It's worth noting that R=2^N: reals is the set of all subsets of integers, simply because any real in binary form appears as a sequence of 1s and 0s that select a subset of N. And for some reason it's not possible to know if there's anything in between N and 2^N. This makes me think that infinite sets grow in discrete exponential jumps: N, 2^N, 2^R and so on. N seems to be the smallest infinite set.