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.

Some sources refer to it as the size of $x$.

Some sources call it the numerical value.

Also see

 * Equivalence of Definitions of Absolute Value Function‎


 * Absolute Value is Many-to-One


 * Absolute Value is Norm

Generalizations

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