In set theory, the complement of a set generally refers to a set of elements which are not elements of . Usually, these elements must be restricted to some set of which is a subset; in this case, we speak of the complement of with respect to . Such a set is sometimes denoted , , , or .
In most standard set theories, one cannot speak of the set of all elements which are not contained in , as this would imply the existance of a set of all sets, which is contradictory, as this leads to Russell's Paradox.
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