Absolute Value Function
Definition
A function defined as $f$ is called the absolute value function, and its values are denoted as shown in $|x|$.
$$ |x| := f(x) = \begin{cases} x &\text{if } x>0 \\ 0 &\text{if } x=0 \\ -x &\text{if } x<0 \end{cases},\quad x\in \mathbb{R} $$
Explanation
Absolute value refers to the magnitude of a real number, and a generalization of this is the norm. The triangle inequality holds.
$$ |x + y| \le |x| + |y|,\quad x \in \mathbb{R} $$