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Topic: Matheology § 210
Replies: 80   Last Post: Feb 8, 2013 5:45 PM

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 William Hughes Posts: 2,268 Registered: 12/7/10
Re: Matheology § 210
Posted: Feb 7, 2013 2:17 PM

On Feb 7, 7:59 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> On 7 Feb., 19:50, William Hughes <wpihug...@gmail.com> wrote:
>
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> > 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:
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> > > > > > <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.

In classical set theory the accessible numbers are listable

Note from the Wikipedia quote

> Constructively it is consistent to assert the
> subcountability of some uncountable collections

(Wikipedia)

Date Subject Author
2/5/13 mueckenh@rz.fh-augsburg.de
2/5/13 fom
2/5/13 mueckenh@rz.fh-augsburg.de
2/5/13 William Hughes
2/5/13 mueckenh@rz.fh-augsburg.de
2/5/13 William Hughes
2/5/13 Virgil
2/5/13 fom
2/5/13 Virgil
2/5/13 fom
2/6/13 mueckenh@rz.fh-augsburg.de
2/6/13 fom
2/6/13 mueckenh@rz.fh-augsburg.de
2/6/13 Virgil
2/6/13 fom
2/7/13 mueckenh@rz.fh-augsburg.de
2/7/13 Virgil
2/7/13 mueckenh@rz.fh-augsburg.de
2/7/13 William Hughes
2/7/13 mueckenh@rz.fh-augsburg.de
2/7/13 William Hughes
2/7/13 mueckenh@rz.fh-augsburg.de
2/7/13 William Hughes
2/7/13 mueckenh@rz.fh-augsburg.de
2/7/13 William Hughes
2/7/13 mueckenh@rz.fh-augsburg.de
2/7/13 William Hughes
2/7/13 mueckenh@rz.fh-augsburg.de
2/7/13 William Hughes
2/7/13 mueckenh@rz.fh-augsburg.de
2/7/13 William Hughes
2/7/13 mueckenh@rz.fh-augsburg.de
2/7/13 William Hughes
2/7/13 mueckenh@rz.fh-augsburg.de
2/7/13 Virgil
2/7/13 mueckenh@rz.fh-augsburg.de
2/7/13 William Hughes
2/8/13 mueckenh@rz.fh-augsburg.de
2/8/13 Virgil
2/8/13 fom
2/8/13 mueckenh@rz.fh-augsburg.de
2/8/13 Michael Stemper
2/8/13 mueckenh@rz.fh-augsburg.de
2/8/13 Virgil
2/8/13 Virgil
2/7/13 Virgil
2/7/13 Virgil
2/7/13 fom
2/8/13 mueckenh@rz.fh-augsburg.de
2/8/13 Virgil
2/7/13 Virgil
2/7/13 fom
2/7/13 Virgil
2/7/13 fom
2/7/13 Virgil
2/8/13 mueckenh@rz.fh-augsburg.de
2/8/13 Virgil
2/7/13 Virgil
2/7/13 fom
2/7/13 Virgil
2/7/13 mueckenh@rz.fh-augsburg.de
2/7/13 fom
2/7/13 mueckenh@rz.fh-augsburg.de
2/7/13 fom
2/7/13 Virgil
2/8/13 mueckenh@rz.fh-augsburg.de
2/7/13 Virgil
2/7/13 fom
2/7/13 fom
2/7/13 fom
2/7/13 fom
2/7/13 fom
2/7/13 fom
2/6/13 Virgil
2/5/13 Virgil
2/6/13 mueckenh@rz.fh-augsburg.de
2/6/13 Virgil
2/7/13 mueckenh@rz.fh-augsburg.de
2/7/13 Virgil
2/8/13 Scott Berg