```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 throughthe infinite nodes.  I can't move to the second path though infinityuntil I've completed the first, that is unless an algorith is proposedthat lets me idenify which infinite paths I've taken without completelytaking them.  I might identify a path by its representation as a rationalnumber.  Unfortunately that leaves out the irrational numbers.
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