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+{"segments": [{"id": 1, "seek": 4730, "start": 19.76, "end": 47.3, "text": "بسم الله الرحمن الرحيم اليوم إن شاء الله موضوعنا اللي هو الأساسي اللي هو التكافؤ العددي للمجموعات آه لكن في كان مثال أو proposition أخير في ال section الماضي خمسة واحد خلينا نشوفه على السريع و ننتقل ل section خمسة اتنين اللي بتحدث عن اللي هو التكافؤ العددي للمجموع فطبعا احنا كنا فيهن نظرية أثبتنا انه فيهن معيار للمجموعة ان تكون finite و يمكن هذا يكون بديل للتعريف", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 45595, 20498, 36145, 13412, 16606, 21984, 3714, 2407, 11242, 45367, 8315, 13672, 1829, 31439, 16247, 3794, 32277, 1829, 13672, 1829, 31439, 16712, 4117, 31845, 33604, 18863, 3215, 16254, 5296, 19528, 7435, 2304, 45367, 9307, 19753, 3224, 44381, 8978, 25961, 50113, 6027, 34051, 24830, 5551, 9778, 13546, 8978, 2423, 3541, 9673, 46958, 1829, 16490, 2304, 3794, 3660, 36764, 24401, 16490, 1211, 9957, 995, 8717, 8592, 38688, 3224, 15844, 21136, 16572, 3615, 4032, 8717, 29399, 4587, 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sets", "probability": 0.87841796875}, {"start": 138.4, "end": 142.14, "word": " فدولة", "probability": 0.82574462890625}, {"start": 142.14, "end": 142.84, "word": " مجموعتين", "probability": 0.8866373697916666}, {"start": 142.84, "end": 143.34, "word": " finite", "probability": 0.982421875}, {"start": 143.34, "end": 144.18, "word": " بدنا", "probability": 0.46142578125}, {"start": 144.18, "end": 144.46, "word": " نثبت", "probability": 0.991943359375}, {"start": 144.46, "end": 144.56, "word": " ان", "probability": 0.615234375}, {"start": 144.56, "end": 145.26, "word": " الاتحاد", "probability": 0.942138671875}, {"start": 145.26, "end": 146.08, "word": " finite", "probability": 0.9765625}], "temperature": 1.0}, {"id": 6, "seek": 16352, "start": 155.28, "end": 163.52, "text": "to prove that A union B is finite", "tokens": [1353, 7081, 300, 316, 11671, 363, 307, 19362], "avg_logprob": -0.3936631944444444, "compression_ratio": 0.8048780487804879, "no_speech_prob": 0.0, "words": [{"start": 155.28, "end": 155.48, "word": "to", "probability": 0.10760498046875}, {"start": 155.48, "end": 156.02, "word": " prove", "probability": 0.91064453125}, {"start": 156.02, "end": 158.16, "word": " that", "probability": 0.9443359375}, {"start": 158.16, "end": 159.68, "word": " A", "probability": 0.73193359375}, {"start": 159.68, "end": 160.56, "word": " union", "probability": 0.7958984375}, {"start": 160.56, "end": 161.24, "word": " B", "probability": 0.54248046875}, {"start": 161.24, "end": 162.28, "word": " is", "probability": 0.9541015625}, {"start": 162.28, "end": 163.52, "word": " finite", "probability": 0.96435546875}], "temperature": 1.0}, {"id": 7, "seek": 19260, "start": 167.46, "end": 192.6, "text": "فهذه البواطيات والمطلوب طبعا إيش معنى finite؟ يا بده تستخدم التعريف هنا ليست infinite أو بده تستخدم النظرية السابقة أثبت أنها يا Phi يا تكافئ أنصب K من الـ K معينة، تمام؟ أه طبعا زي الملاحظة اللي حكيناها أنه لما ناخد الاتحاد مش دايما إذا فيه خمس أو عشر بطلع 15 فبده ناخد بعض الاحتمالات في عين الاعتبار لكن الفكرة الرئيسية احنا حكيناها لكن بدا شوية تفصيلات عشان نشتغل صح", "tokens": [5172, 3224, 24192, 29739, 2407, 41193, 1829, 9307, 16070, 2304, 9566, 1211, 37746, 23032, 3555, 3615, 995, 11933, 1829, 8592, 20449, 1863, 7578, 19362, 22807, 35186, 47525, 3224, 6055, 14851, 9778, 40448, 16712, 3615, 16572, 5172, 34105, 32239, 14851, 13785, 34051, 47525, 3224, 6055, 14851, 9778, 40448, 28239, 19913, 2288, 10632, 21136, 16758, 28671, 5551, 12984, 3555, 2655, 14739, 11296, 35186, 41435, 35186, 6055, 4117, 31845, 19986, 14739, 9381, 3555, 591, 9154, 2423, 39184, 591, 20449, 9957, 3660, 12399, 46811, 10943, 22807, 5551, 3224, 23032, 3555, 3615, 995, 30767, 1829, 9673, 15040, 5016, 19913, 3660, 13672, 1829, 11331, 4117, 1829, 8315, 11296, 14739, 3224, 5296, 15042, 8717, 47283, 3215, 2423, 9307, 5016, 18513, 37893, 11778, 47302, 15042, 11933, 15730, 8978, 3224, 16490, 2304, 3794, 34051, 6225, 46309, 4724, 9566, 1211, 3615, 2119, 6156, 44510, 3224, 8717, 47283, 3215, 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ايه", "probability": 0.8795572916666666}], "temperature": 1.0}, {"id": 15, "seek": 39878, "start": 371.5, "end": 398.78, "text": "وهي مجموعة D وهي A وهي D من الاتحاد التنتين مع بعض لو أخدت هي ال A من الاتحاد مين تم من الاتحاد؟ B ناقص A فإذا هنا هذه ملاحظة أنه we know that واتوقع مرة عالية هي exercise أو لحظة we know that A union B إيش بتساوي؟ A union", "tokens": [2407, 3224, 1829, 3714, 7435, 2304, 2407, 27884, 413, 37037, 1829, 316, 37037, 1829, 413, 9154, 2423, 9307, 5016, 18513, 16712, 29399, 9957, 20449, 45030, 11242, 45164, 5551, 9778, 3215, 2655, 39896, 2423, 316, 9154, 2423, 9307, 5016, 18513, 3714, 9957, 46811, 9154, 2423, 9307, 5016, 18513, 22807, 363, 8717, 995, 4587, 9381, 316, 6156, 28814, 15730, 34105, 29538, 3714, 15040, 5016, 19913, 3660, 14739, 3224, 321, 458, 300, 4032, 9307, 30543, 3615, 3714, 25720, 6225, 6027, 10632, 39896, 5380, 34051, 5296, 5016, 19913, 3660, 321, 458, 300, 316, 11671, 363, 11933, 1829, 8592, 39894, 3794, 995, 45865, 22807, 316, 11671], 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