|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 = 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*.