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 4.6 - Page 205: 7

Answer

Negation: "There exists a least positive rational number." Proof: There is no least positive rational number. Suppose there is a positive rational number $r$ such that, for all positive rational numbers $q$, $r\leq q$. Beginning with the trivial statement $1\lt2$, we can multiply both sides by $r$ to get $r\lt2r$ and then divide both sides by $2$ to get $\frac{r}{2}$

Work Step by Step

We can derive $r\lt2r$ from $1\lt2$ and $\frac{r}{2}$
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