Question

Confusion regarding the proof of Theorem I.32 of Apostol's Calculus.

score 294 · Answer 1 · 2018-05-29 19:03:08

294

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Confusion regarding the proof of Theorem I.32 of Apostol's Calculus.

Published on 29 May 2018 - 19:03

score 199 · Answer 2 · 2018-06-02 13:11:20

199

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Supremum and Infimum of the given set

Published on 02 Jun 2018 - 13:11

score 51 · Answer 3 · 2026-03-25 17:36:51

51

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prove that every countable set $B$ , as $B\subseteq\mathbb{N^{\mathrm{\mathbb{N}}}}/R$ - has a supremum.

Published on 25 Mar 2026 - 17:36

score 134 · Answer 4 · 2018-06-03 14:20:01

134

Views

Supremum of the given set

Published on 03 Jun 2018 - 14:20

score 55 · Answer 5 · 2018-06-03 16:09:54

55

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Why does one take $\inf ||x-a||$ for $d(x,A)$?

Published on 03 Jun 2018 - 16:09

score 75 · Answer 6 · 2018-06-03 16:20:56

75

Views

$\inf_{n}( \log(a_n))=\log (\inf_{n} (a_n))\;?$

Published on 03 Jun 2018 - 16:20

score 438 · Answer 7 · 2018-06-05 19:31:25

438

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$\sup_{y \in Y} \inf_{x \in X}g(x,y) \leq \inf_{x \in X} \sup_{y \in Y} g(x,y)$

Published on 05 Jun 2018 - 19:31

score 170 · Answer 8 · 2018-06-06 15:50:24

170

Views

Least upper and greatest lower bounds

Published on 06 Jun 2018 - 15:50

score 71 · Answer 9 · 2018-06-08 12:29:15

71

Views

If $f:[0,\infty)\to\mathbb R$ is continuous and $\tau:=\inf\left\{t\ge0:|f|\ge\varepsilon\right\}\in(0,\infty)$, is $|f(\tau)|=\varepsilon$?

Published on 08 Jun 2018 - 12:29

score 121 · Answer 10 · 2026-02-23 02:57:43

121

Views

Uniform convergence and boundedness for the sequence of functions $\{f_{n}\}$

Published on 23 Feb 2026 - 2:57

score 50 · Answer 11 · 2018-06-09 11:05:07

50

Views

Calculate $\sup_{(a,b)\in B_2(0,1)}\left\{\max(|a|,|a+b|)\right\}$

Published on 09 Jun 2018 - 11:05

score 52 · Answer 12 · 2018-06-09 20:36:18

52

Views

Help on unit sphere with regards to supremum

Published on 09 Jun 2018 - 20:36

score 358 · Answer 13 · 2018-06-10 00:38:18

358

Views

Can you explain the intuition of Tom Apostol's proof of the Additive Property of sets?

Published on 10 Jun 2018 - 0:38

score 50 · Answer 14 · 2018-06-11 10:58:16

50

Views

$\sup_{(a,b)\in B_2(0,1)}\left\{\max(|a+2b|,|b+2a|)\right\}=2\sqrt{2}$?

Published on 11 Jun 2018 - 10:58

score 1.1k · Answer 15 · 2018-06-15 03:31:07

1.1k

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Showing that $\sup \{ x \in \mathbb{R} : x^2 < 2\} = \sqrt{2}$.

Published on 15 Jun 2018 - 3:31

List Question

Confusion regarding the proof of Theorem I.32 of Apostol's Calculus.

Supremum and Infimum of the given set

prove that every countable set $B$ , as $B\subseteq\mathbb{N^{\mathrm{\mathbb{N}}}}/R$ - has a supremum.

Supremum of the given set

Why does one take $\inf ||x-a||$ for $d(x,A)$?

$\inf_{n}( \log(a_n))=\log (\inf_{n} (a_n))\;?$

$\sup_{y \in Y} \inf_{x \in X}g(x,y) \leq \inf_{x \in X} \sup_{y \in Y} g(x,y)$

Least upper and greatest lower bounds

If $f:[0,\infty)\to\mathbb R$ is continuous and $\tau:=\inf\left\{t\ge0:|f|\ge\varepsilon\right\}\in(0,\infty)$, is $|f(\tau)|=\varepsilon$?

Uniform convergence and boundedness for the sequence of functions $\{f_{n}\}$

Calculate $\sup_{(a,b)\in B_2(0,1)}\left\{\max(|a|,|a+b|)\right\}$

Help on unit sphere with regards to supremum

Can you explain the intuition of Tom Apostol's proof of the Additive Property of sets?

$\sup_{(a,b)\in B_2(0,1)}\left\{\max(|a+2b|,|b+2a|)\right\}=2\sqrt{2}$?

Showing that $\sup \{ x \in \mathbb{R} : x^2 < 2\} = \sqrt{2}$.

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