# Axiom:Axiom of the Empty Set/Set Theory/Formulation 1

Jump to navigation
Jump to search

## Axiom

There exists a set that has no elements:

- $\exists x: \forall y \in x: y \ne y$

## Also known as

In the specific context of set theory, the **Axiom of the Empty Set** is also known as the **axiom of existence**, but there exists another axiom with such a name, used in a different context.

Hence it is preferable not to use that name.

Some sources refer to this as the **axiom of the null set**.

## Also see

## Sources

- 1955: John L. Kelley:
*General Topology*... (previous) ... (next): Chapter $0$: Subsets and Complements; Union and Intersection