axiom of fundierung | axiom of regularity | Fundierungsaxiom | regularity axiom

One of the Zermelo-Fraenkel axioms, also known as the axiom of regularity. In the formal language of set theory, it states that x!=∅⇒exists y(y element x⋀y intersection x = ∅), where ⇒ means implies, exists means exists, ⋀ means AND, intersection denotes intersection, and ∅ is the empty set. More descriptively, "every nonempty set is disjoint from one of its elements." The axiom of foundation can also be stated as "A set contains no infinitely descending (membership) sequence, " or "A set contains a (membership) minimal element, " i.e., there is an element of the set that shares no member with the set.

axiom of choice | Zermelo-Fraenkel axioms