Both sets have the same cardinality ("size"), since they are isomorphic, i.e. can be mapped on to each other one-to-one in a way that is order preserving. Both are aleph_0 (ℵ0 ) in size = cardinality. They are both "denumberable" sets. There are an "infinite" number of different sizes of non-finite sets. Non-finite sets are the only sets wherein a proper subset of another set (a subset that is missing some elements of the containing set) can have the same cardinality as the containing set. This cannot happen in finite sets. You can't apply normal "finite" methods to "non-finite" sets. Check the Wiki page for "Georg Cantor". He was the first mathemetician to explore this subject and now his work is part of the foundations of mathematics, i.e. the Zermelo-Fraenkel axioms.