About

The absolute value function, usually denoted by $|x|$, is a function $\mathbb{R} \to [0, \infty)$ which can be defined in three equivalent ways:

  1. $|x| = \begin{cases}x &\ \text{if}\ x \geq 0,\\\ -x &\ \text{if}\ x <0\end{cases}$,

  2. $|x| = \sqrt{x^2}$, and

  3. $|x| = \max\\{x, -x\\}$.

history | show excerpt | excerpt history