Definition:Absolute Value

Ordered Integral Domain
We can go still further back, and consider the general ordered integral domain:

Also known as
The absolute value of $x$ is sometimes called the modulus or magnitude of $x$, but note that modulus has a more specialized definition in the domain of complex numbers, and that magnitude has a more specialized definition in the context of vectors.

Also see

 * Absolute Value Equals Square Root of Square‎
 * Absolute Value is Norm

Generalizations

 * Definition:Complex Modulus, as shown at Complex Modulus of Real Number equals Absolute Value