No, because I wasn't talking about artificially imposed orderings. One can always define a strict ordering by means of something like

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x < y iff Re(x) < Re(y) or Re(x)=Re(y) and Im(x)<Im(y) However, the usual meaning of x<y for x,y \in C is undefined, except for x,y real. I think the previous poster used the term "natural ordering", I just dropped the adjective "natural", as being unnecessary for the discussion. Cheer On Wed, Jul 13, 2005 at 12:15:01PM +0200, Bruno Marchal wrote: > > Le 13-juil.-05, ? 06:02, Russell Standish a ?crit : > > > >Complex numbers indeed do not have an ordering (being basically > > points on a plane) > > > So you pretend the axiom of choice is false. It is easy to build an > ordering of the complex numbers through it. > > There is no ordering *which satisfies some algebraic desiderata*. But > as a set, you can always ordered it (given that the axiom of choice is > consistent with ZF). > > Bruno > > > http://iridia.ulb.ac.be/~marchal/ -- *PS: A number of people ask me about the attachment to my email, which is of type "application/pgp-signature". Don't worry, it is not a virus. It is an electronic signature, that may be used to verify this email came from me if you have PGP or GPG installed. Otherwise, you may safely ignore this attachment. ---------------------------------------------------------------------------- A/Prof Russell Standish Phone 8308 3119 (mobile) Mathematics 0425 253119 (") UNSW SYDNEY 2052 [EMAIL PROTECTED] Australia http://parallel.hpc.unsw.edu.au/rks International prefix +612, Interstate prefix 02 ----------------------------------------------------------------------------

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