Virgil
Posts:
4,482
Registered:
1/6/11
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Re: Matheology � 198
Posted:
Jan 26, 2013 5:10 PM
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In article
<054da2be-2f0a-4290-b356-10eb0a5e1791@r14g2000yqe.googlegroups.com>,
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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