List questions from limsup-and-liminf

Published on 17 Apr 2013 - 3:29

68

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Suppose that for $a_n\geq b_n$ for all $n$. Show that $\varliminf_{n \to \infty} a_n\geq \varliminf_{n \to \infty} b_n$.

Published on 23 Apr 2013 - 5:47

1k

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Limit Points and lim inf and lim sup

Published on 27 Apr 2013 - 21:45

129

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Is it true that $\cup_{n=N}^{\infty}A_{n}\setminus\cap_{n=N}^{\infty}A_{n}=\cup_{n=N}^{\infty}A_{n}\triangle A_{n+1}$?

Published on 28 Apr 2013 - 9:54

125

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Show that $\liminf a_n \le \liminf s_n$

Published on 07 May 2013 - 2:52

1.1k

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Two questions on $\limsup$: do nested ones commute and sending $n$ to $-\infty$

Published on 09 May 2013 - 13:00

68

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Supremum of $\underset{n \to \infty }{\lim} \underset{x\in [0,1]}{\sup} \left | \frac{x+x^{2}}{1+n+x} \right | $

Published on 10 May 2013 - 5:42

993

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Borel-Cantelli Lemma

Published on 26 Mar 2026 - 22:50

126

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A question on limsup

Published on 18 May 2013 - 13:34

3.6k

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Having trouble understanding upper and lower limits.

Published on 24 May 2013 - 7:15

114

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Does $\lim_{x\to x_0}\limsup_{y\to y_0}f(x,y)=f(x_0,y_0)$?

Published on 29 May 2013 - 7:54

3.6k

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Finding the upper and lower limit of the following sequence.

Published on 31 May 2013 - 23:16

49.3k

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Prove $\limsup\limits_{n \to \infty} (a_n+b_n) \le \limsup\limits_{n \to \infty} a_n + \limsup\limits_{n \to \infty} b_n$

Published on 01 Jun 2013 - 1:00

1.7k

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Subsequential Limits

Published on 01 Jun 2013 - 19:11

771

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List of properties for sup and inf

Published on 05 Jun 2013 - 6:59

List Question

Help Proving Quotient of Sequences Is Finite

Suppose that for $a_n\geq b_n$ for all $n$. Show that $\varliminf_{n \to \infty} a_n\geq \varliminf_{n \to \infty} b_n$.

Limit Points and lim inf and lim sup

Is it true that $\cup_{n=N}^{\infty}A_{n}\setminus\cap_{n=N}^{\infty}A_{n}=\cup_{n=N}^{\infty}A_{n}\triangle A_{n+1}$?

Show that $\liminf a_n \le \liminf s_n$

Two questions on $\limsup$: do nested ones commute and sending $n$ to $-\infty$

Supremum of $\underset{n \to \infty }{\lim} \underset{x\in [0,1]}{\sup} \left | \frac{x+x^{2}}{1+n+x} \right | $

Borel-Cantelli Lemma

A question on limsup

Having trouble understanding upper and lower limits.

Does $\lim_{x\to x_0}\limsup_{y\to y_0}f(x,y)=f(x_0,y_0)$?

Finding the upper and lower limit of the following sequence.

Prove $\limsup\limits_{n \to \infty} (a_n+b_n) \le \limsup\limits_{n \to \infty} a_n + \limsup\limits_{n \to \infty} b_n$

Subsequential Limits

List of properties for sup and inf

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