"Tim Little" <email@example.com> wrote in message news:firstname.lastname@example.org... > On 2010-06-19, Peter Webb <webbfamily@DIESPAMDIEoptusnet.com.au> wrote: >> Bijectable with N and "listable" are not the same. To be "listable" >> the set must be countable and recursively enumerable. > > There is no such requirement for recursive enumerability in Cantor's > work.
> The concept was not even introduced into mathematics until some > time after his death.
> Your insistence that Cantor required lists to > be recursively enumerable is bizarre. >
Which of these two statements do you agree with:
1. You cannot form a list of computable Reals.
2. The computable Reals are countable.
> > - Tim
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 believe that this is because the set of computable numbers is not recursively enumerable, but if you have a better explanation I would love to hear it.