Definition of converge:
For each epsilon > 0 there exists a number N such that n>N implies
|sn -s|<epsilon.
In this case the N you chose was usually a max {constant, f(epsilon)}.
Definition of continuity
For each epsilon > 0 there exists a delta>0 such that x element dom(f) and
|x-x0| < delta implies |f(x)-f(x0)|< epsilon.
In this case the delta you choose is usually a min{constant, f(epsilon)}
I was just wondering how to think about why for one you need a min and the other a max.
Thanks