List questions from supremum-and-infimum

Published on 16 Dec 2015 - 19:50

166

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$ \max \{ \underset{x \in X}{\sup } f(x)\ , \underset{x \in X}{\sup } g(x) \} = \underset{x \in X}{\sup } \{ \max \{ f(x), g(x) \} \}$?

Published on 17 Dec 2015 - 20:21

482

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Is the supremum of a set finite by definition?

Published on 20 Dec 2015 - 17:45

191

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Unique upper bound

Published on 21 Dec 2015 - 3:18

99

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Finding $\inf$ and $\sup$ with the definition

Published on 22 Dec 2015 - 16:58

669

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If $ \sup(A)=\sup(B)$ and $\inf(A)=\inf(B)$ does that mean that $A=B$?

Published on 26 Dec 2015 - 11:22

1k

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In general, when does it hold that $f(\sup(X)) = \sup f(X)$?

Published on 31 Dec 2015 - 20:05

1.4k

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Infimum and Supremum proof

Published on 01 Jan 2016 - 16:20

166

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Let $A,B\subseteq \mathbb{R}$ such that $\forall b\in B ~ \exists a_n$ where $a_n \in A$ and $a_n\to b$ as $n\to\infty$. Prove $\sup(B)\leq \sup(A)$

Published on 03 Jan 2016 - 17:19

141

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Real analysis supremum proof

Published on 03 Jan 2016 - 18:33

49

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Problem in Supremum of cosets .

Published on 04 Jan 2016 - 12:50

40

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Are these two statements involving inf and sup equivalent?

Published on 04 Jan 2016 - 17:10

74

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What does $sup\{|f_1(x)-f(x)|, x \in D\}$ exactly mean?

Published on 07 Jan 2016 - 19:24

1.6k

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How to prove the following properties of infimum and supremum involving the union and intersection of the sets $A_k$

Published on 09 Jan 2016 - 10:13

107

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Show that $\underset{x\in X}{\sup}\left(\underset{y\in Y}{\sup}f(x,y)\right) = \underset{(x,y)\in X\times Y}{\sup} f(x,y)$

Published on 10 Jan 2016 - 1:20

List Question

Sequence approaching infimum

$ \max \{ \underset{x \in X}{\sup } f(x)\ , \underset{x \in X}{\sup } g(x) \} = \underset{x \in X}{\sup } \{ \max \{ f(x), g(x) \} \}$?

Is the supremum of a set finite by definition?

Unique upper bound

Finding $\inf$ and $\sup$ with the definition

If $ \sup(A)=\sup(B)$ and $\inf(A)=\inf(B)$ does that mean that $A=B$?

In general, when does it hold that $f(\sup(X)) = \sup f(X)$?

Infimum and Supremum proof

Let $A,B\subseteq \mathbb{R}$ such that $\forall b\in B ~ \exists a_n$ where $a_n \in A$ and $a_n\to b$ as $n\to\infty$. Prove $\sup(B)\leq \sup(A)$

Real analysis supremum proof

Problem in Supremum of cosets .

Are these two statements involving inf and sup equivalent?

What does $sup\{|f_1(x)-f(x)|, x \in D\}$ exactly mean?

How to prove the following properties of infimum and supremum involving the union and intersection of the sets $A_k$

Show that $\underset{x\in X}{\sup}\left(\underset{y\in Y}{\sup}f(x,y)\right) = \underset{(x,y)\in X\times Y}{\sup} f(x,y)$

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