\begin{definition}[Definition:N-Cube (Euclidean Space)]
Let $R, c \in \R$ be real numbers with $R > 0$.
Let $\struct {\R^n, d}$ be a Euclidean $n$-Space equipped with the usual metric $d$.
An '''$n$-cube''' is a subset of $\struct {\R^n, d}$ defined as the cartesian product of closed real intervals of the form:
:$\ds \prod_{i \mathop = 1}^n \closedint {c - R} {c + R}_i$
where $\closedint {c - R} {c + R}_i$ is an interval in the $i$th factor of $\R^n$.
The $n$-cube can be concisely expressed as:
:$\closedint {c - R} {c + R}^n$
in contexts where the indices of the product are unimportant.
\end{definition}