Date: Apr 4, 2013 2:42 PM
Author: Virgil
Subject: Re: Matheology � 224

In article 
<0ffe7057-d617-486f-96c1-3421254d7f15@cd3g2000vbb.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> 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,
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