List questions from supremum-and-infimum

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If $f$ is continuous on $[a,b]$ and $F(x) = \sup f([a,x])$. Prove that $F$ is continuous on $[a,b]$ .

Published on 10 Nov 2014 - 0:35

82.1k

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"sup" in an equation

Published on 12 Nov 2014 - 11:20

1k

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prove $(\sup{|f(x)|})^2\geq(\sup{f(x)})^2$

Published on 12 Nov 2014 - 18:36

252

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supremum is the only positive root of $z^n=a^m$

Published on 14 Nov 2014 - 6:17

47

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Proving an equality of supremums related to the rate function

Published on 25 Mar 2026 - 9:49

2.1k

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Prove $\sup(f^2(x))\le(\sup(f(x))^2$

Published on 14 Nov 2014 - 18:52

987

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Prove Infimum and Supremum

Published on 16 Nov 2014 - 16:05

3.3k

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Prove the infimum and supremum of the positive rational numbers

Published on 17 Nov 2014 - 16:15

4.7k

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Is supremum part of the set or it is the bigest element out of it?

Published on 17 Nov 2014 - 20:18

33

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Certain property of supremum

Published on 20 Nov 2014 - 22:38

2.7k

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Find $\bigcap_{n=1}^\infty(0,1/n)=\emptyset$

Published on 20 Nov 2014 - 22:46

81

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How to prove the infimum of this subset

Published on 21 Nov 2014 - 9:35

116

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Show that there exists $m\in\mathbb{N}$ such that $a+\frac{m}{2^n}\geq b$

Published on 21 Nov 2014 - 19:28

79

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For every $n$ there exists $k_n \in \mathbb{N}$ such that $a+k_n/2^n$ is an upper bound while $a+(k_n-1)/2^n$ is not

Published on 21 Nov 2014 - 22:33

286

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Finding the supremum of a set

Published on 22 Nov 2014 - 19:15

List Question

If $f$ is continuous on $[a,b]$ and $F(x) = \sup f([a,x])$. Prove that $F$ is continuous on $[a,b]$ .

"sup" in an equation

prove $(\sup{|f(x)|})^2\geq(\sup{f(x)})^2$

supremum is the only positive root of $z^n=a^m$

Proving an equality of supremums related to the rate function

Prove $\sup(f^2(x))\le(\sup(f(x))^2$

Prove Infimum and Supremum

Prove the infimum and supremum of the positive rational numbers

Is supremum part of the set or it is the bigest element out of it?

Certain property of supremum

Find $\bigcap_{n=1}^\infty(0,1/n)=\emptyset$

How to prove the infimum of this subset

Show that there exists $m\in\mathbb{N}$ such that $a+\frac{m}{2^n}\geq b$

For every $n$ there exists $k_n \in \mathbb{N}$ such that $a+k_n/2^n$ is an upper bound while $a+(k_n-1)/2^n$ is not

Finding the supremum of a set

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