Definitions for real numberˈri əl, ril
This page provides all possible meanings and translations of the word real number
real number, real(noun)
any rational or irrational number
An element of the set of real numbers.; the set of real numbers include the rational numbers and the irrational numbers, but not all complex numbers.
A floating-point number.
In mathematics, a real number is a value that represents a quantity along a continuous line. The real numbers include all the rational numbers, such as the integer −5 and the fraction 4/3, and all the irrational numbers such as √2 and π. Real numbers can be thought of as points on an infinitely long line called the number line or real line, where the points corresponding to integers are equally spaced. Any real number can be determined by a possibly infinite decimal representation such as that of 8.632, where each consecutive digit is measured in units one tenth the size of the previous one. The real line can be thought of as a part of the complex plane, and correspondingly, complex numbers include real numbers as a special case. These descriptions of the real numbers are not sufficiently rigorous by the modern standards of pure mathematics. The discovery of a suitably rigorous definition of the real numbers — indeed, the realization that a better definition was needed — was one of the most important developments of 19th century mathematics. The currently standard axiomatic definition is that real numbers form the unique Archimedean complete totally ordered field, up to isomorphism, whereas popular constructive definitions of real numbers include declaring them as equivalence classes of Cauchy sequences of rational numbers, Dedekind cuts, or certain infinite "decimal representations", together with precise interpretations for the arithmetic operations and the order relation. These definitions are equivalent in the realm of classical mathematics.
Sample Sentences & Example Usage
The numbers we have are all estimates; it's hard to get a handle on the real number of cases.
If we can dispel the delusion that learning about computers should be an activity of fiddling with array indexes and worrying whether X is an integer or a real number, we can begin to focus on programming as a source of ideas.
Translations for real number
From our Multilingual Translation Dictionary
- nombre realCatalan, Valencian
- reálné čísloCzech
- reelle ZahlGerman
- πραγματικός αριθμόςGreek
- reela nombroEsperanto
- número realSpanish
- nombre réelFrench
- valós számHungarian
- իրական թիվArmenian
- reāls skaitlisLatvian
- reëel getalDutch
- reelt tallNorwegian
- liczba rzeczywistaPolish
- número realPortuguese
- număr realRomanian
- действительное число, вещественное числоRussian
- реaлни брой, realni brojSerbo-Croatian
- reellt talSwedish
- వాస్తవ సంఖ్యTelugu
- gerçel sayı, gerçek sayı, reel sayıTurkish
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