Burali-Forti paradox

The Burali-Forti paradox demonstrates that the class of all ordinals is not a set. If there were a set of all ordinals, $O r d$ , then it would follow that $O r d$ was itself an ordinal, and therefore that $Ord\\in Ord$ . if sets in general are allowed to contain themselves, ordinals cannot since they are defined so that $\\in$ 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.

单词	BuraliFortiParadox
释义	Burali-Forti paradox The Burali-Forti paradox demonstrates that the class of all ordinals is not a set. If there were a set of all ordinals, $O r d$ , then it would follow that $O r d$ was itself an ordinal, and therefore that $Ord\\in Ord$ . if sets in general are allowed to contain themselves, ordinals cannot since they are defined so that $\\in$ 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.
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