1 (number)
1 (number)



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List of numbers —Integers
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Cardinal  one  
Ordinal  1st (first) 

Numeral system  unary  
Factorization  ∅  
Divisors  1  
Greek numeral  Α´  
Roman numeral  I  
Roman numeral (unicode)  Ⅰ, ⅰ  
Greekprefix  mono/haplo  
Latinprefix  uni  
Binary  1_{2}  
Ternary  1_{3}  
Quaternary  1_{4}  
Quinary  1_{5}  
Senary  1_{6}  
Octal  1_{8}  
Duodecimal  1_{12}  
Hexadecimal  1_{16}  
Vigesimal  1_{20}  
Base 36  1_{36}  
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 calledunit,unity, and(multiplicative) identity) is anumber, and a numerical digit used to represent that number in numerals. It represents a single entity, the unit of counting or measurement. For example, a line segment ofunit lengthis a line segment of length 1. It is also the first of the infinite sequence ofnatural numbers, followed by 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  
Greekprefix  mono/haplo  
Latinprefix  uni  
Binary  1_{2}  
Ternary  1_{3}  
Quaternary  1_{4}  
Quinary  1_{5}  
Senary  1_{6}  
Octal  1_{8}  
Duodecimal  1_{12}  
Hexadecimal  1_{16}  
Vigesimal  1_{20}  
Base 36  1_{36}  
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 
Etymology
The wordonecan be used as a noun, an adjective and a pronoun.^{[1]}
It comes from the English wordan,^{[1]}which comes from the ProtoGermanic root *ainaz.^{[1]}The ProtoGermanic rootainazcomes from the ProtoIndoEuropean root **oino.^{[1]}
As a number
One, sometimes referred to asunity,^{[2]}is the first nonzeronatural number. It is thus theintegerbefore 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 andsquare 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 Brahmic script of ancient India, where it was a simple vertical line. It was transmitted to Europe via Arabic during the Middle Ages.
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 moderntypefaces, in typefaces with text figures, the character usually is of xheight, as, for example, in [[INLINE_IMAGE//upload.wikimedia.org/wikipedia/commons/thumb/8/81/TextFigs148.svg/62pxTextFigs148.svg.png//upload.wikimedia.org/wikipedia/commons/thumb/8/81/TextFigs148.svg/93pxTextFigs148.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/81/TextFigs148.svg/124pxTextFigs148.svg.png 2xHorizontal guidelines with a one fitting within lines, a four extending below guideline, and an eight poking above guidelineh40w62]].
Many older typewriters do not have a separate symbol for1and use the lowercase letterlinstead. It is possible to find cases when the uppercaseJis used, while it may be for decorative purposes.
Mathematics
Mathematically, 1 is:

inarithmetic(algebra) andcalculus, thenatural numberthat follows 0 and precedes 2 and the multiplicative identity element of theintegers,real numbersandcomplex numbers;

more generally, inalgebra, themultiplicative identity(also calledunity), 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 thelogarithmbase 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;

inPrincipia 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, bute(from the GermanEinheit, “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 characteristicnnot equal to 0, the element called 1 has the property thatn1 = 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 typicallynormalizedto fall within the unit interval from 0 to 1, where 1 usually represents the maximum possible value in the range of parameters. Likewise,vectorsare 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 haveintegralone, maximum value one, or square integral one, depending on the application.
Because of the multiplicative identity, iff(x) is a multiplicative function, thenf(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,iand −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 termunit matrixis 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
In category theory, 1 is sometimes used to denote the terminal object of a category.
Innumber theory, 1 is the value of Legendre’s constant, which was introduced in 1808 by AdrienMarie Legendre in expressing the asymptotic behavior of the primecounting 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  

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  

x  1  0.5 
3 
0.25  0.2  0.16 
142857 
0.125 
1 
0.1 
09 
0.083 
076923 
0.0714285  0.06  
x  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  

x  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  
x  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.^{[3]}

The ITU country code for theNorth American Numbering Planarea, 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.^{[4]}^{[5]}

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 ofhydrogen.

+1 is theelectric chargeof 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,hydrogenand helium.

The dwarf planet Ceres has the minorplanet designation 1 Ceres because it was the first asteroid to be discovered.

The Roman numeral I often stands for the firstdiscovered 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 Oneis 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, anartificial intelligenceas an ally of the protagonist Paperinik
In sports

In baseball scoring, the number 1 is assigned to thepitcher.

Inassociation football(soccer) the number 1 is often given to the goalkeeper.

In most competitions ofrugby league(though not the Super League, which uses static squad numbering), the starting fullback wears jersey number 1.

Inrugby 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 ofAmerican football. UnderNational Football Leaguepolicy, it can only be used by aquarterbackor 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).

InFormula One, the previous year’s world champion is allowed to use the number 1.
In film

One A.M.(1916), starringCharlie Chaplin.

One More Time(1970), directed by Jerry Lewis and starring Sammy Davis Jr. and Peter Lawford.

 One Day* (2011), starringAnne Hathawayand Jim Sturgess.
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 theGregorian calendarmonth of January.

1 CE, the first year of theCommon 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 theNorth American Numbering Plan
See also

−1

+1 (disambiguation)

One (word)

Root of unity