In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 26 Jan., 01:46, Virgil <vir...@ligriv.com> wrote: > > > > Of interest is this: If the same set of > > > nodes has to describe both, the Binary Tree with finite paths and that > > > with infinite paths, then it is impossible to discern, alone by nodes, > > > whether we work in the former or the latter. > > > > There is no such thing as a Complete Infinite Binary Tree with finite > > paths. > > So you agree that there is a level omega?
Why should I agree to add another level to the infinitely many finite levels that must already exist in order to have a COMPLETE INFINITE BINARY TREE at all? > > Remember, in the Binary Tree > paths are defined by nodes or edges - and only by them.
Remember that, at least outside Wolkenmuekenheim, in every Complete Infinite Binary Tree each path is, by definition, a MAXIMAL sequence of parent-child linked nodes, and thus in any COMPLETE Infinite Binary Tree no finite set of nodes is a a MAXIMAL sequence of parent-child linked nodes and thus is not a path.
Thus, in any binary tree a path (MAXIMAL sequence of parent-child linked nodes) must start with the root node, and can only end with a leaf node, so that unless WM can identify lots of leaf nodes in his scrambled version of a CIBT, his alleged finite pathed CIBT exists only in Wolkenmuekenheim. --