On 2010-06-21, Virgil <Virgil@home.esc> wrote: > Technically, it isn't Cantor's proof at all, as the only real Cantor > diagonal proof is not about reals but about binary sequences.
Indeed. In fact it would be a lot easier if instead of reals, we talked about sets of natural numbers, and instead of computable reals, we talked about recursively enumerable sets of natural numbers.
The diagonal proof for the uncountability of P(N) is very much simpler, and so there are fewer distractions from the core idea. It is also much closer to Cantor's original proof.
This might help to prevent some of the extraneous confusions Peter has about computable reals, and would help focus on his *central* confusions.
