Question

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

score 298 · Answer 1 · 2026-04-17 11:48:50

298

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

Published on 17 Apr 2026 - 11:48

score 202 · Answer 2 · 2026-04-16 04:33:22

202

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Supremum and Infimum of the given set

Published on 16 Apr 2026 - 4:33

score 53 · Answer 3 · 2026-04-16 06:11:12

53

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

Published on 16 Apr 2026 - 6:11

score 137 · Answer 4 · 2026-04-13 23:06:16

137

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Supremum of the given set

Published on 13 Apr 2026 - 23:06

score 58 · Answer 5 · 2026-04-10 18:06:19

58

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

Published on 10 Apr 2026 - 18:06

score 78 · Answer 6 · 2026-04-17 06:53:19

78

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

Published on 17 Apr 2026 - 6:53

score 440 · Answer 7 · 2026-04-16 03:31:25

440

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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 16 Apr 2026 - 3:31

score 173 · Answer 8 · 2026-04-14 06:49:39

173

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Least upper and greatest lower bounds

Published on 14 Apr 2026 - 6:49

score 74 · Answer 9 · 2026-04-14 18:48:08

74

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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 14 Apr 2026 - 18:48

score 124 · Answer 10 · 2026-04-17 07:06:07

124

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

Published on 17 Apr 2026 - 7:06

score 53 · Answer 11 · 2026-04-16 16:05:01

53

Views

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

Published on 16 Apr 2026 - 16:05

score 55 · Answer 12 · 2026-04-11 05:41:23

55

Views

Help on unit sphere with regards to supremum

Published on 11 Apr 2026 - 5:41

score 361 · Answer 13 · 2026-04-13 17:04:49

361

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

Published on 13 Apr 2026 - 17:04

score 53 · Answer 14 · 2026-04-16 20:08:02

53

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

Published on 16 Apr 2026 - 20:08

score 1.1k · Answer 15 · 2026-04-16 10:30:01

1.1k

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

Published on 16 Apr 2026 - 10:30

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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