{"segments": [{"id": 1, "seek": 4545, "start": 21.63, "end": 45.45, "text": "Okay ان شاء الله اليوم هنعمل مناقشة لبعض المسائل في section اتنين تلاتة و اتنين اربعة زي ما وعدناكم سابقا و نشوف بعض الحلول لبعض المسائل المهمة ففي بسألة", "tokens": [8297, 16472, 13412, 16606, 21984, 45595, 20498, 8032, 1863, 25957, 1211, 3714, 8315, 4587, 8592, 3660, 5296, 3555, 3615, 11242, 9673, 3794, 16373, 1211, 8978, 3541, 1975, 2655, 1863, 9957, 6055, 1211, 9307, 3660, 4032, 1975, 2655, 1863, 9957, 1975, 25513, 27884, 30767, 1829, 19446, 4032, 22488, 8315, 24793, 8608, 16758, 4587, 995, 4032, 8717, 8592, 38688, 45030, 11242, 21542, 1211, 12610, 5296, 3555, 3615, 11242, 9673, 3794, 16373, 1211, 9673, 16095, 3660, 6156, 41185, 4724, 3794, 10721, 37977], "avg_logprob": -0.08623047173023224, "compression_ratio": 1.608433734939759, "no_speech_prob": 0.0, "words": [{"start": 21.63, "end": 22.15, "word": "Okay", "probability": 0.92578125}, {"start": 22.15, "end": 23.17, "word": " ان", "probability": 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في الـ claim أو في الإدعاء تمام؟ وهذا بثبت الجزء الأول في ال part A هاي infimum AS بساوي A في W اللي هو infimum S إذن هذا بثبت الجزء الأول في الفرع A Similarly بالمثل ممكن", "tokens": [2304, 2407, 11242, 5016, 8978, 2423, 39184, 3932, 34051, 8978, 33688, 3215, 3615, 16606, 46811, 10943, 22807, 37037, 15730, 4724, 12984, 3555, 2655, 25724, 11622, 38207, 16247, 12610, 8978, 2423, 644, 316, 8032, 47302, 1536, 332, 449, 7469, 4724, 3794, 995, 45865, 316, 8978, 343, 13672, 1829, 31439, 1536, 332, 449, 318, 11933, 8848, 1863, 23758, 4724, 12984, 3555, 2655, 25724, 11622, 38207, 16247, 12610, 8978, 27188, 2288, 3615, 316, 13157, 20666, 2304, 12984, 1211, 3714, 43020], "avg_logprob": -0.19821714017635736, "compression_ratio": 1.6235294117647059, "no_speech_prob": 0.0, "words": [{"start": 396.63, "end": 397.31, "word": "موضح", "probability": 0.8367919921875}, {"start": 397.31, "end": 397.49, "word": " في", "probability": 0.93017578125}, {"start": 397.49, "end": 397.63, "word": " الـ", 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X في S", "tokens": [9566, 1829, 3555, 1975, 8315, 18871, 16254, 4724, 1829, 6225, 3215, 1211, 8608, 6027, 3555, 1975, 15730, 36764, 24401, 15844, 4724, 1829, 1975, 1829, 11242, 995, 6225, 3215, 1211, 8608, 6027, 3555, 6156, 1211, 2407, 48812, 25513, 2655, 9673, 2655, 3555, 995, 9957, 3660, 29538, 8978, 6225, 3215, 1211, 8608, 6027, 3555, 13672, 1829, 31439, 36764, 24401, 15844, 4724, 1829, 6156, 3224, 1829, 9566, 1211, 3615, 18871, 16254, 4724, 1829, 4386, 4724, 1829, 15844, 4724, 1829, 5551, 9381, 17082, 2288, 9154, 34051, 8608, 995, 45865, 1783, 5296, 28820, 1783, 8978, 318], "avg_logprob": -0.18206522127856378, "compression_ratio": 1.8516129032258064, "no_speech_prob": 0.0, "words": [{"start": 689.92, "end": 690.38, "word": "طيب", "probability": 0.6832275390625}, {"start": 690.38, "end": 690.6, "word": " انا", "probability": 0.640869140625}, {"start": 690.6, "end": 691.06, "word": " عندي", "probability": 0.786376953125}, {"start": 691.06, "end": 691.56, "word": " بي", "probability": 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upper bound للست بي اس و بعدين أخدنا أي upper bound", "tokens": [9566, 3555, 23758, 23758, 8608, 27842, 11296, 261, 11933, 15730, 4724, 1829, 8978, 261, 5551, 9381, 17082, 2288, 9154, 34051, 8608, 995, 45865, 2423, 272, 11933, 15730, 2423, 26890, 3224, 7649, 23758, 5551, 12984, 3555, 2655, 8315, 8978, 3224, 11331, 26108, 2655, 9957, 36145, 3224, 5551, 12610, 44049, 38207, 18863, 3215, 3215, 4724, 1829, 11778, 16758, 20292, 2407, 23758, 6597, 5472, 24976, 14851, 4724, 1829, 24525, 4032, 39182, 9957, 5551, 9778, 3215, 8315, 36632, 6597, 5472], "avg_logprob": -0.26278410329447166, "compression_ratio": 1.6294117647058823, "no_speech_prob": 0.0, "words": [{"start": 888.92, "end": 889.24, "word": "طب", "probability": 0.50238037109375}, {"start": 889.24, "end": 889.66, "word": " هذا", "probability": 0.86962890625}, {"start": 889.66, "end": 890.38, "word": " هذا", "probability": 0.489501953125}, {"start": 890.38, "end": 890.96, "word": " سمنها", "probability": 0.82177734375}, {"start": 890.96, 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"probability": 0.9737955729166666}, {"start": 1308.51, "end": 1311.65, "word": " by", "probability": 0.73095703125}, {"start": 1311.65, "end": 1312.33, "word": " definition", "probability": 0.951171875}, {"start": 1312.33, "end": 1312.95, "word": " حسب", "probability": 0.969970703125}, {"start": 1312.95, "end": 1314.35, "word": " التعريفات", "probability": 0.97314453125}, {"start": 1314.35, "end": 1317.95, "word": " ال", "probability": 0.890625}, {"start": 1317.95, "end": 1318.67, "word": " infimum", "probability": 0.598388671875}], "temperature": 1.0}, {"id": 46, "seek": 133175, "start": 1319.99, "end": 1331.75, "text": "للست S0 أصغر من أو ساوي ال supremum للست S0 الست S0 هذه", "tokens": [1211, 1211, 14851, 318, 15, 5551, 9381, 17082, 2288, 9154, 34051, 8608, 995, 45865, 2423, 23710, 449, 24976, 14851, 318, 15, 2423, 14851, 318, 15, 29538], "avg_logprob": -0.24811921958570127, "compression_ratio": 1.1506849315068493, "no_speech_prob": 0.0, "words": [{"start": 1319.99, "end": 1320.83, 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"word": " هذه", "probability": 0.61572265625}], "temperature": 1.0}, {"id": 47, "seek": 135925, "start": 1335.23, "end": 1359.25, "text": "طبعا هذه ال set S0 subset من S و S bounded إلى S0 bounded ال infimum ل S0 exist و ال suprem ل S0 exist دائما لأي set S0 ال infimum دائما أصغر من أو يساوي ال supremum نعمل رسمة نوضح الكلام هذا", "tokens": [9566, 3555, 3615, 995, 29538, 2423, 992, 318, 15, 25993, 9154, 318, 4032, 318, 37498, 30731, 318, 15, 37498, 2423, 1536, 332, 449, 5296, 318, 15, 2514, 4032, 2423, 23710, 5296, 318, 15, 2514, 11778, 16373, 15042, 5296, 10721, 1829, 992, 318, 15, 2423, 1536, 332, 449, 11778, 16373, 15042, 5551, 9381, 17082, 2288, 9154, 34051, 7251, 3794, 995, 45865, 2423, 23710, 449, 8717, 25957, 1211, 12602, 38251, 3660, 8717, 2407, 11242, 5016, 2423, 28820, 10943, 23758], "avg_logprob": -0.2049278825139388, "compression_ratio": 1.543859649122807, "no_speech_prob": 0.0, "words": [{"start": 1335.23, "end": 1336.15, "word": "طبعا", "probability": 0.769195556640625}, 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" دائما", "probability": 0.7999674479166666}, {"start": 1348.61, "end": 1349.03, "word": " لأي", "probability": 0.81787109375}, {"start": 1349.03, "end": 1349.47, "word": " set", "probability": 0.98095703125}, {"start": 1349.47, "end": 1350.31, "word": " S0", "probability": 0.98974609375}, {"start": 1350.31, "end": 1350.99, "word": " ال", "probability": 0.90478515625}, {"start": 1350.99, "end": 1351.45, "word": " infimum", "probability": 0.97314453125}, {"start": 1351.45, "end": 1351.89, "word": " دائما", "probability": 0.8854166666666666}, {"start": 1351.89, "end": 1352.43, "word": " أصغر", "probability": 0.9620361328125}, {"start": 1352.43, "end": 1352.61, "word": " من", "probability": 0.94775390625}, {"start": 1352.61, "end": 1352.77, "word": " أو", "probability": 0.98193359375}, {"start": 1352.77, "end": 1353.15, "word": " يساوي", "probability": 0.8641357421875}, {"start": 1353.15, "end": 1353.31, "word": " ال", "probability": 0.82080078125}, {"start": 1353.31, "end": 1354.91, "word": " supremum", "probability": 0.6375732421875}, {"start": 1354.91, "end": 1357.21, "word": " نعمل", "probability": 0.9026692708333334}, {"start": 1357.21, "end": 1357.81, "word": " رسمة", "probability": 0.9435221354166666}, {"start": 1357.81, "end": 1358.33, "word": " نوضح", "probability": 0.9464111328125}, {"start": 1358.33, "end": 1358.81, "word": " الكلام", "probability": 0.9518229166666666}, {"start": 1358.81, "end": 1359.25, "word": " هذا", "probability": 0.8876953125}], "temperature": 1.0}, {"id": 48, "seek": 138795, "start": 1364.85, "end": 1387.95, "text": "نعتبر أن هذه هي الست اس وهي ال .. ال .. ال supremum للست اس وهي ال infimum", "tokens": [1863, 34268, 26890, 14739, 29538, 39896, 2423, 14851, 24525, 37037, 1829, 2423, 4386, 2423, 4386, 2423, 23710, 449, 24976, 14851, 24525, 37037, 1829, 2423, 1536, 332, 449], "avg_logprob": -0.39536828973463606, "compression_ratio": 1.435897435897436, "no_speech_prob": 0.0, "words": [{"start": 1364.8500000000001, "end": 1365.65, "word": "نعتبر", "probability": 0.8885091145833334}, {"start": 1365.65, "end": 1365.81, "word": " أن", "probability": 0.308349609375}, {"start": 1365.81, "end": 1366.11, "word": " هذه", "probability": 0.73876953125}, {"start": 1366.11, "end": 1366.41, "word": " هي", "probability": 0.5625}, {"start": 1366.41, "end": 1366.85, "word": " الست", "probability": 0.557861328125}, {"start": 1366.85, "end": 1367.25, "word": " اس", "probability": 0.60009765625}, {"start": 1367.25, "end": 1376.85, "word": " وهي", "probability": 0.7333984375}, {"start": 1376.85, "end": 1378.31, "word": " ال", "probability": 0.9208984375}, {"start": 1378.31, "end": 1378.31, "word": " ..", "probability": 0.56005859375}, {"start": 1378.31, "end": 1380.39, "word": " ال", "probability": 0.8173828125}, {"start": 1380.39, "end": 1380.51, "word": " ..", "probability": 0.407958984375}, {"start": 1380.51, "end": 1380.83, "word": " ال", "probability": 0.640625}, {"start": 1380.83, "end": 1383.37, "word": " supremum", "probability": 0.473388671875}, {"start": 1383.37, "end": 1386.37, "word": " للست", "probability": 0.71923828125}, {"start": 1386.37, "end": 1386.77, "word": " اس", "probability": 0.89306640625}, {"start": 1386.77, "end": 1387.17, "word": " وهي", "probability": 0.85400390625}, {"start": 1387.17, "end": 1387.35, "word": " ال", "probability": 0.974609375}, {"start": 1387.35, "end": 1387.95, "word": " infimum", "probability": 0.7086588541666666}], "temperature": 1.0}, {"id": 49, "seek": 140607, "start": 1391.09, "end": 1406.07, "text": "للـ set S فدائما ال .. دائما ال minimum لأي set هو lower bound لل set وبالتالي أصغر من لو ساوي كل عناصرها", "tokens": [1211, 1211, 39184, 992, 318, 6156, 3215, 16373, 15042, 2423, 4386, 11778, 16373, 15042, 2423, 7285, 5296, 10721, 1829, 992, 31439, 3126, 5472, 24976, 992, 46599, 6027, 2655, 6027, 1829, 5551, 9381, 17082, 2288, 9154, 45164, 8608, 995, 45865, 28242, 18871, 33546, 2288, 11296], "avg_logprob": -0.28038193384806315, "compression_ratio": 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"word": " هو", "probability": 0.93603515625}, {"start": 1400.73, "end": 1401.09, "word": " lower", "probability": 0.93798828125}, {"start": 1401.09, "end": 1401.49, "word": " bound", "probability": 0.94873046875}, {"start": 1401.49, "end": 1401.71, "word": " لل", "probability": 0.84423828125}, {"start": 1401.71, "end": 1402.09, "word": " set", "probability": 0.9072265625}, {"start": 1402.09, "end": 1404.05, "word": " وبالتالي", "probability": 0.91318359375}, {"start": 1404.05, "end": 1404.45, "word": " أصغر", "probability": 0.9752197265625}, {"start": 1404.45, "end": 1404.57, "word": " من", "probability": 0.912109375}, {"start": 1404.57, "end": 1404.73, "word": " لو", "probability": 0.59423828125}, {"start": 1404.73, "end": 1405.15, "word": " ساوي", "probability": 0.7265625}, {"start": 1405.15, "end": 1405.45, "word": " كل", "probability": 0.98828125}, {"start": 1405.45, "end": 1406.07, "word": " عناصرها", "probability": 0.9625244140625}], "temperature": 1.0}, {"id": 50, "seek": 143379, "start": 1407.63, "end": 1433.79, "text": "هو عبارة عن lower bound للست ال supreme للست S هو عبارة عن upper bound للست وبالتالي أكبر من أو ساوي كل عناصرها فواضح أن ال infimum للست S لازم يكون أصغر من أو ساوي ال supremum ونفس الشيء لو أخذنا أي مجموعة جزئية سمنها S0", "tokens": [3224, 2407, 6225, 3555, 9640, 3660, 18871, 3126, 5472, 24976, 14851, 2423, 27756, 24976, 14851, 318, 31439, 6225, 3555, 9640, 3660, 18871, 6597, 5472, 24976, 14851, 46599, 6027, 2655, 6027, 1829, 5551, 4117, 26890, 9154, 34051, 8608, 995, 45865, 28242, 18871, 33546, 2288, 11296, 6156, 2407, 46958, 5016, 14739, 2423, 1536, 332, 449, 24976, 14851, 318, 5296, 31377, 2304, 7251, 30544, 5551, 9381, 17082, 2288, 9154, 34051, 8608, 995, 45865, 2423, 23710, 449, 4032, 1863, 36178, 25124, 1829, 38207, 45164, 5551, 9778, 8848, 8315, 36632, 3714, 7435, 2304, 2407, 27884, 10874, 11622, 19986, 10632, 8608, 27842, 11296, 318, 15], "avg_logprob": -0.15046875402331353, "compression_ratio": 1.703883495145631, 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"word": " فواضح", "probability": 0.9693603515625}, {"start": 1417.47, "end": 1417.65, "word": " أن", "probability": 0.4775390625}, {"start": 1417.65, "end": 1417.77, "word": " ال", "probability": 0.9365234375}, {"start": 1417.77, "end": 1418.27, "word": " infimum", "probability": 0.7821451822916666}, {"start": 1418.27, "end": 1419.41, "word": " للست", "probability": 0.944580078125}, {"start": 1419.41, "end": 1419.75, "word": " S", "probability": 0.93603515625}, {"start": 1419.75, "end": 1420.21, "word": " لازم", "probability": 0.9744466145833334}, {"start": 1420.21, "end": 1420.61, "word": " يكون", "probability": 0.9931640625}, {"start": 1420.61, "end": 1421.13, "word": " أصغر", "probability": 0.9661865234375}, {"start": 1421.13, "end": 1421.29, "word": " من", "probability": 0.9921875}, {"start": 1421.29, "end": 1421.47, "word": " أو", "probability": 0.99462890625}, {"start": 1421.47, "end": 1422.03, "word": " ساوي", "probability": 0.9811197916666666}, {"start": 1422.03, "end": 1422.77, "word": " ال", "probability": 0.85791015625}, {"start": 1422.77, "end": 1423.91, "word": " supremum", "probability": 0.78076171875}, {"start": 1423.91, "end": 1424.75, "word": " ونفس", "probability": 0.8611653645833334}, {"start": 1424.75, "end": 1425.21, "word": " الشيء", "probability": 0.9728190104166666}, {"start": 1425.21, "end": 1425.35, "word": " لو", "probability": 0.8046875}, {"start": 1425.35, "end": 1425.75, "word": " أخذنا", "probability": 0.869140625}, {"start": 1425.75, "end": 1426.03, "word": " أي", "probability": 0.7763671875}, {"start": 1426.03, "end": 1427.67, "word": " مجموعة", "probability": 0.96103515625}, {"start": 1427.67, "end": 1429.13, "word": " جزئية", "probability": 0.9068603515625}, {"start": 1429.13, "end": 1432.97, "word": " سمنها", "probability": 0.85009765625}, {"start": 1432.97, "end": 1433.79, "word": " S0", "probability": 0.793212890625}], "temperature": 1.0}, {"id": 51, "seek": 145962, "start": 1436.18, "end": 1459.62, "text": "يعني هذه المجموعة اسمها S0 فبما أن ال set S bounded إذن S0 bounded وبالتالي ال supremum ل S0 دايما أكبر من أو ساوي ال infimum ل S0 بنفس الطريقة إذن هذا دايما .. هذا دايما صحيح", "tokens": [40228, 22653, 29538, 9673, 7435, 2304, 2407, 27884, 24525, 2304, 11296, 318, 15, 6156, 3555, 15042, 14739, 2423, 992, 318, 37498, 11933, 8848, 1863, 318, 15, 37498, 46599, 6027, 2655, 6027, 1829, 2423, 23710, 449, 5296, 318, 15, 11778, 47302, 15042, 5551, 4117, 26890, 9154, 34051, 8608, 995, 45865, 2423, 1536, 332, 449, 5296, 318, 15, 44945, 36178, 41950, 16572, 28671, 11933, 8848, 1863, 23758, 11778, 47302, 15042, 4386, 23758, 11778, 47302, 15042, 20328, 5016, 1829, 5016], "avg_logprob": -0.1938100909957519, "compression_ratio": 1.5664739884393064, "no_speech_prob": 0.0, "words": [{"start": 1436.18, "end": 1436.58, "word": "يعني", "probability": 0.593505859375}, {"start": 1436.58, "end": 1436.86, "word": " هذه", "probability": 0.75439453125}, {"start": 1436.86, "end": 1437.42, "word": " المجموعة", 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"probability": 0.89931640625}, {"start": 1445.64, "end": 1446.98, "word": " ال", "probability": 0.7783203125}, {"start": 1446.98, "end": 1448.16, "word": " supremum", "probability": 0.6937255859375}, {"start": 1448.16, "end": 1449.38, "word": " ل", "probability": 0.94580078125}, {"start": 1449.38, "end": 1450.4, "word": " S0", "probability": 0.958984375}, {"start": 1450.4, "end": 1451.8, "word": " دايما", "probability": 0.8863932291666666}, {"start": 1451.8, "end": 1452.32, "word": " أكبر", "probability": 0.9039713541666666}, {"start": 1452.32, "end": 1452.46, "word": " من", "probability": 0.78564453125}, {"start": 1452.46, "end": 1452.62, "word": " أو", "probability": 0.90869140625}, {"start": 1452.62, "end": 1453.04, "word": " ساوي", "probability": 0.7916666666666666}, {"start": 1453.04, "end": 1453.2, "word": " ال", "probability": 0.9404296875}, {"start": 1453.2, "end": 1453.8, "word": " infimum", "probability": 0.9021809895833334}, {"start": 1453.8, "end": 1454.0, "word": " ل", 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واضح من التعريفات وهذا الجزء أثبتناه باقي إثبات الجزء الأخير هذا فإذا بنقول finally أخيرا لإثبات الجزء الأخير هذا أنا عندي ال inform ل S is lower bound ل 6S", "tokens": [3615, 8592, 7649, 1975, 5016, 8315, 8717, 24793, 1211, 2423, 26890, 3224, 7649, 1975, 15730, 1975, 5016, 8315, 5551, 12984, 3555, 2655, 8315, 23758, 4032, 46958, 5016, 9154, 16712, 3615, 16572, 5172, 9307, 37037, 15730, 25724, 11622, 38207, 5551, 12984, 3555, 2655, 8315, 3224, 4724, 995, 38436, 11933, 12984, 3555, 9307, 25724, 11622, 38207, 16247, 9778, 13546, 23758, 6156, 28814, 15730, 44945, 39648, 2721, 5551, 9778, 13546, 995, 5296, 28814, 12984, 3555, 9307, 25724, 11622, 38207, 16247, 9778, 13546, 23758, 41850, 18871, 16254, 2423, 1356, 5296, 318, 307, 3126, 5472, 5296, 1386, 50], "avg_logprob": -0.18284574721721894, "compression_ratio": 1.7712765957446808, "no_speech_prob": 0.0, "words": [{"start": 1461.95, "end": 1462.85, "word": "عشان", "probability": 0.9606119791666666}, {"start": 1462.85, "end": 1463.13, 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"end": 1471.31, "word": " أثبتناه", "probability": 0.9703776041666666}, {"start": 1471.31, "end": 1475.15, "word": " باقي", "probability": 0.7610677083333334}, {"start": 1475.15, "end": 1475.79, "word": " إثبات", "probability": 0.85345458984375}, {"start": 1475.79, "end": 1476.35, "word": " الجزء", "probability": 0.9881184895833334}, {"start": 1476.35, "end": 1476.97, "word": " الأخير", "probability": 0.89990234375}, {"start": 1476.97, "end": 1477.67, "word": " هذا", "probability": 0.88671875}, {"start": 1477.67, "end": 1480.93, "word": " فإذا", "probability": 0.7384440104166666}, {"start": 1480.93, "end": 1481.51, "word": " بنقول", "probability": 0.800537109375}, {"start": 1481.51, "end": 1482.09, "word": " finally", "probability": 0.79931640625}, {"start": 1482.09, "end": 1483.39, "word": " أخيرا", "probability": 0.9298095703125}, {"start": 1483.39, "end": 1484.45, "word": " لإثبات", "probability": 0.899609375}, {"start": 1484.45, "end": 1484.79, "word": " الجزء", "probability": 0.9869791666666666}, {"start": 1484.79, "end": 1485.27, "word": " الأخير", "probability": 0.8815104166666666}, {"start": 1485.27, "end": 1485.57, "word": " هذا", "probability": 0.955078125}, {"start": 1485.57, "end": 1485.79, "word": " أنا", "probability": 0.25732421875}, {"start": 1485.79, "end": 1486.09, "word": " عندي", "probability": 0.881103515625}, {"start": 1486.09, "end": 1486.19, "word": " ال", "probability": 0.88037109375}, {"start": 1486.19, "end": 1486.53, "word": " inform", "probability": 0.061492919921875}, {"start": 1486.53, "end": 1486.75, "word": " ل", "probability": 0.61865234375}, {"start": 1486.75, "end": 1487.11, "word": " S", "probability": 0.60888671875}, {"start": 1487.11, "end": 1487.89, "word": " is", "probability": 0.86767578125}, {"start": 1487.89, "end": 1488.27, "word": " lower", "probability": 0.892578125}, {"start": 1488.27, "end": 1488.71, "word": " bound", "probability": 0.90283203125}, {"start": 1488.71, "end": 1488.95, "word": " ل", "probability": 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"probability": 0.8046875}, {"start": 1493.43, "end": 1493.95, "word": " bound", "probability": 0.919921875}, {"start": 1493.95, "end": 1494.41, "word": " لأي", "probability": 0.91357421875}, {"start": 1494.41, "end": 1494.99, "word": " مجموعة", "probability": 0.9314453125}, {"start": 1494.99, "end": 1495.67, "word": " جزئية", "probability": 0.9178466796875}, {"start": 1495.67, "end": 1496.51, "word": " S0", "probability": 0.634521484375}, {"start": 1496.51, "end": 1496.95, "word": " من", "probability": 0.9697265625}, {"start": 1496.95, "end": 1497.35, "word": " S", "probability": 0.96435546875}, {"start": 1497.35, "end": 1500.89, "word": " وبالتالي", "probability": 0.882861328125}, {"start": 1500.89, "end": 1501.53, "word": " إذا", "probability": 0.54693603515625}, {"start": 1501.53, "end": 1502.25, "word": " ال", "probability": 0.97705078125}, {"start": 1502.25, "end": 1502.67, "word": " influence", "probability": 0.068359375}, {"start": 1502.67, "end": 1503.05, "word": " ل", "probability": 0.90185546875}, {"start": 1503.05, "end": 1505.69, "word": " S0", "probability": 0.931884765625}, {"start": 1505.69, "end": 1511.77, "word": " هذا", "probability": 0.29833984375}, {"start": 1511.77, "end": 1512.33, "word": " أكبر", "probability": 0.9684244791666666}, {"start": 1512.33, "end": 1513.85, "word": " lower", "probability": 0.65087890625}, {"start": 1513.85, "end": 1514.39, "word": " bound", "probability": 0.9287109375}, {"start": 1514.39, "end": 1514.57, "word": " ل", "probability": 0.9677734375}, {"start": 1514.57, "end": 1515.27, "word": " S0", "probability": 0.973388671875}, {"start": 1515.27, "end": 1515.97, "word": " هذا", "probability": 0.6552734375}, {"start": 1515.97, "end": 1516.35, "word": " أكبر", "probability": 0.9781901041666666}, {"start": 1516.35, "end": 1516.63, "word": " lower", "probability": 0.92138671875}, {"start": 1516.63, "end": 1516.95, "word": " bound", "probability": 0.9296875}, {"start": 1516.95, "end": 1517.17, "word": " ل", 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"word": " ل", "probability": 0.78564453125}, {"start": 2375.67, "end": 2375.95, "word": " 6", "probability": 0.43017578125}, {"start": 2375.95, "end": 2376.33, "word": " هذه", "probability": 0.67822265625}, {"start": 2376.33, "end": 2377.93, "word": " لأن", "probability": 0.533203125}, {"start": 2377.93, "end": 2378.19, "word": " هذا", "probability": 0.9619140625}, {"start": 2378.19, "end": 2378.63, "word": " بيطلع", "probability": 0.919140625}, {"start": 2378.63, "end": 2379.21, "word": " أكبر", "probability": 0.9200846354166666}, {"start": 2379.21, "end": 2379.61, "word": " من", "probability": 0.9931640625}, {"start": 2379.61, "end": 2379.91, "word": " أو", "probability": 0.9912109375}, {"start": 2379.91, "end": 2380.61, "word": " ساوي", "probability": 0.7976888020833334}, {"start": 2380.61, "end": 2381.79, "word": " ..", "probability": 0.7373046875}, {"start": 2381.79, "end": 2382.27, "word": " هذا", "probability": 0.86962890625}, {"start": 2382.27, "end": 2382.83, "word": " أصغر", "probability": 0.9715576171875}, {"start": 2382.83, "end": 2383.01, "word": " من", "probability": 0.9970703125}, {"start": 2383.01, "end": 2383.17, "word": " أو", "probability": 0.98876953125}, {"start": 2383.17, "end": 2383.65, "word": " ساوي", "probability": 0.9703776041666666}, {"start": 2383.65, "end": 2383.83, "word": " ال", "probability": 0.60888671875}, {"start": 2383.83, "end": 2385.79, "word": " supremum", "probability": 0.719970703125}, {"start": 2385.79, "end": 2389.61, "word": " ل", "probability": 0.91650390625}, {"start": 2389.61, "end": 2390.03, "word": " S", "probability": 0.75439453125}, {"start": 2390.03, "end": 2390.69, "word": " star", "probability": 0.1995849609375}, {"start": 2390.69, "end": 2390.95, "word": " و", "probability": 0.55712890625}, {"start": 2390.95, "end": 2391.21, "word": " U", "probability": 0.87158203125}, {"start": 2391.21, "end": 2393.53, "word": " احنا", "probability": 0.826171875}, {"start": 2393.53, "end": 2393.83, "word": " بدنا", 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"probability": 0.96298828125}, {"start": 2408.29, "end": 2408.77, "word": " كما", "probability": 0.9423828125}, {"start": 2408.77, "end": 2409.75, "word": " يليه", "probability": 0.84130859375}, {"start": 2409.75, "end": 2410.89, "word": " أنا", "probability": 0.68115234375}, {"start": 2410.89, "end": 2411.29, "word": " عندي", "probability": 0.88427734375}, {"start": 2411.29, "end": 2411.75, "word": " هذا", "probability": 0.8984375}, {"start": 2411.75, "end": 2411.83, "word": " ..", "probability": 0.320556640625}, {"start": 2411.83, "end": 2412.19, "word": " هذا", "probability": 0.9208984375}, {"start": 2412.19, "end": 2412.75, "word": " العدد", "probability": 0.958984375}, {"start": 2412.75, "end": 2412.83, "word": " ..", "probability": 0.640625}, {"start": 2412.83, "end": 2413.07, "word": " هذا", "probability": 0.95751953125}, {"start": 2413.07, "end": 2413.67, "word": " العدد", "probability": 0.9894205729166666}, {"start": 2413.67, "end": 2414.19, "word": " عبارة", "probability": 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0.60205078125}, {"start": 2422.27, "end": 2422.59, "word": " upper", "probability": 0.9228515625}, {"start": 2422.59, "end": 2422.97, "word": " bound", "probability": 0.91845703125}, {"start": 2422.97, "end": 2423.69, "word": " إذا", "probability": 0.5987548828125}, {"start": 2423.69, "end": 2423.81, "word": " ن", "probability": 0.98779296875}, {"start": 2423.81, "end": 2424.25, "word": " claim", "probability": 0.755859375}, {"start": 2424.25, "end": 2424.83, "word": " إن", "probability": 0.8046875}, {"start": 2424.83, "end": 2425.37, "word": " ال", "probability": 0.79052734375}, {"start": 2425.37, "end": 2429.33, "word": " supremum", "probability": 0.500457763671875}, {"start": 2429.33, "end": 2430.79, "word": " لست", "probability": 0.719970703125}, {"start": 2430.79, "end": 2431.23, "word": " S", "probability": 0.5361328125}, {"start": 2431.23, "end": 2431.93, "word": " union", "probability": 0.59814453125}, {"start": 2431.93, "end": 2434.85, "word": " لست", "probability": 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"text": "هذا بيقدي أن x أصغر من أو يساوي S لكل x في S and x أصغر من أو يساوي لأ", "tokens": [3224, 15730, 4724, 1829, 4587, 16254, 14739, 2031, 5551, 9381, 17082, 2288, 9154, 34051, 7251, 3794, 995, 45865, 318, 5296, 28820, 2031, 8978, 318, 293, 2031, 5551, 9381, 17082, 2288, 9154, 34051, 7251, 3794, 995, 45865, 5296, 10721], "avg_logprob": -0.14873798688252768, "compression_ratio": 1.3452380952380953, "no_speech_prob": 0.0, "words": [{"start": 2485.69, "end": 2486.19, "word": "هذا", "probability": 0.9150390625}, {"start": 2486.19, "end": 2486.63, "word": " بيقدي", "probability": 0.72509765625}, {"start": 2486.63, "end": 2486.85, "word": " أن", "probability": 0.309814453125}, {"start": 2486.85, "end": 2487.33, "word": " x", "probability": 0.62451171875}, {"start": 2487.33, "end": 2488.03, "word": " أصغر", "probability": 0.9703369140625}, {"start": 2488.03, "end": 2488.29, "word": " من", "probability": 0.9814453125}, {"start": 2488.29, "end": 2488.55, "word": " أو", "probability": 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{"start": 2502.93, "end": 2503.99, "word": " لأ", "probability": 0.939697265625}], "temperature": 1.0}, {"id": 90, "seek": 251712, "start": 2506.04, "end": 2517.12, "text": "عفوا إيش هذا؟ X أصغر من أو ساوي V لكل X في S and U أصغر من أو ساوي V صح؟", "tokens": [3615, 5172, 14407, 11933, 1829, 8592, 23758, 22807, 1783, 5551, 9381, 17082, 2288, 9154, 34051, 8608, 995, 45865, 691, 5296, 28820, 1783, 8978, 318, 293, 624, 5551, 9381, 17082, 2288, 9154, 34051, 8608, 995, 45865, 691, 20328, 5016, 22807], "avg_logprob": -0.1466796901077032, "compression_ratio": 1.3068181818181819, "no_speech_prob": 0.0, "words": [{"start": 2506.04, "end": 2506.92, "word": "عفوا", "probability": 0.7285970052083334}, {"start": 2506.92, "end": 2507.46, "word": " إيش", "probability": 0.7867024739583334}, {"start": 2507.46, "end": 2508.72, "word": " هذا؟", "probability": 0.6373291015625}, {"start": 2508.72, "end": 2509.32, "word": " X", "probability": 0.63330078125}, {"start": 2509.32, "end": 2509.84, "word": " 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أو يساوي ال U فهذا بيقدي إذا ال supremum إذا كان ال V upper bound لل 6 هذه فال supremum", "tokens": [6027, 20292, 39896, 318, 3543, 4032, 624, 20328, 5016, 22807, 5296, 33456, 8032, 47302, 691, 5551, 4117, 26890, 9154, 34051, 7251, 3794, 995, 45865, 318, 3543, 4032, 5551, 4117, 26890, 9154, 34051, 7251, 3794, 995, 45865, 2423, 624, 6156, 3224, 15730, 4724, 1829, 4587, 16254, 11933, 15730, 2423, 23710, 449, 11933, 15730, 25961, 2423, 691, 6597, 5472, 24976, 1386, 29538, 6156, 6027, 23710, 449], "avg_logprob": -0.20240384615384616, "compression_ratio": 1.5472972972972974, "no_speech_prob": 0.0, "words": [{"start": 2553.07, "end": 2553.51, "word": "اللي", "probability": 0.872802734375}, {"start": 2553.51, "end": 2553.87, "word": " هي", "probability": 0.7587890625}, {"start": 2553.87, "end": 2554.19, "word": " S", "probability": 0.58251953125}, {"start": 2554.19, "end": 2554.77, "word": " star", "probability": 0.023834228515625}, {"start": 2554.77, "end": 2555.81, "word": " و", 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upper bound لنفس الست لأن أصغر upper bound أصغر من أو ساوي أي upper bound", "tokens": [1211, 1211, 14851, 8032, 8848, 1829, 13672, 1829, 39896, 318, 3543, 4032, 624, 5551, 9381, 17082, 2288, 9154, 34051, 8608, 995, 45865, 2423, 691, 23758, 5551, 4117, 26890, 6597, 5472, 24976, 14851, 37037, 15730, 6597, 5472, 5296, 1863, 36178, 2423, 14851, 5296, 33456, 5551, 9381, 17082, 2288, 6597, 5472, 5551, 9381, 17082, 2288, 9154, 34051, 8608, 995, 45865, 36632, 6597, 5472], "avg_logprob": -0.22933467525628307, "compression_ratio": 1.7307692307692308, "no_speech_prob": 0.0, "words": [{"start": 2580.81, "end": 2581.53, "word": "للست", "probability": 0.69482421875}, {"start": 2581.53, "end": 2581.93, "word": " هذي", "probability": 0.54345703125}, {"start": 2581.93, "end": 2582.03, "word": " اللي", "probability": 0.8642578125}, {"start": 2582.03, "end": 2582.23, "word": " هي", "probability": 0.83056640625}, {"start": 2582.23, "end": 2582.47, "word": " S", "probability": 0.6708984375}, {"start": 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9778, 3215, 2655, 2423, 23710, 5296, 318, 5551, 9381, 17082, 2288, 4032, 624, 23032, 3555, 3615, 995, 29538, 19362, 992, 295, 957, 3547, 4032, 41185, 6055, 29973, 9957, 4724, 1829, 39648, 45164, 18871, 16254, 19362, 992, 295, 957, 3547, 6156, 6027, 23710, 6055, 3555, 3615, 11296, 3714, 29245, 23328], "avg_logprob": -0.2468077912125536, "compression_ratio": 1.8055555555555556, "no_speech_prob": 0.0, "words": [{"start": 2997.4600000000005, "end": 2998.2000000000003, "word": "أو", "probability": 0.74658203125}, {"start": 2998.2000000000003, "end": 2998.94, "word": " X", "probability": 0.60498046875}, {"start": 2998.94, "end": 2999.48, "word": " أصغر", "probability": 0.9327392578125}, {"start": 2999.48, "end": 2999.68, "word": " من", "probability": 0.98193359375}, {"start": 2999.68, "end": 2999.86, "word": " أو", "probability": 0.89599609375}, {"start": 2999.86, "end": 3000.3, "word": " يساوي", "probability": 0.7435302734375}, {"start": 3000.3, "end": 3000.42, "word": " ال", "probability": 0.4560546875}, {"start": 3000.42, "end": 3000.54, "word": " U", "probability": 0.53076171875}, {"start": 3000.54, "end": 3001.8, "word": " X", "probability": 0.381591796875}, {"start": 3001.8, "end": 3002.28, "word": " بالساوي", "probability": 0.72906494140625}, {"start": 3002.28, "end": 3002.38, "word": " ال", "probability": 0.73486328125}, {"start": 3002.38, "end": 3002.48, "word": " U", "probability": 0.98095703125}, {"start": 3002.48, "end": 3003.18, "word": " بتقدي", "probability": 0.6692708333333334}, {"start": 3003.18, "end": 3004.02, "word": " ان", "probability": 0.56591796875}, {"start": 3004.02, "end": 3004.3, "word": " X", "probability": 0.96923828125}, {"start": 3004.3, "end": 3004.68, "word": " أصغر", "probability": 0.9708251953125}, {"start": 3004.68, "end": 3004.82, "word": " من", "probability": 0.99365234375}, {"start": 3004.82, "end": 3004.96, "word": " أو", "probability": 0.98876953125}, {"start": 3004.96, "end": 3005.36, "word": " يساوي", "probability": 0.9532470703125}, {"start": 3005.36, "end": 3005.44, "word": " ال", "probability": 0.92138671875}, {"start": 3005.44, "end": 3005.72, "word": " U", "probability": 0.97802734375}, {"start": 3005.72, "end": 3006.88, "word": " الان", "probability": 0.4793701171875}, {"start": 3006.88, "end": 3007.02, "word": " لو", "probability": 0.92578125}, {"start": 3007.02, "end": 3007.46, "word": " أخدت", "probability": 0.9090576171875}, {"start": 3007.46, "end": 3007.6, "word": " ال", "probability": 0.818359375}, {"start": 3007.6, "end": 3007.96, "word": " suprem", "probability": 0.724609375}, {"start": 3007.96, "end": 3008.48, "word": " ل", "probability": 0.556640625}, {"start": 3008.48, "end": 3008.9, "word": " S", "probability": 0.77978515625}, {"start": 3008.9, "end": 3009.4, "word": " أصغر", "probability": 0.7067413330078125}, {"start": 3009.4, "end": 3009.54, "word": " و", "probability": 0.68115234375}, {"start": 3009.54, "end": 3009.7, "word": " U", "probability": 0.8095703125}, {"start": 3009.7, "end": 3010.1, "word": " طبعا", "probability": 0.9053955078125}, {"start": 3010.1, "end": 3010.36, "word": " هذه", "probability": 0.301025390625}, {"start": 3010.36, "end": 3011.22, "word": " finite", "probability": 0.96337890625}, {"start": 3011.22, "end": 3011.78, "word": " set", "probability": 0.9755859375}, {"start": 3011.78, "end": 3012.0, "word": " of", "probability": 0.96630859375}, {"start": 3012.0, "end": 3012.24, "word": " real", "probability": 0.9677734375}, {"start": 3012.24, "end": 3012.66, "word": " numbers", "probability": 0.7685546875}, {"start": 3012.66, "end": 3012.92, "word": " وفي", "probability": 0.6453857421875}, {"start": 3012.92, "end": 3013.4, "word": " تمرين", "probability": 0.8448893229166666}, {"start": 3013.4, "end": 3013.8, "word": " بيقول", "probability": 0.8997395833333334}, {"start": 3013.8, "end": 3014.56, "word": " لو", "probability": 0.880859375}, {"start": 3014.56, "end": 3014.86, "word": " عندي", "probability": 0.7398681640625}, {"start": 3014.86, "end": 3015.2, "word": " finite", "probability": 0.98828125}, {"start": 3015.2, "end": 3015.64, "word": " set", "probability": 0.9736328125}, {"start": 3015.64, "end": 3015.8, "word": " of", "probability": 0.97314453125}, {"start": 3015.8, "end": 3015.98, "word": " real", "probability": 0.966796875}, {"start": 3015.98, "end": 3016.48, "word": " numbers", "probability": 0.91015625}, {"start": 3016.48, "end": 3016.78, "word": " فال", "probability": 0.755859375}, {"start": 3016.78, "end": 3017.06, "word": " suprem", "probability": 0.783203125}, {"start": 3017.06, "end": 3017.68, "word": " تبعها", "probability": 0.928466796875}, {"start": 3017.68, "end": 3018.4, "word": " موجود", "probability": 0.9874674479166666}], "temperature": 1.0}, {"id": 110, "seek": 304679, "start": 3018.97, "end": 3046.79, "text": "و ينتمي لل set و ال infimum تبعها أيضا موجود و ينتمي ل .. يعني يكون عنصر في ال set هذا أحد التمارين اللي طبعا ما عليناهوش لكن بإمكانكم تثبتوه by induction فهذه finally ال set إذا ال suprem تبعها exist إلا أن هذا ال suprem أكبر من أو ساوي S star وبالتالي أكبر من أو ساوي X و هذا ال suprem أكبر من أو ساوي U", "tokens": [2407, 7251, 29399, 2304, 1829, 24976, 992, 4032, 2423, 1536, 332, 449, 6055, 3555, 3615, 11296, 36632, 11242, 995, 3714, 29245, 23328, 4032, 7251, 29399, 2304, 1829, 5296, 4386, 37495, 22653, 7251, 30544, 18871, 9381, 2288, 8978, 2423, 992, 23758, 5551, 24401, 16712, 2304, 9640, 9957, 13672, 1829, 23032, 3555, 3615, 995, 19446, 11203, 9957, 40294, 2407, 8592, 44381, 4724, 28814, 2304, 41361, 24793, 6055, 12984, 3555, 2655, 2407, 3224, 538, 33371, 6156, 3224, 24192, 2721, 2423, 992, 11933, 15730, 2423, 23710, 6055, 3555, 3615, 11296, 2514, 11933, 15040, 14739, 23758, 2423, 23710, 5551, 4117, 26890, 9154, 34051, 8608, 995, 45865, 318, 3543, 46599, 6027, 2655, 6027, 1829, 5551, 4117, 26890, 9154, 34051, 8608, 995, 45865, 1783, 4032, 23758, 2423, 23710, 5551, 4117, 26890, 9154, 34051, 8608, 995, 45865, 624], "avg_logprob": -0.2149332127043309, 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{"start": 3033.85, "end": 3034.09, "word": " set", "probability": 0.9873046875}, {"start": 3034.09, "end": 3034.31, "word": " إذا", "probability": 0.69189453125}, {"start": 3034.31, "end": 3034.47, "word": " ال", "probability": 0.865234375}, {"start": 3034.47, "end": 3034.73, "word": " suprem", "probability": 0.828125}, {"start": 3034.73, "end": 3035.25, "word": " تبعها", "probability": 0.9371337890625}, {"start": 3035.25, "end": 3035.77, "word": " exist", "probability": 0.90625}, {"start": 3035.77, "end": 3036.55, "word": " إلا", "probability": 0.504638671875}, {"start": 3036.55, "end": 3036.71, "word": " أن", "probability": 0.68408203125}, {"start": 3036.71, "end": 3036.93, "word": " هذا", "probability": 0.93212890625}, {"start": 3036.93, "end": 3037.09, "word": " ال", "probability": 0.8896484375}, {"start": 3037.09, "end": 3037.39, "word": " suprem", "probability": 0.876953125}, {"start": 3037.39, "end": 3038.01, "word": " أكبر", "probability": 0.9737955729166666}, {"start": 3038.01, "end": 3038.19, "word": " من", "probability": 0.9736328125}, {"start": 3038.19, "end": 3038.39, "word": " أو", "probability": 0.98046875}, {"start": 3038.39, "end": 3039.01, "word": " ساوي", "probability": 0.7952473958333334}, {"start": 3039.01, "end": 3039.35, "word": " S", "probability": 0.59423828125}, {"start": 3039.35, "end": 3039.85, "word": " star", "probability": 0.051971435546875}, {"start": 3039.85, "end": 3040.39, "word": " وبالتالي", "probability": 0.88828125}, {"start": 3040.39, "end": 3040.75, "word": " أكبر", "probability": 0.9723307291666666}, {"start": 3040.75, "end": 3040.87, "word": " من", "probability": 0.9931640625}, {"start": 3040.87, "end": 3041.07, "word": " أو", "probability": 0.9892578125}, {"start": 3041.07, "end": 3041.57, "word": " ساوي", "probability": 0.9703776041666666}, {"start": 3041.57, "end": 3041.99, "word": " X", "probability": 0.94775390625}, {"start": 3041.99, "end": 3042.91, "word": " و", "probability": 0.54443359375}, {"start": 3042.91, "end": 3043.15, "word": " هذا", "probability": 0.9248046875}, {"start": 3043.15, "end": 3043.35, "word": " ال", "probability": 0.91357421875}, {"start": 3043.35, "end": 3043.65, "word": " suprem", "probability": 0.9169921875}, {"start": 3043.65, "end": 3045.61, "word": " أكبر", "probability": 0.9775390625}, {"start": 3045.61, "end": 3045.81, "word": " من", "probability": 0.9970703125}, {"start": 3045.81, "end": 3046.01, "word": " أو", "probability": 0.99609375}, {"start": 3046.01, "end": 3046.47, "word": " ساوي", "probability": 0.95361328125}, {"start": 3046.47, "end": 3046.79, "word": " U", "probability": 0.52734375}], "temperature": 1.0}, {"id": 111, "seek": 306187, "start": 3050.61, "end": 3061.87, "text": "وبالتالي أكبر من أو يساوي ال X اللي هي U أكبر من أو ساوي، إذا الأن هذا الكلام صحيح لكل X ينتمي للإتحاد", "tokens": [37746, 6027, 2655, 6027, 1829, 5551, 4117, 26890, 9154, 34051, 7251, 3794, 995, 45865, 2423, 1783, 13672, 1829, 39896, 624, 5551, 4117, 26890, 9154, 34051, 8608, 995, 45865, 12399, 11933, 15730, 16247, 1863, 23758, 2423, 28820, 10943, 20328, 5016, 1829, 5016, 5296, 28820, 1783, 7251, 29399, 2304, 1829, 24976, 28814, 2655, 5016, 18513], "avg_logprob": -0.2093460703337634, "compression_ratio": 1.6422018348623852, "no_speech_prob": 0.0, "words": [{"start": 3050.61, "end": 3051.57, "word": "وبالتالي", "probability": 0.839794921875}, {"start": 3051.57, "end": 3052.05, "word": " أكبر", "probability": 0.8052571614583334}, {"start": 3052.05, "end": 3052.25, "word": " من", "probability": 0.96923828125}, {"start": 3052.25, "end": 3052.43, "word": " أو", "probability": 0.974609375}, {"start": 3052.43, "end": 3053.11, "word": " يساوي", "probability": 0.8826904296875}, {"start": 3053.11, "end": 3053.89, "word": " ال", "probability": 0.77099609375}, {"start": 3053.89, "end": 3054.21, "word": " X", "probability": 0.619140625}, {"start": 3054.21, "end": 3054.45, "word": " اللي", "probability": 0.508544921875}, {"start": 3054.45, "end": 3054.73, "word": " هي", "probability": 0.83251953125}, {"start": 3054.73, "end": 3054.93, "word": " U", "probability": 0.8984375}, {"start": 3054.93, "end": 3055.29, "word": " أكبر", "probability": 0.9567057291666666}, {"start": 3055.29, "end": 3055.45, "word": " من", "probability": 0.99072265625}, {"start": 3055.45, "end": 3055.61, "word": " أو", "probability": 0.97998046875}, {"start": 3055.61, "end": 3056.19, "word": " ساوي،", "probability": 0.647796630859375}, {"start": 3056.19, "end": 3057.35, "word": " إذا", "probability": 0.65625}, {"start": 3057.35, "end": 3058.11, "word": " الأن", "probability": 0.736083984375}, {"start": 3058.11, "end": 3058.43, "word": " هذا", "probability": 0.93359375}, {"start": 3058.43, "end": 3058.87, "word": " الكلام", "probability": 0.9508463541666666}, {"start": 3058.87, "end": 3059.51, "word": " صحيح", "probability": 0.9951171875}, {"start": 3059.51, "end": 3060.09, "word": " لكل", "probability": 0.97314453125}, {"start": 3060.09, "end": 3060.57, "word": " X", 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bound هو ال infimum هو ال greatest lower bound اذا هنا now if W is", "tokens": [34598, 5472, 5296, 14851, 318, 8717, 19913, 3555, 9566, 5296, 33456, 1783, 16, 5551, 9381, 17082, 2288, 9154, 34051, 8608, 995, 45865, 28242, 18863, 1863, 33546, 2288, 13672, 1829, 8978, 2423, 14851, 6156, 3224, 2407, 4032, 46958, 5016, 16472, 3224, 3126, 5472, 2423, 7649, 1975, 8315, 39894, 12984, 3555, 2655, 16472, 3224, 37893, 4724, 3794, 3126, 5472, 31439, 2423, 1536, 332, 449, 31439, 2423, 6636, 3126, 5472, 1975, 15730, 34105, 586, 498, 343, 307], "avg_logprob": -0.3018750047683716, "compression_ratio": 1.5593220338983051, "no_speech_prob": 0.0, "words": [{"start": 3395.4, "end": 3395.98, "word": "lower", "probability": 0.3759765625}, {"start": 3395.98, "end": 3396.62, "word": " bound", "probability": 0.88916015625}, {"start": 3396.62, "end": 3399.08, "word": " لست", "probability": 0.54638671875}, {"start": 3399.08, "end": 3399.54, "word": " S", "probability": 0.57275390625}, {"start": 3399.54, "end": 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0.720703125}, {"start": 3419.94, "end": 3420.52, "word": " W", "probability": 0.65283203125}, {"start": 3420.52, "end": 3421.62, "word": " is", "probability": 0.9541015625}], "temperature": 1.0}, {"id": 125, "seek": 344964, "start": 3424.4, "end": 3449.64, "text": "any lower bound .. any lower bound of S فهذا معناه أن W أصغر من أو يساوي Xi لكل I بيساوي 1 2 إلى N صح؟", "tokens": [1325, 3126, 5472, 4386, 604, 3126, 5472, 295, 318, 6156, 3224, 15730, 20449, 8315, 3224, 14739, 343, 5551, 9381, 17082, 2288, 9154, 34051, 7251, 3794, 995, 45865, 15712, 5296, 28820, 286, 4724, 1829, 3794, 995, 45865, 502, 568, 30731, 426, 20328, 5016, 22807], "avg_logprob": -0.25035512379624625, "compression_ratio": 1.146341463414634, "no_speech_prob": 0.0, "words": [{"start": 3424.4000000000005, "end": 3425.6400000000003, "word": "any", "probability": 0.496826171875}, {"start": 3425.6400000000003, "end": 3426.88, "word": " lower", "probability": 0.9208984375}, {"start": 3426.88, "end": 3427.52, "word": " bound", "probability": 0.8935546875}, {"start": 3427.52, "end": 3428.12, "word": " ..", "probability": 0.145751953125}, {"start": 3428.12, "end": 3430.6, "word": " any", "probability": 0.771484375}, {"start": 3430.6, "end": 3431.12, "word": " lower", "probability": 0.89208984375}, {"start": 3431.12, "end": 3431.52, "word": " bound", "probability": 0.89306640625}, {"start": 3431.52, "end": 3431.76, "word": " of", "probability": 0.9794921875}, {"start": 3431.76, "end": 3432.2, "word": " S", "probability": 0.75634765625}, {"start": 3432.2, "end": 3436.58, "word": " فهذا", "probability": 0.96826171875}, {"start": 3436.58, "end": 3437.3, "word": " معناه", "probability": 0.990234375}, {"start": 3437.3, "end": 3437.68, "word": " أن", "probability": 0.393310546875}, {"start": 3437.68, "end": 3438.32, "word": " W", "probability": 0.434814453125}, {"start": 3438.32, "end": 3438.98, "word": " أصغر", "probability": 0.9747314453125}, {"start": 3438.98, "end": 3439.18, "word": " من", "probability": 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أو ساوي كل عناصرها و بالتالي therefore w أصغر من أو ساوي x واحد لأن x واحد هو واحد من عناصر الست إذا أنا عندي الان x واحد is lower bound للست", "tokens": [2407, 5551, 9381, 17082, 2288, 9154, 34051, 8608, 995, 45865, 28242, 18871, 33546, 2288, 11296, 4032, 20666, 2655, 6027, 1829, 4412, 261, 5551, 9381, 17082, 2288, 9154, 34051, 8608, 995, 45865, 2031, 36764, 24401, 5296, 33456, 2031, 36764, 24401, 31439, 36764, 24401, 9154, 18871, 33546, 2288, 2423, 14851, 11933, 15730, 41850, 18871, 16254, 2423, 7649, 2031, 36764, 24401, 307, 3126, 5472, 24976, 14851], "avg_logprob": -0.25903321243822575, "compression_ratio": 1.653061224489796, "no_speech_prob": 0.0, "words": [{"start": 3450.51, "end": 3451.25, "word": "و", "probability": 0.316650390625}, {"start": 3451.25, "end": 3453.83, "word": " أصغر", "probability": 0.733306884765625}, {"start": 3453.83, "end": 3453.95, "word": " من", "probability": 0.97900390625}, {"start": 3453.95, "end": 3454.07, "word": " أو", "probability": 0.962890625}, {"start": 3454.07, "end": 3454.33, "word": " ساوي", "probability": 0.8772786458333334}, {"start": 3454.33, "end": 3454.57, "word": " كل", "probability": 0.7109375}, {"start": 3454.57, "end": 3455.21, "word": " عناصرها", "probability": 0.74322509765625}, {"start": 3455.21, "end": 3456.33, "word": " و", "probability": 0.28076171875}, {"start": 3456.33, "end": 3457.09, "word": " بالتالي", "probability": 0.81658935546875}, {"start": 3457.09, "end": 3457.75, "word": " therefore", "probability": 0.379638671875}, {"start": 3457.75, "end": 3458.37, "word": " w", "probability": 0.6044921875}, {"start": 3458.37, "end": 3459.11, "word": " أصغر", "probability": 0.9716796875}, {"start": 3459.11, "end": 3459.27, "word": " من", "probability": 0.9921875}, {"start": 3459.27, "end": 3459.49, "word": " أو", "probability": 0.9833984375}, {"start": 3459.49, "end": 3460.11, "word": " ساوي", "probability": 0.9689127604166666}, {"start": 3460.11, "end": 3460.41, "word": " x", "probability": 0.8291015625}, {"start": 3460.41, "end": 3460.91, "word": " واحد", "probability": 0.80322265625}, {"start": 3460.91, "end": 3462.57, "word": " لأن", "probability": 0.8369140625}, {"start": 3462.57, "end": 3462.83, "word": " x", "probability": 0.94189453125}, {"start": 3462.83, "end": 3463.29, "word": " واحد", "probability": 0.9365234375}, {"start": 3463.29, "end": 3463.59, "word": " هو", "probability": 0.97509765625}, {"start": 3463.59, "end": 3464.31, "word": " واحد", "probability": 0.956298828125}, {"start": 3464.31, "end": 3464.47, "word": " من", "probability": 0.990234375}, {"start": 3464.47, "end": 3464.97, "word": " عناصر", "probability": 0.9910481770833334}, {"start": 3464.97, "end": 3465.37, "word": " الست", "probability": 0.709716796875}, {"start": 3465.37, "end": 3468.13, "word": " إذا", "probability": 0.52288818359375}, {"start": 3468.13, "end": 3468.43, "word": " أنا", "probability": 0.654296875}, {"start": 3468.43, "end": 3468.87, "word": " عندي", "probability": 0.80224609375}, {"start": 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