Question

For bounded real valued function $f$ show that $\omega_f$ is upper continuous

score 215 · Answer 1 · 2026-03-14 14:46:32

For bounded real valued function $f$ show that $\omega_f$ is upper continuous

Published on 14 Mar 2026 - 14:46

score 147 · Answer 2 · 2016-11-20 14:12:35

Calculating $\limsup\limits_{n \to \infty}a_n$ and $\liminf\limits_{n \to \infty}a_n$ with $a_n=\left( \frac{n+(-1)^n}{n} \right)^n$

score 801 · Answer 3 · 2016-11-21 11:47:14

801

Views

Assume $\mathbb{R}$ has the least upper bound property. Show that $[0,1] = \{ x\mid 0 \leq x \leq 1\}$ has the least upper bound property

Published on 21 Nov 2016 - 11:47

score 560 · Answer 4 · 2016-11-22 09:51:38

560

Views

$\limsup$ and $\liminf $ of $\sin ({1\over {n^2}}) $

Published on 22 Nov 2016 - 9:51

score 1.2k · Answer 5 · 2026-03-14 01:09:36

1.2k

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Uniform limit of upper semi-continuous functions

Published on 14 Mar 2026 - 1:09

score 965 · Answer 6 · 2016-11-25 04:28:25

965

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Lim sup of sum of sequences

Published on 25 Nov 2016 - 4:28

score 1.5k · Answer 7 · 2016-11-25 23:38:31

1.5k

Views

Prove that $X$ contains a strictly increasing sequence which converges to $\sup X$

Published on 25 Nov 2016 - 23:38

score 279 · Answer 8 · 2016-11-26 23:23:40

279

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Is the following proof for $\limsup a_n+b_n\ge\liminf a_n+\limsup b_n$ correct?

Published on 26 Nov 2016 - 23:23

score 41 · Answer 9 · 2016-11-27 00:32:26

41

Views

Proof comparing $\limsup$ and $\liminf$ as $n\to\infty$ of $\frac{a_{n+1}-a_n}{c_{n+1}-c_n}$and $\frac{a_n}{c_n}$

Published on 27 Nov 2016 - 0:32

score 660 · Answer 10 · 2016-11-27 00:43:43

660

Views

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

Published on 27 Nov 2016 - 0:43

score 146 · Answer 11 · 2016-11-30 01:09:57

146

Views

Show that $\limsup_{n \to \infty} (x_ny_n) = (\lim_{n \to \infty} x_n)(\limsup_{n \to \infty} y_n).$

Published on 30 Nov 2016 - 1:09

score 40 · Answer 12 · 2016-11-30 09:16:47

40

Views

A problem about the limit of a sequence

Published on 30 Nov 2016 - 9:16

score 188 · Answer 13 · 2016-12-01 21:56:03

188

Views

Limsup = sup(inf) for a series of functions

Published on 01 Dec 2016 - 21:56

score 40 · Answer 14 · 2016-12-04 07:51:51

40

Views

If $\limsup(b_{n})=+\infty$, is $\limsup_{n}(b_{n} S_{n})=+\infty$?

Published on 04 Dec 2016 - 7:51

score 72 · Answer 15 · 2016-12-04 08:39:20

72

Views

Trying to understand a proof about L'Hopital rule

Published on 04 Dec 2016 - 8:39

List Question

For bounded real valued function $f$ show that $\omega_f$ is upper continuous

Calculating $\limsup\limits_{n \to \infty}a_n$ and $\liminf\limits_{n \to \infty}a_n$ with $a_n=\left( \frac{n+(-1)^n}{n} \right)^n$

Assume $\mathbb{R}$ has the least upper bound property. Show that $[0,1] = \{ x\mid 0 \leq x \leq 1\}$ has the least upper bound property

$\limsup$ and $\liminf $ of $\sin ({1\over {n^2}}) $

Uniform limit of upper semi-continuous functions

Lim sup of sum of sequences

Prove that $X$ contains a strictly increasing sequence which converges to $\sup X$

Is the following proof for $\limsup a_n+b_n\ge\liminf a_n+\limsup b_n$ correct?

Proof comparing $\limsup$ and $\liminf$ as $n\to\infty$ of $\frac{a_{n+1}-a_n}{c_{n+1}-c_n}$and $\frac{a_n}{c_n}$

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

Show that $\limsup_{n \to \infty} (x_ny_n) = (\lim_{n \to \infty} x_n)(\limsup_{n \to \infty} y_n).$

A problem about the limit of a sequence

Limsup = sup(inf) for a series of functions

If $\limsup(b_{n})=+\infty$, is $\limsup_{n}(b_{n} S_{n})=+\infty$?

Trying to understand a proof about L'Hopital rule

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