A specialization of intensional or extensional set (q.v.); the collection of mathematical sets. An instance of set can be any arbitrary set of Things. A good way to explain this notion with respect to the Cyc ontology is to contrast set with type of thing (q.v.). First, while the instances of a given collection all have some more-or-less significant (often natural ) property or properties in common, the elements (see Element Of) in a given set might have nothing in common (besides membership in that set). Second, while it is in principle possible for two distinct collections to have exactly the same elements (with respect to a given context), this cannot happen in the case of sets, which are individuated strictly in terms of their extensions (see Extent). Third (and specifically regarding their expression in the CycL language), unlike with collections, rarely will it be desirable to create a new constant to denote a particular set. Instead, a set will often be either (a) intensionally specified by a defining property via The Set Of (q.v.), as in `(The Set Of ?X (And (Isa ?X integer) (Greater Than ?X 42)))', or (b) extensionally specified by enumerating its elements via The Set (q.v.), as in `(The Set 3 4 5)'; see also The Partition and The Covering.