# Thread: lim sup and lim inf

1. ## lim sup and lim inf

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

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

Much Thanks!

2. Originally Posted by studentmath92
What would be the lim inf version of this theorem?
Why don't you make a guess at that statment?