# Axiom:Axiom of Empty Set/Set Theory

## Axiom

In the context of axiomatic set theory, the axiom of the empty set is as follows:

### Formulation 1

There exists a set that has no elements:

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

### Formulation 2

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