A countable union of countable sets is countable. Since the subsets have finite elements, they are essentially a finite union of n, for n \in N, which means they are countable.
This will be the second of a set of questions concerning real analysis. I've been having much trouble understanding how to go about writing the proofs since math classes such as these haven't exactly gone that well for me.
The question reads:
Show that the set of all finite subsets of N is a countable set.
Any help on this would be greatly appreciated. Thanks.