Math Help - Sequences

1. Sequences

Hey all, I'm having a little trouble getting started with this one as I'm really not understanding the hypothesis. Thanks for the help.

Prove that if (sn) is a sequence of distinct terms in R, s is an element in R and every nonempty open subset containing s contains all but finitely many members of the set (sn: n is an element of natural numbers} then sn converges to s.

2. Choose $\epsilon>0$. Then $(s-\epsilon,s+\epsilon)$ excludes finitely many $s_n$. Then there is an integer $N=1+\max\{n:s_n\notin(s-\epsilon,s+\epsilon)\}$ such that if $n\geq N$ then $s-\epsilon.

That's the definition of convergence.