Indefinite and fictitious numbers

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Many languages have words expressing indefinite and fictitious numbers—inexact terms of indefinite size, used for comic effect, for exaggeration, as placeholder names, or when precision is unnecessary or undesirable. One technical term for such words is "non-numerical vague quantifier".[1] Such words designed to indicate large quantities can be called "indefinite hyperbolic numerals".[2]

Specific values used as indefinite[edit]

  • In English, some words that have a precise numerical definition are often used indefinitely: couple, 2;[3] dozen, 12; myriad, 10,000.
  • In various Middle Eastern traditions, the number 40 is used to express a large but unspecific number,[4][5] as in the Hebrew Bible's "forty days and forty nights", Ali Baba and the Forty Thieves, and the Forty Martyrs of Sebaste.[6][7] This usage is sometimes found in English as well (for example, "forty winks").[8][9]
  • In Latin, sescenti (600) was used to mean a very large number, perhaps from the size of a Roman cohort.[10]
  • In Arabic, 1001 is used similarly, as in The Book of One Thousand and One Nights (lit. "a thousand nights and one night").[5] Many modern English book titles use this convention as well: 1,001 Uses for ....
  • In Japanese, 八千, 8000, is used: 八千草 (lit. 8,000 herbs) means a variety of herbs and 八千代 ( lit. 8,000 generations) means eternity.
  • The number 10,000 is used to express an even larger approximate number, as in Hebrew רבבה revâvâh,[11] rendered into Greek as μυριάδες, and to English myriad.[12] Similar usage is found in the East Asian or (lit. 10,000; pinyin: wàn), and the South Asian lakh (lit. 100,000).[13]
  • In Irish, 100,000 (céad míle) is used, as in the phrase céad míle fáilte, "a hundred thousand welcomes" or Gabriel Rosenstock's poetic phrase Irish: mo chéad míle grá ("my hundred thousand loves").[14]
  • In Welsh, cant a mil, literally "a hundred and thousand", is used to mean a large number in a similar way to English "a hundred and one".[15] It is used in phrases such as cant a mil o bethau i'w wneud "a hundred and one things to do" i.e. "many, many things to do".
  • In Swedish, femtioelva is used, meaning "fifty-eleven".
  • In Chinese, 十萬八千里; 十万八千里; shí wàn bā qiān lǐ, 108,000 li, means a great distance.
  • In Thai, ร้อยแปด (roi paed), means both 108, and miscellaneous, various, plentiful.[16]
  • In Hungarian, people often say "26 times" for expressing their impatience or dissatisfaction about a recurring act (for example, "26 times I told you that I know Peter!"). "Csilliárd" is also often used in the same "indefinitely large number" meaning as "zillion" in English. Probably humorous merging of words "csillag" ("star", referring to the large number of stars) and "milliárd" ("billion").

Other specific numbers are occasionally used as indefinite as well. English does this with count nouns that refer to numbers: a dozen/dozens, a score/scores, a hundred/hundreds, and similarly thousand, million, billion. Unlike cardinal numbers, these can be pluralized, in which case they require of before the noun (millions of dollars, but five million dollars), and require the indefinite article "a" in the singular (a million letters (indefinite) but one million letters (definite)).


Umpteen, umteen or umpty[17] is an unspecified but large number, used in a humorous fashion or to imply that it is not worth the effort to pin down the actual figure. Despite the -teen ending, which would seem to indicate that it lies between 12 and 20, umpteen can be much larger.

"Umpty" is first attested in 1905, in the expression "umpty-seven", implying that it is a multiple of ten.[18][19] Ump(ty) came from a verbalization of a dash in Morse code.[18]

"Umpteen", adding the ending -teen, as in "thirteen", is first attested in 1918,[20][17][21] and has become by far the most common form.[22]

In Norwegian, ørten is used in a similar way, playing on the numbers from tretten (13) to nitten (19), but often signifying a much larger number.[23]


Words with the suffix -illion (e.g. zillion,[24] gazillion,[25] jillion,[26] bajillion,[27] squillion,[28] and others) are often used as informal names for unspecified large numbers by analogy to names of large numbers such as million (106), billion (109) and trillion (1012). In Estonian, the compound word mustmiljon ("black million") is used to mean an unfathomably large number.

These words are intended to denote a number that is large enough to be unfathomable and are typically used as hyperbole or for comic effect. They have no precise value or order. They form ordinals and fractions with the usual suffix -th, e.g. "I asked her for the jillionth time", or "-illionaire" to describe a wealthy person.

Sagan's number[edit]

Sagan's number is the number of stars in the observable universe. It is named in honor of Carl Sagan.[29] This number is reasonably well defined, because it is known what stars are and what the observable universe is, but its value is highly uncertain.

  • In 1980, Carl Sagan himself estimated it to be 10 sextillion in short scale (1022).[30]
  • In 2003, it was estimated to be 70 sextillion (7 × 1022).[31][32]
  • In 2010, it was estimated to be 300 sextillion (3 × 1023).[33] This would equal the number of H2 molecules in 1 gram of hydrogen.

Sagan's number is to be distinguished from the sagan unit or the humorous use of the term "sagan" to denote any large quantity—specifically, any number of at least four billion, due to Sagan's association with the phrase "billions and billions".[34][35]

See also[edit]


  1. ^ "Bags of Talent, a Touch of Panic, and a Bit of Luck: The Case of Non-Numerical Vague Quantifiers" from Linguista Pragensia, Nov. 2, 2010 Archived 2012-07-31 at
  2. ^ "The surprising history of indefinite hyperbolic numerals - The Boston Globe". Retrieved 1 April 2018.
  3. ^ "couple (noun)", Merriam-Webster Dictionary, definition 4
  4. ^ A.D. Alderson, Fahir İz, The Concise Oxford Turkish Dictionary, Oxford, 1959, s.v. kırk: "Forty; used especially to denote a large indefinite number
  5. ^ a b "Biblical Criticism", The Classical Journal 36:71:83ff (March 1827) full text
  6. ^ Michael David Coogan, A Brief Introduction to the Old Testament: The Hebrew Bible in Its Context, Oxford, 2008, p. 116
  7. ^ Public Domain Levias, Caspar (1905). "Numbers and numerals". In Singer, Isidore; et al. (eds.). The Jewish Encyclopedia. 9. New York: Funk & Wagnalls. p. 349. Retrieved 2017-04-27. "Forty: Stands in the Bible for a generation (e.g., the forty years of wandering in the desert), hence for any period of time the exact duration of which is unknown (comp. Gen. vii. 4, 12, 17; viii. 6; Ex. xxiv. 18, xxxiv. 28; Deut. ix. 9, 11, 18; x. 10; I Sam. xvii. 16; I Kings xix. 8; Jonah iii. 4). In later literature forty is commonly used as a round number (comp. Giṭ. 39b, 40a; Soṭah 34a; Yer. Ta'an. iv. 8; et al.)."
  8. ^ Oxford English Dictionary, 1st edition, s.v. 'forty' A.b.
  9. ^ Tréguer, Pascal (November 16, 2017). "Meaning and Origin of 'Forty Winks'". Word Histories.
  10. ^ Lewis and Short, A Latin Dictionary, s.v. sescenti
  11. ^ "H7233 רבבה - Strong's Hebrew Lexicon". Retrieved 1 April 2018.
  12. ^ Oxford English Dictionary, 3rd edition, s.v. 'myriad'
  13. ^ Oxford English Dictionary 1st ed., s.v. 'lakh'
  14. ^
  15. ^ "Geiriadur Prifysgol Cymru Online".
  16. ^ "ร้อยแปด - Thai / English dictionary meaning - ร้อยแปด ภาษาอังกฤษ แปล ความหมาย". Retrieved 2019-02-03.
  17. ^ a b "Umpteen". Oxford English Dictionary. Retrieved 14 April 2012. (available online to subscribers)
  18. ^ a b "Umpty". Oxford English Dictionary. Retrieved 14 April 2012. (available online to subscribers)
  19. ^ Warren Harding, quoted in Advertising & Selling 29:28-52:26 (1920)
  20. ^ The American Heritage Dictionary of the English Language (2000), 4th ed. Boston: Houghton Mifflin.
  21. ^ Umpteen, Merriam-Webster. Accessed 2014-06-29.
  22. ^ "Google Ngram Viewer". Retrieved 1 April 2018.
  23. ^ "Det Norske Akademis ordbok: ørten". Retrieved 2019-12-23.
  24. ^ "Definition of ZILLION". Retrieved 1 April 2018.
  25. ^ Included in the standard dictionary included with Microsoft Word word-processing software
  26. ^ Partridge, Eric; Dalzell; Victor, Terry, eds. (2006). The New Partridge Dictionary of Slang and Unconventional English. 2. Taylor & Francis. p. 1103. ISBN 0-415-25938-X.
  27. ^ "Definition of Bajillion". Merriam-Webster. Retrieved 7 March 2021.
  28. ^ "squillion". Oxford Dictionaries. Oxford Dictionaries. Retrieved 4 November 2018.
  29. ^ Michon, Gerard. "Sizing up the Universe - Stars, Sand and Nucleons - Numericana". Retrieved 1 April 2018.
  30. ^ Sagan, Carl. Cosmos. Balantine Books. p. 3. ISBN 0345331354.
  31. ^ "Star survey reaches 70 sextillion: And that's only the stars we can actually see". Sydney, Australia: CNN Science. July 23, 2003. Retrieved October 27, 2014.
  32. ^ "STAR COUNT: ANU ASTRONOMER MAKES BEST YET". Sydney, Australia: Australian National University Media Releases. July 17, 2003. Archived from the original on 9 March 2011. Retrieved October 27, 2015.
  33. ^ "Number Of Stars In The Universe Could Be 300 Sextillion, Triple The Amount Scientists Previously Thought: Study". Huffington Post. December 1, 2010. Archived from the original on 4 December 2010. Retrieved September 3, 2016.
  34. ^ William Safire, ON LANGUAGE; Footprints on the Infobahn, New York Times, April 17, 1994
  35. ^ Sagan at (definition from the Jargon File)