Numeral (linguistics)
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In linguistics, a numeral is a member of a part of speech characterized by the designation of numbers; some examples are the English word 'two' and the compound 'seventyseventh'.^{[1]}^{[2]} Numerals function most typically as a noun (e.g., "twelve", "dozen"), adjective (e.g., "first", "single") or adverb (e.g., "once", "singly") and express numbers and relations to numbers for example: quantity, sequence, frequency, or fraction.^{[3]}
Contents
Identifying numerals
Numerals may be attributive, as in two dogs, or pronominal, as in I saw two (of them).
Many words of different parts of speech indicate number or quantity. Such words are called Quantifiers. Examples are words such as every, most, least, some, etc. Numerals are distinguished from other quantifiers by the fact that they designate a specific number.^{[3]} Examples are words such as five, ten, fifty, one hundred, etc. They may or may not be treated as a distinct part of speech; this may vary, not only with the language, but with the choice of word. For example, 'dozen' serves the function of a noun, 'first' serves the function of an adjective, and 'twice' serves the function of an adverb. In Old Church Slavonic, the cardinal numbers 5 to 10 were feminine nouns; when quantifying a noun, that noun was declined in the genitive plural like other nouns that followed a noun of quantity (one would say the equivalent of "five of people"). In English grammar, the classification "numeral" (viewed as a part of speech) is reserved for those words which have distinct grammatical behavior: when a numeral modifies a noun, it may replace the article: the/some dogs played in the park → twelve dogs played in the park. (Note that *dozen dogs played in the park is not grammatical, so 'dozen' is not a numeral in this sense.) English numerals indicate cardinal numbers. However, not all words for cardinal numbers are necessarily numerals. For example, million is grammatically a noun, and must be preceded by an article or numeral itself.
Numerals may be simple, such as 'eleven', or compound, such as 'twentythree'.
In linguistics, however, numerals are classified according to purpose: examples are ordinal numbers (first, second, third, etc.; from 'third' up, these are also used for fractions), multiplicative numbers (once, twice, and thrice), multipliers (single, double, and triple), and distributive numbers (singly, doubly, and triply). Georgian,^{[4]} Latin, and Romanian (see Romanian distributive numbers) have regular distributive numbers, such as Latin singuli "onebyone", bini "in pairs, twobytwo", terni "three each", etc. In languages other than English, there may be other kinds of number words. For example, in Slavic languages there are collective numbers which describe sets, such as pair or dozen in English (see Russian numerals, Polish numerals).
Some languages have a very limited set of numerals, and in some cases they arguably do not have any numerals at all, but instead use more generic quantifiers, such as 'pair' or 'many'. However, by now most such languages have borrowed the numeral system or part of the numeral system of a national or colonial language, though in a few cases (such as Guarani^{[citation needed]}), a numeral system has been invented internally rather than borrowed. Other languages had an indigenous system but borrowed a second set of numerals anyway. An example is Japanese, which uses either native or Chinesederived numerals depending on what is being counted.
In many languages, such as Chinese, numerals require the use of numeral classifiers. Many sign languages, such as ASL, incorporate numerals.
Basis of counting system
Numeral systems 

Hindu–Arabic numeral system 
East Asian 
Alphabetic 
Former 
Positional systems by base 
Nonstandard positional numeral systems 
List of numeral systems 
Not all languages have numeral systems. Specifically, there is not much need for numeral systems among huntergatherers who do not engage in commerce. Many languages around the world have no numerals above two to four—or at least did not before contact with the colonial societies—and speakers of these languages may have no tradition of using the numerals they did have for counting. Indeed, several languages from the Amazon have been independently reported to have no specific number words other than 'one'. These include Nadëb, precontact Mocoví and Pilagá, Culina and precontact Jarawara, Jabutí, CanelaKrahô, Botocudo (Krenák), Chiquitano, the Campa languages, Arabela, and Achuar.^{[5]} Some languages of Australia, such as Warlpiri, do not have words for quantities above two,^{[6]}^{[7]} as did many Khoisan languages at the time of European contact. Such languages do not have a word class of 'numeral'.
Most languages with both numerals and counting use base 8, 10, 12, or 20. Base 10 appears to come from counting one's fingers, base 20 from the fingers and toes, base 8 from counting the spaces between the fingers (attested in California), and base 12 from counting the knuckles (3 each for the four fingers).^{[8]}
For very large (and very small) numbers, traditional systems have been superseded by the use of scientific notation and the system of SI prefixes. Traditional systems continue to be used in everyday life.
No base
Many languages of Melanesia have (or once had) counting systems based on parts of the body which do not have a numeric base; there are (or were) no numerals, but rather nouns for relevant parts of the body—or simply pointing to the relevant spots—were used for quantities. For example, 1–4 may be the fingers, 5 'thumb', 6 'wrist', 7 'elbow', 8 'shoulder', etc., across the body and down the other arm, so that the opposite little finger represents a number between 17 (Torres Islands) to 23 (Eleman). For numbers beyond this, the torso, legs and toes may be used, or one might count back up the other arm and back down the first, depending on the people.
4: quaternary
Some Austronesian and Melanesian ethnic groups, some Sulawesi and some Papua New Guineans, count with the base number four, using the term asu and aso, the word for dog, as the ubiquitous village dog has four legs.^{[9]} This is argued by anthropologists to be also based on early humans noting the human and animal shared body feature of two arms and two legs as well as its ease in simple arithmetic and counting. As an example of the system's ease a realistic scenario could include a farmer returning from the market with fifty asu heads of pig (200), less 30 asu (120) of pig bartered for 10 asu (40) of goats noting his new pig count total as twenty asu: 80 pigs remaining. The system has a correlation to the dozen counting system and is still in common use in these areas as a natural and easy method of simple arithmetic.^{[9]}^{[10]}
5: quinary
Quinary systems are based on the number 5. It is almost certain the quinary system developed from counting by fingers (five fingers per hand).^{[11]} An example are the Epi languages of Vanuatu, where 5 is luna 'hand', 10 lualuna 'two hand', 15 toluluna 'three hand', etc. 11 is then lualuna tai 'twohand one', and 17 toluluna lua 'threehand two'.
5 is a common auxiliary base, or subbase, where 6 is 'five and one', 7 'five and two', etc. Aztec was a vigesimal (base20) system with subbase 5.
6: senary
The MoreheadMaro languages of Southern New Guinea are examples of the rare base 6 system. Kanum is one these languages. The Sko languages on the North Coast of New Guinea follow a base24 system with a subbase of 6.
7: septenary
Septenary systems are very rare, as few natural objects consistently have seven distinctive features. Traditionally, it occurs in weekrelated timing. It has been suggested that the Palikur language may have a baseseven system, but this is dubious.^{[12]}
8: octal
Octal counting systems are based on the number 8. It is used in the Yuki language of California and in the Pamean languages of Mexico, because the Yuki and Pame keep count by using the four spaces between their fingers rather than the fingers themselves.^{[13]}
9: nonary
It has been suggested that Nenets has a basenine system.^{[12]}
10: decimal
A majority of traditional number systems are decimal. This dates back at least to the ancient Egyptians, who used a wholly decimal system. Anthropologists hypothesize this may be due to humans having five digits per hand, ten in total.^{[11]}^{[14]} There are many regional variations including:
 Western system: based on thousands, with variants (see English numerals)
 Indian system: crore, lakh (see Indian numbering system. Indian numerals)
 East Asian system: based on tenthousands (see below)
12: duodecimal
Duodecimal systems are based on 12.
These include:
 Chepang language of Nepal,
 Mahl language of Minicoy Island in India
 Nigerian Middle Belt areas such as Janji, Kahugu and the Nimbia dialect of Gwandara.
 Melanesia^{[citation needed]}
 reconstructed protoBenue–Congo
Duodecimal numeric systems have some practical advantages over decimal. It is much easier to divide the base digit twelve (which is a highly composite number) by many important divisors in market and trade settings, such as the numbers 2, 3, 4 and 6.
Because of several measurements based on twelve,^{[15]} many Western languages have words for basetwelve units such as dozen, gross and great gross, which allow for rudimentary duodecimal nomenclature, such as "two gross six dozen" for 360. Ancient Romans used a decimal system for integers, but switched to duodecimal for fractions, and correspondingly Latin developed a rich vocabulary for duodecimalbased fractions (see Roman numerals). A notable fictional duodecimal system was that of J. R. R. Tolkien's Elvish languages, which used duodecimal as well as decimal.
20: vigesimal
Vigesimal numbers use the number 20 as the base number for counting. Anthropologists are convinced the system originated from digit counting, as did bases five and ten, twenty being the number of human fingers and toes combined^{[11]}^{[16]} The system is in widespread use across the world. Some include the classical Mesoamerican cultures, still in use today in the modern indigenous languages of their descendants, namely the Nahuatl and Mayan languages (see Maya numerals). A modern national language which uses a full vigesimal system is Dzongkha in Bhutan.
Partial vigesimal systems are found in some European languages: Basque, Celtic languages, French (from Celtic), Danish, and Georgian. In these languages the systems are vigesimal up to 99, then decimal from 100 up. That is, 140 is 'one hundred two score', not *seven score, and there is no numeral for 400.
The term score originates from tally sticks, and is perhaps a remnant of Celtic vigesimal counting. It was widely used to learn the predecimal British currency in this idiom: "a dozen pence and a score of bob", referring to the 20 shillings in a pound. For Americans the term is most known from the opening of the Gettysburg Address: "Four score and seven years ago our fathers...".
24: quadrovigesimal
The Sko languages have a base24 system with a subbase of 6.
32: duotrigesimal
Ngiti has base 32.
60: sexagesimal
Ekari has a base60 system. Sumeria had a base60 system with a decimal subbase (perhaps a conflation of the decimal and a duodecimal systems of its constituent peoples), which was the origin of the numbering of modern degrees, minutes, and seconds.
80: octogesimal
Supyire is said to have a base80 system; it counts in twenties (with 5 and 10 as subbases) up to 80, then by eighties up to 400, and then by 400s (great scores).
kàmpwóò  ŋ̀kwuu  sicyɛɛré  ná  béétàànre  ná  kɛ́  ná  báárìcyɛ̀ɛ̀rè 
fourhundred  eighty  four  and  twentythree  and  ten  and  fivefour 
799 [i.e. 400 + (4 x 80) + (3 x 20) + {10 + (5 + 4)}]’
Larger numerals
English has derived numerals for multiples of its base (fifty, sixty, etc), and some languages have simplex numerals for these, or even for numbers between the multiples of its base. Balinese, for example, currently has a decimal system, with words for 10, 100, and 1000, but has additional simplex numerals for 25 (with a second word for 25 only found in a compound for 75), 35, 45, 50, 150, 175, 200 (with a second found in a compound for 1200), 400, 900, and 1600. In Hindustani, the numerals between 10 and 100 have developed to the extent that they need to be learned independently.
In many languages, numerals up to the base are a distinct part of speech, while the words for powers of the base belong to one of the other word classes. In English, these higher words are hundred 10^{2}, thousand 10^{3}, million 10^{6}, and higher powers of a thousand (short scale) or of a million (long scale—see names of large numbers). These words cannot modify a noun without being preceded by an article or numeral (*hundred dogs played in the park), and so are nouns.
In East Asia, the higher units are hundred, thousand, myriad 10^{4}, and powers of myriad. In India, they are hundred, thousand, lakh 10^{5}, crore 10^{7}, and so on. The Mesoamerican system, still used to some extent in Mayan languages, was based on powers of 20: bak’ 400 (20^{2}), pik 8000 (20^{3}), kalab 160,000 (20^{4}), etc.
See also
Numerals in various languages
A database Numeral Systems of the World's Languages compiled by Eugene S.L. Chan of Hong Kong is hosted by the Max Planck Institute for Evolutionary Anthropology in Leipzig, Germany. The database currently contains data for about 4000 languages.
 ProtoIndoEuropean numerals
 ProtoSemitic numerals
 Japanese numerals
 Korean numerals
 Dzongkha numerals
 Javanese numerals
 Balinese numerals
 Finnish numerals
 Polish numerals
 Yoruba numerals
 Australian Aboriginal enumeration
Related topics
Notes
 ^ Charles Follen: A Practical Grammar of the German Language. Boston, 1828, p. 9, p. 44 and 48. Quote: "PARTS OF SPEECH. There are ten parts of speech, viz. Article, Substantive or Noun, Adjective, Numeral, Pronoun, Verb, Adverb, Preposition, Conjunction, and Interjection.", "NUMERALS. The numbers are divided into cardinal, ordinal, proportional, distributive, and collective. [...] Numerals of proportion and distribution are [...] &c. Observation. The above numerals, in fach or fäl´tig, are regularly declined, like other adjectives."
 ^ Horace Dalmolin: The New English Grammar: With Phonetics, Morphology and Syntax, Tate Publishing & Enterprises, 2009, p. 175 & p. 177. Quote: "76. The different types of words used to compose a sentence, in order to relate an idea or to convey a thought, are known as parts of speech. [...] The parts of speech, with a brief definition, will follow. [...] 87. Numeral: Numerals are words that express the idea of number. There are two types of numerals: cardinal and ordinal. The cardinal numbers (one, two, three...) are used for counting people, objects, etc. Ordinal numbers (first, second, third...) can indicate order, placement in rank, etc."
 ^ ^{a} ^{b} "What is a numeral?".
 ^ Walsinfo.com
 ^ Hammarström (2009, page 197) "Rarities in numeral systems"
 ^ UCL Media Relations, "Aboriginal kids can count without numbers"
 ^ The Science Show, Genetic anomaly could explain severe difficulty with arithmetic, Australian Broadcasting Corporation
 ^ Bernard Comrie, "The Typology of Numeral Systems", p. 3
 ^ ^{a} ^{b} Ryan, Peter. Encyclopaedia of Papua and New Guinea. Melbourne University Press & University of Papua and New Guinea,:1972 ISBN 0522840256.: 3 pages p 219.
 ^ Aleksandr Romanovich Luriicac, Lev Semenovich Vygotskiĭ, Evelyn Rossiter. Ape, primitive man, and child: essays in the history of behavior. CRC Press: 1992: ISBN 1878205439.
 ^ ^{a} ^{b} ^{c} Heath, Thomas, A Manual of Greek Mathematics, Courier Dover: 2003. ISBN 9780486432311 page, p:11
 ^ ^{a} ^{b} Parkvall, M. Limits of Language, 1st edn. 2008. p.291. ISBN 9781590282106
 ^ Ascher, Marcia (1994), Ethnomathematics: A Multicultural View of Mathematical Ideas, Chapman & Hall, ISBN 0412989417
 ^ Scientific American Munn& Co: 1968, vol 219: 219
 ^ such as twelve months in a year, the twelvehour clock, twelve inches to the foot, twelve pence to the shilling
 ^ Georges Ifrah, The Universal History of Numbers: The Modern Number System, Random House, 2000: ISBN 1860467911. 1262 pages
Further reading
 James R. Hurford (2010) [1975]. The Linguistic Theory of Numerals. Cambridge University Press. ISBN 9780521133685.