real number

re·al num·ber

R r

Transcription

- US Pronunciation
- US IPA
- UK Pronunciation
- UK IPA
- [ree-uh l, reel nuhm-ber]
- /ˈri əl, ril ˈnʌm bər/
- /rɪəl ˈnʌmbə(r)/

- US Pronunciation
- US IPA
- [ree-uh l, reel nuhm-ber]
- /ˈri əl, ril ˈnʌm bər/

Definitions of real number words

noun real number a rational number or the limit of a sequence of rational numbers, as opposed to a complex number. 1
noun real number mathematics: rational or irrational number 1
noun Technical meaning of real number (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] | < 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, 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. 1
noun real number a number expressible as a limit of rational numbers 0
noun real number any rational or irrational number not having an imaginary part 0

See all 5 definitions of real number

Information block about the term

Origin of real number

First appearance:

before 1905

One of the 15% newest English words

First recorded in 1905-10

Historical Comparancy

Parts of speech for Real number

noun

adjective

verb

adverb

pronoun

preposition

conjunction

determiner

exclamation

Full grammatical hierarchy of Real number

real number popularity

A pretty common term. Usually people know it’s meaning, but prefer to use a more spread out synonym. About 31% of English native speakers know the meaning and use word.

According to our data about 65% of words is more used. This is a rare but used term. It occurs in the pages of specialized literature and in the speech of educated people.

real number usage trend in Literature

This diagram is provided by Google Ngram Viewer