abstract:In set theory, Cantor's paradox is derivable from the theorem that there is no greatest cardinal number, so that the collection of "infinite sizes" is itself infinite. The difficulty is handled in axiomatic set theory by declaring that this collection is not a set but a proper class; in von Neumann–Bernays–Gödel set theory it follows from this and the axiom of limitation of size that this proper class must be in bijection with the class of all sets.
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the paradox derived from the supposition of an all-inclusive universal set, since every set has more subsets than members while every subset of such a universal set would be a member of it 康托尔悖论
[logic]