Yesterday's post as gotten me into one of my rare stern-logician frames of mind, so I think I'll stick with that today. I wonder if I've ever discussed Cantor's "diagonal" proof in my blogging. If not, I'll make good on that now. Cantor refuted the common idea that "infinity" is a single all-inclusive category. Once we get beyond enumeration we've gotten to "infinity" and there is nothing more to be said. Or, at least, so we're inclined to think. Yes there is, though, Cantor replies, much more to be said. Because for example not every infinity is equal to every other. Some "trans-finite" numbers are bigger than others. The number of real numbers is a larger transfinite number than the number of integers. Why? Well, diagonals! The question is -- could we in principle create a one-to-one correspondence between every real number and every integer that would allow room for every one of each to show up, eventually, ...