Question

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

score 204 · Answer 1 · 2026-03-25 16:14:06

204

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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 25 Mar 2026 - 16:14

score 77 · Answer 2 · 2026-03-25 14:26:01

77

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For which values of reals $ a$ and $ x$ this:${x}^{x^{x^{x^...}}}=a$ could be work?

Published on 25 Mar 2026 - 14:26

score 122 · Answer 3 · 2026-04-14 01:20:12

122

Views

Prove $c,c^c,c^{c^c},c^{c^{c^c}},\ldots \pmod p$ with $p$ prime has period $1$ or $2$

Published on 14 Apr 2026 - 1:20

score 298 · Answer 4 · 2026-04-14 10:55:18

298

Views

Is $\infty$ the solution to ${x}^{{x}^{{x}^{{x}^{x\dots}}}} = i$?

Published on 14 Apr 2026 - 10:55

score 360 · Answer 5 · 2026-03-25 20:41:50

360

Views

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

Published on 25 Mar 2026 - 20:41

score 57 · Answer 6 · 2026-03-25 17:42:09

57

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 25 Mar 2026 - 17:42

score 255 · Answer 7 · 2026-03-25 16:01:59

255

Views

Rightmost decimal digits of Graham's number

Published on 25 Mar 2026 - 16:01

score 61 · Answer 8 · 2026-05-10 15:43:25

61

Views

Tetrating by non-integers?

Published on 10 May 2026 - 15:43

score 122 · Answer 9 · 2026-04-14 12:13:04

122

Views

Find the maximum of $x^{x^{x^{⋰}}}.$

Published on 14 Apr 2026 - 12:13

score 301 · Answer 10 · 2026-04-17 02:55:25

301

Views

Find $\lim_{x\rightarrow 0}x^{x^{x^x}}$

Published on 17 Apr 2026 - 2:55

score 60 · Answer 11 · 2026-04-10 08:43:46

60

Views

How can I find the value of a non-repeating exponent tower?

Published on 10 Apr 2026 - 8:43

score 145 · Answer 12 · 2026-04-15 16:07:32

145

Views

Numerical instability of an extended tetration

Published on 15 Apr 2026 - 16:07

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

58

Views

Non integer Hyper-powers.

Published on 10 May 2026 - 17:55

score 178 · Answer 14 · 2026-05-10 23:43:06

178

Views

Verifying tetration properties

Published on 10 May 2026 - 23:43

score 89 · Answer 15 · 2026-04-14 20:44:12

89

Views

2 different limits for $x^x$ - Could they somehow be applied?

Published on 14 Apr 2026 - 20:44

List Question

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

For which values of reals $ a$ and $ x$ this:${x}^{x^{x^{x^...}}}=a$ could be work?

Prove $c,c^c,c^{c^c},c^{c^{c^c}},\ldots \pmod p$ with $p$ prime has period $1$ or $2$

Is $\infty$ the solution to ${x}^{{x}^{{x}^{{x}^{x\dots}}}} = i$?

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

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

Rightmost decimal digits of Graham's number

Tetrating by non-integers?

Find the maximum of $x^{x^{x^{⋰}}}.$

Find $\lim_{x\rightarrow 0}x^{x^{x^x}}$

How can I find the value of a non-repeating exponent tower?

Numerical instability of an extended tetration

Non integer Hyper-powers.

Verifying tetration properties

2 different limits for $x^x$ - Could they somehow be applied?

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