List questions from supremum-and-infimum

Published on 31 Aug 2016 - 19:09

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Inequality with supreme of linear bounded functions on normed vectorial spaces

Published on 02 Sep 2016 - 4:13

519

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Prove by definition (rigorously) that the supremum of $S:=\lbrace{\frac{1}{a} - \frac{3}{b}:a,b \in \mathbb{N}}\rbrace $ is $1$.

Published on 03 Sep 2016 - 2:30

722

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Global inf-sup condition in Brezzi (Babuška-Brezzi or Ladyzhenskaya-Babuška-Brezzi) Theorem

Published on 04 Sep 2016 - 1:00

984

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Supremum of the product of two sets

Published on 07 Sep 2016 - 19:55

621

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Suggestion on the proof of $\limsup(a_nb_n)\leq \limsup(a_n)\limsup(b_n)$

Published on 29 Mar 2026 - 4:26

70

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Inequality with sup and continuous function

Published on 08 Sep 2016 - 10:00

1.4k

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Infimum of the Ky Fan metric achieved

Published on 11 Sep 2016 - 10:07

80

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Find the $\sup$ of the set.

Published on 11 Sep 2016 - 19:20

1.7k

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If $\sup S\not\in S$ then $\{x \in S: x > \sup{S} - \epsilon\}$ is infinite

Published on 12 Sep 2016 - 5:42

635

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Let $S\subseteq \mathbb R$. Show that $\sup(S') \le \sup(S)$, where $S'$ is the derived set of $S$.

Published on 12 Sep 2016 - 8:44

605

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How to prove that supremum belongs to the set?

Published on 14 Sep 2016 - 7:56

7.4k

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Finding sup, inf, max and min for each sets

Published on 14 Sep 2016 - 22:08

243

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Proving that supremum is $\frac{9}{8}$ of set $D = \{\frac{n^2}{2^n}~|~n \in \mathbb{N}\}$

Published on 16 Sep 2016 - 8:26

221

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Does every neighborhood of a closed set $F$ in a metric space contain an $\varepsilon$-neighborhood of $F$?

Published on 17 Sep 2016 - 0:32

List Question

Infimum of this expression

Inequality with supreme of linear bounded functions on normed vectorial spaces

Prove by definition (rigorously) that the supremum of $S:=\lbrace{\frac{1}{a} - \frac{3}{b}:a,b \in \mathbb{N}}\rbrace $ is $1$.

Global inf-sup condition in Brezzi (Babuška-Brezzi or Ladyzhenskaya-Babuška-Brezzi) Theorem

Supremum of the product of two sets

Suggestion on the proof of $\limsup(a_nb_n)\leq \limsup(a_n)\limsup(b_n)$

Inequality with sup and continuous function

Infimum of the Ky Fan metric achieved

Find the $\sup$ of the set.

If $\sup S\not\in S$ then $\{x \in S: x > \sup{S} - \epsilon\}$ is infinite

Let $S\subseteq \mathbb R$. Show that $\sup(S') \le \sup(S)$, where $S'$ is the derived set of $S$.

How to prove that supremum belongs to the set?

Finding sup, inf, max and min for each sets

Proving that supremum is $\frac{9}{8}$ of set $D = \{\frac{n^2}{2^n}~|~n \in \mathbb{N}\}$

Does every neighborhood of a closed set $F$ in a metric space contain an $\varepsilon$-neighborhood of $F$?

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