<P> In mathematics, the absolute value or modulus x of a real number x is the non-negative value of x without regard to its sign . Namely, x = x for a positive x, x = − x for a negative x (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 . </P> <P> Generalisations of the absolute value for real numbers occur in a wide variety of mathematical settings . For example, an absolute value is also defined for the complex numbers, the quaternions, ordered rings, fields and vector spaces . The absolute value is closely related to the notions of magnitude, distance, and norm in various mathematical and physical contexts . </P>

The absolute value of a real number x is