On Feb 7, 2:54 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > On 7 Feb., 09:10, William Hughes <wpihug...@gmail.com> wrote: > > > On Feb 7, 9:00 am, WM <mueck...@rz.fh-augsburg.de> wrote: > > <snip> > > > > What does that mean for the set of accessible numbers? > > > That this potentially infinite set is not listable. > > Here we stand firm on the grounds of set theory. > > Once upon a time there used to be a logocal identity: The expression > "Set X is countable" used to be equivalent to "Set X can be listed".
You say, X is countable means there are not more X than any natural number. The standard term for this is "sub-countable". Standard terminology is that X is countable iff X is listable. X can be unlistable and sub-countable, so X can be uncountable and sub-countable.
There is nothing contradictory about saying the accessible numbers are uncountable and sub-countable.