Well-ordering follow-up

[franktaw at netscape.net]

Actually, it doesn't work (at least for the reals).  It is possible 
(given the axiom of choice) to well-order the real numbers, but it 
isn't possible to *specify* such an ordering.  So you can't identify a 
number as "the least uninteresting real number under <whatever> well 
ordering", because you can't fill in the <whatever>.

Franklin T. Adams-Watters
16 W. Michigan Ave.
Palatine, IL 60067
847-776-7645

-----Original Message-----
From: Henry Gould <gould at math.wvu.edu>
To: Jim Nastos <nastos at gmail.com>; seqfan at ext.jussieu.fr
Sent: Sun, 12 Mar 2006 19:00:22 -0500
Subject: Re: Well-ordering follow-up

  Jim Nastos wrote:
 > Professor Gould,
 > my apologies: I didn't notice that the well-orderedness of the reals
 > was an axiom-of-choice equivalence, so my objection is withdrawn.
 > J
 >
 > OKAY, THANKS, ANYWAY YOU WANT IT! My original proof still stands?

 Henry


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