Definition:Absolute Value/Definition 1

Definition
Let $x \in \R$ be a real number.

The absolute value of $x$ is denoted $\size x$, and is defined using the usual ordering on the real numbers as follows:
 * $\size x = \begin{cases}

x & : x > 0 \\ 0 & : x = 0 \\ -x & : x < 0 \end{cases}$

Also see

 * Equivalence of Definitions of Absolute Value Function‎