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Set Theory Glossary

complement

(set theory) The complement of a set A is the set of all elements of the universe which are not in A.
difference

(set theory) The difference of sets A and B is the set of all elements of A which are not also elements of B.
element

(set theory) a member of a set.
empty set

The set with no elements.
idempotent

A value is idempotent under a binary operation if the result of applying that operation to the value is the same value.
Intersection

(set theory) The intersection of sets A and B is the set of all elements of A which are also elements of B.
proper subset

The set A is a proper subset of set B iff A is a subset of B, but B is not a subset of A.
proper superset

The set A is a proper superset of set B iff A is a superset of B, but B is not a superset of A.
relative complement

(set theory) The relative complement of set A in set B is the set of all elements of B which are not also elements of A.
set

An abstract collection of elements.
set equality

Two sets A and B are equal iff A is a subset of B, and B is a subset of A.
set theory

The study of the behavior of sets and their relationships.
subset

The set A is a subset of set B iff every member of A is also a member of B.
superset

The set A is a superset of set B iff every member of B is also a member of A.
symmetric difference

(set theory) The symmetric difference of sets A and B is the set of all elements of A or B which are not in both A and B.
union

(set theory) The union of sets A and B is the set of all elements of A and all elements of B.
universal set

The set which, in a certain context, contains everything of interest.

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