Ah ok, thanks Chris, thought that might be the reference but wasn't sure. Jon, that's not quite a proof that he gave though. The famous proof is known as Camtor's diagonalisation argument, and it's a proof by contradiction. The usual development is to go over some infinite hotel cases to first show how it's a slippery concept (countable many countable infinities is still countable), then show (again to push the intuition) naturals and rationals have same size, and finally to show it can't be done for naturals and reals with a diagonalization proof: Usually do it for just the reals from 0 to 1 (without loss of generality). Assume you have a 1-1 mapping from N to the interval. List out all the reals in decimal notation according to this mapping, r1 on first row, r2 on next, etc. Define new real by taking the "diagonal" of this and changing the value. This number is nowhere in your list 🤯 Worth looking up for a proper proof with all the little details. The next question is usually, "are there infinities between these two? Known as continuum hypothesis, and it drive Cantor mad, they say. It's been shown since that it's consistent and independent that there are or there aren't 🤯