Question

Can we say that if a sequence in $(X,\frac d{1+d})$ is cauchy, then is also in $(X,d)$?

score 52 · Answer 1 · 2017-11-11 18:19:05

52

Views

Can we say that if a sequence in $(X,\frac d{1+d})$ is cauchy, then is also in $(X,d)$?

Published on 11 Nov 2017 - 18:19

score 102 · Answer 2 · 2017-11-13 10:05:11

102

Views

A confusion about the proof of "Every Cauchy sequence converges"

Published on 13 Nov 2017 - 10:05

score 30 · Answer 3 · 2017-11-14 21:50:23

30

Views

Prove that sequence $\frac{a_{n+1}}{a_n} \le r$ converges to $0$

Published on 14 Nov 2017 - 21:50

score 3.4k · Answer 4 · 2017-11-15 09:27:20

3.4k

Views

Does a continuous function take Cauchy sequences to Cauchy sequences?

Published on 15 Nov 2017 - 9:27

score 232 · Answer 5 · 2017-11-15 17:20:40

232

Views

Prove that this sequence is Cauchy

Published on 15 Nov 2017 - 17:20

score 49 · Answer 6 · 2026-03-29 08:35:37

49

Views

Do these objects keep their properties if we apply an homeomorphism on them: $(u_n)$ convergent, $(u_n)$ bounded, and $(u_n)$ Cauchy.

Published on 29 Mar 2026 - 8:35

score 77 · Answer 7 · 2026-04-03 18:12:14

77

Views

Cauchy's convergence test can I say that?

Published on 03 Apr 2026 - 18:12

score 137 · Answer 8 · 2017-11-20 22:15:42

137

Views

prove that $a_{n}$ converges using Cauchy's convergence test

Published on 20 Nov 2017 - 22:15

score 60 · Answer 9 · 2017-11-21 23:30:13

60

Views

prove that $\lim_{n\to \infty} a_{n}=$finite

Published on 21 Nov 2017 - 23:30

score 223 · Answer 10 · 2026-03-29 08:35:21

223

Views

Connected components of a metric space are complete subspaces.

Published on 29 Mar 2026 - 8:35

score 52 · Answer 11 · 2026-03-29 08:45:07

52

Views

Show if $(Y,\rho')$ is complete metric space then, so is $(X,\rho)$ if $f: X\rightarrow Y$ is continuous.

Published on 29 Mar 2026 - 8:45

score 233 · Answer 12 · 2017-11-23 20:33:15

233

Views

Proving a sequence is a Cauchy sequence from other theorems

Published on 23 Nov 2017 - 20:33

score 38 · Answer 13 · 2017-11-23 21:03:46

38

Views

Prove that ${\xi_i}$ is complete system in $l_2$

Published on 23 Nov 2017 - 21:03

score 418 · Answer 14 · 2017-11-24 11:34:58

418

Views

Sufficient condition that a sequence is a Cauchy sequence

Published on 24 Nov 2017 - 11:34

score 100 · Answer 15 · 2017-11-24 18:06:51

100

Views

Infinite number of terms of a Cauchy sequence in a union of disjoint closed sets

Published on 24 Nov 2017 - 18:06

List Question

Can we say that if a sequence in $(X,\frac d{1+d})$ is cauchy, then is also in $(X,d)$?

A confusion about the proof of "Every Cauchy sequence converges"

Prove that sequence $\frac{a_{n+1}}{a_n} \le r$ converges to $0$

Does a continuous function take Cauchy sequences to Cauchy sequences?

Prove that this sequence is Cauchy

Do these objects keep their properties if we apply an homeomorphism on them: $(u_n)$ convergent, $(u_n)$ bounded, and $(u_n)$ Cauchy.

Cauchy's convergence test can I say that?

prove that $a_{n}$ converges using Cauchy's convergence test

prove that $\lim_{n\to \infty} a_{n}=$finite

Connected components of a metric space are complete subspaces.

Show if $(Y,\rho')$ is complete metric space then, so is $(X,\rho)$ if $f: X\rightarrow Y$ is continuous.

Proving a sequence is a Cauchy sequence from other theorems

Prove that ${\xi_i}$ is complete system in $l_2$

Sufficient condition that a sequence is a Cauchy sequence

Infinite number of terms of a Cauchy sequence in a union of disjoint closed sets

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