Appendix:Glossary of set theory

This is a glossary of set theory.

A

 * axiom of choice : One of the axioms in axiomatic set theory, equivalent to the statement that an arbitrary direct product of non-empty sets is non-empty.

C

 * Cartesian product : The set of all possible pairs of elements whose components are members of two sets.
 * complement : Given two sets, the set containing one set's elements that are not members of the other set.
 * complement : The set containing exactly those elements of the universal set not in the given set.

D

 * disjoint : Of two or more sets, having no members in common; having an intersection equal to the empty set.

E

 * element : One of the objects in a set.
 * equivalence class : Any one of the subsets into which an equivalence relation partitions a set, each of these subsets containing all the elements of the set that are equivalent under the equivalence relation.
 * equivalence relation : A binary relation that is reflexive, symmetric and transitive.

I

 * intersection : The set containing all the elements that are common to two or more sets.

M

 * member : An element of a set.

O

 * ordered pair : A tuple consisting of two elements.

P

 * partition : A collection of non-empty, disjoint subsets of a set whose union is the set itself (i.e. all elements of the set are contained in exactly one of the subsets).


 * power set : The set of all subsets of a set.

R

 * relation : A set of ordered tuples.

S

 * set : A possibly infinite collection of objects, disregarding their order and repetition.


 * subset : With respect to another set, a set such that each of its elements is also an element of the other set.


 * superset : With respect to another set, a set such that each of the elements of the other set is also an element of the set.

T

 * tuple : A finite sequence of elements; a finite ordered set.

U

 * union : The set containing all of the elements of two or more sets.

V

 * Venn diagram : A diagram representing sets by circles or ellipses.