Quote by Char. Limit
This is probably what makes infinity so hard to understand. Yes, there are exactly as many even numbers as there are integers. There are also as many rational numbers as there are integers.

It's historically interesting to note that Galileo pondered these issues hundreds of years ago. He noted that the square numbers 1, 4, 9, 16, 25, ... were a proper subset of the whole numbers, yet could also be put into 11 correspondence with the whole numbers.
http://en.wikipedia.org/wiki/Galileo's_paradox