Definition:Singleton Class

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

Also see

• Singleton Class can be Formed from Set

• Definition:Singleton

• 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