Category:Definitions/Axiom of Foundation

This category contains definitions related to the Axiom of Foundation.
Related results can be found in Category:Axiom of Foundation.

For all non-empty sets, there is an element of the set that shares no element with the set.

That is:

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

The antecedent states that $S$ is not empty.