List questions from supremum-and-infimum

Published on 01 May 2020 - 13:45

53

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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 02 May 2020 - 1:04

30

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Calculating Lim Sup of a certain expression

Published on 02 May 2020 - 9:38

43

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If $0\leq x\leq1/2$, then why $\inf_{k\in\mathbb{Z}}|x+k|=x$?

Published on 30 Mar 2026 - 2:07

158

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Necessity of Archimedean property in construction of Reals?

Published on 28 Mar 2026 - 21:51

44

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Show $\sup_{x > a}\frac{\sin x}{x} < 1$

Published on 04 May 2020 - 16:05

271

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Recursive sequence does not converge

Published on 04 May 2020 - 17:55

21

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If $\inf_{k\in\mathbb{Z}}|x-y+k|\leq\frac{1}{2N}$, then $\inf_{k\in\mathbb{Z}}|Nx-Ny+k| = N\inf_{k\in\mathbb{Z}}|x-y+k|$.

Published on 04 May 2020 - 19:26

68

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Proving $\|L\| = \sup\left\{\frac{\|L(x)\|}{\|x\|}\colon x\ne 0\right\}$

Published on 05 May 2020 - 23:12

206

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Supremum of continuous function on an unbounded interval

Published on 07 May 2020 - 19:54

97

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$\int^1_0f$ to 1 decimal place

Published on 30 Mar 2026 - 7:54

107

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Prove that the infimum of set of powers is $0$

Published on 10 May 2020 - 22:50

73

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Let $f$ be continuous on $\mathbb{R}$, and $\inf_\mathbb{R}f(x)<0$. Prove that $\exists c$ such that $f(c)<0$

Published on 30 Mar 2026 - 2:07

129

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Infimum and Supremum of sets

Published on 12 May 2020 - 0:18

208

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Application of Montel's Theorem

Published on 23 Feb 2026 - 6:56

List Question

Supremum Norm Identity

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

Calculating Lim Sup of a certain expression

If $0\leq x\leq1/2$, then why $\inf_{k\in\mathbb{Z}}|x+k|=x$?

Necessity of Archimedean property in construction of Reals?

Show $\sup_{x > a}\frac{\sin x}{x} < 1$

Recursive sequence does not converge

If $\inf_{k\in\mathbb{Z}}|x-y+k|\leq\frac{1}{2N}$, then $\inf_{k\in\mathbb{Z}}|Nx-Ny+k| = N\inf_{k\in\mathbb{Z}}|x-y+k|$.

Proving $\|L\| = \sup\left\{\frac{\|L(x)\|}{\|x\|}\colon x\ne 0\right\}$

Supremum of continuous function on an unbounded interval

$\int^1_0f$ to 1 decimal place

Prove that the infimum of set of powers is $0$

Let $f$ be continuous on $\mathbb{R}$, and $\inf_\mathbb{R}f(x)<0$. Prove that $\exists c$ such that $f(c)<0$

Infimum and Supremum of sets

Application of Montel's Theorem

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