List questions from supremum-and-infimum

Published on 28 Dec 2017 - 17:31

190

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Notation question: Does $\inf$ require a subscript?

Published on 29 Dec 2017 - 11:34

817

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How can I show diameter of subset is less then diameter of superset?

Published on 30 Dec 2017 - 20:16

38

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Proof Verification: Let $A = [0 , a), \ a \in \Re$ with $a > 0$, then Sup A = a

Published on 02 Jan 2018 - 23:27

775

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Mathematical Analysis by Walter Rudin, Theorem 1.11: Upper/Lower Bounds and Supremum/Infimum.

Published on 03 Apr 2026 - 22:39

61

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Is my proof for $\sup(A) \le \sup(B)$ if $A \subseteq B$ correct?

Published on 04 Jan 2018 - 17:38

83

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is it true that $a < \sup A \implies \exists b \in A \; \text{such that} \; a <b$?

Published on 06 Jan 2018 - 18:36

173

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For $S\subseteq T\subseteq\mathbb{Q}$, it is possible for $\sup_T S$ to exist, but $\sup_\mathbb{Q} S$ does not?

Published on 10 Sep 2010 - 3:27

88.3k

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How can I prove $\sup(A+B)=\sup A+\sup B$ if $A+B=\{a+b\mid a\in A, b\in B\}$

Published on 23 Feb 2026 - 7:54

6.7k

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How to prove $a \lt b$ for all $a \in A, b \in B$ implies $\sup A \leq \inf B$?

Published on 13 Sep 2010 - 18:18

12.6k

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Sequence converging to the supremum

Published on 07 Dec 2010 - 18:39

50.4k

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max and min versus sup and inf

Published on 23 Jan 2011 - 10:18

15.5k

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Product of sets and supremum

Published on 03 Apr 2026 - 23:00

2.6k

Views

When is $\sup(f) \sup (g) = \sup(fg)$?

Published on 15 Aug 2011 - 19:51

2.6k

Views

Prove that $\sup(S)=1$ if $S=\{x \in \mathbb{R}\mid x^2 < x\}$

Published on 26 Sep 2011 - 2:56

List Question

Supremum question with Arithmetic-Geometric means

Notation question: Does $\inf$ require a subscript?

How can I show diameter of subset is less then diameter of superset?

Proof Verification: Let $A = [0 , a), \ a \in \Re$ with $a > 0$, then Sup A = a

Mathematical Analysis by Walter Rudin, Theorem 1.11: Upper/Lower Bounds and Supremum/Infimum.

Is my proof for $\sup(A) \le \sup(B)$ if $A \subseteq B$ correct?

is it true that $a < \sup A \implies \exists b \in A \; \text{such that} \; a <b$?

For $S\subseteq T\subseteq\mathbb{Q}$, it is possible for $\sup_T S$ to exist, but $\sup_\mathbb{Q} S$ does not?

How can I prove $\sup(A+B)=\sup A+\sup B$ if $A+B=\{a+b\mid a\in A, b\in B\}$

How to prove $a \lt b$ for all $a \in A, b \in B$ implies $\sup A \leq \inf B$?

Sequence converging to the supremum

max and min versus sup and inf

Product of sets and supremum

When is $\sup(f) \sup (g) = \sup(fg)$?

Prove that $\sup(S)=1$ if $S=\{x \in \mathbb{R}\mid x^2 < x\}$

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