\begin{definition}[Definition:N-Ary Operation Induced by Binary Operation]
Let $\struct {G, \oplus}$ be a magma.
Let $n \ge 1$ be a natural number.
Let $G^n$ be the $n$th cartesian power of $G$.
The '''$n$-ary operation induced by $\oplus$''' is the $n$-ary operation $\oplus_n: G^n \to G$ defined as:
:$\map {\oplus_n} f = \ds \bigoplus_{i \mathop = 1}^n \map f i$
where $\bigoplus$ denotes indexed iteration of $f$ from $1$ to $n$.
\end{definition}