On 2 Apr., 01:54, Virgil <vir...@ligriv.com> wrote:
> > I am not at all sure that it is even possible to build any binary tree > this way but it is clearly impossible to built a COMPLETE INFINITE > BINARY TREE, this way.
Given the foundations of matheology, it is possible to construct every node / every finite path of a Binary Tree that is complete with respect to its nodes. > > For one thing, in a CIBT, every path is by definition maximal in the > sense that no additional node can be added to a path without making the > result not a path, and is also minimal in the sense that no node can be > removed from it without making the result not a path. > > In WM's "trees", every FISON (Finite Initial Sequncee Of Nodes) appears > to be a path, which is quite differnt notion of path.
Call it as you like. I call it finite path as an abbreviation of FIS of an infinite path. > > > It is impossible to write them out. Yes. But they are constructed like > > the finite paths. It is impossible to prohibit infinite paths (of > > rationals and of irrationals) to be constructed when the complete set > > of nodes of the Binary Tree is constructed by means of all finite > > paths. Therefore it is impossible to distinguish infinite paths by > > nodes other than be naming infinite sets of nodes. Alas there are only > > countably many names available. > > Thus not all CIBT-paths are nameable, just like not all real numbers are > nameable.
They are not even distinguishable by nodes. They are purest belief.