additive function

A unary function that preserves the addition operation; a unary function f such that for any x and y: f(x + y) = f(x) + f(y).

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  • Additive function — Different definitions exist depending on the specific field of application. Traditionally, an additive function is a function that preserves the addition operation:: f ( x + y ) = f ( x ) + f ( y )for any two elements x and y in the domain. An… …   Wikipedia

  • countably additive function — Math. a set function that upon operating on the union of a countable number of disjoint sets gives the same result as the sum of the functional values of each set. Cf. finitely additive function. * * * …   Universalium

  • finitely additive function — Math. a set function that upon operating on the union of a finite number of disjoint sets gives the same result as the sum of the functional values of each set. Cf. countably additive function. * * * …   Universalium

  • countably additive function — Math. a set function that upon operating on the union of a countable number of disjoint sets gives the same result as the sum of the functional values of each set. Cf. finitely additive function …   Useful english dictionary

  • finitely additive function — Math. a set function that upon operating on the union of a finite number of disjoint sets gives the same result as the sum of the functional values of each set. Cf. countably additive function …   Useful english dictionary

  • Additive — may refer to:* Additive function, a function which preserves addition * Additive inverse, an arithmetic concept * Additive category, a preadditive category with finite biproducts * Additive rhythm, a larger period of time constructed from smaller …   Wikipedia

  • Additive synthesis — is a technique of audio synthesis which creates musical timbre.The timbre of an instrument is composed of multiple harmonics or partials , in different quantities, that change over time. Additive synthesis emulates such timbres by combining… …   Wikipedia

  • 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

  • additive — additively, adv. /ad i tiv/, n. 1. something that is added, as one substance to another, to alter or improve the general quality or to counteract undesirable properties: an additive that thins paint. 2. Nutrition. a. Also called food additive. a… …   Universalium

  • 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

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