"Virgil" <Virgil@home.esc> wrote in message news:Virgil-22B7E6.14010020062010@bignews.usenetmonster.com... > In article > <ccb88bb1-d8a6-4f04-bc6a-ca3346f7c8ad@c10g2000yqi.googlegroups.com>, > WM <mueckenh@rz.fh-augsburg.de> 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.
Exactly the same as mine.
Cantor calculates the anti-diagonal to n places (for all n) using only the first n digits of the first n items. So do I.
