Question

Cauchy sequence such that don't have limes in C[0,1]

score 81 · Answer 1 · 2014-05-26 18:56:40

81

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Cauchy sequence such that don't have limes in C[0,1]

Published on 26 May 2014 - 18:56

score 101 · Answer 2 · 2014-05-28 22:50:54

101

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Imaginary unit $i$ is not a limit of a real Cauchy sequence

Published on 28 May 2014 - 22:50

score 1.1k · Answer 3 · 2014-05-29 22:31:34

1.1k

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Let $V:= (C([0,1]),\|\cdot\|$) with $\|f\|:= \int_0^1|f(x)| \ dx$. Consider the function $f_n$ and show that V is not a Banach Space.

Published on 29 May 2014 - 22:31

score 55 · Answer 4 · 2014-06-01 14:37:25

55

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Convergence of series $\sum a_rb_r$

Published on 01 Jun 2014 - 14:37

score 227 · Answer 5 · 2014-06-10 04:58:41

227

Views

Completeness: Nets vs. Sequences

Published on 10 Jun 2014 - 4:58

score 147 · Answer 6 · 2014-06-16 03:38:22

147

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Let $a_n=\frac{a_{n-1}+a_{n-2}}{2}$ for each positive integer $n\geq 2$. Show that $\{a_n\}_{n=1}^{\infty}$ is Cauchy

Published on 16 Jun 2014 - 3:38

score 172 · Answer 7 · 2014-06-19 05:18:19

172

Views

Can I take Inverse Limits as Cauchy sequences literally?

Published on 19 Jun 2014 - 5:18

score 287 · Answer 8 · 2014-06-22 05:23:39

287

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Determine whether $f_n(x) = \frac {nx}{1+(nx)^2}$ is cauchy in $[ C^0([−1, 1], \mathbb {R} ), d_\infty]$

Published on 22 Jun 2014 - 5:23

score 49 · Answer 9 · 2014-06-22 08:22:13

49

Views

If $\{X_n\}$ is a Cauchy seq of r.vs a.s., then why does it converge to some r.v?

Published on 22 Jun 2014 - 8:22

score 4.7k · Answer 10 · 2026-03-26 06:29:12

4.7k

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Completeness of the set of convergent sequences

Published on 26 Mar 2026 - 6:29

score 1.1k · Answer 11 · 2014-07-04 15:41:48

1.1k

Views

Limit of $x_n = 0.5(x_{n-1} + x_{n-2})$ - help finishing proof...

Published on 04 Jul 2014 - 15:41

score 693 · Answer 12 · 2014-07-06 16:31:15

693

Views

Sequence of bounded linear operators implicating Cauchy sequence in $\mathbb K$

Published on 06 Jul 2014 - 16:31

score 157 · Answer 13 · 2014-07-07 01:05:25

157

Views

Prove $a_{n+1} = \frac{4+3 a_n}{3+2 a_n}$ is a Cauchy sequence

Published on 07 Jul 2014 - 1:05

score 538 · Answer 14 · 2014-07-07 13:45:56

538

Views

$\{a_n\}$ is a Cauchy sequence, if $a_{n+2} = \frac{a_n + a_{n+1}}{2}$

Published on 07 Jul 2014 - 13:45

score 83 · Answer 15 · 2014-07-12 18:19:48

83

Views

Proof sequence is cauchy

Published on 12 Jul 2014 - 18:19

List Question

Cauchy sequence such that don't have limes in C[0,1]

Imaginary unit $i$ is not a limit of a real Cauchy sequence

Let $V:= (C([0,1]),\|\cdot\|$) with $\|f\|:= \int_0^1|f(x)| \ dx$. Consider the function $f_n$ and show that V is not a Banach Space.

Convergence of series $\sum a_rb_r$

Completeness: Nets vs. Sequences

Let $a_n=\frac{a_{n-1}+a_{n-2}}{2}$ for each positive integer $n\geq 2$. Show that $\{a_n\}_{n=1}^{\infty}$ is Cauchy

Can I take Inverse Limits as Cauchy sequences literally?

Determine whether $f_n(x) = \frac {nx}{1+(nx)^2}$ is cauchy in $[ C^0([−1, 1], \mathbb {R} ), d_\infty]$

If $\{X_n\}$ is a Cauchy seq of r.vs a.s., then why does it converge to some r.v?

Completeness of the set of convergent sequences

Limit of $x_n = 0.5(x_{n-1} + x_{n-2})$ - help finishing proof...

Sequence of bounded linear operators implicating Cauchy sequence in $\mathbb K$

Prove $a_{n+1} = \frac{4+3 a_n}{3+2 a_n}$ is a Cauchy sequence

$\{a_n\}$ is a Cauchy sequence, if $a_{n+2} = \frac{a_n + a_{n+1}}{2}$

Proof sequence is cauchy

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