Question

Existence of supremum in matrix norm definition

score 30 · Answer 1 · 2026-03-26 09:17:45

Existence of supremum in matrix norm definition

Published on 26 Mar 2026 - 9:17

score 111 · Answer 2 · 2023-02-18 19:04:07

Running supremum of a right-continuous function: prove that $\left\{x\geq 0\left|\sup_{0\leq y\leq x}f(y)\geq K\right.\right\}$ is closed.

score 44 · Answer 3 · 2023-02-20 23:30:50

44

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Maximizing a function via an intermediate bound

Published on 20 Feb 2023 - 23:30

score 212 · Answer 4 · 2023-02-28 06:49:35

212

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Draw a triangle in the region bounded by a polynomial curve and a straight line. What is the supremum of the ratio of their areas?

Published on 28 Feb 2023 - 6:49

score 39 · Answer 5 · 2023-03-01 15:06:09

39

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Boundary of open set in $\mathbb{R}$

Published on 01 Mar 2023 - 15:06

score 95 · Answer 6 · 2023-03-03 15:10:20

95

Views

maximum Fourier coefficient among all bounded real continuous periodic functions

Published on 03 Mar 2023 - 15:10

score 39 · Answer 7 · 2023-03-05 16:54:31

39

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If $[f(t) > l \implies f'(t) <0]$, then $\sup_{t \in [0, T]} f(t) \le \max \{f(0), l\}$

Published on 05 Mar 2023 - 16:54

score 61 · Answer 8 · 2023-03-07 11:42:15

61

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Infimum plus constant

Published on 07 Mar 2023 - 11:42

score 48 · Answer 9 · 2026-04-01 09:34:29

48

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A (classical) bound on the jumps of a cadlag function: $\left|\Delta f(t)\right|\leq 2\,\sup_{0\leq s\leq t}\left|f(s)\right|$.

Published on 01 Apr 2026 - 9:34

score 106 · Answer 10 · 2023-03-08 22:24:35

106

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Show that the set $A:=\{ x \in \mathbb{Q}_{>0} \, | \, x^2 \geq 2 \}$ has no greatest lower bound in $\mathbb{Q}$

Published on 08 Mar 2023 - 22:24

score 97 · Answer 11 · 2026-02-23 06:18:38

97

Views

Triangle Inequality for this metric

Published on 23 Feb 2026 - 6:18

score 74 · Answer 12 · 2023-03-10 13:43:48

74

Views

On the supremum of cadlag function with bounded jumps

Published on 10 Mar 2023 - 13:43

score 81 · Answer 13 · 2023-03-14 18:41:48

81

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The distribution function of a running supremum of a diffusion process in a particular limit.

Published on 14 Mar 2023 - 18:41

score 370 · Answer 14 · 2023-03-16 16:42:06

370

Views

Are inf and sup continuous functionals in general?

Published on 16 Mar 2023 - 16:42

score 63 · Answer 15 · 2023-03-20 20:34:14

63

Views

If $A, B \subseteq \mathbb{R}$ are bounded intervals with $A \cap B \neq \varnothing$, then $\sup(A \cap B) = \min\{\sup A, \sup B\}$

Published on 20 Mar 2023 - 20:34

List Question

Existence of supremum in matrix norm definition

Running supremum of a right-continuous function: prove that $\left\{x\geq 0\left|\sup_{0\leq y\leq x}f(y)\geq K\right.\right\}$ is closed.

Maximizing a function via an intermediate bound

Draw a triangle in the region bounded by a polynomial curve and a straight line. What is the supremum of the ratio of their areas?

Boundary of open set in $\mathbb{R}$

maximum Fourier coefficient among all bounded real continuous periodic functions

If $[f(t) > l \implies f'(t) <0]$, then $\sup_{t \in [0, T]} f(t) \le \max \{f(0), l\}$

Infimum plus constant

A (classical) bound on the jumps of a cadlag function: $\left|\Delta f(t)\right|\leq 2\,\sup_{0\leq s\leq t}\left|f(s)\right|$.

Show that the set $A:=\{ x \in \mathbb{Q}_{>0} \, | \, x^2 \geq 2 \}$ has no greatest lower bound in $\mathbb{Q}$

Triangle Inequality for this metric

On the supremum of cadlag function with bounded jumps

The distribution function of a running supremum of a diffusion process in a particular limit.

Are inf and sup continuous functionals in general?

If $A, B \subseteq \mathbb{R}$ are bounded intervals with $A \cap B \neq \varnothing$, then $\sup(A \cap B) = \min\{\sup A, \sup B\}$

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