# 函數列逐點收斂基礎 · 脈衝 R02 本批已通過 Schema、去重、來源快照與獨立答案重算；仍未標記為人工審定。 本題庫已有對應的中英逐步詳解。原題的 candidate 與英文 ai_candidate 狀態保留；AI 覆核、有限計算與 Lean 形式證明分開標示。 batch-20261014-advance-20261103-r02-pointwise-convergence-of-functions-foundations · 2026-10-14 · 100 題 ## 1. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-domain-evaluate；資料={"limit":[0,1],"coefficients":[1,-2],"shift":2,"n":1,"point":0}。請依 [n,point,f_n_x,limit_x,error] 欄序回答。 查看答案與解釋(1, 0, 1/3, 0, 1/3) Wave5第三層核對=(1, 0, 1/3, 0, 1/3)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0001/) 函數列逐點收斂 · qf-mod34-pointwise-finite-domain-evaluate · candidate ## 2. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-domain-evaluate；資料={"limit":[1,2],"coefficients":[2,-3],"shift":2,"n":2,"point":1}。請依 [n,point,f_n_x,limit_x,error] 欄序回答。 查看答案與解釋(2, 1, 5/4, 2, -3/4) Wave5第三層核對=(2, 1, 5/4, 2, -3/4)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0002/) 函數列逐點收斂 · qf-mod34-pointwise-finite-domain-evaluate · candidate ## 3. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-domain-evaluate；資料={"limit":[2,3],"coefficients":[3,-4],"shift":2,"n":3,"point":0}。請依 [n,point,f_n_x,limit_x,error] 欄序回答。 查看答案與解釋(3, 0, 13/5, 2, 3/5) Wave5第三層核對=(3, 0, 13/5, 2, 3/5)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0003/) 函數列逐點收斂 · qf-mod34-pointwise-finite-domain-evaluate · candidate ## 4. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-domain-evaluate；資料={"limit":[3,4],"coefficients":[4,-5],"shift":2,"n":4,"point":1}。請依 [n,point,f_n_x,limit_x,error] 欄序回答。 查看答案與解釋(4, 1, 19/6, 4, -5/6) Wave5第三層核對=(4, 1, 19/6, 4, -5/6)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0004/) 函數列逐點收斂 · qf-mod34-pointwise-finite-domain-evaluate · candidate ## 5. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-domain-evaluate；資料={"limit":[4,5],"coefficients":[5,-6],"shift":2,"n":5,"point":0}。請依 [n,point,f_n_x,limit_x,error] 欄序回答。 查看答案與解釋(5, 0, 33/7, 4, 5/7) Wave5第三層核對=(5, 0, 33/7, 4, 5/7)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0005/) 函數列逐點收斂 · qf-mod34-pointwise-finite-domain-evaluate · candidate ## 6. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-domain-evaluate；資料={"limit":[5,6],"coefficients":[6,-7],"shift":2,"n":6,"point":1}。請依 [n,point,f_n_x,limit_x,error] 欄序回答。 查看答案與解釋(6, 1, 41/8, 6, -7/8) Wave5第三層核對=(6, 1, 41/8, 6, -7/8)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0006/) 函數列逐點收斂 · qf-mod34-pointwise-finite-domain-evaluate · candidate ## 7. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-domain-evaluate；資料={"limit":[6,7],"coefficients":[7,-8],"shift":2,"n":7,"point":0}。請依 [n,point,f_n_x,limit_x,error] 欄序回答。 查看答案與解釋(7, 0, 61/9, 6, 7/9) Wave5第三層核對=(7, 0, 61/9, 6, 7/9)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0007/) 函數列逐點收斂 · qf-mod34-pointwise-finite-domain-evaluate · candidate ## 8. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-domain-evaluate；資料={"limit":[7,8],"coefficients":[8,-9],"shift":2,"n":8,"point":1}。請依 [n,point,f_n_x,limit_x,error] 欄序回答。 查看答案與解釋(8, 1, 71/10, 8, -9/10) Wave5第三層核對=(8, 1, 71/10, 8, -9/10)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0008/) 函數列逐點收斂 · qf-mod34-pointwise-finite-domain-evaluate · candidate ## 9. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-domain-evaluate；資料={"limit":[8,9],"coefficients":[9,-10],"shift":2,"n":9,"point":0}。請依 [n,point,f_n_x,limit_x,error] 欄序回答。 查看答案與解釋(9, 0, 97/11, 8, 9/11) Wave5第三層核對=(9, 0, 97/11, 8, 9/11)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0009/) 函數列逐點收斂 · qf-mod34-pointwise-finite-domain-evaluate · candidate ## 10. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-domain-evaluate；資料={"limit":[9,10],"coefficients":[10,-11],"shift":2,"n":10,"point":1}。請依 [n,point,f_n_x,limit_x,error] 欄序回答。 查看答案與解釋(10, 1, 109/12, 10, -11/12) Wave5第三層核對=(10, 1, 109/12, 10, -11/12)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0010/) 函數列逐點收斂 · qf-mod34-pointwise-finite-domain-evaluate · candidate ## 11. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-domain-evaluate；資料={"limit":[10,11],"coefficients":[11,-12],"shift":2,"n":11,"point":0}。請依 [n,point,f_n_x,limit_x,error] 欄序回答。 查看答案與解釋(11, 0, 141/13, 10, 11/13) Wave5第三層核對=(11, 0, 141/13, 10, 11/13)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0011/) 函數列逐點收斂 · qf-mod34-pointwise-finite-domain-evaluate · candidate ## 12. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-domain-evaluate；資料={"limit":[11,12],"coefficients":[12,-13],"shift":2,"n":12,"point":1}。請依 [n,point,f_n_x,limit_x,error] 欄序回答。 查看答案與解釋(12, 1, 155/14, 12, -13/14) Wave5第三層核對=(12, 1, 155/14, 12, -13/14)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0012/) 函數列逐點收斂 · qf-mod34-pointwise-finite-domain-evaluate · candidate ## 13. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-domain-evaluate；資料={"limit":[12,13],"coefficients":[13,-14],"shift":2,"n":13,"point":0}。請依 [n,point,f_n_x,limit_x,error] 欄序回答。 查看答案與解釋(13, 0, 193/15, 12, 13/15) Wave5第三層核對=(13, 0, 193/15, 12, 13/15)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0013/) 函數列逐點收斂 · qf-mod34-pointwise-finite-domain-evaluate · candidate ## 14. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-domain-evaluate；資料={"limit":[13,14],"coefficients":[14,-15],"shift":2,"n":14,"point":1}。請依 [n,point,f_n_x,limit_x,error] 欄序回答。 查看答案與解釋(14, 1, 209/16, 14, -15/16) Wave5第三層核對=(14, 1, 209/16, 14, -15/16)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0014/) 函數列逐點收斂 · qf-mod34-pointwise-finite-domain-evaluate · candidate ## 15. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-domain-evaluate；資料={"limit":[14,15],"coefficients":[15,-16],"shift":2,"n":15,"point":0}。請依 [n,point,f_n_x,limit_x,error] 欄序回答。 查看答案與解釋(15, 0, 253/17, 14, 15/17) Wave5第三層核對=(15, 0, 253/17, 14, 15/17)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0015/) 函數列逐點收斂 · qf-mod34-pointwise-finite-domain-evaluate · candidate ## 16. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-domain-evaluate；資料={"limit":[15,16],"coefficients":[16,-17],"shift":2,"n":16,"point":1}。請依 [n,point,f_n_x,limit_x,error] 欄序回答。 查看答案與解釋(16, 1, 271/18, 16, -17/18) Wave5第三層核對=(16, 1, 271/18, 16, -17/18)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0016/) 函數列逐點收斂 · qf-mod34-pointwise-finite-domain-evaluate · candidate ## 17. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-domain-evaluate；資料={"limit":[16,17],"coefficients":[17,-18],"shift":2,"n":17,"point":0}。請依 [n,point,f_n_x,limit_x,error] 欄序回答。 查看答案與解釋(17, 0, 321/19, 16, 17/19) Wave5第三層核對=(17, 0, 321/19, 16, 17/19)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0017/) 函數列逐點收斂 · qf-mod34-pointwise-finite-domain-evaluate · candidate ## 18. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-domain-evaluate；資料={"limit":[17,18],"coefficients":[18,-19],"shift":2,"n":18,"point":1}。請依 [n,point,f_n_x,limit_x,error] 欄序回答。 查看答案與解釋(18, 1, 341/20, 18, -19/20) Wave5第三層核對=(18, 1, 341/20, 18, -19/20)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0018/) 函數列逐點收斂 · qf-mod34-pointwise-finite-domain-evaluate · candidate ## 19. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-domain-evaluate；資料={"limit":[18,19],"coefficients":[19,-20],"shift":2,"n":19,"point":0}。請依 [n,point,f_n_x,limit_x,error] 欄序回答。 查看答案與解釋(19, 0, 397/21, 18, 19/21) Wave5第三層核對=(19, 0, 397/21, 18, 19/21)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0019/) 函數列逐點收斂 · qf-mod34-pointwise-finite-domain-evaluate · candidate ## 20. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-domain-evaluate；資料={"limit":[19,20],"coefficients":[20,-21],"shift":2,"n":20,"point":1}。請依 [n,point,f_n_x,limit_x,error] 欄序回答。 查看答案與解釋(20, 1, 419/22, 20, -21/22) Wave5第三層核對=(20, 1, 419/22, 20, -21/22)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0020/) 函數列逐點收斂 · qf-mod34-pointwise-finite-domain-evaluate · candidate ## 21. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-domain-evaluate；資料={"limit":[20,21],"coefficients":[21,-22],"shift":2,"n":21,"point":0}。請依 [n,point,f_n_x,limit_x,error] 欄序回答。 查看答案與解釋(21, 0, 481/23, 20, 21/23) Wave5第三層核對=(21, 0, 481/23, 20, 21/23)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0021/) 函數列逐點收斂 · qf-mod34-pointwise-finite-domain-evaluate · candidate ## 22. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-domain-evaluate；資料={"limit":[21,22],"coefficients":[22,-23],"shift":2,"n":22,"point":1}。請依 [n,point,f_n_x,limit_x,error] 欄序回答。 查看答案與解釋(22, 1, 505/24, 22, -23/24) Wave5第三層核對=(22, 1, 505/24, 22, -23/24)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0022/) 函數列逐點收斂 · qf-mod34-pointwise-finite-domain-evaluate · candidate ## 23. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-domain-evaluate；資料={"limit":[22,23],"coefficients":[23,-24],"shift":2,"n":23,"point":0}。請依 [n,point,f_n_x,limit_x,error] 欄序回答。 查看答案與解釋(23, 0, 573/25, 22, 23/25) Wave5第三層核對=(23, 0, 573/25, 22, 23/25)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0023/) 函數列逐點收斂 · qf-mod34-pointwise-finite-domain-evaluate · candidate ## 24. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-domain-evaluate；資料={"limit":[23,24],"coefficients":[24,-25],"shift":2,"n":24,"point":1}。請依 [n,point,f_n_x,limit_x,error] 欄序回答。 查看答案與解釋(24, 1, 599/26, 24, -25/26) Wave5第三層核對=(24, 1, 599/26, 24, -25/26)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0024/) 函數列逐點收斂 · qf-mod34-pointwise-finite-domain-evaluate · candidate ## 25. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-domain-evaluate；資料={"limit":[24,25],"coefficients":[25,-26],"shift":2,"n":25,"point":0}。請依 [n,point,f_n_x,limit_x,error] 欄序回答。 查看答案與解釋(25, 0, 673/27, 24, 25/27) Wave5第三層核對=(25, 0, 673/27, 24, 25/27)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0025/) 函數列逐點收斂 · qf-mod34-pointwise-finite-domain-evaluate · candidate ## 26. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-epsilon-witness；資料={"limit":[0,1],"coefficients":[1,-2],"shift":2,"epsilon":[1,10],"point":0}。請依 [point,epsilon,N,error_at_N,strict_tail,certificate] 欄序回答。 查看答案與解釋(0, 1/10, 9, 1/11, 是, forall_n_ge_N) Wave5第三層核對=(0, 1/10, 9, 1/11, 是, forall_n_ge_N)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0026/) 函數列逐點收斂 · qf-mod34-pointwise-epsilon-witness · candidate ## 27. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-epsilon-witness；資料={"limit":[1,2],"coefficients":[2,-3],"shift":2,"epsilon":[1,11],"point":1}。請依 [point,epsilon,N,error_at_N,strict_tail,certificate] 欄序回答。 查看答案與解釋(1, 1/11, 32, 3/34, 是, forall_n_ge_N) Wave5第三層核對=(1, 1/11, 32, 3/34, 是, forall_n_ge_N)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0027/) 函數列逐點收斂 · qf-mod34-pointwise-epsilon-witness · candidate ## 28. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-epsilon-witness；資料={"limit":[2,3],"coefficients":[3,-4],"shift":2,"epsilon":[1,12],"point":0}。請依 [point,epsilon,N,error_at_N,strict_tail,certificate] 欄序回答。 查看答案與解釋(0, 1/12, 35, 3/37, 是, forall_n_ge_N) Wave5第三層核對=(0, 1/12, 35, 3/37, 是, forall_n_ge_N)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0028/) 函數列逐點收斂 · qf-mod34-pointwise-epsilon-witness · candidate ## 29. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-epsilon-witness；資料={"limit":[3,4],"coefficients":[4,-5],"shift":2,"epsilon":[1,13],"point":1}。請依 [point,epsilon,N,error_at_N,strict_tail,certificate] 欄序回答。 查看答案與解釋(1, 1/13, 64, 5/66, 是, forall_n_ge_N) Wave5第三層核對=(1, 1/13, 64, 5/66, 是, forall_n_ge_N)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0029/) 函數列逐點收斂 · qf-mod34-pointwise-epsilon-witness · candidate ## 30. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-epsilon-witness；資料={"limit":[4,5],"coefficients":[5,-6],"shift":2,"epsilon":[1,14],"point":0}。請依 [point,epsilon,N,error_at_N,strict_tail,certificate] 欄序回答。 查看答案與解釋(0, 1/14, 69, 5/71, 是, forall_n_ge_N) Wave5第三層核對=(0, 1/14, 69, 5/71, 是, forall_n_ge_N)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0030/) 函數列逐點收斂 · qf-mod34-pointwise-epsilon-witness · candidate ## 31. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-epsilon-witness；資料={"limit":[5,6],"coefficients":[6,-7],"shift":2,"epsilon":[1,15],"point":1}。請依 [point,epsilon,N,error_at_N,strict_tail,certificate] 欄序回答。 查看答案與解釋(1, 1/15, 104, 7/106, 是, forall_n_ge_N) Wave5第三層核對=(1, 1/15, 104, 7/106, 是, forall_n_ge_N)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0031/) 函數列逐點收斂 · qf-mod34-pointwise-epsilon-witness · candidate ## 32. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-epsilon-witness；資料={"limit":[6,7],"coefficients":[7,-8],"shift":2,"epsilon":[1,16],"point":0}。請依 [point,epsilon,N,error_at_N,strict_tail,certificate] 欄序回答。 查看答案與解釋(0, 1/16, 111, 7/113, 是, forall_n_ge_N) Wave5第三層核對=(0, 1/16, 111, 7/113, 是, forall_n_ge_N)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0032/) 函數列逐點收斂 · qf-mod34-pointwise-epsilon-witness · candidate ## 33. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-epsilon-witness；資料={"limit":[7,8],"coefficients":[8,-9],"shift":2,"epsilon":[1,17],"point":1}。請依 [point,epsilon,N,error_at_N,strict_tail,certificate] 欄序回答。 查看答案與解釋(1, 1/17, 152, 9/154, 是, forall_n_ge_N) Wave5第三層核對=(1, 1/17, 152, 9/154, 是, forall_n_ge_N)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0033/) 函數列逐點收斂 · qf-mod34-pointwise-epsilon-witness · candidate ## 34. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-epsilon-witness；資料={"limit":[8,9],"coefficients":[9,-10],"shift":2,"epsilon":[1,18],"point":0}。請依 [point,epsilon,N,error_at_N,strict_tail,certificate] 欄序回答。 查看答案與解釋(0, 1/18, 161, 9/163, 是, forall_n_ge_N) Wave5第三層核對=(0, 1/18, 161, 9/163, 是, forall_n_ge_N)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0034/) 函數列逐點收斂 · qf-mod34-pointwise-epsilon-witness · candidate ## 35. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-epsilon-witness；資料={"limit":[9,10],"coefficients":[10,-11],"shift":2,"epsilon":[1,19],"point":1}。請依 [point,epsilon,N,error_at_N,strict_tail,certificate] 欄序回答。 查看答案與解釋(1, 1/19, 208, 11/210, 是, forall_n_ge_N) Wave5第三層核對=(1, 1/19, 208, 11/210, 是, forall_n_ge_N)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0035/) 函數列逐點收斂 · qf-mod34-pointwise-epsilon-witness · candidate ## 36. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-epsilon-witness；資料={"limit":[10,11],"coefficients":[11,-12],"shift":2,"epsilon":[1,20],"point":0}。請依 [point,epsilon,N,error_at_N,strict_tail,certificate] 欄序回答。 查看答案與解釋(0, 1/20, 219, 11/221, 是, forall_n_ge_N) Wave5第三層核對=(0, 1/20, 219, 11/221, 是, forall_n_ge_N)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0036/) 函數列逐點收斂 · qf-mod34-pointwise-epsilon-witness · candidate ## 37. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-epsilon-witness；資料={"limit":[11,12],"coefficients":[12,-13],"shift":2,"epsilon":[1,21],"point":1}。請依 [point,epsilon,N,error_at_N,strict_tail,certificate] 欄序回答。 查看答案與解釋(1, 1/21, 272, 13/274, 是, forall_n_ge_N) Wave5第三層核對=(1, 1/21, 272, 13/274, 是, forall_n_ge_N)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0037/) 函數列逐點收斂 · qf-mod34-pointwise-epsilon-witness · candidate ## 38. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-epsilon-witness；資料={"limit":[12,13],"coefficients":[13,-14],"shift":2,"epsilon":[1,22],"point":0}。請依 [point,epsilon,N,error_at_N,strict_tail,certificate] 欄序回答。 查看答案與解釋(0, 1/22, 285, 13/287, 是, forall_n_ge_N) Wave5第三層核對=(0, 1/22, 285, 13/287, 是, forall_n_ge_N)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0038/) 函數列逐點收斂 · qf-mod34-pointwise-epsilon-witness · candidate ## 39. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-epsilon-witness；資料={"limit":[13,14],"coefficients":[14,-15],"shift":2,"epsilon":[1,23],"point":1}。請依 [point,epsilon,N,error_at_N,strict_tail,certificate] 欄序回答。 查看答案與解釋(1, 1/23, 344, 15/346, 是, forall_n_ge_N) Wave5第三層核對=(1, 1/23, 344, 15/346, 是, forall_n_ge_N)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0039/) 函數列逐點收斂 · qf-mod34-pointwise-epsilon-witness · candidate ## 40. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-epsilon-witness；資料={"limit":[14,15],"coefficients":[15,-16],"shift":2,"epsilon":[1,24],"point":0}。請依 [point,epsilon,N,error_at_N,strict_tail,certificate] 欄序回答。 查看答案與解釋(0, 1/24, 359, 15/361, 是, forall_n_ge_N) Wave5第三層核對=(0, 1/24, 359, 15/361, 是, forall_n_ge_N)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0040/) 函數列逐點收斂 · qf-mod34-pointwise-epsilon-witness · candidate ## 41. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-epsilon-witness；資料={"limit":[15,16],"coefficients":[16,-17],"shift":2,"epsilon":[1,25],"point":1}。請依 [point,epsilon,N,error_at_N,strict_tail,certificate] 欄序回答。 查看答案與解釋(1, 1/25, 424, 17/426, 是, forall_n_ge_N) Wave5第三層核對=(1, 1/25, 424, 17/426, 是, forall_n_ge_N)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0041/) 函數列逐點收斂 · qf-mod34-pointwise-epsilon-witness · candidate ## 42. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-epsilon-witness；資料={"limit":[16,17],"coefficients":[17,-18],"shift":2,"epsilon":[1,26],"point":0}。請依 [point,epsilon,N,error_at_N,strict_tail,certificate] 欄序回答。 查看答案與解釋(0, 1/26, 441, 17/443, 是, forall_n_ge_N) Wave5第三層核對=(0, 1/26, 441, 17/443, 是, forall_n_ge_N)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0042/) 函數列逐點收斂 · qf-mod34-pointwise-epsilon-witness · candidate ## 43. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-epsilon-witness；資料={"limit":[17,18],"coefficients":[18,-19],"shift":2,"epsilon":[1,27],"point":1}。請依 [point,epsilon,N,error_at_N,strict_tail,certificate] 欄序回答。 查看答案與解釋(1, 1/27, 512, 19/514, 是, forall_n_ge_N) Wave5第三層核對=(1, 1/27, 512, 19/514, 是, forall_n_ge_N)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0043/) 函數列逐點收斂 · qf-mod34-pointwise-epsilon-witness · candidate ## 44. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-epsilon-witness；資料={"limit":[18,19],"coefficients":[19,-20],"shift":2,"epsilon":[1,28],"point":0}。請依 [point,epsilon,N,error_at_N,strict_tail,certificate] 欄序回答。 查看答案與解釋(0, 1/28, 531, 19/533, 是, forall_n_ge_N) Wave5第三層核對=(0, 1/28, 531, 19/533, 是, forall_n_ge_N)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0044/) 函數列逐點收斂 · qf-mod34-pointwise-epsilon-witness · candidate ## 45. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-epsilon-witness；資料={"limit":[19,20],"coefficients":[20,-21],"shift":2,"epsilon":[1,29],"point":1}。請依 [point,epsilon,N,error_at_N,strict_tail,certificate] 欄序回答。 查看答案與解釋(1, 1/29, 608, 21/610, 是, forall_n_ge_N) Wave5第三層核對=(1, 1/29, 608, 21/610, 是, forall_n_ge_N)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0045/) 函數列逐點收斂 · qf-mod34-pointwise-epsilon-witness · candidate ## 46. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-epsilon-witness；資料={"limit":[20,21],"coefficients":[21,-22],"shift":2,"epsilon":[1,30],"point":0}。請依 [point,epsilon,N,error_at_N,strict_tail,certificate] 欄序回答。 查看答案與解釋(0, 1/30, 629, 21/631, 是, forall_n_ge_N) Wave5第三層核對=(0, 1/30, 629, 21/631, 是, forall_n_ge_N)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0046/) 函數列逐點收斂 · qf-mod34-pointwise-epsilon-witness · candidate ## 47. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-epsilon-witness；資料={"limit":[21,22],"coefficients":[22,-23],"shift":2,"epsilon":[1,31],"point":1}。請依 [point,epsilon,N,error_at_N,strict_tail,certificate] 欄序回答。 查看答案與解釋(1, 1/31, 712, 23/714, 是, forall_n_ge_N) Wave5第三層核對=(1, 1/31, 712, 23/714, 是, forall_n_ge_N)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0047/) 函數列逐點收斂 · qf-mod34-pointwise-epsilon-witness · candidate ## 48. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-epsilon-witness；資料={"limit":[22,23],"coefficients":[23,-24],"shift":2,"epsilon":[1,32],"point":0}。請依 [point,epsilon,N,error_at_N,strict_tail,certificate] 欄序回答。 查看答案與解釋(0, 1/32, 735, 23/737, 是, forall_n_ge_N) Wave5第三層核對=(0, 1/32, 735, 23/737, 是, forall_n_ge_N)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0048/) 函數列逐點收斂 · qf-mod34-pointwise-epsilon-witness · candidate ## 49. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-epsilon-witness；資料={"limit":[23,24],"coefficients":[24,-25],"shift":2,"epsilon":[1,33],"point":1}。請依 [point,epsilon,N,error_at_N,strict_tail,certificate] 欄序回答。 查看答案與解釋(1, 1/33, 824, 25/826, 是, forall_n_ge_N) Wave5第三層核對=(1, 1/33, 824, 25/826, 是, forall_n_ge_N)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0049/) 函數列逐點收斂 · qf-mod34-pointwise-epsilon-witness · candidate ## 50. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-epsilon-witness；資料={"limit":[24,25],"coefficients":[25,-26],"shift":2,"epsilon":[1,34],"point":0}。請依 [point,epsilon,N,error_at_N,strict_tail,certificate] 欄序回答。 查看答案與解釋(0, 1/34, 849, 25/851, 是, forall_n_ge_N) Wave5第三層核對=(0, 1/34, 849, 25/851, 是, forall_n_ge_N)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0050/) 函數列逐點收斂 · qf-mod34-pointwise-epsilon-witness · candidate ## 51. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-domain-uniform-max；資料={"limit":[0,1],"coefficients":[1,-2],"shift":2,"epsilon":[1,10]}。請依 [epsilon,pointwise_witnesses,max_N,uniform_on_finite_domain,boundary] 欄序回答。 查看答案與解釋(1/10, [[0, 9], [1, 19]], 19, 是, finite_domain_maximum_only_not_infinite_domain_theorem) Wave5第三層核對=(1/10, [[0, 9], [1, 19]], 19, 是, finite_domain_maximum_only_not_infinite_domain_theorem)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0051/) 函數列逐點收斂 · qf-mod34-pointwise-finite-domain-uniform-max · candidate ## 52. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-domain-uniform-max；資料={"limit":[1,2],"coefficients":[2,-3],"shift":2,"epsilon":[1,11]}。請依 [epsilon,pointwise_witnesses,max_N,uniform_on_finite_domain,boundary] 欄序回答。 查看答案與解釋(1/11, [[0, 21], [1, 32]], 32, 是, finite_domain_maximum_only_not_infinite_domain_theorem) Wave5第三層核對=(1/11, [[0, 21], [1, 32]], 32, 是, finite_domain_maximum_only_not_infinite_domain_theorem)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0052/) 函數列逐點收斂 · qf-mod34-pointwise-finite-domain-uniform-max · candidate ## 53. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-domain-uniform-max；資料={"limit":[2,3],"coefficients":[3,-4],"shift":2,"epsilon":[1,12]}。請依 [epsilon,pointwise_witnesses,max_N,uniform_on_finite_domain,boundary] 欄序回答。 查看答案與解釋(1/12, [[0, 35], [1, 47]], 47, 是, finite_domain_maximum_only_not_infinite_domain_theorem) Wave5第三層核對=(1/12, [[0, 35], [1, 47]], 47, 是, finite_domain_maximum_only_not_infinite_domain_theorem)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0053/) 函數列逐點收斂 · qf-mod34-pointwise-finite-domain-uniform-max · candidate ## 54. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-domain-uniform-max；資料={"limit":[3,4],"coefficients":[4,-5],"shift":2,"epsilon":[1,13]}。請依 [epsilon,pointwise_witnesses,max_N,uniform_on_finite_domain,boundary] 欄序回答。 查看答案與解釋(1/13, [[0, 51], [1, 64]], 64, 是, finite_domain_maximum_only_not_infinite_domain_theorem) Wave5第三層核對=(1/13, [[0, 51], [1, 64]], 64, 是, finite_domain_maximum_only_not_infinite_domain_theorem)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0054/) 函數列逐點收斂 · qf-mod34-pointwise-finite-domain-uniform-max · candidate ## 55. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-domain-uniform-max；資料={"limit":[4,5],"coefficients":[5,-6],"shift":2,"epsilon":[1,14]}。請依 [epsilon,pointwise_witnesses,max_N,uniform_on_finite_domain,boundary] 欄序回答。 查看答案與解釋(1/14, [[0, 69], [1, 83]], 83, 是, finite_domain_maximum_only_not_infinite_domain_theorem) Wave5第三層核對=(1/14, [[0, 69], [1, 83]], 83, 是, finite_domain_maximum_only_not_infinite_domain_theorem)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0055/) 函數列逐點收斂 · qf-mod34-pointwise-finite-domain-uniform-max · candidate ## 56. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-domain-uniform-max；資料={"limit":[5,6],"coefficients":[6,-7],"shift":2,"epsilon":[1,15]}。請依 [epsilon,pointwise_witnesses,max_N,uniform_on_finite_domain,boundary] 欄序回答。 查看答案與解釋(1/15, [[0, 89], [1, 104]], 104, 是, finite_domain_maximum_only_not_infinite_domain_theorem) Wave5第三層核對=(1/15, [[0, 89], [1, 104]], 104, 是, finite_domain_maximum_only_not_infinite_domain_theorem)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0056/) 函數列逐點收斂 · qf-mod34-pointwise-finite-domain-uniform-max · candidate ## 57. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-domain-uniform-max；資料={"limit":[6,7],"coefficients":[7,-8],"shift":2,"epsilon":[1,16]}。請依 [epsilon,pointwise_witnesses,max_N,uniform_on_finite_domain,boundary] 欄序回答。 查看答案與解釋(1/16, [[0, 111], [1, 127]], 127, 是, finite_domain_maximum_only_not_infinite_domain_theorem) Wave5第三層核對=(1/16, [[0, 111], [1, 127]], 127, 是, finite_domain_maximum_only_not_infinite_domain_theorem)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0057/) 函數列逐點收斂 · qf-mod34-pointwise-finite-domain-uniform-max · candidate ## 58. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-domain-uniform-max；資料={"limit":[7,8],"coefficients":[8,-9],"shift":2,"epsilon":[1,17]}。請依 [epsilon,pointwise_witnesses,max_N,uniform_on_finite_domain,boundary] 欄序回答。 查看答案與解釋(1/17, [[0, 135], [1, 152]], 152, 是, finite_domain_maximum_only_not_infinite_domain_theorem) Wave5第三層核對=(1/17, [[0, 135], [1, 152]], 152, 是, finite_domain_maximum_only_not_infinite_domain_theorem)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0058/) 函數列逐點收斂 · qf-mod34-pointwise-finite-domain-uniform-max · candidate ## 59. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-domain-uniform-max；資料={"limit":[8,9],"coefficients":[9,-10],"shift":2,"epsilon":[1,18]}。請依 [epsilon,pointwise_witnesses,max_N,uniform_on_finite_domain,boundary] 欄序回答。 查看答案與解釋(1/18, [[0, 161], [1, 179]], 179, 是, finite_domain_maximum_only_not_infinite_domain_theorem) Wave5第三層核對=(1/18, [[0, 161], [1, 179]], 179, 是, finite_domain_maximum_only_not_infinite_domain_theorem)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0059/) 函數列逐點收斂 · qf-mod34-pointwise-finite-domain-uniform-max · candidate ## 60. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-domain-uniform-max；資料={"limit":[9,10],"coefficients":[10,-11],"shift":2,"epsilon":[1,19]}。請依 [epsilon,pointwise_witnesses,max_N,uniform_on_finite_domain,boundary] 欄序回答。 查看答案與解釋(1/19, [[0, 189], [1, 208]], 208, 是, finite_domain_maximum_only_not_infinite_domain_theorem) Wave5第三層核對=(1/19, [[0, 189], [1, 208]], 208, 是, finite_domain_maximum_only_not_infinite_domain_theorem)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0060/) 函數列逐點收斂 · qf-mod34-pointwise-finite-domain-uniform-max · candidate ## 61. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-domain-uniform-max；資料={"limit":[10,11],"coefficients":[11,-12],"shift":2,"epsilon":[1,20]}。請依 [epsilon,pointwise_witnesses,max_N,uniform_on_finite_domain,boundary] 欄序回答。 查看答案與解釋(1/20, [[0, 219], [1, 239]], 239, 是, finite_domain_maximum_only_not_infinite_domain_theorem) Wave5第三層核對=(1/20, [[0, 219], [1, 239]], 239, 是, finite_domain_maximum_only_not_infinite_domain_theorem)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0061/) 函數列逐點收斂 · qf-mod34-pointwise-finite-domain-uniform-max · candidate ## 62. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-domain-uniform-max；資料={"limit":[11,12],"coefficients":[12,-13],"shift":2,"epsilon":[1,21]}。請依 [epsilon,pointwise_witnesses,max_N,uniform_on_finite_domain,boundary] 欄序回答。 查看答案與解釋(1/21, [[0, 251], [1, 272]], 272, 是, finite_domain_maximum_only_not_infinite_domain_theorem) Wave5第三層核對=(1/21, [[0, 251], [1, 272]], 272, 是, finite_domain_maximum_only_not_infinite_domain_theorem)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0062/) 函數列逐點收斂 · qf-mod34-pointwise-finite-domain-uniform-max · candidate ## 63. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-domain-uniform-max；資料={"limit":[12,13],"coefficients":[13,-14],"shift":2,"epsilon":[1,22]}。請依 [epsilon,pointwise_witnesses,max_N,uniform_on_finite_domain,boundary] 欄序回答。 查看答案與解釋(1/22, [[0, 285], [1, 307]], 307, 是, finite_domain_maximum_only_not_infinite_domain_theorem) Wave5第三層核對=(1/22, [[0, 285], [1, 307]], 307, 是, finite_domain_maximum_only_not_infinite_domain_theorem)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0063/) 函數列逐點收斂 · qf-mod34-pointwise-finite-domain-uniform-max · candidate ## 64. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-domain-uniform-max；資料={"limit":[13,14],"coefficients":[14,-15],"shift":2,"epsilon":[1,23]}。請依 [epsilon,pointwise_witnesses,max_N,uniform_on_finite_domain,boundary] 欄序回答。 查看答案與解釋(1/23, [[0, 321], [1, 344]], 344, 是, finite_domain_maximum_only_not_infinite_domain_theorem) Wave5第三層核對=(1/23, [[0, 321], [1, 344]], 344, 是, finite_domain_maximum_only_not_infinite_domain_theorem)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0064/) 函數列逐點收斂 · qf-mod34-pointwise-finite-domain-uniform-max · candidate ## 65. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-domain-uniform-max；資料={"limit":[14,15],"coefficients":[15,-16],"shift":2,"epsilon":[1,24]}。請依 [epsilon,pointwise_witnesses,max_N,uniform_on_finite_domain,boundary] 欄序回答。 查看答案與解釋(1/24, [[0, 359], [1, 383]], 383, 是, finite_domain_maximum_only_not_infinite_domain_theorem) Wave5第三層核對=(1/24, [[0, 359], [1, 383]], 383, 是, finite_domain_maximum_only_not_infinite_domain_theorem)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0065/) 函數列逐點收斂 · qf-mod34-pointwise-finite-domain-uniform-max · candidate ## 66. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-domain-uniform-max；資料={"limit":[15,16],"coefficients":[16,-17],"shift":2,"epsilon":[1,25]}。請依 [epsilon,pointwise_witnesses,max_N,uniform_on_finite_domain,boundary] 欄序回答。 查看答案與解釋(1/25, [[0, 399], [1, 424]], 424, 是, finite_domain_maximum_only_not_infinite_domain_theorem) Wave5第三層核對=(1/25, [[0, 399], [1, 424]], 424, 是, finite_domain_maximum_only_not_infinite_domain_theorem)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0066/) 函數列逐點收斂 · qf-mod34-pointwise-finite-domain-uniform-max · candidate ## 67. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-domain-uniform-max；資料={"limit":[16,17],"coefficients":[17,-18],"shift":2,"epsilon":[1,26]}。請依 [epsilon,pointwise_witnesses,max_N,uniform_on_finite_domain,boundary] 欄序回答。 查看答案與解釋(1/26, [[0, 441], [1, 467]], 467, 是, finite_domain_maximum_only_not_infinite_domain_theorem) Wave5第三層核對=(1/26, [[0, 441], [1, 467]], 467, 是, finite_domain_maximum_only_not_infinite_domain_theorem)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0067/) 函數列逐點收斂 · qf-mod34-pointwise-finite-domain-uniform-max · candidate ## 68. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-domain-uniform-max；資料={"limit":[17,18],"coefficients":[18,-19],"shift":2,"epsilon":[1,27]}。請依 [epsilon,pointwise_witnesses,max_N,uniform_on_finite_domain,boundary] 欄序回答。 查看答案與解釋(1/27, [[0, 485], [1, 512]], 512, 是, finite_domain_maximum_only_not_infinite_domain_theorem) Wave5第三層核對=(1/27, [[0, 485], [1, 512]], 512, 是, finite_domain_maximum_only_not_infinite_domain_theorem)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0068/) 函數列逐點收斂 · qf-mod34-pointwise-finite-domain-uniform-max · candidate ## 69. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-domain-uniform-max；資料={"limit":[18,19],"coefficients":[19,-20],"shift":2,"epsilon":[1,28]}。請依 [epsilon,pointwise_witnesses,max_N,uniform_on_finite_domain,boundary] 欄序回答。 查看答案與解釋(1/28, [[0, 531], [1, 559]], 559, 是, finite_domain_maximum_only_not_infinite_domain_theorem) Wave5第三層核對=(1/28, [[0, 531], [1, 559]], 559, 是, finite_domain_maximum_only_not_infinite_domain_theorem)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0069/) 函數列逐點收斂 · qf-mod34-pointwise-finite-domain-uniform-max · candidate ## 70. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-domain-uniform-max；資料={"limit":[19,20],"coefficients":[20,-21],"shift":2,"epsilon":[1,29]}。請依 [epsilon,pointwise_witnesses,max_N,uniform_on_finite_domain,boundary] 欄序回答。 查看答案與解釋(1/29, [[0, 579], [1, 608]], 608, 是, finite_domain_maximum_only_not_infinite_domain_theorem) Wave5第三層核對=(1/29, [[0, 579], [1, 608]], 608, 是, finite_domain_maximum_only_not_infinite_domain_theorem)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0070/) 函數列逐點收斂 · qf-mod34-pointwise-finite-domain-uniform-max · candidate ## 71. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-domain-uniform-max；資料={"limit":[20,21],"coefficients":[21,-22],"shift":2,"epsilon":[1,30]}。請依 [epsilon,pointwise_witnesses,max_N,uniform_on_finite_domain,boundary] 欄序回答。 查看答案與解釋(1/30, [[0, 629], [1, 659]], 659, 是, finite_domain_maximum_only_not_infinite_domain_theorem) Wave5第三層核對=(1/30, [[0, 629], [1, 659]], 659, 是, finite_domain_maximum_only_not_infinite_domain_theorem)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0071/) 函數列逐點收斂 · qf-mod34-pointwise-finite-domain-uniform-max · candidate ## 72. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-domain-uniform-max；資料={"limit":[21,22],"coefficients":[22,-23],"shift":2,"epsilon":[1,31]}。請依 [epsilon,pointwise_witnesses,max_N,uniform_on_finite_domain,boundary] 欄序回答。 查看答案與解釋(1/31, [[0, 681], [1, 712]], 712, 是, finite_domain_maximum_only_not_infinite_domain_theorem) Wave5第三層核對=(1/31, [[0, 681], [1, 712]], 712, 是, finite_domain_maximum_only_not_infinite_domain_theorem)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0072/) 函數列逐點收斂 · qf-mod34-pointwise-finite-domain-uniform-max · candidate ## 73. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-domain-uniform-max；資料={"limit":[22,23],"coefficients":[23,-24],"shift":2,"epsilon":[1,32]}。請依 [epsilon,pointwise_witnesses,max_N,uniform_on_finite_domain,boundary] 欄序回答。 查看答案與解釋(1/32, [[0, 735], [1, 767]], 767, 是, finite_domain_maximum_only_not_infinite_domain_theorem) Wave5第三層核對=(1/32, [[0, 735], [1, 767]], 767, 是, finite_domain_maximum_only_not_infinite_domain_theorem)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0073/) 函數列逐點收斂 · qf-mod34-pointwise-finite-domain-uniform-max · candidate ## 74. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-domain-uniform-max；資料={"limit":[23,24],"coefficients":[24,-25],"shift":2,"epsilon":[1,33]}。請依 [epsilon,pointwise_witnesses,max_N,uniform_on_finite_domain,boundary] 欄序回答。 查看答案與解釋(1/33, [[0, 791], [1, 824]], 824, 是, finite_domain_maximum_only_not_infinite_domain_theorem) Wave5第三層核對=(1/33, [[0, 791], [1, 824]], 824, 是, finite_domain_maximum_only_not_infinite_domain_theorem)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0074/) 函數列逐點收斂 · qf-mod34-pointwise-finite-domain-uniform-max · candidate ## 75. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-domain-uniform-max；資料={"limit":[24,25],"coefficients":[25,-26],"shift":2,"epsilon":[1,34]}。請依 [epsilon,pointwise_witnesses,max_N,uniform_on_finite_domain,boundary] 欄序回答。 查看答案與解釋(1/34, [[0, 849], [1, 883]], 883, 是, finite_domain_maximum_only_not_infinite_domain_theorem) Wave5第三層核對=(1/34, [[0, 849], [1, 883]], 883, 是, finite_domain_maximum_only_not_infinite_domain_theorem)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0075/) 函數列逐點收斂 · qf-mod34-pointwise-finite-domain-uniform-max · candidate ## 76. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-prefix-boundary；資料={"limit":[0,1],"coefficients":[1,-2],"shift":2,"prefix_length":1}。請依 [prefix_length,value_rows,sufficient,boundary] 欄序回答。 查看答案與解釋(1, [[0, [1/2]], [1, [0]]], 否, finite_prefix_not_pointwise_convergence_certificate) Wave5第三層核對=(1, [[0, [1/2]], [1, [0]]], 否, finite_prefix_not_pointwise_convergence_certificate)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0076/) 函數列逐點收斂 · qf-mod34-pointwise-finite-prefix-boundary · candidate ## 77. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-prefix-boundary；資料={"limit":[1,2],"coefficients":[2,-3],"shift":2,"prefix_length":2}。請依 [prefix_length,value_rows,sufficient,boundary] 欄序回答。 查看答案與解釋(2, [[0, [2, 5/3]], [1, [1/2, 1]]], 否, finite_prefix_not_pointwise_convergence_certificate) Wave5第三層核對=(2, [[0, [2, 5/3]], [1, [1/2, 1]]], 否, finite_prefix_not_pointwise_convergence_certificate)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0077/) 函數列逐點收斂 · qf-mod34-pointwise-finite-prefix-boundary · candidate ## 78. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-prefix-boundary；資料={"limit":[2,3],"coefficients":[3,-4],"shift":2,"prefix_length":3}。請依 [prefix_length,value_rows,sufficient,boundary] 欄序回答。 查看答案與解釋(3, [[0, [7/2, 3, 11/4]], [1, [1, 5/3, 2]]], 否, finite_prefix_not_pointwise_convergence_certificate) Wave5第三層核對=(3, [[0, [7/2, 3, 11/4]], [1, [1, 5/3, 2]]], 否, finite_prefix_not_pointwise_convergence_certificate)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0078/) 函數列逐點收斂 · qf-mod34-pointwise-finite-prefix-boundary · candidate ## 79. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-prefix-boundary；資料={"limit":[3,4],"coefficients":[4,-5],"shift":2,"prefix_length":4}。請依 [prefix_length,value_rows,sufficient,boundary] 欄序回答。 查看答案與解釋(4, [[0, [5, 13/3, 4, 19/5]], [1, [3/2, 7/3, 11/4, 3]]], 否, finite_prefix_not_pointwise_convergence_certificate) Wave5第三層核對=(4, [[0, [5, 13/3, 4, 19/5]], [1, [3/2, 7/3, 11/4, 3]]], 否, finite_prefix_not_pointwise_convergence_certificate)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0079/) 函數列逐點收斂 · qf-mod34-pointwise-finite-prefix-boundary · candidate ## 80. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-prefix-boundary；資料={"limit":[4,5],"coefficients":[5,-6],"shift":2,"prefix_length":5}。請依 [prefix_length,value_rows,sufficient,boundary] 欄序回答。 查看答案與解釋(5, [[0, [13/2, 17/3, 21/4, 5, 29/6]], [1, [2, 3, 7/2, 19/5, 4]]], 否, finite_prefix_not_pointwise_convergence_certificate) Wave5第三層核對=(5, [[0, [13/2, 17/3, 21/4, 5, 29/6]], [1, [2, 3, 7/2, 19/5, 4]]], 否, finite_prefix_not_pointwise_convergence_certificate)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0080/) 函數列逐點收斂 · qf-mod34-pointwise-finite-prefix-boundary · candidate ## 81. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-prefix-boundary；資料={"limit":[5,6],"coefficients":[6,-7],"shift":2,"prefix_length":6}。請依 [prefix_length,value_rows,sufficient,boundary] 欄序回答。 查看答案與解釋(6, [[0, [8, 7, 13/2, 31/5, 6, 41/7]], [1, [5/2, 11/3, 17/4, 23/5, 29/6, 5]]], 否, finite_prefix_not_pointwise_convergence_certificate) Wave5第三層核對=(6, [[0, [8, 7, 13/2, 31/5, 6, 41/7]], [1, [5/2, 11/3, 17/4, 23/5, 29/6, 5]]], 否, finite_prefix_not_pointwise_convergence_certificate)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0081/) 函數列逐點收斂 · qf-mod34-pointwise-finite-prefix-boundary · candidate ## 82. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-prefix-boundary；資料={"limit":[6,7],"coefficients":[7,-8],"shift":2,"prefix_length":7}。請依 [prefix_length,value_rows,sufficient,boundary] 欄序回答。 查看答案與解釋(7, [[0, [19/2, 25/3, 31/4, 37/5, 43/6, 7, 55/8]], [1, [3, 13/3, 5, 27/5, 17/3, 41/7, 6]]], 否, finite_prefix_not_pointwise_convergence_certificate) Wave5第三層核對=(7, [[0, [19/2, 25/3, 31/4, 37/5, 43/6, 7, 55/8]], [1, [3, 13/3, 5, 27/5, 17/3, 41/7, 6]]], 否, finite_prefix_not_pointwise_convergence_certificate)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0082/) 函數列逐點收斂 · qf-mod34-pointwise-finite-prefix-boundary · candidate ## 83. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-prefix-boundary；資料={"limit":[7,8],"coefficients":[8,-9],"shift":2,"prefix_length":8}。請依 [prefix_length,value_rows,sufficient,boundary] 欄序回答。 查看答案與解釋(8, [[0, [11, 29/3, 9, 43/5, 25/3, 57/7, 8, 71/9]], [1, [7/2, 5, 23/4, 31/5, 13/2, 47/7, 55/8, 7]]], 否, finite_prefix_not_pointwise_convergence_certificate) Wave5第三層核對=(8, [[0, [11, 29/3, 9, 43/5, 25/3, 57/7, 8, 71/9]], [1, [7/2, 5, 23/4, 31/5, 13/2, 47/7, 55/8, 7]]], 否, finite_prefix_not_pointwise_convergence_certificate)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0083/) 函數列逐點收斂 · qf-mod34-pointwise-finite-prefix-boundary · candidate ## 84. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-prefix-boundary；資料={"limit":[8,9],"coefficients":[9,-10],"shift":2,"prefix_length":9}。請依 [prefix_length,value_rows,sufficient,boundary] 欄序回答。 查看答案與解釋(9, [[0, [25/2, 11, 41/4, 49/5, 19/2, 65/7, 73/8, 9, 89/10]], [1, [4, 17/3, 13/2, 7, 22/3, 53/7, 31/4, 71/9, 8]]], 否, finite_prefix_not_pointwise_convergence_certificate) Wave5第三層核對=(9, [[0, [25/2, 11, 41/4, 49/5, 19/2, 65/7, 73/8, 9, 89/10]], [1, [4, 17/3, 13/2, 7, 22/3, 53/7, 31/4, 71/9, 8]]], 否, finite_prefix_not_pointwise_convergence_certificate)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0084/) 函數列逐點收斂 · qf-mod34-pointwise-finite-prefix-boundary · candidate ## 85. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-prefix-boundary；資料={"limit":[9,10],"coefficients":[10,-11],"shift":2,"prefix_length":10}。請依 [prefix_length,value_rows,sufficient,boundary] 欄序回答。 查看答案與解釋(10, [[0, [14, 37/3, 23/2, 11, 32/3, 73/7, 41/4, 91/9, 10, 109/11]], [1, [9/2, 19/3, 29/4, 39/5, 49/6, 59/7, 69/8, 79/9, 89/10, 9]]], 否, finite_prefix_not_pointwise_convergence_certificate) Wave5第三層核對=(10, [[0, [14, 37/3, 23/2, 11, 32/3, 73/7, 41/4, 91/9, 10, 109/11]], [1, [9/2, 19/3, 29/4, 39/5, 49/6, 59/7, 69/8, 79/9, 89/10, 9]]], 否, finite_prefix_not_pointwise_convergence_certificate)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0085/) 函數列逐點收斂 · qf-mod34-pointwise-finite-prefix-boundary · candidate ## 86. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-prefix-boundary；資料={"limit":[10,11],"coefficients":[11,-12],"shift":2,"prefix_length":11}。請依 [prefix_length,value_rows,sufficient,boundary] 欄序回答。 查看答案與解釋(11, [[0, [31/2, 41/3, 51/4, 61/5, 71/6, 81/7, 91/8, 101/9, 111/10, 11, 131/12]], [1, [5, 7, 8, 43/5, 9, 65/7, 19/2, 29/3, 49/5, 109/11, 10]]], 否, finite_prefix_not_pointwise_convergence_certificate) Wave5第三層核對=(11, [[0, [31/2, 41/3, 51/4, 61/5, 71/6, 81/7, 91/8, 101/9, 111/10, 11, 131/12]], [1, [5, 7, 8, 43/5, 9, 65/7, 19/2, 29/3, 49/5, 109/11, 10]]], 否, finite_prefix_not_pointwise_convergence_certificate)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0086/) 函數列逐點收斂 · qf-mod34-pointwise-finite-prefix-boundary · candidate ## 87. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-prefix-boundary；資料={"limit":[11,12],"coefficients":[12,-13],"shift":2,"prefix_length":12}。請依 [prefix_length,value_rows,sufficient,boundary] 欄序回答。 查看答案與解釋(12, [[0, [17, 15, 14, 67/5, 13, 89/7, 25/2, 37/3, 61/5, 133/11, 12, 155/13]], [1, [11/2, 23/3, 35/4, 47/5, 59/6, 71/7, 83/8, 95/9, 107/10, 119/11, 131/12, 11]]], 否, finite_prefix_not_pointwise_convergence_certificate) Wave5第三層核對=(12, [[0, [17, 15, 14, 67/5, 13, 89/7, 25/2, 37/3, 61/5, 133/11, 12, 155/13]], [1, [11/2, 23/3, 35/4, 47/5, 59/6, 71/7, 83/8, 95/9, 107/10, 119/11, 131/12, 11]]], 否, finite_prefix_not_pointwise_convergence_certificate)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0087/) 函數列逐點收斂 · qf-mod34-pointwise-finite-prefix-boundary · candidate ## 88. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-prefix-boundary；資料={"limit":[12,13],"coefficients":[13,-14],"shift":2,"prefix_length":13}。請依 [prefix_length,value_rows,sufficient,boundary] 欄序回答。 查看答案與解釋(13, [[0, [37/2, 49/3, 61/4, 73/5, 85/6, 97/7, 109/8, 121/9, 133/10, 145/11, 157/12, 13, 181/14]], [1, [6, 25/3, 19/2, 51/5, 32/3, 11, 45/4, 103/9, 58/5, 129/11, 71/6, 155/13, 12]]], 否, finite_prefix_not_pointwise_convergence_certificate) Wave5第三層核對=(13, [[0, [37/2, 49/3, 61/4, 73/5, 85/6, 97/7, 109/8, 121/9, 133/10, 145/11, 157/12, 13, 181/14]], [1, [6, 25/3, 19/2, 51/5, 32/3, 11, 45/4, 103/9, 58/5, 129/11, 71/6, 155/13, 12]]], 否, finite_prefix_not_pointwise_convergence_certificate)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0088/) 函數列逐點收斂 · qf-mod34-pointwise-finite-prefix-boundary · candidate ## 89. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-prefix-boundary；資料={"limit":[13,14],"coefficients":[14,-15],"shift":2,"prefix_length":14}。請依 [prefix_length,value_rows,sufficient,boundary] 欄序回答。 查看答案與解釋(14, [[0, [20, 53/3, 33/2, 79/5, 46/3, 15, 59/4, 131/9, 72/5, 157/11, 85/6, 183/13, 14, 209/15]], [1, [13/2, 9, 41/4, 11, 23/2, 83/7, 97/8, 37/3, 25/2, 139/11, 51/4, 167/13, 181/14, 13]]], 否, finite_prefix_not_pointwise_convergence_certificate) Wave5第三層核對=(14, [[0, [20, 53/3, 33/2, 79/5, 46/3, 15, 59/4, 131/9, 72/5, 157/11, 85/6, 183/13, 14, 209/15]], [1, [13/2, 9, 41/4, 11, 23/2, 83/7, 97/8, 37/3, 25/2, 139/11, 51/4, 167/13, 181/14, 13]]], 否, finite_prefix_not_pointwise_convergence_certificate)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0089/) 函數列逐點收斂 · qf-mod34-pointwise-finite-prefix-boundary · candidate ## 90. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-prefix-boundary；資料={"limit":[14,15],"coefficients":[15,-16],"shift":2,"prefix_length":15}。請依 [prefix_length,value_rows,sufficient,boundary] 欄序回答。 查看答案與解釋(15, [[0, [43/2, 19, 71/4, 17, 33/2, 113/7, 127/8, 47/3, 31/2, 169/11, 61/4, 197/13, 211/14, 15, 239/16]], [1, [7, 29/3, 11, 59/5, 37/3, 89/7, 13, 119/9, 67/5, 149/11, 41/3, 179/13, 97/7, 209/15, 14]]], 否, finite_prefix_not_pointwise_convergence_certificate) Wave5第三層核對=(15, [[0, [43/2, 19, 71/4, 17, 33/2, 113/7, 127/8, 47/3, 31/2, 169/11, 61/4, 197/13, 211/14, 15, 239/16]], [1, [7, 29/3, 11, 59/5, 37/3, 89/7, 13, 119/9, 67/5, 149/11, 41/3, 179/13, 97/7, 209/15, 14]]], 否, finite_prefix_not_pointwise_convergence_certificate)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0090/) 函數列逐點收斂 · qf-mod34-pointwise-finite-prefix-boundary · candidate ## 91. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-prefix-boundary；資料={"limit":[15,16],"coefficients":[16,-17],"shift":2,"prefix_length":16}。請依 [prefix_length,value_rows,sufficient,boundary] 欄序回答。 查看答案與解釋(16, [[0, [23, 61/3, 19, 91/5, 53/3, 121/7, 17, 151/9, 83/5, 181/11, 49/3, 211/13, 113/7, 241/15, 16, 271/17]], [1, [15/2, 31/3, 47/4, 63/5, 79/6, 95/7, 111/8, 127/9, 143/10, 159/11, 175/12, 191/13, 207/14, 223/15, 239/16, 15]]], 否, finite_prefix_not_pointwise_convergence_certificate) Wave5第三層核對=(16, [[0, [23, 61/3, 19, 91/5, 53/3, 121/7, 17, 151/9, 83/5, 181/11, 49/3, 211/13, 113/7, 241/15, 16, 271/17]], [1, [15/2, 31/3, 47/4, 63/5, 79/6, 95/7, 111/8, 127/9, 143/10, 159/11, 175/12, 191/13, 207/14, 223/15, 239/16, 15]]], 否, finite_prefix_not_pointwise_convergence_certificate)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0091/) 函數列逐點收斂 · qf-mod34-pointwise-finite-prefix-boundary · candidate ## 92. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-prefix-boundary；資料={"limit":[16,17],"coefficients":[17,-18],"shift":2,"prefix_length":17}。請依 [prefix_length,value_rows,sufficient,boundary] 欄序回答。 查看答案與解釋(17, [[0, [49/2, 65/3, 81/4, 97/5, 113/6, 129/7, 145/8, 161/9, 177/10, 193/11, 209/12, 225/13, 241/14, 257/15, 273/16, 17, 305/18]], [1, [8, 11, 25/2, 67/5, 14, 101/7, 59/4, 15, 76/5, 169/11, 31/2, 203/13, 110/7, 79/5, 127/8, 271/17, 16]]], 否, finite_prefix_not_pointwise_convergence_certificate) Wave5第三層核對=(17, [[0, [49/2, 65/3, 81/4, 97/5, 113/6, 129/7, 145/8, 161/9, 177/10, 193/11, 209/12, 225/13, 241/14, 257/15, 273/16, 17, 305/18]], [1, [8, 11, 25/2, 67/5, 14, 101/7, 59/4, 15, 76/5, 169/11, 31/2, 203/13, 110/7, 79/5, 127/8, 271/17, 16]]], 否, finite_prefix_not_pointwise_convergence_certificate)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0092/) 函數列逐點收斂 · qf-mod34-pointwise-finite-prefix-boundary · candidate ## 93. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-prefix-boundary；資料={"limit":[17,18],"coefficients":[18,-19],"shift":2,"prefix_length":18}。請依 [prefix_length,value_rows,sufficient,boundary] 欄序回答。 查看答案與解釋(18, [[0, [26, 23, 43/2, 103/5, 20, 137/7, 77/4, 19, 94/5, 205/11, 37/2, 239/13, 128/7, 91/5, 145/8, 307/17, 18, 341/19]], [1, [17/2, 35/3, 53/4, 71/5, 89/6, 107/7, 125/8, 143/9, 161/10, 179/11, 197/12, 215/13, 233/14, 251/15, 269/16, 287/17, 305/18, 17]]], 否, finite_prefix_not_pointwise_convergence_certificate) Wave5第三層核對=(18, [[0, [26, 23, 43/2, 103/5, 20, 137/7, 77/4, 19, 94/5, 205/11, 37/2, 239/13, 128/7, 91/5, 145/8, 307/17, 18, 341/19]], [1, [17/2, 35/3, 53/4, 71/5, 89/6, 107/7, 125/8, 143/9, 161/10, 179/11, 197/12, 215/13, 233/14, 251/15, 269/16, 287/17, 305/18, 17]]], 否, finite_prefix_not_pointwise_convergence_certificate)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0093/) 函數列逐點收斂 · qf-mod34-pointwise-finite-prefix-boundary · candidate ## 94. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-prefix-boundary；資料={"limit":[18,19],"coefficients":[19,-20],"shift":2,"prefix_length":19}。請依 [prefix_length,value_rows,sufficient,boundary] 欄序回答。 查看答案與解釋(19, [[0, [55/2, 73/3, 91/4, 109/5, 127/6, 145/7, 163/8, 181/9, 199/10, 217/11, 235/12, 253/13, 271/14, 289/15, 307/16, 325/17, 343/18, 19, 379/20]], [1, [9, 37/3, 14, 15, 47/3, 113/7, 33/2, 151/9, 17, 189/11, 52/3, 227/13, 123/7, 53/3, 71/4, 303/17, 161/9, 341/19, 18]]], 否, finite_prefix_not_pointwise_convergence_certificate) Wave5第三層核對=(19, [[0, [55/2, 73/3, 91/4, 109/5, 127/6, 145/7, 163/8, 181/9, 199/10, 217/11, 235/12, 253/13, 271/14, 289/15, 307/16, 325/17, 343/18, 19, 379/20]], [1, [9, 37/3, 14, 15, 47/3, 113/7, 33/2, 151/9, 17, 189/11, 52/3, 227/13, 123/7, 53/3, 71/4, 303/17, 161/9, 341/19, 18]]], 否, finite_prefix_not_pointwise_convergence_certificate)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0094/) 函數列逐點收斂 · qf-mod34-pointwise-finite-prefix-boundary · candidate ## 95. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-prefix-boundary；資料={"limit":[19,20],"coefficients":[20,-21],"shift":2,"prefix_length":20}。請依 [prefix_length,value_rows,sufficient,boundary] 欄序回答。 查看答案與解釋(20, [[0, [29, 77/3, 24, 23, 67/3, 153/7, 43/2, 191/9, 21, 229/11, 62/3, 267/13, 143/7, 61/3, 81/4, 343/17, 181/9, 381/19, 20, 419/21]], [1, [19/2, 13, 59/4, 79/5, 33/2, 17, 139/8, 53/3, 179/10, 199/11, 73/4, 239/13, 37/2, 93/5, 299/16, 319/17, 113/6, 359/19, 379/20, 19]]], 否, finite_prefix_not_pointwise_convergence_certificate) Wave5第三層核對=(20, [[0, [29, 77/3, 24, 23, 67/3, 153/7, 43/2, 191/9, 21, 229/11, 62/3, 267/13, 143/7, 61/3, 81/4, 343/17, 181/9, 381/19, 20, 419/21]], [1, [19/2, 13, 59/4, 79/5, 33/2, 17, 139/8, 53/3, 179/10, 199/11, 73/4, 239/13, 37/2, 93/5, 299/16, 319/17, 113/6, 359/19, 379/20, 19]]], 否, finite_prefix_not_pointwise_convergence_certificate)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0095/) 函數列逐點收斂 · qf-mod34-pointwise-finite-prefix-boundary · candidate ## 96. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-prefix-boundary；資料={"limit":[20,21],"coefficients":[21,-22],"shift":2,"prefix_length":21}。請依 [prefix_length,value_rows,sufficient,boundary] 欄序回答。 查看答案與解釋(21, [[0, [61/2, 27, 101/4, 121/5, 47/2, 23, 181/8, 67/3, 221/10, 241/11, 87/4, 281/13, 43/2, 107/5, 341/16, 361/17, 127/6, 401/19, 421/20, 21, 461/22]], [1, [10, 41/3, 31/2, 83/5, 52/3, 125/7, 73/4, 167/9, 94/5, 19, 115/6, 251/13, 136/7, 293/15, 157/8, 335/17, 178/9, 377/19, 199/10, 419/21, 20]]], 否, finite_prefix_not_pointwise_convergence_certificate) Wave5第三層核對=(21, [[0, [61/2, 27, 101/4, 121/5, 47/2, 23, 181/8, 67/3, 221/10, 241/11, 87/4, 281/13, 43/2, 107/5, 341/16, 361/17, 127/6, 401/19, 421/20, 21, 461/22]], [1, [10, 41/3, 31/2, 83/5, 52/3, 125/7, 73/4, 167/9, 94/5, 19, 115/6, 251/13, 136/7, 293/15, 157/8, 335/17, 178/9, 377/19, 199/10, 419/21, 20]]], 否, finite_prefix_not_pointwise_convergence_certificate)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0096/) 函數列逐點收斂 · qf-mod34-pointwise-finite-prefix-boundary · candidate ## 97. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-prefix-boundary；資料={"limit":[21,22],"coefficients":[22,-23],"shift":2,"prefix_length":22}。請依 [prefix_length,value_rows,sufficient,boundary] 欄序回答。 查看答案與解釋(22, [[0, [32, 85/3, 53/2, 127/5, 74/3, 169/7, 95/4, 211/9, 116/5, 23, 137/6, 295/13, 158/7, 337/15, 179/8, 379/17, 200/9, 421/19, 221/10, 463/21, 22, 505/23]], [1, [21/2, 43/3, 65/4, 87/5, 109/6, 131/7, 153/8, 175/9, 197/10, 219/11, 241/12, 263/13, 285/14, 307/15, 329/16, 351/17, 373/18, 395/19, 417/20, 439/21, 461/22, 21]]], 否, finite_prefix_not_pointwise_convergence_certificate) Wave5第三層核對=(22, [[0, [32, 85/3, 53/2, 127/5, 74/3, 169/7, 95/4, 211/9, 116/5, 23, 137/6, 295/13, 158/7, 337/15, 179/8, 379/17, 200/9, 421/19, 221/10, 463/21, 22, 505/23]], [1, [21/2, 43/3, 65/4, 87/5, 109/6, 131/7, 153/8, 175/9, 197/10, 219/11, 241/12, 263/13, 285/14, 307/15, 329/16, 351/17, 373/18, 395/19, 417/20, 439/21, 461/22, 21]]], 否, finite_prefix_not_pointwise_convergence_certificate)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0097/) 函數列逐點收斂 · qf-mod34-pointwise-finite-prefix-boundary · candidate ## 98. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-prefix-boundary；資料={"limit":[22,23],"coefficients":[23,-24],"shift":2,"prefix_length":23}。請依 [prefix_length,value_rows,sufficient,boundary] 欄序回答。 查看答案與解釋(23, [[0, [67/2, 89/3, 111/4, 133/5, 155/6, 177/7, 199/8, 221/9, 243/10, 265/11, 287/12, 309/13, 331/14, 353/15, 375/16, 397/17, 419/18, 441/19, 463/20, 485/21, 507/22, 23, 551/24]], [1, [11, 15, 17, 91/5, 19, 137/7, 20, 61/3, 103/5, 229/11, 21, 275/13, 149/7, 107/5, 43/2, 367/17, 65/3, 413/19, 109/5, 153/7, 241/11, 505/23, 22]]], 否, finite_prefix_not_pointwise_convergence_certificate) Wave5第三層核對=(23, [[0, [67/2, 89/3, 111/4, 133/5, 155/6, 177/7, 199/8, 221/9, 243/10, 265/11, 287/12, 309/13, 331/14, 353/15, 375/16, 397/17, 419/18, 441/19, 463/20, 485/21, 507/22, 23, 551/24]], [1, [11, 15, 17, 91/5, 19, 137/7, 20, 61/3, 103/5, 229/11, 21, 275/13, 149/7, 107/5, 43/2, 367/17, 65/3, 413/19, 109/5, 153/7, 241/11, 505/23, 22]]], 否, finite_prefix_not_pointwise_convergence_certificate)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0098/) 函數列逐點收斂 · qf-mod34-pointwise-finite-prefix-boundary · candidate ## 99. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-prefix-boundary；資料={"limit":[23,24],"coefficients":[24,-25],"shift":2,"prefix_length":24}。請依 [prefix_length,value_rows,sufficient,boundary] 欄序回答。 查看答案與解釋(24, [[0, [35, 31, 29, 139/5, 27, 185/7, 26, 77/3, 127/5, 277/11, 25, 323/13, 173/7, 123/5, 49/2, 415/17, 73/3, 461/19, 121/5, 169/7, 265/11, 553/23, 24, 599/25]], [1, [23/2, 47/3, 71/4, 19, 119/6, 143/7, 167/8, 191/9, 43/2, 239/11, 263/12, 287/13, 311/14, 67/3, 359/16, 383/17, 407/18, 431/19, 91/4, 479/21, 503/22, 527/23, 551/24, 23]]], 否, finite_prefix_not_pointwise_convergence_certificate) Wave5第三層核對=(24, [[0, [35, 31, 29, 139/5, 27, 185/7, 26, 77/3, 127/5, 277/11, 25, 323/13, 173/7, 123/5, 49/2, 415/17, 73/3, 461/19, 121/5, 169/7, 265/11, 553/23, 24, 599/25]], [1, [23/2, 47/3, 71/4, 19, 119/6, 143/7, 167/8, 191/9, 43/2, 239/11, 263/12, 287/13, 311/14, 67/3, 359/16, 383/17, 407/18, 431/19, 91/4, 479/21, 503/22, 527/23, 551/24, 23]]], 否, finite_prefix_not_pointwise_convergence_certificate)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0099/) 函數列逐點收斂 · qf-mod34-pointwise-finite-prefix-boundary · candidate ## 100. 函數列逐點收斂 同一有限domain上的symbolic rational function tail。操作=pointwise-finite-prefix-boundary；資料={"limit":[24,25],"coefficients":[25,-26],"shift":2,"prefix_length":25}。請依 [prefix_length,value_rows,sufficient,boundary] 欄序回答。 查看答案與解釋(25, [[0, [73/2, 97/3, 121/4, 29, 169/6, 193/7, 217/8, 241/9, 53/2, 289/11, 313/12, 337/13, 361/14, 77/3, 409/16, 433/17, 457/18, 481/19, 101/4, 529/21, 553/22, 577/23, 601/24, 25, 649/26]], [1, [12, 49/3, 37/2, 99/5, 62/3, 149/7, 87/4, 199/9, 112/5, 249/11, 137/6, 23, 162/7, 349/15, 187/8, 399/17, 212/9, 449/19, 237/10, 499/21, 262/11, 549/23, 287/12, 599/25, 24]]], 否, finite_prefix_not_pointwise_convergence_certificate) Wave5第三層核對=(25, [[0, [73/2, 97/3, 121/4, 29, 169/6, 193/7, 217/8, 241/9, 53/2, 289/11, 313/12, 337/13, 361/14, 77/3, 409/16, 433/17, 457/18, 481/19, 101/4, 529/21, 553/22, 577/23, 601/24, 25, 649/26]], [1, [12, 49/3, 37/2, 99/5, 62/3, 149/7, 87/4, 199/9, 112/5, 249/11, 137/6, 23, 162/7, 349/15, 187/8, 399/17, 212/9, 449/19, 237/10, 499/21, 262/11, 549/23, 287/12, 599/25, 24]]], 否, finite_prefix_not_pointwise_convergence_certificate)；依完整明示資料重算；逐點量詞保留N依x與epsilon且tail對所有n大於等於N；有限domain最大witness不外推無限domain；有限prefix不足。 [本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261103-r02-pointwise-convergence-of-functions-0100/) 函數列逐點收斂 · qf-mod34-pointwise-finite-prefix-boundary · candidate [原始題目 JSONL](https://ocme.evemisslab.com/data/questions/batches/batch-20261014-advance-20261103-r02-pointwise-convergence-of-functions-foundations/questions.jsonl) · [驗收報告](https://ocme.evemisslab.com/data/questions/batches/batch-20261014-advance-20261103-r02-pointwise-convergence-of-functions-foundations/validation-report.json)