Definition:Absolute Value/Number Classes

Definition
The absolute value function applies to the various number classes as follows:


 * Natural numbers $\N$: All elements of $\N$ are greater than or equal to zero, so the concept is irrelevant.
 * Integers $\Z$: As defined here.
 * Rational numbers $\Q$: As defined here.
 * Real numbers $\R$: As defined here.


 * Complex numbers $\C$: As $\C$ is not an ordered set, the definition of the absolute value function based upon whether a complex number is greater than or less than zero cannot be applied.

The notation $\cmod z$, where $z \in \C$, is defined as the modulus of $z$ and has a different meaning.