Assume that $\{\forall s (\emptyset \in s)[\math]. Let <script type="math/tex">f(\hat{s})[\math] denote <script type="math/tex">\{x|x\textup{ is not a set.}\}[\math]. By definition, <script type="math/tex">f(\hat{s})[\math] is a set and thus the first axiom holds, so that <script type="math/tex">\emptyset \in f(\hat{s})[\math]. By definition, the empty set <script type="math/tex">\emptyset[\math] is a set and thus <script type="math/tex">\emptyset \in f(\hat{s})[\math] is not the set of all non-set items, which is a contradiction.<br /> <br /> Therefore, are all mathematical objects sets?$