On Jun 25, 11:22 pm, "Peter Webb" <webbfam...@DIESPAMDIEoptusnet.com.au> wrote: > "Virgil" <Vir...@home.esc> wrote in message > > news:Virgil-71EA75.email@example.com... > > > In article > > <b3413a4e-567b-4dfb-8037-21f14b826...@g1g2000prg.googlegroups.com>, > > Newberry <newberr...@gmail.com> wrote: > > >> > > No. (3) is not true, as it is based on a false premise (that the > >> > > computable > >> > > Reals can be listed). > > > How is countability any different from listability for an infinite set? > > > Does not countability of an infinite set S imply a surjections from N > > to S? And then does not such a surjection imply a listing? > > It implies a listing must exist, but does not provide such a listing.
Does such a listing have an anti-diagonal?
> The computable Reals are countable, but you cannot form them into a list of > all computable Reals (and nothing else) where each item on the list can be > computed. > > In order to list a set, it has to be recursively enumerable. Being countable > is not sufficient.