lim sup and lim inf

**studentmath92** · May 18th 2010, 01:28 PM

Let ( $s_n$ ) be a bounded sequence and let $L =lim sups_n$ . Then for every $\epsilon> 0$ , we have $L-\epsilon$ $<s_n$ $\le$ $L+\epsilon$ for infinitely many $n$

What would be the lim inf version of this theorem and how would you go about proving it?

Much Thanks!

**Plato** · May 18th 2010, 01:46 PM

Originally Posted by studentmath92

What would be the lim inf version of this theorem?

Why don't you make a guess at that statment?

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