List questions from supremum-and-infimum

Published on 02 Jan 2020 - 17:08

87

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Proving that $\liminf (1/a_n) = 1/ \lim \sup (a_n)$ for any positive sequence $(a_n)$?

Published on 28 Mar 2026 - 2:23

88

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Understanding infimum in a complete lattice

Published on 27 Mar 2026 - 16:29

461

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What is the supremum of $A=\{\cos{n},n\in\Bbb{N}\}$

Published on 26 Mar 2026 - 8:00

58

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Is $\max_{s \in [0,1]} B_s = B_1$ where $B_s \sim \mathcal{N}(0,s)$

Published on 05 Jan 2020 - 17:23

52

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Supremum and convergence theorem

Published on 05 Jan 2020 - 17:52

181

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If $F$ is a distribution function and $t>0$, can we show that $F(F^{-1}(t))\ge t$?

Published on 27 Mar 2026 - 22:23

35

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About two different proofs of Archimedean property

Published on 06 Jan 2020 - 11:20

270

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Find the supremum of $h(z)$.

Published on 07 Jan 2020 - 6:05

363

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Triangle inequality for suprema?

Published on 22 Mar 2026 - 20:21

319

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Taking a limit inside an infimum.

Published on 28 Mar 2026 - 2:21

180

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What is the supremum of $f(z)$?

Published on 08 Jan 2020 - 12:40

69

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Solution verification: $\sup S\;\&\;\inf S,\;S:=\left\{\frac{a}{a+b}+\frac{b}{b+c}+\frac{c}{c+a}:\;a,b,c\in\langle 0,+\infty\rangle\right\}$

Published on 09 Jan 2020 - 19:11

886

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Interchange the lim inf and supremum

Published on 28 Mar 2026 - 2:22

1.6k

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Find supremum and infimum for $C={\frac{x^2+1}{x^2+2}: x \in \mathbb{R}}.$

Published on 12 Jan 2020 - 12:30

List Question

Supremum of set of products of elements of two sets

Proving that $\liminf (1/a_n) = 1/ \lim \sup (a_n)$ for any positive sequence $(a_n)$?

Understanding infimum in a complete lattice

What is the supremum of $A=\{\cos{n},n\in\Bbb{N}\}$

Is $\max_{s \in [0,1]} B_s = B_1$ where $B_s \sim \mathcal{N}(0,s)$

Supremum and convergence theorem

If $F$ is a distribution function and $t>0$, can we show that $F(F^{-1}(t))\ge t$?

About two different proofs of Archimedean property

Find the supremum of $h(z)$.

Triangle inequality for suprema?

Taking a limit inside an infimum.

What is the supremum of $f(z)$?

Solution verification: $\sup S\;\&\;\inf S,\;S:=\left\{\frac{a}{a+b}+\frac{b}{b+c}+\frac{c}{c+a}:\;a,b,c\in\langle 0,+\infty\rangle\right\}$

Interchange the lim inf and supremum

Find supremum and infimum for $C={\frac{x^2+1}{x^2+2}: x \in \mathbb{R}}.$

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