Burali-Forti paradox

The Burali - Forti paradox in naive set theory describes the contradiction upon which fails the formation of the set of all ordinals. It is named after its discoverer Cesare Burali - Forti, who showed in 1897 that such a set of all ordinals correspond to an ordinal itself to the greater successor ordinal could be formed which would be less than or equal, from which the Impossible inequality followed.

Georg Cantor described the paradox independently of Burali - Forti in 1899 as a generalization of the first Cantor'schen antinomy of 1897, in which he proved that the class of all cardinal numbers is not a lot. This class can be seen as proper subclass of ordinals.

In the axiomatic Zermelo set theory or Zermelo -Fraenkel set theory (ZF ) can the Burali - Forti paradox as evidence understand that no set of all ordinals exist. In quantity gauges that work with classes, it provides the proof that the class of all ordinals is a proper class.