An empty set has no elements

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• Empty set — ∅ redirects here. For similar looking symbols, see Ø (disambiguation). The empty set is the set containing no elements. In mathematics, and more specifically set theory, the empty set is the unique set having no elements; its size or cardinality… …   Wikipedia

• set theory — the branch of mathematics that deals with relations between sets. [1940 45] * * * Branch of mathematics that deals with the properties of sets. It is most valuable as applied to other areas of mathematics, which borrow from and adapt its… …   Universalium

• Axiom of empty set — In set theory, the axiom of empty set is one of the axioms of Zermelo–Fraenkel set theory and one of the axioms of Kripke–Platek set theory. Formal statement In the formal language of the Zermelo–Fraenkel axioms, the axiom reads::exist x, forall… …   Wikipedia

• Set (mathematics) — This article gives an introduction to what mathematicians call intuitive or naive set theory; for a more detailed account see Naive set theory. For a rigorous modern axiomatic treatment of sets, see Set theory. The intersection of two sets is… …   Wikipedia

• Empty product — In mathematics, an empty product, or nullary product, is the result of multiplying no factors. It is equal to the multiplicative identity 1, given that it exists for the multiplication operation in question, just as the empty sum the result of… …   Wikipedia

• Empty sum — Not to be confused with Zero sum. In mathematics, an empty sum, or nullary sum, is a summation involving no terms at all. The value of any empty sum of numbers is conventionally taken to be zero. For summations defined in terms of addition of… …   Wikipedia

• Set theory — This article is about the branch of mathematics. For musical set theory, see Set theory (music). A Venn diagram illustrating the intersection of two sets. Set theory is the branch of mathematics that studies sets, which are collections of objects …   Wikipedia

• Set notation — Sets are fundamental objects in mathematics. Intuitively, a set is merely a collection of elements or members . There are various conventions for textually denoting sets. In any particular situation, an author typically chooses from among these… …   Wikipedia

• Set-theoretic definition of natural numbers — Several ways have been proposed to define the natural numbers using set theory.The contemporary standardIn standard (ZF) set theory the natural numbersare defined recursively by 0 = {} (the empty set) and n +1 = n ∪ { n }. Then n = {0,1,..., n… …   Wikipedia

• set — /set/, v., set, setting, n., adj., interj. v.t. 1. to put (something or someone) in a particular place: to set a vase on a table. 2. to place in a particular position or posture: Set the baby on his feet. 3. to place in some relation to something …   Universalium

• Binary set — A binary set is a set with (exactly) two distinct elements, or, equivalently, a set whose cardinality is two.Examples: * The set { a , b } is binary. * The set { a , a } is not binary, since it is the same set as { a }, and is thus a singleton.In …   Wikipedia