In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> There is no need to say what numbers belong to mathematics - in > mathematics.
There is every need, at least if one is to be clear about what mathematics consists of, which WM clearly wants to avoid.
> There is no need to say what paths belong to the Binary > Tree - in mathemativs.
It is necessary in mathematics, even if not in mathemativs, to define what one means by a path in a tree, the usual definition being a maximal chain of parent-child nodes, though WM's allows non-maximal such chains.
>Every path that you can form by unioning finite paths
In a standard Complete Infinite Binary Tree, at least using the standard definition of paths, no union of two or more distinct paths can ever be a path.
What WM is talking about might well be called FISONs, finite initial sequences of nodes, though not paths in a COMPLETE INFINITE BINARY TREE, in which case a union of two of them would be another FISON only if one is a sub-FISON of the other.
> is of course a path of the Binary Tree. Every node you point to, > is a node of a path, in fact even of a finite path.
There cannot be any finite paths in a CIBT, only finite FISONs.
> And this does not > change, whether or not the Binary Tree is defined so or so.
If no COMPLETE INFINITE BINARY TREE is defined at all, there are no paths or FISONs or nodes or anything, at least not outside odd places like Wolkenmuekenheim, --