# Absolute value

The absolute value of a real number $x$ is denoted by $|x|$ and is defined as $|x| = \begin{cases} x &\text{if x \geq 0}\\ -x & \text{if x < 0.} \end{cases}$

Therefore, the absolute value is always greater than or equal to zero, and describes how far away the corresponding number is from the origin.

The absolute value of a real number is sometimes referred to as its modulus.