ABSTRACT

Most of the sets (classes) you are likely to think of will not be members of themselves: the set of whole numbers is not a whole number, the set of nations is not a nation and the set of Frenchwomen is not a Frenchwoman. But the set of everything which is not a Frenchwoman is a member of itself, since it is not a Frenchwoman; so is the set of sets, since it is a set. However, the set of those sets which are not members of themselves is both self-membered and not self-membered.