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Topic: Matheology � 233
Replies: 36   Last Post: Apr 2, 2013 5:56 PM

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mueckenh@rz.fh-augsburg.de

Posts: 13,481
Registered: 1/29/05
Re: Matheology § 233
Posted: Mar 30, 2013 6:31 PM
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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?

Regards, WM



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