“A set is an identification of zero or more objects (elements, entities, depending on context) that can be referred to as a group by name (usually a symbol) and which are drawn from some pre-defined universe of objects. Such objects are then said to be the members of the set. The set members have one or more properties in common. It is, however, possible that the sole defining property of a set can be simply that the definer of a set has explicitly designated as members certain (one or more) objects that do not share any properties, so the only property shared by the set members is the designation property (DP) -- each member then has the property of having been designated member of the set. More explicitly, for any set, an assertion of set membership has definitional priority over the necessity of any other properties being shared among the members.” --David McGoveran
Thus, members of a set are "drawn from some pre-defined universe of objects" on the basis of shared properties (that define their type and are required for set membership) -- if nothing else, at least a designation property (DP). These properties distinguish members of the set from those in the universe that are not.
