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.