# real number

[ree-uh l, reel] /ˈri əl, ril/
noun, Mathematics
1.
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
1905-1910
1905-10
Dictionary.com Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2015.
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Examples from the Web for real number
Contemporary Examples
• The real number is much higher as many items are stolen from undocumented “virgin” sites.

• Remes, by the way, says he and the others lawyers believe that the real number of hunger strikers is closer to 130.

April 28, 2013
• In 2011, women reported 3,000 instances; the real number is thought to be 19,000.

February 22, 2013
• The economist Justin Wolfers estimates based on combining the two that the real number is more like 30,000.

April 4, 2013
• But an RJC board member told the investigative website Open Secrets that the real number was more like \$15 million.

November 7, 2012
Historical Examples
• We find in a cover by General Sheaffe, that the first report of the cannon taken was one-third short of the real number.

Ferdinand Brock Tupper
• Although their reports place their loss at over 4,000, it falls short of the real number.

Samuel Gibbs French
• The real number of churches where there is Holy Communion every Sunday is, by recent returns, about 430.

Philip Freeman
• The teacher names successively several numbers, and asks, whether they think the real number will be greater or less.

Jacob Abbott
• The real number was 76, six having been dropped on subsequent political excitements.

British Dictionary definitions for real number

## real number

noun
1.
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   (rē'əl)    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
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real number in Technology
mathematics
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.
(1997-03-12)
The Free On-line Dictionary of Computing, © Denis Howe 2010 http://foldoc.org
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### Difficulty index for real number

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### Word Value for real

4
5
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