List questions from supremum-and-infimum

Published on 05 Nov 2021 - 18:23

71

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Supremum and infimum of expected value of an indicator

Published on 05 Nov 2021 - 20:21

548

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Find $\inf$ and $\sup$ of $a_n = \frac{a_{n-1} + a_{n-2}}{a_{n-3}}$

Published on 05 Nov 2021 - 23:57

33

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Proving minium and supremum of a set

Published on 07 Nov 2021 - 9:37

36

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Integrability of a family of functions, parameterized by the points of the compact

Published on 27 Mar 2026 - 7:50

374

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$\sup(A+B) = \sup(A) + \sup(B)$

Published on 12 Nov 2021 - 2:47

37

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Proving of disproving a claim regarding limits

Published on 15 Nov 2021 - 0:38

507

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Sup and inf of $A=\{a_n:=\frac{(n^2+(-1)^n(n-1)^2}{3n^{(1+(-1)^n)}+2n},\ n\in\mathbb{N}\setminus\{0\}\}$

Published on 15 Nov 2021 - 11:04

142

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For arbitrary metric spaces, if $\sup E\not\in E$, then must $\sup E$ be a limit point of $E$?

Published on 15 Nov 2021 - 17:54

100

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How to determine $\sup_{x \in \mathbb{R}} \left|\frac{\sin \left(x^{2}+1\right)}{x^{2}+1}\right|$

Published on 17 Nov 2021 - 16:59

54

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Is there a $n_\varepsilon\in\mathbb{N}$?

Published on 19 Nov 2021 - 14:18

32

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Continuity in different metrics:

Published on 20 Nov 2021 - 17:30

293

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is there example that inequality $\sup\{\inf\{f(x,y) : x \in X\}: y \in Y\} \le \inf\{\sup\{f(x,y) : y \in Y\}: x \in X\}$ be strict?

Published on 21 Nov 2021 - 17:20

173

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Theorem 6.6 of Baby Rudin

Published on 22 Nov 2021 - 19:51

62

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Infimum of $\{\frac{11}{n + 3} : n \in \mathbb{N}\}$

Published on 23 Nov 2021 - 12:58

List Question

Handling of suprema and infima in a proof of $\int_{a}^{b}(f+g)=\int_{a}^{b}f+\int_{a}^{b}g$

Supremum and infimum of expected value of an indicator

Find $\inf$ and $\sup$ of $a_n = \frac{a_{n-1} + a_{n-2}}{a_{n-3}}$

Proving minium and supremum of a set

Integrability of a family of functions, parameterized by the points of the compact

$\sup(A+B) = \sup(A) + \sup(B)$

Proving of disproving a claim regarding limits

Sup and inf of $A=\{a_n:=\frac{(n^2+(-1)^n(n-1)^2}{3n^{(1+(-1)^n)}+2n},\ n\in\mathbb{N}\setminus\{0\}\}$

For arbitrary metric spaces, if $\sup E\not\in E$, then must $\sup E$ be a limit point of $E$?

How to determine $\sup_{x \in \mathbb{R}} \left|\frac{\sin \left(x^{2}+1\right)}{x^{2}+1}\right|$

Is there a $n_\varepsilon\in\mathbb{N}$?

Continuity in different metrics:

is there example that inequality $\sup\{\inf\{f(x,y) : x \in X\}: y \in Y\} \le \inf\{\sup\{f(x,y) : y \in Y\}: x \in X\}$ be strict?

Theorem 6.6 of Baby Rudin

Infimum of $\{\frac{11}{n + 3} : n \in \mathbb{N}\}$

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