Absolute value - Knowlpedia

The absolute value on $\mathbb R$ is the function $|\cdot|:\mathbb R\to[0,\infty)$ defined by

|x|=\begin{cases} x,& x\ge 0,\\ -x,& x<0. \end{cases}

Examples

$|-3|=|3|=3$ .
The distance between $2$ and $5$ in $\mathbb R$ is $|2-5|=3$ .

Remarks

The formula $d(x,y)=|x-y|$ defines the usual metric on $\mathbb R$ . Absolute value also appears in $\varepsilon$ - $\delta$ definitions such as the limit at a point.