Question

The factors of a tetration plus an integer

score 90 · Answer 1 · 2026-05-11 06:16:44

90

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The factors of a tetration plus an integer

Published on 11 May 2026 - 6:16

score 142 · Answer 2 · 2026-05-10 18:17:24

142

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Nested Tetration properties

Published on 10 May 2026 - 18:17

score 205 · Answer 3 · 2026-05-11 07:22:37

205

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Tetration convergence: prove $\lim_{x\rightarrow0} {}^{n}x = \begin{cases} 1, & n \text{ even} \\ 0, & n \text{ odd} \end{cases}$

Published on 11 May 2026 - 7:22

score 62 · Answer 4 · 2026-03-26 22:58:27

62

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What will be the minimum value of the function $f(x)=\arcsin(x)\uparrow\uparrow(2k)$ as $k \to \infty$?

Published on 26 Mar 2026 - 22:58

score 360 · Answer 5 · 2026-03-26 22:53:37

360

Views

Area enclosed by a function containing two power towers: $f(x)=(−\ln(x↑↑(2k)))↑↑(2k+1)$

Published on 26 Mar 2026 - 22:53

score 360 · Answer 6 · 2026-03-25 20:41:50

360

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How to express the infinite power tower $a^{{{{{{(a+1)}^{(a+2)}}^{(a+3)}}^{.}}^{.}}^{.}}$?

Published on 25 Mar 2026 - 20:41

score 172 · Answer 7 · 2026-03-26 22:54:18

Determine the smallest positive integer $ m $ for which $\underbrace{100^{100^{\ldots^{100}}}}_m>\underbrace{3^{3^{\ldots^3}}}_{100}$

score 74 · Answer 8 · 2026-03-26 22:53:40

74

Views

How to evaluate the infinite sequence of 0^(-1)^(-2)^(-3)^(-4)^{.}^{.}^{.}?

Published on 26 Mar 2026 - 22:53

score 58 · Answer 9 · 2026-05-11 08:40:52

58

Views

How to find the maximum arc length of ${^{\infty}x}+{^{\infty}y}={^{\infty}r}$ and the value of $r$ at which it occurs?

Published on 11 May 2026 - 8:40

score 417 · Answer 10 · 2026-04-09 03:35:50

417

Views

Ackermann-Péter Function: Proof by induction, power tower

Published on 09 Apr 2026 - 3:35

score 205 · Answer 11 · 2026-04-09 01:53:12

205

Views

Proving a modified Ackermann function using induction

Published on 09 Apr 2026 - 1:53

score 223 · Answer 12 · 2026-05-10 15:47:45

223

Views

Is 2(6)3 (2↑↑↑↑3) equal to 2^65536? And if yes, is 2(n)3 equal to 2 to the power of how many time 2 is repeated in the power tower?

Published on 10 May 2026 - 15:47

score 58 · Answer 13 · 2026-05-10 17:55:40

58

Views

Non integer Hyper-powers.

Published on 10 May 2026 - 17:55

score 111 · Answer 14 · 2026-03-25 20:41:47

111

Views

Sum of power tower which tends to $1$

Published on 25 Mar 2026 - 20:41

score 96 · Answer 15 · 2026-03-26 22:54:18

96

Views

Simple power tower $x^{1-x+x^{1-x+x^{1-x+x^{1-x+\cdots}}}}=x$

Published on 26 Mar 2026 - 22:54

List Question

The factors of a tetration plus an integer

Nested Tetration properties

Tetration convergence: prove $\lim_{x\rightarrow0} {}^{n}x = \begin{cases} 1, & n \text{ even} \\ 0, & n \text{ odd} \end{cases}$

What will be the minimum value of the function $f(x)=\arcsin(x)\uparrow\uparrow(2k)$ as $k \to \infty$?

Area enclosed by a function containing two power towers: $f(x)=(−\ln(x↑↑(2k)))↑↑(2k+1)$

How to express the infinite power tower $a^{{{{{{(a+1)}^{(a+2)}}^{(a+3)}}^{.}}^{.}}^{.}}$?

Determine the smallest positive integer $ m $ for which $\underbrace{100^{100^{\ldots^{100}}}}_m>\underbrace{3^{3^{\ldots^3}}}_{100}$

How to evaluate the infinite sequence of 0^(-1)^(-2)^(-3)^(-4)^{.}^{.}^{.}?

How to find the maximum arc length of ${^{\infty}x}+{^{\infty}y}={^{\infty}r}$ and the value of $r$ at which it occurs?

Ackermann-Péter Function: Proof by induction, power tower

Proving a modified Ackermann function using induction

Is 2(6)3 (2↑↑↑↑3) equal to 2^65536? And if yes, is 2(n)3 equal to 2 to the power of how many time 2 is repeated in the power tower?

Non integer Hyper-powers.

Sum of power tower which tends to $1$

Simple power tower $x^{1-x+x^{1-x+x^{1-x+x^{1-x+\cdots}}}}=x$

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