empty set

The set that has no members (there is only one, since sets are different only if they have different members). The existence of this set as a mathematical object can be puzzling if one is (incorrectly) inclined to visualize a set as a kind of heap.

Philosophy dictionary. . 2011.

Look at other dictionaries:

  • empty set — empty set, Mathematics. a set that has no members; null set. The set of natural numbers less than 0 is an empty set …   Useful english dictionary

  • 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

  • empty set — tuščioji aibė statusas T sritis automatika atitikmenys: angl. empty set vok. Leerensemble, n rus. пустое множество, n pranc. ensemble vide, m …   Automatikos terminų žodynas

  • empty set — /ɛmpti ˈsɛt/ (say emptee set) noun → null set …   Australian English dictionary

  • empty set — noun The unique set that contains no elements. Notation: Ø or Syn: null set …   Wiktionary

  • 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

  • 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

  • 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

  • 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

  • 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

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