Question

find supremum and infimum of sets (and min/max if they exist)

score 51 · Answer 1 · 2019-11-17 20:05:11

51

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find supremum and infimum of sets (and min/max if they exist)

Published on 17 Nov 2019 - 20:05

score 339 · Answer 2 · 2019-11-18 22:30:33

339

Views

Interchanging limsup of a sequence with $L^{\infty}$ norm

Published on 18 Nov 2019 - 22:30

score 63 · Answer 3 · 2019-11-27 21:56:39

63

Views

Limes $1- \frac{(-1)^n}{\sqrt{n}}$ and $\frac{2^n + (-3)^n}{(-2)^n + 3^n}$ and $n - 3 \lfloor \frac{n}{3} \rfloor$

Published on 27 Nov 2019 - 21:56

score 68 · Answer 4 · 2019-11-28 10:30:40

68

Views

Proof $\lim_{n \to \infty} a_n = \lim_{n \to \infty} \sup a_n = \lim_{n \to \infty} \inf a_n$

Published on 28 Nov 2019 - 10:30

score 277 · Answer 5 · 2019-11-30 11:24:07

277

Views

liminf and limsup of sequence of numbers and sets

Published on 30 Nov 2019 - 11:24

score 108 · Answer 6 · 2019-12-01 11:49:34

108

Views

Is $\liminf_{n \to \infty} \arctan(x_n) = \arctan( \liminf_{n \to \infty} x_n)$?

Published on 01 Dec 2019 - 11:49

score 130 · Answer 7 · 2019-12-01 23:24:38

130

Views

series and lim sup proof

Published on 01 Dec 2019 - 23:24

score 58 · Answer 8 · 2019-12-07 18:58:13

58

Views

Indirect argument for proof that $\limsup\{a_n+b_n\} < \limsup\{a_n\}+\limsup\{b_n\}$.

Published on 07 Dec 2019 - 18:58

score 667 · Answer 9 · 2019-12-08 03:16:28

667

Views

Prove $\liminf(a_n+b_n) \geq \liminf(a_n)+\liminf(b_n)$ for bounded sequences $a_n$ and $b_n$

Published on 08 Dec 2019 - 3:16

score 514 · Answer 10 · 2019-12-08 04:15:01

514

Views

Counterexamples of reverse Fatou lemma

Published on 08 Dec 2019 - 4:15

score 164 · Answer 11 · 2019-12-09 09:50:21

164

Views

Prove/Disprove $\lim \sup a_n = -\lim \inf -a_n$

Published on 09 Dec 2019 - 9:50

score 137 · Answer 12 · 2026-03-27 17:04:20

137

Views

If $F$ is purely discontinuous, then $\limsup_{t\to\infty}f(t)=1$.

Published on 27 Mar 2026 - 17:04

score 661 · Answer 13 · 2019-12-11 03:23:07

661

Views

Using $\limsup |a_n|^{1/n}$ to find radius of convergence of a power series.

Published on 11 Dec 2019 - 3:23

score 43 · Answer 14 · 2019-12-12 10:23:54

43

Views

Prove that L is partial limit of $a_n$

Published on 12 Dec 2019 - 10:23

score 421 · Answer 15 · 2026-03-25 09:39:52

421

Views

Reverse of Gabriel's Horn/Toricelli's Trumpet - need explanation of the proof

Published on 25 Mar 2026 - 9:39

List Question

find supremum and infimum of sets (and min/max if they exist)

Interchanging limsup of a sequence with $L^{\infty}$ norm

Limes $1- \frac{(-1)^n}{\sqrt{n}}$ and $\frac{2^n + (-3)^n}{(-2)^n + 3^n}$ and $n - 3 \lfloor \frac{n}{3} \rfloor$

Proof $\lim_{n \to \infty} a_n = \lim_{n \to \infty} \sup a_n = \lim_{n \to \infty} \inf a_n$

liminf and limsup of sequence of numbers and sets

Is $\liminf_{n \to \infty} \arctan(x_n) = \arctan( \liminf_{n \to \infty} x_n)$?

series and lim sup proof

Indirect argument for proof that $\limsup\{a_n+b_n\} < \limsup\{a_n\}+\limsup\{b_n\}$.

Prove $\liminf(a_n+b_n) \geq \liminf(a_n)+\liminf(b_n)$ for bounded sequences $a_n$ and $b_n$

Counterexamples of reverse Fatou lemma

Prove/Disprove $\lim \sup a_n = -\lim \inf -a_n$

If $F$ is purely discontinuous, then $\limsup_{t\to\infty}f(t)=1$.

Using $\limsup |a_n|^{1/n}$ to find radius of convergence of a power series.

Prove that L is partial limit of $a_n$

Reverse of Gabriel's Horn/Toricelli's Trumpet - need explanation of the proof

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