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Topic: Matheology § 198
Replies: 40   Last Post: Jan 26, 2013 6:54 PM

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 Virgil Posts: 8,833 Registered: 1/6/11
Re: Matheology � 198
Posted: Jan 26, 2013 5:10 PM

In article
WM <mueckenh@rz.fh-augsburg.de> 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.
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