第 17593 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":[17,18],"coefficients":[18,-19],"shift":2,"prefix_length":18}。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":[17,18],"coefficients":[18,-19],"shift":2,"prefix_length":18}。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=[17, 18];signed coefficients=[18, -19];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(18, 2)

finite prefix point0 index0 signed correction = 9

finite prefix point0 index0 function value := sum(17, 9)

finite prefix point0 index0 function value = 26

finite prefix point0 index0 reverse signed error := sub(26, 17)

finite prefix point0 index0 reverse signed error = 9

finite prefix point0 index0:original point=0;n=0;limit=17;signed coefficient=18

f_n(x)=26;f_n(x)-limit=9;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(18, 3)

finite prefix point0 index1 signed correction = 6

finite prefix point0 index1 function value := sum(17, 6)

finite prefix point0 index1 function value = 23

finite prefix point0 index1 reverse signed error := sub(23, 17)

finite prefix point0 index1 reverse signed error = 6

finite prefix point0 index1:original point=0;n=1;limit=17;signed coefficient=18

f_n(x)=23;f_n(x)-limit=6;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(18, 4)

finite prefix point0 index2 signed correction = 9/2

finite prefix point0 index2 function value := sum(17, 9/2)

finite prefix point0 index2 function value = 43/2

finite prefix point0 index2 reverse signed error := sub(43/2, 17)

finite prefix point0 index2 reverse signed error = 9/2

finite prefix point0 index2:original point=0;n=2;limit=17;signed coefficient=18

f_n(x)=43/2;f_n(x)-limit=9/2;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(18, 5)

finite prefix point0 index3 signed correction = 18/5

finite prefix point0 index3 function value := sum(17, 18/5)

finite prefix point0 index3 function value = 103/5

finite prefix point0 index3 reverse signed error := sub(103/5, 17)

finite prefix point0 index3 reverse signed error = 18/5

finite prefix point0 index3:original point=0;n=3;limit=17;signed coefficient=18

f_n(x)=103/5;f_n(x)-limit=18/5;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(18, 6)

finite prefix point0 index4 signed correction = 3

finite prefix point0 index4 function value := sum(17, 3)

finite prefix point0 index4 function value = 20

finite prefix point0 index4 reverse signed error := sub(20, 17)

finite prefix point0 index4 reverse signed error = 3

finite prefix point0 index4:original point=0;n=4;limit=17;signed coefficient=18

f_n(x)=20;f_n(x)-limit=3;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(18, 7)

finite prefix point0 index5 signed correction = 18/7

finite prefix point0 index5 function value := sum(17, 18/7)

finite prefix point0 index5 function value = 137/7

finite prefix point0 index5 reverse signed error := sub(137/7, 17)

finite prefix point0 index5 reverse signed error = 18/7

finite prefix point0 index5:original point=0;n=5;limit=17;signed coefficient=18

f_n(x)=137/7;f_n(x)-limit=18/7;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(18, 8)

finite prefix point0 index6 signed correction = 9/4

finite prefix point0 index6 function value := sum(17, 9/4)

finite prefix point0 index6 function value = 77/4

finite prefix point0 index6 reverse signed error := sub(77/4, 17)

finite prefix point0 index6 reverse signed error = 9/4

finite prefix point0 index6:original point=0;n=6;limit=17;signed coefficient=18

f_n(x)=77/4;f_n(x)-limit=9/4;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(18, 9)

finite prefix point0 index7 signed correction = 2

finite prefix point0 index7 function value := sum(17, 2)

finite prefix point0 index7 function value = 19

finite prefix point0 index7 reverse signed error := sub(19, 17)

finite prefix point0 index7 reverse signed error = 2

finite prefix point0 index7:original point=0;n=7;limit=17;signed coefficient=18

f_n(x)=19;f_n(x)-limit=2;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(18, 10)

finite prefix point0 index8 signed correction = 9/5

finite prefix point0 index8 function value := sum(17, 9/5)

finite prefix point0 index8 function value = 94/5

finite prefix point0 index8 reverse signed error := sub(94/5, 17)

finite prefix point0 index8 reverse signed error = 9/5

finite prefix point0 index8:original point=0;n=8;limit=17;signed coefficient=18

f_n(x)=94/5;f_n(x)-limit=9/5;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(18, 11)

finite prefix point0 index9 signed correction = 18/11

finite prefix point0 index9 function value := sum(17, 18/11)

finite prefix point0 index9 function value = 205/11

finite prefix point0 index9 reverse signed error := sub(205/11, 17)

finite prefix point0 index9 reverse signed error = 18/11

finite prefix point0 index9:original point=0;n=9;limit=17;signed coefficient=18

f_n(x)=205/11;f_n(x)-limit=18/11;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(18, 12)

finite prefix point0 index10 signed correction = 3/2

finite prefix point0 index10 function value := sum(17, 3/2)

finite prefix point0 index10 function value = 37/2

finite prefix point0 index10 reverse signed error := sub(37/2, 17)

finite prefix point0 index10 reverse signed error = 3/2

finite prefix point0 index10:original point=0;n=10;limit=17;signed coefficient=18

f_n(x)=37/2;f_n(x)-limit=3/2;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(18, 13)

finite prefix point0 index11 signed correction = 18/13

finite prefix point0 index11 function value := sum(17, 18/13)

finite prefix point0 index11 function value = 239/13

finite prefix point0 index11 reverse signed error := sub(239/13, 17)

finite prefix point0 index11 reverse signed error = 18/13

finite prefix point0 index11:original point=0;n=11;limit=17;signed coefficient=18

f_n(x)=239/13;f_n(x)-limit=18/13;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(18, 14)

finite prefix point0 index12 signed correction = 9/7

finite prefix point0 index12 function value := sum(17, 9/7)

finite prefix point0 index12 function value = 128/7

finite prefix point0 index12 reverse signed error := sub(128/7, 17)

finite prefix point0 index12 reverse signed error = 9/7

finite prefix point0 index12:original point=0;n=12;limit=17;signed coefficient=18

f_n(x)=128/7;f_n(x)-limit=9/7;this error field remains SIGNED

finite prefix point0 index13 denominator := sum(13, 2)

finite prefix point0 index13 denominator = 15

finite prefix point0 index13 signed correction := div(18, 15)

finite prefix point0 index13 signed correction = 6/5

finite prefix point0 index13 function value := sum(17, 6/5)

finite prefix point0 index13 function value = 91/5

finite prefix point0 index13 reverse signed error := sub(91/5, 17)

finite prefix point0 index13 reverse signed error = 6/5

finite prefix point0 index13:original point=0;n=13;limit=17;signed coefficient=18

f_n(x)=91/5;f_n(x)-limit=6/5;this error field remains SIGNED

finite prefix point0 index14 denominator := sum(14, 2)

finite prefix point0 index14 denominator = 16

finite prefix point0 index14 signed correction := div(18, 16)

finite prefix point0 index14 signed correction = 9/8

finite prefix point0 index14 function value := sum(17, 9/8)

finite prefix point0 index14 function value = 145/8

finite prefix point0 index14 reverse signed error := sub(145/8, 17)

finite prefix point0 index14 reverse signed error = 9/8

finite prefix point0 index14:original point=0;n=14;limit=17;signed coefficient=18

f_n(x)=145/8;f_n(x)-limit=9/8;this error field remains SIGNED

finite prefix point0 index15 denominator := sum(15, 2)

finite prefix point0 index15 denominator = 17

finite prefix point0 index15 signed correction := div(18, 17)

finite prefix point0 index15 signed correction = 18/17

finite prefix point0 index15 function value := sum(17, 18/17)

finite prefix point0 index15 function value = 307/17

finite prefix point0 index15 reverse signed error := sub(307/17, 17)

finite prefix point0 index15 reverse signed error = 18/17

finite prefix point0 index15:original point=0;n=15;limit=17;signed coefficient=18

f_n(x)=307/17;f_n(x)-limit=18/17;this error field remains SIGNED

finite prefix point0 index16 denominator := sum(16, 2)

finite prefix point0 index16 denominator = 18

finite prefix point0 index16 signed correction := div(18, 18)

finite prefix point0 index16 signed correction = 1

finite prefix point0 index16 function value := sum(17, 1)

finite prefix point0 index16 function value = 18

finite prefix point0 index16 reverse signed error := sub(18, 17)

finite prefix point0 index16 reverse signed error = 1

finite prefix point0 index16:original point=0;n=16;limit=17;signed coefficient=18

f_n(x)=18;f_n(x)-limit=1;this error field remains SIGNED

finite prefix point0 index17 denominator := sum(17, 2)

finite prefix point0 index17 denominator = 19

finite prefix point0 index17 signed correction := div(18, 19)

finite prefix point0 index17 signed correction = 18/19

finite prefix point0 index17 function value := sum(17, 18/19)

finite prefix point0 index17 function value = 341/19

finite prefix point0 index17 reverse signed error := sub(341/19, 17)

finite prefix point0 index17 reverse signed error = 18/19

finite prefix point0 index17:original point=0;n=17;limit=17;signed coefficient=18

f_n(x)=341/19;f_n(x)-limit=18/19;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(-19, 2)

finite prefix point1 index0 signed correction = -19/2

finite prefix point1 index0 function value := sum(18, -19/2)

finite prefix point1 index0 function value = 17/2

finite prefix point1 index0 reverse signed error := sub(17/2, 18)

finite prefix point1 index0 reverse signed error = -19/2

finite prefix point1 index0:original point=1;n=0;limit=18;signed coefficient=-19

f_n(x)=17/2;f_n(x)-limit=-19/2;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(-19, 3)

finite prefix point1 index1 signed correction = -19/3

finite prefix point1 index1 function value := sum(18, -19/3)

finite prefix point1 index1 function value = 35/3

finite prefix point1 index1 reverse signed error := sub(35/3, 18)

finite prefix point1 index1 reverse signed error = -19/3

finite prefix point1 index1:original point=1;n=1;limit=18;signed coefficient=-19

f_n(x)=35/3;f_n(x)-limit=-19/3;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(-19, 4)

finite prefix point1 index2 signed correction = -19/4

finite prefix point1 index2 function value := sum(18, -19/4)

finite prefix point1 index2 function value = 53/4

finite prefix point1 index2 reverse signed error := sub(53/4, 18)

finite prefix point1 index2 reverse signed error = -19/4

finite prefix point1 index2:original point=1;n=2;limit=18;signed coefficient=-19

f_n(x)=53/4;f_n(x)-limit=-19/4;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(-19, 5)

finite prefix point1 index3 signed correction = -19/5

finite prefix point1 index3 function value := sum(18, -19/5)

finite prefix point1 index3 function value = 71/5

finite prefix point1 index3 reverse signed error := sub(71/5, 18)

finite prefix point1 index3 reverse signed error = -19/5

finite prefix point1 index3:original point=1;n=3;limit=18;signed coefficient=-19

f_n(x)=71/5;f_n(x)-limit=-19/5;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(-19, 6)

finite prefix point1 index4 signed correction = -19/6

finite prefix point1 index4 function value := sum(18, -19/6)

finite prefix point1 index4 function value = 89/6

finite prefix point1 index4 reverse signed error := sub(89/6, 18)

finite prefix point1 index4 reverse signed error = -19/6

finite prefix point1 index4:original point=1;n=4;limit=18;signed coefficient=-19

f_n(x)=89/6;f_n(x)-limit=-19/6;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(-19, 7)

finite prefix point1 index5 signed correction = -19/7

finite prefix point1 index5 function value := sum(18, -19/7)

finite prefix point1 index5 function value = 107/7

finite prefix point1 index5 reverse signed error := sub(107/7, 18)

finite prefix point1 index5 reverse signed error = -19/7

finite prefix point1 index5:original point=1;n=5;limit=18;signed coefficient=-19

f_n(x)=107/7;f_n(x)-limit=-19/7;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(-19, 8)

finite prefix point1 index6 signed correction = -19/8

finite prefix point1 index6 function value := sum(18, -19/8)

finite prefix point1 index6 function value = 125/8

finite prefix point1 index6 reverse signed error := sub(125/8, 18)

finite prefix point1 index6 reverse signed error = -19/8

finite prefix point1 index6:original point=1;n=6;limit=18;signed coefficient=-19

f_n(x)=125/8;f_n(x)-limit=-19/8;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(-19, 9)

finite prefix point1 index7 signed correction = -19/9

finite prefix point1 index7 function value := sum(18, -19/9)

finite prefix point1 index7 function value = 143/9

finite prefix point1 index7 reverse signed error := sub(143/9, 18)

finite prefix point1 index7 reverse signed error = -19/9

finite prefix point1 index7:original point=1;n=7;limit=18;signed coefficient=-19

f_n(x)=143/9;f_n(x)-limit=-19/9;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(-19, 10)

finite prefix point1 index8 signed correction = -19/10

finite prefix point1 index8 function value := sum(18, -19/10)

finite prefix point1 index8 function value = 161/10

finite prefix point1 index8 reverse signed error := sub(161/10, 18)

finite prefix point1 index8 reverse signed error = -19/10

finite prefix point1 index8:original point=1;n=8;limit=18;signed coefficient=-19

f_n(x)=161/10;f_n(x)-limit=-19/10;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(-19, 11)

finite prefix point1 index9 signed correction = -19/11

finite prefix point1 index9 function value := sum(18, -19/11)

finite prefix point1 index9 function value = 179/11

finite prefix point1 index9 reverse signed error := sub(179/11, 18)

finite prefix point1 index9 reverse signed error = -19/11

finite prefix point1 index9:original point=1;n=9;limit=18;signed coefficient=-19

f_n(x)=179/11;f_n(x)-limit=-19/11;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(-19, 12)

finite prefix point1 index10 signed correction = -19/12

finite prefix point1 index10 function value := sum(18, -19/12)

finite prefix point1 index10 function value = 197/12

finite prefix point1 index10 reverse signed error := sub(197/12, 18)

finite prefix point1 index10 reverse signed error = -19/12

finite prefix point1 index10:original point=1;n=10;limit=18;signed coefficient=-19

f_n(x)=197/12;f_n(x)-limit=-19/12;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(-19, 13)

finite prefix point1 index11 signed correction = -19/13

finite prefix point1 index11 function value := sum(18, -19/13)

finite prefix point1 index11 function value = 215/13

finite prefix point1 index11 reverse signed error := sub(215/13, 18)

finite prefix point1 index11 reverse signed error = -19/13

finite prefix point1 index11:original point=1;n=11;limit=18;signed coefficient=-19

f_n(x)=215/13;f_n(x)-limit=-19/13;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(-19, 14)

finite prefix point1 index12 signed correction = -19/14

finite prefix point1 index12 function value := sum(18, -19/14)

finite prefix point1 index12 function value = 233/14

finite prefix point1 index12 reverse signed error := sub(233/14, 18)

finite prefix point1 index12 reverse signed error = -19/14

finite prefix point1 index12:original point=1;n=12;limit=18;signed coefficient=-19

f_n(x)=233/14;f_n(x)-limit=-19/14;this error field remains SIGNED

finite prefix point1 index13 denominator := sum(13, 2)

finite prefix point1 index13 denominator = 15

finite prefix point1 index13 signed correction := div(-19, 15)

finite prefix point1 index13 signed correction = -19/15

finite prefix point1 index13 function value := sum(18, -19/15)

finite prefix point1 index13 function value = 251/15

finite prefix point1 index13 reverse signed error := sub(251/15, 18)

finite prefix point1 index13 reverse signed error = -19/15

finite prefix point1 index13:original point=1;n=13;limit=18;signed coefficient=-19

f_n(x)=251/15;f_n(x)-limit=-19/15;this error field remains SIGNED

finite prefix point1 index14 denominator := sum(14, 2)

finite prefix point1 index14 denominator = 16

finite prefix point1 index14 signed correction := div(-19, 16)

finite prefix point1 index14 signed correction = -19/16

finite prefix point1 index14 function value := sum(18, -19/16)

finite prefix point1 index14 function value = 269/16

finite prefix point1 index14 reverse signed error := sub(269/16, 18)

finite prefix point1 index14 reverse signed error = -19/16

finite prefix point1 index14:original point=1;n=14;limit=18;signed coefficient=-19

f_n(x)=269/16;f_n(x)-limit=-19/16;this error field remains SIGNED

finite prefix point1 index15 denominator := sum(15, 2)

finite prefix point1 index15 denominator = 17

finite prefix point1 index15 signed correction := div(-19, 17)

finite prefix point1 index15 signed correction = -19/17

finite prefix point1 index15 function value := sum(18, -19/17)

finite prefix point1 index15 function value = 287/17

finite prefix point1 index15 reverse signed error := sub(287/17, 18)

finite prefix point1 index15 reverse signed error = -19/17

finite prefix point1 index15:original point=1;n=15;limit=18;signed coefficient=-19

f_n(x)=287/17;f_n(x)-limit=-19/17;this error field remains SIGNED

finite prefix point1 index16 denominator := sum(16, 2)

finite prefix point1 index16 denominator = 18

finite prefix point1 index16 signed correction := div(-19, 18)

finite prefix point1 index16 signed correction = -19/18

finite prefix point1 index16 function value := sum(18, -19/18)

finite prefix point1 index16 function value = 305/18

finite prefix point1 index16 reverse signed error := sub(305/18, 18)

finite prefix point1 index16 reverse signed error = -19/18

finite prefix point1 index16:original point=1;n=16;limit=18;signed coefficient=-19

f_n(x)=305/18;f_n(x)-limit=-19/18;this error field remains SIGNED

finite prefix point1 index17 denominator := sum(17, 2)

finite prefix point1 index17 denominator = 19

finite prefix point1 index17 signed correction := div(-19, 19)

finite prefix point1 index17 signed correction = -1

finite prefix point1 index17 function value := sum(18, -1)

finite prefix point1 index17 function value = 17

finite prefix point1 index17 reverse signed error := sub(17, 18)

finite prefix point1 index17 reverse signed error = -1

finite prefix point1 index17:original point=1;n=17;limit=18;signed coefficient=-19

f_n(x)=17;f_n(x)-limit=-1;this error field remains SIGNED

finite observed length=18;complete domain-order rows=[[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]]]

prefix-alone sufficiency=否;finite_prefix_not_pointwise_convergence_certificate

逐步反向核對

• S182 · 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。
• S181 · 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。
• S180 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index17 reverse signed error，不以小數近似替代。
• S179 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index17 function value，不以小數近似替代。
• S178 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index17 signed correction，不以小數近似替代。
• S177 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index17 denominator，不以小數近似替代。
• S176 · 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。
• S175 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index16 reverse signed error，不以小數近似替代。
• S174 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index16 function value，不以小數近似替代。
• S173 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index16 signed correction，不以小數近似替代。
• S172 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index16 denominator，不以小數近似替代。
• S171 · 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。
• S170 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index15 reverse signed error，不以小數近似替代。
• S169 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index15 function value，不以小數近似替代。
• S168 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index15 signed correction，不以小數近似替代。
• S167 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index15 denominator，不以小數近似替代。
• S166 · 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。
• S165 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index14 reverse signed error，不以小數近似替代。
• S164 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index14 function value，不以小數近似替代。
• S163 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index14 signed correction，不以小數近似替代。
• S162 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index14 denominator，不以小數近似替代。
• S161 · 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。
• S160 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index13 reverse signed error，不以小數近似替代。
• S159 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index13 function value，不以小數近似替代。
• S158 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index13 signed correction，不以小數近似替代。
• S157 · premise_and_result_audit — 以精確有理數重算 finite prefix point1 index13 denominator，不以小數近似替代。
• S156 · 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。
• S155 · 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。
• S154 · 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。
• S153 · 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。
• S152 · 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。
• S151 · 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。
• S150 · 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。
• S149 · 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。
• S148 · 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。
• S147 · 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。
• S146 · 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。
• S145 · 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。
• S144 · 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。
• S143 · 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。
• S142 · 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。
• S141 · 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。
• S140 · 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。
• S139 · 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。
• S138 · 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。
• S137 · 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。
• S136 · 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。
• S135 · 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。
• S134 · 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。
• S133 · 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。
• S132 · 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。
• 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 index7 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 index7 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 index7 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 index7 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 index6 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 index6 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 index6 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 index6 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 index5 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 index5 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 index5 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 index5 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 index4 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 index4 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 index4 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 index4 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 index3 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 index3 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 index3 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 index3 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 index2 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 index2 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 index2 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 index2 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 index1 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 index1 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 index1 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 index1 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 index0 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 index0 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 index0 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 index0 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 point0 index17 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 point0 index17 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 point0 index17 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 point0 index17 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 point0 index16 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 point0 index16 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 point0 index16 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 point0 index16 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 point0 index15 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 point0 index15 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 point0 index15 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 point0 index15 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 point0 index14 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 point0 index14 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 point0 index14 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 point0 index14 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 point0 index13 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 point0 index13 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 point0 index13 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 point0 index13 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

(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。