Although the term can be used for any equivalence relation's set of equivalence classes, possibly with further structure, the intent of using the term is generally to compare that type of equivalence relation on a set , either to an equivalence relation that induces some structure on the set of equivalence classes from a structure of the same kind on , or to the orbits of a group action. Both the sense of a structure preserved by an equivalence relation, and the study of invariants under group actions, lead to the definition of invariants of equivalence relations given above.