In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 18 Jun., 05:22, "Peter Webb" <webbfam...@DIESPAMDIEoptusnet.com.au> > wrote: > > > Since by definition, "listability" = "countability", Cantor's proof of > > > unlistability proves uncountability. > > > > Really? Where did you get that from? > > From Cantor. > > > > The computable Reals cannot be listed. > > > > Therefore according to you they are uncountable.
If one defines countability of a set standardly, it requires existence of a surjection from the set of naturals to the set in question.
So proof that there can be no such surjection is clearly sufficient to show that a set is not countable.
> No. There is no uncountability. That needs to be understood.
There is certainly such a definition, but in order to eliminate uncountability, WM would first have to eliminate infiniteness, which he also fails to do.
> Uncomputable numbers are not numbers, because nobody knows what they > are.
A real number, a, is said to be computable if it can be approximated by some computable function in the following manner: given any (positive) integer n, the function produces an integer k such that: (k-1)/n <= a <= (k+1)/n