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This article is about the number. For the year AD 1, and other uses, see One (disambiguation) and Number One (disambiguation).

This article contains special characters. Without proper rendering support, you may see question marks, boxes, or other symbols.
← 0 1 2 →
−1 0 1 2 3 4 5 6 7 8 9 →
Cardinalone
Ordinal1st
(first)
Numeral systemunary
Factorization∅
Divisors1
Greek numeralΑ´
Roman numeralI, i
Greek prefixmono-/haplo-
Latin prefixuni-
Binary12
Ternary13
Senary16
Octal18
Duodecimal112
Hexadecimal116
Greek numeralα'
Arabic, Kurdish, Persian, Sindhi, Urdu١
Assamese & Bengali১
Chinese numeral一/弌/壹
Devanāgarī१
Ge'ez፩
GeorgianႠ/ⴀ/ა(Ani)
Hebrewא
Japanese numeral一/壱
Kannada೧
Khmer១
ArmenianԱ
Malayalam൧
Meitei꯱
Thai๑
Tamil௧
Telugu೧
Babylonian numeral𒐕
Egyptian hieroglyph, Aegean numeral, Chinese counting rod𓏤
Mayan numeral•
Morse code. _ _ _ _
British Sign Language

1 (one, unit, unity) is a number representing a single unit of counting or measurement. 1 is the first and smallest positive integer. It is also sometimes considered the first of the infinite sequence of natural numbers, followed by 2, although by other definitions 1 is the second natural number. It commonly denotes the first, leading, or top thing in a group. 1 is by convention not considered a prime number.[citation needed]

In advanced mathematics, an identity element is often denoted 1, even if it is not a number.

As a word

Etymology

One originates from the Old English word an, derived from the Germanic root *ainaz, from the Proto-Indo-European root *oi-no- (meaning "one, unique").[1]

Modern usage

Linguistically, one is a cardinal number used for counting and expressing the number of items in a collection of things.[2] One is commonly used as a determiner for singular countable nouns, as in one day at a time.[3] One is also a gender-neutral pronoun used to refer to an unspecified person or to people in general as in one should take care of oneself.[4] Words that derive their meaning from one include alone, which signifies all one in the sense of being by oneself, none meaning not one, once denoting one time, and atone meaning to become at one with the someone. Combining alone with only (implying one-like) leads to lonely, conveying a sense of solitude.[5] Other common numeral prefixes for the number 1 include uni- (e.g., unicycle, universe, unicorn), sol- (e.g., solo dance), derived from Latin, or mono- (e.g., monorail, monogamy, monopoly) derived from Greek.[6][7]

In mathematics

Table of basic calculations

Multiplication 1 2 3 4 5 6 7 8 9 10 11 1000
1 × x 1 2 3 4 5 6 7 8 9 10 11 1000
Division 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
1 ÷ x 1 0.5 0.3 0.25 0.2 0.16 0.142857 0.125 0.1 0.1 0.09 0.083 0.076923 0.0714285 0.06
x ÷ 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Exponentiation 1 2 3 4 5 6 7 8 9 10 11 20
1x 1 1 1 1 1 1 1 1 1 1 1 1
x1 1 2 3 4 5 6 7 8 9 10 11 20

Symbols and representation

Decorative clay/stone circular off-white sundial with bright gold stylized sunburst in center of the 24-hour clock face, one through twelve clockwise on right, and one through twelve again clockwise on left, with J shapes where ones' digits would be expected when numbering the clock hours. Shadow suggests 3 PM toward the lower left.
The 24-hour tower clock in Venice, using J as a symbol for 1
This Woodstock typewriter from the 1940s lacks a separate key for the numeral 1.
Hoefler Text, a typeface designed in 1991, uses text figures and represents the numeral 1 as similar to a small-caps I.
See also: History of the Hindu–Arabic numeral system

Among the earliest known record of a numeral system, is the Sumerian decimal-sexagesimal system on clay tablets dating from the first half of the third millennium BCE.[14] The Archaic Sumerian numerals for 1 and 60 both consisted of horizontal semi-circular symbols.[15] By c. 2350 BCE, the older Sumerian curviform numerals were replaced with cuneiform symbols, with 1 and 60 both represented by the same symbol . The Sumerian cuneiform system is a direct ancestor to the Eblaite and Assyro-Babylonian Semitic cuneiform decimal systems.[16] Surviving Babylonian documents date mostly from Old Babylonian (c. 1500 BCE) and the Seleucid (c. 300 BCE) eras.[14] The Babylonian cuneiform script notation for numbers used the same symbol for 1 and 60 as in the Sumerian system.[17]

The most commonly used glyph in the modern Western world to represent the number 1 is the Arabic numeral, a vertical line, often with a serif at the top and sometimes a short horizontal line at the bottom. It can be traced back to the Brahmic script of ancient India, as represented by Ashoka as a simple vertical line in his Edicts of Ashoka in c. 250 BCE.[18] This script's numeral shapes were transmitted to Europe via the Maghreb and Al-Andalus during the Middle Ages, through scholarly works written in Arabic.[citation needed] In some countries, the serif at the top may be extended into a long upstroke as long as the vertical line. This variation can lead to confusion with the glyph used for seven in other countries and so to provide a visual distinction between the two the digit 7 may be written with a horizontal stroke through the vertical line.[citation needed]

In modern typefaces, the shape of the character for the digit 1 is typically typeset as a lining figure with an ascender, such that the digit is the same height and width as a capital letter. However, in typefaces with text figures (also known as Old style numerals or non-lining figures), the glyph usually is of x-height and designed to follow the rhythm of the lowercase, as, for example, in Horizontal guidelines with a one fitting within lines, a four extending below guideline, and an eight poking above guideline.[19] In old-style typefaces (e.g., Hoefler Text), the typeface for numeral 1 resembles a small caps version of I, featuring parallel serifs at the top and bottom, while the capital I retains a full-height form. This is a relic from the Roman numerals system where I represents 1.[20][21] The modern digit '1' did not become widespread until the mid-1950s. As such, many older typewriters do not have dedicated key for the numeral 1 might be absent, requiring the use of the lowercase letter l or uppercase I as substitutes.[21] The lower case "j" can be considered a swash variant of a lower-case Roman numeral "i", often employed for the final i of a "lower-case" Roman numeral. It is also possible to find historic examples of the use of j or J as a substitute for the Arabic numeral 1.[22][23][24][25]

In technology

In digital technology, data is represented by binary code, i.e., a base-2 numeral system with numbers represented by a sequence of 1s and 0s. Digitised data is represented in physical devices, such as computers, as pulses of electricity through switching devices such as transistors or logic gates where "1" represents the value for "on". As such, the numerical value of true is equal to 1 in many programming languages.[26][27]

In science

In philosophy

In the philosophy of Plotinus (and that of other neoplatonists), The One is the ultimate reality and source of all existence.[28] Philo of Alexandria (20 BC – AD 50) regarded the number one as God's number, and the basis for all numbers ("De Allegoriis Legum", ii.12 [i.66]).

The Neopythagorean philosopher Nicomachus of Gerasa claimed that one is not a number, but the source of number. He also believed the number two is the embodiment of the origin of otherness. His number theory was recovered by Boethius in his Latin translation of Nicomachus's treatise Introduction to Arithmetic.[29]

See also

Wikimedia Commons has media related to:
1 (number) (category)
Wikiquote has quotations related to 1 (number).

References

  1. ^ "Online Etymology Dictionary". etymonline.com. Douglas Harper. Archived from the original on 2013-12-30. Retrieved 2013-12-30.
  2. ^ Hurford 1994, pp. 23–24.
  3. ^ Huddleston, Pullum & Reynolds 2022, p. 117.
  4. ^ Huddleston, Pullum & Reynolds 2022, p. 140.
  5. ^ Conway & Guy 1996, pp. 3–4.
  6. ^ Chrisomalis, Stephen. "Numerical Adjectives, Greek and Latin Number Prefixes". The Phrontistery. Archived from the original on 2022-01-29. Retrieved 2022-02-24.
  7. ^ Conway & Guy 1996, p. 4.
  8. ^ Graham, Knuth & Patashnik 1988, p. 111.
  9. ^ Horn & Johnson 2012, p. 8.
  10. ^ Awodey 2010, p. 33.
  11. ^ Miller 2015, p. 4.
  12. ^ Gaitsgory & Lurie 2019, pp. 204–307.
  13. ^ Kottwitz 1988.
  14. ^ a b Conway & Guy 1996, p. 17.
  15. ^ Chrisomalis 2010, p. 241.
  16. ^ Chrisomalis 2010, p. 244.
  17. ^ Chrisomalis 2010, p. 249.
  18. ^ Acharya, Eka Ratna (2018). "Evidences of Hierarchy of Brahmi Numeral System". Journal of the Institute of Engineering. 14: 136–142. doi:10.3126/jie.v14i1.20077.
  19. ^ Cullen 2007, p. 93.
  20. ^ "Fonts by Hoefler&Co". www.typography.com. Retrieved 2023-11-21.
  21. ^ a b Company, Post Haste Telegraph (April 2, 2017). "Why Old Typewriters Lack A "1" Key". {{cite web}}: |last= has generic name (help)
  22. ^ Köhler, Christian (November 23, 1693). "Der allzeitfertige Rechenmeister" – via Google Books.
  23. ^ "Naeuw-keurig reys-boek: bysonderlijk dienstig voor kooplieden, en reysende persoonen, sijnde een trysoor voor den koophandel, in sigh begrijpende alle maate, en gewighte, Boekhouden, Wissel, Asseurantie ... : vorders hoe men ... kan reysen ... door Neederlandt, Duytschlandt, Vrankryk, Spanjen, Portugael en Italiën ..." by Jan ten Hoorn. November 23, 1679 – via Google Books.
  24. ^ "Articvli Defensionales Peremptoriales & Elisivi, Bvrgermaister vnd Raths zu Nürmberg, Contra Brandenburg, In causa die Fraiszlich Obrigkait [et]c: Produ. 7. Feb. Anno [et]c. 33". Heußler. November 23, 1586 – via Google Books.
  25. ^ August (Herzog), Braunschweig-Lüneburg (November 23, 1624). "Gustavi Seleni Cryptomenytices Et Cryptographiae Libri IX.: In quibus & planißima Steganographiae a Johanne Trithemio ... magice & aenigmatice olim conscriptae, Enodatio traditur; Inspersis ubique Authoris ac Aliorum, non contemnendis inventis". Johann & Heinrich Stern – via Google Books.
  26. ^ Woodford, Chris (2006), Digital Technology, Evans Brothers, p. 9, ISBN 978-0-237-52725-9, retrieved 2016-03-24
  27. ^ Godbole 2002, p. 34.
  28. ^ Olson 2017.
  29. ^ British Society for the History of Science (July 1, 1977). "From Abacus to Algorism: Theory and Practice in Medieval Arithmetic". The British Journal for the History of Science. 10 (2). Cambridge University Press: Abstract. doi:10.1017/S0007087400015375. S2CID 145065082. Archived from the original on May 16, 2021. Retrieved May 16, 2021.

Sources

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