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"probability": 0.9947916666666666}, {"start": 408.09, "end": 408.57, "word": " اتنين", "probability": 0.9814453125}, {"start": 408.57, "end": 410.29, "word": " و", "probability": 0.6572265625}, {"start": 410.29, "end": 410.75, "word": " هذا", "probability": 0.9599609375}], "temperature": 1.0}, {"id": 15, "seek": 42412, "start": 413.3, "end": 424.12, "text": "أصغر من أو ساوي اتنين وبالتالي هذا أصغر من أو ساوي جدر الأربعة اللي هو أصغر من أو ساوي اتنين", "tokens": [10721, 9381, 17082, 2288, 9154, 34051, 8608, 995, 45865, 1975, 2655, 1863, 9957, 46599, 6027, 2655, 6027, 1829, 23758, 5551, 9381, 17082, 2288, 9154, 34051, 8608, 995, 45865, 10874, 3215, 2288, 16247, 25513, 27884, 13672, 1829, 31439, 5551, 9381, 17082, 2288, 9154, 34051, 8608, 995, 45865, 1975, 2655, 1863, 9957], "avg_logprob": -0.059666053629388996, "compression_ratio": 1.853932584269663, "no_speech_prob": 0.0, "words": [{"start": 413.3, "end": 413.98, "word": "أصغر", "probability": 0.9263916015625}, {"start": 413.98, "end": 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"text": "بعدين بنلاحظ انه قيمة ال sequence بتكبر كل ما اه فممكن اثبات انه claim تاني اذا ال sequence bounded claim x in اصغر منها و ساوي x in زاد واحد for every n", "tokens": [3555, 22488, 9957, 44945, 15040, 5016, 19913, 16472, 3224, 12174, 32640, 3660, 2423, 8310, 39894, 4117, 26890, 28242, 19446, 1975, 3224, 6156, 2304, 43020, 1975, 12984, 3555, 9307, 16472, 3224, 3932, 6055, 7649, 1829, 1975, 15730, 2423, 8310, 37498, 3932, 2031, 294, 1975, 9381, 17082, 2288, 9154, 11296, 4032, 8608, 995, 45865, 2031, 294, 30767, 18513, 36764, 24401, 337, 633, 297], "avg_logprob": -0.2762096706897982, "compression_ratio": 1.4125, "no_speech_prob": 0.0, "words": [{"start": 503.38, "end": 503.9, "word": "بعدين", "probability": 0.8836263020833334}, {"start": 503.9, "end": 504.44, "word": " بنلاحظ", "probability": 0.8682861328125}, {"start": 504.44, "end": 504.8, "word": " انه", "probability": 0.4012451171875}, {"start": 504.8, "end": 505.16, "word": " قيمة", "probability": 0.97802734375}, {"start": 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او ساوي XK انا XK انا نحط شريط اكبر XK زياد اتنين", "tokens": [2407, 1783, 42, 30767, 1829, 18513, 36764, 24401, 23758, 1975, 1829, 3224, 22807, 39896, 9566, 1211, 3615, 1975, 9381, 17082, 2288, 9154, 1783, 42, 30767, 1829, 18513, 36764, 24401, 1975, 4117, 26890, 9154, 1975, 2407, 8608, 995, 45865, 1783, 42, 1975, 8315, 1783, 42, 1975, 8315, 8717, 5016, 9566, 13412, 16572, 9566, 1975, 4117, 26890, 1783, 42, 30767, 1829, 18513, 1975, 2655, 1863, 9957], "avg_logprob": -0.23221153846153847, "compression_ratio": 1.6759259259259258, "no_speech_prob": 0.0, "words": [{"start": 692.94, "end": 693.24, "word": "و", "probability": 0.91650390625}, {"start": 693.24, "end": 693.82, "word": " XK", "probability": 0.685302734375}, {"start": 693.82, "end": 694.26, "word": " زياد", "probability": 0.67919921875}, {"start": 694.26, "end": 694.72, "word": " واحد", "probability": 0.814697265625}, {"start": 694.72, "end": 695.02, "word": " هذا", "probability": 0.640625}, {"start": 695.02, "end": 696.42, 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"probability": 0.799072265625}, {"start": 721.18, "end": 721.66, "word": " زيادة", "probability": 0.72869873046875}, {"start": 721.66, "end": 722.12, "word": " واحد", "probability": 0.962646484375}, {"start": 722.12, "end": 723.32, "word": " بأكبر", "probability": 0.8829345703125}, {"start": 723.32, "end": 723.48, "word": " من", "probability": 0.97998046875}, {"start": 723.48, "end": 723.66, "word": " أو", "probability": 0.94677734375}, {"start": 723.66, "end": 724.1, "word": " ساوي", "probability": 0.958984375}, {"start": 724.1, "end": 724.68, "word": " XK", "probability": 0.96435546875}, {"start": 724.68, "end": 724.88, "word": " من", "probability": 0.95947265625}, {"start": 724.88, "end": 725.02, "word": " ال", "probability": 0.52099609375}, {"start": 725.02, "end": 725.4, "word": " induction", "probability": 0.98291015625}, {"start": 725.4, "end": 726.08, "word": " hypothesis", "probability": 0.93115234375}, {"start": 726.08, "end": 727.22, "word": " من", "probability": 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" إذاً", "probability": 0.5673014322916666}, {"start": 750.21, "end": 750.71, "word": " this", "probability": 0.7666015625}, {"start": 750.71, "end": 753.59, "word": " completes", "probability": 0.9609375}, {"start": 753.59, "end": 757.25, "word": " this", "probability": 0.63623046875}, {"start": 757.25, "end": 757.89, "word": " completes", "probability": 0.98046875}, {"start": 757.89, "end": 758.17, "word": " the", "probability": 0.73046875}, {"start": 758.17, "end": 758.61, "word": " induction", "probability": 0.966796875}], "temperature": 1.0}, {"id": 29, "seek": 78958, "start": 763.32, "end": 789.58, "text": "وبالتالي إذا هيك بنكون أثبتنا ال claim بتاعي إن أنا في عندي two claims أول شي sequence bounded والتاني بيقول إن ال sequence increasing وبالتالي therefore إذا لو سمينا هذا claim one وهذا claim two", "tokens": [37746, 6027, 2655, 6027, 1829, 11933, 15730, 39896, 4117, 44945, 30544, 5551, 12984, 3555, 2655, 8315, 2423, 3932, 39894, 45761, 1829, 36145, 41850, 8978, 18871, 16254, 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{"start": 773.78, "end": 773.92, "word": " إن", "probability": 0.578125}, {"start": 773.92, "end": 774.04, "word": " ال", "probability": 0.93896484375}, {"start": 774.04, "end": 774.34, "word": " sequence", "probability": 0.94775390625}, {"start": 774.34, "end": 775.2, "word": " increasing", "probability": 0.9619140625}, {"start": 775.2, "end": 777.2, "word": " وبالتالي", "probability": 0.90966796875}, {"start": 777.2, "end": 778.7, "word": " therefore", "probability": 0.71875}, {"start": 778.7, "end": 785.2, "word": " إذا", "probability": 0.606201171875}, {"start": 785.2, "end": 785.4, "word": " لو", "probability": 0.99609375}, {"start": 785.4, "end": 785.86, "word": " سمينا", "probability": 0.8128662109375}, {"start": 785.86, "end": 786.12, "word": " هذا", "probability": 0.86474609375}, {"start": 786.12, "end": 786.54, "word": " claim", "probability": 0.97021484375}, {"start": 786.54, "end": 787.0, "word": " one", "probability": 0.7958984375}, {"start": 787.0, "end": 788.76, "word": 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sequence", "probability": 0.414794921875}, {"start": 814.71, "end": 815.25, "word": " x", "probability": 0.454833984375}, {"start": 815.25, "end": 815.65, "word": " in", "probability": 0.418701171875}, {"start": 815.65, "end": 818.35, "word": " convergence", "probability": 0.61376953125}, {"start": 818.35, "end": 821.53, "word": " say", "probability": 0.75048828125}, {"start": 821.53, "end": 824.29, "word": " دعنا", "probability": 0.9607747395833334}, {"start": 824.29, "end": 825.07, "word": " نسمي", "probability": 0.9755859375}, {"start": 825.07, "end": 825.19, "word": " ال", "probability": 0.84033203125}, {"start": 825.19, "end": 825.45, "word": " limit", "probability": 0.9443359375}, {"start": 825.45, "end": 826.13, "word": " تبعتها", "probability": 0.91455078125}], "temperature": 1.0}, {"id": 31, "seek": 85332, "start": 827.62, "end": 853.32, "text": "limit x in بساوي x طبعا هذا بيطلع عدد حقيقي الان بنوجد قيمة limit x هذه فبنرجع to find to find x لإيجاد قيمة ال x بناخد ال limit", 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find", "probability": 0.9501953125}, {"start": 843.64, "end": 846.62, "word": " to", "probability": 0.71435546875}, {"start": 846.62, "end": 847.04, "word": " find", "probability": 0.9501953125}, {"start": 847.04, "end": 847.42, "word": " x", "probability": 0.962890625}, {"start": 847.42, "end": 848.06, "word": " لإيجاد", "probability": 0.95}, {"start": 848.06, "end": 848.58, "word": " قيمة", "probability": 0.99560546875}, {"start": 848.58, "end": 848.74, "word": " ال", "probability": 0.91162109375}, {"start": 848.74, "end": 849.06, "word": " x", "probability": 0.41748046875}, {"start": 849.06, "end": 852.88, "word": " بناخد", "probability": 0.93408203125}, {"start": 852.88, "end": 853.02, "word": " ال", "probability": 0.7470703125}, {"start": 853.02, "end": 853.32, "word": " limit", "probability": 0.9599609375}], "temperature": 1.0}, {"id": 32, "seek": 86822, "start": 855.58, "end": 868.22, "text": "take limit of both sides of", "tokens": [27612, 4948, 295, 1293, 4881, 295], "avg_logprob": -0.35881695577076506, "compression_ratio": 0.8181818181818182, "no_speech_prob": 0.0, "words": [{"start": 855.58, "end": 856.2, "word": "take", "probability": 0.271728515625}, {"start": 856.2, "end": 857.92, "word": " limit", "probability": 0.970703125}, {"start": 857.92, "end": 861.34, "word": " of", "probability": 0.96435546875}, {"start": 861.34, "end": 861.72, "word": " both", "probability": 0.91796875}, {"start": 861.72, "end": 862.32, "word": " sides", "probability": 0.919921875}, {"start": 862.32, "end": 868.22, "word": " of", "probability": 0.9091796875}], "temperature": 1.0}, {"id": 33, "seek": 89080, "start": 875.54, "end": 890.8, "text": "بناخد ال limit لطرفين of both sides of المعادلة xn زي الواحد بساوي square root ل two plus xn to get", "tokens": [3555, 1863, 47283, 3215, 2423, 4948, 5296, 9566, 28480, 9957, 295, 1293, 4881, 295, 9673, 3615, 18513, 37977, 2031, 77, 30767, 1829, 2423, 14407, 24401, 4724, 3794, 995, 45865, 3732, 5593, 5296, 732, 1804, 2031, 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"start": 961.69, "end": 988.15, "text": "الـ xn أكبر من أو ساوي واحد أصغر من أو ساوي اتنين لكل n هذا من claim one بيقدي ان ال limit حسب نظرية سابقة هذا بيقدي ان ال limit ل xn أصغر من أو ساوي اتنين أكبر من أو ساوي الواحد", "tokens": [6027, 39184, 2031, 77, 5551, 4117, 26890, 9154, 34051, 8608, 995, 45865, 36764, 24401, 5551, 9381, 17082, 2288, 9154, 34051, 8608, 995, 45865, 1975, 2655, 1863, 9957, 5296, 28820, 297, 23758, 9154, 3932, 472, 4724, 1829, 4587, 16254, 16472, 2423, 4948, 11331, 35457, 8717, 19913, 2288, 10632, 8608, 16758, 28671, 23758, 4724, 1829, 4587, 16254, 16472, 2423, 4948, 5296, 2031, 77, 5551, 9381, 17082, 2288, 9154, 34051, 8608, 995, 45865, 1975, 2655, 1863, 9957, 5551, 4117, 26890, 9154, 34051, 8608, 995, 45865, 2423, 14407, 24401], "avg_logprob": -0.12000363623333532, "compression_ratio": 1.972972972972973, "no_speech_prob": 0.0, "words": [{"start": 961.69, "end": 962.13, "word": "الـ", "probability": 0.676513671875}, {"start": 962.13, "end": 962.87, "word": " xn", "probability": 0.49072265625}, {"start": 962.87, "end": 963.69, "word": " أكبر", "probability": 0.9269205729166666}, {"start": 963.69, "end": 963.93, "word": " من", "probability": 0.9228515625}, {"start": 963.93, "end": 964.17, "word": " أو", "probability": 0.97119140625}, {"start": 964.17, "end": 964.73, "word": " ساوي", "probability": 0.8427734375}, {"start": 964.73, "end": 965.35, "word": " واحد", "probability": 0.92431640625}, {"start": 965.35, "end": 967.13, "word": " أصغر", "probability": 0.950439453125}, {"start": 967.13, "end": 967.37, "word": " من", "probability": 0.99658203125}, {"start": 967.37, "end": 967.59, "word": " أو", "probability": 0.9794921875}, {"start": 967.59, "end": 968.23, "word": " ساوي", "probability": 0.9601236979166666}, {"start": 968.23, "end": 968.75, "word": " اتنين", "probability": 0.95263671875}, {"start": 968.75, "end": 969.35, "word": " لكل", "probability": 0.969970703125}, {"start": 969.35, "end": 969.75, "word": " n", "probability": 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ممكن نحل باقي الأسئلة زي مثلا سؤال واحد و اتنين و تلاتة و خمسة و ستة و سابعة okay تمام في أي أسئلة تانية في هذا section السؤال تسعة", "tokens": [2407, 39896, 4117, 44945, 30544, 5551, 12984, 3555, 2655, 8315, 36145, 2423, 8310, 307, 9652, 6930, 4032, 39896, 49610, 3215, 8315, 2423, 4948, 6055, 3555, 34268, 11296, 20666, 2304, 12984, 1211, 3714, 43020, 8717, 5016, 1211, 4724, 995, 38436, 16247, 3794, 19986, 37977, 30767, 1829, 50113, 15040, 8608, 33604, 6027, 36764, 24401, 4032, 1975, 2655, 1863, 9957, 4032, 6055, 1211, 9307, 3660, 4032, 16490, 2304, 3794, 3660, 4032, 8608, 2655, 3660, 4032, 8608, 16758, 27884, 1392, 46811, 10943, 8978, 36632, 5551, 3794, 19986, 37977, 6055, 7649, 10632, 8978, 23758, 3541, 21136, 33604, 6027, 6055, 3794, 27884], "avg_logprob": -0.1481153350515464, "compression_ratio": 1.6093023255813954, "no_speech_prob": 0.0, "words": [{"start": 1017.51, "end": 1017.73, "word": "و", "probability": 0.84912109375}, {"start": 1017.73, "end": 1017.95, "word": " هيك", 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"probability": 0.9353841145833334}, {"start": 1057.92, "end": 1058.46, "word": " تسعة", "probability": 0.9454752604166666}, {"start": 1058.46, "end": 1085.54, "word": " هاي", "probability": 0.4742431640625}, {"start": 1085.54, "end": 1086.08, "word": " السؤال", "probability": 0.873046875}, {"start": 1086.08, "end": 1086.6, "word": " تسعة", "probability": 0.9884440104166666}], "temperature": 1.0}, {"id": 41, "seek": 111208, "start": 1087.85, "end": 1112.09, "text": "السيقشن تلاتة تلاتة السؤال هذا بيقول let a be infinite infinite subset of R و ال set هذه bounded", "tokens": [6027, 3794, 1829, 4587, 8592, 1863, 6055, 1211, 9307, 3660, 6055, 1211, 9307, 3660, 21136, 33604, 6027, 23758, 4724, 1829, 39648, 718, 257, 312, 13785, 13785, 25993, 295, 497, 4032, 2423, 992, 29538, 37498], "avg_logprob": -0.28950894049235754, "compression_ratio": 1.303921568627451, "no_speech_prob": 0.0, "words": [{"start": 1087.85, "end": 1088.75, "word": "السيقشن", "probability": 0.6556803385416666}, {"start": 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1106.75, "end": 1107.37, "word": " R", "probability": 0.66748046875}, {"start": 1107.37, "end": 1109.47, "word": " و", "probability": 0.425048828125}, {"start": 1109.47, "end": 1109.87, "word": " ال", "probability": 0.8203125}, {"start": 1109.87, "end": 1110.27, "word": " set", "probability": 0.9541015625}, {"start": 1110.27, "end": 1110.93, "word": " هذه", "probability": 0.448486328125}, {"start": 1110.93, "end": 1112.09, "word": " bounded", "probability": 0.9130859375}], "temperature": 1.0}, {"id": 42, "seek": 113360, "start": 1114.79, "end": 1133.61, "text": "أو bounded above محدودة من أعلى and let ال U", "tokens": [10721, 2407, 37498, 3673, 3714, 24401, 23328, 3660, 9154, 5551, 3615, 23942, 293, 718, 2423, 624], "avg_logprob": -0.26769301470588236, "compression_ratio": 0.8695652173913043, "no_speech_prob": 0.0, "words": [{"start": 1114.79, "end": 1115.15, "word": "أو", "probability": 0.6826171875}, {"start": 1115.15, "end": 1115.53, "word": " bounded", "probability": 0.55078125}, 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"end": 1419.52, "text": "بعدين now for إبسلون بساوي واحد على تلاتة أكبر من سفر it choose إذا في اللمّة هذه خدوا إبسلون بساوي تلت it choose X تلاتة ينتمي إلى A", "tokens": [3555, 22488, 9957, 586, 337, 11933, 3555, 3794, 1211, 11536, 4724, 3794, 995, 45865, 36764, 24401, 15844, 6055, 1211, 9307, 3660, 5551, 4117, 26890, 9154, 8608, 5172, 2288, 309, 2826, 11933, 15730, 8978, 13672, 2304, 11703, 3660, 29538, 16490, 3215, 14407, 11933, 3555, 3794, 1211, 11536, 4724, 3794, 995, 45865, 6055, 1211, 2655, 309, 2826, 1783, 6055, 1211, 9307, 3660, 7251, 29399, 2304, 1829, 30731, 316], "avg_logprob": -0.19706156271607128, "compression_ratio": 1.4726027397260273, "no_speech_prob": 0.0, "words": [{"start": 1399.44, "end": 1400.72, "word": "بعدين", "probability": 0.966796875}, {"start": 1400.72, "end": 1402.0, "word": " now", "probability": 0.6201171875}, {"start": 1402.0, "end": 1404.52, "word": " for", "probability": 0.919921875}, {"start": 1404.52, "end": 1405.74, "word": " إبسلون", 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{"start": 1425.35, "end": 1425.83, "word": " تلاتة", "probability": 0.8157958984375}, {"start": 1425.83, "end": 1426.07, "word": " هذا", "probability": 0.59375}, {"start": 1426.07, "end": 1426.45, "word": " ممكن", "probability": 0.983154296875}, {"start": 1426.45, "end": 1427.07, "word": " اختاره", "probability": 0.924072265625}, {"start": 1427.07, "end": 1427.51, "word": " اكبر", "probability": 0.8605143229166666}, {"start": 1427.51, "end": 1427.69, "word": " من", "probability": 0.98486328125}, {"start": 1427.69, "end": 1427.85, "word": " او", "probability": 0.804443359375}, {"start": 1427.85, "end": 1428.33, "word": " ساوي", "probability": 0.9261067708333334}, {"start": 1428.33, "end": 1428.59, "word": " X", "probability": 0.72900390625}, {"start": 1428.59, "end": 1429.15, "word": " اتنين", "probability": 0.8758544921875}, {"start": 1429.15, "end": 1430.77, "word": " and", "probability": 0.806640625}, {"start": 1430.77, "end": 1433.63, "word": " U", "probability": 0.79296875}, {"start": 1433.63, "end": 1434.11, "word": " اللي", "probability": 0.949951171875}, {"start": 1434.11, "end": 1434.57, "word": " هو", "probability": 0.9873046875}, {"start": 1434.57, "end": 1436.05, "word": " U", "probability": 0.90625}, {"start": 1436.05, "end": 1436.83, "word": " سالب", "probability": 0.94287109375}, {"start": 1436.83, "end": 1438.31, "word": " تلت", "probability": 0.9724934895833334}, {"start": 1438.31, "end": 1439.33, "word": " اصغر", "probability": 0.947998046875}, {"start": 1439.33, "end": 1439.53, "word": " من", "probability": 0.99609375}, {"start": 1439.53, "end": 1439.85, "word": " X", "probability": 0.994140625}, {"start": 1439.85, "end": 1440.89, "word": " تلاتة", "probability": 0.9661865234375}, {"start": 1440.89, "end": 1443.09, "word": " صح؟", "probability": 0.695556640625}, {"start": 1443.09, "end": 1445.43, "word": " continuing", "probability": 0.33984375}, {"start": 1445.43, "end": 1447.81, "word": " in", "probability": 0.35986328125}, {"start": 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بساوي واحد على ك أكبر من السفر", "tokens": [2994, 17889, 4724, 3794, 995, 45865, 36764, 24401, 15844, 9122, 5551, 4117, 26890, 9154, 21136, 5172, 2288], "avg_logprob": -0.363715272810724, "compression_ratio": 0.8918918918918919, "no_speech_prob": 0.0, "words": [{"start": 1486.82, "end": 1487.34, "word": "for", "probability": 0.3291015625}, {"start": 1487.34, "end": 1487.86, "word": " epsilon", "probability": 0.48583984375}, {"start": 1487.86, "end": 1488.66, "word": " بساوي", "probability": 0.70556640625}, {"start": 1488.66, "end": 1489.22, "word": " واحد", "probability": 0.93408203125}, {"start": 1489.22, "end": 1489.42, "word": " على", "probability": 0.59228515625}, {"start": 1489.42, "end": 1489.78, "word": " ك", "probability": 0.6376953125}, {"start": 1489.78, "end": 1491.48, "word": " أكبر", "probability": 0.7938639322916666}, {"start": 1491.48, "end": 1491.66, "word": " من", "probability": 0.99169921875}, {"start": 1491.66, "end": 1492.74, "word": " السفر", "probability": 0.8361002604166666}], "temperature": 1.0}, {"id": 55, "seek": 152353, "start": 1496.07, "end": 1523.53, "text": "there exists xk أكبر من او ساوي xk زايد واحد such that absolute u سالب واحد على k أصغر من xk وهذا صحيح for every k ينتمي إلى n تمام؟", "tokens": [15456, 8198, 2031, 74, 5551, 4117, 26890, 9154, 1975, 2407, 8608, 995, 45865, 2031, 74, 30767, 995, 25708, 36764, 24401, 1270, 300, 8236, 344, 8608, 6027, 3555, 36764, 24401, 15844, 350, 5551, 9381, 17082, 2288, 9154, 2031, 74, 37037, 15730, 20328, 5016, 1829, 5016, 337, 633, 350, 7251, 29399, 2304, 1829, 30731, 297, 46811, 10943, 22807], "avg_logprob": -0.17269736842105263, "compression_ratio": 1.2751677852348993, "no_speech_prob": 0.0, "words": [{"start": 1496.07, "end": 1496.45, "word": "there", "probability": 0.355224609375}, {"start": 1496.45, "end": 1496.97, "word": " exists", "probability": 0.6552734375}, {"start": 1496.97, "end": 1498.03, "word": " xk", "probability": 0.77099609375}, {"start": 1498.03, "end": 1499.41, "word": " أكبر", "probability": 0.8792317708333334}, {"start": 1499.41, "end": 1499.63, "word": " من", "probability": 0.94189453125}, {"start": 1499.63, "end": 1501.37, "word": " او", "probability": 0.550048828125}, {"start": 1501.37, "end": 1501.65, "word": " ساوي", "probability": 0.7521158854166666}, {"start": 1501.65, "end": 1502.05, "word": " xk", "probability": 0.847412109375}, {"start": 1502.05, "end": 1502.49, "word": " زايد", "probability": 0.7390950520833334}, {"start": 1502.49, "end": 1502.99, "word": " واحد", "probability": 0.9521484375}, {"start": 1502.99, "end": 1504.03, "word": " such", "probability": 0.9326171875}, {"start": 1504.03, "end": 1505.07, "word": " that", "probability": 0.95849609375}, {"start": 1505.07, "end": 1506.35, "word": " absolute", "probability": 0.712890625}, {"start": 1506.35, "end": 1508.35, "word": " u", "probability": 0.67138671875}, {"start": 1508.35, "end": 1508.97, "word": " سالب", "probability": 0.9034830729166666}, {"start": 1508.97, "end": 1509.47, "word": " واحد", "probability": 0.982666015625}, {"start": 1509.47, "end": 1509.67, "word": " على", "probability": 0.8271484375}, {"start": 1509.67, "end": 1510.21, "word": " k", "probability": 0.69287109375}, {"start": 1510.21, "end": 1511.63, "word": " أصغر", "probability": 0.96826171875}, {"start": 1511.63, "end": 1511.99, "word": " من", "probability": 0.99560546875}, {"start": 1511.99, "end": 1513.67, "word": " xk", "probability": 0.966796875}, {"start": 1513.67, "end": 1514.95, "word": " وهذا", "probability": 0.819580078125}, {"start": 1514.95, "end": 1515.57, "word": " صحيح", "probability": 0.9969482421875}, {"start": 1515.57, "end": 1515.95, "word": " for", "probability": 0.966796875}, {"start": 1515.95, "end": 1516.49, "word": " every", "probability": 0.82421875}, {"start": 1516.49, "end": 1517.17, "word": " k", "probability": 0.95458984375}, {"start": 1517.17, "end": 1518.61, "word": " ينتمي", "probability": 0.963134765625}, {"start": 1518.61, "end": 1518.85, "word": " إلى", "probability": 0.896484375}, {"start": 1518.85, "end": 1519.17, "word": " n", "probability": 0.417724609375}, {"start": 1519.17, "end": 1523.53, "word": " تمام؟", "probability": 0.91796875}], "temperature": 1.0}, {"id": 56, "seek": 155670, "start": 1532.82, "end": 1556.7, "text": "طيب أنا عندي .. خلّيني أمسح اللمّة هذه طيب إذا أنا عندي U نيجاتيب واحد على K طلع أصغر من XK", "tokens": [9566, 1829, 3555, 41850, 18871, 16254, 4386, 16490, 1211, 11703, 9957, 1829, 5551, 2304, 3794, 5016, 13672, 2304, 11703, 3660, 29538, 23032, 1829, 3555, 11933, 15730, 41850, 18871, 16254, 624, 8717, 1829, 7435, 9307, 1829, 3555, 36764, 24401, 15844, 591, 23032, 1211, 3615, 5551, 9381, 17082, 2288, 9154, 1783, 42], "avg_logprob": -0.26639092202280085, "compression_ratio": 1.3220338983050848, "no_speech_prob": 0.0, "words": [{"start": 1532.82, "end": 1533.26, "word": "طيب", "probability": 0.8347981770833334}, {"start": 1533.26, "end": 1533.5, "word": " أنا", "probability": 0.5849609375}, {"start": 1533.5, "end": 1534.2, "word": " عندي", "probability": 0.8818359375}, {"start": 1534.2, "end": 1540.12, "word": " ..", "probability": 0.466064453125}, {"start": 1540.12, "end": 1542.6, "word": " خلّيني", "probability": 0.71220703125}, {"start": 1542.6, "end": 1543.08, "word": " أمسح", "probability": 0.943115234375}, {"start": 1543.08, "end": 1543.6, "word": " اللمّة", "probability": 0.76824951171875}, {"start": 1543.6, "end": 1544.4, "word": " هذه", "probability": 0.8505859375}, {"start": 1544.4, "end": 1550.56, "word": " طيب", "probability": 0.8932291666666666}, {"start": 1550.56, "end": 1550.92, "word": " إذا", "probability": 0.673583984375}, {"start": 1550.92, "end": 1551.36, "word": " أنا", "probability": 0.8681640625}, {"start": 1551.36, "end": 1551.88, "word": " عندي", "probability": 0.937744140625}, {"start": 1551.88, "end": 1553.1, "word": " U", "probability": 0.51513671875}, {"start": 1553.1, "end": 1553.74, "word": " نيجاتيب", "probability": 0.6347249348958334}, {"start": 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"probability": 0.931640625}, {"start": 1577.96, "end": 1578.36, "word": " ..", "probability": 0.5810546875}, {"start": 1578.36, "end": 1578.56, "word": " و", "probability": 0.97265625}, {"start": 1578.56, "end": 1579.08, "word": " XK", "probability": 0.986083984375}, {"start": 1579.08, "end": 1579.62, "word": " عنصر", "probability": 0.9943033854166666}, {"start": 1579.62, "end": 1580.02, "word": " في", "probability": 0.98876953125}, {"start": 1580.02, "end": 1580.42, "word": " A", "probability": 0.6279296875}, {"start": 1580.42, "end": 1581.24, "word": " إذا", "probability": 0.69775390625}, {"start": 1581.24, "end": 1581.38, "word": " ال", "probability": 0.6298828125}, {"start": 1581.38, "end": 1581.76, "word": " XK", "probability": 0.994140625}, {"start": 1581.76, "end": 1582.1, "word": " لازم", "probability": 0.9890950520833334}, {"start": 1582.1, "end": 1582.3, "word": " يكون", "probability": 0.993408203125}, {"start": 1582.3, "end": 1582.7, "word": " أصغر", "probability": 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{"start": 1596.13, "end": 1596.47, "word": " n", "probability": 0.775390625}, {"start": 1596.47, "end": 1598.67, "word": " مظبوط", "probability": 0.7635986328125}, {"start": 1598.67, "end": 1599.25, "word": " صحيح", "probability": 0.873046875}, {"start": 1599.25, "end": 1601.81, "word": " so", "probability": 0.181640625}, {"start": 1601.81, "end": 1603.33, "word": " احنا", "probability": 0.8968098958333334}, {"start": 1603.33, "end": 1603.85, "word": " اثبتنا", "probability": 0.90634765625}, {"start": 1603.85, "end": 1604.13, "word": " هيك", "probability": 0.68505859375}, {"start": 1604.13, "end": 1604.29, "word": " ان", "probability": 0.73828125}, {"start": 1604.29, "end": 1604.83, "word": " يوجد", "probability": 0.9777018229166666}, {"start": 1604.83, "end": 1605.63, "word": " sequence", "probability": 0.9033203125}, {"start": 1605.63, "end": 1606.57, "word": " يوجد", "probability": 0.9659830729166666}, {"start": 1606.57, "end": 1608.41, "word": " increasing", "probability": 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"end": 1857.51, "text": "لو كتبنا اول تلت اربع خمس حدود نقدر نشوف وين يعني ال sequence محصورة بين اي اعداد ايه هو ال upper bound و ال lower bound لل sequence فمثلا لو بدي احسب الحد رقم اي حد واحد اكبر من واحد طب الحد التاني بساوي اتنين سالب واحد على اكس واحد", "tokens": [1211, 2407, 9122, 2655, 3555, 8315, 1975, 12610, 6055, 1211, 2655, 1975, 25513, 3615, 16490, 2304, 3794, 11331, 3215, 23328, 8717, 28543, 2288, 8717, 8592, 38688, 4032, 9957, 37495, 22653, 2423, 8310, 3714, 5016, 9381, 13063, 3660, 49374, 1975, 1829, 1975, 22488, 18513, 1975, 1829, 3224, 31439, 2423, 6597, 5472, 4032, 2423, 3126, 5472, 24976, 8310, 6156, 2304, 12984, 15040, 45164, 4724, 16254, 1975, 5016, 35457, 21542, 3215, 12602, 4587, 2304, 1975, 1829, 11331, 3215, 36764, 24401, 1975, 4117, 26890, 9154, 36764, 24401, 23032, 3555, 21542, 3215, 16712, 7649, 1829, 4724, 3794, 995, 45865, 1975, 2655, 1863, 9957, 8608, 6027, 3555, 36764, 24401, 15844, 1975, 4117, 3794, 36764, 24401], "avg_logprob": -0.15340908549048685, 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0.78076171875}], "temperature": 1.0}, {"id": 83, "seek": 232446, "start": 2306.08, "end": 2324.46, "text": "الان من ال claims واحد و اتنين تطلع now x in is decreasing and bounded", "tokens": [6027, 7649, 9154, 2423, 9441, 36764, 24401, 4032, 1975, 2655, 1863, 9957, 6055, 9566, 1211, 3615, 586, 2031, 294, 307, 23223, 293, 37498], "avg_logprob": -0.23046874503294626, "compression_ratio": 1.0, "no_speech_prob": 0.0, "words": [{"start": 2306.08, "end": 2307.48, "word": "الان", "probability": 0.5389404296875}, {"start": 2307.48, "end": 2307.66, "word": " من", "probability": 0.86083984375}, {"start": 2307.66, "end": 2307.8, "word": " ال", "probability": 0.64599609375}, {"start": 2307.8, "end": 2308.1, "word": " claims", "probability": 0.84130859375}, {"start": 2308.1, "end": 2308.58, "word": " واحد", "probability": 0.95068359375}, {"start": 2308.58, "end": 2308.74, "word": " و", "probability": 0.91357421875}, {"start": 2308.74, "end": 2309.14, "word": " اتنين", "probability": 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1863, 9957, 370, 538, 1108, 310, 546, 32181, 20904, 2031, 77, 9652, 2880, 584, 4948, 2031, 77, 20666, 3794, 995, 45865, 2031, 337, 512, 2031, 7251, 29399, 2304, 1829, 2423, 7578, 497, 2423, 7649, 44945, 7435, 1829, 3555, 12174, 32640, 3660, 2423, 4948, 13672, 1829, 39896, 2423, 1783], "avg_logprob": -0.25808190785605334, "compression_ratio": 1.37012987012987, "no_speech_prob": 0.0, "words": [{"start": 2328.23, "end": 2328.67, "word": "حسب", "probability": 0.6669921875}, {"start": 2328.67, "end": 2328.95, "word": " claim", "probability": 0.455078125}, {"start": 2328.95, "end": 2329.55, "word": " واحد", "probability": 0.86083984375}, {"start": 2329.55, "end": 2329.67, "word": " و", "probability": 0.96826171875}, {"start": 2329.67, "end": 2329.91, "word": " claim", "probability": 0.76708984375}, {"start": 2329.91, "end": 2330.41, "word": " اتنين", "probability": 0.958740234375}, {"start": 2330.41, "end": 2330.81, "word": " so", "probability": 0.07147216796875}, {"start": 2330.81, "end": 2332.21, "word": " by", "probability": 0.8076171875}, {"start": 2332.21, "end": 2332.87, "word": " monotone", "probability": 0.8758138020833334}, {"start": 2332.87, "end": 2333.57, "word": " convergence", "probability": 0.9482421875}, {"start": 2333.57, "end": 2334.19, "word": " theorem", "probability": 0.92041015625}, {"start": 2334.19, "end": 2336.51, "word": " xn", "probability": 0.5023193359375}, {"start": 2336.51, "end": 2337.87, "word": " converges", "probability": 0.8955078125}, {"start": 2337.87, "end": 2340.83, "word": " say", "probability": 0.84619140625}, {"start": 2340.83, "end": 2341.63, "word": " limit", "probability": 0.96533203125}, {"start": 2341.63, "end": 2343.61, "word": " xn", "probability": 0.95458984375}, {"start": 2343.61, "end": 2344.37, "word": " بالساوي", "probability": 0.73443603515625}, {"start": 2344.37, "end": 2344.83, "word": " x", "probability": 0.951171875}, {"start": 2344.83, "end": 2345.93, "word": " for", "probability": 0.7666015625}, {"start": 2345.93, "end": 2346.31, "word": " some", "probability": 0.87548828125}, {"start": 2346.31, "end": 2346.71, "word": " x", "probability": 0.98876953125}, {"start": 2346.71, "end": 2347.37, "word": " ينتمي", "probability": 0.9549560546875}, {"start": 2347.37, "end": 2347.63, "word": " الى", "probability": 0.665283203125}, {"start": 2347.63, "end": 2347.93, "word": " R", "probability": 0.55224609375}, {"start": 2347.93, "end": 2349.49, "word": " الان", "probability": 0.61572265625}, {"start": 2349.49, "end": 2350.15, "word": " بنجيب", "probability": 0.80682373046875}, {"start": 2350.15, "end": 2350.67, "word": " قيمة", "probability": 0.9949544270833334}, {"start": 2350.67, "end": 2350.81, "word": " ال", "probability": 0.75830078125}, {"start": 2350.81, "end": 2351.17, "word": " limit", "probability": 0.9580078125}, {"start": 2351.17, "end": 2353.97, "word": " اللي", "probability": 0.820556640625}, {"start": 2353.97, "end": 2354.15, "word": " هي", "probability": 0.7763671875}, {"start": 2354.15, "end": 2354.31, "word": " ال", "probability": 0.88525390625}, {"start": 2354.31, "end": 2354.61, "word": " X", "probability": 0.50439453125}], "temperature": 1.0}, {"id": 85, "seek": 238473, "start": 2356.0, "end": 2384.74, "text": "فنرجع لل inductive formula to find x we have من ال inductive formula أنا عندي ال limit ل x n plus one equals two بالساوية اتنين minus", "tokens": [5172, 1863, 47341, 3615, 24976, 31612, 488, 8513, 281, 915, 2031, 321, 362, 9154, 2423, 31612, 488, 8513, 41850, 18871, 16254, 2423, 4948, 5296, 2031, 297, 1804, 472, 6915, 732, 20666, 3794, 995, 2407, 10632, 1975, 2655, 1863, 9957, 3175], "avg_logprob": -0.25628810975609756, "compression_ratio": 1.2462686567164178, "no_speech_prob": 0.0, "words": [{"start": 2356.0, "end": 2356.76, "word": "فنرجع", "probability": 0.8988037109375}, {"start": 2356.76, "end": 2356.98, "word": " لل", "probability": 0.84033203125}, {"start": 2356.98, "end": 2357.72, "word": " inductive", "probability": 0.57891845703125}, {"start": 2357.72, "end": 2358.26, "word": " formula", "probability": 0.95361328125}, {"start": 2358.26, "end": 2362.76, "word": " to", "probability": 0.75927734375}, {"start": 2362.76, "end": 2365.36, "word": " find", "probability": 0.9306640625}, {"start": 2365.36, "end": 2368.36, "word": " x", "probability": 0.56396484375}, {"start": 2368.36, "end": 2369.86, "word": " we", "probability": 0.693359375}, {"start": 2369.86, "end": 2370.38, "word": " have", "probability": 0.96875}, {"start": 2370.38, "end": 2370.7, "word": " من", "probability": 0.98974609375}, {"start": 2370.7, "end": 2370.84, "word": " ال", "probability": 0.8212890625}, {"start": 2370.84, "end": 2371.38, "word": " inductive", "probability": 0.942626953125}, {"start": 2371.38, "end": 2371.9, "word": " formula", "probability": 0.96875}, {"start": 2371.9, "end": 2373.62, "word": " أنا", "probability": 0.5283203125}, {"start": 2373.62, "end": 2374.06, "word": " عندي", "probability": 0.89794921875}, {"start": 2374.06, "end": 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"seek": 240119, "start": 2386.24, "end": 2401.2, "text": "واحد على limit xm هذا لما اخد ال limit للطرفين في ال inductive formula طب هذا طرف الشمال بساوي x و الطرف اليمين واحد على x", "tokens": [14407, 24401, 15844, 4948, 2031, 76, 23758, 5296, 15042, 1975, 9778, 3215, 2423, 4948, 24976, 9566, 28480, 9957, 8978, 2423, 31612, 488, 8513, 23032, 3555, 23758, 23032, 28480, 25124, 2304, 6027, 4724, 3794, 995, 45865, 2031, 4032, 41950, 28480, 2423, 32640, 9957, 36764, 24401, 15844, 2031], "avg_logprob": -0.30236038502226487, "compression_ratio": 1.4538461538461538, "no_speech_prob": 0.0, "words": [{"start": 2386.24, "end": 2387.1, "word": "واحد", "probability": 0.560699462890625}, {"start": 2387.1, "end": 2387.34, "word": " على", "probability": 0.62890625}, {"start": 2387.34, "end": 2387.84, "word": " limit", "probability": 0.9189453125}, {"start": 2387.84, "end": 2389.62, "word": " xm", "probability": 0.35711669921875}, {"start": 2389.62, "end": 2389.88, "word": " هذا", "probability": 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0.806640625}, {"start": 2396.64, "end": 2397.14, "word": " الشمال", "probability": 0.87451171875}, {"start": 2397.14, "end": 2397.62, "word": " بساوي", "probability": 0.7833251953125}, {"start": 2397.62, "end": 2398.04, "word": " x", "probability": 0.857421875}, {"start": 2398.04, "end": 2399.26, "word": " و", "probability": 0.6298828125}, {"start": 2399.26, "end": 2399.64, "word": " الطرف", "probability": 0.884033203125}, {"start": 2399.64, "end": 2400.18, "word": " اليمين", "probability": 0.8546549479166666}, {"start": 2400.18, "end": 2400.64, "word": " واحد", "probability": 0.96875}, {"start": 2400.64, "end": 2400.82, "word": " على", "probability": 0.83154296875}, {"start": 2400.82, "end": 2401.2, "word": " x", "probability": 0.95654296875}], "temperature": 1.0}, {"id": 87, "seek": 242601, "start": 2402.31, "end": 2426.01, "text": "الان حل المعادلة هاد في X اضرب في X بطلع عندي X تربيع سالب اتنين X موجة بواحد بساوي سفر وانت بتحلل الى X موجة باتنين X سالب واحد الكل تربيع بساوي سفر فبطلع X بساوي واحد", "tokens": [6027, 7649, 11331, 1211, 9673, 3615, 18513, 37977, 8032, 18513, 8978, 1783, 1975, 11242, 25513, 8978, 1783, 4724, 9566, 1211, 3615, 18871, 16254, 1783, 6055, 2288, 21292, 3615, 8608, 6027, 3555, 1975, 2655, 1863, 9957, 1783, 3714, 29245, 3660, 4724, 14407, 24401, 4724, 3794, 995, 45865, 8608, 5172, 2288, 4032, 7649, 2655, 39894, 5016, 1211, 1211, 2423, 7578, 1783, 3714, 29245, 3660, 4724, 9307, 1863, 9957, 1783, 8608, 6027, 3555, 36764, 24401, 2423, 28820, 6055, 2288, 21292, 3615, 4724, 3794, 995, 45865, 8608, 5172, 2288, 6156, 3555, 9566, 1211, 3615, 1783, 4724, 3794, 995, 45865, 36764, 24401], "avg_logprob": -0.13807398597804868, "compression_ratio": 2.0206896551724136, "no_speech_prob": 0.0, "words": [{"start": 2402.31, "end": 2402.73, "word": "الان", "probability": 0.812255859375}, {"start": 2402.73, "end": 2403.01, "word": " حل", "probability": 0.84814453125}, {"start": 2403.01, "end": 2403.53, "word": " المعادلة", "probability": 0.8994140625}, 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0.615576171875}, {"start": 2487.61, "end": 2488.05, "word": " تلاتة", "probability": 0.8646240234375}, {"start": 2488.05, "end": 2488.39, "word": " اربعة", "probability": 0.8426106770833334}, {"start": 2488.39, "end": 2488.63, "word": " فش", "probability": 0.3045654296875}, {"start": 2488.63, "end": 2488.81, "word": " ولا", "probability": 0.8134765625}, {"start": 2488.81, "end": 2489.11, "word": " سؤال", "probability": 0.9925130208333334}, {"start": 2489.11, "end": 2493.87, "word": " عندكم", "probability": 0.96826171875}, {"start": 2493.87, "end": 2504.03, "word": " فحللكم", "probability": 0.683837890625}, {"start": 2504.03, "end": 2504.35, "word": " سؤال", "probability": 0.8974609375}, {"start": 2504.35, "end": 2504.95, "word": " يحداش", "probability": 0.7523600260416666}, {"start": 2504.95, "end": 2505.83, "word": " لانه", "probability": 0.6713053385416666}, {"start": 2505.83, "end": 2507.01, "word": " واضح", "probability": 0.9820963541666666}, {"start": 2507.01, "end": 2507.17, 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"seek": 254634, "start": 2517.8, "end": 2546.34, "text": "إذن سؤال 11 سيكشن تلاتة أربعة suppose افترضي ان xn أكبر من أو ساوي سفر for every natural number n and ال limit لل sequence", "tokens": [28814, 8848, 1863, 8608, 33604, 6027, 2975, 8608, 1829, 4117, 8592, 1863, 6055, 1211, 9307, 3660, 5551, 25513, 27884, 7297, 1975, 5172, 2655, 43042, 1829, 16472, 2031, 77, 5551, 4117, 26890, 9154, 34051, 8608, 995, 45865, 8608, 5172, 2288, 337, 633, 3303, 1230, 297, 293, 2423, 4948, 24976, 8310], "avg_logprob": -0.3324999874830246, "compression_ratio": 1.1712328767123288, "no_speech_prob": 0.0, "words": [{"start": 2517.8, "end": 2518.38, "word": "إذن", "probability": 0.5275472005208334}, {"start": 2518.38, "end": 2520.02, "word": " سؤال", "probability": 0.84765625}, {"start": 2520.02, "end": 2520.32, "word": " 11", "probability": 0.442626953125}, {"start": 2520.32, "end": 2521.04, "word": " سيكشن", "probability": 0.6455078125}, {"start": 2521.04, "end": 2521.62, "word": " تلاتة", "probability": 0.79742431640625}, {"start": 2521.62, "end": 2522.24, "word": " أربعة", "probability": 0.8678385416666666}, {"start": 2522.24, "end": 2527.28, "word": " suppose", "probability": 0.388916015625}, {"start": 2527.28, "end": 2530.86, "word": " افترضي", "probability": 0.87724609375}, {"start": 2530.86, "end": 2531.24, "word": " ان", "probability": 0.439697265625}, {"start": 2531.24, "end": 2532.82, "word": " xn", "probability": 0.337646484375}, {"start": 2532.82, "end": 2534.46, "word": " أكبر", "probability": 0.89404296875}, {"start": 2534.46, "end": 2534.66, "word": " من", "probability": 0.7294921875}, {"start": 2534.66, "end": 2534.8, "word": " أو", "probability": 0.958984375}, {"start": 2534.8, "end": 2535.2, "word": " ساوي", "probability": 0.87744140625}, {"start": 2535.2, "end": 2535.74, "word": " سفر", "probability": 0.82275390625}, {"start": 2535.74, "end": 2537.04, "word": " for", "probability": 0.9423828125}, {"start": 2537.04, "end": 2537.68, "word": " every", "probability": 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2564.33, "word": " sequence", "probability": 0.90087890625}, {"start": 2564.33, "end": 2565.29, "word": " xn", "probability": 0.963134765625}, {"start": 2565.29, "end": 2568.49, "word": " convergence", "probability": 0.76123046875}], "temperature": 1.0}, {"id": 93, "seek": 263190, "start": 2622.52, "end": 2631.9, "text": "Okay خلّينا نشوف ال .. طيب احنا نشوف solution", "tokens": [8297, 16490, 1211, 11703, 9957, 995, 8717, 8592, 38688, 2423, 4386, 23032, 1829, 3555, 1975, 5016, 8315, 8717, 8592, 38688, 3827], "avg_logprob": -0.26136363500898535, "compression_ratio": 1.0625, "no_speech_prob": 0.0, "words": [{"start": 2622.52, "end": 2623.44, "word": "Okay", "probability": 0.705078125}, {"start": 2623.44, "end": 2624.36, "word": " خلّينا", "probability": 0.69140625}, {"start": 2624.36, "end": 2624.82, "word": " نشوف", "probability": 0.9532877604166666}, {"start": 2624.82, "end": 2625.08, "word": " ال", "probability": 0.412353515625}, {"start": 2625.08, "end": 2625.34, "word": " ..", 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من الفرض by hypothesis من الفرض أنا عندي xn أكبر من أو ساوى سفر لكل n في n فهذا بيدّي", "tokens": [39237, 10943, 22807, 23032, 1829, 3555, 41850, 18871, 16254, 9154, 27188, 43042, 538, 17291, 9154, 27188, 43042, 41850, 18871, 16254, 2031, 77, 5551, 4117, 26890, 9154, 34051, 8608, 995, 2407, 7578, 8608, 5172, 2288, 5296, 28820, 297, 8978, 297, 6156, 3224, 15730, 4724, 25708, 11703, 1829], "avg_logprob": -0.1999667559532409, "compression_ratio": 1.3412698412698412, "no_speech_prob": 0.0, "words": [{"start": 2776.73, "end": 2777.81, "word": "تمام؟", "probability": 0.6678873697916666}, {"start": 2777.81, "end": 2778.89, "word": " طيب", "probability": 0.9392903645833334}, {"start": 2778.89, "end": 2779.81, "word": " أنا", "probability": 0.44970703125}, {"start": 2779.81, "end": 2780.15, "word": " عندي", "probability": 0.94677734375}, {"start": 2780.15, "end": 2780.31, "word": " من", "probability": 0.98828125}, {"start": 2780.31, "end": 2780.83, "word": " الفرض", "probability": 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0.8274739583333334}, {"start": 2801.41, "end": 2801.99, "word": " لكل", "probability": 0.983154296875}, {"start": 2801.99, "end": 2802.43, "word": " n", "probability": 0.79833984375}, {"start": 2802.43, "end": 2802.71, "word": " في", "probability": 0.9423828125}, {"start": 2802.71, "end": 2803.15, "word": " n", "probability": 0.75146484375}, {"start": 2803.15, "end": 2805.05, "word": " فهذا", "probability": 0.9508463541666666}, {"start": 2805.05, "end": 2805.69, "word": " بيدّي", "probability": 0.69775390625}], "temperature": 1.0}, {"id": 100, "seek": 283450, "start": 2807.56, "end": 2834.5, "text": "إنه X2N و أيضا X2N-1 أكبر من أو يساوي سفر لكل N في ال natural numbers وهذا بيقدي بدوره إلى إنه ال X اللي هي من هنا X بيساوي ليه بيساوي limit X2N", "tokens": [28814, 1863, 3224, 1783, 17, 45, 4032, 36632, 11242, 995, 1783, 17, 45, 12, 16, 5551, 4117, 26890, 9154, 34051, 7251, 3794, 995, 45865, 8608, 5172, 2288, 5296, 28820, 426, 8978, 2423, 3303, 3547, 37037, 15730, 4724, 1829, 4587, 16254, 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2814.86, "word": " أو", "probability": 0.95751953125}, {"start": 2814.86, "end": 2815.26, "word": " يساوي", "probability": 0.8587646484375}, {"start": 2815.26, "end": 2815.78, "word": " سفر", "probability": 0.8282877604166666}, {"start": 2815.78, "end": 2817.0, "word": " لكل", "probability": 0.9794921875}, {"start": 2817.0, "end": 2817.4, "word": " N", "probability": 0.841796875}, {"start": 2817.4, "end": 2817.88, "word": " في", "probability": 0.92578125}, {"start": 2817.88, "end": 2818.46, "word": " ال", "probability": 0.95654296875}, {"start": 2818.46, "end": 2818.76, "word": " natural", "probability": 0.3330078125}, {"start": 2818.76, "end": 2819.52, "word": " numbers", "probability": 0.70947265625}, {"start": 2819.52, "end": 2821.94, "word": " وهذا", "probability": 0.8583984375}, {"start": 2821.94, "end": 2822.58, "word": " بيقدي", "probability": 0.71112060546875}, {"start": 2822.58, "end": 2823.62, "word": " بدوره", "probability": 0.9588216145833334}, {"start": 2823.62, "end": 2825.1, "word": " إلى", "probability": 0.9521484375}, {"start": 2825.1, "end": 2825.68, "word": " إنه", "probability": 0.677734375}, {"start": 2825.68, "end": 2827.06, "word": " ال", "probability": 0.72998046875}, {"start": 2827.06, "end": 2827.56, "word": " X", "probability": 0.93798828125}, {"start": 2827.56, "end": 2829.04, "word": " اللي", "probability": 0.871826171875}, {"start": 2829.04, "end": 2829.32, "word": " هي", "probability": 0.77392578125}, {"start": 2829.32, "end": 2829.56, "word": " من", "probability": 0.986328125}, {"start": 2829.56, "end": 2829.86, "word": " هنا", "probability": 0.9970703125}, {"start": 2829.86, "end": 2830.3, "word": " X", "probability": 0.88623046875}, {"start": 2830.3, "end": 2831.04, "word": " بيساوي", "probability": 0.82880859375}, {"start": 2831.04, "end": 2831.34, "word": " ليه", "probability": 0.7423095703125}, {"start": 2831.34, "end": 2831.84, "word": " بيساوي", "probability": 0.933203125}, {"start": 2831.84, "end": 2832.28, "word": " limit", "probability": 0.8173828125}, {"start": 2832.28, "end": 2834.5, "word": " X2N", "probability": 0.9148763020833334}], "temperature": 1.0}, {"id": 101, "seek": 286181, "start": 2836.87, "end": 2861.81, "text": "هي عندي هذا هو هذا من هان بطلع عندي limit x2n بساوي x و من هان بطلع عندي limit سالب x2n سالب واحد بساوي x او", "tokens": [3224, 1829, 18871, 16254, 23758, 31439, 23758, 9154, 8032, 7649, 4724, 9566, 1211, 3615, 18871, 16254, 4948, 2031, 17, 77, 4724, 3794, 995, 45865, 2031, 4032, 9154, 8032, 7649, 4724, 9566, 1211, 3615, 18871, 16254, 4948, 8608, 6027, 3555, 2031, 17, 77, 8608, 6027, 3555, 36764, 24401, 4724, 3794, 995, 45865, 2031, 1975, 2407], "avg_logprob": -0.18409090909090908, "compression_ratio": 1.7835051546391754, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2836.87, "end": 2837.21, "word": "هي", "probability": 0.56597900390625}, {"start": 2837.21, "end": 2837.69, "word": " عندي", "probability": 0.824462890625}, {"start": 2837.69, "end": 2842.69, "word": " هذا", "probability": 0.666015625}, {"start": 2842.69, "end": 2843.01, "word": " هو", "probability": 0.974609375}, {"start": 2843.01, "end": 2843.49, "word": " هذا", "probability": 0.96484375}, {"start": 2843.49, "end": 2845.05, "word": " من", "probability": 0.9033203125}, {"start": 2845.05, "end": 2845.47, "word": " هان", "probability": 0.564453125}, {"start": 2845.47, "end": 2846.17, "word": " بطلع", "probability": 0.8546142578125}, {"start": 2846.17, "end": 2846.55, "word": " عندي", "probability": 0.874267578125}, {"start": 2846.55, "end": 2847.03, "word": " limit", "probability": 0.9658203125}, {"start": 2847.03, "end": 2849.89, "word": " x2n", "probability": 0.5244140625}, {"start": 2849.89, "end": 2850.43, "word": " بساوي", "probability": 0.80908203125}, {"start": 2850.43, "end": 2850.87, "word": " x", "probability": 0.919921875}, {"start": 2850.87, "end": 2851.73, "word": " و", "probability": 0.95849609375}, {"start": 2851.73, "end": 2851.93, "word": " من", "probability": 0.52490234375}, {"start": 2851.93, "end": 2852.23, "word": " هان", "probability": 0.9208984375}, {"start": 2852.23, "end": 2852.65, "word": " بطلع", "probability": 0.9801025390625}, {"start": 2852.65, "end": 2853.07, "word": " عندي", "probability": 0.974365234375}, {"start": 2853.07, "end": 2854.31, "word": " limit", "probability": 0.9833984375}, {"start": 2854.31, "end": 2856.15, "word": " سالب", "probability": 0.8279622395833334}, {"start": 2856.15, "end": 2857.65, "word": " x2n", "probability": 0.9527994791666666}, {"start": 2857.65, "end": 2858.19, "word": " سالب", "probability": 0.9334309895833334}, {"start": 2858.19, "end": 2858.59, "word": " واحد", "probability": 0.8759765625}, {"start": 2858.59, "end": 2859.13, "word": " بساوي", "probability": 0.9759521484375}, {"start": 2859.13, "end": 2859.55, "word": " x", "probability": 0.97021484375}, {"start": 2859.55, "end": 2861.81, "word": " او", "probability": 0.778564453125}], "temperature": 1.0}, {"id": 102, "seek": 289301, "start": 2865.51, "end": 2893.01, "text": "السالب واحد بيطلع برا ال limit فبطلع عندي limit x2n سالب واحد بساوي سالب x مظبوط؟ إذا هاي عندي أنا limit x2n سا��ب واحد هذا بيطلع بساوي سالب x أو لأ في الأول ال x بساوي limit x2n وهذا بيطلع أكبر من أو ساوي سفر", "tokens": [6027, 3794, 6027, 3555, 36764, 24401, 4724, 1829, 9566, 1211, 3615, 4724, 23557, 2423, 4948, 6156, 3555, 9566, 1211, 3615, 18871, 16254, 4948, 2031, 17, 77, 8608, 6027, 3555, 36764, 24401, 4724, 3794, 995, 45865, 8608, 6027, 3555, 2031, 3714, 19913, 3555, 2407, 9566, 22807, 11933, 15730, 8032, 47302, 18871, 16254, 41850, 4948, 2031, 17, 77, 8608, 6027, 3555, 36764, 24401, 23758, 4724, 1829, 9566, 1211, 3615, 4724, 3794, 995, 45865, 8608, 6027, 3555, 2031, 34051, 5296, 10721, 8978, 16247, 12610, 2423, 2031, 4724, 3794, 995, 45865, 4948, 2031, 17, 77, 37037, 15730, 4724, 1829, 9566, 1211, 3615, 5551, 4117, 26890, 9154, 34051, 8608, 995, 45865, 8608, 5172, 2288], "avg_logprob": -0.22372158792885868, "compression_ratio": 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limit تبعتها إذا كانت convergent ال limit تبعتها تطلع غير سالبة و كذلك سالب x اللي هي بتساوي limit x2n سالب واحد برضه أنا عندي x2n سالب واحد كلهم", "tokens": [1211, 33456, 41850, 18871, 16254, 2031, 17, 77, 5551, 4117, 26890, 9154, 34051, 3794, 3615, 11296, 1958, 5296, 28820, 297, 6156, 1211, 15042, 6055, 30544, 2423, 8310, 11331, 3215, 23328, 11296, 32771, 13546, 8608, 6027, 49401, 6156, 6027, 4948, 6055, 3555, 34268, 11296, 11933, 15730, 25961, 2655, 9652, 6930, 2423, 4948, 6055, 3555, 34268, 11296, 6055, 9566, 1211, 3615, 32771, 13546, 8608, 6027, 49401, 4032, 9122, 8848, 23275, 8608, 6027, 3555, 2031, 13672, 1829, 39896, 39894, 3794, 995, 45865, 4948, 2031, 17, 77, 8608, 6027, 3555, 36764, 24401, 4724, 43042, 3224, 41850, 18871, 16254, 2031, 17, 77, 8608, 6027, 3555, 36764, 24401, 28242, 16095], "avg_logprob": -0.18482142516544886, "compression_ratio": 1.8341708542713568, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2893.72, "end": 2894.1, "word": "لأن", 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