There is one advantage in the above direct argument, as against deduction from Zermelo's theorem, that the above argument does not demand the universal truth of the multiplicative axiom, but only its truth as applied to a set of
classes. It may happen that the axiom holds for
classes, though not for larger numbers of classes. For this reason it is better, when it is possible, to content ourselves with the more restricted assumption. The assumption made in the above direct argument is that a product of
factors is never zero unless one of the factors is zero. We may state this assumption in the form: "
is a multipliable number," where a number
