# 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 $b$.

### Class Theory Definition

A doubleton is 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.