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IEVref:102-01-11ID:
Language:enStatus: Standard
Term: addition
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Definition: 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@ .


Publication date:2008-08
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Internal notes:2017-02-20: Editorial revisions in accordance with the information provided in C00019 (IEV 102) - evaluation. JGO
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