KnowraElementElementAn element is an object that belongs to a specified set. In set theory, membership is written with the symbol ∈.BriefConnectSet: A collection of distinct objects treated as a mathematical object. An element is defined by belonging to a set.Membership symbol: The symbol ∈, used to state that an object belongs to a set. It is the standard notation for saying that an object is an element.Subset relation: The relation in which every element of one set also belongs to another set. An element is an object in a set; a subset is a set whose elements lie there.Natural number: A number used for counting, commonly including zero or beginning with one. Natural numbers can be treated as elements of sets such as the integers.Set membership: The relation that holds between an object and a set when the object belongs to that set. Membership is the relation that makes an object an element of a set.Extensionality: The set-theoretic principle that sets with the same elements are equal. It makes a set depend on its elements, not on how it is described.Set equality: Equality between sets, determined by whether they have exactly the same elements. Being an element of a set is different from being equal to that set.Cartesian product: The set of ordered pairs formed by choosing one element from each of two sets. Its elements combine membership in two sets into ordered pairs.Subset: A set whose every element also belongs to another set. An element of a subset is also an element of the containing set.Ordered pair: A mathematical object that records two entries in a specified order. Ordered pairs can themselves be elements of sets, including Cartesian products.Show all 20Linked from 10 pagesAncient Greek mathematicsBroader topic: It systematized earlier mathematics into the most influential surviving Greek textbook.Pythagorean theoremRelated: Its proof became a durable model for presenting the theorem deductively.Parallel postulateBroader topic: Its opening books establish the setting and consequences of the fifth postulate.Unique factorizationBroader topic: Its number-theory books establish results about primes and divisibility.AM–GM inequalityBroader topic: Book VI contains an early geometric result underlying the two-variable inequality.Euclid's theoremBroader topic: Book IX contains the classic proof that primes are infinite.Euclid–Euler theoremBroader topic: Its Book IX contains the direction of the theorem later associated with Euclid.Playfair's axiomBroader topic: Its fifth postulate prompted centuries of attempts to clarify parallelism.Show all 10