>Actually, I'm just paraphrasing my advanced calaculus book. They say that C is not ordered, and there are several ways to show this (but they don't explain further). But all ordered number fields must obey 4 properties of inequalities, as I said:

That's true only if we consider the field C. I was talking about an order on the set C. In this case, there are only 3 inequalities (axioms): reflexivity, tranzitivity and antisymmetry.

>>Which means 0 <= i. How is this?

0+0*i <= 0+1*i

>>I never said that C and R are isomorphic. I said RxR is isomorphic with C. (An element in RxR is an order pair: (x,y).)
>>
>I don't quite follow. What does C plane look like here?

If z is from C and z=a+b*i, then we associate to z the pair (a,b) from RxR. And this is one isomorphism between C and RxR. And this is why C is called sometimes: the plane of the complex numbers.

Vlad