List questions from solution-verification

Published on 02 May 2020 - 0:37

54

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Let $a_{n} = 1/n$. Thus $\sup(a_{n})_{n=1}^{\infty} = 1$ and $\inf(a_{n})_{n=1}^{\infty}$ = 0.

Published on 30 Mar 2026 - 14:11

729

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Prove the Extended Pigeonhole Principle with Induction

Published on 11 Apr 2026 - 16:50

94

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Let $a_{n}$ be a sequence which converges to $c$. Then $c$ is a limit point of $a_{n}$ and it is its unique limit point.

Published on 28 Mar 2026 - 12:49

115

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If $f(x)$ is Integrable, $\int_{0}^{\infty}f(x)dx$ converges and $g(x) \geq x \Rightarrow \lim_{x \to \infty} \int_{x}^{g(x)}f(t)dt = 0$

Published on 07 Apr 2026 - 17:51

39

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Bounded sets on $\mathbb R$ proof-verification

Published on 02 May 2020 - 4:25

364

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If $P(A)=P(B)=1$, then $P(A\cap B)=1$

Published on 02 May 2020 - 4:46

346

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Fundamental group of sphere with antipodal points on the equator

Published on 08 Apr 2026 - 21:19

31

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Calculating Lim Sup of a certain expression

Published on 30 Mar 2026 - 14:18

158

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If $x+y+z=1$ Find the maximum of $\frac{x-y}{\sqrt{x+y}}+\frac{y-z}{\sqrt{y+z}}+\frac{z-x}{\sqrt{z+x}}$

Published on 30 Mar 2026 - 0:22

48

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Question involving $n \geq N \implies y_n > M$, for $y_n \rightarrow \infty$ as $n \rightarrow \infty$

Published on 02 May 2020 - 12:15

48

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Proof of double counting formula

Published on 09 Apr 2026 - 6:44

43

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High school olympiad homogeneity $\frac{a}{b+2c}+\frac{b}{c+2a}+\frac{c}{a+2b} \geq 1$

Published on 02 May 2020 - 15:21

73

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Separability of countable product my attempt

Published on 02 May 2020 - 16:50

96

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The Heine-Borel theorem: how do we prove it?

Published on 02 May 2020 - 17:18

List Question

Proving Abel's lemma

Let $a_{n} = 1/n$. Thus $\sup(a_{n})_{n=1}^{\infty} = 1$ and $\inf(a_{n})_{n=1}^{\infty}$ = 0.

Prove the Extended Pigeonhole Principle with Induction

Let $a_{n}$ be a sequence which converges to $c$. Then $c$ is a limit point of $a_{n}$ and it is its unique limit point.

If $f(x)$ is Integrable, $\int_{0}^{\infty}f(x)dx$ converges and $g(x) \geq x \Rightarrow \lim_{x \to \infty} \int_{x}^{g(x)}f(t)dt = 0$

Bounded sets on $\mathbb R$ proof-verification

If $P(A)=P(B)=1$, then $P(A\cap B)=1$

Fundamental group of sphere with antipodal points on the equator

Calculating Lim Sup of a certain expression

If $x+y+z=1$ Find the maximum of $\frac{x-y}{\sqrt{x+y}}+\frac{y-z}{\sqrt{y+z}}+\frac{z-x}{\sqrt{z+x}}$

Question involving $n \geq N \implies y_n > M$, for $y_n \rightarrow \infty$ as $n \rightarrow \infty$

Proof of double counting formula

High school olympiad homogeneity $\frac{a}{b+2c}+\frac{b}{c+2a}+\frac{c}{a+2b} \geq 1$

Separability of countable product my attempt

The Heine-Borel theorem: how do we prove it?

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