Question

Why are upper bounds only defined on subsets of preordered sets?

score 169 · Answer 1 · 2021-02-11 23:43:43

169

Views

Why are upper bounds only defined on subsets of preordered sets?

Published on 11 Feb 2021 - 23:43

score 104 · Answer 2 · 2021-02-12 09:24:34

104

Views

Existence of a local maximum on an open ball

Published on 12 Feb 2021 - 9:24

score 53 · Answer 3 · 2026-03-26 08:23:13

53

Views

$\sup_{\Gamma}\sum |\phi(x_i)-\phi(x_{i-1})|=\infty$ but $\lim_{|\Gamma|\to 0}\sum (\phi(x_i)-\phi(x_{i-1}))$ exists

Published on 26 Mar 2026 - 8:23

score 215 · Answer 4 · 2026-04-01 08:05:44

215

Views

Completing a proof on integrability: $f$ is Riemann integrable under the mesh definition iff $\sup L_\Gamma = \inf U_\Gamma$

Published on 01 Apr 2026 - 8:05

score 30 · Answer 5 · 2021-02-16 12:04:28

30

Views

$d$ forms a metric space on The set of bounded sequences.

Published on 16 Feb 2021 - 12:04

score 86 · Answer 6 · 2021-02-16 17:03:20

86

Views

A question about infimum and supremum.

Published on 16 Feb 2021 - 17:03

score 43 · Answer 7 · 2026-04-06 17:45:57

43

Views

Comparing two events

Published on 06 Apr 2026 - 17:45

score 63 · Answer 8 · 2026-04-06 08:04:49

63

Views

Clarity on a property of infimum and supremum

Published on 06 Apr 2026 - 8:04

score 166 · Answer 9 · 2021-02-23 20:06:40

166

Views

If $A$ and $B$ are sets of real positive numbers, bounded and $C:=\{x\cdot y | x \in A, y \in B\}$ show that $sup(A) sup(B)= sup(C)$

Published on 23 Feb 2021 - 20:06

score 37 · Answer 10 · 2021-02-24 07:26:37

37

Views

Is $\sup_{\{x \in S : |f(x)|\leq |\inf_S f|\}} |f(x)| = |\inf_S f|$?

Published on 24 Feb 2021 - 7:26

score 91 · Answer 11 · 2021-02-24 10:02:54

91

Views

Why is $\sup_{n \in \mathbb{N}} E[|X_n|^p] \leq B < \infty$ different from $\sup_{n \in \mathbb{N}} E[|X_n|^p] < \infty$ as a requirement?

Published on 24 Feb 2021 - 10:02

score 244 · Answer 12 · 2026-04-01 13:08:10

244

Views

Supremum of $x^2y^2(x^2+y^2)$

Published on 01 Apr 2026 - 13:08

score 354 · Answer 13 · 2021-02-26 09:29:02

354

Views

Determine whether the given set is bounded and find its supremum and its infimum.

Published on 26 Feb 2021 - 9:29

score 105 · Answer 14 · 2026-04-06 17:52:46

105

Views

Show that $a = \sup \{ a_n | n \in \mathbb{N} \} = \limsup\limits_{n \to \infty} a_n$

Published on 06 Apr 2026 - 17:52

score 405 · Answer 15 · 2021-03-03 08:27:36

405

Views

Prove $|f(x)-f(y)|<\varepsilon \implies \sup f - \inf f \leq \varepsilon$

Published on 03 Mar 2021 - 8:27

List Question

Why are upper bounds only defined on subsets of preordered sets?

Existence of a local maximum on an open ball

$\sup_{\Gamma}\sum |\phi(x_i)-\phi(x_{i-1})|=\infty$ but $\lim_{|\Gamma|\to 0}\sum (\phi(x_i)-\phi(x_{i-1}))$ exists

Completing a proof on integrability: $f$ is Riemann integrable under the mesh definition iff $\sup L_\Gamma = \inf U_\Gamma$

$d$ forms a metric space on The set of bounded sequences.

A question about infimum and supremum.

Comparing two events

Clarity on a property of infimum and supremum

If $A$ and $B$ are sets of real positive numbers, bounded and $C:=\{x\cdot y | x \in A, y \in B\}$ show that $sup(A) sup(B)= sup(C)$

Is $\sup_{\{x \in S : |f(x)|\leq |\inf_S f|\}} |f(x)| = |\inf_S f|$?

Why is $\sup_{n \in \mathbb{N}} E[|X_n|^p] \leq B < \infty$ different from $\sup_{n \in \mathbb{N}} E[|X_n|^p] < \infty$ as a requirement?

Supremum of $x^2y^2(x^2+y^2)$

Determine whether the given set is bounded and find its supremum and its infimum.

Show that $a = \sup \{ a_n | n \in \mathbb{N} \} = \limsup\limits_{n \to \infty} a_n$

Prove $|f(x)-f(y)|<\varepsilon \implies \sup f - \inf f \leq \varepsilon$

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