1
| ||||
---|---|---|---|---|
೧ | ||||
Khmer | ១ | |||
Armenian | Ա | |||
Malayalam | ൧ | |||
Meitei | ꯱ | |||
Thai | ๑ | |||
Tamil | ௧ | |||
Telugu | ೧ | |||
Babylonian numeral | 𒐕 | |||
Egyptian hieroglyph, Aegean numeral, Chinese counting rod | 𓏤 | |||
Mayan numeral | • | |||
Morse code | . _ _ _ _ |
1 (one, unit, unity) is a
The fundamental mathematical property of 1 is to be a
The unique mathematical properties of the number have led to its unique uses in other fields, ranging from science to sports. It commonly denotes the first, leading, or top thing in a group.
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
Symbols and representation
Among the earliest known record of a numeral system, is the
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.[12] 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
In mathematics
Mathematically, the number 1 has unique properties and significance. In normal arithmetic (algebra), the number 1 is the first natural number after 0 (zero) and can be used to make up all other integers (e.g., ; ; etc.). The product of 0 numbers (the empty product) is 1 and the factorial 0! evaluates to 1, as a special case of the empty product.[20] Any number multiplied or divided by 1 remains unchanged (). This makes it a mathematical unit, and for this reason, 1 is often called unity. Consequently, if is a multiplicative function, then must be equal to 1. This distinctive feature leads to 1 being is its own factorial (), its own square () and square root (), its own cube () and cube root (), and so forth. By definition, 1 is the
In algebraic structures such as multiplicative groups and monoids the identity element is often denoted 1, but e (from the German Einheit, "unity") is also traditional. However, 1 is especially common for the multiplicative identity of a ring, i.e., when an addition and 0 are also present. Moreover, if a ring has characteristic n not equal to 0, the element represented by 1 has the property that n1 = 1n = 0 (where this 0 denotes the additive identity of the ring). Important examples that involve this concept are finite fields.[citation needed] A matrix of ones or all-ones matrix is defined as a matrix composed entirely of 1s.[22]
Formalizations of the natural numbers have their own representations of 1. For example, in the original formulation of the Peano axioms, 1 serves as the starting point in the sequence of natural numbers.[23] Peano later revised his axioms to state 0 as the "first" natural number such that 1 is the successor of 0.[24] In the Von Neumann cardinal assignment of natural numbers, numbers are defined as the set containing all preceding numbers, with 1 represented as the singleton {0}.[25] In lambda calculus and computability theory, natural numbers are represented by Church encoding as functions, where the Church numeral for 1 is represented by the function applied to an argument once (1).
The simplest way to represent the natural numbers is by the
The number 1 can be represented in decimal form by two recurring notations: 1.000..., where the digit 0 repeats infinitely after the decimal point, and 0.999..., which contains an infinite repetition of the digit 9 after the decimal point. The latter arises from the definition of decimal numbers as the limits of their summed components, such that "0.999..." and "1" represent exactly the same number.[28]
Primality
Although 1 appears to meet the naïve definition of a prime number, being evenly divisible only by 1 and itself (also 1), by convention 1 is neither a
Other mathematical attributes and uses
In many mathematical and engineering problems, numeric values are typically normalized to fall within the
In
The definition of a
In numerical data, 1 is the most common leading digit in many sets of data (occurring about 30% of the time), a consequence of Benford's law.[39]
1 is the only known
]The generating function that has all coefficients equal to 1 is a geometric series, given by [citation needed]
The zeroth metallic mean is 1, with the golden section equal to the continued fraction [1;1,1,...], and the infinitely nested square root [citation needed]
The series of unit fractions that most rapidly converge to 1 are the reciprocals of Sylvester's sequence, which generate the infinite Egyptian fraction .[citation needed]
Table of basic calculations
Multiplication | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 50 | 100 | 1000 | |||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 × x | 1 | 2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 50 | 100
|
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 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1x | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | |
x1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
In technology
In digital technology, data is represented by
In science
- Dimensionless quantitiesare also known as quantities of dimension one.
- Hydrogen, the first element of the periodic table, has an atomic number of 1.
- Group 1 of the alkali metals.
- Period 1 of the periodic table consists of just two elements, hydrogen and helium.
In philosophy
In the philosophy of
The Neopythagorean philosopher
See also
References
- ^ "Online Etymology Dictionary". etymonline.com. Douglas Harper. Archived from the original on 2013-12-30. Retrieved 2013-12-30.
- ^ Hurford 1994, pp. 23–24.
- ^ Huddleston, Pullum & Reynolds 2022, p. 117.
- ^ Huddleston, Pullum & Reynolds 2022, p. 140.
- ^ Conway & Guy 1996, pp. 3–4.
- ^ Chrisomalis, Stephen. "Numerical Adjectives, Greek and Latin Number Prefixes". The Phrontistery. Archived from the original on 2022-01-29. Retrieved 2022-02-24.
- ^ Conway & Guy 1996, p. 4.
- ^ a b Conway & Guy 1996, p. 17.
- ^ Chrisomalis 2010, p. 241.
- ^ Chrisomalis 2010, p. 244.
- ^ Chrisomalis 2010, p. 249.
- .
- ^ Cullen 2007, p. 93.
- ^ "Fonts by Hoefler&Co". www.typography.com. Retrieved 2023-11-21.
- ^ a b Company, Post Haste Telegraph (April 2, 2017). "Why Old Typewriters Lack A "1" Key".
- ^ Köhler, Christian (November 23, 1693). "Der allzeitfertige Rechenmeister" – via Google Books.
- ^ "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.
- ^ "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.
- ^ 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.
- ^ Graham, Knuth & Patashnik 1988, p. 111.
- ^ Weisstein, Eric W. "1". mathworld.wolfram.com. Archived from the original on 2020-07-26. Retrieved 2020-09-22.
- ^ Horn & Johnson 2012, p. 8.
- ^ Peano 1889, p. 1.
- ^ Peano 1908, p. 27.
- ^ Halmos 1974, p. 32.
- ^ Hindley & Seldin 2008, p. 48.
- ^ Hodges 2009, p. 14.
- ^ Stillwell 1994, p. 42.
- ^ Caldwell & Xiong 2012, pp. 8–9.
- ^ Caldwell & Xiong 2012, pp. 2, 7.
- ^ Sierpiński 1988, p. 245.
- ^ Sandifer 2007, p. 59.
- ^ Graham, Knuth & Patashnik 1988, p. 381.
- ^ Blokhintsev 2012, p. 35.
- ^ Sung & Smith 2019.
- ^ Awodey 2010, p. 33.
- ^ La Vallée Poussin, C. Mém. Couronnés Acad. Roy. Belgique 59, 1–74, 1899
- JSTOR 2321863.
- ^ Miller 2015, p. 4.
- ^ Gaitsgory & Lurie 2019, pp. 204–307.
- ^ Kottwitz 1988.
- ISBN 978-0-237-52725-9, retrieved 2016-03-24
- ^ Godbole 2002, p. 34.
- ^ Olson 2017.
- from the original on May 16, 2021. Retrieved May 16, 2021.
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