The existence of a bijection between two sets is what &quot;same size&quot; means in set theory.  Yes, there are non-prime integers, but you can establish a bijection between the two, so their cardinalities are equal (both have a cardinality of aleph zero).<p>The reals, on the other hand, cannot be placed in a bijection with the natural numbers, and there are therefore &quot;more&quot; reals than naturals (i.e. there is an injection from the naturals to the reals, but not from the reals to the naturals -- any function from reals to naturals must have some pair x ≠ y with f(x) = f(y)).