\begin{definition}[Definition:Cover of Set]
Let $S$ be a set.
A '''cover for $S$''' is a set of sets $\CC$ such that:
:$\ds S \subseteq \bigcup \CC$
where $\bigcup \CC$ denotes the union of $\CC$.
We say that '''$S$ is covered by $\CC$'''.
\end{definition}