In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 20 Jun., 02:04, "Mike Terry" > > > > No, you're misunderstanding the meaning of computable. > > > > Hopefully you will be OK with the following definition: > > > > A real number r is computable if there is a TM (Turing machine) > > T which given n as input, will produce as output > > the n'th digit of r. > > Whatever might be the true meaning: The Turing machine need a finite > definition. Therefore the computable number has a finite definition. > > There are only countable many finite definitions. And every diagonal > of a defined Cantor list has also a finite definition.
Cantor's argument does not require that any member of a list of reals be computable beyond a finite number of decimal places, so enough of each can be finitely defined for the proof to work.