**Additive identity** — In mathematics the additive identity of a set which is equipped with the operation of addition is an element which, when added to any element x in the set, yields x . One of the most familiar additive identities is the number 0 from elementary… … Wikipedia

**additive identity** — noun An element of an algebraic structure, generally denoted 0, which is an identity for an additive operation (generally denoted +). That is, x + 0 = 0 + x = x for any x in the structure … Wiktionary

**additive identity** — noun Date: 1953 an identity element (as 0 in the group of whole numbers under the operation of addition) that in a given mathematical system leaves unchanged any element to which it is added … New Collegiate Dictionary

**additive identity** — Math. an element that when added to a given element in a specified set leaves that element unchanged, as zero in the real number system. [1955 60] * * * … Universalium

**Additive inverse** — In mathematics, the additive inverse, or opposite, of a number a is the number that, when added to a, yields zero. The additive inverse of a is denoted −a. For example, the additive inverse of 7 is −7, because 7 + (−7) = 0, and the additive… … Wikipedia

**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 (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

**Additive category** — In mathematics, specifically in category theory, an additive category is a preadditive category C such that any finitely many objects A 1,..., A n of C have a biproduct A 1 ⊕ ⋯ ⊕ A n in C. (Recall that a category C is preadditive if all its… … Wikipedia

**additiveidentity** — additive identity n. An element that in a given mathematical system leaves unchanged any element to which it is added. * * * … Universalium

**Ring (mathematics)** — This article is about algebraic structures. For geometric rings, see Annulus (mathematics). For the set theory concept, see Ring of sets. Polynomials, represented here by curves, form a ring under addition and multiplication. In mathematics, a… … Wikipedia