The Burali-Forti Paradox

The Burali-Forti Paradox

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Medium:  Paradox
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Release Message:  If the ordinal numbers formed a set, it would be an ordinal number that is smaller than itself. Authored by Cesare Burali-Forti.
Description:  In set theory, a field of mathematics, the Burali-Forti paradox demonstrates that naively constructing "the set of all ordinal numbers" leads to a contradiction and therefore shows an antinomy in a system that allows its construction. It is named after Cesare Burali-Forti, who discovered it in 1897. (Naive set theory)