The Burali-Forti paradox demonstrates that the class of all ordinals is not a set. If there were a set of all ordinals, , then it would follow that was itself an ordinal, and therefore that . 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.
|Date of creation||2013-03-22 13:04:28|
|Last modified on||2013-03-22 13:04:28|
|Last modified by||Henry (455)|