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Prove that if a, b E iQ, and a > b, then there. are infinitely many x E iQ such that a >

Chapter 31, Problem 31.19

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QUESTION:

Prove that if a, b E iQ, and a > b, then there. are infinitely many x E iQ such that a > x > b[Suggestion: If c and d are rational, then so IS (c + d)J2.]

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QUESTION:

Prove that if a, b E iQ, and a > b, then there. are infinitely many x E iQ such that a > x > b[Suggestion: If c and d are rational, then so IS (c + d)J2.]

ANSWER:

Step 1 of 2

Proof: (Density property of Q) Suppose a and b be distinct rational numbers and b < a.

 Let , then

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