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

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


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

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