preceding all others in time or space or degree; "the first house on the right"; "the first day of spring"; "his first political race"; "her first baby"; "the first time"; "the first meetings of the new party"; "the first phase of his training"
the first or highest in an ordering or series; "He wanted to be the first" (同)number_one
the first element in a countable series; "the first of the month" (同)number_one, number 1
an honours degree of the highest class (同)first-class honours degree
indicating the beginning unit in a series (同)1st
before anything else; "first we must consider the garter snake" (同)firstly, foremost, first of all, first off
the initial time; "when Felix first saw a garter snake" (同)for_the_first_time
ranking above all others; "was first in her class"; "the foremost figure among marine artists"; "the top graduate" (同)foremost, world-class
before another in time, space, or importance; "I was here first"; "lets do this job first"
highest in pitch or chief among parts or voices or instruments or orchestra sections; "first soprano"; "the first violin section"; "played first horn"
This article is about the number. For the year, see AD 1. For other uses, see One (disambiguation) and Number One (disambiguation).
Natural number
← 0
1
2 →
-1 0 1 2 3 4 5 6 7 8 9 →
List of numbers — Integers
← 0 10 20 30 40 50 60 70 80 90 →
Cardinal
one
Ordinal
1st (first)
Numeral system
unary
Factorization
∅
Divisors
1
Greek numeral
Α´
Roman numeral
I
Roman numeral (unicode)
Ⅰ, ⅰ
Greek prefix
mono-/haplo-
Latin prefix
uni-
Binary
12
Ternary
13
Quaternary
14
Quinary
15
Senary
16
Octal
18
Duodecimal
112
Hexadecimal
116
Vigesimal
120
Base 36
136
Greek numeral
α'
Persian
١
Arabic & Kurdish
١
Urdu
Sindhi
١
Assamese & Bengali
১
Chinese numeral
一/弌/壹
Devanāgarī
१
Ge'ez
፩
Georgian
Ⴁ/ⴁ/ბ(Bani)
Hebrew
א
Japanese numeral
一/壱
Kannada
೧
Khmer
១
Korean
일/하나
Malayalam
൧
Thai
๑
Tamil
௧
1 (one, also called unit, unity, and (multiplicative) identity) is a number, numeral, and glyph. It represents a single entity, the unit of counting or measurement. For example, a line segment of unit length is a line segment of length 1. It is also the first of the infinite sequence of natural numbers, followed by 2.
Contents
1Etymology
2As a number
3As a digit
4Mathematics
4.1Table of basic calculations
5In technology
6In science
7In philosophy
8In literature
9In comics
10In sports
11In other fields
12See also
13References
14External links
Etymology
The word one can be used as a noun, an adjective and a pronoun.[1]
It comes from the English word an,[1] which comes from the Proto-Germanic root *ainaz.[1] The Proto-Germanic root *ainaz comes from the Proto-Indo-European root *oi-no-.[1]
Compare the Proto-Germanic root *ainaz to Old Frisian an, Gothic ains, Danish en, Dutch een, German eins and Old Norse einn.
Compare the Proto-Indo-European root *oi-no- (which means "one, single"[1]) to Greek oinos (which means "ace" on dice[1]), Latin unus (one[1]), Old Persian aivam, Old Church Slavonic -inu and ino-, Lithuanian vienas, Old Irish oin and Breton un (one[1]).
As a number
One, sometimes referred to as unity,[2] is the first non-zero natural number. It is thus the integer before two and after zero, and the first positive odd number.
Any number multiplied by one remains that number, as one is the identity for multiplication. As a result, 1 is its own factorial, its own square and square root, its own cube and cube root, and so on. One is also the result of the empty product, as any number multiplied by one is itself. It is also the only natural number that is neither composite nor prime with respect to division, but instead considered a unit (meaning of ring theory).
As a digit
The glyph used today in the Western world to represent the number 1, a vertical line, often with a serif at the top and sometimes a short horizontal line at the bottom, traces its roots back to the Indians, who wrote 1 as a horizontal line, much like the Chinese character 一. The Gupta wrote it as a curved line, and the Nagari sometimes added a small circle on the left (rotated a quarter turn to the right, this 9-look-alike became the present day numeral 1 in the Gujarati and Punjabi scripts). The Nepali also rotated it to the right but kept the circle small.[3] This eventually became the top serif in the modern numeral, but the occasional short horizontal line at the bottom probably originates from similarity with the Roman numeral I. In some countries, the serif at the top is sometimes extended into a long upstroke, sometimes as long as the vertical line, which can lead to confusion with the glyph for seven in other countries. Where the 1 is written with a long upstroke, the number 7 has a horizontal stroke through the vertical line.
While the shape of the 1 character has an ascender in most modern typefaces, in typefaces with text figures, the character usually is of x-height, as, for example, in .
The 24-hour tower clock in Venice, using J as a symbol for 1.
Many older typewriters do not have a separate symbol for 1 and use the lowercase letter l instead. It is possible to find cases when the uppercase J is used, while it may be for decorative purposes.
Mathematics
Mathematically, 1 is:
in arithmetic (algebra) and calculus, the natural number that follows 0 and precedes 2 and the multiplicative identity element of the integers, real numbers and complex numbers;
more generally, in algebra, the multiplicative identity (also called unity), usually of a group or a ring.
Tallying is often referred to as "base 1", since only one mark – the tally itself – is needed. This is more formally referred to as a unary numeral system. Unlike base 2 or base 10, this is not a positional notation.
Since the base 1 exponential function (1x) always equals 1, its inverse does not exist (which would be called the logarithm base 1 if it did exist).
There are two ways to write the real number 1 as a recurring decimal: as 1.000..., and as 0.999....
Formalizations of the natural numbers have their own representations of 1:
in the Peano axioms, 1 is the successor of 0;
in Principia Mathematica, 1 is defined as the set of all singletons (sets with one element);
in the Von Neumann cardinal assignment of natural numbers, 1 is defined as the set {0}.
In a multiplicative group or monoid, the identity element is sometimes 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. When such a ring has characteristic n not equal to 0, the element called 1 has the property that n1 = 1n = 0 (where this 0 is the additive identity of the ring). Important examples are finite fields.
1 is the first figurate number of every kind, such as triangular number, pentagonal number and centered hexagonal number, to name just a few.
In many mathematical and engineering problems, numeric values are typically normalized to fall within the unit interval from 0 to 1, where 1 usually represents the maximum possible value in the range of parameters. Likewise, vectors are often normalized to give unit vectors, that is vectors of magnitude one, because these often have more desirable properties. Functions, too, are often normalized by the condition that they have integral one, maximum value one, or square integral one, depending on the application.
Because of the multiplicative identity, if f(x) is a multiplicative function, then f(1) must equal 1.
It is also the first and second number in the Fibonacci sequence (0 is the zeroth) and is the first number in many other mathematical sequences.
1 is neither a prime number nor a composite number, but a unit (meaning of ring theory), like −1 and, in the Gaussian integers, i and −i. The fundamental theorem of arithmetic guarantees unique factorization over the integers only up to units. (For example, 4 = 22, but if units are included, is also equal to, say, (−1)6 × 123 × 22, among infinitely many similar "factorizations".)
The definition of a field requires that 1 must not be equal to 0. Thus, there are no fields of characteristic 1. Nevertheless, abstract algebra can consider the field with one element, which is not a singleton and is not a set at all.
1 is the only positive integer divisible by exactly one positive integer (whereas prime numbers are divisible by exactly two positive integers, composite numbers are divisible by more than two positive integers, and zero is divisible by all positive integers). 1 was formerly considered prime by some mathematicians, using the definition that a prime is divisible only by 1 and itself. However, this complicates the fundamental theorem of arithmetic, so modern definitions exclude units.
By definition, 1 is the magnitude, absolute value, or norm of a unit complex number, unit vector, and a unit matrix (more usually called an identity matrix). Note that the term unit matrix is sometimes used to mean something quite different.
By definition, 1 is the probability of an event that is almost certain to occur.
1 is the most common leading digit in many sets of data, a consequence of Benford's law.
1 is the only known Tamagawa number for a simply connected algebraic group over a number field.
The generating function that has all coefficients 1 is given by
This power series converges and has finite value if and only if, .
In category theory, 1 is sometimes used to denote the terminal object of a category.
In number theory, 1 is the value of Legendre's constant, which was introduced in 1808 by Adrien-Marie Legendre in expressing the asymptotic behavior of the prime-counting function. Legendre's constant was originally conjectured to be approximately 1.08366, but was proven to equal exactly 1 in 1899.
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
The resin identification code used in recycling to identify polyethylene terephthalate.[4]
The ITU country code for the North American Numbering Plan area, which includes the United States, Canada, and parts of the Caribbean
A binary code is a sequence of 1 and 0 that is used in computers for representing any kind of data.
In many physical devices, 1 represents the value for "on", which means that electricity is flowing.[5][6]
The numerical value of true in many programming languages.
1 is the ASCII code of "Start of Header".
In science
Dimensionless quantities are also known as quantities of dimension one.
1 is the atomic number of hydrogen.
+1 is the electric charge of positrons and protons.
Group 1 of the periodic table consists of the alkali metals.
Period 1 of the periodic table consists of just two elements, hydrogen and helium.
The dwarf planet Ceres has the minor-planet designation 1 Ceres because it was the first asteroid to be discovered.
The Roman numeral I often stands for the first-discovered satellite of a planet or minor planet (such as Neptune I, a.k.a. Triton). For some earlier discoveries, the Roman numerals originally reflected the increasing distance from the primary instead.
In philosophy
In the philosophy of Plotinus and a number of other neoplatonists, The One is the ultimate reality and source of all existence. 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]).
In literature
Number One is a character in the book series Lorien Legacies by Pittacus Lore.
Number 1 is also a character in the series "Artemis Fowl" by Eoin Colfer.
In a 1968 song by Harry Nilsson and recorded by Three Dog Night, the number one is identified as "the loneliest number".
We Are Number One is a 2014 song from the children's TV show LazyTown, which gained popularity as a meme.
In comics
A character in the Italian comic book Alan Ford (authors Max Bunker and Magnus), very old disabled man, the supreme leader of the group TNT.
A character in the Italian comic series PKNA and its sequels, an artificial intelligence as an ally of the protagonist Paperinik
In sports
In baseball scoring, the number 1 is assigned to the pitcher.
In association football (soccer) the number 1 is often given to the goalkeeper.
In most competitions of rugby league (though not the Super League, which uses static squad numbering), the starting fullback wears jersey number 1.
In rugby union, the starting loosehead prop wears the jersey number 1.
1 is the lowest number permitted for use by players of the National Hockey League (NHL); the league prohibited the use of 00 and 0 in the late 1990s. (The highest number permitted is 98.)
1 is the lowest number permitted for use at most levels of American football. Under National Football League policy, it can only be used by a quarterback or kicking player (during preseason play, restrictions are looser, and players of other positions can wear the number and can also, if no other options exist, wear 0).
In Formula One, the previous year's world champion is allowed to use the number 1.
In other fields
1 is the value of an ace in many playing card games, such as cribbage.
List of highways numbered 1
List of public transport routes numbered 1
1 is often used to denote the Gregorian calendar month of January.
1 CE, the first year of the Common Era
01, the former dialing code for Greater London
PRS One, a German paraglider design
+1 is the code for international telephone calls to countries in the North American Numbering Plan
See also
Mathematics portal
−1
+1 (disambiguation)
One (word)
Root of unity
References
Wikimedia Commons has media related to:
1 (number) (category)
^ abcdefgh"Online Etymology Dictionary". etymonline.com. Douglas Harper.
^Skoog, Douglas. Principles of Instrumental Analysis. Brooks/Cole, 2007, p. 758.
^Ifrah, Georges; et al. (1998). The Universal History of Numbers: From Prehistory to the Invention of the Computer. Translated by Bellos, David. yes. London: The Harvill Press. p. 392, Fig. 24.61.
^"Plastic Packaging Resins" (PDF). American Chemistry Council. Archived from the original (PDF) on 2011-07-21.
^Woodford, Chris (2006), Digital Technology, Evans Brothers, p. 9, ISBN 978-0-237-52725-9
^Godbole, Achyut S. (1 September 2002), Data Comms & Networks, Tata McGraw-Hill Education, p. 34, ISBN 978-1-259-08223-8
External links
Wikiquote has quotations related to: 1 (number)
The Number 1
The Positive Integer 1
Prime curiosities: 1
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at first / first / firstly / for the first time の違い・意味・使い方について 英検やGTECの英作文の書き方を勉強している生徒や、長文読解をしている生徒から質問されることが多いat first / first / firstly / for the first time …
