Actually, there are different orders of infinity. http://en.wikipedia.org/wiki/Aleph_number
has a pretty reasonable treatment of the subject. It's a bit tough to wrap your mind around, but consider this. There are an infinite number of integers. Between each pair of integers, there are an infinite number of irrational numbers. Therefore, there are more irrational numbers than there are integers. But there are an infinite number of integers. But there are more irrational numbers. An so on, to infinity.