OK. I know all mostly about infinite sets. Mama always said, “Infinite is as infinite does.” I have always loved Cantor’s sieve and the correspondence that it refers to. But I have a question for those numerical theory types.

As one looks at pairs of infinite sets and sets them up into one-to-one relationships with each other it is possible to show that each is bigger than the other. I say that of course with tongue firmly in cheek. It is to me one of the best proofs of transfinite analysis (if that is the term) that if you can show that each set is bigger than the other, than they are clearly the same size. I am thinking here of the fun you can have with the natural numbers and integers, to be specific.

I only recently found out about the method to correspond points on a real line to all points on a two-dimensional plane, or any number of real valued axes. I was really tickled to finally hear about it. It made my day.

I am curious if the same sort of fun exists for **C**. Can you show with naïve math that two sets of size **C**are each bigger than the other?