Burali-Forti paradox

The Burali-Forti paradoxMathworldPlanetmath demonstrates that the class of all ordinalsMathworldPlanetmathPlanetmath is not a set. If there were a set of all ordinals, Ord, then it would follow that Ord was itself an ordinal, and therefore that OrdOrd. if sets in general are allowed to contain themselves, ordinals cannot since they are defined so that is well founded over them.

This paradox is similar to both Russell’s paradox and Cantor’s paradox, although it predates both. All of these paradoxes prove that a certain object is “too large” to be a set.

Title Burali-Forti paradoxMathworldPlanetmath
Canonical name BuraliFortiParadox
Date of creation 2013-03-22 13:04:28
Last modified on 2013-03-22 13:04:28
Owner Henry (455)
Last modified by Henry (455)
Numerical id 8
Author Henry (455)
Entry type Definition
Classification msc 03-00