Question: Let p,q be rational numbers. Consider the statement . For every rin mathbb {Q}, if r > q, then r is greater or equal p.

Let p,q be rational numbers. Consider the statement . For every r\in \mathbb {Q}, if r > q, then r is greater or equal p.

Prove that if (P) holds, then p q.

(Hint: you should try proof by contradiction; namely, assume p > q and show that (P) cannot be true.)

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