Question

Prove that $\liminf x_n \le \liminf a_n \le \limsup a_n \le \limsup x_n$

score 740 · Answer 1 · 2016-11-04 13:51:30

740

Views

Prove that $\liminf x_n \le \liminf a_n \le \limsup a_n \le \limsup x_n$

Published on 04 Nov 2016 - 13:51

score 341 · Answer 2 · 2016-11-04 15:18:08

341

Views

$\limsup \cos(\frac{n\pi}{60})$

Published on 04 Nov 2016 - 15:18

score 103 · Answer 3 · 2026-02-24 13:49:05

103

Views

Show mean of a sequence of sets is zero but mean of countably infinite set is infinity if increasing

Published on 24 Feb 2026 - 13:49

score 829 · Answer 4 · 2016-11-06 08:29:01

829

Views

Supremum/Infimum with an inequality subscript

Published on 06 Nov 2016 - 8:29

score 68 · Answer 5 · 2016-11-06 17:42:18

68

Views

Prove if $\{s_n\}$ is monotonically increasing. Then $\{s_n\}$ converges if and only if it is bounded.

Published on 06 Nov 2016 - 17:42

score 47 · Answer 6 · 2016-11-06 23:38:27

47

Views

Trouble Understanding Limit Surperior

Published on 06 Nov 2016 - 23:38

score 70 · Answer 7 · 2016-11-09 05:49:03

70

Views

Product of $\limsup_{x\to\infty} x_n $

Published on 09 Nov 2016 - 5:49

score 539 · Answer 8 · 2016-11-12 20:35:27

539

Views

Proof for sequences: $\limsup_{n \to \infty}(b_n - a_n) \le \limsup_{n \to \infty}{b_n} - \liminf_{n \to \infty}{a_n}$

Published on 12 Nov 2016 - 20:35

score 88 · Answer 9 · 2016-11-13 03:49:15

88

Views

Is this proof correct: $\liminf {\frac{\sin(\frac{\pi n}{8})n^n}{n!}} = 0$?

Published on 13 Nov 2016 - 3:49

score 107 · Answer 10 · 2016-11-13 22:17:43

107

Views

Is it true that $ \left\{{\inf\limits_{n \in \mathbb N}}{h_n} \leq c \right\} = \bigcup_\limits{n=1}^{\infty} \left\{ h_n \leq c \right\} $?

Published on 13 Nov 2016 - 22:17

score 739 · Answer 11 · 2016-11-15 19:09:10

739

Views

Supremum of $\sqrt{n} -\left\lfloor\sqrt{n}\right\rfloor $

Published on 15 Nov 2016 - 19:09

score 34 · Answer 12 · 2016-11-18 14:50:34

34

Views

Meaning of $\sup_{g \in G} \inf_{f \in F} \| f - g \|$ where $F$ and $G$ are functional spaces

Published on 18 Nov 2016 - 14:50

score 38 · Answer 13 · 2016-11-19 14:21:39

38

Views

Compute $\liminf_{n\to \infty }n^{1/3}\max\{X_n,X_{n+1},X_{n+2}\}$ and $\liminf_{n\to \infty }\log(n)n^{1/3}\max\{X_n,X_{n+1},X_{n+2}\}$

Published on 19 Nov 2016 - 14:21

score 684 · Answer 14 · 2016-11-19 16:10:20

684

Views

Show that a subset of an ordered set has at most one smallest element and at most one largest element

Published on 19 Nov 2016 - 16:10

score 377 · Answer 15 · 2016-11-20 02:05:29

377

Views

Proof that $\limsup\limits_{n \to \infty}{a_n} = \lim_{N \to \infty} \sup{\{a_n: n \ge N\}}$

Published on 20 Nov 2016 - 2:05

List Question

Prove that $\liminf x_n \le \liminf a_n \le \limsup a_n \le \limsup x_n$

$\limsup \cos(\frac{n\pi}{60})$

Show mean of a sequence of sets is zero but mean of countably infinite set is infinity if increasing

Supremum/Infimum with an inequality subscript

Prove if $\{s_n\}$ is monotonically increasing. Then $\{s_n\}$ converges if and only if it is bounded.

Trouble Understanding Limit Surperior

Product of $\limsup_{x\to\infty} x_n $

Proof for sequences: $\limsup_{n \to \infty}(b_n - a_n) \le \limsup_{n \to \infty}{b_n} - \liminf_{n \to \infty}{a_n}$

Is this proof correct: $\liminf {\frac{\sin(\frac{\pi n}{8})n^n}{n!}} = 0$?

Is it true that $ \left\{{\inf\limits_{n \in \mathbb N}}{h_n} \leq c \right\} = \bigcup_\limits{n=1}^{\infty} \left\{ h_n \leq c \right\} $?

Supremum of $\sqrt{n} -\left\lfloor\sqrt{n}\right\rfloor $

Meaning of $\sup_{g \in G} \inf_{f \in F} \| f - g \|$ where $F$ and $G$ are functional spaces

Compute $\liminf_{n\to \infty }n^{1/3}\max\{X_n,X_{n+1},X_{n+2}\}$ and $\liminf_{n\to \infty }\log(n)n^{1/3}\max\{X_n,X_{n+1},X_{n+2}\}$

Show that a subset of an ordered set has at most one smallest element and at most one largest element

Proof that $\limsup\limits_{n \to \infty}{a_n} = \lim_{N \to \infty} \sup{\{a_n: n \ge N\}}$

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