On 8 Jun., 00:15, Virgil <virg...@nowhere.com> wrote:
> In a maximal infinite binary tree a path can have only one "end" and > all paths have the same end: the root node.
That is the beginning. If you dislike the name "end", then speak of X = "path without its first n nodes".
There are infinitely many nodes mapped on every X, namely those which belong to that X. The X exhaust the complete binary tree, because there is no node that remains unmapped. The X of every real number you wish, including 1/3, 1/sqrt(2), 1/pi and so on, is among all paths constructed.