Question

Does $ a_{\lfloor n + \sqrt{n/2}\rfloor} \le a_n\left(1 + \frac{b}{n^{\frac{1}{2}+\varepsilon}}\right) $ imply that $a_n$ is bounded?

score 122 · Answer 1 · 2021-07-12 07:38:33

122

Views

Does $ a_{\lfloor n + \sqrt{n/2}\rfloor} \le a_n\left(1 + \frac{b}{n^{\frac{1}{2}+\varepsilon}}\right) $ imply that $a_n$ is bounded?

Published on 12 Jul 2021 - 7:38

score 87 · Answer 2 · 2021-07-15 16:11:40

87

Views

Subsequence theorem: Typo in textbook proof or my mistake?

Published on 15 Jul 2021 - 16:11

score 127 · Answer 3 · 2021-07-17 18:58:44

127

Views

$\liminf s_n = \limsup s_n = +\infty$ implies that the limit of the sequence is also $+\infty$

Published on 17 Jul 2021 - 18:58

score 36 · Answer 4 · 2021-07-22 15:05:13

36

Views

some confusion of limsup and its connection with limit points and subsequential limits

Published on 22 Jul 2021 - 15:05

score 496 · Answer 5 · 2026-02-23 23:51:39

496

Views

A continuous, convex functional on a Banach space is weakly lower semicontinuous

Published on 23 Feb 2026 - 23:51

score 291 · Answer 6 · 2021-07-22 19:20:12

291

Views

Show that the $\limsup$ is the supremum of the set of limit points

Published on 22 Jul 2021 - 19:20

score 83 · Answer 7 · 2026-04-01 09:10:03

83

Views

Limit of characteristic functions $1_{A_n} $ its the characteristic function of the limit $1_{\lim A_n}$

Published on 01 Apr 2026 - 9:10

score 106 · Answer 8 · 2021-07-28 16:51:17

106

Views

Prove that, for two sequences, lim inf s_n<lim t_n

Published on 28 Jul 2021 - 16:51

score 22 · Answer 9 · 2021-08-03 09:28:09

22

Views

Meaning of $\limsup_{j,k\to \infty}\, \lvert \lvert u_{m_j} - u_{m_k} \rvert\rvert_{L^q(V)}\leq \delta$

Published on 03 Aug 2021 - 9:28

score 294 · Answer 10 · 2021-08-09 17:46:21

294

Views

Show that $\liminf a_n$ and $\limsup b_n$ are finite

Published on 09 Aug 2021 - 17:46

score 16 · Answer 11 · 2026-03-07 15:14:32

16

Views

Show that $\limsup_{t\to T_0-}\left\|u(t,\;\cdot\;)\right\|_\infty<\infty$ is not possible here

Published on 07 Mar 2026 - 15:14

score 147 · Answer 12 · 2021-08-12 16:09:18

147

Views

What does $\liminf_{x\to0+}-\frac{f'(x)}x>0$ informally mean?

Published on 12 Aug 2021 - 16:09

score 100 · Answer 13 · 2021-08-30 19:38:22

100

Views

Probability of $\limsup[X_n \geq n]$

Published on 30 Aug 2021 - 19:38

score 45 · Answer 14 · 2021-08-31 01:06:26

45

Views

About $\liminf$ for functions. Why this statement holds?

Published on 31 Aug 2021 - 1:06

score 63 · Answer 15 · 2021-09-09 11:01:17

63

Views

Relevance of the deduction of similar theorems than Maier's theorem for other constellations of primes

Published on 09 Sep 2021 - 11:01

List Question

Does $ a_{\lfloor n + \sqrt{n/2}\rfloor} \le a_n\left(1 + \frac{b}{n^{\frac{1}{2}+\varepsilon}}\right) $ imply that $a_n$ is bounded?

Subsequence theorem: Typo in textbook proof or my mistake?

$\liminf s_n = \limsup s_n = +\infty$ implies that the limit of the sequence is also $+\infty$

some confusion of limsup and its connection with limit points and subsequential limits

A continuous, convex functional on a Banach space is weakly lower semicontinuous

Show that the $\limsup$ is the supremum of the set of limit points

Limit of characteristic functions $1_{A_n} $ its the characteristic function of the limit $1_{\lim A_n}$

Prove that, for two sequences, lim inf s_n<lim t_n

Meaning of $\limsup_{j,k\to \infty}\, \lvert \lvert u_{m_j} - u_{m_k} \rvert\rvert_{L^q(V)}\leq \delta$

Show that $\liminf a_n$ and $\limsup b_n$ are finite

Show that $\limsup_{t\to T_0-}\left\|u(t,\;\cdot\;)\right\|_\infty<\infty$ is not possible here

What does $\liminf_{x\to0+}-\frac{f'(x)}x>0$ informally mean?

Probability of $\limsup[X_n \geq n]$

About $\liminf$ for functions. Why this statement holds?

Relevance of the deduction of similar theorems than Maier's theorem for other constellations of primes

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