An ordered field is a field F, and a subset PCF, called a positive set, such that (a) If x, y EP, then x + y € P; (b) If x, y EP, then x y € P; . (c) For any x E F, exactly one of the following must hold true: xEP, or x = P, or x = = 0. Also recall that for a, b E F, We define a < b to mean an b - a € P. Prove that: if c < 0 and a < b,then ca> cb.

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