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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(choose chapter or problem)
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.]
Questions & Answers
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