Definition:Absolute Value/Ordered Integral Domain

Definition
Let $\struct {D, +, \times, \le}$ be an ordered integral domain whose zero is $0_D$.

Then for all $a \in D$, the absolute value of $a$ is defined as:


 * $\size a = \begin{cases}

a & : 0_D \le a \\ -a & : a < 0_D \end{cases}$ where $a > 0_D$ denotes that $\neg \paren {a \le 0_D}$.

Also see

 * Integers form Ordered Integral Domain
 * Rational Numbers form Ordered Integral Domain
 * Real Numbers form Ordered Integral Domain

from which it follows that the definition for numbers is compatible with this.