Axiom:Axiom of the Empty Set

Axiom
There exists a set that has no elements:


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

Also defined as
It can equivalently be specified:
 * $\exists x: \forall y \in x: y \ne y$

Also known as
This axiom is akso known as the Axiom of the Empty Set.

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


 * Empty set