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

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mueckenh@rz.fh-augsburg.de

Posts: 15,457
Registered: 1/29/05
Re: Matheology § 191
Posted: Jan 12, 2013 12:03 PM
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On 12 Jan., 16:24, Ben Bacarisse <ben.use...@bsb.me.uk> wrote:
> WM <mueck...@rz.fh-augsburg.de> writes:
> > Matheology § 191
>
> > The complete infinite Binary Tree can be constructed by first
> > constructing all aleph_0 finite paths and then appending to each path
> > all aleph_0 finiteley definable tails from 000... to 111...

>
> >         0
> >       1, 2
> >   3, 4, 5, 6
> > 7, ...

>
> > This Binary Tree contains aleph_0 * aleph_0 = aleph_0 paths.
>
> No, it contains aleph_0 * whatever the cardinality of the set of tails
> is.  Talk about begging the question!


A tail can be defined by a finite word *only*. Nobody can quote an
infinite string digit by digit - although most mathematicians believe
that instinctively when pondering about set theory (but never when
doing analysis).

Therefore every definition of a tail belongs to the set of finite
words and hence to a set of cardinality less than aleph_0. (In fact
during the lifetime of the universe the set of used words will remain
finite.)

Regards, WM


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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