Definitions for real number
ˈri əl, rilre·al num·ber

Princeton's WordNetRate this definition:0.0 / 0 votes

1. real number, realnoun

   any rational or irrational number

WiktionaryRate this definition:0.0 / 0 votes

1. real numbernoun

   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.

2. real numbernoun

   A floating-point number.

WikipediaRate this definition:0.0 / 0 votes

1. Real number

   In mathematics, a real number is a number that can be used to measure a continuous one-dimensional quantity such as a distance, duration or temperature. Here, continuous means that values can have arbitrarily small variations. Every real number can be almost uniquely represented by an infinite decimal expansion.The real numbers are fundamental in calculus (and more generally in all mathematics), in particular by their role in the classical definitions of limits, continuity and derivatives.The set of real numbers is denoted R or R {\displaystyle \mathbb {R} } and is sometimes called "the reals". The adjective real in this context was introduced in the 17th century by René Descartes to distinguish real numbers, associated with physical reality, from imaginary numbers (such as the square roots of −1), which seemed like a theoretical contrivance unrelated to physical reality.The real numbers include the rational numbers, such as the integer −5 and the fraction 4 / 3. The rest of the real numbers are called irrational numbers, and include algebraic numbers (such as the square root √2 = 1.414...) and transcendental numbers (such as π = 3.1415...).Real numbers can be thought of as all points on an infinitely long line called the number line or real line, where the points corresponding to integers (..., −2, −1, 0, 1, 2, ...) are equally spaced. Conversely, analytic geometry is the association of points on lines (especially axis lines) to real numbers such that geometric displacements are proportional to differences between corresponding numbers. The informal descriptions above of the real numbers are not sufficient for ensuring the correctness of proofs of theorems involving real numbers. The realization that a better definition was needed, and the elaboration of such a definition was a major development of 19th-century mathematics and is the foundation of real analysis, the study of real functions and real-valued sequences. A current axiomatic definition is that real numbers form the unique (up to an isomorphism) Dedekind-complete ordered field. Other common definitions of real numbers include equivalence classes of Cauchy sequences (of rational numbers), Dedekind cuts, and infinite decimal representations. All these definitions satisfy the axiomatic definition and are thus equivalent.

ChatGPTRate this definition:0.0 / 0 votes

1. real number

   A real number is any value of a continuous quantity that can represent a distance along a line. This includes all the numbers that can be written as a decimal, including both rational numbers (like 7, 0.75, -0.3333) and irrational numbers (like square roots, π and e), but not imaginary numbers. Real numbers can be positive, negative or zero.

WikidataRate this definition:4.0 / 1 vote

1. Real 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.

Matched Categories

1. • Complex Number

How to pronounce real number?

1. Alex

   US English

   David

   US English

   Mark

   US English

   Daniel

   British

   Libby

   British

   Mia

   British

   Karen

   Australian

   Hayley

   Australian

   Natasha

   Australian

   Veena

   Indian

   Priya

   Indian

   Neerja

   Indian

   Zira

   US English

   Oliver

   British

   Wendy

   British

   Fred

   US English

   Tessa

   South African

How to say real number in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of real number in Chaldean Numerology is: 8

2. Pythagorean Numerology

   The numerical value of real number in Pythagorean Numerology is: 1

Examples of real number in a Sentence

1. Harold Abelson:

   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.

2. Reinhard Steurer:

   For the The EU, the real number is 52.8 %, normally, when a government says' we reduce by 55 %,' it means 55 % less emissions. In this case, they do a little trick and count in [ carbon ] sinks.

3. Susan Montgomery:

   The numbers we have are all estimates; it's hard to get a handle on the real number of cases.

4. Jean Su:

   We think the real number [ of shutoffs ] should be around 3.4 million households.

5. Michael Tan:

   The real number is 65 days.

References

1. ^ Princeton's WordNet
   http://wordnetweb.princeton.edu/perl/webwn?s=real number
2. ^ Wiktionary
   https://en.wiktionary.org/wiki/Real_Number
3. ^ Wikipedia
   https://en.wikipedia.org/wiki/Real_Number
4. ^ ChatGPT
   https://chat.openai.com
5. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=real number