The absolute value of a number represents its distance from 0 on the number line, regardless of direction.

It is defined piecewise as:

This means:

• If $x$ is positive or zero, $|x| = x$
• If $x$ is negative, $|x| = -x$ (which makes it positive)

Absolute value is often used in contexts involving:

• Distance between numbers
• Inequalities (e.g., $|x - a| < \delta$ in limits)
• Piecewise definitions
• Symmetry of graphs