Appendix:Glossary of set theory

This is a glossary of set theory.

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

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.