partition

A partition $P$ of a set $S$ is a collection of pairwise disjoint nonempty sets such that $\cup P = S$ .

Any partition $P$ of a set $S$ introduces an equivalence relation on $S$ , where each $A \in P$ is an equivalence class. Similarly, given an equivalence relation on $S$ , the collection of distinct equivalence classes is a partition of $S$ .