List questions from supremum-and-infimum

Published on 04 Nov 2018 - 21:04

39

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Why is $f(x)=\inf \{ r \in \mathbb{Q} ;x \in U(r)\}$?

Published on 05 Nov 2018 - 11:21

43

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Limits, supremum and Lebesgue measure

Published on 06 Nov 2018 - 18:39

45

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Let $f$ be a mapping, $\beta$ be an ordinal, $X=\{\alpha\mid f(\alpha)\le \beta\}$, and $\gamma=\sup X$. Is $\gamma\in X$?

Published on 25 Mar 2026 - 23:58

71

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what will be the supremum of $a_n $ ?

Published on 08 Nov 2018 - 11:25

130

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If maximum of an ordered, set exists, this is equal to the supremum.

Published on 08 Nov 2018 - 17:46

37

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Is it possible to show sup$(\bigcup_{n\in\mathbb{N}}A_n)=$sup$\{$sup$A_n|n\in\mathbb{N}\}$ by induction?

Published on 13 Nov 2018 - 20:13

187

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Supremum and infimum of a set

Published on 14 Nov 2018 - 7:36

44

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Is $f$ continuous at $0$?

Published on 14 Nov 2018 - 18:09

158

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norm of element in equivalent class in quotient space

Published on 25 Mar 2026 - 14:37

310

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Real analysis use of sup and inf

Published on 15 Nov 2018 - 13:42

23

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Prove property of $A$ implies $\inf A \le 2$

Published on 17 Nov 2018 - 13:12

303

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sup and inf of $A=\left\{\frac{m^4+2n^2}{2m^2-m^2n+n^2}:m,n \in\Bbb N\right\}$

Published on 17 Nov 2018 - 21:44

179

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Is the supremum of an almost surely continuous random function random variable?

Published on 18 Nov 2018 - 11:07

135

Views

Find infA when $A=\{\frac{m^2-n}{m^2+n^2}:m,n\in \Bbb N,m>2n>1\} $

Published on 18 Nov 2018 - 21:48

List Question

What are the conditions on $f$ for $\sup f$ and $f(\sup)$ be interchangeable?

Why is $f(x)=\inf \{ r \in \mathbb{Q} ;x \in U(r)\}$?

Limits, supremum and Lebesgue measure

Let $f$ be a mapping, $\beta$ be an ordinal, $X=\{\alpha\mid f(\alpha)\le \beta\}$, and $\gamma=\sup X$. Is $\gamma\in X$?

what will be the supremum of $a_n $ ?

If maximum of an ordered, set exists, this is equal to the supremum.

Is it possible to show sup$(\bigcup_{n\in\mathbb{N}}A_n)=$sup$\{$sup$A_n|n\in\mathbb{N}\}$ by induction?

Supremum and infimum of a set

Is $f$ continuous at $0$?

norm of element in equivalent class in quotient space

Real analysis use of sup and inf

Prove property of $A$ implies $\inf A \le 2$

sup and inf of $A=\left\{\frac{m^4+2n^2}{2m^2-m^2n+n^2}:m,n \in\Bbb N\right\}$

Is the supremum of an almost surely continuous random function random variable?

Find infA when $A=\{\frac{m^2-n}{m^2+n^2}:m,n\in \Bbb N,m>2n>1\} $

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