Definition:Singleton

Definition
A singleton is a set that contains exactly one element.

The singleton containing only the element $a$ can be written $\set a$.

When this happens, we must be careful to distinguish between the element itself, that is, $a$, and the set containing it, that is, $\set a$.

The set $\set a$ is known as the singleton of $a$.

Formal Definition
The concept of the singleton set can be formalized rigorously as:


 * $\set A := \set {x : x = A}$

With this definition, the singleton of proper classes is equal to the empty set.

Also known as
Some authors use the term unit set.

Also see

 * Existence of Singleton Set