Question

Proof that subspace of $L^2\{\mathbb{R}\}$ is Hilbert space

score 153 · Answer 1 · 2021-11-07 20:51:42

153

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Proof that subspace of $L^2\{\mathbb{R}\}$ is Hilbert space

Published on 07 Nov 2021 - 20:51

score 168 · Answer 2 · 2021-11-09 16:29:22

168

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If $(f_n)$ is Cauchy and converges a.e. to $f$, there is a Cauchy subsequence $(f_{\psi (n), x})_n$ converging to $f_x$ in $\mathcal L_1$ and a.e.

Published on 09 Nov 2021 - 16:29

score 87 · Answer 3 · 2021-11-10 19:01:13

87

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If $\sum_n\|x_n-x_{n-1}\|^2<\infty$, is $(x_n)$ Cauchy?

Published on 10 Nov 2021 - 19:01

score 232 · Answer 4 · 2026-03-30 08:31:28

232

Views

$L^1_{loc}(\mathbb{R})$ is a Fréchet space

Published on 30 Mar 2026 - 8:31

score 46 · Answer 5 · 2021-11-15 01:00:53

46

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Question About Equivalence

Published on 15 Nov 2021 - 1:00

score 93 · Answer 6 · 2021-11-15 09:59:47

93

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$\text { Prove } u_{n}=\frac{\cos 5}{5}+\frac{\cos 5^{2}}{5^{2}}+\cdots+\frac{\cos 5^{n}}{5^{n}} \text { is convergent in } \mathbb{R} \text {. } $

Published on 15 Nov 2021 - 9:59

score 129 · Answer 7 · 2021-11-17 05:27:40

129

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If any two sequences converge to the same limit, prove they are concurrent.

Published on 17 Nov 2021 - 5:27

score 63 · Answer 8 · 2021-11-24 20:04:47

63

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Is this sequence Cauchy?

Published on 24 Nov 2021 - 20:04

score 52 · Answer 9 · 2026-04-05 20:14:27

52

Views

Shortcut to recognize a cauchy sequence?

Published on 05 Apr 2026 - 20:14

score 102 · Answer 10 · 2021-11-27 03:45:17

102

Views

Let the sequence $\{a_n\}$ be defined as $a_1=1$ and $a_{n+1} = \frac{6a_n+3}{a_n+4}$. Show that $a_n \lt 3$ and the sequence is increasing.

Published on 27 Nov 2021 - 3:45

score 226 · Answer 11 · 2021-11-28 22:52:02

226

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If the difference between two consecutive elements tends to 0, then the sequence converges? Mistake in proof

Published on 28 Nov 2021 - 22:52

score 40 · Answer 12 · 2021-11-29 19:08:12

40

Views

Understanding the class of all convergent sequences in a discrete space.

Published on 29 Nov 2021 - 19:08

score 96 · Answer 13 · 2021-12-01 05:38:07

96

Views

Proof that sequence is a Cauchy sequence.

Published on 01 Dec 2021 - 5:38

score 128 · Answer 14 · 2021-12-01 18:46:55

128

Views

Sow that if $\mathcal{H}$ is not finite-dimensional, then there exists a sequence in $B$ that does not have a convergent subsequence.

Published on 01 Dec 2021 - 18:46

score 82 · Answer 15 · 2021-12-01 19:46:26

82

Views

Prove that the metric space is Cauchy: $d(x,y)=|\frac{x}{3+x}-\frac{y}{3+y}|$

Published on 01 Dec 2021 - 19:46

List Question

Proof that subspace of $L^2\{\mathbb{R}\}$ is Hilbert space

If $(f_n)$ is Cauchy and converges a.e. to $f$, there is a Cauchy subsequence $(f_{\psi (n), x})_n$ converging to $f_x$ in $\mathcal L_1$ and a.e.

If $\sum_n\|x_n-x_{n-1}\|^2<\infty$, is $(x_n)$ Cauchy?

$L^1_{loc}(\mathbb{R})$ is a Fréchet space

Question About Equivalence

$\text { Prove } u_{n}=\frac{\cos 5}{5}+\frac{\cos 5^{2}}{5^{2}}+\cdots+\frac{\cos 5^{n}}{5^{n}} \text { is convergent in } \mathbb{R} \text {. } $

If any two sequences converge to the same limit, prove they are concurrent.

Is this sequence Cauchy?

Shortcut to recognize a cauchy sequence?

Let the sequence $\{a_n\}$ be defined as $a_1=1$ and $a_{n+1} = \frac{6a_n+3}{a_n+4}$. Show that $a_n \lt 3$ and the sequence is increasing.

If the difference between two consecutive elements tends to 0, then the sequence converges? Mistake in proof

Understanding the class of all convergent sequences in a discrete space.

Proof that sequence is a Cauchy sequence.

Sow that if $\mathcal{H}$ is not finite-dimensional, then there exists a sequence in $B$ that does not have a convergent subsequence.

Prove that the metric space is Cauchy: $d(x,y)=|\frac{x}{3+x}-\frac{y}{3+y}|$

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