On 2010-06-18, Peter Webb <webbfamily@DIESPAMDIEoptusnet.com.au> wrote: > There are a countable number of computable Reals.
> You can apply the Cantor construction to any purported list of all > computable Reals to form a computable Real not on the list.
No, you can apply the Cantor construction to any purported list of all computable Reals to form a *non*computable Real not on the list.
> This proves that the computable Reals cannot be listed.
It proves no such thing.
> It does *not* prove the computable Reals are uncountable, and in > fact they are not.
Of course the computable reals are countable. I never claimed otherwise. You are the one claiming that they cannot be listed, a statement equivalent to their uncountability.
> In exactly the same manner, Cantor proved that the Reals cannot be > listed. This does *not* automatically mean they are uncountable, > any more than the same proof applied to computable Reals proves they > are uncountable. These are different concepts. (Although they were > not when Cantor produced his proof).
Computability as a concept did not even exist when Cantor produced his proof. You are extremely confused.