Question

Closure and Subsets of Normed Vector Spaces

score 415 · Answer 1 · 2026-05-06 04:31:47

415

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Closure and Subsets of Normed Vector Spaces

Published on 06 May 2026 - 4:31

score 1.2k · Answer 2 · 2026-05-07 10:11:31

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 07 May 2026 - 10:11

score 78 · Answer 3 · 2026-04-29 12:22:17

78

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

Published on 29 Apr 2026 - 12:22

score 145 · Answer 4 · 2026-04-29 12:22:30

145

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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 29 Apr 2026 - 12:22

score 93 · Answer 5 · 2026-04-29 12:22:16

93

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

Published on 29 Apr 2026 - 12:22

score 1.2k · Answer 6 · 2026-05-06 02:33:46

1.2k

Views

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

Published on 06 May 2026 - 2:33

score 116 · Answer 7 · 2026-05-10 09:30:16

116

Views

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

Published on 10 May 2026 - 9:30

score 174 · Answer 8 · 2026-04-29 12:22:17

174

Views

Proving that sequence with given criteria is Cauchy?

Published on 29 Apr 2026 - 12:22

score 125 · Answer 9 · 2026-04-29 12:22:30

125

Views

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

Published on 29 Apr 2026 - 12:22

score 281 · Answer 10 · 2026-05-10 12:50:53

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 130 · Answer 11 · 2026-05-10 11:25:07

130

Views

Understanding Uniformly Cauchy

Published on 10 May 2026 - 11:25

score 55 · Answer 12 · 2026-05-10 11:40:50

55

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Purpose of separating cauchy and convergent sequences

Published on 10 May 2026 - 11:40

score 5.1k · Answer 13 · 2026-05-10 11:41:15

5.1k

Views

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

Published on 10 May 2026 - 11:41

score 60 · Answer 14 · 2026-05-10 11:40:04

60

Views

Proving by definition that sequence is Cauchy

Published on 10 May 2026 - 11:40

score 134 · Answer 15 · 2026-05-10 11:38:59

134

Views

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

Published on 10 May 2026 - 11:38

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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