On 2010-06-19, Peter Webb <webbfamily@DIESPAMDIEoptusnet.com.au> wrote: > Which of these two statements do you agree with: > > 1. You cannot form a list of computable Reals. > > 2. The computable Reals are countable.
Answering the same questions for the fourth time now, 1 is false, 2 is true.
> You have failed to explain why Cantor's diagonal proof "proves" the > Reals are uncountable, but the same proof applied to computable > Reals does *not* prove the Computable Reals are uncountable.
I have, multiple times now. The antidiagonal of a list of computable reals is not necessarily a computable real. Your insistence that it must be is almost certainly because you don't know what a computable real is. (There are other possibilities, even less flattering to your math skills)
In particular, the antidiagonal of a list of all computable reals is never a computable real.