Definition:Symmetric Function/Absolute

Definition
Let $f: \R^n \to \R$ be a real-valued function.

Let $f$ be such that, for all $\mathbf x := \tuple {x_1, x_2, \ldots, x_n} \in \R^n$:
 * $\map f {\mathbf x} = \map f {\mathbf y}$

where $\mathbf y$ is a permutation of $\tuple {x_1, x_2, \ldots, x_n}$.

Then $f$ is an absolutely symmetric function.