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 4.5 - Page 197: 2

Answer

$floor(\frac{17}{4})=floor(4.25)=4$ $ceiling(\frac{17}{4})=ceiling(4.25)=5$

Work Step by Step

By definition, $floor(x)$ is the largest integer less than or equal to $x$, and $ceiling(x)$ is the smallest integer greater than or equal to $x$. Note that $\frac{17}{4}=4.25$. Hence, we "fall to the floor" of $4.25$ to get $4$, and "rise to the ceiling" of $4.25$ to get $5$.
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