Question

Can someone verify if my proof is accurate?

score 44 · Answer 1 · 2024-02-21 05:07:56

44

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Can someone verify if my proof is accurate?

Published on 21 Feb 2024 - 5:07

score 169 · Answer 2 · 2024-03-01 08:13:20

169

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A question on a step in proving $L^\infty$ is complete.

Published on 01 Mar 2024 - 8:13

score 67 · Answer 3 · 2024-03-07 03:46:02

67

Views

Theorem 3.11 (c): Rudin's PMA

Published on 07 Mar 2024 - 3:46

score 83 · Answer 4 · 2024-03-09 10:28:32

83

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$\mathbb{Q}$ is dense in $K$ if each element in $K$ is the limit of a Cauchy sequence in $\mathbb{Q}$.

Published on 09 Mar 2024 - 10:28

score 27 · Answer 5 · 2026-02-23 07:22:31

27

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$A_n-A_{n-1} = q^nA_n-aq^{n-1}A_{n-1}$ for Cauchy sequence

Published on 23 Feb 2026 - 7:22

score 64 · Answer 6 · 2026-02-25 09:50:04

64

Views

How to correctly choose number for Cauchy sequence for infinitesimal functions? Will it be $x=y=[sin(t)]$ or $x=y=[t]$?

Published on 25 Feb 2026 - 9:50

score 56 · Answer 7 · 2026-03-29 13:39:16

56

Views

How is it possible that Cauchy sequence represents two different numbers?

Published on 29 Mar 2026 - 13:39

score 74 · Answer 8 · 2024-03-25 23:22:39

74

Views

Proposition 5.4.9. Analysis I - Terence Tao.

Published on 25 Mar 2024 - 23:22

score 25 · Answer 9 · 2026-02-25 00:13:34

25

Views

Show that the sequence $(f_n)_{n \in \mathbb{N}} \in (C^0([0,2]),||\cdot||_1)$, is a Cauchy-sequence, but does not converge

Published on 25 Feb 2026 - 0:13

score 384 · Answer 10 · 2015-01-03 14:50:08

384

Views

Is being a Cauchy sequence equivalent to $ \lim_{n\to+\infty}d(x_{n+k},x_n)=0$ for every $k$?

Published on 03 Jan 2015 - 14:50

score 119 · Answer 11 · 2015-01-04 07:40:48

119

Views

Cauchy Continuous function is continuous??

Published on 04 Jan 2015 - 7:40

score 70 · Answer 12 · 2015-01-07 15:45:29

70

Views

Showing that sequence is convergent by proving it is Cauchy sequence

Published on 07 Jan 2015 - 15:45

score 72 · Answer 13 · 2015-01-13 14:06:53

72

Views

Convergence of a sequence given by recursive relation

Published on 13 Jan 2015 - 14:06

score 282 · Answer 14 · 2015-01-15 11:58:57

282

Views

My proof of: Every convergent real sequence is a Cauchy sequence.

Published on 15 Jan 2015 - 11:58

score 109 · Answer 15 · 2015-01-17 06:15:21

109

Views

Is the projection of a cauchy sequence in a normed finite dimensional vector space along some subspace also cauchy?

Published on 17 Jan 2015 - 6:15

List Question

Can someone verify if my proof is accurate?

A question on a step in proving $L^\infty$ is complete.

Theorem 3.11 (c): Rudin's PMA

$\mathbb{Q}$ is dense in $K$ if each element in $K$ is the limit of a Cauchy sequence in $\mathbb{Q}$.

$A_n-A_{n-1} = q^nA_n-aq^{n-1}A_{n-1}$ for Cauchy sequence

How to correctly choose number for Cauchy sequence for infinitesimal functions? Will it be $x=y=[sin(t)]$ or $x=y=[t]$?

How is it possible that Cauchy sequence represents two different numbers?

Proposition 5.4.9. Analysis I - Terence Tao.

Show that the sequence $(f_n)_{n \in \mathbb{N}} \in (C^0([0,2]),||\cdot||_1)$, is a Cauchy-sequence, but does not converge

Is being a Cauchy sequence equivalent to $ \lim_{n\to+\infty}d(x_{n+k},x_n)=0$ for every $k$?

Cauchy Continuous function is continuous??

Showing that sequence is convergent by proving it is Cauchy sequence

Convergence of a sequence given by recursive relation

My proof of: Every convergent real sequence is a Cauchy sequence.

Is the projection of a cauchy sequence in a normed finite dimensional vector space along some subspace also cauchy?

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