Absolute Value

Definition

The absolute value $a\in \mathbb{R}$, denoted by $|a|$, is defined by $|a|:=\{\begin{array}{ll}-a,& a<0\\ 0,& a=0\\ a,& a>0\end{array}$

We see from the definition of absolute value that, $\forall a\in \mathbb{R}$,

• $|a|\ge 0$
• $|-a|=|a|$
• $|a|=0⟺a=0$