# Definition:Singleton Class

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## Contents

## Definition

Let $a$ be a set.

The class $\set a$ is a **singleton (class)**.

It can be referred to as **singleton $a$**.

## Also known as

**Singleton $a$** can also be referred to as **bracket $a$**, but **singleton $a$** is preferred, as it is less ambiguous.

## Examples

### Singleton Class of Empty Set

The singleton class $\O$ is the class whose only element is the empty set $\O$.

## Also see

- Results about
**singleton classes**can be found here.

## Sources

- 2010: Raymond M. Smullyan and Melvin Fitting:
*Set Theory and the Continuum Problem*(revised ed.) ... (previous) ... (next): Chapter $2$: Some Basics of Class-Set Theory: $\S 4$ The pairing axiom