# Axiom:Axiom of the Empty Set/Set Theory/Formulation 2

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## Axiom

There exists a set that has no elements:

- $\exists x: \forall y: \paren {\neg \paren {y \in x} }$

## 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

- Weisstein, Eric W. "Axiom of the Empty Set." From
*MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/AxiomoftheEmptySet.html