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Re: Cantor's Proofs
Posted:
Oct 17, 2011 1:49 AM
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"Graham Cooper" <grahamcooper7@gmail.com> wrote in message
news:ffb9190a-1fd1-482a-a6d5-e045cbd642c8@31g2000prt.googlegroups.com...
On Oct 17, 2:42 pm, "Peter Webb"
<webbfam...@optusnetDIESPAMDIE.com.au> wrote:
> > No, he would say that the computable reals are listable
> > but not listable by a computable list.
>
> So they're not computable then?
>
> ___________________________________
> The numbers are computable. It is the list itself which is not computable.
> If it was, we could diagonalise the list to form a computable number not
> on
> the list, violating our assumption that the list contains all computable
> numbers.
>
OK then, define the missing diagonals from infinitely_many turing
machines that output equivalent lists (given an input sequence N) by
each turing machine emulating every turing machine (in different
representations and orderings) to each produce every computable real
indexed by N.
_____________________________________________
I can't compute the diagonal because I cannot compute a list of all
computable reals. Nor can you. That is the point.
Herc
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