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

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Virgil

Posts: 9,012
Registered: 1/6/11
Re: Matheology � 233
Posted: Mar 31, 2013 1:29 AM
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WM <mueck...@rz.fh-augsburg.de> wrote:


> 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.

Anti-diagonals derive ONLY from lists, never from trees,
and paths of the type referred to exist only in trees, not in lists.


The entries in any list are WELL-ORDERED.

The paths in any Complete Infinite Binary Tree are DENSELY ORDERED.

Those order types, well-ordering versus dense orderings, are entirely
incompatible.

So questions, like WM's, which confuse and conflate them, are nonsense.

At least everywhere outside Wolkenmuekenheim.
--





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