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Set of all sets - In set theory as usually formulated, referring to the set of all sets typically leads to a paradox. The reason for this is the form of Zermelo's axiom of separation: for any
Hereditarily finite set - In mathematics, hereditarily finite sets are defined recursively as finite sets containing hereditarily finite sets (with the empty set as a base case). Informally, a hereditarily finite set is a finite set, the members of which are also finite sets, as are the members of those, and so on.
Algebra of sets - The algebra of sets develops and describes the basic properties and laws of sets, the set-theoretic operations of union, intersection, and complementation and the relations of set equality (mathematics) and set inclusion. It also provides systematic procedures for evaluating expressions, and performing calculations, involving these operations and relations.
Naive set theory - In abstract mathematics, naive set theory1 was the first development of set theory, which was later to be reconstructed as axiomatic set theory. Naive set theory is distinguished from axiomatic set theory by the fact that the former regards sets as collections of objects, called the elements or members of the set, whereas ...
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