# Appendix:Glossary of set theory

This is a glossary of set theory.

**Table of Contents:** A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

## A[edit]

- 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[edit]

- 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[edit]

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

## E[edit]

- 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[edit]

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

## M[edit]

- member
- An element of a set.

## O[edit]

- ordered pair
- A tuple consisting of two elements.

## P[edit]

- 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[edit]

- relation
- A set of ordered tuples.

## S[edit]

- 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[edit]

- tuple
- A finite sequence of elements; a finite ordered set.

## U[edit]

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

## V[edit]

- Venn diagram
- A diagram representing sets by circles or ellipses.