第 17588 題：函數列逐點收斂

原題與已知條件

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。

• G001 — 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。

定義與適用範圍

沿用原題明示的論域、假設與來源 MKO 定義。本題已完成第二對話數理與中英語義覆核，並由原始參數逐題獨立重算模型、答案與每個算術步驟；原題仍為 candidate。

• mko-pointwise-convergence-of-functions

逐步推導

same COMPLETE finite domain Fin(2);original aligned limits=[12, 13];signed coefficients=[13, -14];positive shift=2

declared for EVERY n>=0:f_n(x)=limit[x]+coefficient[x]/(n+shift);signed error=f_n(x)-limit[x]=coefficient[x]/(n+shift)

finite prefix point0 index0 denominator := sum(0, 2)

finite prefix point0 index0 denominator = 2

finite prefix point0 index0 signed correction := div(13, 2)

finite prefix point0 index0 signed correction = 13/2

finite prefix point0 index0 function value := sum(12, 13/2)

finite prefix point0 index0 function value = 37/2

finite prefix point0 index0 reverse signed error := sub(37/2, 12)

finite prefix point0 index0 reverse signed error = 13/2

finite prefix point0 index0:original point=0;n=0;limit=12;signed coefficient=13

f_n(x)=37/2;f_n(x)-limit=13/2;this error field remains SIGNED

finite prefix point0 index1 denominator := sum(1, 2)

finite prefix point0 index1 denominator = 3

finite prefix point0 index1 signed correction := div(13, 3)

finite prefix point0 index1 signed correction = 13/3

finite prefix point0 index1 function value := sum(12, 13/3)

finite prefix point0 index1 function value = 49/3

finite prefix point0 index1 reverse signed error := sub(49/3, 12)

finite prefix point0 index1 reverse signed error = 13/3

finite prefix point0 index1:original point=0;n=1;limit=12;signed coefficient=13

f_n(x)=49/3;f_n(x)-limit=13/3;this error field remains SIGNED

finite prefix point0 index2 denominator := sum(2, 2)

finite prefix point0 index2 denominator = 4

finite prefix point0 index2 signed correction := div(13, 4)

finite prefix point0 index2 signed correction = 13/4

finite prefix point0 index2 function value := sum(12, 13/4)

finite prefix point0 index2 function value = 61/4

finite prefix point0 index2 reverse signed error := sub(61/4, 12)

finite prefix point0 index2 reverse signed error = 13/4

finite prefix point0 index2:original point=0;n=2;limit=12;signed coefficient=13

f_n(x)=61/4;f_n(x)-limit=13/4;this error field remains SIGNED

finite prefix point0 index3 denominator := sum(3, 2)

finite prefix point0 index3 denominator = 5

finite prefix point0 index3 signed correction := div(13, 5)

finite prefix point0 index3 signed correction = 13/5

finite prefix point0 index3 function value := sum(12, 13/5)

finite prefix point0 index3 function value = 73/5

finite prefix point0 index3 reverse signed error := sub(73/5, 12)

finite prefix point0 index3 reverse signed error = 13/5

finite prefix point0 index3:original point=0;n=3;limit=12;signed coefficient=13

f_n(x)=73/5;f_n(x)-limit=13/5;this error field remains SIGNED

finite prefix point0 index4 denominator := sum(4, 2)

finite prefix point0 index4 denominator = 6

finite prefix point0 index4 signed correction := div(13, 6)

finite prefix point0 index4 signed correction = 13/6

finite prefix point0 index4 function value := sum(12, 13/6)

finite prefix point0 index4 function value = 85/6

finite prefix point0 index4 reverse signed error := sub(85/6, 12)

finite prefix point0 index4 reverse signed error = 13/6

finite prefix point0 index4:original point=0;n=4;limit=12;signed coefficient=13

f_n(x)=85/6;f_n(x)-limit=13/6;this error field remains SIGNED

finite prefix point0 index5 denominator := sum(5, 2)

finite prefix point0 index5 denominator = 7

finite prefix point0 index5 signed correction := div(13, 7)

finite prefix point0 index5 signed correction = 13/7

finite prefix point0 index5 function value := sum(12, 13/7)

finite prefix point0 index5 function value = 97/7

finite prefix point0 index5 reverse signed error := sub(97/7, 12)

finite prefix point0 index5 reverse signed error = 13/7

finite prefix point0 index5:original point=0;n=5;limit=12;signed coefficient=13

f_n(x)=97/7;f_n(x)-limit=13/7;this error field remains SIGNED

finite prefix point0 index6 denominator := sum(6, 2)

finite prefix point0 index6 denominator = 8

finite prefix point0 index6 signed correction := div(13, 8)

finite prefix point0 index6 signed correction = 13/8

finite prefix point0 index6 function value := sum(12, 13/8)

finite prefix point0 index6 function value = 109/8

finite prefix point0 index6 reverse signed error := sub(109/8, 12)

finite prefix point0 index6 reverse signed error = 13/8

finite prefix point0 index6:original point=0;n=6;limit=12;signed coefficient=13

f_n(x)=109/8;f_n(x)-limit=13/8;this error field remains SIGNED

finite prefix point0 index7 denominator := sum(7, 2)

finite prefix point0 index7 denominator = 9

finite prefix point0 index7 signed correction := div(13, 9)

finite prefix point0 index7 signed correction = 13/9

finite prefix point0 index7 function value := sum(12, 13/9)

finite prefix point0 index7 function value = 121/9

finite prefix point0 index7 reverse signed error := sub(121/9, 12)

finite prefix point0 index7 reverse signed error = 13/9

finite prefix point0 index7:original point=0;n=7;limit=12;signed coefficient=13

f_n(x)=121/9;f_n(x)-limit=13/9;this error field remains SIGNED

finite prefix point0 index8 denominator := sum(8, 2)

finite prefix point0 index8 denominator = 10

finite prefix point0 index8 signed correction := div(13, 10)

finite prefix point0 index8 signed correction = 13/10

finite prefix point0 index8 function value := sum(12, 13/10)

finite prefix point0 index8 function value = 133/10

finite prefix point0 index8 reverse signed error := sub(133/10, 12)

finite prefix point0 index8 reverse signed error = 13/10

finite prefix point0 index8:original point=0;n=8;limit=12;signed coefficient=13

f_n(x)=133/10;f_n(x)-limit=13/10;this error field remains SIGNED

finite prefix point0 index9 denominator := sum(9, 2)

finite prefix point0 index9 denominator = 11

finite prefix point0 index9 signed correction := div(13, 11)

finite prefix point0 index9 signed correction = 13/11

finite prefix point0 index9 function value := sum(12, 13/11)

finite prefix point0 index9 function value = 145/11

finite prefix point0 index9 reverse signed error := sub(145/11, 12)

finite prefix point0 index9 reverse signed error = 13/11

finite prefix point0 index9:original point=0;n=9;limit=12;signed coefficient=13

f_n(x)=145/11;f_n(x)-limit=13/11;this error field remains SIGNED

finite prefix point0 index10 denominator := sum(10, 2)

finite prefix point0 index10 denominator = 12

finite prefix point0 index10 signed correction := div(13, 12)

finite prefix point0 index10 signed correction = 13/12

finite prefix point0 index10 function value := sum(12, 13/12)

finite prefix point0 index10 function value = 157/12

finite prefix point0 index10 reverse signed error := sub(157/12, 12)

finite prefix point0 index10 reverse signed error = 13/12

finite prefix point0 index10:original point=0;n=10;limit=12;signed coefficient=13

f_n(x)=157/12;f_n(x)-limit=13/12;this error field remains SIGNED

finite prefix point0 index11 denominator := sum(11, 2)

finite prefix point0 index11 denominator = 13

finite prefix point0 index11 signed correction := div(13, 13)

finite prefix point0 index11 signed correction = 1

finite prefix point0 index11 function value := sum(12, 1)

finite prefix point0 index11 function value = 13

finite prefix point0 index11 reverse signed error := sub(13, 12)

finite prefix point0 index11 reverse signed error = 1

finite prefix point0 index11:original point=0;n=11;limit=12;signed coefficient=13

f_n(x)=13;f_n(x)-limit=1;this error field remains SIGNED

finite prefix point0 index12 denominator := sum(12, 2)

finite prefix point0 index12 denominator = 14

finite prefix point0 index12 signed correction := div(13, 14)

finite prefix point0 index12 signed correction = 13/14

finite prefix point0 index12 function value := sum(12, 13/14)

finite prefix point0 index12 function value = 181/14

finite prefix point0 index12 reverse signed error := sub(181/14, 12)

finite prefix point0 index12 reverse signed error = 13/14

finite prefix point0 index12:original point=0;n=12;limit=12;signed coefficient=13

f_n(x)=181/14;f_n(x)-limit=13/14;this error field remains SIGNED

finite prefix point1 index0 denominator := sum(0, 2)

finite prefix point1 index0 denominator = 2

finite prefix point1 index0 signed correction := div(-14, 2)

finite prefix point1 index0 signed correction = -7

finite prefix point1 index0 function value := sum(13, -7)

finite prefix point1 index0 function value = 6

finite prefix point1 index0 reverse signed error := sub(6, 13)

finite prefix point1 index0 reverse signed error = -7

finite prefix point1 index0:original point=1;n=0;limit=13;signed coefficient=-14

f_n(x)=6;f_n(x)-limit=-7;this error field remains SIGNED

finite prefix point1 index1 denominator := sum(1, 2)

finite prefix point1 index1 denominator = 3

finite prefix point1 index1 signed correction := div(-14, 3)

finite prefix point1 index1 signed correction = -14/3

finite prefix point1 index1 function value := sum(13, -14/3)

finite prefix point1 index1 function value = 25/3

finite prefix point1 index1 reverse signed error := sub(25/3, 13)

finite prefix point1 index1 reverse signed error = -14/3

finite prefix point1 index1:original point=1;n=1;limit=13;signed coefficient=-14

f_n(x)=25/3;f_n(x)-limit=-14/3;this error field remains SIGNED

finite prefix point1 index2 denominator := sum(2, 2)

finite prefix point1 index2 denominator = 4

finite prefix point1 index2 signed correction := div(-14, 4)

finite prefix point1 index2 signed correction = -7/2

finite prefix point1 index2 function value := sum(13, -7/2)

finite prefix point1 index2 function value = 19/2

finite prefix point1 index2 reverse signed error := sub(19/2, 13)

finite prefix point1 index2 reverse signed error = -7/2

finite prefix point1 index2:original point=1;n=2;limit=13;signed coefficient=-14

f_n(x)=19/2;f_n(x)-limit=-7/2;this error field remains SIGNED

finite prefix point1 index3 denominator := sum(3, 2)

finite prefix point1 index3 denominator = 5

finite prefix point1 index3 signed correction := div(-14, 5)

finite prefix point1 index3 signed correction = -14/5

finite prefix point1 index3 function value := sum(13, -14/5)

finite prefix point1 index3 function value = 51/5

finite prefix point1 index3 reverse signed error := sub(51/5, 13)

finite prefix point1 index3 reverse signed error = -14/5

finite prefix point1 index3:original point=1;n=3;limit=13;signed coefficient=-14

f_n(x)=51/5;f_n(x)-limit=-14/5;this error field remains SIGNED

finite prefix point1 index4 denominator := sum(4, 2)

finite prefix point1 index4 denominator = 6

finite prefix point1 index4 signed correction := div(-14, 6)

finite prefix point1 index4 signed correction = -7/3

finite prefix point1 index4 function value := sum(13, -7/3)

finite prefix point1 index4 function value = 32/3

finite prefix point1 index4 reverse signed error := sub(32/3, 13)

finite prefix point1 index4 reverse signed error = -7/3

finite prefix point1 index4:original point=1;n=4;limit=13;signed coefficient=-14

f_n(x)=32/3;f_n(x)-limit=-7/3;this error field remains SIGNED

finite prefix point1 index5 denominator := sum(5, 2)

finite prefix point1 index5 denominator = 7

finite prefix point1 index5 signed correction := div(-14, 7)

finite prefix point1 index5 signed correction = -2

finite prefix point1 index5 function value := sum(13, -2)

finite prefix point1 index5 function value = 11

finite prefix point1 index5 reverse signed error := sub(11, 13)

finite prefix point1 index5 reverse signed error = -2

finite prefix point1 index5:original point=1;n=5;limit=13;signed coefficient=-14

f_n(x)=11;f_n(x)-limit=-2;this error field remains SIGNED

finite prefix point1 index6 denominator := sum(6, 2)

finite prefix point1 index6 denominator = 8

finite prefix point1 index6 signed correction := div(-14, 8)

finite prefix point1 index6 signed correction = -7/4

finite prefix point1 index6 function value := sum(13, -7/4)

finite prefix point1 index6 function value = 45/4

finite prefix point1 index6 reverse signed error := sub(45/4, 13)

finite prefix point1 index6 reverse signed error = -7/4

finite prefix point1 index6:original point=1;n=6;limit=13;signed coefficient=-14

f_n(x)=45/4;f_n(x)-limit=-7/4;this error field remains SIGNED

finite prefix point1 index7 denominator := sum(7, 2)

finite prefix point1 index7 denominator = 9

finite prefix point1 index7 signed correction := div(-14, 9)

finite prefix point1 index7 signed correction = -14/9

finite prefix point1 index7 function value := sum(13, -14/9)

finite prefix point1 index7 function value = 103/9

finite prefix point1 index7 reverse signed error := sub(103/9, 13)

finite prefix point1 index7 reverse signed error = -14/9

finite prefix point1 index7:original point=1;n=7;limit=13;signed coefficient=-14

f_n(x)=103/9;f_n(x)-limit=-14/9;this error field remains SIGNED

finite prefix point1 index8 denominator := sum(8, 2)

finite prefix point1 index8 denominator = 10

finite prefix point1 index8 signed correction := div(-14, 10)

finite prefix point1 index8 signed correction = -7/5

finite prefix point1 index8 function value := sum(13, -7/5)

finite prefix point1 index8 function value = 58/5

finite prefix point1 index8 reverse signed error := sub(58/5, 13)

finite prefix point1 index8 reverse signed error = -7/5

finite prefix point1 index8:original point=1;n=8;limit=13;signed coefficient=-14

f_n(x)=58/5;f_n(x)-limit=-7/5;this error field remains SIGNED

finite prefix point1 index9 denominator := sum(9, 2)

finite prefix point1 index9 denominator = 11

finite prefix point1 index9 signed correction := div(-14, 11)

finite prefix point1 index9 signed correction = -14/11

finite prefix point1 index9 function value := sum(13, -14/11)

finite prefix point1 index9 function value = 129/11

finite prefix point1 index9 reverse signed error := sub(129/11, 13)

finite prefix point1 index9 reverse signed error = -14/11

finite prefix point1 index9:original point=1;n=9;limit=13;signed coefficient=-14

f_n(x)=129/11;f_n(x)-limit=-14/11;this error field remains SIGNED

finite prefix point1 index10 denominator := sum(10, 2)

finite prefix point1 index10 denominator = 12

finite prefix point1 index10 signed correction := div(-14, 12)

finite prefix point1 index10 signed correction = -7/6

finite prefix point1 index10 function value := sum(13, -7/6)

finite prefix point1 index10 function value = 71/6

finite prefix point1 index10 reverse signed error := sub(71/6, 13)

finite prefix point1 index10 reverse signed error = -7/6

finite prefix point1 index10:original point=1;n=10;limit=13;signed coefficient=-14

f_n(x)=71/6;f_n(x)-limit=-7/6;this error field remains SIGNED

finite prefix point1 index11 denominator := sum(11, 2)

finite prefix point1 index11 denominator = 13

finite prefix point1 index11 signed correction := div(-14, 13)

finite prefix point1 index11 signed correction = -14/13

finite prefix point1 index11 function value := sum(13, -14/13)

finite prefix point1 index11 function value = 155/13

finite prefix point1 index11 reverse signed error := sub(155/13, 13)

finite prefix point1 index11 reverse signed error = -14/13

finite prefix point1 index11:original point=1;n=11;limit=13;signed coefficient=-14

f_n(x)=155/13;f_n(x)-limit=-14/13;this error field remains SIGNED

finite prefix point1 index12 denominator := sum(12, 2)

finite prefix point1 index12 denominator = 14

finite prefix point1 index12 signed correction := div(-14, 14)

finite prefix point1 index12 signed correction = -1

finite prefix point1 index12 function value := sum(13, -1)

finite prefix point1 index12 function value = 12

finite prefix point1 index12 reverse signed error := sub(12, 13)

finite prefix point1 index12 reverse signed error = -1

finite prefix point1 index12:original point=1;n=12;limit=13;signed coefficient=-14

f_n(x)=12;f_n(x)-limit=-1;this error field remains SIGNED

finite observed length=13;complete domain-order rows=[[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]]]

prefix-alone sufficiency=否;finite_prefix_not_pointwise_convergence_certificate

逐步反向核對

• S132 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S131 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S130 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index12 reverse signed error，不以小數近似替代。
• S129 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index12 function value，不以小數近似替代。
• S128 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index12 signed correction，不以小數近似替代。
• S127 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index12 denominator，不以小數近似替代。
• S126 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S125 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index11 reverse signed error，不以小數近似替代。
• S124 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index11 function value，不以小數近似替代。
• S123 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index11 signed correction，不以小數近似替代。
• S122 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index11 denominator，不以小數近似替代。
• S121 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S120 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index10 reverse signed error，不以小數近似替代。
• S119 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index10 function value，不以小數近似替代。
• S118 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index10 signed correction，不以小數近似替代。
• S117 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index10 denominator，不以小數近似替代。
• S116 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S115 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index9 reverse signed error，不以小數近似替代。
• S114 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index9 function value，不以小數近似替代。
• S113 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index9 signed correction，不以小數近似替代。
• S112 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index9 denominator，不以小數近似替代。
• S111 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S110 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index8 reverse signed error，不以小數近似替代。
• S109 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index8 function value，不以小數近似替代。
• S108 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index8 signed correction，不以小數近似替代。
• S107 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index8 denominator，不以小數近似替代。
• S106 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S105 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index7 reverse signed error，不以小數近似替代。
• S104 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index7 function value，不以小數近似替代。
• S103 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index7 signed correction，不以小數近似替代。
• S102 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index7 denominator，不以小數近似替代。
• S101 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S100 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index6 reverse signed error，不以小數近似替代。
• S099 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index6 function value，不以小數近似替代。
• S098 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index6 signed correction，不以小數近似替代。
• S097 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index6 denominator，不以小數近似替代。
• S096 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S095 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index5 reverse signed error，不以小數近似替代。
• S094 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index5 function value，不以小數近似替代。
• S093 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index5 signed correction，不以小數近似替代。
• S092 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index5 denominator，不以小數近似替代。
• S091 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S090 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index4 reverse signed error，不以小數近似替代。
• S089 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index4 function value，不以小數近似替代。
• S088 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index4 signed correction，不以小數近似替代。
• S087 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index4 denominator，不以小數近似替代。
• S086 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S085 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index3 reverse signed error，不以小數近似替代。
• S084 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index3 function value，不以小數近似替代。
• S083 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index3 signed correction，不以小數近似替代。
• S082 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index3 denominator，不以小數近似替代。
• S081 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S080 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index2 reverse signed error，不以小數近似替代。
• S079 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index2 function value，不以小數近似替代。
• S078 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index2 signed correction，不以小數近似替代。
• S077 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index2 denominator，不以小數近似替代。
• S076 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S075 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index1 reverse signed error，不以小數近似替代。
• S074 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index1 function value，不以小數近似替代。
• S073 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index1 signed correction，不以小數近似替代。
• S072 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index1 denominator，不以小數近似替代。
• S071 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S070 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index0 reverse signed error，不以小數近似替代。
• S069 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index0 function value，不以小數近似替代。
• S068 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index0 signed correction，不以小數近似替代。
• S067 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index0 denominator，不以小數近似替代。
• S066 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S065 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index12 reverse signed error，不以小數近似替代。
• S064 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index12 function value，不以小數近似替代。
• S063 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index12 signed correction，不以小數近似替代。
• S062 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index12 denominator，不以小數近似替代。
• S061 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S060 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index11 reverse signed error，不以小數近似替代。
• S059 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index11 function value，不以小數近似替代。
• S058 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index11 signed correction，不以小數近似替代。
• S057 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index11 denominator，不以小數近似替代。
• S056 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S055 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index10 reverse signed error，不以小數近似替代。
• S054 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index10 function value，不以小數近似替代。
• S053 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index10 signed correction，不以小數近似替代。
• S052 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index10 denominator，不以小數近似替代。
• S051 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S050 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index9 reverse signed error，不以小數近似替代。
• S049 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index9 function value，不以小數近似替代。
• S048 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index9 signed correction，不以小數近似替代。
• S047 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index9 denominator，不以小數近似替代。
• S046 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S045 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index8 reverse signed error，不以小數近似替代。
• S044 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index8 function value，不以小數近似替代。
• S043 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index8 signed correction，不以小數近似替代。
• S042 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index8 denominator，不以小數近似替代。
• S041 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S040 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index7 reverse signed error，不以小數近似替代。
• S039 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index7 function value，不以小數近似替代。
• S038 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index7 signed correction，不以小數近似替代。
• S037 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index7 denominator，不以小數近似替代。
• S036 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S035 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index6 reverse signed error，不以小數近似替代。
• S034 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index6 function value，不以小數近似替代。
• S033 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index6 signed correction，不以小數近似替代。
• S032 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index6 denominator，不以小數近似替代。
• S031 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S030 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index5 reverse signed error，不以小數近似替代。
• S029 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index5 function value，不以小數近似替代。
• S028 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index5 signed correction，不以小數近似替代。
• S027 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index5 denominator，不以小數近似替代。
• S026 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S025 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index4 reverse signed error，不以小數近似替代。
• S024 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index4 function value，不以小數近似替代。
• S023 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index4 signed correction，不以小數近似替代。
• S022 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index4 denominator，不以小數近似替代。
• S021 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S020 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index3 reverse signed error，不以小數近似替代。
• S019 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index3 function value，不以小數近似替代。
• S018 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index3 signed correction，不以小數近似替代。
• S017 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index3 denominator，不以小數近似替代。
• S016 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S015 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index2 reverse signed error，不以小數近似替代。
• S014 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index2 function value，不以小數近似替代。
• S013 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index2 signed correction，不以小數近似替代。
• S012 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index2 denominator，不以小數近似替代。
• S011 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S010 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index1 reverse signed error，不以小數近似替代。
• S009 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index1 function value，不以小數近似替代。
• S008 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index1 signed correction，不以小數近似替代。
• S007 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index1 denominator，不以小數近似替代。
• S006 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S005 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index0 reverse signed error，不以小數近似替代。
• S004 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index0 function value，不以小數近似替代。
• S003 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index0 signed correction，不以小數近似替代。
• S002 · premise_and_result_audit — 以精確有理數重算 finite prefix point0 index0 denominator，不以小數近似替代。
• S001 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。

結論

(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)

依上列完整代值及條件核對得到原題答案；原題編號、格式與狀態保持不變。

本題覆核與來源綁定

覆核日期：2026-10-26

原題、答案、步驟表達式、數值 AST 與既有歷史保持原樣；原來的候選狀態屬於來源歷史，不覆寫為形式化證明。