List questions from proof-verification

Published on 25 Mar 2026 - 13:55

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For what ordinals does $1+\alpha=\alpha$ hold? For what ordinals does $2\alpha=\alpha$ hold?

Published on 25 Mar 2026 - 9:29

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Is it possible to shorten the solution for this 2014 RMO question?

Published on 26 Mar 2026 - 4:32

29

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Prove that for every $y \in [0, g(1)-g(0)]$, there exists $x\in[0,1]$ such that $g'(x)=y$.

Published on 30 Mar 2026 - 5:02

37

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Suppose $H \leq G$. For $g \in G$, prove $gH \leq G$ if and only if $g \in H$.

Published on 14 May 2018 - 14:40

51

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If $G$ is a finite $p$-group with $Z(G) = [G,G]$, then $\exp(G/Z(G)) = \exp(Z(G))$.

Published on 26 Mar 2026 - 15:16

1.7k

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Proving that the closure of a connected set in a metric space is connected.

Published on 31 Mar 2026 - 23:54

123

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Proof for $Z^2$ not being cyclic

Published on 14 May 2018 - 20:28

32

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Proof Verification and Help: Differentiation

Published on 01 Apr 2026 - 20:09

177

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Prove that a closed ball is an open set in ultrametric space

Published on 15 May 2018 - 0:21

47

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Is there a place I could get my proofs critiqued?

Published on 26 Mar 2026 - 11:07

157

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Where is $ze^{\overline{z}}$ differentiable?

Published on 26 Mar 2026 - 4:30

114

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Functional equation: $f(x^2+f(y))=y+f^2(x)$.

Published on 25 Mar 2026 - 11:16

46

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For $\frac{a}{b}>\frac{c}{d}$ I can write $\frac{c}{d} = \frac{a}{d'}$ with $d'=b+\epsilon$, $\epsilon>0$

Published on 26 Mar 2026 - 8:23

67

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Proof Verification: Derivative theorem

Published on 30 Mar 2026 - 5:00

List Question

How do I show that $n$ is prime if and only if $\phi(n) = n − 1$?

For what ordinals does $1+\alpha=\alpha$ hold? For what ordinals does $2\alpha=\alpha$ hold?

Is it possible to shorten the solution for this 2014 RMO question?

Prove that for every $y \in [0, g(1)-g(0)]$, there exists $x\in[0,1]$ such that $g'(x)=y$.

Suppose $H \leq G$. For $g \in G$, prove $gH \leq G$ if and only if $g \in H$.

If $G$ is a finite $p$-group with $Z(G) = [G,G]$, then $\exp(G/Z(G)) = \exp(Z(G))$.

Proving that the closure of a connected set in a metric space is connected.

Proof for $Z^2$ not being cyclic

Proof Verification and Help: Differentiation

Prove that a closed ball is an open set in ultrametric space

Is there a place I could get my proofs critiqued?

Where is $ze^{\overline{z}}$ differentiable?

Functional equation: $f(x^2+f(y))=y+f^2(x)$.

For $\frac{a}{b}>\frac{c}{d}$ I can write $\frac{c}{d} = \frac{a}{d'}$ with $d'=b+\epsilon$, $\epsilon>0$

Proof Verification: Derivative theorem

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