List questions from supremum-and-infimum

Published on 30 Mar 2015 - 17:01

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${\rm sup}\ A\cap B = {\rm min}\ \{ {\rm sup} (A), {\rm sup}(B) \} $

Published on 01 Apr 2015 - 8:05

288

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Equality of sets supremum and infimum

Published on 02 Apr 2015 - 22:29

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Existence of a sequence that converges to infimum of a function

Published on 06 Apr 2015 - 6:32

1.6k

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Why is the infimum in the Hopf-Lax formula a minimum?

Published on 25 Mar 2026 - 14:22

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Prove $\sup S \leq \inf T$, if $s \leq t$, $\forall s \in S$ and $\forall t \in T$

Published on 07 Apr 2015 - 11:17

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What exactly is the meaning of the following $\inf\{ s_n : n > N\}$ and $\sup\{ s_n : n > N\}$

Published on 08 Apr 2015 - 14:25

204

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Supremums and subsets

Published on 12 Apr 2015 - 22:35

220

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Supremum/Infimum and min/max

Published on 12 Apr 2015 - 23:01

671

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Let $A= [0,1] - \{1/n │n \in \mathbb{N}\}$. Find $\sup(A)$, $\inf(A)$, $\min(A)$, $\max(A)$.

Published on 13 Apr 2015 - 0:30

526

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Limit of monotonic function

Published on 14 Apr 2015 - 19:26

66

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Calculate $\sup\limits_{x\in(0,+\infty)}\frac{x^2 e^{-n/x}}{n^2+x^2}$

Published on 15 Apr 2015 - 7:57

1.9k

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Sup and inf of $n \sin(1/n)$

Published on 19 Apr 2015 - 9:19

104

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Monotonic everywhere function

Published on 19 Apr 2015 - 14:23

58

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If the set $B=\{f(x) : x\in A\}$ has supremum and $C=\{k+f(x): x\in A\}$, then what is $\sup C$?

Published on 20 Apr 2015 - 1:46

List Question

If $A$ has no max and $B$ is finite, then $\sup(A)=\sup(A\setminus B)$

${\rm sup}\ A\cap B = {\rm min}\ \{ {\rm sup} (A), {\rm sup}(B) \} $

Equality of sets supremum and infimum

Existence of a sequence that converges to infimum of a function

Why is the infimum in the Hopf-Lax formula a minimum?

Prove $\sup S \leq \inf T$, if $s \leq t$, $\forall s \in S$ and $\forall t \in T$

What exactly is the meaning of the following $\inf\{ s_n : n > N\}$ and $\sup\{ s_n : n > N\}$

Supremums and subsets

Supremum/Infimum and min/max

Let $A= [0,1] - \{1/n │n \in \mathbb{N}\}$. Find $\sup(A)$, $\inf(A)$, $\min(A)$, $\max(A)$.

Limit of monotonic function

Calculate $\sup\limits_{x\in(0,+\infty)}\frac{x^2 e^{-n/x}}{n^2+x^2}$

Sup and inf of $n \sin(1/n)$

Monotonic everywhere function

If the set $B=\{f(x) : x\in A\}$ has supremum and $C=\{k+f(x): x\in A\}$, then what is $\sup C$?

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