 identity element

A member of a structure which, when applied to any other element via a binary operation induces an identity mapping; more specifically, given an operation ,, an element I is
a left identity if I , x = x for any x in the structure
See Also: neutral element
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identity element — n. an element of a mathematical system that does not change the other elements in the system when it operates on them: zero is the identity element for addition (x + 0 = x) and one is the identity element for multiplication (y × 1 = y) … English World dictionary
Identity element — In mathematics, an identity element (or neutral element) is a special type of element of a set with respect to a binary operation on that set. It leaves other elements unchanged when combined with them. This is used for groups and related… … Wikipedia
identity element — noun an operator that leaves unchanged the element on which it operates the identity under numerical multiplication is 1 • Syn: ↑identity, ↑identity operator • Hypernyms: ↑operator * * * noun see identity 8 * * … Useful english dictionary
identity element — loginis ekvivalentumo elementas statusas T sritis automatika atitikmenys: angl. biconditional gate; equality gate; equivalence element; equivalence gate; equivalent to element; exclusive NOR gate; identity element; material equivalence element… … Automatikos terminų žodynas
identity element — noun Date: 1902 an element (as 0 in the set of all integers under addition or 1 in the set of positive integers under multiplication) that leaves any element of the set to which it belongs unchanged when combined with it by a specified operation … New Collegiate Dictionary
identity element — Math. identity (def. 9b). [1900 05] * * * … Universalium
Identity — may refer to:Philosophy* Identity (philosophy), the sameness of two things * Identity theory of mind, in the philosophy of mind, holds that the mind is identical to the brain * Personal identity (philosophy) * Identity (social science) * Identity … Wikipedia
Identity (mathematics) — For other uses, see Identity (disambiguation). In mathematics, the term identity has several different important meanings: An identity is a relation which is tautologically true. This means that whatever the number or value may be, the answer… … Wikipedia
Identity function — In mathematics, an identity function, also called identity map or identity transformation, is a function that always returns the same value that was used as its argument. In terms of equations, the function is given by f ( x ) = x… … Wikipedia
identity — /uy den ti tee, i den /, n., pl. identities. 1. the state or fact of remaining the same one or ones, as under varying aspects or conditions: The identity of the fingerprints on the gun with those on file provided evidence that he was the killer.… … Universalium