Definition:Doubleton

Definition
A doubleton is a set that contains exactly two elements.

The doubleton containing the distinct elements $a$ and $b$ can be written $\left\{{a, b}\right\}$.

The set $\left\{{a, b}\right\}$ is known as the doubleton of $a$ and $b$.

Set Theory Definition
The doubleton can be defined as a class:


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

Also known as
Doubletons are also frequently referred to as unordered pairs, or even simply pairs if no ambiguity results.

Also see

 * Axiom:Axiom of Pairing


 * Union of Disjoint Singletons is Doubleton for a proof from the ZF axioms that $\left\{{a}\right\} \cup \left\{{b}\right\} = \left\{{a, b}\right\}$ when $a \ne b$.