The graph of the absolute value function for real numbers.
In mathematics, the absolute value or modulus|x| of a real numberx is the non-negative value of x without regard to its sign. Namely, |x| = x for a positivex, |x| = −x for a negativex (in which case −x is positive), and |0| = 0. For example, the absolute value of 3 is 3, and the absolute value of −3 is also 3. The absolute value of a number may be thought of as its distance from zero.
For any real numberx the absolute value of x is denoted by | x | (a vertical bar on each side of the quantity) and is defined as
The absolute value of x is always either positive or zero, but never negative.
From an analytic geometry point of view, the absolute value of a real number is that number's distance from zero along the real number line. The absolute value of the difference of two real numbers is the distance between them.