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Topic: Matheology § 233
Replies: 20   Last Post: Apr 4, 2013 10:16 AM

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 mueckenh@rz.fh-augsburg.de Posts: 18,076 Registered: 1/29/05
Re: Matheology § 233
Posted: Apr 2, 2013 4:14 PM

On 2 Apr., 01:54, Virgil <vir...@ligriv.com> wrote:

>
> I am not at all sure that it is even possible to build  any binary tree
> this way but it is clearly impossible to built a COMPLETE INFINITE
> BINARY TREE, this way.

Given the foundations of matheology, it is possible to construct every
node / every finite path of a Binary Tree that is complete with
respect to its nodes.
>
> For one thing, in a CIBT, every path is by definition maximal in the
> sense that no additional node can be added to a path without making the
> result not a path, and is also minimal in the sense that no node can be
> removed from it without making the result not a path.
>
> In WM's "trees", every FISON (Finite Initial Sequncee Of Nodes) appears
> to be a path, which is quite differnt notion of path.

Call it as you like. I call it finite path as an abbreviation of FIS
of an infinite path.
>
> > It is impossible to write them out. Yes. But they are constructed like
> > the finite paths. It is impossible to prohibit infinite paths (of
> > rationals and of irrationals) to be constructed when the complete set
> > of nodes of the Binary Tree is constructed by means of all finite
> > paths. Therefore it is impossible to distinguish infinite paths by
> > nodes other than be naming infinite sets of nodes. Alas there are only
> > countably many names available.

>
> Thus not all CIBT-paths are nameable, just like not all real numbers are
> nameable.

They are not even distinguishable by nodes. They are purest belief.

Regards, WM