Axiom:Axiom of the Empty Set

Axiom
There exists a set that has no elements.


 * $$\exists x: \forall y: \left({\neg \left({y \in x}\right)}\right)$$

Otherwise known as the Axiom of the Empty Set.

This can be deduced from the Axiom of Infinity and Axiom of Subsets and some treatments exclude it from the list.

It can alternatively be specified:
 * $$\exists x: \forall y \in x: y \ne y$$

Also see

 * Empty set