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Re: Matheology § 210
Posted:
Feb 7, 2013 9:13 AM
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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.
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