Virgil
Posts:
4,482
Registered:
1/6/11
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Re: Matheology � 210
Posted:
Feb 7, 2013 7:38 PM
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In article
<c00c57de-f177-4019-b022-e7f76ae7acd4@fn10g2000vbb.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 7 Feb., 19:50, William Hughes <wpihug...@gmail.com> wrote:
> > On Feb 7, 7:28 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> >
> >
> >
> >
> >
> > > On 7 Feb., 19:14, William Hughes <wpihug...@gmail.com> wrote:
> >
> > > > 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.-
> >
> > > You are in error again. There is the axiom of power set. For any F,
> > > there is P such that D e P if and only if D c F. According to it every
> > > subset of the countable set F exists. Will you dispute that the finite
> > > definitions of numbers are a subset of F?
> >
> > Yes. A subset must be constructable.-
>
> Sorry, we are in classical set theory. There nothing must be
> constructable.
>
>
> Perhaps you are interested in definition and domain of application of
> "subcountable"?
>
> In constructive mathematics
But only WM claims t be constrained to constructable mathematics here,
and has not the power to constrain anyone else.
And even WM does not follow those constraints consistently.
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