A partition of a set $X$ is a subset $\mathcal S$ of the power set $\mathcal P(X)$ such that
- $A\in \mathcal S$ implies that $A\neq \emptyset$;
- For every $x\in X$, there is a unique $A\in \mathcal S$ such that $x\in A$. (Equivalently, the union of the sets $A\in \mathcal S$ is $X$ and the intersection of any two elements of $\mathcal S$ is empty.)