Virgil
Posts:
4,482
Registered:
1/6/11
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Re: Matheology � 191
Posted:
Jan 13, 2013 3:47 PM
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In article
<91cc9673-aa94-45c5-ba92-f50a1c7012ea@b8g2000yqh.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 12 Jan., 22:58, Virgil <vir...@ligriv.com> wrote:
> > In article
> > <f62302b5-c3c6-4b54-8437-6f9d7bc00...@4g2000yqv.googlegroups.com>,
> >
> > WM <mueck...@rz.fh-augsburg.de> wrote:
> > > 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.
> >
> > Aleph_0 * aleph_0 = aleph_0 but 2 ^ aleph_0 > aleph_0, and that is the
> > number of paths.
>
> Can you name, define, or at least "discern" one of the paths missing
> in my Binary Tree? Note: I do not hide my receipe of construction any
> longer. I use every tail that can be described and communicated in any
> language.
If your set of paths ( as infinite binary sequences) is capable of being
listed then that very capability proves, a la Cantor, that it is
incomplete, and if it cannot be listed then it is, by definition, not
countable.
> >
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