Let \(\frac ab\in \mathbb Q\). Based on the order relation for rational numbers, we can define the absolute value of \(q\) as a function \(|~|:\mathbb Q\mapsto\mathbb Q_+\)
\[\left|\frac ab\right| := \begin{cases} \frac ab & \text{ if } \frac ab \ge 0 \\ -\frac ab & \text{ if } \frac ab < 0. \end{cases}\]
Corollaries: 1
Corollaries: 1
Definitions: 2
Examples: 3
Proofs: 4 5
