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Area Mathematics - General concepts and linear algebra / Sets and operations

IEV ref102-01-11

en
addition
operation, usually denoted by the plus symbol +, performed on a set and assigning a unique element a + b of the set to any elements a and b of the set, with the following properties:

  • associativity: a + (b + c) = (a + b) + c, where c is also an element of the set,
  • commutativity: a + b = b + a

Note 1 to entry: An addition is defined for natural numbers and extended to other classes of numbers and to mathematical entities such as vectors and matrices, and also to quantities of the same kind. An addition may be defined even for a finite set, for example the set of two elements 0 and 1 with addition modulo 2, i.e. 1 + 1 = 0.

Note 2 to entry: The addition of entities a and b is expressed by the words "a plus b". The symbol Σ is used to denote successive additions, for example a 2 + a 3 ++ a 7 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaadggadaWgaaWcba GaaGOmaaqabaGccqGHRaWkcaWGHbWaaSbaaSqaaiaaiodaaeqaaOGa ey4kaSIaeSOjGSKaey4kaSIaamyyamaaBaaaleaacaaI3aaabeaaaa a@3E9C@ is denoted by i=2 7 a i MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaamaaqahabaGaamyyam aaBaaaleaacaWGPbaabeaaaeaacaWGPbGaeyypa0JaaGOmaaqaaiaa iEdaa0GaeyyeIuoaaaa@3CF8@ .


fr
addition, f
opération, généralement notée par le symbole plus +, effectuée sur un ensemble et attribuant un élément unique a + b de l'ensemble à tout couple d'éléments a et b de l'ensemble, avec les propriétés suivantes:

  • associativité: a + (b + c) = (a +b) + c, où c est aussi un élément de l'ensemble,
  • commutativité: a + b = b + a

Note 1 à l'article: Une addition est définie pour les nombres entiers naturels et étendue à d'autres classes de nombres et à des entités mathématiques telles que vecteurs et matrices, ainsi qu'aux grandeurs de même nature. Une addition peut même être définie pour un ensemble fini, par exemple l'ensemble des deux éléments 0 et 1 muni de l'addition modulo 2, c’est à dire 1 + 1 = 0.

Note 2 à l'article: L'addition des entités a et b est exprimée par les mots «a plus b». Le symbole Σ est utilisé pour noter des additions successives, par exemple a 2 + a 3 ++ a 7 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaadggadaWgaaWcba GaaGOmaaqabaGccqGHRaWkcaWGHbWaaSbaaSqaaiaaiodaaeqaaOGa ey4kaSIaeSOjGSKaey4kaSIaamyyamaaBaaaleaacaaI3aaabeaaaa a@3E9C@ est noté i=2 7 a i MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaamaaqahabaGaamyyam aaBaaaleaacaWGPbaabeaaaeaacaWGPbGaeyypa0JaaGOmaaqaaiaa iEdaa0GaeyyeIuoaaaa@3CF8@ .


de
Addition, f

es
adición

ja
加法

pl
dodawanie

pt
adição

sr
сабирање, с јд

sv
addition

zh
加法

Publication date: 2008-08
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