By the Axiom of Extensionality, this is equal to the set {B, A}.

This also allows for the creation of singleton sets. If A is any object, then Pairing means that {A, A} is a set, so by Extensionality {A} is a set.

See all of Axiom of Pairing, no other writeups in this node.

One of the Zermelo-Fraenkel axioms of set theory, and the most basic of those that allow for the creation of new sets from old. It states that if A and B are any objects then the pair {A, B} is a set.

By the Axiom of Extensionality, this is equal to the set {B, A}.

This also allows for the creation of singleton sets. If A is any object, then Pairing means that {A, A} is a set, so by Extensionality {A} is a set.