Sometimes used as a synonym for set. But a class is contrasted with a set in classical set theory. A class of things may answer to a condition but not form a set, if various restrictions designed to avoid the logical paradoxes are not met. Intuitively this usually means that the class may never be treated as a completed totality. But in some set theories classes are completed totalities, but are too big to be sets: paradox is avoided by not allowing them to be members of other sets. See also separation, axiom of.