Date: Mar 24, 2013 10:45 PM
Author: Virgil
Subject: Re: Matheology � 224

In article 
<4e692da8-beb2-4097-b9eb-c263c86d24b3@i5g2000pbj.googlegroups.com>,
"Ross A. Finlayson" <ross.finlayson@gmail.com> wrote:

> On Mar 24, 4:16 pm, Virgil <vir...@ligriv.com> wrote:
> > In article
> > <ab63154d-ab7e-4a03-be1b-17ac93226...@hd10g2000pbc.googlegroups.com>,
> >  "Ross A. Finlayson" <ross.finlay...@gmail.com> wrote:
> >
> >
> >
> >
> >
> >
> >
> >
> >

> > > On Mar 24, 2:51 pm, fom <fomJ...@nyms.net> wrote:
> > > > On 3/24/2013 4:34 PM, WM wrote:
> >
> > > > > On 24 Mrz., 21:29, Virgil <vir...@ligriv.com> wrote:
> > > > >> In article
> > > > >> <729f073f-8948-4eb9-991a-2bd249ac5...@c6g2000yqh.googlegroups.com>,

> >
> > > > >> A binary tree that contains one path of each positive natural number
> > > > >> length will necessarily also contain exactly one path of infinite
> > > > >> length.

> >
> > > > > Like the sequence
> > > > > 0.1
> > > > > 0.11
> > > > > 0.111
> > > > > ...
> > > > > that necessarily also contains its limit?

> >
> > > A binary tree that contains one path, of all zero-branches, of each
> > > finite length, will necessarily contain a path of 0-branches of
> > > infinite length.

> >
> > Better is
> >
> >     root
> >       |  \
> >       0   1
> >       |  \
> >       0   1
> >       |  \
> >       0   1
> >       |  \
> >       0   1
> >       |  \
> >       0   1
> >       |  \
> >       0   1
> >       |  \
> >       0   1
> >       |  \
> >
> >   And so on
> >
> > --

>
>
> A binary tree, of all 0's or 1's (0- or 1- branches) with paths of
> each finite length, has a path of infinite length


How acute of you to notice.
--