Date: Dec 12, 2012 8:13 PM
Author: george
Subject: Re: On the infinite binary Tree
On Dec 12, 12:07 pm, WM <mueck...@rz.fh-augsburg.de> wrote:

> > Let's see:

>

> > Lets take the first degree binary tree which is the following

>

> > 0. One node, no paths

>

> We could say 1 degenerated or empty path. Set theorists like empty

> things.

Exactly. As surely as there is an empty string of length 0 or an an

empty set of cardinality 0,

there is a null path from the root to the root. The tree with 1 node

has ONE path.

The point here is that EVERY finite binary tree has EXACTLY THE SAME

number of nodes as paths,

since EVERY PATH ENDS AT A NODE, injectively&surjectively&bijectively.

There is an obvious and natural bijection between a path and the node

where it ends.

This makes WM's talk about "limits" even stupider than usual --

obviously the limit of

a sequence WHOSE EVERY ELEMENT is 1 IS ONE. The elements were the

ratio of number of paths

to number of nodes.