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Topic: Matheology � 300
Replies: 14   Last Post: Jul 23, 2013 1:31 AM

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Virgil

Posts: 9,012
Registered: 1/6/11
Re: Matheology � 300
Posted: Jul 23, 2013 1:31 AM
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In article <145ccf00-437a-4ba9-92c7-4dfaf133fd9f@googlegroups.com>,
mueckenh@rz.fh-augsburg.de wrote:

> On Monday, 22 July 2013 21:45:08 UTC+2, Virgil wrote:
> > It is the structure of the Complete Infinite Binary Tree which cannot
> > exist with only binary rational paths, since the existence of all the
> > binary rational approximations to an irrational in such a tree requires
> > the existence of the path for that irrational as well.

>
> Paths of irrationals in mathematics are not defined by "structure". That is
> purest matheology.


They may not be in WM's wild weird world of WMytheology, but they are
in the wider worlds of mathematics that allow such sets as |N and 2^|N.
>
> For every finite step n in the construction of the Binary Tree (by nodes or
> by FIS or by paths of rationals), there is no irrational path. They sneak in
> only after all finite steps.


Quite true.

But a binary tree cannot contain all finite paths without containing all
infinite paths just like a unary tree cannot contain all FISONs as
subsets without containing |N.



> That is obvious nonsense. But if it was not
> nonsense, then the same could happen in every Cantor-list.


Not until lists (which are really just unary trees) become binary trees.

Which they are not.
--





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