# Absolute value

From Encyclopedia of Mathematics

*modulus, of a real number *

The non-negative number, denoted by , which is defined as follows: If , ; if , . The absolute value (modulus) of a complex number , where and are real numbers, is the number . Absolute values obey the following relations

A generalization of the concept of the absolute value to the case of arbitrary fields exists, cf. Norm on a field.

**How to Cite This Entry:**

Absolute value.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Absolute_value&oldid=17245