\begin{definition}[Definition:Real Function/Multivariable]
Let $f: S_1 \times S_2 \times \cdots \times S_n \to \R$ be a mapping where $S_1, S_2, \ldots, S_n \subseteq \R$.
Then $f$ is defined as a '''(real) function of $n$ (independent) variables'''. 
The expression:
:$y = \map f {x_1, x_2, \ldots, x_n}$
means:
:(The dependent variable) $y$ is a function of (the independent variables) $x_1, x_2, \ldots, x_n$.
\end{definition}