In set theory, a universal set is a set which contains all objects, including itself. In set theory as usually formulated, the conception of a universal set leads to Russell's paradox and is consequently not allowed. However, some non-standard variants of set theory include a universal set.
== Notation ==
There is no standard notation for the universal set of a given set theory. Common symbols include V, U and ξ.
== Reasons for nonexistence ==
Zermelo–Fraenkel set theory and related set theories, which are based on the idea of the cumulative hierarchy, do not allow for the existence of ...