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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 1, 2013 7:54 PM

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

> On 1 Apr., 17:05, William Hughes <wpihug...@gmail.com> wrote:
> > On Mar 27, 8:55 am, WM <mueck...@rz.fh-augsburg.de> wrote:
> >

> > > Matheology § 233
> >
> > > The set of all termination decimals is a subset of Q. If the set of
> > > all terminating decimals of the unit interval is arranged as set of
> > > all terminating paths of the decimal tree,

> >
> > It is, of course, impossible to write this out
> > (there number of terminating decimals is infinite).
> >

> But it is possible to construct the Binary Tree according to this
> method.

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.

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.

> It is impossible to write them out. Yes. But they are constructed like
> the finita 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.

Nothing in the vast extent of mathematics outide Wolkenmuekenheim
requires that all things be nameable.
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