Mathematics is a rich source of counter-intuitive facts.
There are some infinities that are "bigger" than others.
http://en.wikipedia.org/wiki/Infinit..._the_continuum
Take the natural numbers (counting numbers - whole numbers) - one can have an infinite number of them.
Now consider the real numbers (those numbers that can have arbitrary decimal precision). There are an infinite number of numbers between 0 and 1 and between 1 and 2 - in fact between any two decimal numbers.
These two infinities are of different scale.
Cantor had real resistance to this idea.
Mark C.