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Topic: Matheology § 191
Replies: 91   Last Post: Jan 18, 2013 2:44 AM

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Virgil

Posts: 9,012
Registered: 1/6/11
Re: Matheology � 191
Posted: Jan 13, 2013 5:44 PM
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In article
<0fa84faa-2103-4a2a-9c16-b6d498f23dd4@4g2000yqv.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:


> > The definition of a set being countable is that there is a surjection
> > from |N to that set.
> >
> > Thus in order to PROVE a set is countable one must show a surjection
> > from |N to that set, which is just a listing, possibly with repetitions,
> > of that sets members.
> >
> > But any listing of the paths of a Complete Infinite Binary Tree (as
> > infinite binary sequences) proves itself incomplete.
> >
> > Thus the set of paths cannot be made to fit the "countable" definition.

>
> Above you see the enumeration of the set
>
> 0.
> 0.0
> 0.1
> 0.00
> 0.01
> 0.10
> 0.11
> ...
>
> Regards, WM


Since every path of a Complete Infinite Binary Tree must have infintely
many nodes (or, equivalently, infinitely many branchings), your list of
finite objects contains none of them
--




Date Subject Author
1/12/13
Read Matheology § 191
mueckenh@rz.fh-augsburg.de
1/12/13
Read Re: Matheology § 191
Zaljohar@gmail.com
1/12/13
Read Re: Matheology § 191
mueckenh@rz.fh-augsburg.de
1/12/13
Read Re: Matheology � 191
Virgil
1/12/13
Read Re: Matheology § 191
mueckenh@rz.fh-augsburg.de
1/12/13
Read Re: Matheology § 191
Zaljohar@gmail.com
1/12/13
Read Re: Matheology § 191
mueckenh@rz.fh-augsburg.de
1/12/13
Read Re: Matheology � 191
Virgil
1/13/13
Read Re: Matheology § 191
Zaljohar@gmail.com
1/13/13
Read Re: Matheology § 191
mueckenh@rz.fh-augsburg.de
1/13/13
Read Re: Matheology � 191
Virgil
1/13/13
Read Re: Matheology § 191
mueckenh@rz.fh-augsburg.de
1/13/13
Read Re: Matheology � 191
Virgil
1/14/13
Read Re: Matheology § 191
mueckenh@rz.fh-augsburg.de
1/14/13
Read Re: Matheology � 191
Virgil
1/15/13
Read Re: Matheology § 191
mueckenh@rz.fh-augsburg.de
1/15/13
Read Re: Matheology � 191
Virgil
1/15/13
Read Re: Matheology § 191
mueckenh@rz.fh-augsburg.de
1/15/13
Read Re: WMatheology � 191
Virgil
1/15/13
Read Re: WMatheology § 191
mueckenh@rz.fh-augsburg.de
1/15/13
Read Re: WMatheology � 191
Virgil
1/15/13
Read Re: WMatheology § 191
mueckenh@rz.fh-augsburg.de
1/15/13
Read Re: WMatheology � 191
Virgil
1/16/13
Read Re: WMatheology § 191
mueckenh@rz.fh-augsburg.de
1/16/13
Read Re: WMatheology � 191
Virgil
1/16/13
Read Re: WMatheology § 191
mueckenh@rz.fh-augsburg.de
1/16/13
Read Re: WMatheology � 191
Virgil
1/16/13
Read Re: WMatheology § 191
mueckenh@rz.fh-augsburg.de
1/16/13
Read Re: WMatheology � 191
Virgil
1/17/13
Read Re: WMatheology � 191
Ralf Bader
1/17/13
Read Re: WMatheology §Organization: Anon
Virgil
1/17/13
Read Re: WMatheology § 191
mueckenh@rz.fh-augsburg.de
1/17/13
Read Re: WMatheology § 191
fom
1/17/13
Read Re: WMatheology § 191
mueckenh@rz.fh-augsburg.de
1/17/13
Read Re: WMatheology § 191
fom
1/17/13
Read Re: WMatheology § 191
mueckenh@rz.fh-augsburg.de
1/17/13
Read Re: WMatheology � 191
Virgil
1/18/13
Read Re: WMatheology § 191
Ralf Bader
1/18/13
Read Re: WMatheology § 191
Virgil
1/17/13
Read Re: WMatheology S 191
Jesse F. Hughes
1/17/13
Read Re: WMatheology S 191
mueckenh@rz.fh-augsburg.de
1/17/13
Read Re: WMatheology S 191
Jesse F. Hughes
1/17/13
Read Re: WMatheology S 191
mueckenh@rz.fh-augsburg.de
1/17/13
Read Re: WMatheology S 191
Jesse F. Hughes
1/17/13
Read Re: WMatheology S 191
Virgil
1/17/13
Read Re: WMatheology S 191
Virgil
1/17/13
Read Re: WMatheology � 191
Virgil
1/17/13
Read Re: WMatheology � 191
Virgil
1/17/13
Read Re: WMatheology § 191
mueckenh@rz.fh-augsburg.de
1/17/13
Read Re: WMatheology � 191
Virgil
1/13/13
Read Re: Matheology § 191
Zaljohar@gmail.com
1/13/13
Read Re: Matheology § 191
mueckenh@rz.fh-augsburg.de
1/13/13
Read Re: Matheology � 191
Virgil
1/13/13
Read Re: Matheology § 191
mueckenh@rz.fh-augsburg.de
1/13/13
Read Re: Matheology � 191
Virgil
1/14/13
Read Re: Matheology § 191
mueckenh@rz.fh-augsburg.de
1/14/13
Read Re: Matheology � 191
Virgil
1/13/13
Read Re: Matheology § 191
mueckenh@rz.fh-augsburg.de
1/13/13
Read Re: Matheology � 191
Virgil
1/13/13
Read Re: Matheology � 191
Virgil
1/12/13
Read Re: Matheology � 191
Virgil
1/13/13
Read Re: Matheology § 191
mueckenh@rz.fh-augsburg.de
1/13/13
Read Re: Matheology � 191
Virgil
1/13/13
Read Re: Matheology § 191
mueckenh@rz.fh-augsburg.de
1/13/13
Read Re: Matheology � 191
Virgil
1/14/13
Read Re: Matheology § 191
mueckenh@rz.fh-augsburg.de
1/14/13
Read Re: Matheology � 191
Virgil
1/14/13
Read Re: Matheology § 191
mueckenh@rz.fh-augsburg.de
1/14/13
Read Re: Matheology � 191
Virgil
1/15/13
Read Re: Matheology § 191
mueckenh@rz.fh-augsburg.de
1/15/13
Read Re: WMatheology � 191
Virgil
1/15/13
Read Re: WMatheology § 191
mueckenh@rz.fh-augsburg.de
1/15/13
Read Re: WMatheology � 191
Virgil
1/15/13
Read Re: WMatheology § 191
mueckenh@rz.fh-augsburg.de
1/15/13
Read Re: WMatheology � 191
Virgil
1/12/13
Read Re: Matheology § 191
Ben Bacarisse
1/12/13
Read Re: Matheology § 191
mueckenh@rz.fh-augsburg.de
1/12/13
Read Re: Matheology � 191
Virgil
1/13/13
Read Re: Matheology § 191
mueckenh@rz.fh-augsburg.de
1/13/13
Read Re: Matheology � 191
Virgil
1/12/13
Read Re: Matheology � 191
David C. Ullrich
1/12/13
Read Re: Matheology § 191
mueckenh@rz.fh-augsburg.de
1/12/13
Read Re: Matheology � 191
Virgil
1/13/13
Read Re: Matheology § 191
mueckenh@rz.fh-augsburg.de
1/13/13
Read Re: Matheology � 191
Virgil
1/14/13
Read Re: Matheology § 191
mueckenh@rz.fh-augsburg.de
1/14/13
Read Re: Matheology � 191
Virgil
1/14/13
Read Re: Matheology § 191
mueckenh@rz.fh-augsburg.de
1/14/13
Read Re: Matheology � 191
Virgil
1/12/13
Read Re: Matheology � 191
Virgil
1/13/13
Read Re: Matheology § 191
mueckenh@rz.fh-augsburg.de
1/13/13
Read Re: Matheology � 191
Virgil

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