Burali-Forti paradox

{{set theory}} The following paradox: Let ''L'' be the set of all ordinal numbers. This set is well-ordered, so it has an ordinal number ''γ''. Since ''L'' is the set of all ordinal numbers, ''L'' contains ''γ''. But ''γ'' is equal to the well-ordered set of all ordinal numbers ''β'' smaller than ''γ''. Thus, ''L'' is order isomorphic to one of its proper subsets, a contradiction.