On 2010-06-19, Peter Webb <webbfamily@DIESPAMDIEoptusnet.com.au> wrote: > So Cantor's proof when applied to computable Reals proves exactly > what in your opinion?
That there is a real not on the list.
> I might remind you that as the form of proof is identical to that > used by Cantor for all Reals, whatever you believe that Cantor's > proof applied to computable Reals proves, his proof applied to all > Reals must prove the same thing.
It does prove exactly the same thing: in both cases, all such lists omit at least one real.
> Its the same proof, after all, except limitting the set to just > computable Reals.
No, there is a slight difference: the antidiagonal is a real number. It does not necessarily produce a computable real number.
Why, in your opinion, does the construction fail for rational numbers?