List questions from cauchy-sequences

Published on 24 Jul 2018 - 17:03

377

Views

When do we need to show a function is well-defined?

Published on 30 Jul 2018 - 6:06

378

Views

Centers of nested balls in a normed space make a Cauchy sequence.

Published on 31 Jul 2018 - 8:49

101

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floor of a Cauchy sequence is Cauchy?

Published on 31 Jul 2018 - 16:16

912

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Concerning the existence of a divergent monotone sequence with a Cauchy subsequence.

Published on 31 Jul 2018 - 18:00

219

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If a sequence is such that $a_n = \frac{a_{n-1}+a_{n-2}}{2}$, then find the limit of sequence

Published on 01 Aug 2018 - 12:27

107

Views

Will a “continuous” Cauchy sequence construction generate the real numbers?

Published on 01 Aug 2018 - 22:44

413

Views

If $(2x_{n+1}-x_n)$ converges to $x$, then show that $(x_n)$ converges to $x$.

Published on 05 Aug 2018 - 7:03

276

Views

Does $|x_n - x_m| \leq \frac 12 |x_{n-1} - x_{m-1}|$ imply $(x_n)$ is Cauchy?

Published on 05 Aug 2018 - 10:52

109

Views

Find non convergent Cauchy sequence

Published on 06 Aug 2018 - 15:49

938

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Why we define the completeness of a space by the converge of a Cauchy sequence rather than a normal sequence?

Published on 10 Aug 2018 - 3:51

209

Views

Show that $a_n = \frac{n}{2n+1}+\frac{1}{n^3}$ is a Cauchy Sequence

Published on 10 Aug 2018 - 6:04

52

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Prove that the limit function is discontinuous

Published on 13 Aug 2018 - 2:33

556

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Proof that real Cauchy sequences converge using the definitions only

Published on 15 Aug 2018 - 9:26

242

Views

Is this a valid convergence test (for sequences)?

Published on 23 Aug 2018 - 20:58

List Question

What do you call the algebraic structure physical space modeled after?

When do we need to show a function is well-defined?

Centers of nested balls in a normed space make a Cauchy sequence.

floor of a Cauchy sequence is Cauchy?

Concerning the existence of a divergent monotone sequence with a Cauchy subsequence.

If a sequence is such that $a_n = \frac{a_{n-1}+a_{n-2}}{2}$, then find the limit of sequence

Will a “continuous” Cauchy sequence construction generate the real numbers?

If $(2x_{n+1}-x_n)$ converges to $x$, then show that $(x_n)$ converges to $x$.

Does $|x_n - x_m| \leq \frac 12 |x_{n-1} - x_{m-1}|$ imply $(x_n)$ is Cauchy?

Find non convergent Cauchy sequence

Why we define the completeness of a space by the converge of a Cauchy sequence rather than a normal sequence?

Show that $a_n = \frac{n}{2n+1}+\frac{1}{n^3}$ is a Cauchy Sequence

Prove that the limit function is discontinuous

Proof that real Cauchy sequences converge using the definitions only

Is this a valid convergence test (for sequences)?

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