Question

$s + \frac{1}{n}$ is an upper bound for $A$ and $s - \frac{1}{n}$ is not an upper bound for $A$. Show $s = \sup A.$

score 1.5k · Answer 1 · 2018-02-08 01:52:26

1.5k

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$s + \frac{1}{n}$ is an upper bound for $A$ and $s - \frac{1}{n}$ is not an upper bound for $A$. Show $s = \sup A.$

Published on 08 Feb 2018 - 1:52

score 56 · Answer 2 · 2026-03-21 22:30:29

56

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Finding Infimum of set

Published on 21 Mar 2026 - 22:30

score 5.1k · Answer 3 · 2018-02-11 22:35:04

5.1k

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Formally Proving $1$ is the supremum of $(0, 1)$ in $\mathbb{R}$

Published on 11 Feb 2018 - 22:35

score 78 · Answer 4 · 2018-02-14 07:41:21

78

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Determine the Supremum and Infimum of a sequence

Published on 14 Feb 2018 - 7:41

score 30 · Answer 5 · 2018-02-19 15:32:51

30

Views

The limit of a sequence of $\sup X_n$ where each $X_n$ is a real subset

Published on 19 Feb 2018 - 15:32

score 65 · Answer 6 · 2018-02-19 16:58:43

65

Views

Supremum of the sample mean without first moment assumption.

Published on 19 Feb 2018 - 16:58

score 285 · Answer 7 · 2018-02-20 19:41:22

285

Views

If $F \subset \mathbb{R}$ and bounded, then sup $F \in \bar{F}$

Published on 20 Feb 2018 - 19:41

score 322 · Answer 8 · 2026-03-25 03:02:57

322

Views

Infimum of infima of all subsets

Published on 25 Mar 2026 - 3:02

score 60 · Answer 9 · 2018-02-22 07:57:01

60

Views

some confusion about infimum and supremum concepts>

Published on 22 Feb 2018 - 7:57

score 99 · Answer 10 · 2018-02-22 18:36:14

99

Views

if $\sup(S) = \infty$, then there is a sequence $s_n \in S$ such that its limit is $\infty$?

Published on 22 Feb 2018 - 18:36

score 74 · Answer 11 · 2018-02-23 10:16:05

74

Views

Proving the infimum of a function of four variables is positive

Published on 23 Feb 2018 - 10:16

score 123 · Answer 12 · 2026-03-21 20:51:46

123

Views

supremum of two sets

Published on 21 Mar 2026 - 20:51

score 74 · Answer 13 · 2018-02-24 16:42:13

74

Views

Prove that for $A:= \{\operatorname{frac}(n\sqrt2)\mid n \in \mathbb{Z}\} $ we have $0.99 \leq \sup(A) \leq 1$

Published on 24 Feb 2018 - 16:42

score 1.4k · Answer 14 · 2018-02-25 04:47:42

1.4k

Views

Why do we use supremum instead of maximum in Riemann Integration?

Published on 25 Feb 2018 - 4:47

score 90 · Answer 15 · 2018-03-01 05:36:27

90

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Let $a^2<2, b=2(a+1)/(a+2)$. Show $b^2<2$ (assignment)

Published on 01 Mar 2018 - 5:36

List Question

$s + \frac{1}{n}$ is an upper bound for $A$ and $s - \frac{1}{n}$ is not an upper bound for $A$. Show $s = \sup A.$

Finding Infimum of set

Formally Proving $1$ is the supremum of $(0, 1)$ in $\mathbb{R}$

Determine the Supremum and Infimum of a sequence

The limit of a sequence of $\sup X_n$ where each $X_n$ is a real subset

Supremum of the sample mean without first moment assumption.

If $F \subset \mathbb{R}$ and bounded, then sup $F \in \bar{F}$

Infimum of infima of all subsets

some confusion about infimum and supremum concepts>

if $\sup(S) = \infty$, then there is a sequence $s_n \in S$ such that its limit is $\infty$?

Proving the infimum of a function of four variables is positive

supremum of two sets

Prove that for $A:= \{\operatorname{frac}(n\sqrt2)\mid n \in \mathbb{Z}\} $ we have $0.99 \leq \sup(A) \leq 1$

Why do we use supremum instead of maximum in Riemann Integration?

Let $a^2<2, b=2(a+1)/(a+2)$. Show $b^2<2$ (assignment)

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