List questions from proof-verification

Published on 25 Mar 2026 - 3:00

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Proof Verification: $\lim_{x \to 0} \cos(1/x) $ does not converge

Published on 11 Apr 2018 - 6:57

358

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A continuous function on a closed interval is bounded proof verify

Published on 11 Apr 2018 - 7:50

74

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If $f: \mathbb{R} \to \mathbb{R}$ is continuous and $f(q)=0 \forall q \in \mathbb{Q}$, prove that $f(x)=0 \forall x \in \mathbb{R}$

Published on 11 Apr 2018 - 8:42

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Prove that the supremum of a set of nested square roots is 2

Published on 25 Mar 2026 - 16:46

89

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Inequality proof by induction of $n!>2^n+3^n$

Published on 26 Mar 2026 - 16:06

162

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Proving that $a_{n+1}=a^{2}_{n}+\frac{1}{4}$ diverges to $+\infty$

Published on 30 Mar 2026 - 13:40

244

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Prove $n\geq 3$ is prime or the largest non-trivial factor of $n$ is at least $3\sqrt{n}$

Published on 25 Mar 2026 - 9:30

85

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Show that sequence converges, hence find the limit.

Published on 25 Mar 2026 - 12:16

75

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How to prove a series is convergent?

Published on 11 Apr 2018 - 17:00

644

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If $f(xy)=xf(y)$ for all $x,y\in \mathbb{R}$, then $f(x+y)=f(x)+f(y)$

Published on 26 Mar 2026 - 1:12

62

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Proving that $\sup\limits_{n\geq 1}\{a_n+b_n\}\neq \sup\limits_{n\geq 1}a_n+\sup\limits_{n\geq 1}b_n$

Published on 25 Mar 2026 - 16:46

50

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Inductive proof for $2n-3<2^{n-2}$ for $n ≥ 5$

Published on 26 Mar 2026 - 17:35

107

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$A$ is a finite $\implies$ $f(A)$ is finite

Published on 12 Apr 2018 - 1:37

383

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Prove that there do not exist non-trivial groups $H$ and $K$ such that $\mathbb{Q}\cong H\times K$.

Published on 25 Mar 2026 - 16:56

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How to write the proof for $|x|>a \implies x >a$ or $x<-a$

Proof Verification: $\lim_{x \to 0} \cos(1/x) $ does not converge

A continuous function on a closed interval is bounded proof verify

If $f: \mathbb{R} \to \mathbb{R}$ is continuous and $f(q)=0 \forall q \in \mathbb{Q}$, prove that $f(x)=0 \forall x \in \mathbb{R}$

Prove that the supremum of a set of nested square roots is 2

Inequality proof by induction of $n!>2^n+3^n$

Proving that $a_{n+1}=a^{2}_{n}+\frac{1}{4}$ diverges to $+\infty$

Prove $n\geq 3$ is prime or the largest non-trivial factor of $n$ is at least $3\sqrt{n}$

Show that sequence converges, hence find the limit.

How to prove a series is convergent?

If $f(xy)=xf(y)$ for all $x,y\in \mathbb{R}$, then $f(x+y)=f(x)+f(y)$

Proving that $\sup\limits_{n\geq 1}\{a_n+b_n\}\neq \sup\limits_{n\geq 1}a_n+\sup\limits_{n\geq 1}b_n$

Inductive proof for $2n-3<2^{n-2}$ for $n ≥ 5$

$A$ is a finite $\implies$ $f(A)$ is finite

Prove that there do not exist non-trivial groups $H$ and $K$ such that $\mathbb{Q}\cong H\times K$.

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