Question

Let $f_n \in L_p(X, \mathbb{X}, \mu)$, $1 \leq p < \infty$, and let $\beta _n$ defined for $E \in \mathbb{X}$ by

score 428 · Answer 1 · 2018-10-15 21:04:39

428

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Let $f_n \in L_p(X, \mathbb{X}, \mu)$, $1 \leq p < \infty$, and let $\beta _n$ defined for $E \in \mathbb{X}$ by

Published on 15 Oct 2018 - 21:04

score 71 · Answer 2 · 2018-10-19 23:57:58

71

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Question about Cauchy sequences are convergent in $\mathbb{R}^k$

Published on 19 Oct 2018 - 23:57

score 143 · Answer 3 · 2018-10-20 17:27:52

143

Views

Convergence of recursive sequence involving cosine

Published on 20 Oct 2018 - 17:27

score 722 · Answer 4 · 2018-10-21 01:24:54

722

Views

Let $(x_n)$ be Cauchy with a subsequence $(x_{n_k})$ such that $\lim_{k\to\infty} (x_{n_k}) = a$. Show that $\lim_{n\to\infty} (x_{n}) = a$

Published on 21 Oct 2018 - 1:24

score 1.1k · Answer 5 · 2018-10-21 02:25:52

1.1k

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Let $(a_n)$ be a sequence such that $\lim_{N\rightarrow \infty} \sum_{n=1}^N |a_n - a_{n+1}| < \infty$. Show that $(a_n)$ is Cauchy.

Published on 21 Oct 2018 - 2:25

score 255 · Answer 6 · 2018-10-21 03:59:15

255

Views

$\sum_{n=1}^{\infty} \left\{ e-(1+\frac{1}{n})^n \right\}$. is this converge or diverge

Published on 21 Oct 2018 - 3:59

score 102 · Answer 7 · 2018-10-23 01:25:57

102

Views

Find a divergent sequence whose distance lessens with each subsequent term

Published on 23 Oct 2018 - 1:25

score 173 · Answer 8 · 2018-10-24 08:29:28

173

Views

Equivalent statement on Cauchy sequence

Published on 24 Oct 2018 - 8:29

score 310 · Answer 9 · 2018-10-24 22:43:17

310

Views

If f is a uniform continuous function on (a,b), then f is bounded on (a,b).

Published on 24 Oct 2018 - 22:43

score 244 · Answer 10 · 2026-03-25 18:14:33

244

Views

If (X,d) is a metric space and $K \subseteq X$ is compact. Show that $K$ is complete.

Published on 25 Mar 2026 - 18:14

score 2.9k · Answer 11 · 2026-03-25 18:09:34

2.9k

Views

Prove $(l^{\infty},d_{\infty})$ is complete (metric space)

Published on 25 Mar 2026 - 18:09

score 384 · Answer 12 · 2018-10-25 22:07:17

384

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Show that $C^1[a,b]$ with the uniform norm is not a Banach space

Published on 25 Oct 2018 - 22:07

score 630 · Answer 13 · 2018-10-26 20:21:49

630

Views

How to show that $C_0 (U) $ is a Banach space

Published on 26 Oct 2018 - 20:21

score 78 · Answer 14 · 2018-10-27 21:37:52

78

Views

Proof that in Сauchy metric space the union of a sequence of closed sets with no internal points has no internal points

Published on 27 Oct 2018 - 21:37

score 104 · Answer 15 · 2018-11-04 15:59:49

104

Views

Use Cauchy Criterion to prove that $1+\frac{2^2}{2!}+\frac{2^3}{3!}+\cdots+\frac{2^n}{n!}$ converges

Published on 04 Nov 2018 - 15:59

List Question

Let $f_n \in L_p(X, \mathbb{X}, \mu)$, $1 \leq p < \infty$, and let $\beta _n$ defined for $E \in \mathbb{X}$ by

Question about Cauchy sequences are convergent in $\mathbb{R}^k$

Convergence of recursive sequence involving cosine

Let $(x_n)$ be Cauchy with a subsequence $(x_{n_k})$ such that $\lim_{k\to\infty} (x_{n_k}) = a$. Show that $\lim_{n\to\infty} (x_{n}) = a$

Let $(a_n)$ be a sequence such that $\lim_{N\rightarrow \infty} \sum_{n=1}^N |a_n - a_{n+1}| < \infty$. Show that $(a_n)$ is Cauchy.

$\sum_{n=1}^{\infty} \left\{ e-(1+\frac{1}{n})^n \right\}$. is this converge or diverge

Find a divergent sequence whose distance lessens with each subsequent term

Equivalent statement on Cauchy sequence

If f is a uniform continuous function on (a,b), then f is bounded on (a,b).

If (X,d) is a metric space and $K \subseteq X$ is compact. Show that $K$ is complete.

Prove $(l^{\infty},d_{\infty})$ is complete (metric space)

Show that $C^1[a,b]$ with the uniform norm is not a Banach space

How to show that $C_0 (U) $ is a Banach space

Proof that in Сauchy metric space the union of a sequence of closed sets with no internal points has no internal points

Use Cauchy Criterion to prove that $1+\frac{2^2}{2!}+\frac{2^3}{3!}+\cdots+\frac{2^n}{n!}$ converges

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