"Peter Webb" <webbfamily@DIESPAMDIEoptusnet.com.au> wrote in message news:4c1d8758$0$14086$afc38c87@news.optusnet.com.au... > > "Tim Little" <tim@little-possums.net> wrote in message > news:slrni1qqsn.jrj.tim@soprano.little-possums.net... > > On 2010-06-19, Peter Webb <webbfamily@DIESPAMDIEoptusnet.com.au> wrote: > >> Of course it is computable. Cantor provides a simple construction > >> for the number. > > > > Only if the list itself is a recursively enumerable function. > > Cantor's proof makes no such assumption. > > > > Yes it does. It requires that the nth digit of the nth term can be > calculated.
Not so - the proof simply needs the n'th digit of the n'th term to EXIST. It is then possible to prove the EXISTENCE of the missing real number (via the antidiagonal argument). His proof should not be read as instructions for a "C" program or some such! :-) It's an existence proof, not really an "algorithm" at all in the sense I would use the word...
> This is not quite as strong as being re, but it is close. In any > event, it is exactly the same restriction as I place on the purported list > of all computable Reals.
No, you require the list itself to be computable, so that given m,n as input you can compute "the n'th digit of the m'th number". That's MUCH more than Cantor requires.
