John von Neumann proposed a different interpretation, based upon an elegant recursive idea: every number is the set of smaller numbers. On this conception, the empty set ∅ is the smallest number, for it has no elements and therefore, according to the slogan, there are no numbers smaller than it. Next is {∅}, since the only element of this set (and hence the only number less than it) is ∅. Continuing in this way, one finds the natural numbers: The successor of any number n is the set n∪{n},
