Definition:Doubleton/Class Theory

Definition
Let $a$ and $b$ be sets.

The class $\set {a, b}$ is a doubleton (class).

It is defined as the class of all $x$ such that $x = a$ or $x = b$:


 * $\set {a, b} = \set {x: x = a \lor x = b: a \ne b}$

Also see

 * Axiom:Axiom of Pairing (Class Theory)


 * Union of Disjoint Singletons is Doubleton for a proof from the Zermelo-Fraenkel axioms that $\set a \cup \set b = \set {a, b}$ when $a \ne b$.