Definition:Trivial Partition/Partition of Singletons

Definition
Let $S$ be a set such that $S \ne \varnothing$.

The partition of singletons on $S$ is defined as:
 * $\mathcal P = \left\{{\left\{{x}\right\}: x \in S}\right\}$

That is, it is a partition such that every element of $\mathcal P$ is a singleton.