a. The Archimedean property for the rational numbers states that for all rational

Chapter 5, Problem 22

(choose chapter or problem)

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

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