In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 4 Apr., 19:40, William Hughes <wpihug...@gmail.com> wrote: > > On Apr 4, 6:43 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > On 4 Apr., 18:21, William Hughes <wpihug...@gmail.com> wrote: > > > > > > On Apr 4, 5:19 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > > > > > On 4 Apr., 16:08, William Hughes <wpihug...@gmail.com> wrote: > > > > > There is no need to say what numbers belong to mathematics - in > > > > > mathematics. There is no need to say what paths belong to the Binary > > > > > Tree > > > > > > However, you keep talking about two types of paths, > > > > > Not at all. I talk about sets of nodes that are in the Binary Tree. > > > > Indeed, and some of these subsets of nodes are paths and > > some are not. > > In the Binary Tree there is no stop at any path.
By the time one has a path one has infinitely many nodes in it, at least for a CIBT. > > > You talk about subsets of nodes with a last node > > and subsets of nodes without a last node. However, > > you refuse outright to indicate what makes a subset of nodes > > a path (certainly not all subsets of nodes are paths). > > All nodes that belong to a finite path
There are no such things as finite paths in any Complete Infinite Binary Tree.
> belong to an infinite path > too. That is the character of the Binary Tree. There is no further > limitation possible. There is no further indication necessary or > possible. > > Abandon your untenable position.
It may be untenable inside Wolkenmuekenheim, but nowhere else, and much of what WM claims is untenable anywhere else.
> Or try (and fail) to define a limit > that distinguishes both Binary Trees.
The only binary tree of interest here is the Complete Infinite Binary Tree in which each path is order isomorphic to |N. --