List questions from limsup-and-liminf

Published on 21 Jul 2020 - 0:43

106

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Why limsup of subsequence unbounded above doesn't have infinity as its limit?

Published on 21 Jul 2020 - 18:13

5.6k

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Why does every oscillating sequence diverge?

Published on 22 Jul 2020 - 18:24

46

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What is being "minimized" when discussing a confidence set?

Published on 24 Jul 2020 - 5:02

362

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Big $O$ notation and limit superior

Published on 28 Jul 2020 - 14:21

774

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Liminf of union of two sequences

Published on 30 Jul 2020 - 0:35

470

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Proof of $\limsup s_n = \lim _{N \rightarrow \infty} \sup \{s_n: n >N \}$. What does $n>{}$natural number mean? Is the solution wrong?

Published on 30 Jul 2020 - 16:08

205

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Prove that $u$ is upper semicontinuous on $\Delta(0,\rho)$.

Published on 10 Jul 2016 - 20:40

114

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On a superior limit involving the multiplication formula for the Gamma function and the divisors $d\mid n$ of a positive integer

Published on 26 Mar 2026 - 8:00

170

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Radius of convergence of integral series; problem with limsup

Published on 14 Jul 2016 - 10:42

619

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L^1 convergence and limsup of convergent sequence

Published on 16 Jul 2016 - 10:48

508

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Proofs involving limsup and liminf

Published on 17 Jul 2016 - 15:18

537

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A surprising inequality about a $\limsup$ for any sequence of positive numbers

Published on 19 Jul 2016 - 0:57

105

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inf, sup, max, min for $\bigcap_{n \in \mathbb N}\left[-\frac{1}{3^n},4+\frac{1}{2n}\right)$

Published on 21 Jul 2016 - 21:45

305

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Relation between Supremum and limit superior

Published on 22 Jul 2016 - 9:30

List Question

lim inferior and Lim superior

Why limsup of subsequence unbounded above doesn't have infinity as its limit?

Why does every oscillating sequence diverge?

What is being "minimized" when discussing a confidence set?

Big $O$ notation and limit superior

Liminf of union of two sequences

Proof of $\limsup s_n = \lim _{N \rightarrow \infty} \sup \{s_n: n >N \}$. What does $n>{}$natural number mean? Is the solution wrong?

Prove that $u$ is upper semicontinuous on $\Delta(0,\rho)$.

On a superior limit involving the multiplication formula for the Gamma function and the divisors $d\mid n$ of a positive integer

Radius of convergence of integral series; problem with limsup

L^1 convergence and limsup of convergent sequence

Proofs involving limsup and liminf

A surprising inequality about a $\limsup$ for any sequence of positive numbers

inf, sup, max, min for $\bigcap_{n \in \mathbb N}\left[-\frac{1}{3^n},4+\frac{1}{2n}\right)$

Relation between Supremum and limit superior

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