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real number One of the infinitely divisible range of values between positive and negative infinity, used to represent continuous physical quantities such as distance, time and temperature. Between any two real numbers there are infinitely many more real numbers. The integers ("counting numbers") are real numbers with no fractional part and real numbers ("measuring numbers") are complex numbers with no imaginary part. Real numbers can be divided into rational numbers and irrational numbers. Real numbers are usually represented (approximately) by computers as floating-point numbers. Strictly, real numbers are the equivalence classes of the Cauchy sequences of {rationals} under the equivalence relation "~", where a ~ b if and only if a-b is {Cauchy} with limit 0. The real numbers are the minimal {topologically closed} field containing the rational field. A sequence, r, of rationals (i.e. a function, r, from the natural numbers to
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