I think what you mean is you used to think that the set of non-negative even integers was "smaller" than the set of natural numbers. The reason you can do this is because the set of non-negative even integers has the same cardinality as the set of naturals (both are countably infinite): http://en.wikipedia.org/wiki/Cardinality

The same is true of the rational numbers, by the way. There is a famous proof of the fact that there are infinite sets with larger cardinality that the naturals (the reals for example): http://en.wikipedia.org/wiki/Cantor's_diagonal_argument