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Topic: On the infinite binary Tree
Replies: 64   Last Post: Dec 17, 2012 11:06 AM

 Messages: [ Previous | Next ]
 forbisgaryg@gmail.com Posts: 43 Registered: 11/26/12
Re: On the infinite binary Tree
Posted: Dec 14, 2012 1:17 PM

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
>
>
>
>
>
> 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.

Date Subject Author
12/12/12 Zaljohar@gmail.com
12/12/12 mueckenh@rz.fh-augsburg.de
12/12/12 Virgil
12/12/12 mueckenh@rz.fh-augsburg.de
12/12/12 Zaljohar@gmail.com
12/13/12 mueckenh@rz.fh-augsburg.de
12/13/12 trj
12/13/12 Virgil
12/13/12 mueckenh@rz.fh-augsburg.de
12/13/12 Virgil
12/13/12 mueckenh@rz.fh-augsburg.de
12/13/12 mueckenh@rz.fh-augsburg.de
12/13/12 Virgil
12/13/12 Zaljohar@gmail.com
12/13/12 mueckenh@rz.fh-augsburg.de
12/13/12 Zaljohar@gmail.com
12/13/12 mueckenh@rz.fh-augsburg.de
12/13/12 Virgil
12/13/12 Virgil
12/13/12 mueckenh@rz.fh-augsburg.de
12/13/12 Virgil
12/13/12 Virgil
12/13/12 Virgil
12/13/12 Zaljohar@gmail.com
12/13/12 mueckenh@rz.fh-augsburg.de
12/13/12 Virgil
12/13/12 Zaljohar@gmail.com
12/13/12 mueckenh@rz.fh-augsburg.de
12/13/12 Virgil
12/14/12 mueckenh@rz.fh-augsburg.de
12/13/12 Zaljohar@gmail.com
12/13/12 mueckenh@rz.fh-augsburg.de
12/13/12 Virgil
12/14/12 Zaljohar@gmail.com
12/14/12 Zaljohar@gmail.com
12/15/12 mueckenh@rz.fh-augsburg.de
12/15/12 Virgil
12/14/12 mueckenh@rz.fh-augsburg.de
12/14/12 Tanu R.
12/14/12 Virgil
12/15/12 mueckenh@rz.fh-augsburg.de
12/15/12 Virgil
12/12/12 Virgil
12/13/12 mueckenh@rz.fh-augsburg.de
12/12/12 george
12/13/12 Zaljohar@gmail.com
12/13/12 mueckenh@rz.fh-augsburg.de
12/13/12 george
12/14/12 mueckenh@rz.fh-augsburg.de
12/14/12 Virgil
12/14/12 mueckenh@rz.fh-augsburg.de
12/14/12 Tanu R.
12/14/12 Virgil
12/15/12 mueckenh@rz.fh-augsburg.de
12/15/12 Virgil
12/15/12 Tanu R.
12/14/12 Charlie-Boo
12/14/12 forbisgaryg@gmail.com
12/15/12 ross.finlayson@gmail.com
12/15/12 forbisgaryg@gmail.com
12/15/12 ross.finlayson@gmail.com
12/16/12 forbisgaryg@gmail.com
12/17/12 ross.finlayson@gmail.com
12/16/12 Ciekaw
12/16/12 Virgil