<P> In Zermelo set theory, the existence of the empty set is assured by the axiom of empty set, and its uniqueness follows from the axiom of extensionality . However, the axiom of empty set can be shown redundant in either of two ways: </P> <Ul> <Li> There is already an axiom implying the existence of at least one set . Given such an axiom together with the axiom of separation, the existence of the empty set is easily proved . </Li> <Li> In the presence of urelements, it is easy to prove that at least one set exists, viz . the set of all urelements (assuming there is not a proper class of them). Again, given the axiom of separation, the empty set is easily proved . </Li> </Ul> <Li> There is already an axiom implying the existence of at least one set . Given such an axiom together with the axiom of separation, the existence of the empty set is easily proved . </Li> <Li> In the presence of urelements, it is easy to prove that at least one set exists, viz . the set of all urelements (assuming there is not a proper class of them). Again, given the axiom of separation, the empty set is easily proved . </Li>

Can an empty set be an element of a set