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IEVref:102-02-05ID:
Language:enStatus: Standard
Term: real number
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Definition: element of the unique totally ordered set consisting of the rational numbers and all limits of infinite sequences of rational numbers, with the same operations as for rational numbers

Note 1 to entry: The rational numbers are also real numbers. Irrational numbers, i.e. real numbers other than rational numbers, are for example 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaamaakaaabaacbaqcLb sacaWFYaaaleqaaaaa@3A33@ = 1,414 2..., π = 3,141 5..., e = 2,718 2... For such numbers, the sequence of digits after the decimal sign is infinite without any periodic repetition.

Note 2 to entry: The set of real numbers is denoted by ℝ (R with left vertical bar and right part doubled), or R, or sometimes R with left vertical bar doubled. This set without zero is denoted by an asterisk to the symbol, for example ℝ*.


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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