Question

Closure and Subsets of Normed Vector Spaces

score 392 · Answer 1 · 2026-03-22 17:13:45

392

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Closure and Subsets of Normed Vector Spaces

Published on 22 Mar 2026 - 17:13

score 1.2k · Answer 2 · 2026-03-22 12:55:41

1.2k

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Proof check - If two sequences A and B are equivalent, then the first one is a Cauchy sequence if and only if the second one is a Cauchy sequence too

Published on 22 Mar 2026 - 12:55

score 72 · Answer 3 · 2026-03-20 10:49:40

72

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Proof check - The multiplication of two real numbers is a real number (Cauchy sequences)

Published on 20 Mar 2026 - 10:49

score 138 · Answer 4 · 2026-03-20 21:50:32

138

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If $\|x_k - x_{k-1}\| \le \frac{1} {k^2}$, what is the limit of $\lim_{k \to \infty} (k x_k - (k-1) x_{k-1})$?

Published on 20 Mar 2026 - 21:50

score 87 · Answer 5 · 2026-03-20 06:37:05

87

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Prove that $f$ has a fixed-point $x_0$ with $x_0 > 0$

Published on 20 Mar 2026 - 6:37

score 1.1k · Answer 6 · 2026-03-20 08:30:50

1.1k

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Proving that the sequence $\{\frac{3n+5}{2n+6}\}$ is Cauchy.

Published on 20 Mar 2026 - 8:30

score 108 · Answer 7 · 2026-03-22 10:40:00

108

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Why can't all pointwise continuous functions preserve Cauchy sequences?

Published on 22 Mar 2026 - 10:40

score 168 · Answer 8 · 2026-03-20 22:32:36

168

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Proving that sequence with given criteria is Cauchy?

Published on 20 Mar 2026 - 22:32

score 119 · Answer 9 · 2026-03-20 06:38:12

119

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Determining whether sequence $a_n=\sum_{k=1}^n\frac n{n^2+k}$ is convergent or not.

Published on 20 Mar 2026 - 6:38

score 271 · Answer 10 · 2026-03-24 03:28:43

How does the Cauchy criterion for double series imply that the comparison test can be applied to double series if the terms are nonnegative?

score 120 · Answer 11 · 2026-03-22 13:24:43

120

Views

Understanding Uniformly Cauchy

Published on 22 Mar 2026 - 13:24

score 47 · Answer 12 · 2026-03-17 13:22:03

47

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Purpose of separating cauchy and convergent sequences

Published on 17 Mar 2026 - 13:22

score 5.1k · Answer 13 · 2026-03-17 09:51:59

5.1k

Views

Showing that a totally bounded set is relatively compact (closure is compact)

Published on 17 Mar 2026 - 9:51

score 50 · Answer 14 · 2026-03-17 11:01:15

50

Views

Proving by definition that sequence is Cauchy

Published on 17 Mar 2026 - 11:01

score 126 · Answer 15 · 2026-03-17 09:41:26

126

Views

Understanding why $\mathbb{R}^2$ is complete

Published on 17 Mar 2026 - 9:41

List Question

Closure and Subsets of Normed Vector Spaces

Proof check - If two sequences A and B are equivalent, then the first one is a Cauchy sequence if and only if the second one is a Cauchy sequence too

Proof check - The multiplication of two real numbers is a real number (Cauchy sequences)

If $\|x_k - x_{k-1}\| \le \frac{1} {k^2}$, what is the limit of $\lim_{k \to \infty} (k x_k - (k-1) x_{k-1})$?

Prove that $f$ has a fixed-point $x_0$ with $x_0 > 0$

Proving that the sequence $\{\frac{3n+5}{2n+6}\}$ is Cauchy.

Why can't all pointwise continuous functions preserve Cauchy sequences?

Proving that sequence with given criteria is Cauchy?

Determining whether sequence $a_n=\sum_{k=1}^n\frac n{n^2+k}$ is convergent or not.

How does the Cauchy criterion for double series imply that the comparison test can be applied to double series if the terms are nonnegative?

Understanding Uniformly Cauchy

Purpose of separating cauchy and convergent sequences

Showing that a totally bounded set is relatively compact (closure is compact)

Proving by definition that sequence is Cauchy

Understanding why $\mathbb{R}^2$ is complete

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