This article will be permanently flagged as inappropriate and made unaccessible to everyone. Are you certain this article is inappropriate? Excessive Violence Sexual Content Political / Social
Email Address:
Article Id: WHEBN0000723043 Reproduction Date:
In set theory and related branches of mathematics, a collection F of subsets of a given set S is called a family of subsets of S, or a family of sets over S. More generally, a collection of any sets whatsoever is called a family of sets.
The term "collection" is used here because, in some contexts, a family of sets may be allowed to contain repeated copies of any given member,^{[1]}^{[2]}^{[3]} and in other contexts it may form a proper class rather than a set.
Certain types of objects from other areas of mathematics are equivalent to families of sets, in that they can be described purely as a collection of sets of objects of some type:
Axiom of choice, Mathematical logic, Category theory, Mathematics, Foundations of mathematics
Logic, Set theory, Statistics, Number theory, Mathematical logic
Set theory, Mathematics, Set (mathematics), Mathematical logic, Logical consequence
Epistemology, Metaphysics, Ludwig Wittgenstein, Philosophy of science, David Hume
Set theory, Pi, Venn diagram, Empty set, Axiomatic set theory
Set theory, Mathematics, Set (mathematics), Empty set, Complement (set theory)
Fano plane, Mathematics, Binary relation, Family of sets, Euclidean plane
Subset, Vector space, PlanetMath, Family of sets, Set (mathematics)