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real number

[ree-uh l, reel] /ˈri əl, ril/
noun, Mathematics
a rational number or the limit of a sequence of rational numbers, as opposed to a complex number.
Also called real.
Origin of real number
1905-10 Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2015.
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Examples from the web for real number
  • So, you see, the real number continuum is full of holes.
  • These winter sports require great balance, and they can do a real number on your knees.
  • For example, there's an infinite number of integers and also an infinite number of points on the real number line.
  • Figuring your real number, of course, takes a bit more work.
  • The exponent is a real number that can be positive or negative.
  • The real number of cases and deaths was probably much higher.
British Dictionary definitions for real number

real number

a number expressible as a limit of rational numbers See number (sense 1)
Collins English Dictionary - Complete & Unabridged 2012 Digital Edition
© William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012
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real number in Science
real number
A number that can be written as a terminating or nonterminating decimal; a rational or irrational number. The numbers 2, -12.5, 3/7 , and pi (π) are all real numbers.
The American Heritage® Science Dictionary
Copyright © 2002. Published by Houghton Mifflin. All rights reserved.
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real number in Technology
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 the rationals) is said to be Cauchy precisely if, for any tolerance delta there is a size, N, beyond which: for any n, m exceeding N,
| r[n] - r[m] | A Cauchy sequence, r, has limit x precisely if, for any tolerance delta there is a size, N, beyond which: for any n exceeding N,
| r[n] - x | (i.e. r would remain Cauchy if any of its elements, no matter how late, were replaced by x).
It is possible to perform addition on the reals, because the equivalence class of a sum of two sequences can be shown to be the equivalence class of the sum of any two sequences equivalent to the given originals: ie, a~b and c~d implies a+c~b+d; likewise a.c~b.d so we can perform multiplication. Indeed, there is a natural embedding of the rationals in the reals (via, for any rational, the sequence which takes no other value than that rational) which suffices, when extended via continuity, to import most of the algebraic properties of the rationals to the reals.
The Free On-line Dictionary of Computing, © Denis Howe 2010
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