Question: The binary operator > defines an ordered relation on R. This depends on a subset R , positive real numbers, that satisfy the following conditions:

The binary operator > defines an ordered relation on R. This depends on a subset R , positive real numbers, that satisfy the following conditions: (a) For any x = 0, either x or x, but not both, belongs to R . (b) If x and y belong to R , so does x y. (c) If x and y belong to R , so does x y. Then the existence of R tells us that x > y if and only if xy is in R . Prove that C cannot be ordered. That is, show that C does not contain a nonempty set V that satisfies the three properties of an ordered relation

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