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Definition: number from The Penguin Dictionary of Mathematics
1. (natural number)

A positive integer.

2.

A member of the set of all complex numbers. The real numbers are numbers that do not involve -1. These are classified into rational numbers and irrational numbers.

3.

See cardinal number.

4.

See ordinal number.

Summary Article: NUMBER
From The Cambridge Encyclopedia of the Language Sciences

Number is a grammatical feature that quantifies the denotation of a linguistic element. It can refer to entities or events, and in language we find both nominal number (very common, discussed in the following) and verbal number (less common, realized on the verb to indicate the number of events or the number of participants; also called pluractionality).

Languages vary with regard to the part of their nominal inventory that is involved in the number system. In different languages, the split into nominals that do and do not express number may occur at different points of the animacy hierarchy: speaker (first person pronouns) > addressee (second person pronouns) > third person pronouns > kin > rational > human > animate > inanimate. Furthermore, not all nouns are number differentiable. Two types of noun are traditionally distinguished: count nouns and mass nouns, the latter regarded as lacking the number distinction. At the level of semantics, the count–mass distinction can be captured with two semantic features boundedness and internal structure (Jackendoff 1991), which corresponds to the distinction between temporally bounded and unbounded events in verbal semantics. But countability is really a characteristic of nominal phrases (Allan 1980), since many nouns can appear in both count and mass syntactic contexts, for example, Would you like a cake/some cake? We need a bigger table/ There is not enough table for everyone to sit at.

When nominal number is found expressed on the noun or the noun phrase as such, it is considered inherent. When found on other elements of the noun phrase or on the verb, it is contextual. The expressions of nominal number can involve special number words (of different syntactic status); syntactic means (i.e., agreement, found most commonly on demonstratives and verbs but also on articles, adjectives, pronouns, nouns in possessive constructions, adverbs, adpositions, and complementizers); a variety of morphological means (inflections, stem changes, zero expressions, clitics); and lexical means (e.g., suppletion). Number is often marked in more than one way within one language.

All nominal number systems are built on the primary opposition between singular (expressing the quantity one) and plural (more than one). Other attested number values are dual (two), trial (three), and paucal (a few). There may be further divisions into paucal and greater paucal, plural and greater plural (the last value may imply an excessive number, or all possible instances of the referent). No genuine quadrals (four) have been found. The largest number systems involve five values. In many languages, the absence of plural marking does not necessarily imply the singular, but the form may be outside the number opposition and express general number, that is, the meaning of the noun without reference to number.

Associatives, distributives, and collectives – all sometimes listed as additional values of number – are better analyzed as independent features. Associativity expresses the meaning “X and the group associated with X”; distributives indicate that entities (whether count or mass ones), events, qualities, or locations are to be construed as distinct in space, sort, or time; and collectives indicate that the members of a group are to be construed together as a unit. Many languages have markers for these categories in addition to various number markers.

© Cambridge University Press 2011

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