On Jun 27, 5:25 am, "Peter Webb" <webbfam...@DIESPAMDIEoptusnet.com.au> wrote: > "Newberry" <newberr...@gmail.com> wrote in message > > news:email@example.com... > On Jun 25, 11:22 pm, "Peter Webb" > > > > > > <webbfam...@DIESPAMDIEoptusnet.com.au> wrote: > > "Virgil" <Vir...@home.esc> wrote in message > > >news:Virgil-71EA75.firstname.lastname@example.org... > > > > 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? > > ________________________________ > How can something which doesn't exist have some property?
This is what you said: "It implies a listing must EXIST, but does not provide such a listing. [Emphasis added.]
> > > 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.- Hide quoted text - > > - Show quoted text -- Hide quoted text - > > - Show quoted text -