\begin{definition}[Definition:Additive Function (Conventional)]
Let $f: S \to S$ be a mapping on an algebraic structure $\struct {S, +}$.
Then $f$ is an '''additive function''' {{iff}} it preserves the addition operation:
:$\forall x, y \in S: \map f {x + y} = \map f x + \map f y$
\end{definition}