Question 17598: A Long Prefix Still Does Not Replace the All-n Tail

Original question and givens

Use the same complete finite domain Fin(2)={0,…,1}, with aligned limit values=[22, 23], coefficients=[23, -24], positive shift=2, and f_n(x)=limit[x]+coefficients[x]/(n+shift) for every n≥0. Values and tail bounds are exact rationals. Pointwise witnesses may depend on both x and epsilon. A finite maximum of all pointwise witnesses gives a common witness only on this finite domain; it is not a general infinite-domain implication. A finite observed prefix alone is not a convergence certificate. prefix_length=23, beginning at n=0. Give (prefix_length,value_rows,sufficient?,finite_prefix_not_pointwise_convergence_certificate), with each row [point,values_in_n_order].

• G001 — Use the same complete finite domain Fin(2)={0,…,1}, with aligned limit values=[22, 23], coefficients=[23, -24], positive shift=2, and f_n(x)=limit[x]+coefficients[x]/(n+shift) for every n≥0. Values and tail bounds are exact rationals. Pointwise witnesses may depend on both x and epsilon. A finite maximum of all pointwise witnesses gives a common witness only on this finite domain; it is not a general infinite-domain implication. A finite observed prefix alone is not a convergence certificate. prefix_length=23, beginning at n=0. Give (prefix_length,value_rows,sufficient?,finite_prefix_not_pointwise_convergence_certificate), with each row [point,values_in_n_order].

Definition and scope

Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.

• mko-pointwise-convergence-of-functions

Step-by-step derivation

same COMPLETE finite domain Fin(2);original aligned limits=[22, 23];signed coefficients=[23, -24];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(23, 2)

finite prefix point0 index0 signed correction = 23/2

finite prefix point0 index0 function value := sum(22, 23/2)

finite prefix point0 index0 function value = 67/2

finite prefix point0 index0 reverse signed error := sub(67/2, 22)

finite prefix point0 index0 reverse signed error = 23/2

finite prefix point0 index0:original point=0;n=0;limit=22;signed coefficient=23

f_n(x)=67/2;f_n(x)-limit=23/2;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(23, 3)

finite prefix point0 index1 signed correction = 23/3

finite prefix point0 index1 function value := sum(22, 23/3)

finite prefix point0 index1 function value = 89/3

finite prefix point0 index1 reverse signed error := sub(89/3, 22)

finite prefix point0 index1 reverse signed error = 23/3

finite prefix point0 index1:original point=0;n=1;limit=22;signed coefficient=23

f_n(x)=89/3;f_n(x)-limit=23/3;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(23, 4)

finite prefix point0 index2 signed correction = 23/4

finite prefix point0 index2 function value := sum(22, 23/4)

finite prefix point0 index2 function value = 111/4

finite prefix point0 index2 reverse signed error := sub(111/4, 22)

finite prefix point0 index2 reverse signed error = 23/4

finite prefix point0 index2:original point=0;n=2;limit=22;signed coefficient=23

f_n(x)=111/4;f_n(x)-limit=23/4;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(23, 5)

finite prefix point0 index3 signed correction = 23/5

finite prefix point0 index3 function value := sum(22, 23/5)

finite prefix point0 index3 function value = 133/5

finite prefix point0 index3 reverse signed error := sub(133/5, 22)

finite prefix point0 index3 reverse signed error = 23/5

finite prefix point0 index3:original point=0;n=3;limit=22;signed coefficient=23

f_n(x)=133/5;f_n(x)-limit=23/5;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(23, 6)

finite prefix point0 index4 signed correction = 23/6

finite prefix point0 index4 function value := sum(22, 23/6)

finite prefix point0 index4 function value = 155/6

finite prefix point0 index4 reverse signed error := sub(155/6, 22)

finite prefix point0 index4 reverse signed error = 23/6

finite prefix point0 index4:original point=0;n=4;limit=22;signed coefficient=23

f_n(x)=155/6;f_n(x)-limit=23/6;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(23, 7)

finite prefix point0 index5 signed correction = 23/7

finite prefix point0 index5 function value := sum(22, 23/7)

finite prefix point0 index5 function value = 177/7

finite prefix point0 index5 reverse signed error := sub(177/7, 22)

finite prefix point0 index5 reverse signed error = 23/7

finite prefix point0 index5:original point=0;n=5;limit=22;signed coefficient=23

f_n(x)=177/7;f_n(x)-limit=23/7;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(23, 8)

finite prefix point0 index6 signed correction = 23/8

finite prefix point0 index6 function value := sum(22, 23/8)

finite prefix point0 index6 function value = 199/8

finite prefix point0 index6 reverse signed error := sub(199/8, 22)

finite prefix point0 index6 reverse signed error = 23/8

finite prefix point0 index6:original point=0;n=6;limit=22;signed coefficient=23

f_n(x)=199/8;f_n(x)-limit=23/8;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(23, 9)

finite prefix point0 index7 signed correction = 23/9

finite prefix point0 index7 function value := sum(22, 23/9)

finite prefix point0 index7 function value = 221/9

finite prefix point0 index7 reverse signed error := sub(221/9, 22)

finite prefix point0 index7 reverse signed error = 23/9

finite prefix point0 index7:original point=0;n=7;limit=22;signed coefficient=23

f_n(x)=221/9;f_n(x)-limit=23/9;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(23, 10)

finite prefix point0 index8 signed correction = 23/10

finite prefix point0 index8 function value := sum(22, 23/10)

finite prefix point0 index8 function value = 243/10

finite prefix point0 index8 reverse signed error := sub(243/10, 22)

finite prefix point0 index8 reverse signed error = 23/10

finite prefix point0 index8:original point=0;n=8;limit=22;signed coefficient=23

f_n(x)=243/10;f_n(x)-limit=23/10;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(23, 11)

finite prefix point0 index9 signed correction = 23/11

finite prefix point0 index9 function value := sum(22, 23/11)

finite prefix point0 index9 function value = 265/11

finite prefix point0 index9 reverse signed error := sub(265/11, 22)

finite prefix point0 index9 reverse signed error = 23/11

finite prefix point0 index9:original point=0;n=9;limit=22;signed coefficient=23

f_n(x)=265/11;f_n(x)-limit=23/11;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(23, 12)

finite prefix point0 index10 signed correction = 23/12

finite prefix point0 index10 function value := sum(22, 23/12)

finite prefix point0 index10 function value = 287/12

finite prefix point0 index10 reverse signed error := sub(287/12, 22)

finite prefix point0 index10 reverse signed error = 23/12

finite prefix point0 index10:original point=0;n=10;limit=22;signed coefficient=23

f_n(x)=287/12;f_n(x)-limit=23/12;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(23, 13)

finite prefix point0 index11 signed correction = 23/13

finite prefix point0 index11 function value := sum(22, 23/13)

finite prefix point0 index11 function value = 309/13

finite prefix point0 index11 reverse signed error := sub(309/13, 22)

finite prefix point0 index11 reverse signed error = 23/13

finite prefix point0 index11:original point=0;n=11;limit=22;signed coefficient=23

f_n(x)=309/13;f_n(x)-limit=23/13;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(23, 14)

finite prefix point0 index12 signed correction = 23/14

finite prefix point0 index12 function value := sum(22, 23/14)

finite prefix point0 index12 function value = 331/14

finite prefix point0 index12 reverse signed error := sub(331/14, 22)

finite prefix point0 index12 reverse signed error = 23/14

finite prefix point0 index12:original point=0;n=12;limit=22;signed coefficient=23

f_n(x)=331/14;f_n(x)-limit=23/14;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(23, 15)

finite prefix point0 index13 signed correction = 23/15

finite prefix point0 index13 function value := sum(22, 23/15)

finite prefix point0 index13 function value = 353/15

finite prefix point0 index13 reverse signed error := sub(353/15, 22)

finite prefix point0 index13 reverse signed error = 23/15

finite prefix point0 index13:original point=0;n=13;limit=22;signed coefficient=23

f_n(x)=353/15;f_n(x)-limit=23/15;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(23, 16)

finite prefix point0 index14 signed correction = 23/16

finite prefix point0 index14 function value := sum(22, 23/16)

finite prefix point0 index14 function value = 375/16

finite prefix point0 index14 reverse signed error := sub(375/16, 22)

finite prefix point0 index14 reverse signed error = 23/16

finite prefix point0 index14:original point=0;n=14;limit=22;signed coefficient=23

f_n(x)=375/16;f_n(x)-limit=23/16;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(23, 17)

finite prefix point0 index15 signed correction = 23/17

finite prefix point0 index15 function value := sum(22, 23/17)

finite prefix point0 index15 function value = 397/17

finite prefix point0 index15 reverse signed error := sub(397/17, 22)

finite prefix point0 index15 reverse signed error = 23/17

finite prefix point0 index15:original point=0;n=15;limit=22;signed coefficient=23

f_n(x)=397/17;f_n(x)-limit=23/17;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(23, 18)

finite prefix point0 index16 signed correction = 23/18

finite prefix point0 index16 function value := sum(22, 23/18)

finite prefix point0 index16 function value = 419/18

finite prefix point0 index16 reverse signed error := sub(419/18, 22)

finite prefix point0 index16 reverse signed error = 23/18

finite prefix point0 index16:original point=0;n=16;limit=22;signed coefficient=23

f_n(x)=419/18;f_n(x)-limit=23/18;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(23, 19)

finite prefix point0 index17 signed correction = 23/19

finite prefix point0 index17 function value := sum(22, 23/19)

finite prefix point0 index17 function value = 441/19

finite prefix point0 index17 reverse signed error := sub(441/19, 22)

finite prefix point0 index17 reverse signed error = 23/19

finite prefix point0 index17:original point=0;n=17;limit=22;signed coefficient=23

f_n(x)=441/19;f_n(x)-limit=23/19;this error field remains SIGNED

finite prefix point0 index18 denominator := sum(18, 2)

finite prefix point0 index18 denominator = 20

finite prefix point0 index18 signed correction := div(23, 20)

finite prefix point0 index18 signed correction = 23/20

finite prefix point0 index18 function value := sum(22, 23/20)

finite prefix point0 index18 function value = 463/20

finite prefix point0 index18 reverse signed error := sub(463/20, 22)

finite prefix point0 index18 reverse signed error = 23/20

finite prefix point0 index18:original point=0;n=18;limit=22;signed coefficient=23

f_n(x)=463/20;f_n(x)-limit=23/20;this error field remains SIGNED

finite prefix point0 index19 denominator := sum(19, 2)

finite prefix point0 index19 denominator = 21

finite prefix point0 index19 signed correction := div(23, 21)

finite prefix point0 index19 signed correction = 23/21

finite prefix point0 index19 function value := sum(22, 23/21)

finite prefix point0 index19 function value = 485/21

finite prefix point0 index19 reverse signed error := sub(485/21, 22)

finite prefix point0 index19 reverse signed error = 23/21

finite prefix point0 index19:original point=0;n=19;limit=22;signed coefficient=23

f_n(x)=485/21;f_n(x)-limit=23/21;this error field remains SIGNED

finite prefix point0 index20 denominator := sum(20, 2)

finite prefix point0 index20 denominator = 22

finite prefix point0 index20 signed correction := div(23, 22)

finite prefix point0 index20 signed correction = 23/22

finite prefix point0 index20 function value := sum(22, 23/22)

finite prefix point0 index20 function value = 507/22

finite prefix point0 index20 reverse signed error := sub(507/22, 22)

finite prefix point0 index20 reverse signed error = 23/22

finite prefix point0 index20:original point=0;n=20;limit=22;signed coefficient=23

f_n(x)=507/22;f_n(x)-limit=23/22;this error field remains SIGNED

finite prefix point0 index21 denominator := sum(21, 2)

finite prefix point0 index21 denominator = 23

finite prefix point0 index21 signed correction := div(23, 23)

finite prefix point0 index21 signed correction = 1

finite prefix point0 index21 function value := sum(22, 1)

finite prefix point0 index21 function value = 23

finite prefix point0 index21 reverse signed error := sub(23, 22)

finite prefix point0 index21 reverse signed error = 1

finite prefix point0 index21:original point=0;n=21;limit=22;signed coefficient=23

f_n(x)=23;f_n(x)-limit=1;this error field remains SIGNED

finite prefix point0 index22 denominator := sum(22, 2)

finite prefix point0 index22 denominator = 24

finite prefix point0 index22 signed correction := div(23, 24)

finite prefix point0 index22 signed correction = 23/24

finite prefix point0 index22 function value := sum(22, 23/24)

finite prefix point0 index22 function value = 551/24

finite prefix point0 index22 reverse signed error := sub(551/24, 22)

finite prefix point0 index22 reverse signed error = 23/24

finite prefix point0 index22:original point=0;n=22;limit=22;signed coefficient=23

f_n(x)=551/24;f_n(x)-limit=23/24;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(-24, 2)

finite prefix point1 index0 signed correction = -12

finite prefix point1 index0 function value := sum(23, -12)

finite prefix point1 index0 function value = 11

finite prefix point1 index0 reverse signed error := sub(11, 23)

finite prefix point1 index0 reverse signed error = -12

finite prefix point1 index0:original point=1;n=0;limit=23;signed coefficient=-24

f_n(x)=11;f_n(x)-limit=-12;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(-24, 3)

finite prefix point1 index1 signed correction = -8

finite prefix point1 index1 function value := sum(23, -8)

finite prefix point1 index1 function value = 15

finite prefix point1 index1 reverse signed error := sub(15, 23)

finite prefix point1 index1 reverse signed error = -8

finite prefix point1 index1:original point=1;n=1;limit=23;signed coefficient=-24

f_n(x)=15;f_n(x)-limit=-8;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(-24, 4)

finite prefix point1 index2 signed correction = -6

finite prefix point1 index2 function value := sum(23, -6)

finite prefix point1 index2 function value = 17

finite prefix point1 index2 reverse signed error := sub(17, 23)

finite prefix point1 index2 reverse signed error = -6

finite prefix point1 index2:original point=1;n=2;limit=23;signed coefficient=-24

f_n(x)=17;f_n(x)-limit=-6;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(-24, 5)

finite prefix point1 index3 signed correction = -24/5

finite prefix point1 index3 function value := sum(23, -24/5)

finite prefix point1 index3 function value = 91/5

finite prefix point1 index3 reverse signed error := sub(91/5, 23)

finite prefix point1 index3 reverse signed error = -24/5

finite prefix point1 index3:original point=1;n=3;limit=23;signed coefficient=-24

f_n(x)=91/5;f_n(x)-limit=-24/5;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(-24, 6)

finite prefix point1 index4 signed correction = -4

finite prefix point1 index4 function value := sum(23, -4)

finite prefix point1 index4 function value = 19

finite prefix point1 index4 reverse signed error := sub(19, 23)

finite prefix point1 index4 reverse signed error = -4

finite prefix point1 index4:original point=1;n=4;limit=23;signed coefficient=-24

f_n(x)=19;f_n(x)-limit=-4;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(-24, 7)

finite prefix point1 index5 signed correction = -24/7

finite prefix point1 index5 function value := sum(23, -24/7)

finite prefix point1 index5 function value = 137/7

finite prefix point1 index5 reverse signed error := sub(137/7, 23)

finite prefix point1 index5 reverse signed error = -24/7

finite prefix point1 index5:original point=1;n=5;limit=23;signed coefficient=-24

f_n(x)=137/7;f_n(x)-limit=-24/7;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(-24, 8)

finite prefix point1 index6 signed correction = -3

finite prefix point1 index6 function value := sum(23, -3)

finite prefix point1 index6 function value = 20

finite prefix point1 index6 reverse signed error := sub(20, 23)

finite prefix point1 index6 reverse signed error = -3

finite prefix point1 index6:original point=1;n=6;limit=23;signed coefficient=-24

f_n(x)=20;f_n(x)-limit=-3;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(-24, 9)

finite prefix point1 index7 signed correction = -8/3

finite prefix point1 index7 function value := sum(23, -8/3)

finite prefix point1 index7 function value = 61/3

finite prefix point1 index7 reverse signed error := sub(61/3, 23)

finite prefix point1 index7 reverse signed error = -8/3

finite prefix point1 index7:original point=1;n=7;limit=23;signed coefficient=-24

f_n(x)=61/3;f_n(x)-limit=-8/3;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(-24, 10)

finite prefix point1 index8 signed correction = -12/5

finite prefix point1 index8 function value := sum(23, -12/5)

finite prefix point1 index8 function value = 103/5

finite prefix point1 index8 reverse signed error := sub(103/5, 23)

finite prefix point1 index8 reverse signed error = -12/5

finite prefix point1 index8:original point=1;n=8;limit=23;signed coefficient=-24

f_n(x)=103/5;f_n(x)-limit=-12/5;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(-24, 11)

finite prefix point1 index9 signed correction = -24/11

finite prefix point1 index9 function value := sum(23, -24/11)

finite prefix point1 index9 function value = 229/11

finite prefix point1 index9 reverse signed error := sub(229/11, 23)

finite prefix point1 index9 reverse signed error = -24/11

finite prefix point1 index9:original point=1;n=9;limit=23;signed coefficient=-24

f_n(x)=229/11;f_n(x)-limit=-24/11;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(-24, 12)

finite prefix point1 index10 signed correction = -2

finite prefix point1 index10 function value := sum(23, -2)

finite prefix point1 index10 function value = 21

finite prefix point1 index10 reverse signed error := sub(21, 23)

finite prefix point1 index10 reverse signed error = -2

finite prefix point1 index10:original point=1;n=10;limit=23;signed coefficient=-24

f_n(x)=21;f_n(x)-limit=-2;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(-24, 13)

finite prefix point1 index11 signed correction = -24/13

finite prefix point1 index11 function value := sum(23, -24/13)

finite prefix point1 index11 function value = 275/13

finite prefix point1 index11 reverse signed error := sub(275/13, 23)

finite prefix point1 index11 reverse signed error = -24/13

finite prefix point1 index11:original point=1;n=11;limit=23;signed coefficient=-24

f_n(x)=275/13;f_n(x)-limit=-24/13;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(-24, 14)

finite prefix point1 index12 signed correction = -12/7

finite prefix point1 index12 function value := sum(23, -12/7)

finite prefix point1 index12 function value = 149/7

finite prefix point1 index12 reverse signed error := sub(149/7, 23)

finite prefix point1 index12 reverse signed error = -12/7

finite prefix point1 index12:original point=1;n=12;limit=23;signed coefficient=-24

f_n(x)=149/7;f_n(x)-limit=-12/7;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(-24, 15)

finite prefix point1 index13 signed correction = -8/5

finite prefix point1 index13 function value := sum(23, -8/5)

finite prefix point1 index13 function value = 107/5

finite prefix point1 index13 reverse signed error := sub(107/5, 23)

finite prefix point1 index13 reverse signed error = -8/5

finite prefix point1 index13:original point=1;n=13;limit=23;signed coefficient=-24

f_n(x)=107/5;f_n(x)-limit=-8/5;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(-24, 16)

finite prefix point1 index14 signed correction = -3/2

finite prefix point1 index14 function value := sum(23, -3/2)

finite prefix point1 index14 function value = 43/2

finite prefix point1 index14 reverse signed error := sub(43/2, 23)

finite prefix point1 index14 reverse signed error = -3/2

finite prefix point1 index14:original point=1;n=14;limit=23;signed coefficient=-24

f_n(x)=43/2;f_n(x)-limit=-3/2;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(-24, 17)

finite prefix point1 index15 signed correction = -24/17

finite prefix point1 index15 function value := sum(23, -24/17)

finite prefix point1 index15 function value = 367/17

finite prefix point1 index15 reverse signed error := sub(367/17, 23)

finite prefix point1 index15 reverse signed error = -24/17

finite prefix point1 index15:original point=1;n=15;limit=23;signed coefficient=-24

f_n(x)=367/17;f_n(x)-limit=-24/17;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(-24, 18)

finite prefix point1 index16 signed correction = -4/3

finite prefix point1 index16 function value := sum(23, -4/3)

finite prefix point1 index16 function value = 65/3

finite prefix point1 index16 reverse signed error := sub(65/3, 23)

finite prefix point1 index16 reverse signed error = -4/3

finite prefix point1 index16:original point=1;n=16;limit=23;signed coefficient=-24

f_n(x)=65/3;f_n(x)-limit=-4/3;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(-24, 19)

finite prefix point1 index17 signed correction = -24/19

finite prefix point1 index17 function value := sum(23, -24/19)

finite prefix point1 index17 function value = 413/19

finite prefix point1 index17 reverse signed error := sub(413/19, 23)

finite prefix point1 index17 reverse signed error = -24/19

finite prefix point1 index17:original point=1;n=17;limit=23;signed coefficient=-24

f_n(x)=413/19;f_n(x)-limit=-24/19;this error field remains SIGNED

finite prefix point1 index18 denominator := sum(18, 2)

finite prefix point1 index18 denominator = 20

finite prefix point1 index18 signed correction := div(-24, 20)

finite prefix point1 index18 signed correction = -6/5

finite prefix point1 index18 function value := sum(23, -6/5)

finite prefix point1 index18 function value = 109/5

finite prefix point1 index18 reverse signed error := sub(109/5, 23)

finite prefix point1 index18 reverse signed error = -6/5

finite prefix point1 index18:original point=1;n=18;limit=23;signed coefficient=-24

f_n(x)=109/5;f_n(x)-limit=-6/5;this error field remains SIGNED

finite prefix point1 index19 denominator := sum(19, 2)

finite prefix point1 index19 denominator = 21

finite prefix point1 index19 signed correction := div(-24, 21)

finite prefix point1 index19 signed correction = -8/7

finite prefix point1 index19 function value := sum(23, -8/7)

finite prefix point1 index19 function value = 153/7

finite prefix point1 index19 reverse signed error := sub(153/7, 23)

finite prefix point1 index19 reverse signed error = -8/7

finite prefix point1 index19:original point=1;n=19;limit=23;signed coefficient=-24

f_n(x)=153/7;f_n(x)-limit=-8/7;this error field remains SIGNED

finite prefix point1 index20 denominator := sum(20, 2)

finite prefix point1 index20 denominator = 22

finite prefix point1 index20 signed correction := div(-24, 22)

finite prefix point1 index20 signed correction = -12/11

finite prefix point1 index20 function value := sum(23, -12/11)

finite prefix point1 index20 function value = 241/11

finite prefix point1 index20 reverse signed error := sub(241/11, 23)

finite prefix point1 index20 reverse signed error = -12/11

finite prefix point1 index20:original point=1;n=20;limit=23;signed coefficient=-24

f_n(x)=241/11;f_n(x)-limit=-12/11;this error field remains SIGNED

finite prefix point1 index21 denominator := sum(21, 2)

finite prefix point1 index21 denominator = 23

finite prefix point1 index21 signed correction := div(-24, 23)

finite prefix point1 index21 signed correction = -24/23

finite prefix point1 index21 function value := sum(23, -24/23)

finite prefix point1 index21 function value = 505/23

finite prefix point1 index21 reverse signed error := sub(505/23, 23)

finite prefix point1 index21 reverse signed error = -24/23

finite prefix point1 index21:original point=1;n=21;limit=23;signed coefficient=-24

f_n(x)=505/23;f_n(x)-limit=-24/23;this error field remains SIGNED

finite prefix point1 index22 denominator := sum(22, 2)

finite prefix point1 index22 denominator = 24

finite prefix point1 index22 signed correction := div(-24, 24)

finite prefix point1 index22 signed correction = -1

finite prefix point1 index22 function value := sum(23, -1)

finite prefix point1 index22 function value = 22

finite prefix point1 index22 reverse signed error := sub(22, 23)

finite prefix point1 index22 reverse signed error = -1

finite prefix point1 index22:original point=1;n=22;limit=23;signed coefficient=-24

f_n(x)=22;f_n(x)-limit=-1;this error field remains SIGNED

finite observed length=23;complete domain-order rows=[[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]]]

prefix-alone sufficiency=No;finite_prefix_not_pointwise_convergence_certificate

Reverse checks

• S232 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S231 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S230 · premise_and_result_audit — Recompute finite prefix point1 index22 reverse signed error with exact rational arithmetic, not rounded decimals.
• S229 · premise_and_result_audit — Recompute finite prefix point1 index22 function value with exact rational arithmetic, not rounded decimals.
• S228 · premise_and_result_audit — Recompute finite prefix point1 index22 signed correction with exact rational arithmetic, not rounded decimals.
• S227 · premise_and_result_audit — Recompute finite prefix point1 index22 denominator with exact rational arithmetic, not rounded decimals.
• S226 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S225 · premise_and_result_audit — Recompute finite prefix point1 index21 reverse signed error with exact rational arithmetic, not rounded decimals.
• S224 · premise_and_result_audit — Recompute finite prefix point1 index21 function value with exact rational arithmetic, not rounded decimals.
• S223 · premise_and_result_audit — Recompute finite prefix point1 index21 signed correction with exact rational arithmetic, not rounded decimals.
• S222 · premise_and_result_audit — Recompute finite prefix point1 index21 denominator with exact rational arithmetic, not rounded decimals.
• S221 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S220 · premise_and_result_audit — Recompute finite prefix point1 index20 reverse signed error with exact rational arithmetic, not rounded decimals.
• S219 · premise_and_result_audit — Recompute finite prefix point1 index20 function value with exact rational arithmetic, not rounded decimals.
• S218 · premise_and_result_audit — Recompute finite prefix point1 index20 signed correction with exact rational arithmetic, not rounded decimals.
• S217 · premise_and_result_audit — Recompute finite prefix point1 index20 denominator with exact rational arithmetic, not rounded decimals.
• S216 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S215 · premise_and_result_audit — Recompute finite prefix point1 index19 reverse signed error with exact rational arithmetic, not rounded decimals.
• S214 · premise_and_result_audit — Recompute finite prefix point1 index19 function value with exact rational arithmetic, not rounded decimals.
• S213 · premise_and_result_audit — Recompute finite prefix point1 index19 signed correction with exact rational arithmetic, not rounded decimals.
• S212 · premise_and_result_audit — Recompute finite prefix point1 index19 denominator with exact rational arithmetic, not rounded decimals.
• S211 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S210 · premise_and_result_audit — Recompute finite prefix point1 index18 reverse signed error with exact rational arithmetic, not rounded decimals.
• S209 · premise_and_result_audit — Recompute finite prefix point1 index18 function value with exact rational arithmetic, not rounded decimals.
• S208 · premise_and_result_audit — Recompute finite prefix point1 index18 signed correction with exact rational arithmetic, not rounded decimals.
• S207 · premise_and_result_audit — Recompute finite prefix point1 index18 denominator with exact rational arithmetic, not rounded decimals.
• S206 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S205 · premise_and_result_audit — Recompute finite prefix point1 index17 reverse signed error with exact rational arithmetic, not rounded decimals.
• S204 · premise_and_result_audit — Recompute finite prefix point1 index17 function value with exact rational arithmetic, not rounded decimals.
• S203 · premise_and_result_audit — Recompute finite prefix point1 index17 signed correction with exact rational arithmetic, not rounded decimals.
• S202 · premise_and_result_audit — Recompute finite prefix point1 index17 denominator with exact rational arithmetic, not rounded decimals.
• S201 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S200 · premise_and_result_audit — Recompute finite prefix point1 index16 reverse signed error with exact rational arithmetic, not rounded decimals.
• S199 · premise_and_result_audit — Recompute finite prefix point1 index16 function value with exact rational arithmetic, not rounded decimals.
• S198 · premise_and_result_audit — Recompute finite prefix point1 index16 signed correction with exact rational arithmetic, not rounded decimals.
• S197 · premise_and_result_audit — Recompute finite prefix point1 index16 denominator with exact rational arithmetic, not rounded decimals.
• S196 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S195 · premise_and_result_audit — Recompute finite prefix point1 index15 reverse signed error with exact rational arithmetic, not rounded decimals.
• S194 · premise_and_result_audit — Recompute finite prefix point1 index15 function value with exact rational arithmetic, not rounded decimals.
• S193 · premise_and_result_audit — Recompute finite prefix point1 index15 signed correction with exact rational arithmetic, not rounded decimals.
• S192 · premise_and_result_audit — Recompute finite prefix point1 index15 denominator with exact rational arithmetic, not rounded decimals.
• S191 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S190 · premise_and_result_audit — Recompute finite prefix point1 index14 reverse signed error with exact rational arithmetic, not rounded decimals.
• S189 · premise_and_result_audit — Recompute finite prefix point1 index14 function value with exact rational arithmetic, not rounded decimals.
• S188 · premise_and_result_audit — Recompute finite prefix point1 index14 signed correction with exact rational arithmetic, not rounded decimals.
• S187 · premise_and_result_audit — Recompute finite prefix point1 index14 denominator with exact rational arithmetic, not rounded decimals.
• S186 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S185 · premise_and_result_audit — Recompute finite prefix point1 index13 reverse signed error with exact rational arithmetic, not rounded decimals.
• S184 · premise_and_result_audit — Recompute finite prefix point1 index13 function value with exact rational arithmetic, not rounded decimals.
• S183 · premise_and_result_audit — Recompute finite prefix point1 index13 signed correction with exact rational arithmetic, not rounded decimals.
• S182 · premise_and_result_audit — Recompute finite prefix point1 index13 denominator with exact rational arithmetic, not rounded decimals.
• S181 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S180 · premise_and_result_audit — Recompute finite prefix point1 index12 reverse signed error with exact rational arithmetic, not rounded decimals.
• S179 · premise_and_result_audit — Recompute finite prefix point1 index12 function value with exact rational arithmetic, not rounded decimals.
• S178 · premise_and_result_audit — Recompute finite prefix point1 index12 signed correction with exact rational arithmetic, not rounded decimals.
• S177 · premise_and_result_audit — Recompute finite prefix point1 index12 denominator with exact rational arithmetic, not rounded decimals.
• S176 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S175 · premise_and_result_audit — Recompute finite prefix point1 index11 reverse signed error with exact rational arithmetic, not rounded decimals.
• S174 · premise_and_result_audit — Recompute finite prefix point1 index11 function value with exact rational arithmetic, not rounded decimals.
• S173 · premise_and_result_audit — Recompute finite prefix point1 index11 signed correction with exact rational arithmetic, not rounded decimals.
• S172 · premise_and_result_audit — Recompute finite prefix point1 index11 denominator with exact rational arithmetic, not rounded decimals.
• S171 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S170 · premise_and_result_audit — Recompute finite prefix point1 index10 reverse signed error with exact rational arithmetic, not rounded decimals.
• S169 · premise_and_result_audit — Recompute finite prefix point1 index10 function value with exact rational arithmetic, not rounded decimals.
• S168 · premise_and_result_audit — Recompute finite prefix point1 index10 signed correction with exact rational arithmetic, not rounded decimals.
• S167 · premise_and_result_audit — Recompute finite prefix point1 index10 denominator with exact rational arithmetic, not rounded decimals.
• S166 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S165 · premise_and_result_audit — Recompute finite prefix point1 index9 reverse signed error with exact rational arithmetic, not rounded decimals.
• S164 · premise_and_result_audit — Recompute finite prefix point1 index9 function value with exact rational arithmetic, not rounded decimals.
• S163 · premise_and_result_audit — Recompute finite prefix point1 index9 signed correction with exact rational arithmetic, not rounded decimals.
• S162 · premise_and_result_audit — Recompute finite prefix point1 index9 denominator with exact rational arithmetic, not rounded decimals.
• S161 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S160 · premise_and_result_audit — Recompute finite prefix point1 index8 reverse signed error with exact rational arithmetic, not rounded decimals.
• S159 · premise_and_result_audit — Recompute finite prefix point1 index8 function value with exact rational arithmetic, not rounded decimals.
• S158 · premise_and_result_audit — Recompute finite prefix point1 index8 signed correction with exact rational arithmetic, not rounded decimals.
• S157 · premise_and_result_audit — Recompute finite prefix point1 index8 denominator with exact rational arithmetic, not rounded decimals.
• S156 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S155 · premise_and_result_audit — Recompute finite prefix point1 index7 reverse signed error with exact rational arithmetic, not rounded decimals.
• S154 · premise_and_result_audit — Recompute finite prefix point1 index7 function value with exact rational arithmetic, not rounded decimals.
• S153 · premise_and_result_audit — Recompute finite prefix point1 index7 signed correction with exact rational arithmetic, not rounded decimals.
• S152 · premise_and_result_audit — Recompute finite prefix point1 index7 denominator with exact rational arithmetic, not rounded decimals.
• S151 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S150 · premise_and_result_audit — Recompute finite prefix point1 index6 reverse signed error with exact rational arithmetic, not rounded decimals.
• S149 · premise_and_result_audit — Recompute finite prefix point1 index6 function value with exact rational arithmetic, not rounded decimals.
• S148 · premise_and_result_audit — Recompute finite prefix point1 index6 signed correction with exact rational arithmetic, not rounded decimals.
• S147 · premise_and_result_audit — Recompute finite prefix point1 index6 denominator with exact rational arithmetic, not rounded decimals.
• S146 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S145 · premise_and_result_audit — Recompute finite prefix point1 index5 reverse signed error with exact rational arithmetic, not rounded decimals.
• S144 · premise_and_result_audit — Recompute finite prefix point1 index5 function value with exact rational arithmetic, not rounded decimals.
• S143 · premise_and_result_audit — Recompute finite prefix point1 index5 signed correction with exact rational arithmetic, not rounded decimals.
• S142 · premise_and_result_audit — Recompute finite prefix point1 index5 denominator with exact rational arithmetic, not rounded decimals.
• S141 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S140 · premise_and_result_audit — Recompute finite prefix point1 index4 reverse signed error with exact rational arithmetic, not rounded decimals.
• S139 · premise_and_result_audit — Recompute finite prefix point1 index4 function value with exact rational arithmetic, not rounded decimals.
• S138 · premise_and_result_audit — Recompute finite prefix point1 index4 signed correction with exact rational arithmetic, not rounded decimals.
• S137 · premise_and_result_audit — Recompute finite prefix point1 index4 denominator with exact rational arithmetic, not rounded decimals.
• S136 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S135 · premise_and_result_audit — Recompute finite prefix point1 index3 reverse signed error with exact rational arithmetic, not rounded decimals.
• S134 · premise_and_result_audit — Recompute finite prefix point1 index3 function value with exact rational arithmetic, not rounded decimals.
• S133 · premise_and_result_audit — Recompute finite prefix point1 index3 signed correction with exact rational arithmetic, not rounded decimals.
• S132 · premise_and_result_audit — Recompute finite prefix point1 index3 denominator with exact rational arithmetic, not rounded decimals.
• S131 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S130 · premise_and_result_audit — Recompute finite prefix point1 index2 reverse signed error with exact rational arithmetic, not rounded decimals.
• S129 · premise_and_result_audit — Recompute finite prefix point1 index2 function value with exact rational arithmetic, not rounded decimals.
• S128 · premise_and_result_audit — Recompute finite prefix point1 index2 signed correction with exact rational arithmetic, not rounded decimals.
• S127 · premise_and_result_audit — Recompute finite prefix point1 index2 denominator with exact rational arithmetic, not rounded decimals.
• S126 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S125 · premise_and_result_audit — Recompute finite prefix point1 index1 reverse signed error with exact rational arithmetic, not rounded decimals.
• S124 · premise_and_result_audit — Recompute finite prefix point1 index1 function value with exact rational arithmetic, not rounded decimals.
• S123 · premise_and_result_audit — Recompute finite prefix point1 index1 signed correction with exact rational arithmetic, not rounded decimals.
• S122 · premise_and_result_audit — Recompute finite prefix point1 index1 denominator with exact rational arithmetic, not rounded decimals.
• S121 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S120 · premise_and_result_audit — Recompute finite prefix point1 index0 reverse signed error with exact rational arithmetic, not rounded decimals.
• S119 · premise_and_result_audit — Recompute finite prefix point1 index0 function value with exact rational arithmetic, not rounded decimals.
• S118 · premise_and_result_audit — Recompute finite prefix point1 index0 signed correction with exact rational arithmetic, not rounded decimals.
• S117 · premise_and_result_audit — Recompute finite prefix point1 index0 denominator with exact rational arithmetic, not rounded decimals.
• S116 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S115 · premise_and_result_audit — Recompute finite prefix point0 index22 reverse signed error with exact rational arithmetic, not rounded decimals.
• S114 · premise_and_result_audit — Recompute finite prefix point0 index22 function value with exact rational arithmetic, not rounded decimals.
• S113 · premise_and_result_audit — Recompute finite prefix point0 index22 signed correction with exact rational arithmetic, not rounded decimals.
• S112 · premise_and_result_audit — Recompute finite prefix point0 index22 denominator with exact rational arithmetic, not rounded decimals.
• S111 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S110 · premise_and_result_audit — Recompute finite prefix point0 index21 reverse signed error with exact rational arithmetic, not rounded decimals.
• S109 · premise_and_result_audit — Recompute finite prefix point0 index21 function value with exact rational arithmetic, not rounded decimals.
• S108 · premise_and_result_audit — Recompute finite prefix point0 index21 signed correction with exact rational arithmetic, not rounded decimals.
• S107 · premise_and_result_audit — Recompute finite prefix point0 index21 denominator with exact rational arithmetic, not rounded decimals.
• S106 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S105 · premise_and_result_audit — Recompute finite prefix point0 index20 reverse signed error with exact rational arithmetic, not rounded decimals.
• S104 · premise_and_result_audit — Recompute finite prefix point0 index20 function value with exact rational arithmetic, not rounded decimals.
• S103 · premise_and_result_audit — Recompute finite prefix point0 index20 signed correction with exact rational arithmetic, not rounded decimals.
• S102 · premise_and_result_audit — Recompute finite prefix point0 index20 denominator with exact rational arithmetic, not rounded decimals.
• S101 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S100 · premise_and_result_audit — Recompute finite prefix point0 index19 reverse signed error with exact rational arithmetic, not rounded decimals.
• S099 · premise_and_result_audit — Recompute finite prefix point0 index19 function value with exact rational arithmetic, not rounded decimals.
• S098 · premise_and_result_audit — Recompute finite prefix point0 index19 signed correction with exact rational arithmetic, not rounded decimals.
• S097 · premise_and_result_audit — Recompute finite prefix point0 index19 denominator with exact rational arithmetic, not rounded decimals.
• S096 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S095 · premise_and_result_audit — Recompute finite prefix point0 index18 reverse signed error with exact rational arithmetic, not rounded decimals.
• S094 · premise_and_result_audit — Recompute finite prefix point0 index18 function value with exact rational arithmetic, not rounded decimals.
• S093 · premise_and_result_audit — Recompute finite prefix point0 index18 signed correction with exact rational arithmetic, not rounded decimals.
• S092 · premise_and_result_audit — Recompute finite prefix point0 index18 denominator with exact rational arithmetic, not rounded decimals.
• S091 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S090 · premise_and_result_audit — Recompute finite prefix point0 index17 reverse signed error with exact rational arithmetic, not rounded decimals.
• S089 · premise_and_result_audit — Recompute finite prefix point0 index17 function value with exact rational arithmetic, not rounded decimals.
• S088 · premise_and_result_audit — Recompute finite prefix point0 index17 signed correction with exact rational arithmetic, not rounded decimals.
• S087 · premise_and_result_audit — Recompute finite prefix point0 index17 denominator with exact rational arithmetic, not rounded decimals.
• S086 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S085 · premise_and_result_audit — Recompute finite prefix point0 index16 reverse signed error with exact rational arithmetic, not rounded decimals.
• S084 · premise_and_result_audit — Recompute finite prefix point0 index16 function value with exact rational arithmetic, not rounded decimals.
• S083 · premise_and_result_audit — Recompute finite prefix point0 index16 signed correction with exact rational arithmetic, not rounded decimals.
• S082 · premise_and_result_audit — Recompute finite prefix point0 index16 denominator with exact rational arithmetic, not rounded decimals.
• S081 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S080 · premise_and_result_audit — Recompute finite prefix point0 index15 reverse signed error with exact rational arithmetic, not rounded decimals.
• S079 · premise_and_result_audit — Recompute finite prefix point0 index15 function value with exact rational arithmetic, not rounded decimals.
• S078 · premise_and_result_audit — Recompute finite prefix point0 index15 signed correction with exact rational arithmetic, not rounded decimals.
• S077 · premise_and_result_audit — Recompute finite prefix point0 index15 denominator with exact rational arithmetic, not rounded decimals.
• S076 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S075 · premise_and_result_audit — Recompute finite prefix point0 index14 reverse signed error with exact rational arithmetic, not rounded decimals.
• S074 · premise_and_result_audit — Recompute finite prefix point0 index14 function value with exact rational arithmetic, not rounded decimals.
• S073 · premise_and_result_audit — Recompute finite prefix point0 index14 signed correction with exact rational arithmetic, not rounded decimals.
• S072 · premise_and_result_audit — Recompute finite prefix point0 index14 denominator with exact rational arithmetic, not rounded decimals.
• S071 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S070 · premise_and_result_audit — Recompute finite prefix point0 index13 reverse signed error with exact rational arithmetic, not rounded decimals.
• S069 · premise_and_result_audit — Recompute finite prefix point0 index13 function value with exact rational arithmetic, not rounded decimals.
• S068 · premise_and_result_audit — Recompute finite prefix point0 index13 signed correction with exact rational arithmetic, not rounded decimals.
• S067 · premise_and_result_audit — Recompute finite prefix point0 index13 denominator with exact rational arithmetic, not rounded decimals.
• S066 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S065 · premise_and_result_audit — Recompute finite prefix point0 index12 reverse signed error with exact rational arithmetic, not rounded decimals.
• S064 · premise_and_result_audit — Recompute finite prefix point0 index12 function value with exact rational arithmetic, not rounded decimals.
• S063 · premise_and_result_audit — Recompute finite prefix point0 index12 signed correction with exact rational arithmetic, not rounded decimals.
• S062 · premise_and_result_audit — Recompute finite prefix point0 index12 denominator with exact rational arithmetic, not rounded decimals.
• S061 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S060 · premise_and_result_audit — Recompute finite prefix point0 index11 reverse signed error with exact rational arithmetic, not rounded decimals.
• S059 · premise_and_result_audit — Recompute finite prefix point0 index11 function value with exact rational arithmetic, not rounded decimals.
• S058 · premise_and_result_audit — Recompute finite prefix point0 index11 signed correction with exact rational arithmetic, not rounded decimals.
• S057 · premise_and_result_audit — Recompute finite prefix point0 index11 denominator with exact rational arithmetic, not rounded decimals.
• S056 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S055 · premise_and_result_audit — Recompute finite prefix point0 index10 reverse signed error with exact rational arithmetic, not rounded decimals.
• S054 · premise_and_result_audit — Recompute finite prefix point0 index10 function value with exact rational arithmetic, not rounded decimals.
• S053 · premise_and_result_audit — Recompute finite prefix point0 index10 signed correction with exact rational arithmetic, not rounded decimals.
• S052 · premise_and_result_audit — Recompute finite prefix point0 index10 denominator with exact rational arithmetic, not rounded decimals.
• S051 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S050 · premise_and_result_audit — Recompute finite prefix point0 index9 reverse signed error with exact rational arithmetic, not rounded decimals.
• S049 · premise_and_result_audit — Recompute finite prefix point0 index9 function value with exact rational arithmetic, not rounded decimals.
• S048 · premise_and_result_audit — Recompute finite prefix point0 index9 signed correction with exact rational arithmetic, not rounded decimals.
• S047 · premise_and_result_audit — Recompute finite prefix point0 index9 denominator with exact rational arithmetic, not rounded decimals.
• S046 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S045 · premise_and_result_audit — Recompute finite prefix point0 index8 reverse signed error with exact rational arithmetic, not rounded decimals.
• S044 · premise_and_result_audit — Recompute finite prefix point0 index8 function value with exact rational arithmetic, not rounded decimals.
• S043 · premise_and_result_audit — Recompute finite prefix point0 index8 signed correction with exact rational arithmetic, not rounded decimals.
• S042 · premise_and_result_audit — Recompute finite prefix point0 index8 denominator with exact rational arithmetic, not rounded decimals.
• S041 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S040 · premise_and_result_audit — Recompute finite prefix point0 index7 reverse signed error with exact rational arithmetic, not rounded decimals.
• S039 · premise_and_result_audit — Recompute finite prefix point0 index7 function value with exact rational arithmetic, not rounded decimals.
• S038 · premise_and_result_audit — Recompute finite prefix point0 index7 signed correction with exact rational arithmetic, not rounded decimals.
• S037 · premise_and_result_audit — Recompute finite prefix point0 index7 denominator with exact rational arithmetic, not rounded decimals.
• S036 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S035 · premise_and_result_audit — Recompute finite prefix point0 index6 reverse signed error with exact rational arithmetic, not rounded decimals.
• S034 · premise_and_result_audit — Recompute finite prefix point0 index6 function value with exact rational arithmetic, not rounded decimals.
• S033 · premise_and_result_audit — Recompute finite prefix point0 index6 signed correction with exact rational arithmetic, not rounded decimals.
• S032 · premise_and_result_audit — Recompute finite prefix point0 index6 denominator with exact rational arithmetic, not rounded decimals.
• S031 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S030 · premise_and_result_audit — Recompute finite prefix point0 index5 reverse signed error with exact rational arithmetic, not rounded decimals.
• S029 · premise_and_result_audit — Recompute finite prefix point0 index5 function value with exact rational arithmetic, not rounded decimals.
• S028 · premise_and_result_audit — Recompute finite prefix point0 index5 signed correction with exact rational arithmetic, not rounded decimals.
• S027 · premise_and_result_audit — Recompute finite prefix point0 index5 denominator with exact rational arithmetic, not rounded decimals.
• S026 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S025 · premise_and_result_audit — Recompute finite prefix point0 index4 reverse signed error with exact rational arithmetic, not rounded decimals.
• S024 · premise_and_result_audit — Recompute finite prefix point0 index4 function value with exact rational arithmetic, not rounded decimals.
• S023 · premise_and_result_audit — Recompute finite prefix point0 index4 signed correction with exact rational arithmetic, not rounded decimals.
• S022 · premise_and_result_audit — Recompute finite prefix point0 index4 denominator with exact rational arithmetic, not rounded decimals.
• S021 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S020 · premise_and_result_audit — Recompute finite prefix point0 index3 reverse signed error with exact rational arithmetic, not rounded decimals.
• S019 · premise_and_result_audit — Recompute finite prefix point0 index3 function value with exact rational arithmetic, not rounded decimals.
• S018 · premise_and_result_audit — Recompute finite prefix point0 index3 signed correction with exact rational arithmetic, not rounded decimals.
• S017 · premise_and_result_audit — Recompute finite prefix point0 index3 denominator with exact rational arithmetic, not rounded decimals.
• S016 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S015 · premise_and_result_audit — Recompute finite prefix point0 index2 reverse signed error with exact rational arithmetic, not rounded decimals.
• S014 · premise_and_result_audit — Recompute finite prefix point0 index2 function value with exact rational arithmetic, not rounded decimals.
• S013 · premise_and_result_audit — Recompute finite prefix point0 index2 signed correction with exact rational arithmetic, not rounded decimals.
• S012 · premise_and_result_audit — Recompute finite prefix point0 index2 denominator with exact rational arithmetic, not rounded decimals.
• S011 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S010 · premise_and_result_audit — Recompute finite prefix point0 index1 reverse signed error with exact rational arithmetic, not rounded decimals.
• S009 · premise_and_result_audit — Recompute finite prefix point0 index1 function value with exact rational arithmetic, not rounded decimals.
• S008 · premise_and_result_audit — Recompute finite prefix point0 index1 signed correction with exact rational arithmetic, not rounded decimals.
• S007 · premise_and_result_audit — Recompute finite prefix point0 index1 denominator with exact rational arithmetic, not rounded decimals.
• S006 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S005 · premise_and_result_audit — Recompute finite prefix point0 index0 reverse signed error with exact rational arithmetic, not rounded decimals.
• S004 · premise_and_result_audit — Recompute finite prefix point0 index0 function value with exact rational arithmetic, not rounded decimals.
• S003 · premise_and_result_audit — Recompute finite prefix point0 index0 signed correction with exact rational arithmetic, not rounded decimals.
• S002 · premise_and_result_audit — Recompute finite prefix point0 index0 denominator with exact rational arithmetic, not rounded decimals.
• S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.

Result

(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]]], No, finite_prefix_not_pointwise_convergence_certificate)

The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.

This question review and source binding

Review date: 2026-10-26

Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.