Answer
See explanation below.
Work Step by Step
Suppose there were two distinct integers n and m
such that |r−n|<1/2 and |r−m|<1/2
Then |n−m|≤|r−n|+|r−m|<1/2+1/2=1
But as n and m are two distinct integers we have a contradiction since |n−m|≥1
Discrete Mathematics and Its Applications, Seventh Edition
by Rosen, Kenneth
Published by
McGraw-Hill Education
ISBN 10:
0073383090
ISBN 13:
978-0-07338-309-5
Chapter 1 - Section 1.8 - Proof Methods and Strategy - Exercises - Page 108: 18
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