Absolut-Betrag in \(\mathbb{R}\)

\begin{align*} \vert x \vert \coloneqq& \begin{cases} \hphantom{-}x & \mbox{if } x > 0\\ - x & \mbox{if } x < 0 \end{cases} \\ \vert x \vert \Leftrightarrow& \mathrm{max}(x,-x) \end{align*}