In article <7fa0f961-d798-4f6c-9b92-fba5a603db47@e5g2000yqn.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 17 Jun., 05:26, Tim Little <t...@little-possums.net> wrote: > > On 2010-06-15, Peter Webb <webbfam...@DIESPAMDIEoptusnet.com.au> wrote: > > > > > No. You cannot form a list of all computable Reals. If you could do > > > this, then you could use a diagonal argument to construct a > > > computable Real not in the list. > > > > You can form a list of all computable reals (in the sense of > > mathematical existence). However, such a list is not itself > > computable. > > That does not matter. > There exists a list containing all computable reals in all possible > languages. > Therefore the set of reals that can serve as doiagonals of a Cantor > list is countable. > > Regards, WM
Note, "all possible languages" is much too ambiguous to define a valid set of objects, so there is no such "set" of objects to list.
