We define an ordered field as the following: Definition An ordered field is a field F, together with a subset PC F, called the positive sel, such that R1: Vr, y P, x+yEP; R2: Va, y P, x y P; R3: Vr EF, exactly one of the following must hold true: EP, or - EP, or x = 0. Also for a, b F, We define a