Question

A simple theoretical optimization problem

score 34 · Answer 1 · 2020-10-02 15:33:24

34

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A simple theoretical optimization problem

Published on 02 Oct 2020 - 15:33

score 866 · Answer 2 · 2020-10-02 16:13:15

866

Views

How to show this $\sup_{x} [ \sup_{y} f(x,y)] = \sup_{y} [ \sup_{x} f(x,y)]$?

Published on 02 Oct 2020 - 16:13

score 428 · Answer 3 · 2026-04-06 17:50:14

428

Views

Show that $\ M$ =sup $\ E$ iff for all $\varepsilon \gt$ 0 there is an $\ x$ in $\ E$ such that $\ M$ $\ - \varepsilon \lt x \le M$

Published on 06 Apr 2026 - 17:50

score 39 · Answer 4 · 2020-10-04 03:31:49

Let $a,b\in\mathbb{R}$ not both $0$ and $f(\vec{x})=ax_1+bx_2$ and $A= \{f(\vec{x}):\vec{x}\in B(\vec{0},1)\}$. Determine $\inf A$ and $\sup A$

score 115 · Answer 5 · 2020-10-06 11:26:46

115

Views

Show that if $S \subset Z$ is bounded above, then $S$ has a maximum, i.e., $\sup S in S$.

Published on 06 Oct 2020 - 11:26

score 730 · Answer 6 · 2020-10-07 14:20:04

730

Views

Complex numbers - supremum

Published on 07 Oct 2020 - 14:20

score 159 · Answer 7 · 2020-10-07 18:26:43

159

Views

1.14 Theorem (Rudin's Complex analysis book)

Published on 07 Oct 2020 - 18:26

score 31 · Answer 8 · 2020-10-08 06:43:03

31

Views

Sequence of events $\{C_n\}_n\in\mathbb{N}$: why $\mathbb{P}\left(\bigcup_{m\ge n}C_m\right)\ge\sup_{m\ge n} \mathbb{P}\left(C_m\right)$?

Published on 08 Oct 2020 - 6:43

score 419 · Answer 9 · 2020-10-08 20:57:36

419

Views

Supremum and infimum of the following set

Published on 08 Oct 2020 - 20:57

score 265 · Answer 10 · 2020-10-09 08:05:18

265

Views

Find infimum of the set $A=\left \{ \frac{1}{n+1}, n \in \mathbb{N} \right \}$.

Published on 09 Oct 2020 - 8:05

score 90 · Answer 11 · 2020-10-09 13:00:47

90

Views

Prove that $A = \bigg \{ \frac{n}{1 - n^2} \hspace{.1cm} | \hspace{.1cm} n \in \mathbb{N}, n \ge 2 \bigg \}$ has a supremum equal to $0$.

Published on 09 Oct 2020 - 13:00

score 176 · Answer 12 · 2020-10-11 02:53:36

176

Views

How do I show $\sup(\bigcup_{n=0}^{\infty} A_n) \leqslant \sum_{n=0}^\infty \sup(A_n)$?

Published on 11 Oct 2020 - 2:53

score 68 · Answer 13 · 2020-10-11 08:52:02

68

Views

How to obtain $\theta=0$?

Published on 11 Oct 2020 - 8:52

score 302 · Answer 14 · 2020-10-11 17:29:13

302

Views

Show that a function with a limit either has maximum or supremum equals limit

Published on 11 Oct 2020 - 17:29

score 194 · Answer 15 · 2020-10-14 19:36:32

194

Views

Let $S = \{x \in \mathbb{R}| x < a_n \hspace{2mm}\text{for infinitely many $a_n$}\}$. Find a subsequence converging to $\sup S$

Published on 14 Oct 2020 - 19:36

List Question

A simple theoretical optimization problem

How to show this $\sup_{x} [ \sup_{y} f(x,y)] = \sup_{y} [ \sup_{x} f(x,y)]$?

Show that $\ M$ =sup $\ E$ iff for all $\varepsilon \gt$ 0 there is an $\ x$ in $\ E$ such that $\ M$ $\ - \varepsilon \lt x \le M$

Let $a,b\in\mathbb{R}$ not both $0$ and $f(\vec{x})=ax_1+bx_2$ and $A= \{f(\vec{x}):\vec{x}\in B(\vec{0},1)\}$. Determine $\inf A$ and $\sup A$

Show that if $S \subset Z$ is bounded above, then $S$ has a maximum, i.e., $\sup S in S$.

Complex numbers - supremum

1.14 Theorem (Rudin's Complex analysis book)

Sequence of events $\{C_n\}_n\in\mathbb{N}$: why $\mathbb{P}\left(\bigcup_{m\ge n}C_m\right)\ge\sup_{m\ge n} \mathbb{P}\left(C_m\right)$?

Supremum and infimum of the following set

Find infimum of the set $A=\left \{ \frac{1}{n+1}, n \in \mathbb{N} \right \}$.

Prove that $A = \bigg \{ \frac{n}{1 - n^2} \hspace{.1cm} | \hspace{.1cm} n \in \mathbb{N}, n \ge 2 \bigg \}$ has a supremum equal to $0$.

How do I show $\sup(\bigcup_{n=0}^{\infty} A_n) \leqslant \sum_{n=0}^\infty \sup(A_n)$?

How to obtain $\theta=0$?

Show that a function with a limit either has maximum or supremum equals limit

Let $S = \{x \in \mathbb{R}| x < a_n \hspace{2mm}\text{for infinitely many $a_n$}\}$. Find a subsequence converging to $\sup S$

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