Absolute value

In mathematics, the absolute value, or modulus (UK), of a number is that number without a negative sign. So, for example, 3 is the absolute value of both 3 and -3.

It can be defined as follows: For any real number a, the absolute value of a (denoted |a|) is equal to a itself if a ≥ 0, and to -a, if a < 0 (see also: inequality). |a| is never negative, as absolute values are always either positive or zero. In other words, the solution to |a| < 0 is that a is equal to the empty set, as there is no quantity which has a negative absolute value.

The absolute value can be regarded as the distance of a number from zero; indeed the notion of distance in mathematics is a generalisation of the properties of the absolute value. It is thus a concept useful to scientists, for whom it serves as a measure of the magnitude of any quantity, whether scalar or vector.