Discrete Mathematics with Applications 4th Edition

Published by Cengage Learning
ISBN 10: 0-49539-132-8
ISBN 13: 978-0-49539-132-6

Chapter 4 - Elementary Number Theory and Methods of Proof - Exercise Set 4.4 - Page 190: 45

Answer

See below.

Work Step by Step

Case1: if $r=0$, we have $|r|=0\le c$; Case2: if $r\gt0$, we have $|r|=r\le c$; Case3: if $r\lt0$, we have $|r|=-r$, since $-c\le r$, we have $c\ge -r$, thus $|r|=-r\le c$; Based on the above, in any case of $r$, we have $|r|\le c$.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.