User cpiegore

12 votes

1 answer

1k views

Does an iterated exponential $z^{z^{z^{...}}}$ always have a finite period

asked Jun 10, 2016 at 0:46

11 votes

3 answers

1k views

Number system with $e^x = 0$ for some $x$

asked Mar 21, 2016 at 22:52

10 votes

2 answers

14k views

Dividing a circle into $3$ equal pieces using $2$ parallel lines

asked Jul 13, 2016 at 0:14

9 votes

5 answers

460 views

Proving that $\cos(\frac{\arctan(\frac{11}{2})}{3}) = \frac{2}{\sqrt{5}}$

asked Feb 11, 2016 at 4:07

8 votes

3 answers

3k views

Convergence properties of $z^{z^{z^{...}}}$ and is it "chaotic"

asked Apr 25, 2016 at 2:20

6 votes

2 answers

436 views

Examples of functions that do not belong to any Baire class

asked Sep 21, 2016 at 20:40

5 votes

1 answer

681 views

Function that is continuous only on the transcendental numbers

asked Feb 16, 2016 at 23:12

4 votes

3 answers

1k views

Proving that if $|W(-\ln z)| < 1$ then $z^{z^{z^{z^...}}}$ is convergent

asked Feb 27, 2016 at 5:13

4 votes

5 answers

2k views

If $f:\mathbb{R}\mapsto\mathbb{R}$ is a non-constant periodic function than $\lim_{x \to \infty} f(x)$ does not exist

asked Mar 3, 2016 at 20:55

3 votes

1 answer

498 views

Infinite tetration of $-2.5$

asked Jul 14, 2016 at 1:01

3 votes

1 answer

382 views

Prove if $t = W(-\log z)$, $|t| = 1$, and $t^n \ne 1$ than $z^{z^{z^{...}}}$ does not converge

asked Aug 17, 2016 at 18:41

3 votes

1 answer

529 views

Understanding Baker and Rippon's proof of a result in iteration theory

asked Oct 12, 2016 at 2:26

2 votes

2 answers

813 views

Convergence or divergence of infinite power towers of complex numbers $z^{z^{z^{z{...}}}}$

asked Feb 13, 2016 at 3:58

1 vote

1 answer

3k views

Limit of $\frac{\tan(x)-x}{x^3}$ as $x$ approaches $0$ without L'Hospital's Rule [duplicate]

asked Feb 14, 2016 at 18:35

1 vote

0 answers

95 views

Fast formula for gamma function [duplicate]

asked Sep 5, 2015 at 2:33

1 vote

1 answer

58 views

Homogeneity of $f(x,y) = \frac{3x^2y}{x^2+y^2}$

asked Feb 11, 2016 at 3:07

1 vote

0 answers

160 views

What would be different about mathematics if there was no way of avoiding Russell’s Paradox

asked Nov 24, 2017 at 22:59

1 vote

2 answers

317 views

Prove $\int_a^b f(x)\,\mathrm dx=\int_a^cf(x)\,\mathrm dx+\int_c^bf(x)\,\mathrm dx$ without the Fundamental Theorem of Calculus

asked Jun 4, 2020 at 22:50

1 vote

0 answers

134 views

Prove the Fundamental Theorem of Calculus without using $\int_a^b f(x)\,\mathrm dx=\int_a^cf(x)\,\mathrm dx+\int_c^bf(x)\,\mathrm dx$

asked Nov 23, 2021 at 18:58

0 votes

1 answer

145 views

If $A,B \subset \mathbb{R}^n$ are disjoint non-empty and open then $\exists x \in \mathbb{R}^n$ such that $x \notin A \cup B$

asked Nov 24, 2017 at 17:57

0 votes

1 answer

87 views

Graph of $f(x,y) = \frac{3x^2 y}{x^2+y^2}$ near the origin

asked Feb 2, 2016 at 19:19

0 votes

1 answer

125 views

Continuity of $x - y\lceil \frac{x}{y} \rceil$

asked Feb 14, 2016 at 22:38

0 votes

1 answer

527 views

If $|t| = |W(-\ln z)| = 1$ and $t^n =1$ then $z^{z^{z^{...}}}$ is convergent

asked Jun 14, 2016 at 20:21

0 votes

1 answer

2k views

What exactly is a "chaotic" sequence?

asked Apr 25, 2016 at 4:21

-4 votes

1 answer

581 views

Topological space that is not sequential and not $T_0$ [closed]

asked Sep 4, 2015 at 23:37

Stack Exchange Network

25 Questions

Does an iterated exponential $z^{z^{z^{...}}}$ always have a finite period

Number system with $e^x = 0$ for some $x$

Dividing a circle into $3$ equal pieces using $2$ parallel lines

Proving that $\cos(\frac{\arctan(\frac{11}{2})}{3}) = \frac{2}{\sqrt{5}}$

Convergence properties of $z^{z^{z^{...}}}$ and is it "chaotic"

Examples of functions that do not belong to any Baire class

Function that is continuous only on the transcendental numbers

Proving that if $|W(-\ln z)| < 1$ then $z^{z^{z^{z^...}}}$ is convergent

If $f:\mathbb{R}\mapsto\mathbb{R}$ is a non-constant periodic function than $\lim_{x \to \infty} f(x)$ does not exist

Infinite tetration of $-2.5$

Prove if $t = W(-\log z)$, $|t| = 1$, and $t^n \ne 1$ than $z^{z^{z^{...}}}$ does not converge

Understanding Baker and Rippon's proof of a result in iteration theory

Convergence or divergence of infinite power towers of complex numbers $z^{z^{z^{z{...}}}}$

Limit of $\frac{\tan(x)-x}{x^3}$ as $x$ approaches $0$ without L'Hospital's Rule [duplicate]

Fast formula for gamma function [duplicate]

Homogeneity of $f(x,y) = \frac{3x^2y}{x^2+y^2}$

What would be different about mathematics if there was no way of avoiding Russell’s Paradox

Prove $\int_a^b f(x)\,\mathrm dx=\int_a^cf(x)\,\mathrm dx+\int_c^bf(x)\,\mathrm dx$ without the Fundamental Theorem of Calculus

Prove the Fundamental Theorem of Calculus without using $\int_a^b f(x)\,\mathrm dx=\int_a^cf(x)\,\mathrm dx+\int_c^bf(x)\,\mathrm dx$

If $A,B \subset \mathbb{R}^n$ are disjoint non-empty and open then $\exists x \in \mathbb{R}^n$ such that $x \notin A \cup B$

Graph of $f(x,y) = \frac{3x^2 y}{x^2+y^2}$ near the origin

Continuity of $x - y\lceil \frac{x}{y} \rceil$

If $|t| = |W(-\ln z)| = 1$ and $t^n =1$ then $z^{z^{z^{...}}}$ is convergent

What exactly is a "chaotic" sequence?

Topological space that is not sequential and not $T_0$ [closed]