Take all the even numbers. That's a subset of all whole numbers. Is it a finite set? Clearly not. Both are infinite; the population of even numbers is 50%. Sometimes infinity/infinity = 0.5.

The set of prime integers is a strict subset of the set of integers, and yet both are infinite (they have the same cardinality even--that is, they are the same size, in one sense of 'size').

Ex: {n ∈ R ∣ n is odd}