Russell's paradox is the most elementary contradiction that results from naive set theory. It is an immediate consequence of a schema of unrestricted comprehension (where all classes become sets). It, in part, justifies the exploration of axiomatic systems such as [ZFC](ZFC.md "ZFC"). It was first discovered by Bertrand Russell when reviewing Frege's "Die Grunderland der Arithmetik". ## Statement of the paradox Take the set of all sets that are not elements of themselves. Given the schema of unrestricted comprehension, any class is a member of this class if and only if it is not a member of itself. Therefore, this class is a member of itself if and only if it is not a member of itself, creating a contradiction.