Appendix:Glossary of set theory
This is a glossary of set theory.
- 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.
- Cartesian product
- The set of all possible pairs of elements whose components are members of two sets.
- Given two sets, the set containing one set's elements that are not members of the other set.
- The set containing exactly those elements of the universal set not in the given set.
- Of two or more sets, having no members in common; having an intersection equal to the empty set.
- 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.
- The set containing all the elements that are common to two or more sets.
- An element of a set.
- ordered pair
- A tuple consisting of two elements.
- 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.
- A set of ordered tuples.
- A possibly infinite collection of objects, disregarding their order and repetition.
- With respect to another set, a set such that each of its elements is also an element of the other set.
- With respect to another set, a set such that each of the elements of the other set is also an element of the set.
- A finite sequence of elements; a finite ordered set.
- The set containing all of the elements of two or more sets.
- Venn diagram
- A diagram representing sets by circles or ellipses.