Singleton

set-theory

Definition

Singleton

A singleton is a set with cardinality one. A set $S$ is a singleton precisely when there exists an object $x$ such that

$$S=\{x\}⟺|S|=1.$$

The object $x$ is the unique element of $S$: $x\in S$, while $\{x\}$ denotes the set that contains it. The element and its singleton must not be confused.