 2288], "avg_logprob": -0.31473214285714285, "compression_ratio": 1.3064516129032258, "no_speech_prob": 0.0, "words": [{"start": 2173.33, "end": 2174.35, "word": "بما", "probability": 0.873779296875}, {"start": 2174.35, "end": 2174.57, "word": " أن", "probability": 0.71044921875}, {"start": 2174.57, "end": 2175.07, "word": " السفر", "probability": 0.7891438802083334}, {"start": 2175.07, "end": 2175.67, "word": " ينتمي", "probability": 0.896484375}, {"start": 2175.67, "end": 2176.63, "word": " للتقاطع", "probability": 0.89775390625}, {"start": 2176.63, "end": 2181.21, "word": " يجب", "probability": 0.8070475260416666}, {"start": 2181.21, "end": 2185.21, "word": " أن", "probability": 0.64990234375}, {"start": 2185.21, "end": 2185.63, "word": " يكون", "probability": 0.870849609375}, {"start": 2185.63, "end": 2186.37, "word": " التقاطع", "probability": 0.9700927734375}, {"start": 2186.37, "end": 2186.55, "word": " من", "probability": 0.73974609375}, {"start": 2186.55, "end": 2186.83, "word": " N", "probability": 0.2003173828125}, {"start": 2186.83, "end": 2187.31, "word": " بساوي", "probability": 0.6513519287109375}, {"start": 2187.31, "end": 2187.75, "word": " واحد", "probability": 0.801513671875}, {"start": 2187.75, "end": 2188.33, "word": " infinity", "probability": 0.2408447265625}, {"start": 2188.33, "end": 2189.65, "word": " ل", "probability": 0.814453125}, {"start": 2189.65, "end": 2189.99, "word": " I", "probability": 0.556640625}, {"start": 2189.99, "end": 2190.37, "word": " N", "probability": 0.548828125}, {"start": 2190.37, "end": 2191.07, "word": " بساوي", "probability": 0.8807373046875}, {"start": 2191.07, "end": 2191.59, "word": " بس", "probability": 0.667236328125}, {"start": 2191.59, "end": 2192.77, "word": " single", "probability": 0.476806640625}, {"start": 2192.77, "end": 2193.15, "word": " tone", "probability": 0.28466796875}, {"start": 2193.15, "end": 2193.61, "word": " سفر", "probability": 0.8494466145833334}], "temperature": 1.0}, {"id": 77, "seek": 220611, "start": 2199.67, "end": 2206.11, "text": "طبعا ممكن اعطيتكم انا برهان زي هذا بس كان بدل 1 على جدر ال N 1 على N", "tokens": [9566, 3555, 3615, 995, 3714, 43020, 1975, 3615, 9566, 36081, 24793, 1975, 8315, 4724, 2288, 3224, 7649, 30767, 1829, 23758, 4724, 3794, 25961, 47525, 1211, 502, 15844, 10874, 3215, 2288, 2423, 426, 502, 15844, 426], "avg_logprob": -0.1705729237033261, "compression_ratio": 1.2777777777777777, "no_speech_prob": 0.0, "words": [{"start": 2199.67, "end": 2200.11, "word": "طبعا", "probability": 0.90478515625}, {"start": 2200.11, "end": 2200.47, "word": " ممكن", "probability": 0.953369140625}, {"start": 2200.47, "end": 2201.03, "word": " اعطيتكم", "probability": 0.8548828125}, {"start": 2201.03, "end": 2201.21, "word": " انا", "probability": 0.865234375}, {"start": 2201.21, "end": 2201.69, "word": " برهان", "probability": 0.9378662109375}, {"start": 2201.69, "end": 2201.99, "word": " زي", "probability": 0.932373046875}, {"start": 2201.99, "end": 2202.37, "word": " هذا", "probability": 0.93798828125}, {"start": 2202.37, "end": 2202.93, "word": " بس", "probability": 0.860595703125}, {"start": 2202.93, "end": 2203.11, "word": " كان", "probability": 0.96630859375}, {"start": 2203.11, "end": 2203.55, "word": " بدل", "probability": 0.95703125}, {"start": 2203.55, "end": 2204.49, "word": " 1", "probability": 0.440673828125}, {"start": 2204.49, "end": 2204.71, "word": " على", "probability": 0.54638671875}, {"start": 2204.71, "end": 2205.01, "word": " جدر", "probability": 0.92041015625}, {"start": 2205.01, "end": 2205.13, "word": " ال", "probability": 0.451416015625}, {"start": 2205.13, "end": 2205.25, "word": " N", "probability": 0.66650390625}, {"start": 2205.25, "end": 2205.51, "word": " 1", "probability": 0.69873046875}, {"start": 2205.51, "end": 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"end": 2226.6, "word": " بساوي", "probability": 0.76708984375}, {"start": 2226.6, "end": 2227.06, "word": " سفر", "probability": 0.8645833333333334}, {"start": 2227.06, "end": 2227.6, "word": " و", "probability": 0.958984375}, {"start": 2227.6, "end": 2227.88, "word": " عملنا", "probability": 0.9264322916666666}, {"start": 2227.88, "end": 2228.26, "word": " برهان", "probability": 0.94287109375}, {"start": 2228.26, "end": 2229.0, "word": " بالتناقض", "probability": 0.965234375}, {"start": 2229.0, "end": 2230.18, "word": " افرضي", "probability": 0.76025390625}, {"start": 2230.18, "end": 2230.28, "word": " إن", "probability": 0.39111328125}, {"start": 2230.28, "end": 2230.38, "word": " ال", "probability": 0.57568359375}, {"start": 2230.38, "end": 2230.54, "word": " x", "probability": 0.85205078125}, {"start": 2230.54, "end": 2231.1, "word": " مابسويش", "probability": 0.78857421875}, {"start": 2231.1, "end": 2231.48, "word": " سفر", "probability": 0.97314453125}, {"start": 2231.48, "end": 2232.34, "word": " إذا", "probability": 0.653076171875}, {"start": 2232.34, "end": 2232.8, "word": " أكبر", "probability": 0.9529622395833334}, {"start": 2232.8, "end": 2233.0, "word": " من", "probability": 0.99609375}, {"start": 2233.0, "end": 2233.38, "word": " سفر", "probability": 0.9807942708333334}, {"start": 2233.38, "end": 2233.52, "word": " و", "probability": 0.98876953125}, {"start": 2233.52, "end": 2233.88, "word": " وصلنا", "probability": 0.8182779947916666}, {"start": 2233.88, "end": 2234.1, "word": " إلى", "probability": 0.92626953125}, {"start": 2234.1, "end": 2234.66, "word": " تناقض", "probability": 0.9483642578125}, {"start": 2234.66, "end": 2234.9, "word": " by", "probability": 0.79541015625}, {"start": 2234.9, "end": 2235.62, "word": " Archimedean", "probability": 0.91552734375}, {"start": 2235.62, "end": 2236.1, "word": " property", "probability": 0.623046875}], "temperature": 1.0}, {"id": 79, "seek": 226550, "start": 2237.08, "end": 2265.5, "text": "إذا في برهان تاني لكن أنا حبيت أعطيكم البرهان هذا التاني اللي ما خناش زيه طبعا صح إذا أنا عندكم برهانين طيب هاي كمان الجزء بيه من السؤال هذا أنا في عندي sequence xn sequence mr", "tokens": [28814, 15730, 8978, 4724, 2288, 3224, 7649, 6055, 7649, 1829, 44381, 41850, 11331, 21292, 2655, 5551, 3615, 9566, 1829, 24793, 2423, 26890, 3224, 7649, 23758, 16712, 7649, 1829, 13672, 1829, 19446, 16490, 1863, 33599, 30767, 1829, 3224, 23032, 3555, 3615, 995, 20328, 5016, 11933, 15730, 41850, 43242, 24793, 4724, 2288, 3224, 7649, 9957, 23032, 1829, 3555, 8032, 47302, 9122, 2304, 7649, 25724, 11622, 38207, 4724, 1829, 3224, 9154, 21136, 33604, 6027, 23758, 41850, 8978, 18871, 16254, 8310, 2031, 77, 8310, 33660], "avg_logprob": -0.25800304587294415, "compression_ratio": 1.7267441860465116, "no_speech_prob": 0.0, "words": [{"start": 2237.08, "end": 2237.32, "word": "إذا", "probability": 0.40179443359375}, {"start": 2237.32, "end": 2237.5, "word": " في", "probability": 0.5576171875}, {"start": 2237.5, "end": 2237.94, "word": " برهان", "probability": 0.926513671875}, {"start": 2237.94, "end": 2238.28, "word": " تاني", "probability": 0.9412434895833334}, {"start": 2238.28, "end": 2238.52, "word": " لكن", "probability": 0.76416015625}, {"start": 2238.52, "end": 2238.78, "word": " أنا", "probability": 0.56787109375}, {"start": 2238.78, "end": 2239.94, "word": " حبيت", "probability": 0.7328287760416666}, {"start": 2239.94, "end": 2240.74, "word": " أعطيكم", "probability": 0.82314453125}, {"start": 2240.74, "end": 2241.32, "word": " البرهان", "probability": 0.9107666015625}, {"start": 2241.32, "end": 2241.82, "word": " هذا", "probability": 0.74365234375}, {"start": 2241.82, "end": 2242.26, "word": " التاني", "probability": 0.9762369791666666}, {"start": 2242.26, "end": 2242.38, "word": " اللي", "probability": 0.883544921875}, {"start": 2242.38, "end": 2242.5, "word": " ما", "probability": 0.73974609375}, {"start": 2242.5, "end": 2242.92, "word": " خناش", "probability": 0.6118977864583334}, {"start": 2242.92, "end": 2243.44, "word": " زيه", "probability": 0.9853515625}, {"start": 2243.44, "end": 2246.84, "word": " طبعا", "probability": 0.83380126953125}, {"start": 2246.84, "end": 2250.92, "word": " صح", "probability": 0.83251953125}, {"start": 2250.92, "end": 2251.62, "word": " إذا", "probability": 0.5316162109375}, {"start": 2251.62, "end": 2251.78, "word": " أنا", "probability": 0.2198486328125}, {"start": 2251.78, "end": 2252.2, "word": " عندكم", "probability": 0.978271484375}, {"start": 2252.2, "end": 2253.48, "word": " برهانين", "probability": 0.95693359375}, {"start": 2253.48, "end": 2257.34, "word": " طيب", "probability": 0.8763020833333334}, {"start": 2257.34, "end": 2257.54, "word": " هاي", "probability": 0.640380859375}, {"start": 2257.54, "end": 2258.12, "word": " كمان", "probability": 0.9861653645833334}, {"start": 2258.12, "end": 2259.74, "word": " الجزء", "probability": 0.9186197916666666}, {"start": 2259.74, "end": 2260.06, "word": " بيه", "probability": 0.7696940104166666}, {"start": 2260.06, "end": 2260.18, "word": " من", "probability": 0.9755859375}, {"start": 2260.18, "end": 2260.66, "word": " السؤال", "probability": 0.9959309895833334}, {"start": 2260.66, "end": 2261.2, "word": " هذا", "probability": 0.94921875}, {"start": 2261.2, "end": 2262.2, "word": " أنا", "probability": 0.61279296875}, {"start": 2262.2, "end": 2262.38, "word": " في", "probability": 0.927734375}, {"start": 2262.38, "end": 2262.7, "word": " عندي", "probability": 0.843994140625}, {"start": 2262.7, "end": 2263.24, "word": " sequence", "probability": 0.955078125}, {"start": 2263.24, "end": 2264.02, "word": " xn", "probability": 0.4530029296875}, {"start": 2264.02, "end": 2264.8, "word": " sequence", "probability": 0.869140625}, {"start": 2264.8, "end": 2265.5, "word": " mr", "probability": 0.80419921875}], "temperature": 1.0}, {"id": 80, "seek": 228821, "start": 2266.72, "end": 2288.22, "text": "وعندي xn أصغر من أو ساوي سفر لكل n وبدنا نثبت إنه إذا كان limit xn بساوي x then ال x بتطلع أيضا أصغر من أو ساوي سفر", "tokens": [2407, 3615, 1863, 16254, 2031, 77, 5551, 9381, 17082, 2288, 9154, 34051, 8608, 995, 45865, 8608, 5172, 2288, 5296, 28820, 297, 4032, 44510, 8315, 8717, 12984, 3555, 2655, 36145, 3224, 11933, 15730, 25961, 4948, 2031, 77, 4724, 3794, 995, 45865, 2031, 550, 2423, 2031, 39894, 9566, 1211, 3615, 36632, 11242, 995, 5551, 9381, 17082, 2288, 9154, 34051, 8608, 995, 45865, 8608, 5172, 2288], "avg_logprob": -0.139282223302871, "compression_ratio": 1.4724409448818898, "no_speech_prob": 0.0, "words": [{"start": 2266.72, "end": 2267.56, "word": "وعندي", "probability": 0.755615234375}, {"start": 2267.56, "end": 2268.36, "word": " xn", "probability": 0.624755859375}, {"start": 2268.36, "end": 2269.04, "word": " أصغر", "probability": 0.959716796875}, {"start": 2269.04, "end": 2269.22, "word": " من", "probability": 0.982421875}, {"start": 2269.22, "end": 2269.42, "word": " أو", "probability": 0.951171875}, {"start": 2269.42, "end": 2269.82, "word": " ساوي", "probability": 0.849609375}, {"start": 2269.82, "end": 2270.3, "word": " سفر", "probability": 0.76953125}, {"start": 2270.3, "end": 2270.84, "word": " لكل", "probability": 0.982666015625}, {"start": 2270.84, "end": 2271.26, "word": " n", "probability": 0.67626953125}, {"start": 2271.26, "end": 2273.56, "word": " وبدنا", "probability": 0.74267578125}, {"start": 2273.56, "end": 2274.2, "word": " نثبت", "probability": 0.994873046875}, {"start": 2274.2, "end": 2275.88, "word": " إنه", "probability": 0.6751708984375}, {"start": 2275.88, "end": 2278.86, "word": " إذا", "probability": 0.883056640625}, {"start": 2278.86, "end": 2279.24, "word": " كان", "probability": 0.994140625}, {"start": 2279.24, "end": 2279.66, "word": " limit", "probability": 0.9375}, {"start": 2279.66, "end": 2281.44, "word": " xn", "probability": 0.94970703125}, {"start": 2281.44, "end": 2282.26, "word": " بساوي", "probability": 0.840576171875}, {"start": 2282.26, "end": 2282.72, "word": " x", "probability": 0.97412109375}, {"start": 2282.72, "end": 2283.14, "word": " then", "probability": 0.56201171875}, {"start": 2283.14, "end": 2285.36, "word": " ال", "probability": 0.8564453125}, {"start": 2285.36, "end": 2285.64, "word": " x", "probability": 0.73486328125}, {"start": 2285.64, "end": 2286.16, "word": " بتطلع", "probability": 0.96337890625}, {"start": 2286.16, "end": 2286.62, "word": " أيضا", "probability": 0.81689453125}, {"start": 2286.62, "end": 2287.14, "word": " أصغر", "probability": 0.9912109375}, {"start": 2287.14, "end": 2287.32, "word": " من", "probability": 0.9912109375}, {"start": 2287.32, "end": 2287.5, "word": " أو", "probability": 0.99169921875}, {"start": 2287.5, "end": 2287.86, "word": " ساوي", "probability": 0.95703125}, {"start": 2287.86, "end": 2288.22, "word": " سفر", "probability": 0.9654947916666666}], "temperature": 1.0}, {"id": 81, "seek": 231365, "start": 2289.55, "end": 2313.65, "text": "أنا في عندى sequence of real numbers كل حدودها غير ثالثة و ال sequence converge ل X بالدفعة ان ال limit ايضا بتطلع غير ثالثة فهي البرهان proof برهان بالتناقض assume on contrary", "tokens": [10721, 8315, 8978, 43242, 7578, 8310, 295, 957, 3547, 28242, 11331, 3215, 23328, 11296, 32771, 13546, 38637, 6027, 12984, 3660, 4032, 2423, 8310, 41881, 5296, 1783, 20666, 3215, 5172, 27884, 16472, 2423, 4948, 1975, 1829, 11242, 995, 39894, 9566, 1211, 3615, 32771, 13546, 38637, 6027, 12984, 3660, 6156, 3224, 1829, 2423, 26890, 3224, 7649, 8177, 4724, 2288, 3224, 7649, 20666, 2655, 8315, 4587, 11242, 6552, 322, 19506], "avg_logprob": -0.26378677215646296, "compression_ratio": 1.4382022471910112, "no_speech_prob": 0.0, "words": [{"start": 2289.55, "end": 2290.67, "word": "أنا", "probability": 0.5367431640625}, {"start": 2290.67, "end": 2290.81, "word": " في", "probability": 0.7666015625}, {"start": 2290.81, "end": 2291.07, "word": " عندى", "probability": 0.45361328125}, {"start": 2291.07, "end": 2291.39, "word": " sequence", "probability": 0.92333984375}, {"start": 2291.39, "end": 2291.73, "word": " of", "probability": 0.94580078125}, {"start": 2291.73, "end": 2291.95, "word": " real", "probability": 0.96923828125}, {"start": 2291.95, "end": 2292.53, "word": " numbers", "probability": 0.814453125}, {"start": 2292.53, "end": 2293.09, "word": " كل", "probability": 0.580078125}, {"start": 2293.09, "end": 2293.63, "word": " حدودها", "probability": 0.991455078125}, {"start": 2293.63, "end": 2293.91, "word": " غير", "probability": 0.99658203125}, {"start": 2293.91, "end": 2294.61, "word": " ثالثة", "probability": 0.7718505859375}, {"start": 2294.61, "end": 2295.23, "word": " و", "probability": 0.427490234375}, {"start": 2295.23, "end": 2295.35, "word": " ال", "probability": 0.7900390625}, {"start": 2295.35, "end": 2295.67, "word": " sequence", "probability": 0.97509765625}, {"start": 2295.67, "end": 2296.27, "word": " converge", "probability": 0.88916015625}, {"start": 2296.27, "end": 2296.43, "word": " ل", "probability": 0.8603515625}, {"start": 2296.43, "end": 2296.73, "word": " X", "probability": 0.58740234375}, {"start": 2296.73, "end": 2297.49, "word": " بالدفعة", "probability": 0.51190185546875}, {"start": 2297.49, "end": 2297.75, "word": " ان", "probability": 0.2449951171875}, {"start": 2297.75, "end": 2297.93, "word": " ال", "probability": 0.5029296875}, {"start": 2297.93, "end": 2298.33, "word": " limit", "probability": 0.95703125}, {"start": 2298.33, "end": 2299.17, "word": " ايضا", "probability": 0.875732421875}, {"start": 2299.17, "end": 2299.65, "word": " بتطلع", "probability": 0.9151611328125}, {"start": 2299.65, "end": 2300.01, "word": " غير", "probability": 0.99658203125}, {"start": 2300.01, "end": 2300.83, "word": " ثالثة", "probability": 0.978515625}, {"start": 2300.83, "end": 2301.93, "word": " فهي", "probability": 0.8346354166666666}, {"start": 2301.93, "end": 2302.55, "word": " البرهان", "probability": 0.909423828125}, {"start": 2302.55, "end": 2303.19, "word": " proof", "probability": 0.4658203125}, {"start": 2303.19, "end": 2307.85, "word": " برهان", "probability": 0.830078125}, {"start": 2307.85, "end": 2308.67, "word": " بالتناقض", "probability": 0.972265625}, {"start": 2308.67, "end": 2309.33, "word": " assume", "probability": 0.7353515625}, {"start": 2309.33, "end": 2312.93, "word": " on", "probability": 0.8955078125}, {"start": 2312.93, "end": 2313.65, "word": " contrary", "probability": 0.869140625}], "temperature": 1.0}, {"id": 82, "seek": 233778, "start": 2316.4, "end": 2337.78, "text": "إن X أكبر من سفر و بدنا نصل إلى تناقض افرض إن X أكبر من سفر طيب let epsilon بساوي X ع 2 هذا بطل عدل موجب", "tokens": [28814, 1863, 1783, 5551, 4117, 26890, 9154, 8608, 5172, 2288, 4032, 47525, 8315, 8717, 36520, 30731, 6055, 8315, 4587, 11242, 1975, 5172, 43042, 36145, 1783, 5551, 4117, 26890, 9154, 8608, 5172, 2288, 23032, 1829, 3555, 718, 17889, 4724, 3794, 995, 45865, 1783, 6225, 568, 23758, 4724, 9566, 1211, 6225, 3215, 1211, 3714, 29245, 3555], "avg_logprob": -0.28096591992811726, "compression_ratio": 1.3658536585365855, "no_speech_prob": 0.0, "words": [{"start": 2316.4, "end": 2316.7, "word": "إن", "probability": 0.6688232421875}, {"start": 2316.7, "end": 2317.12, "word": " X", "probability": 0.5810546875}, {"start": 2317.12, "end": 2317.58, "word": " أكبر", "probability": 0.9095052083333334}, {"start": 2317.58, "end": 2317.8, "word": " من", "probability": 0.99267578125}, {"start": 2317.8, "end": 2318.22, "word": " سفر", "probability": 0.73974609375}, {"start": 2318.22, "end": 2319.56, "word": " و", "probability": 0.533203125}, {"start": 2319.56, "end": 2320.12, "word": " بدنا", "probability": 0.6639404296875}, {"start": 2320.12, "end": 2320.56, "word": " نصل", "probability": 0.971435546875}, {"start": 2320.56, "end": 2320.92, "word": " إلى", "probability": 0.86474609375}, {"start": 2320.92, "end": 2322.42, "word": " تناقض", "probability": 0.9573974609375}, {"start": 2322.42, "end": 2325.86, "word": " افرض", "probability": 0.7652180989583334}, {"start": 2325.86, "end": 2326.1, "word": " إن", "probability": 0.220703125}, {"start": 2326.1, "end": 2326.5, "word": " X", "probability": 0.935546875}, {"start": 2326.5, "end": 2326.98, "word": " أكبر", "probability": 0.9703776041666666}, {"start": 2326.98, "end": 2327.22, "word": " من", "probability": 0.9970703125}, {"start": 2327.22, "end": 2328.04, "word": " سفر", "probability": 0.9676106770833334}, {"start": 2328.04, "end": 2329.9, "word": " طيب", "probability": 0.7284342447916666}, {"start": 2329.9, "end": 2332.58, "word": " let", "probability": 0.708984375}, {"start": 2332.58, "end": 2333.86, "word": " epsilon", "probability": 0.2449951171875}, {"start": 2333.86, "end": 2335.3, "word": " بساوي", "probability": 0.7298583984375}, {"start": 2335.3, "end": 2335.64, "word": " X", "probability": 0.845703125}, {"start": 2335.64, "end": 2335.78, "word": " ع", "probability": 0.6064453125}, {"start": 2335.78, "end": 2336.28, "word": " 2", "probability": 0.560546875}, {"start": 2336.28, "end": 2336.62, "word": " هذا", "probability": 0.54248046875}, {"start": 2336.62, "end": 2336.94, "word": " بطل", "probability": 0.7449544270833334}, {"start": 2336.94, "end": 2337.26, "word": " عدل", "probability": 0.7701822916666666}, {"start": 2337.26, "end": 2337.78, "word": " موجب", "probability": 0.9842122395833334}], "temperature": 1.0}, {"id": 83, "seek": 235046, "start": 2339.4, "end": 2350.46, "text": "بما أنه since .. since xn converges ل x إذا يوجد capital N يعتمد على إبسلون", "tokens": [3555, 15042, 14739, 3224, 1670, 4386, 1670, 2031, 77, 9652, 2880, 5296, 2031, 11933, 15730, 7251, 29245, 3215, 4238, 426, 7251, 34268, 2304, 3215, 15844, 11933, 3555, 3794, 1211, 11536], "avg_logprob": -0.22442035617366915, "compression_ratio": 1.0098039215686274, "no_speech_prob": 0.0, "words": [{"start": 2339.4, "end": 2339.88, "word": "بما", "probability": 0.9853515625}, {"start": 2339.88, "end": 2340.32, "word": " أنه", "probability": 0.681640625}, {"start": 2340.32, 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