Set Partition/Examples/Partition into Singletons

Example of Set Partition
Let $S$ be a set.

Consider the family of subsets $\family {\set x}_{x \mathop \in S}$ indexed by $S$ itself.

Then $\family {\set x}_{x \mathop \in S}$ is a partitioning of $S$ into singletons.

Its associated partition is:
 * $\set {\set x: x \in S}$