Use the results of exercise and the well-ordering principle for the integers to show that...

Use the results of exercise and the well-ordering principle for the integers to show that given any rational number r, there is an integer m such that m ≤ r 1.

Exercise

a. The Archimedean property for the rational numbers states that for all rational numbers r, there is an integer n such that n > r. Prove this property.

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b. Prove that given any rational number r, the number – r is also rational.

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c. Use the results of parts (a) and (b) to prove that given any rational number r, there is an integer m such that m.