Question

Infimum and supremum of the set $\{(\frac{1}{n},1-\frac{1}{n}):n\in \mathbb{N}\} $ with dictionary order in $\mathbb{R}^2$

score 457 · Answer 1 · 2020-01-12 13:08:05

457

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Infimum and supremum of the set $\{(\frac{1}{n},1-\frac{1}{n}):n\in \mathbb{N}\} $ with dictionary order in $\mathbb{R}^2$

Published on 12 Jan 2020 - 13:08

score 93 · Answer 2 · 2020-01-12 19:55:02

93

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How come $\inf \{ E(X+c)^2 / (a+c)^2 : c \geq 0 \}$ is attained at $ c= \sigma ^2 / a $?

Published on 12 Jan 2020 - 19:55

score 66 · Answer 3 · 2020-01-13 14:17:59

66

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What does the union and intersection of a single sequence of real number mean?

Published on 13 Jan 2020 - 14:17

score 1.1k · Answer 4 · 2020-01-14 00:39:40

1.1k

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Prove that $\sup S \leq \inf T$

Published on 14 Jan 2020 - 0:39

score 98 · Answer 5 · 2020-01-14 21:10:46

98

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$S:=\{3\ln n-\ln(m^2+2m+4n^3): m,n\in\mathbb N\}\;\sup S,\inf S=?$

Published on 14 Jan 2020 - 21:10

score 252 · Answer 6 · 2020-01-14 23:11:40

252

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Extremums of $\sin(\frac{n\pi}{6}): n \in \mathbb{Z}$, and $\frac{1}{n} + \sin(\frac{n\pi}{2}) : n \in \mathbb{N}$

Published on 14 Jan 2020 - 23:11

score 35 · Answer 7 · 2020-01-16 01:46:07

35

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Example of a sequence that fit to these criteria

Published on 16 Jan 2020 - 1:46

score 44 · Answer 8 · 2020-01-16 06:36:26

44

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$\lim_{x \to 0+} w(a, \delta) = 0$ iff f is continuous at $a$

Published on 16 Jan 2020 - 6:36

score 42 · Answer 9 · 2020-01-16 13:48:27

42

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Supremum and subset(Proof verification)

Published on 16 Jan 2020 - 13:48

score 83 · Answer 10 · 2020-01-16 17:58:28

83

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$S:=\left\{\left(m+n\right)^{\frac1{mn}}:\;m,n\in\mathbb N\right\}\inf S,\sup S$

Published on 16 Jan 2020 - 17:58

score 320 · Answer 11 · 2020-01-20 22:29:23

320

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I have no clue how to show this supremum and infimum theorem

Published on 20 Jan 2020 - 22:29

score 190 · Answer 12 · 2020-01-21 01:14:04

190

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Inf and sup of an intersection and union of 2 sets

Published on 21 Jan 2020 - 1:14

score 88 · Answer 13 · 2020-01-21 16:31:35

88

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Proving infimum and supremum of a set

Published on 21 Jan 2020 - 16:31

score 4.4k · Answer 14 · 2020-01-21 19:25:35

4.4k

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Let $A$ be a non-empty subset of the real numbers that is bounded below. Let $-A = \{ -x \mid x \in A\}$ Prove that $\text{inf}(A) = -\text{sup}(-A)$

Published on 21 Jan 2020 - 19:25

score 48 · Answer 15 · 2020-01-23 20:50:28

48

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How to find supremum of a certain sequence

Published on 23 Jan 2020 - 20:50

List Question

Infimum and supremum of the set $\{(\frac{1}{n},1-\frac{1}{n}):n\in \mathbb{N}\} $ with dictionary order in $\mathbb{R}^2$

How come $\inf \{ E(X+c)^2 / (a+c)^2 : c \geq 0 \}$ is attained at $ c= \sigma ^2 / a $?

What does the union and intersection of a single sequence of real number mean?

Prove that $\sup S \leq \inf T$

$S:=\{3\ln n-\ln(m^2+2m+4n^3): m,n\in\mathbb N\}\;\sup S,\inf S=?$

Extremums of $\sin(\frac{n\pi}{6}): n \in \mathbb{Z}$, and $\frac{1}{n} + \sin(\frac{n\pi}{2}) : n \in \mathbb{N}$

Example of a sequence that fit to these criteria

$\lim_{x \to 0+} w(a, \delta) = 0$ iff f is continuous at $a$

Supremum and subset(Proof verification)

$S:=\left\{\left(m+n\right)^{\frac1{mn}}:\;m,n\in\mathbb N\right\}\inf S,\sup S$

I have no clue how to show this supremum and infimum theorem

Inf and sup of an intersection and union of 2 sets

Proving infimum and supremum of a set

Let $A$ be a non-empty subset of the real numbers that is bounded below. Let $-A = \{ -x \mid x \in A\}$ Prove that $\text{inf}(A) = -\text{sup}(-A)$

How to find supremum of a certain sequence

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