Question

Show that the operator norm can be defined in terms of a minimum

score 1k · Answer 1 · 2017-03-23 17:35:44

1k

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Show that the operator norm can be defined in terms of a minimum

Published on 23 Mar 2017 - 17:35

score 6.5k · Answer 2 · 2017-03-23 17:54:04

6.5k

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absolute value of supremum is smaller than or equal to supremum of absolute values

Published on 23 Mar 2017 - 17:54

score 257 · Answer 3 · 2017-03-24 14:58:18

257

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How to prove that the metric $d=\sup \lbrace d_i(x_i,y_i) \rbrace$ satisfy the triangle inequality?

Published on 24 Mar 2017 - 14:58

score 1.3k · Answer 4 · 2017-03-30 04:16:36

1.3k

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The infimum and supremum of a set containing rational numbers whose squares satisfies a certain property.

Published on 30 Mar 2017 - 4:16

score 223 · Answer 5 · 2017-03-30 05:48:08

223

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The supremum and infimum of a set that contains a variable and an inequality.

Published on 30 Mar 2017 - 5:48

score 67 · Answer 6 · 2017-03-31 15:06:08

67

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Why $\inf \{f^2(x) : x \in A\} = [\inf \{f(x) : x \in A\}^2]$

Published on 31 Mar 2017 - 15:06

score 1.7k · Answer 7 · 2017-04-01 20:41:57

1.7k

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Prove: $\sup (A \cup B) = \max\{\sup(A),\sup(B) \}$ where $A,B \subseteq \mathbb{R}$

Published on 01 Apr 2017 - 20:41

score 113 · Answer 8 · 2017-04-01 23:59:59

Prove: If $A + B = \{a + b \mid a \in A, b \in B \}, \text{ then }\sup (A + B) = \sup (A) + \sup (B)$, where $A,B$ are bounded sets in $\mathbb{R}$

score 115 · Answer 9 · 2026-03-29 22:28:56

115

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Unsure if this proof works for proving $\sup\geq\inf$

Published on 29 Mar 2026 - 22:28

score 96 · Answer 10 · 2017-04-05 15:47:31

96

Views

Find with proofs the infimum, supremum of $E = {a^{n} : n \in \mathbb{N}}$

Published on 05 Apr 2017 - 15:47

score 1.9k · Answer 11 · 2017-04-07 04:18:12

1.9k

Views

Finding the norm of the shift operator on $l^\infty$, $(x_1,x_2, \dots)\mapsto (x_2,x_3,\dots)$

Published on 07 Apr 2017 - 4:18

score 754 · Answer 12 · 2017-04-07 06:50:36

754

Views

interchanging of sup and inf in an optimization problem

Published on 07 Apr 2017 - 6:50

score 448 · Answer 13 · 2026-03-25 16:45:45

448

Views

Understanding a proof about contraction mapping theorem

Published on 25 Mar 2026 - 16:45

score 146 · Answer 14 · 2023-02-09 00:33:46

146

Views

Median of symmetric distribution, where median is defined using inverse of CDF

Published on 09 Feb 2023 - 0:33

score 79 · Answer 15 · 2023-02-13 14:08:02

79

Views

Finding the supremum and infimum of $\{1/n + (-1)^n \mid n \in \mathbb{Z}_{+}\} \subset \mathbb{Q}$

Published on 13 Feb 2023 - 14:08

List Question

Show that the operator norm can be defined in terms of a minimum

absolute value of supremum is smaller than or equal to supremum of absolute values

How to prove that the metric $d=\sup \lbrace d_i(x_i,y_i) \rbrace$ satisfy the triangle inequality?

The infimum and supremum of a set containing rational numbers whose squares satisfies a certain property.

The supremum and infimum of a set that contains a variable and an inequality.

Why $\inf \{f^2(x) : x \in A\} = [\inf \{f(x) : x \in A\}^2]$

Prove: $\sup (A \cup B) = \max\{\sup(A),\sup(B) \}$ where $A,B \subseteq \mathbb{R}$

Prove: If $A + B = \{a + b \mid a \in A, b \in B \}, \text{ then }\sup (A + B) = \sup (A) + \sup (B)$, where $A,B$ are bounded sets in $\mathbb{R}$

Unsure if this proof works for proving $\sup\geq\inf$

Find with proofs the infimum, supremum of $E = {a^{n} : n \in \mathbb{N}}$

Finding the norm of the shift operator on $l^\infty$, $(x_1,x_2, \dots)\mapsto (x_2,x_3,\dots)$

interchanging of sup and inf in an optimization problem

Understanding a proof about contraction mapping theorem

Median of symmetric distribution, where median is defined using inverse of CDF

Finding the supremum and infimum of $\{1/n + (-1)^n \mid n \in \mathbb{Z}_{+}\} \subset \mathbb{Q}$

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