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IEVref:102-01-18ID:
Language:enStatus: Standard
Term: multiplication
Synonym1:
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Definition: operation performed on a set, assigning a unique element of the set to any ordered pair of elements a and b of the set, with the following properties:

  • associativity: a(bc)=(ab)c MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaadggacqGHflY1ca GGOaGaamOyaiabgwSixlaadogacaGGPaGaeyypa0Jaaiikaiaadgga cqGHflY1caWGIbGaaiykaiabgwSixlaadogaaaa@4B17@ , where c is also an element of the set,
  • if an addition is performed on the set, distributivity: a(b+c)=ab+ac MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaadggacqGHflY1ca GGOaGaamOyaiabgUcaRiaadogacaGGPaGaeyypa0JaamyyaiabgwSi xlaadkgacqGHRaWkcaWGHbGaeyyXICTaam4yaaaa@4A1E@ and (a+b)c=ac+bc MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaacIcacaWGHbGaey 4kaSIaamOyaiaacMcacqGHflY1caWGJbGaeyypa0JaamyyaiabgwSi xlaadogacqGHRaWkcaWGIbGaeyyXICTaam4yaaaa@4A20@

Note 1 to entry: Multiplication is defined for natural numbers and extended to other classes of numbers and to mathematical entities such as polynomials and matrices. Multiplication is also defined for quantities and units, even if they are not of the same kind, so that addition cannot be defined.

Note 2 to entry: Multiplication is not necessarily commutative, for example in the case of matrices.

Note 3 to entry: Each element in a multiplication of two or more elements is called a factor. The term "factor" is also used for a quotient of two quantities of the same kind (see IEV 112-01-04). In the multiplication of two elements, the first is called "multiplier" and the second "multiplicator".

Note 4 to entry: The multiplication of entities a and b is expressed by the words "a multiplied by b" or "a times b" and denoted by ab, a × b, or ab. The symbol ∏ is used to denote successive multiplications, for example a2a3a4a5a6a7 is denoted by i=2 7 a i MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaamaarahabaGaamyyam aaBaaaleaacaWGPbaabeaaaeaacaWGPbGaeyypa0tcLboacaaIYaaa leaajug4aiaaiEdaa0Gaey4dIunaaaa@430B@ .


Publication date:2008-08
Source:
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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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