The second approach to the problem took as its base the notion of class, and defines a set as a class which belongs to other classes, while a proper class is defined as a class which does not belong to other classes. Under the Zermelo–Fraenkel approach, the axioms impede the construction of a set of all sets which do not belong to themselves. In contrast, under the von Neumann approach, the <answer>class of all sets which do not belong to themselves can be constructed, but it is a proper class and not a set.</answer>
Under Von Neumann's approach can a class of all sets that do not belong to themselves be constructed?
class of all sets which do not belong to themselves can be constructed, but it is a proper class and not a set.