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Topic: Matheology � 233
Replies: 37   Last Post: May 12, 2014 10:24 AM

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Virgil

Posts: 8,833
Registered: 1/6/11
Re: Matheology � 233
Posted: Mar 30, 2013 8:56 PM
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In article
<2bc13fff-5cbb-43dd-a06a-218c68c99849@m9g2000vbc.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 30 Mrz., 22:11, Virgil <vir...@ligriv.com> wrote:
>

> > > > Thus there is always at least one bit of any listed entry disagreeing
> > > > with the antidiagonanl, just as the Cantor proof requires.

> >
> > > In a list containing every rational: Is there always, i.e., up to
> > > every digit, an infinite set of paths identical with the anti-
> > > diagonal? Yes or no?

> >
> > The set of paths in any Complete Infinite Binary Tree which agree with
> > any particular path up to its nth node is equinumerous with the set of
> > all paths in the entire tree i.e., is uncountably infinite.

>
> This was the question: In a list containing every rational: Is there
> always, i.e., up to every digit, an infinite set of paths identical
> with the anti-diagonal? Yes or no?


Lists and trees are different. And anti-diagonals derive from lists, not
trees.
The entries in list are well ordered.
The entries in a Complete Infinite Binary Tree are densely ordered.
Those order types are incompatible.
So questions, like WM's, which confuse them, are nonsense.
At least outside Wolkenmuekenheim.
--





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