List questions from supremum-and-infimum

Published on 19 Mar 2021 - 5:15

171

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Changing variable in a supremum integral inequality

Published on 19 Mar 2021 - 10:24

65

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Infimium between two sets with a bijection

Published on 20 Mar 2021 - 19:34

34

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Finding lub and glb

Published on 22 Mar 2021 - 6:58

39

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Calculating $\left\Vert \sum_{n=1}^\infty \frac{x_n-\lim_{n \rightarrow\infty} x_n}{2^n} \right\Vert_\infty$

Published on 22 Mar 2021 - 20:26

43

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Calculating $\Vert\sum_n^\infty(-1)^nx_n \Vert_\infty$

Published on 23 Mar 2021 - 11:30

133

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When do we know that $\sup_{x \in \mathbb{R}} f(x) \in f(\mathbb{R})$? And is there a argsup function or something equivalent?

Published on 26 Mar 2021 - 18:21

90

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Proof or counterexample to $ \int_a^t |f(x)|dx \leq \sup_t|\int f(x)dx| $

Published on 30 Mar 2026 - 7:56

1.8k

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Minimum of empty set in $\infty$ why is that?

Published on 29 Mar 2021 - 16:19

30

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If $\tau:=\{t\ge t_0:f(t)\in B\}$, can we show that $f(\min(t,\tau))\not\in B$ for all $t$?

Published on 03 Apr 2026 - 2:00

97

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Limit definition: how to say that supremum is finite?

Published on 30 Mar 2021 - 21:21

72

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A question about a net in a topological space

Published on 30 Mar 2021 - 22:30

52

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How to prove that $u(\epsilon') = \inf\{f(s) - f(s+\epsilon'): s \in [0,t]\} > 0$ for strictly decreasing function $f$?

Published on 07 Apr 2026 - 17:16

179

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The set $\{\frac{1}{x^2-3}: x\in\mathbb{Q}\}$ is bounded? Explain.

Published on 03 Apr 2021 - 19:42

43

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Let $A=\{a_k:k \in \mathbb{N}\}$ be a countable set of strictly positive real numbers such that $\mbox{inf}(A) = 0$. Prove an accumulation point.

Published on 04 Apr 2021 - 17:40

List Question

continuity, supremum/infimum

Changing variable in a supremum integral inequality

Infimium between two sets with a bijection

Finding lub and glb

Calculating $\left\Vert \sum_{n=1}^\infty \frac{x_n-\lim_{n \rightarrow\infty} x_n}{2^n} \right\Vert_\infty$

Calculating $\Vert\sum_n^\infty(-1)^nx_n \Vert_\infty$

When do we know that $\sup_{x \in \mathbb{R}} f(x) \in f(\mathbb{R})$? And is there a argsup function or something equivalent?

Proof or counterexample to $ \int_a^t |f(x)|dx \leq \sup_t|\int f(x)dx| $

Minimum of empty set in $\infty$ why is that?

If $\tau:=\{t\ge t_0:f(t)\in B\}$, can we show that $f(\min(t,\tau))\not\in B$ for all $t$?

Limit definition: how to say that supremum is finite?

A question about a net in a topological space

How to prove that $u(\epsilon') = \inf\{f(s) - f(s+\epsilon'): s \in [0,t]\} > 0$ for strictly decreasing function $f$?

The set $\{\frac{1}{x^2-3}: x\in\mathbb{Q}\}$ is bounded? Explain.

Let $A=\{a_k:k \in \mathbb{N}\}$ be a countable set of strictly positive real numbers such that $\mbox{inf}(A) = 0$. Prove an accumulation point.

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