Question

Prove sequence converges if $0 < a_{n+1} < a_n + \frac{1}{2^n}$

score 82 · Answer 1 · 2022-02-12 09:05:28

82

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Prove sequence converges if $0 < a_{n+1} < a_n + \frac{1}{2^n}$

Published on 12 Feb 2022 - 9:05

score 81 · Answer 2 · 2022-02-16 05:09:08

81

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Cantor intersection theorem holds iff $(X, d)$ is a complete metric space

Published on 16 Feb 2022 - 5:09

score 37 · Answer 3 · 2022-02-18 22:40:22

37

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Is this sequence Cauchy given this $\max$ norm?

Published on 18 Feb 2022 - 22:40

score 36 · Answer 4 · 2022-02-18 23:26:17

36

Views

Is this sequence Cauchy given this integral norm?

Published on 18 Feb 2022 - 23:26

score 180 · Answer 5 · 2026-03-26 14:33:03

180

Views

Numerical analysis bisection method sequence points inequality

Published on 26 Mar 2026 - 14:33

score 41 · Answer 6 · 2022-02-23 10:42:40

41

Views

To what limit does this sequence converge to?

Published on 23 Feb 2022 - 10:42

score 118 · Answer 7 · 2022-03-04 19:00:39

118

Views

Proving space of polynomials is not complete with the integral metric. Problem with proving a sequence is Cauchy.

Published on 04 Mar 2022 - 19:00

score 31 · Answer 8 · 2022-03-07 13:33:19

31

Views

Continuity of the periodization of an integrable, vanishing and continuous function

Published on 07 Mar 2022 - 13:33

score 43 · Answer 9 · 2022-03-08 23:13:23

43

Views

A Cauchy Sequence is a Cauchy Sequence in a space iff is a Cauchy sequence in another space.

Published on 08 Mar 2022 - 23:13

score 179 · Answer 10 · 2026-03-30 11:58:18

179

Views

Show that $(Y,||\cdot||_Y)$ is a Banach space

Published on 30 Mar 2026 - 11:58

score 293 · Answer 11 · 2022-03-11 06:06:37

293

Views

For $C^1[a,b]$, define $||f||= ||f||_{sup}+||f'||_{sup}$. Prove that the norm is in fact a norm and that $C^1[a,b]$ is a complete normed linear space

Published on 11 Mar 2022 - 6:06

score 84 · Answer 12 · 2022-03-15 18:19:16

84

Views

Show that $X$ is Banach Space

Published on 15 Mar 2022 - 18:19

score 38 · Answer 13 · 2026-03-30 11:53:23

38

Views

Help understanding why this sequence converges

Published on 30 Mar 2026 - 11:53

score 111 · Answer 14 · 2022-03-27 19:15:38

111

Views

When a Pseudo-Cauchy sequence converges?

Published on 27 Mar 2022 - 19:15

score 52 · Answer 15 · 2022-03-28 17:39:27

52

Views

If $(f_n)_{n\in \mathbb{N}}$ is a Cauchy sequence of functions in a complete metric space, then does $\sup_{x\in X}d(f_n(x), f_m(x)) < \epsilon$ hold?

Published on 28 Mar 2022 - 17:39

List Question

Prove sequence converges if $0 < a_{n+1} < a_n + \frac{1}{2^n}$

Cantor intersection theorem holds iff $(X, d)$ is a complete metric space

Is this sequence Cauchy given this $\max$ norm?

Is this sequence Cauchy given this integral norm?

Numerical analysis bisection method sequence points inequality

To what limit does this sequence converge to?

Proving space of polynomials is not complete with the integral metric. Problem with proving a sequence is Cauchy.

Continuity of the periodization of an integrable, vanishing and continuous function

A Cauchy Sequence is a Cauchy Sequence in a space iff is a Cauchy sequence in another space.

Show that $(Y,||\cdot||_Y)$ is a Banach space

For $C^1[a,b]$, define $||f||= ||f||_{sup}+||f'||_{sup}$. Prove that the norm is in fact a norm and that $C^1[a,b]$ is a complete normed linear space

Show that $X$ is Banach Space

Help understanding why this sequence converges

When a Pseudo-Cauchy sequence converges?

If $(f_n)_{n\in \mathbb{N}}$ is a Cauchy sequence of functions in a complete metric space, then does $\sup_{x\in X}d(f_n(x), f_m(x)) < \epsilon$ hold?

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