Charles, Interesting point-- but, all of these theories would be weaker then the standard axioms, and so there would be *even more* about numbers left undefined in them.
--Abram On Tue, Oct 28, 2008 at 10:46 PM, Charles Hixson <[EMAIL PROTECTED]> wrote: > Excuse me, but I thought there were subsets of Number theory which were > strong enough to contain all the integers, and perhaps all the rational, but > which weren't strong enough to prove Gödel's incompleteness theorem in. I > seem to remember, though, that you can't get more than a finite number of > irrationals in such a theory. And I think that there are limitations on > what operators can be defined. > > Still, depending on what you mean my Number, that would seem to mean that > Number was well-defined. Just not in Number Theory, but that's because > Number Theory itself wasn't well-defined. ------------------------------------------- agi Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: https://www.listbox.com/member/?member_id=8660244&id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
