 Viewed in this way, the reasoning of the paradox is in direct violation of Cantor’s theorem. The latter theorem is usually thought of as the principle that the cardinality of the power set of a set is greater than that of the set; and applied to an infinite set, this leads to the sequence of ever larger infinite cardinal numbers. But in its most basic form—from which the result about cardinality follows as a corollary—Cantor’s theorem is the following set theoretical principle: