List questions from supremum-and-infimum

Published on 01 Oct 2021 - 7:56

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Proving central limit theorem in a specific case( fourier analysis course)

Published on 03 Apr 2026 - 5:15

101

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limit of supremum of Green's function, $\lim_{\epsilon \to 0} (\sup_{z \in \partial B(x,\epsilon)} |G(x,z)|$) for $n \geq 3$

Published on 26 Mar 2026 - 0:53

84

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Understanding Archimedean Priniciple Proof in WikiProof

Published on 09 Oct 2021 - 18:35

868

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Prove that for any $x \in \mathbb{R}$, $x = \sup \{q \in \mathbb{Q} : q < x\}$

Published on 10 Oct 2021 - 22:31

223

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Formal proof for supremum of $A=\{1+\frac{1}{n}:n\in\mathbb{N}\}$ is $2$.

Published on 12 Oct 2021 - 6:00

35

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Regarding the supremum of the given function

Published on 28 Mar 2026 - 2:03

185

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If $u$ is rational, can we show $\inf\{t:x(t)\in B\}\le u$ iff $x(s)\in B$ for some rational $s\le u$?

Published on 12 Oct 2021 - 15:38

565

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When does sup and function commute?

Published on 26 Mar 2026 - 1:26

142

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Moving a limit inside integral and uniform convergence.

Published on 26 Feb 2026 - 2:51

107

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Show that there exists a strictly increasing function $g$ such that $\sup_{\|x\|>1}\frac{\|x\|}{g(f(x))}<\infty$

Published on 14 Oct 2021 - 14:55

39

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Supremum of a function over $[0,T]$

Published on 15 Oct 2021 - 15:39

56

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Property of $\sup_{n\geq 1}\left(\sum_{i=1}^na_ip^{-i}\right)$ for $p>1$

Published on 15 Oct 2021 - 21:22

39

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Proving something is a lower or upper bound.

Published on 16 Oct 2021 - 0:24

38

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Supremum of Absolutely Continuous Function

Published on 16 Oct 2021 - 19:55

List Question

Prove that $1$ is the supremum of $\frac{n-1}{n+1}$

Proving central limit theorem in a specific case( fourier analysis course)

limit of supremum of Green's function, $\lim_{\epsilon \to 0} (\sup_{z \in \partial B(x,\epsilon)} |G(x,z)|$) for $n \geq 3$

Understanding Archimedean Priniciple Proof in WikiProof

Prove that for any $x \in \mathbb{R}$, $x = \sup \{q \in \mathbb{Q} : q < x\}$

Formal proof for supremum of $A=\{1+\frac{1}{n}:n\in\mathbb{N}\}$ is $2$.

Regarding the supremum of the given function

If $u$ is rational, can we show $\inf\{t:x(t)\in B\}\le u$ iff $x(s)\in B$ for some rational $s\le u$?

When does sup and function commute?

Moving a limit inside integral and uniform convergence.

Show that there exists a strictly increasing function $g$ such that $\sup_{\|x\|>1}\frac{\|x\|}{g(f(x))}<\infty$

Supremum of a function over $[0,T]$

Property of $\sup_{n\geq 1}\left(\sum_{i=1}^na_ip^{-i}\right)$ for $p>1$

Proving something is a lower or upper bound.

Supremum of Absolutely Continuous Function

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