Question

Meaning of Infinite Union/Intersection of sets

score 5.1k · Answer 1 · 2017-03-05 21:15:44

5.1k

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Meaning of Infinite Union/Intersection of sets

Published on 05 Mar 2017 - 21:15

score 3.6k · Answer 2 · 2017-03-05 22:20:40

3.6k

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Infinite Union/Intersection vs Infinite summation

Published on 05 Mar 2017 - 22:20

score 2.2k · Answer 3 · 2017-03-05 23:49:39

2.2k

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If $\limsup = \infty$ then sequence is unbounded and $\infty$ is the subsequential limit of sequence.

Published on 05 Mar 2017 - 23:49

score 48 · Answer 4 · 2017-03-06 09:47:08

48

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If, for every $n$, $f_n\to0$ at infinity and $|f_n(x_n)|\geq C$, can one deduce that $(x_n)$ is bounded?

Published on 06 Mar 2017 - 9:47

score 186 · Answer 5 · 2017-03-07 13:10:23

186

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Looking for a sequence with $4$ limit points

Published on 07 Mar 2017 - 13:10

score 528 · Answer 6 · 2017-03-07 16:10:23

528

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Studying sequences, lim sup and lim inf

Published on 07 Mar 2017 - 16:10

score 31 · Answer 7 · 2017-03-08 20:58:53

31

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Studying sequences in analysis

Published on 08 Mar 2017 - 20:58

score 2.1k · Answer 8 · 2017-03-08 21:52:24

2.1k

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Finding limit using inequalities: $\liminf \frac{a_{n+1}}{a_n} \le \liminf (a_n)^ {1/n}\le\limsup (a_n)^ {1/n}\le \limsup \frac{a_{n+1}}{a_n}$

Published on 08 Mar 2017 - 21:52

score 204 · Answer 9 · 2017-03-13 05:51:36

204

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Equivalence for upper semicontinuous functions

Published on 13 Mar 2017 - 5:51

score 33 · Answer 10 · 2017-03-15 21:55:14

33

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Supremum and Limit superior

Published on 15 Mar 2017 - 21:55

score 172 · Answer 11 · 2026-03-29 03:35:29

172

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What are the applications / usages of the limes superior?

Published on 29 Mar 2026 - 3:35

score 202 · Answer 12 · 2017-03-17 15:21:53

202

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Show that $\limsup_{n\rightarrow\infty} a_n^\frac{1}{n} \leq \limsup_{n\rightarrow\infty} (a_{n+1} / a_n).$

Published on 17 Mar 2017 - 15:21

score 265 · Answer 13 · 2017-03-18 15:58:41

265

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Example of sequence of sets $(A_n)$ such that $\liminf{A_n}$ and $\limsup{A_n}$ have a specific property

Published on 18 Mar 2017 - 15:58

score 93 · Answer 14 · 2017-03-19 16:38:17

93

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Show that $\lim\inf X_{n}\subseteq \lim\sup X_{n}$ always.

Published on 19 Mar 2017 - 16:38

score 589 · Answer 15 · 2017-03-19 23:15:09

589

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Understanding $\lim \inf$ and $\lim \sup$

Published on 19 Mar 2017 - 23:15

List Question

Meaning of Infinite Union/Intersection of sets

Infinite Union/Intersection vs Infinite summation

If $\limsup = \infty$ then sequence is unbounded and $\infty$ is the subsequential limit of sequence.

If, for every $n$, $f_n\to0$ at infinity and $|f_n(x_n)|\geq C$, can one deduce that $(x_n)$ is bounded?

Looking for a sequence with $4$ limit points

Studying sequences, lim sup and lim inf

Studying sequences in analysis

Finding limit using inequalities: $\liminf \frac{a_{n+1}}{a_n} \le \liminf (a_n)^ {1/n}\le\limsup (a_n)^ {1/n}\le \limsup \frac{a_{n+1}}{a_n}$

Equivalence for upper semicontinuous functions

Supremum and Limit superior

What are the applications / usages of the limes superior?

Show that $\limsup_{n\rightarrow\infty} a_n^\frac{1}{n} \leq \limsup_{n\rightarrow\infty} (a_{n+1} / a_n).$

Example of sequence of sets $(A_n)$ such that $\liminf{A_n}$ and $\limsup{A_n}$ have a specific property

Show that $\lim\inf X_{n}\subseteq \lim\sup X_{n}$ always.

Understanding $\lim \inf$ and $\lim \sup$

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