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.