function with integer domain

Hi guys!

So i've been asked to prove that every function f:Z->R is continuous using the epsilon-delta notion of continuity.

I'm just a little confused about the specifics of the proof.
For instance, for arbitrary integers p and x, suppose |x-p|<d.
If d<1 then we know x=p since they're integers.
And so f(x)-f(p)=0

But how can you account for the case when |x-p|>1. Can I just assume d<1?

Thanks alot!