 Although it took several decades from Cantor’s work to find a system of axioms for set theory that avoids these paradoxes (see the entries on   the early development of set theory and  set theory),  Cantor already saw, in this unreachability of the totality of all ordinals or cardinals, a notion of “absolute infinity”. Although in his system, there are many infinite sets that are tractable and graspable at many different levels, starting with the natural numbers (which Aristotle had thought was merely potential rather than actual), he discovered an even greater Aristotelian potential infinity. This led to the distinction between a “set” as a totality that can be grasped in the relevant sense, and a “proper class”, which is too large even for a system that encompasses each of Cantor’s many infinities.