n. a relation of qualitative identity that defines a partition of its domain, so that the elements are equivalent for the purposes of the theory. It may then be possible to select one from each equivalence class as its canonical element; alternatively, the equivalence class may itself be taken to be the element of the factor space. For example, the rationals may be defined either as the sets of ordered pairs <kn, km > for integral k, m, n, or else may be taken to be the unique members of these sets for which m and n are relatively prime. The rationals are thus identical relative to, or unique up to, common factors.