Definition:Singleton Class
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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
- 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