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Re: Matheology § 210
Posted:
Feb 7, 2013 1:14 PM
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On Feb 7, 5:57 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> On 7 Feb., 15:56, William Hughes <wpihug...@gmail.com> wrote:
>
> > On Feb 7, 3:25 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>
> > <snip>
>
> > >... a subset S of the countable set F of finite words bijects with
> > > the set D of definable numbers
>
> by definition.
>
>
>
> > Nope. Every D corresponds to some finite word.
>
> No, D is a set or at least a collection. A definable number is an
> element of D.
>
> > However, S,
> > the collection of all the correspondences, may not be a subset
> > of F (subsets must be computable).
>
> Need not be a subset. It is sufficient to know that there are not more
> than countably many correspondences,
There is no set of correspondences thus there is no number
of correspondences. You cannot know anything about
the number of correspondences.
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