In the midst of the crisis the Russell's paradox caused, Ernst Zermelo and Abraham Fraenkel created a much more simple, as compared to Russell's and Whitehead's "Principia Mathematica", set of axioms, also avoiding this paradox. At least until now, nobody was able to discover any other contradictions and paradoxes resulting from their axioms. Therefore, Zermelo-Fraenkel Axioms are today a standard form of axiomatic set theory.
It is now time to revise our first definition of the set and provide a more thorough fundament of the set theory, based on these axioms.
