equivalence class

An equivalence class is a subset for which an equivalence relation holds.

Formally,
an element $a\in X$ has equivalence class $[a]\subseteq X$ defined with by equivalence relation $\sim$ such that

i.e., two elements of a given set belong to the same equivalence class if and only if they are equivalent to each other.

Equivalence classes form a partition of a set, i.e. each element belongs uniquely to one equivalence class.