\begin{definition}[Definition:Set Partition/Definition 1]
Let $S$ be a set.
A '''partition''' of $S$ is a set of subsets $\Bbb S$ of $S$ such that:
:$(1): \quad$ $\Bbb S$ is pairwise disjoint: $\forall S_1, S_2 \in \Bbb S: S_1 \cap S_2 = \O$ when $S_1 \ne S_2$
:$(2): \quad$ The union of $\Bbb S$ forms the whole set $S$: $\ds \bigcup \Bbb S = S$
:$(3): \quad$ None of the elements of $\Bbb S$ is empty: $\forall T \in \Bbb S: T \ne \O$.
\end{definition}