How to prove that, if a sequence of integers converges, then its limit is an integer?
Suppose sequence is $z_n$ and limit is $z$. This is same as proving if $\forall\epsilon>0, $ there exists a $N$ s.t. $n>N$ implies $|z_n-z|<\epsilon$
I have no idea how to start. I was trying to use contradiction and suppose that limit is not an integer, and then pick $\epsilon $ that makes the limit an integer. But I don't know how to make inequality $|z_n-z|<\epsilon$ into equality.