The point is to see what modifications are necessary to add urelements You could define urelements as sets with no members Then you must not only drop the axom of Foundation but also change the axiom of extensionality since all urelements have the same members i e none yet they are distinct Then you are not in Zermelo set theory at all and you will have to change the definition of the von Neumann universe accordingly by excluding urelements Or you could say each urelement is its own sole member and keep all the axioms of Zermelo Fraenkel except Foundation Then you can keep the usual definition of the von Neumann universe since these urelements are plainly not well founded sets