# 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 known as

A doubleton is also known as an unordered pair, or even simply pair set or pair if no ambiguity results.