Date: Dec 14, 2012 1:17 PM
Author: forbisgaryg@gmail.com
Subject: Re: On the infinite binary Tree

On Friday, December 14, 2012 6:30:11 AM UTC-8, Charlie-Boo wrote:
> On Dec 12, 5:26 am, Zuhair <zaljo...@gmail.com> wrote:
>
>
>

> > Lets take the third degree binary tree
>
> >
>
> >      0
>
> >    /    \
>
> >   0     1
>
> >  / \    / \
>
> > 0  1 0  1
>
> >
>
> > Now this has 7 nodes BUT 8 paths, those are
>
> >
>
> > 0-0
>
> > 0-1
>
> > 1-0
>
> > 1-1
>
> > 0-0-0
>
> > 0-0-1
>
> > 0-1-0
>
> > 0-1-1
>
>
>
> Only 2 start with 1 and 6 start with 0. Shouldn't it be 50-50? If
>
> you start with 0 then all start with 0. You seem to be inconsistent
>
> in your manipulations of the tree.


four of his paths start at second level nodes.

> You need to diagonalize the binary tree rather than the list of real
>
> numbers - and account for multiple trees representing the same
>
> number. Or just ignore the real number interpretation and deal with
>
> binary strings without regard to numbers.
>
>
>
> My many examples of diagonalization in different contexts is a model
>
> to do just that. It's always good to generalize.


My concern is how one shows there are countably many paths through
the infinite nodes. I can't move to the second path though infinity
until I've completed the first, that is unless an algorith is proposed
that lets me idenify which infinite paths I've taken without completely
taking them. I might identify a path by its representation as a rational
number. Unfortunately that leaves out the irrational numbers.