In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> 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.
What in mathematics is not a matter of belief? Even small natural numbers have no physical existence but are merely creations of the mind.
And if other minds than WM's can create what WM does not and cannot either comprehend or imagine, that is only WM's loss. --