[FOM] Re: Excluded middle & cardinality of the reals

Mark van Atten Mark.vanAtten at univ-paris1.fr
Wed Jun 30 02:27:32 EDT 2004

Andrej Bauer (Mon, 28 Jun 2004 09:32:03 +0200) asked:

> Perhaps someone out there knows: is there a known constructive proof
> that the set of reals (any kind of reals) is not countable?

If one thinks of the decimal expansions of the reals as choice sequences,
a continuity principle suffices to show that the reals cannot be enumerated.

Brouwer began using this argument as an alternative to the diagonal method
in his course on set theory of 1916-1917.


IHPST (Paris 1/CNRS), http://www-ihpst.univ-paris1.fr
13 rue du Four, F-75006 Paris, France

Ce message a été vérifié par MailScanner
pour des virus ou des polluriels et rien de
suspect n'a été trouvé.

More information about the FOM mailing list