Burali-Forti paradox

Etymology
Named after, who in 1897 published a paper proving a theorem which, unknown to him, contradicted a previously proved result by.

Proper noun

 * 1)  The paradox that supposing the existence of a set of all ordinal numbers leads to a contradiction; construed as meaning that it is not a properly defined set.
 * 2) * 1984, Michael Hallett, Cantorian Set Theory and Limitation of Size, (Clarendon Press), 1986, Paperback, page 186,
 * Like them, Mirimanoff concentrates on the Burali-Forti paradox, and like Russell's analysis before, Mirimanoff shows how. in terms of size, the Burali-Forti paradox is basic and that if we solve this the other paradoxes will be solved too.
 * 1) * 1994 [Routledge], (editor), Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences, Volume 1, 2003,, Paperback, page 632,
 * In the first place, Berry rejected Russell's solution to the Burali-Forti paradox, claiming that it was easy to prove that the set of all ordinal numbers was a well-ordered set (and that Cantor had actually done it).