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

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 Virgil Posts: 8,833 Registered: 1/6/11
Re: Matheology � 233
Posted: Apr 3, 2013 2:48 PM

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

> On 3 Apr., 00:03, Virgil <vir...@ligriv.com> wrote:
> > In article
> >
> >
> >
> >
> >
> >  WM <mueck...@rz.fh-augsburg.de> wrote:

> > > 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.
> >
> > What in mathematics is not a matter of belief?

>
> Given that an enumeration of all rational numbers is believed to form
> a Cantor-list

But it is not given.

The only such "ennumeration" that I know of is summarily restricted to
rationals between 0 and 1 inclusive, and is ambiguous in that what I
like to call binary rationals but fom prefers to call dyadic rationals
in that range all have dual representations.

So I certainly do not believe it

> then the following is not a matter of belief.

Since the claim of "given" is false, what follows is irrelevant.
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