 In contrast, under the von Neumann approach, the class of all sets which do not belong to themselves can be constructed, but it is a "proper class" and not a set.With this contribution of von Neumann, the axiomatic system of the theory of sets avoided the contradictions of earlier systems and became usable as a foundation for mathematics, despite the lack of a proof of its consistency.The next question was whether it provided definitive answers to all mathematical questions that could be posed in it, or whether it might be improved by adding stronger axioms that could be used to prove a broader class of theorems.