Choose . Then excludes finitely many . Then there is an integer such that if then .
That's the definition of convergence.
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.