
Definition of BuraliForti paradox
1. Noun. (set theory) The following paradox: Let ''L'' be the set of all ordinal numbers. This set is wellordered, 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 wellordered set of all ordinal numbers ''β'' smaller than ''γ''. Thus, ''L'' is order isomorphism order isomorphic to one of its proper subsets, a contradiction. ¹
¹ Source: wiktionary.com
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