[rvbissell]

That's an interesting statement about rationals. My intuition would be to consider them a subset of the reals, and for natural numbers to be a subset of the rationals. How is my intuition failing me, in this case?

EDIT: found the answer: with Cantor's diagonalization, you can count all the rationals -- effectively mapping each one to a natural number. Since this mapping is demonstrably possible, they have the same cardinality.