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

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mueckenh@rz.fh-augsburg.de

Posts: 15,304
Registered: 1/29/05
Re: Matheology § 210
Posted: Feb 7, 2013 11:57 AM
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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, because the upper limit would be
"all elements of F".

>  Hence we know D is
> sub-countable, but we do not know D is countable.


You intermingle elements D and sets D in a really refreshing way.
Nevertheless, we know that all correspondences together cannot
surpass aleph_0.

According to this definition the real numbers are subcountable. All
paths of the Binary Tree cross every finite level in a finite number
of nodes. Aleph_0 is not reached at any finite level - and there is
nothing, in particular no path, beyond every level. Nevertheless there
is no list of all paths.

A typical case of subcountability.

Regards, WM


Date Subject Author
2/5/13
Read Matheology § 210
mueckenh@rz.fh-augsburg.de
2/5/13
Read Re: Matheology § 210
fom
2/5/13
Read Re: Matheology § 210
mueckenh@rz.fh-augsburg.de
2/5/13
Read Re: Matheology § 210
William Hughes
2/5/13
Read Re: Matheology § 210
mueckenh@rz.fh-augsburg.de
2/5/13
Read Re: Matheology § 210
William Hughes
2/5/13
Read Re: Matheology � 210
Virgil
2/5/13
Read Re: Matheology § 210
fom
2/5/13
Read Re: Matheology � 210
Virgil
2/5/13
Read Re: Matheology § 210
fom
2/6/13
Read Re: Matheology § 210
mueckenh@rz.fh-augsburg.de
2/6/13
Read Re: Matheology § 210
fom
2/6/13
Read Re: Matheology § 210
mueckenh@rz.fh-augsburg.de
2/6/13
Read Re: Matheology � 210
Virgil
2/6/13
Read Re: Matheology § 210
fom
2/7/13
Read Re: Matheology § 210
mueckenh@rz.fh-augsburg.de
2/7/13
Read Re: Matheology � 210
Virgil
2/7/13
Read Re: Matheology § 210
mueckenh@rz.fh-augsburg.de
2/7/13
Read Re: Matheology § 210
William Hughes
2/7/13
Read Re: Matheology § 210
mueckenh@rz.fh-augsburg.de
2/7/13
Read Re: Matheology § 210
William Hughes
2/7/13
Read Re: Matheology § 210
mueckenh@rz.fh-augsburg.de
2/7/13
Read Re: Matheology § 210
William Hughes
2/7/13
Read Re: Matheology § 210
mueckenh@rz.fh-augsburg.de
2/7/13
Read Re: Matheology § 210
William Hughes
2/7/13
Read Re: Matheology § 210
mueckenh@rz.fh-augsburg.de
2/7/13
Read Re: Matheology § 210
William Hughes
2/7/13
Read Re: Matheology § 210
mueckenh@rz.fh-augsburg.de
2/7/13
Read Re: Matheology § 210
William Hughes
2/7/13
Read Re: Matheology § 210
mueckenh@rz.fh-augsburg.de
2/7/13
Read Re: Matheology § 210
William Hughes
2/7/13
Read Re: Matheology § 210
mueckenh@rz.fh-augsburg.de
2/7/13
Read Re: Matheology § 210
William Hughes
2/7/13
Read Re: Matheology § 210
mueckenh@rz.fh-augsburg.de
2/7/13
Read Re: Matheology � 210
Virgil
2/7/13
Read Re: Matheology § 210
mueckenh@rz.fh-augsburg.de
2/7/13
Read Re: Matheology § 210
William Hughes
2/8/13
Read Re: Matheology § 210
mueckenh@rz.fh-augsburg.de
2/8/13
Read Re: Matheology � 210
Virgil
2/8/13
Read Re: Matheology § 210
fom
2/8/13
Read Re: Matheology § 210
mueckenh@rz.fh-augsburg.de
2/8/13
Read Re: Re: Matheology § 210
Michael Stemper
2/8/13
Read Re: Matheology § 210
mueckenh@rz.fh-augsburg.de
2/8/13
Read Re: Matheology � 210
Virgil
2/8/13
Read Re: Matheology � 210
Virgil
2/7/13
Read Re: Matheology � 210
Virgil
2/7/13
Read Re: Matheology � 210
Virgil
2/7/13
Read Re: Matheology § 210
fom
2/8/13
Read Re: Matheology § 210
mueckenh@rz.fh-augsburg.de
2/8/13
Read Re: Matheology � 210
Virgil
2/7/13
Read Re: Matheology � 210
Virgil
2/7/13
Read Re: Matheology § 210
fom
2/7/13
Read Re: Matheology � 210
Virgil
2/7/13
Read Re: Matheology § 210
fom
2/7/13
Read Re: Matheology � 210
Virgil
2/8/13
Read Re: Matheology § 210
mueckenh@rz.fh-augsburg.de
2/8/13
Read Re: Matheology � 210
Virgil
2/7/13
Read Re: WMytheology � 210
Virgil
2/7/13
Read Re: WMytheology § 210
fom
2/7/13
Read Re: Matheology � 210
Virgil
2/7/13
Read Re: Matheology § 210
mueckenh@rz.fh-augsburg.de
2/7/13
Read Re: Matheology § 210
fom
2/7/13
Read Re: Matheology § 210
mueckenh@rz.fh-augsburg.de
2/7/13
Read Re: Matheology § 210
fom
2/8/13
Read Re: Matheology § 210
Ralf Bader
2/7/13
Read Re: Matheology � 210
Virgil
2/8/13
Read Re: Matheology § 210
mueckenh@rz.fh-augsburg.de
2/7/13
Read Re: Matheology � 210
Virgil
2/7/13
Read Re: Matheology § 210
fom
2/7/13
Read Re: Matheology § 210
fom
2/7/13
Read Re: Matheology § 210
fom
2/7/13
Read Re: Matheology § 210
fom
2/7/13
Read Re: Matheology § 210
fom
2/7/13
Read Re: Matheology § 210
fom
2/6/13
Read Re: Matheology � 210
Virgil
2/5/13
Read Re: Matheology � 210
Virgil
2/6/13
Read Re: Matheology § 210
mueckenh@rz.fh-augsburg.de
2/6/13
Read Re: Matheology � 210
Virgil
2/7/13
Read Re: Matheology § 210
mueckenh@rz.fh-augsburg.de
2/7/13
Read Re: WM's WMytheology
Virgil
2/8/13
Read Re: Matheology § 210
Scott Berg

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