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IEVref: | 102-02-05 | ID: | |

Language: | en | Status: 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 $\sqrt{2}$ = 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 | ||

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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Note 1 to entry: The rational numbers are also real numbers. Irrational numbers, i.e. real numbers other than rational numbers, are for example $\sqrt{2}$ = 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*.