Absolute Values

The absolute value of a real number is the distance between its corresponding point on the number line and the number 0. The absolute value of the real number a is denoted by |a|.

From the diagram, it is clear that the absolute value of nonnegative numbers is the number itself, while the absolute value of negative integers is the negative of the number. Thus, the absolute value of a real number can be defined as follows:

For all real numbers a,
(1) If a >= 0, then |a| = a.
(2) If a < 0, then |a| = -a.

Examples:
| 2 | = 2
| -4.5 | = 4.5
| 0 | = 0