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Topic: This Week's Finds in Mathematical Physics (Week 236)
Replies: 29   Last Post: Aug 24, 2006 9:00 AM

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 G. A. Edgar Posts: 2,510 Registered: 12/8/04
Re: Order-preserving embeddings of ordinals in the real numbers
Posted: Jul 28, 2006 2:00 PM
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In article <eadai0\$g34\$1@news.ks.uiuc.edu>, David Madore
<david.madore@ens.fr> wrote:

> > Which ordinals can we do this for?
>
> If you're asking which ordinals are order-isomorphic to a subset of
> the real numbers, the answer is simple (at least, assuming the axiom
> of choice): exactly the countable ordinals.

And more generally: any countable totally ordered set can be imbedded
in the rationals.

--
G. A. Edgar http://www.math.ohio-state.edu/~edgar/

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