Question

Filter, dual ideal,definition of $\liminf_I \lambda$

score 71 · Answer 1 · 2026-03-28 05:21:48

71

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Filter, dual ideal,definition of $\liminf_I \lambda$

Published on 28 Mar 2026 - 5:21

score 45 · Answer 2 · 2015-05-28 19:40:19

45

Views

Limit superior and inferior of a sequence that satisfies the asymptotic formula $\sum\limits_{n\leq x} a_n \sim x $

Published on 28 May 2015 - 19:40

score 54 · Answer 3 · 2015-05-29 06:33:13

54

Views

Yes or No: The following $\infty\triangleq\sup{\mathbb{R}}$ and $-\infty\triangleq \inf\mathbb{R}$ holds

Published on 29 May 2015 - 6:33

score 52 · Answer 4 · 2015-06-02 10:33:44

52

Views

When working with the limites inferior and superior, how do you procede?

Published on 02 Jun 2015 - 10:33

score 64 · Answer 5 · 2015-06-02 14:01:01

64

Views

If $a_n \geq b_n$, $b_n \leq |c_n|$ with $c_n \to 0$, does this imply $\liminf a_n \geq 0?$

Published on 02 Jun 2015 - 14:01

score 63 · Answer 6 · 2015-06-04 09:18:25

63

Views

Asymptotic sums and liminf

Published on 04 Jun 2015 - 9:18

score 64 · Answer 7 · 2015-06-04 17:52:57

64

Views

My attempt at finding $\underline{\lim_{n \to \infty}}A_n$ and $\overline{\lim_{n \to \infty}}A_n$ $A_n=B$ for $n$ even; $A_n=C$ for $n$ odd.

Published on 04 Jun 2015 - 17:52

score 132 · Answer 8 · 2015-06-05 14:54:27

132

Views

Find $\liminf\limits_{n\to\infty} (x_{n})$ and $\limsup\limits_{n\to\infty}(x_{n})$ for a sequence $x_{n}=1-n\sin\frac{n\pi}{4}$

Published on 05 Jun 2015 - 14:54

score 75 · Answer 9 · 2015-06-06 17:54:34

75

Views

Let $ f:I \to \mathbb{R} , I=(0,1) $ be uniformly continuous. Then exists $ \lim_{n\to\infty} f(\frac{1}{n}) $

Published on 06 Jun 2015 - 17:54

score 79 · Answer 10 · 2015-06-08 10:40:39

79

Views

(analysis) sequence a(n) is bounbed and sequence b(n) converges. Show that a(n)≤b(n) (∀ n ∈ ℕ) ⇒lim supa(n)≤lim b(n)

Published on 08 Jun 2015 - 10:40

score 263 · Answer 11 · 2015-06-15 17:07:31

263

Views

Is there any connection between these two limsup definitions?

Published on 15 Jun 2015 - 17:07

score 223 · Answer 12 · 2015-06-16 18:48:04

223

Views

Do we need to have a subsequence such that $\lim_{k\to\infty}\left\|x_{n_k}\right\|=\liminf_{n\to\infty}\left\|x_n\right\|$?

Published on 16 Jun 2015 - 18:48

score 169 · Answer 13 · 2015-06-25 04:41:57

169

Views

proof that $\limsup a_n=\sup\{a_n,a_{n+1},...\}$

Published on 25 Jun 2015 - 4:41

score 69 · Answer 14 · 2015-06-25 17:56:03

69

Views

What is bigger, $\liminf $ or $\inf ( \liminf )$

Published on 25 Jun 2015 - 17:56

score 150 · Answer 15 · 2026-03-26 16:09:52

150

Views

$P\left(\limsup \left(X_n=0, X_ {n+1}=1,X_ {n+2}=0 \right)\right)$

Published on 26 Mar 2026 - 16:09

List Question

Filter, dual ideal,definition of $\liminf_I \lambda$

Limit superior and inferior of a sequence that satisfies the asymptotic formula $\sum\limits_{n\leq x} a_n \sim x $

Yes or No: The following $\infty\triangleq\sup{\mathbb{R}}$ and $-\infty\triangleq \inf\mathbb{R}$ holds

When working with the limites inferior and superior, how do you procede?

If $a_n \geq b_n$, $b_n \leq |c_n|$ with $c_n \to 0$, does this imply $\liminf a_n \geq 0?$

Asymptotic sums and liminf

My attempt at finding $\underline{\lim_{n \to \infty}}A_n$ and $\overline{\lim_{n \to \infty}}A_n$ $A_n=B$ for $n$ even; $A_n=C$ for $n$ odd.

Find $\liminf\limits_{n\to\infty} (x_{n})$ and $\limsup\limits_{n\to\infty}(x_{n})$ for a sequence $x_{n}=1-n\sin\frac{n\pi}{4}$

Let $ f:I \to \mathbb{R} , I=(0,1) $ be uniformly continuous. Then exists $ \lim_{n\to\infty} f(\frac{1}{n}) $

(analysis) sequence a(n) is bounbed and sequence b(n) converges. Show that a(n)≤b(n) (∀ n ∈ ℕ) ⇒lim supa(n)≤lim b(n)

Is there any connection between these two limsup definitions?

Do we need to have a subsequence such that $\lim_{k\to\infty}\left\|x_{n_k}\right\|=\liminf_{n\to\infty}\left\|x_n\right\|$?

proof that $\limsup a_n=\sup\{a_n,a_{n+1},...\}$

What is bigger, $\liminf $ or $\inf ( \liminf )$

$P\left(\limsup \left(X_n=0, X_ {n+1}=1,X_ {n+2}=0 \right)\right)$

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