Question

Does all non-convergent sequences have this property?(does all non-convergent sequences oscillate between two fixed numbers?)

score 108 · Answer 1 · 2015-09-11 19:58:35

108

Views

Does all non-convergent sequences have this property?(does all non-convergent sequences oscillate between two fixed numbers?)

Published on 11 Sep 2015 - 19:58

score 101 · Answer 2 · 2015-09-15 06:34:57

101

Views

Is limsup ${x_n}$ real-valued on the space of bounded sequences?

Published on 15 Sep 2015 - 6:34

score 457 · Answer 3 · 2015-09-16 20:29:05

457

Views

Equivalence between two definitions for the limit of a sequence

Published on 16 Sep 2015 - 20:29

score 272 · Answer 4 · 2015-09-18 00:06:38

272

Views

Does average value always exist?

Published on 18 Sep 2015 - 0:06

score 153 · Answer 5 · 2015-09-18 00:51:26

153

Views

Inequality for Limit inferior

Published on 18 Sep 2015 - 0:51

score 236 · Answer 6 · 2015-09-19 01:28:07

236

Views

Let $A_n$ be a sequence of Events. Find the Lim Sup

Published on 19 Sep 2015 - 1:28

score 123 · Answer 7 · 2015-09-19 11:20:50

123

Views

$a_n\leq b_n$ for almost all $n\in\mathbb{N}\implies \limsup_n a_n\leq\limsup_n b_n$?

Published on 19 Sep 2015 - 11:20

score 240 · Answer 8 · 2015-09-20 22:36:40

240

Views

How to show that if a sequence of events converges, then the $\limsup$ and $\liminf$ must converge to the same limit?

Published on 20 Sep 2015 - 22:36

score 818 · Answer 9 · 2026-03-25 12:47:22

818

Views

Integrable slowly varying function

Published on 25 Mar 2026 - 12:47

score 736 · Answer 10 · 2015-09-22 20:11:36

736

Views

Show that lim inf $a_{n}$ $\leq$ lim sup $a_{n}$

Published on 22 Sep 2015 - 20:11

score 25 · Answer 11 · 2015-09-23 21:14:17

25

Views

Need help proving sequences involving inferiors

Published on 23 Sep 2015 - 21:14

score 95 · Answer 12 · 2015-09-24 15:40:13

95

Views

If $\{a_{n}\} \to \pm \infty$, then show that $\liminf a_{n} =\limsup a_{n} = \pm \infty$

Published on 24 Sep 2015 - 15:40

score 132 · Answer 13 · 2026-03-26 14:25:17

132

Views

Show the probability of liminfA is 1

Published on 26 Mar 2026 - 14:25

score 1.6k · Answer 14 · 2015-09-25 16:58:05

1.6k

Views

Show that the lim inf $\{a_n\}$ is the smallest cluster point

Published on 25 Sep 2015 - 16:58

score 1.8k · Answer 15 · 2015-09-29 02:44:53

1.8k

Views

Let $(s_n)$ be a sequence of nonnegative numbers, and $\sigma_n=\frac{1}{n}(s_1+s_2+\cdots +s_n)$. Show that $\liminf s_n \le \liminf \sigma_n$.

Published on 29 Sep 2015 - 2:44

List Question

Does all non-convergent sequences have this property?(does all non-convergent sequences oscillate between two fixed numbers?)

Is limsup ${x_n}$ real-valued on the space of bounded sequences?

Equivalence between two definitions for the limit of a sequence

Does average value always exist?

Inequality for Limit inferior

Let $A_n$ be a sequence of Events. Find the Lim Sup

$a_n\leq b_n$ for almost all $n\in\mathbb{N}\implies \limsup_n a_n\leq\limsup_n b_n$?

How to show that if a sequence of events converges, then the $\limsup$ and $\liminf$ must converge to the same limit?

Integrable slowly varying function

Show that lim inf $a_{n}$ $\leq$ lim sup $a_{n}$

Need help proving sequences involving inferiors

If $\{a_{n}\} \to \pm \infty$, then show that $\liminf a_{n} =\limsup a_{n} = \pm \infty$

Show the probability of liminfA is 1

Show that the lim inf $\{a_n\}$ is the smallest cluster point

Let $(s_n)$ be a sequence of nonnegative numbers, and $\sigma_n=\frac{1}{n}(s_1+s_2+\cdots +s_n)$. Show that $\liminf s_n \le \liminf \sigma_n$.

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