>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.
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As I suspected, we're in different math zones...you're in algebra and I'm in calculus.
(Oops -- one of my cats is having a fight outside)
The more I compare two books, one on each area, the more I see they're different worlds. I never thought too much about it when I took courses...

>>>Which means 0 <= i. How is this?
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>0+0*i <= 0+1*i
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Okay, maybe in algebra's world. In calculus, this does not hold, since i is defined more precisely. (That disagreement is kind of interesting)

>>I don't quite follow. What does C plane look like here?
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>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.
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Gotcha. In the calculus sequence of courses we usually mapped C by magnitudes into R, but yours works too.