NUMBER1 A concept associated with quantity, size, measurement, etc., and represented by a word such as three, a symbol such as 3, a group of words such as eighty-three point five, or a group of symbols such as 83.5. Every number, regardless of the language in which it is expressed, occupies a unique position in a series, such as 3 in the series 1, 2, 3, 4, 5, …, enabling it to be used in such arithmetical processes as addition, subtraction, multiplication, and division. There are two basic kinds of number in such languages as English and French: cardinal numbers (the term deriving ultimately from Latin cardo/cardinis a hinge: that is, something on which other things turn or depend), denoting quantity and not order (as in 1, 2, 3, 4); and ordinal numbers (the term deriving ultimately from Latin ordo/ordinis order), denoting relative position in a sequence (as in 1st, 2nd, 3rd, 4th). Grammatically, the number system of a language contrasts with its system of quantifiers: for example, one house with a house, and two/three/forty people, etc., with some people, several people, and many people, etc.

Numbers as words

A spoken number is a WORD or phrase in a language, but a written number may be realized as either a word or phrase or a symbol or groups of symbols, usually a figure such as 1, 2, 12, 21. Written words are generally used for low numbers, from one to ten or twelve (as in the phrases three blind mice, the seven wonders of the world, and the twelve signs of the Zodiac). They are also often used for numbers up to 100 (with hyphenation for compound forms such as twenty-one and eighty-three) and for large round figures as in a thousand years and four million visitors a year. Words may or may not be used to express percentages, which may be given as ten per cent, 10 per cent, or 10% depending on house style or personal preference. Most house styles and editors aim for consistency in whichever forms they have chosen.

Numbers as symbols

Arabic figures are commonly used for numbers above ten or twelve (as in The ship sank with the loss of 18 lives), before abbreviations (as in 8 pm for eight o'clock in the evening, 7K for seven thousand, and 3m for three million), and for dates, addresses, and exact sums of money. Large numbers such as 118,985 are usually given as figures; when spoken, there is one significant difference between British and American usage: BrE always has and after hundred, as in one hundred and eighteen thousand, nine hundred and eighty-five, while AmE generally does not, as in one hundred eighteen thousand, nine hundred eighty-five. In large numbers, commas are generally used after the figures representing millions and thousands (1,345,905), but spaces are also, perhaps increasingly, used for this purpose (1 345 905); commas or spaces may or may not be used for thousands alone (2,345 and 2 345), for which solid numbers are also common (2345). Telephone numbers are generally written with spaces between regional and local numbers (01223 245999), and reference numbers are generally solid (N707096). Plural s after a set of numbers is often preceded by an apostrophe, as in 3's and 4's or the 1980's, but many house styles and individuals now favour 3s and 4s and the 1980s.

Numbers in -illion

Formerly, BrE and AmE differed greatly in their use of numbers representing multiples of million: for example, in Britain, France, and Germany, billion was ‘one million million’, or 10¹² (10 to the power 12), while in the US and Canada it was ‘one thousand million’ or 10⁹. The North American equivalent to the British billion was the trillion. In the last decades of the 20c, however, the North American use has become universal, providing the set million, billion, trillion, quadrillion, quintillion, sextillion, septillion, octillion, nonillion, decillion. The -illion pattern has prompted some word-play, especially in AmE, that makes use of various initial consonants and syllables: ‘The savings-and-loan industry bailout, which as of yesterday afternoon was expected to cost taxpayers $752.6 trillion skillion, is now expected to cost $964.3 hillion jillion bazillion’ ( Dave Barry, ‘Give or Take a Whomptillion’, International Herald Tribune, 13 June 1990). The widely-used zillion, with its end-of-alphabet prefix, usually suggests the ultimate in facetious scale, but Barry's ba-adds even more force. See LETTER 1, QUANTIFIER.

number entity describing the magnitude or position of a mathematical object or extensions of these concepts.

The Natural Numbers

Cardinal numbers describe the size of a collection of objects; two such collections have the same (cardinal) number of objects if their members can be matched in a one-to-one correspondence. Ordinal numbers refer to position relative to an ordering, as first, second, third, etc. The finite cardinal and ordinal numbers are called the natural numbers and are represented by the symbols 1, 2, 3, 4, etc. Both types can be generalized to infinite collections, but in this case an essential distinction occurs that requires a different notation for the two types (see transfinite number ).

The Integers and Rational Numbers

To the natural numbers one adjoins their negatives and zero to form the integers. The ratios a / b of the integers, where a and b are integers and b  ≠ 0, constitute the rational numbers; the integers are those rational numbers for which b  = 1. The rational numbers may also be represented by repeating decimals; e.g., 1/2 = 0.5000 … , 2/3 = 0.6666 … , 2/7 = 0.285714285714 … (see decimal system ).

The Real Numbers

The real numbers are those representable by an infinite decimal expansion, which may be repeating or nonrepeating; they are in a one-to-one correspondence with the points on a straight line and are sometimes referred to as the continuum. Real numbers that have a nonrepeating decimal expansion are called irrational, i.e., they cannot be represented by any ratio of integers. The Greeks knew of the existence of irrational numbers through geometry; e.g., 2 is the length of the diagonal of a unit square. The proof that 2 is unable to be represented by such a ratio was the first proof of the existence of irrational numbers, and it caused tremendous upheaval in the mathematical thinking of that time.

The Complex Numbers

Numbers of the form z  =  x  +  yi, where x and y are real and i  =  -1 , such as 8 + 7 i (or 8 + 7 -1 ), are called complex numbers; x is called the real part of z and yi the imaginary part. The real numbers are thus complex numbers with y  = 0; e.g., the real number 4 can be expressed as the complex number 4 + 0 i. The complex numbers are in a one-to-one correspondence with the points of a plane, with one axis defining the real parts of the numbers and one axis defining the imaginary parts. Mathematicians have extended this concept even further, as in quaternions .

The Algebraic and Transcendental Numbers

A real or complex number z is called algebraic if it is the root of a polynomial equation zⁿ  +  a_n - 1z^n - 1  + … +  a₁z  +  a₀  = 0, where the coefficients a₀ , a₁ , …  a_n - 1 are all rational; if z cannot be a root of such an equation, it is said to be transcendental. The number 2 is algebraic because it is a root of the equation z²  + 2 = 0; similarly, i, a root of z²  + 1 = 0, is also algebraic. However, F. Lindemann showed (1882) that π is transcendental, and using this fact he proved the impossibility of "squaring the circle" by straight edge and compass alone (see geometric problems of antiquity ). The number e has also been found to be transcendental, although it still remains unknown whether e  + π is transcendental.



See G. Ifrah, The Universal History of Numbers (1999).

num·ber / ˈnəmbər/ • n. 1. an arithmetical value, expressed by a word, symbol, or figure, representing a particular quantity and used in counting and making calculations and for showing order in a series or for identification: she dialed the number carefully | an even number. ∎  (numbers) dated arithmetic: the boy was adept at numbers. 2. a quantity or amount: the company is seeking to increase the number of women on its staff | the exhibition attracted vast numbers of visitors. ∎  (a number of) several: we have discussed the matter on a number of occasions. ∎  a group or company of people: there were some distinguished names among our number. ∎  (numbers) a large quantity or amount, often in contrast to a smaller one; numerical preponderance: the weight of numbers turned the battle against them. 3. a single issue of a magazine: the October number of “Travel.” ∎  a song, dance, piece of music, etc., esp. one of several in a performance: they go from one melodious number to another. ∎  inf. a thing, typically an item of clothing, of a particular type, regarded with approval or admiration: Yvonne was wearing a little black number. 4. Gram. a distinction of word form denoting reference to one person or thing or to more than one. See also singular (sense 2), plural, count noun, and mass noun. ∎  a particular form so classified. • v. [tr.] 1. amount to (a specified figure or quantity); comprise: the demonstrators numbered more than 5,000. ∎  include or classify as a member of a group: the orchestra numbers Brahms among its past conductors. 2. (often be numbered) mark with a number or assign a number to, typically to indicate position in a series: each document was numbered consecutively. ∎  count: strategies like ours can be numbered on the fingers of one hand. ∎  assess or estimate the size or quantity of (something) to be a specified figure: he numbers the fleet at a thousand. PHRASES: any number of any particular whole quantity of: the game can involve any number of players. ∎  a large and unlimited quantity or amount of: the results can be read any number of ways. by numbers following simple instructions identified by numbers or as if identified: painting by numbers.by the numbers following standard operating procedure. ∎  all together with a shouted-out count. someone's/something's days are numbered someone or something will not survive or remain in a position of power or advantage for much longer: my days as director were numbered. do a number on inf. treat someone badly, typically by deceiving, humiliating, or criticizing them in a calculated and thorough way. have someone's number inf. understand a person's real motives or character and thereby gain some advantage. have someone's number on it inf. (of a bomb, bullet, or other missile) destined to find a specified person as its target. someone's number is up inf. the time has come when someone is doomed to die or suffer some other disaster or setback. without number too many to count: they forgot the message times without number.

NUMBER2. A grammatical category used in describing parts of speech that show contrasts of PLURAL, SINGULAR, dual, etc. In English, the number system is basically a two-term contrast of singular and plural, shown in nouns and some pronouns and determiners, and to some extent in verbs. Even dual words, such as both, either, neither, take singular or plural verb CONCORD: both taking the plural; either, neither usually taking the singular. English nouns, as far as number is concerned, can be divided into: singular only, plural only, and words that can be both. Singular-only nouns are: (1) Uncountable nouns which can occur with such uncountable-specific words as much, little: much money, little sugar. (2) Most proper nouns: Edinburgh, the Thames (in which other restrictions apply). Plural only nouns are: (1) Countable: people in six people, but not in the European peoples. (2) Usually uncountable: not enough clothes (not *six clothes); many thanks (not *five thanks); trousers (a pair of trousers and not usually three trousers). The vast majority of countable nouns can be both singular and plural (book/books, fox/foxes, mouse/mice), but a few have no distinct plural form (as with one sheep/three sheep). Many nouns, however, have both countable and uncountable uses, in which case they may have a plural in some uses (What an excellent wine/What excellent wines!) but not in others (I never drink wine). Pronouns having distinct singular and plural forms include personal, reflexive, and possessive. Number contrast is neutralized with you, but the second-person reflexive forms distinguish yourself and yourselves. Demonstrative pronouns also have separate forms, singular this, that being used both with singular countable nouns (this restaurant) and with uncountable nouns (this food). Number contrast in verbs, except in the verb be, is confined to the distinct third-person singular tense form (look/looks). See PRONOUN, QUANTIFIER.

number Symbol representing a quantity used in counting or calculation. All ancient cultures devised their own number systems for the purposes of counting and measuring. From the basic process of counting we get the natural numbers. This concept can be extended to define an integer, a rational number, a real number and a complex number. See also binary system; irrational number; prime number

number sum of individuals or units; full tale or count XIII; multitude, aggregate; aspect or property of things as units; symbol of arithmetical value XIV; (pl.) groups of musical notes, melody; metrical periods, verses XVI. ME. no(u)mbre, numbre — AN. numbre, (O)F. nombre :- L. numerus.
So number vb. XIII. — (O)F. nombrer :- L. numerāre.

number •blubber, clubber, grubber, lubber, rubber, scrubber, snubber •Columba, cumber, encumber, Humber, lumbar, lumber, number, outnumber, rumba, slumber, umber •cucumber • landlubber •Addis Ababa • Córdoba •Aqaba • djellaba • mastaba •Berber, disturber, Djerba, Thurber