In article <email@example.com>, "Peter Webb" <webbfamily@DIESPAMDIEoptusnet.com.au> wrote:
> "Virgil" <Virgil@home.esc> wrote in message > news:Virgil-22B7E6.firstname.lastname@example.org... > > 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. > > 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.
Technically speaking,CANTOR'S anti-diagonal argument involves only binary sequences, not real numbers at all, though the real number form of the argument is almost always attributed to him.