List questions from cauchy-sequences

Published on 08 Mar 2026 - 21:11

363

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Prove the following statement about Cauchy sequences...

Published on 18 Mar 2026 - 23:55

165

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A peculiar characterization of open balls in a Banach space

Published on 03 Mar 2026 - 3:36

146

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Completion of a metric space $\mathbb{R}$ with a special metric

Published on 19 Mar 2026 - 0:00

56

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Show that the interest rate sequence is Cauchy

Published on 01 Apr 2026 - 12:41

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$C[0,1]$ with $L^1$ norm is not Banach space.

Published on 18 Mar 2026 - 23:47

3.7k

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Can a sequence converge but be not Cauchy? Any examples?

Published on 18 Mar 2026 - 23:47

148

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Proving $\lim_{n \to \infty} \frac{n}{4^n}=0$

Published on 18 Oct 2015 - 3:18

58

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Show that $(3x_{n}+4y_{n})$ is also Cauchy sequence.

Published on 18 Oct 2015 - 15:17

135

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Closed Subset of $l^{1}$ Space

Published on 19 Oct 2015 - 4:04

493

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Show that the sequence $a_n=1+\frac1{\sqrt{2}} +\frac1{\sqrt{3}} + \dots + \frac1{\sqrt{n}}$ is not Cauchy

Published on 19 Oct 2015 - 17:03

345

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Is the alternating sequence Cauchy?

Published on 20 Oct 2015 - 0:01

87

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Product of "Non-Cauchy" and Cauchy Sequencs: Always Cauchy, Always "Non-Cauchy", Sometimes Cauchy?

Published on 20 Oct 2015 - 0:23

224

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If $f$ is discontinuous only at certain points, does $f(\text{Cauchy})$ "kill" the Cauchy properties?

Published on 20 Oct 2015 - 1:32

164

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Understanding the proof for a sequence to be Cauchy

Published on 21 Oct 2015 - 7:32

List Question

Proving the nested interval theorem

Prove the following statement about Cauchy sequences...

A peculiar characterization of open balls in a Banach space

Completion of a metric space $\mathbb{R}$ with a special metric

Show that the interest rate sequence is Cauchy

$C[0,1]$ with $L^1$ norm is not Banach space.

Can a sequence converge but be not Cauchy? Any examples?

Proving $\lim_{n \to \infty} \frac{n}{4^n}=0$

Show that $(3x_{n}+4y_{n})$ is also Cauchy sequence.

Closed Subset of $l^{1}$ Space

Show that the sequence $a_n=1+\frac1{\sqrt{2}} +\frac1{\sqrt{3}} + \dots + \frac1{\sqrt{n}}$ is not Cauchy

Is the alternating sequence Cauchy?

Product of "Non-Cauchy" and Cauchy Sequencs: Always Cauchy, Always "Non-Cauchy", Sometimes Cauchy?

If $f$ is discontinuous only at certain points, does $f(\text{Cauchy})$ "kill" the Cauchy properties?

Understanding the proof for a sequence to be Cauchy

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