I love square numbers, but taking them to infinity has me floored. For every number, there is a corresponding square, so 1 to one correspondence in that direction. But there are many many numbers which are not squares - 2,3,5,6,7,8 for which there is no correspondence with the natural numbers, so how can there be the same cardinality? One set is so much greater than the other this side of infinity! Can you save my sanity?
ES