Date: Dec 12, 2012 8:13 PM
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
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.