real number - meaning and definition. What is real number
Diclib.com
ChatGPT AI Dictionary
Enter a word or phrase in any language 👆
Language:

Translation and analysis of words by ChatGPT artificial intelligence

On this page you can get a detailed analysis of a word or phrase, produced by the best artificial intelligence technology to date:

  • how the word is used
  • frequency of use
  • it is used more often in oral or written speech
  • word translation options
  • usage examples (several phrases with translation)
  • etymology

What (who) is real number - definition


real number         
  • A symbol for the set of real numbers
  • Real numbers <math>(\mathbb{R})</math> include the rational numbers <math>(\mathbb{Q})</math>, which include the integers <math>(\mathbb{Z})</math>, which in turn include the natural numbers <math>(\mathbb{N})</math>
  • Real numbers can be thought of as all points on a number line
QUANTITY ALONG A CONTINUOUS LINE
Real numbers; Real Numbers; Bounded real-valued data; Real number field; Real (numbers); ℝ; Field of reals; Axiomatic real number; Complete ordered field; The complete ordered field; Reall numbers; Real number system; Real (number); Real Number System; Set of real numbers; R (math); R (maths)
<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} "real number", where a real number 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] | < delta 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 | < delta (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, areal numberb and creal numberd implies a+creal numberb+d; likewise a.creal numberb.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)
Real number         
  • A symbol for the set of real numbers
  • Real numbers <math>(\mathbb{R})</math> include the rational numbers <math>(\mathbb{Q})</math>, which include the integers <math>(\mathbb{Z})</math>, which in turn include the natural numbers <math>(\mathbb{N})</math>
  • Real numbers can be thought of as all points on a number line
QUANTITY ALONG A CONTINUOUS LINE
Real numbers; Real Numbers; Bounded real-valued data; Real number field; Real (numbers); ℝ; Field of reals; Axiomatic real number; Complete ordered field; The complete ordered field; Reall numbers; Real number system; Real (number); Real Number System; Set of real numbers; R (math); R (maths)
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line (or alternatively, a quantity that can be represented as an infinite decimal expansion). The adjective real in this context was introduced in the 17th century by René Descartes, who distinguished between real and imaginary roots of polynomials.
Positive real numbers         
REAL NUMBER STRICTLY GREATER THAN ZERO
Logarithmic measure; Ratio scale; Positive reals; Positive real axis; Positive numbers; Positive real number
In mathematics, the set of positive real numbers, \R_{>0} = \left\{ x \in \R \mid x > 0 \right\}, is the subset of those real numbers that are greater than zero. The non-negative real numbers, \R_{\geq 0} = \left\{ x \in \R \mid x \geq 0 \right\}, also include zero.

Wikipedia

Real number
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line (or alternatively, a quantity that can be represented as an infinite decimal expansion). The adjective real in this context was introduced in the 17th century by René Descartes, who distinguished between real and imaginary roots of polynomials.
Examples of use of real number
1. "The real number might be bigger than this," he said.
2. Activists say the real number is up to 60 million.
3. "Everyone can guess, but what is the real number?
4. But the real number of quangos could be far higher.
5. Bezeq spat back that the real number was vastly smaller.