Question

Let $s_{0}$ and $s_{1}$ be arbitrary and $s_{n+1}$=($s_{n} $+ $s_{n-1}$ ) /2 n>=1 show Cauchy

score 73 · Answer 1 · 2018-10-05 19:53:53

73

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Let $s_{0}$ and $s_{1}$ be arbitrary and $s_{n+1}$=($s_{n} $+ $s_{n-1}$ ) /2 n>=1 show Cauchy

Published on 05 Oct 2018 - 19:53

score 724 · Answer 2 · 2026-03-25 18:09:34

724

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Why can't completeness be defined on topological spaces without using metrics?

Published on 25 Mar 2026 - 18:09

score 295 · Answer 3 · 2026-03-25 18:08:14

295

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What sequences are Cauchy in all metrics for a given topology?

Published on 25 Mar 2026 - 18:08

score 187 · Answer 4 · 2018-10-07 10:41:11

187

Views

For a sequence, how should we check that the distance between two consecutive terms $a_{n+2}$ and $a_{n+1}$ is less than $a_{n+1}$ and $a_n$?

Published on 07 Oct 2018 - 10:41

score 23 · Answer 5 · 2018-10-07 15:08:03

23

Views

Clarification on how a particular space is defined

Published on 07 Oct 2018 - 15:08

score 112 · Answer 6 · 2018-10-08 10:58:18

112

Views

Cauchy sequences always have a largest or smallest element past an arbitrary index

Published on 08 Oct 2018 - 10:58

score 212 · Answer 7 · 2018-10-08 17:00:21

212

Views

Triangle Inequality for proving Cauchy Criterion for Series

Published on 08 Oct 2018 - 17:00

score 59 · Answer 8 · 2018-10-09 17:08:49

59

Views

proving limits of sequences using cauchy criterion

Published on 09 Oct 2018 - 17:08

score 80 · Answer 9 · 2026-03-25 18:09:33

80

Views

C($\mathbb{R}$) is complete under the discrete metric.

Published on 25 Mar 2026 - 18:09

score 85 · Answer 10 · 2018-10-13 22:42:59

85

Views

proving convergence by showing a sequence is Cauchy

Published on 13 Oct 2018 - 22:42

score 61 · Answer 11 · 2018-10-14 00:07:42

61

Views

Prove that the following set $A = \{x \in \mathbb{R} \setminus\mathbb{Q}\mid x^2 \leq \frac{1}{4} \} \subset \mathbb{R}$ is complete.

Published on 14 Oct 2018 - 0:07

score 95 · Answer 12 · 2018-10-14 21:07:03

95

Views

Prove the sequence is Cauchy

Published on 14 Oct 2018 - 21:07

score 1k · Answer 13 · 2018-10-14 22:13:48

1k

Views

Show that a recursive sequence $(x_n)$ is Cauchy

Published on 14 Oct 2018 - 22:13

score 155 · Answer 14 · 2018-10-14 23:01:59

155

Views

Understanding a Cauchy Sequence Proof

Published on 14 Oct 2018 - 23:01

score 249 · Answer 15 · 2018-10-15 01:33:04

249

Views

If $\sum x_n$ converges, is the even partial sums of the sequence squared Cauchy?

Published on 15 Oct 2018 - 1:33

List Question

Let $s_{0}$ and $s_{1}$ be arbitrary and $s_{n+1}$=($s_{n} $+ $s_{n-1}$ ) /2 n>=1 show Cauchy

Why can't completeness be defined on topological spaces without using metrics?

What sequences are Cauchy in all metrics for a given topology?

For a sequence, how should we check that the distance between two consecutive terms $a_{n+2}$ and $a_{n+1}$ is less than $a_{n+1}$ and $a_n$?

Clarification on how a particular space is defined

Cauchy sequences always have a largest or smallest element past an arbitrary index

Triangle Inequality for proving Cauchy Criterion for Series

proving limits of sequences using cauchy criterion

C($\mathbb{R}$) is complete under the discrete metric.

proving convergence by showing a sequence is Cauchy

Prove that the following set $A = \{x \in \mathbb{R} \setminus\mathbb{Q}\mid x^2 \leq \frac{1}{4} \} \subset \mathbb{R}$ is complete.

Prove the sequence is Cauchy

Show that a recursive sequence $(x_n)$ is Cauchy

Understanding a Cauchy Sequence Proof

If $\sum x_n$ converges, is the even partial sums of the sequence squared Cauchy?

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