Question

Every increasing and bounded from above sequence $(x_k)_{k \in \mathbb N}$ in $R$ has a supremum

score 77 · Answer 1 · 2019-08-26 20:10:20

77

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Every increasing and bounded from above sequence $(x_k)_{k \in \mathbb N}$ in $R$ has a supremum

Published on 26 Aug 2019 - 20:10

score 41 · Answer 2 · 2019-08-28 23:15:37

41

Views

Applying the definition of convergence for a sequence

Published on 28 Aug 2019 - 23:15

score 117 · Answer 3 · 2019-09-04 20:18:14

117

Views

Cauchy series:How to determine the convergence of the series?

Published on 04 Sep 2019 - 20:18

score 89 · Answer 4 · 2019-09-05 01:33:45

89

Views

Proof verification - Cauchy sequence

Published on 05 Sep 2019 - 1:33

score 74 · Answer 5 · 2019-09-05 05:19:06

74

Views

Show $\{x_n\}$ converges if $\left| x_{n+1}-x_n \right| \lt \left(\frac{3}{4}\right)^n \ \forall n \in \mathbb{N}$

Published on 05 Sep 2019 - 5:19

score 95 · Answer 6 · 2019-09-07 02:32:52

95

Views

Cauchy sequence less than a convergent series in a metric space $(X, d)$

Published on 07 Sep 2019 - 2:32

score 92 · Answer 7 · 2019-09-08 02:15:16

92

Views

Showing that $x_n = \frac{(-1)^n}{\sqrt{n}}$ is Cauchy

Published on 08 Sep 2019 - 2:15

score 105 · Answer 8 · 2019-09-10 07:43:47

105

Views

About subsequence of a Cauchy sequence

Published on 10 Sep 2019 - 7:43

score 514 · Answer 9 · 2019-09-11 01:45:44

514

Views

Show scalar multiplication sequence of a Cauchy sequence is also a Cauchy sequence.

Published on 11 Sep 2019 - 1:45

score 130 · Answer 10 · 2026-03-25 12:14:32

130

Views

Find a transfinite monotone subsequence.

Published on 25 Mar 2026 - 12:14

score 71 · Answer 11 · 2019-09-19 17:28:00

71

Views

Cauchy preserving implies continuity of function

Published on 19 Sep 2019 - 17:28

score 86 · Answer 12 · 2019-09-20 10:11:20

86

Views

${x_n}$ is a sequence such that $|x_{n+1} - x_n| \leq \frac{1}{2}|x_n - x_{n-1}|$. Prove $x_n$ is convergent.

Published on 20 Sep 2019 - 10:11

score 52 · Answer 13 · 2019-09-21 06:18:15

52

Views

How to prove $B_n$ is a cauchy sequence given $|B_n - B_{n-1}| < \frac{1}{n!}$

Published on 21 Sep 2019 - 6:18

score 87 · Answer 14 · 2019-09-21 22:26:23

87

Views

Cauchy sequences of real and rationals

Published on 21 Sep 2019 - 22:26

score 178 · Answer 15 · 2019-09-22 14:16:33

178

Views

Question about $l_\infty$ as a complete metric space

Published on 22 Sep 2019 - 14:16

List Question

Every increasing and bounded from above sequence $(x_k)_{k \in \mathbb N}$ in $R$ has a supremum

Applying the definition of convergence for a sequence

Cauchy series:How to determine the convergence of the series?

Proof verification - Cauchy sequence

Show $\{x_n\}$ converges if $\left| x_{n+1}-x_n \right| \lt \left(\frac{3}{4}\right)^n \ \forall n \in \mathbb{N}$

Cauchy sequence less than a convergent series in a metric space $(X, d)$

Showing that $x_n = \frac{(-1)^n}{\sqrt{n}}$ is Cauchy

About subsequence of a Cauchy sequence

Show scalar multiplication sequence of a Cauchy sequence is also a Cauchy sequence.

Find a transfinite monotone subsequence.

Cauchy preserving implies continuity of function

${x_n}$ is a sequence such that $|x_{n+1} - x_n| \leq \frac{1}{2}|x_n - x_{n-1}|$. Prove $x_n$ is convergent.

How to prove $B_n$ is a cauchy sequence given $|B_n - B_{n-1}| < \frac{1}{n!}$

Cauchy sequences of real and rationals

Question about $l_\infty$ as a complete metric space

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