'1' ('one') is a
number,
numeral, and the name of the
glyph representing that number. It is the
natural number following
0 (number) and preceding
2.
It represents a single entity. One is sometimes referred to as 'unity' or 'unit' as an adjective. For example, a
line segment of "unit length" is a line segment of length 1.
In mathematics
For any number ''x'':
[1]
:''x''·1 = 1·''x'' = ''x'' (This expresses the fact that 1 is the
multiplicative identity.) As a consequence of this, 1 is a 1-
automorphic number in any
positional numeral system.
:''x''/1 = ''x'' (see
division)
:''x''
1 = ''x'', 1
''x'' = 1, and for nonzero ''x'', ''x''
0 = 1 (see
exponentiation)
:''x''↑↑1 = ''x'' and 1↑↑''x'' = 1 (see
tetration).
Using ordinary
addition, we have 1 + 1 =
2.
One cannot be used as the base of a positional
numeral system in the ordinary way.
Sometimes
tallying is referred to as "base 1", since only one mark (the tally) is needed, but this doesn't work in the same way as other positional numeral systems.
Related to this, one cannot take
logarithms with base 1, since the "exponential function" with base 1 is the constant function 1.
In the
real number system, 1 can be represented in two ways as a
recurring decimal: as 1.000... and as
0.999... This identity is not immediately obvious to many people, and a full understanding of why it is true requires an understanding of the properties of the real numbers. See the article
0.999... for more details.
In the
Von Neumann representation of natural numbers, 1 is defined as the
set {0}. This set has
cardinality 1 and
hereditary rank 1. Sets like this with a single element are called
singletons.
In
Principia Mathematica, 1 is defined as the set of all
singletons.
In a multiplicative
group or
monoid, the
identity element is sometimes denoted "1", but "''e''" (from the German ''Einheit'', unity) is more traditional. However, "1" is especially common for the multiplicative identity of a
ring. (Note that this multiplicative identity is also often called "unity".)
One is its own
factorial, and its own square and cube (and so on, as 1 × 1 × ... × 1 = 1). One is the first
figurate number of every kind, such as
triangular number,
pentagonal number and
centered hexagonal number to name just a few.
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 numbers in the
Fibonacci sequence, and is the first number in a lot of mathematical sequences. As a matter of convention, Sloane's early ''Handbook of Integer Sequences'' added an initial 1 to any sequence that didn't already have it, and considered these initial 1's in its lexicographic ordering. Sloane's later ''Encyclopedia of Integer Sequences'' and its Web counterpart, the ''
On-Line Encyclopedia of Integer Sequences'', ignore initial ones in their lexicographic ordering of sequences, because such initial ones often correspond to trivial cases.
One is the
empty product.
One is the smallest positive odd integer.
One is a
harmonic divisor number.
One is most often used for representing 'true' as a
Boolean datatype in
computer science.
One is currently considered neither a
prime number, nor a
composite number — although it used to be considered
prime. Defining a prime as a number that is only divisible by one and itself, one ''is'' a prime. However, for purposes of
factorization and especially the
fundamental theorem of arithmetic, it is more convenient to not think of one as a prime factor, or to think of it as an implicit factor that's always there but need not be written down. To exclude the number one from the list of prime numbers, primality is defined as a number having exactly two distinct positive divisors, one and itself. The last professional
mathematician to publicly label 1 a prime number was
Henri Lebesgue in 1899. (
Carl Sagan included one in a list of prime numbers in his book ''Contact'' in 1985.)
One is one of three possible return values of the
Möbius function. Passed an integer that is
square-free with an even number of distinct prime factors, the Möbius function returns one.
One is the only odd number that is in the range of
Euler's totient function φ(''x''), in the cases ''x'' = 1 and ''x'' = 2.
One is the only 1-perfect number (see
multiply perfect number).
By definition, 1 is the
magnitude or
absolute value of a
unit vector and a
unit matrix (more usually called an ''identity matrix''). Note that the term ''unit matrix'' is usually used to mean something
quite different.
One is the value of the
sine and
cosine at π/2 and 0 radians, respectively.
One is the most common leading digit in many sets of data, a consequence of
Benford's law.
Sequence of natural numbers always ends with the number 1 (
Collatz conjecture).
See also
−1.
List of basic calculations
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Exponentiation
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Evolution of the glyph
Evolution1glyph.png
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 Brahmin Indians, who wrote 1 as a horizontal line (in
Chinese today this is the way it is written). 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. 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 European countries (e.g.,
Germany) the little 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
TextFigs148.png
.
In science
★ set equal to celerity (c), the speed of light, in Heaviside notation to simplify calculations.
★ the factor in ratios for unit conversions.
★ the total density ratio for a flat universe.
★ The
atomic number of
hydrogen
★ Group '1' in the
Periodic Table consists of hydrogen and the
alkali metals whose usual
valence is +1.
★ Period '1', the shortest row in the Periodic Table, consists only of hydrogen and helium.
★ A
haploid has one set of
chromosomes in the
nucleus.
Astronomy
★
Messier object M1, a magnitude 7.0
supernova remnant in the constellation
Taurus, also known as the
Crab Nebula.
★ The
New General Catalogue object NGC 1, a 13th
magnitude spiral galaxy in the
constellation Pegasus
★ The
Saros number of the
solar eclipse series which began on
-2872 June 4 and ended on
-1592 July 11. The duration of Saros series 1 was 1280.1 years, and it contained 73 solar eclipses.
★ The Saros
number of the
lunar eclipse series which began on
-2588 March 2 and ended on
-1272 April 30. The duration of Saros series 1 was 1316.2 years, and it contained 74 lunar eclipses.
★ The first
space shuttle mission
STS-1
In religion
Many religions ascribe symbolic meanings to the concept of 'one-ness'.
★
Islam's core belief is in the
One God.
Allah is the Arabic translation (term) for the word: GOD.
★ In
Judaism's credo, the
Shema Yisrael,
God is described as being "one" (Deut. 6:4)
★ In
Christianity,
Jesus is God's only begotten Son; God the Father, God the Son, and the Holy Spirit as One
★ In
Sikhism's philosophy, there is only one God.
★ In many
Gnostic systems and heresiologies, God is known as the Monad, the One
★ All is One according to
Monism and
Theosophy.
In culture
Some
Ancient Greeks did not consider one as a number: they considered it to be the ''unit'',
two being the first proper number as it represented a multiplicity.
In modern culture, one represents unity, togetherness, and absence of separation or discrimination, e.g. "We are all one" or "everyone".
Something is 'unique' if it is the only one of its kind. More loosely and exaggeratedly (especially in
advertising), the term is used for something very special.
One is also an (archaic) expression of the
first person singular ("One is not amused") and of the
second person singular ("Does one take sugar?").
In
Western culture, it is believed by many that the maximum number of girlfriends or boyfriends one may have at one time is 1. Also, it is strongly believed that you can be married to only 1 person at any time - this is called
monogamy. Being married to more than one person at any time is called
bigamy or
polygamy. This is illegal in many Western societies.
Among children, or when otherwise calling for subtlety, the phrase "number 1" can refer to the act of
urination. This can derive from a traditional U.S. elementary school practice of holding up one or two fingers to indicate the approximate time of a requested absence.
"Number 1" can also refer to oneself, or that something is first in its class, the latter being used often as a cheer in sports games.
On a twelve-hour
clock, 1:00 signals that one full
hour has passed since the last change of the "AM" or "PM"
meridian. On a twenty-four-hour clock, it signals that one full hour has passed since
midnight.
One is used as a
pronoun in
English grammar to refer to an unspecified person: see ''
generic you''.
In music
★ In harmonic analysis of tonal music, the
tonic chord is referred to as I.
★ In
funk music, being "On The One" denotes a four-to-the-bar
bass guitar-driven beat with emphasis on first
note. The term can also describe being "plugged in" to the
music, achieving a state of
nirvana.
★ "One is the loneliest number that you'll ever do", reads the first line of "One" by
Harry Nilsson, which was covered by
Three Dog Night. The number also appears in the title of
songs by
U2 (voted greatest song in history by a
Channel 4 poll in
2001),
Metallica,
Creed,
Marvin Hamlisch (in the musical ''
A Chorus Line''),
Alanis Morissette, and the
Bee Gees. "#1 Zero" is a song by
Audioslave. It was also the title of a best-selling compilation album of all
Beatles songs that reached number 1 in the UK or US charts (see
List of Number 1 Hits (USA)).
★ The song ''
Green grow the rushes, O'' has the line "One is one and all alone and evermore shall be so."
★ The last
George Jones and
Tammy Wynette duet album was called "One" and included a love song of the same name.
In politics
★
ONE Campaign is an antipoverty coalition.
★ as
Air Force One, is the callsign of any
United States Air Force aircraft carrying the
President of the United States.
★ the house number of
Number One Observatory Circle, the
US Vice-President's residence.
★ The
1st Amendment of the American
constitution.
In currency
★ The denomination of the
Danish Krone coin, featuring a hole in the center.
★ the denomination of
U.S. dollar bill with
George Washington's portrait, and the denomination of coin with
Sacagawea's portrait. It is also the denomination of the older
Eisenhower and
Susan B. Anthony tender coins and the
American Silver Eagle bullion coin.
★ the denomination of
Canadian dollar coin with a swimming loon on the reverse, hence its universally employed nickname, the "
loonie"
★ in cents of a U.S. dollar, the denomination of coin with
Abraham Lincoln's portrait, commonly known as a
penny.
★ in cents of a
Canadian dollar, the denomination of coin with two maple leaves on the reverse, also known as a
penny.
In sports
In NASCAR, its Martin Truex Jr's number in the NEXTEL Cup Series. J.J. Yeley's number in the Busch Series, and Aaron Fike's number in the Craftsman Truck Series.
In some sports, one is the number of a specific position: in
rugby league the number of the fullback; in
rugby union, the number of the
loosehead prop; in
baseball, the number representing the
pitcher's position; in
basketball, the number representing the
point guard's position; in
football, the number of the
goalkeeper.
Hockey goalies have traditionally worn the number. However, its popularity has been waning in recent years.
It is the retired baseball jersey number of
Ozzie Smith and
Richie Ashburn.
The number worn by Del Unser, outfielder for the Cleveland Indians in 1972.
The number was worn by former
CFL and
NFL quarterback
Warren Moon who held the record for most passing yards in North American Professional Football history until 2006, when he was surpassed by Damon Allen.
In
2004, fans of the
Philadelphia Eagles NFL team used the phrase "One" to show support for the team as they inched closer to the
Super Bowl. The full text of the phrase was "One Team. One City. One Dream."
After a victory, especially the
championship finals, the winning team will often
pose for a team photo. They usually crowd around the
trophy and raise their
index finger while holding up the number one. This symbolic gesture is used to demonstrate a team's sense of pride in itself. Typically, this type of celebration is considered a
default.
In
Formula 1, the number one is used to designate the car of the previous year's champion.
In
Motocross, the number on the champion of last year's number plate (unless he chooses to have a red background or to not any any symbol of winning).
The number worn by
NBA stars
Chauncey Billups,
Amare Stoudemire, and
Tracy McGrady.
The number worn by retired
NBA player
Muggsy Bogues.
In technology
One is the
DVD region of the United States and Canada.
In the
DOS Shell and many
Microsoft Windows programs, the
function key F1 calls up online help.
Some
cellular phones associate the "1" key with various symbols (i.e. the
pound sign, the
ampersand, etc.) when users engage in
text messaging.
One is the
code for international direct dial phone calls to countries participating in the
North American Numbering Plan, such as the
United States and Canada.
In the
Rich Text Format specification, 1 is the language code for the
Arabic language. All codes for dialects of Arabic are congruent to 1 mod 256.
In
ASCII (American Standard Code for Information Interchange), 1 is a non printing character representing 'Start of Heading' or 'SOH'
A common railway
gauge is .
In other fields
One is:
★ the designation of many roads; see
List of highways numbered 1
★ the address of
Apsley House, known simply as Number 1, London
★ a
subway service in
New York City. See
1 (New York City Subway service)
★
'one' train operating company in the United Kingdom
★ an
enneagram personality type
★ part of a nickname for the U.S. Army's First Infantry Division, "
The Big Red One"
★ as a word in all capitals, ''
ONE'', a trademark of
Nestlé Purina PetCare for a line of pet food products (acronym for the "optimum nutritional effectiveness" they are claimed to possess)
★ In
Astrology,
Aries is the first sign of the
Zodiac
★ In Tarot, card No. 1 is "the Magician"
Historical years
AD '
1' or the immediately previous year
1 BC,
1901,
2001, etc.
Etymology
The Old English ''án'' is in
Old Frisian ''ân,'' ''ên,'' Old Saxon ''ên'' (Middle Dutch, Dutch ''een''), Old High German (Middle High German, German) ''ein,'' Old Norse ''einn'':–''ein-r'' (Danish ''een,'' Sw. ''en''), Gothic ''ain-s'':–Old Teutonic ''
★ ain-oz'':–pre-Teutonic ''
★ oinos'' = Latin ''ūnus'' (Old Latin ''oinos''); Old Irish ''óen,'' Old Slavic ''inu,'' Lithuanian ''venas'' one; cf. Greek ''
oἶνoς, oἴνη,'' ace. Old English ''án'' became in regular course in south and midland dialect ''on,'' exemplified before 1200. By the 15th century, ''on,'' ''oon,'' in southwest and west, had developed (through ''on,'' ''uon,'' ''uön,'' ''won,'' ''wun'') an initial ''w'' (cf. the southwest ''wuk,'' ''wuts'' = ''oak,'' ''oats''), which only occasionally appears in the spelling, but is now the standard pronunciation. The first orthoepist to refer to it was apparently Jones 1701: earlier grammarians, down to Christopher Cooper, 1685, give to ''one'' the sound that it has in ''alone,'' ''atone,'' and ''only''; Thomas Dyche in 1710 has [] beside []. In the north, ''ān'' was retained in Middle English; but through the narrowing of the originally long ''ā'' to [] ''ân'' has sunk in dialectal utterance through ''ane,'' to ''eane,'' ''eän,'' ''yan,'' ''yen,'' the development of [jɛn] in the north being the counterpart of that of [] in the south. In Old English, ''án'' had the full adjective inflexions, definite and indefinite, remains of which persisted in the south to ca. 1300, and in Kent still later; but, in north and midland England, the uninflected ''ān,'' ''ōn,'' with the definite form ''āne,'' ''ōne'' (Old English ''ána,'' ''áne''), is found in the accusative and dative, as well as the nominative by 1200. Already also, ''ān,'' ''ōn'' were reduced before a consonant to ''ā,'' ''ō'' (''oo''), which did not die out till the 16th century.
In the north the separation of ''ân'' and ''â'' was more permanent; at the present day in Scots the full form ''ane,'' ''eane,'' etc., is only used absolutely or in the
predicate, ''ae,'' ''eae,'' is the attributive form before consonants and vowels alike: ''ae day,'' ''ae yeir,'' ''we hae ane''; so in north English dialects with ''yà'' and ''yàn''. From the early ''an,'' ''a,'' pronounced proclitically without stress, arose the “indefinite article” ''an, a''. In the northern dialect the numeral and article were long written alike, the stress or emphasis alone distinguishing them; in 16th century Scots both were written ''ane''. By more or less permanent coalescence of a preceding ''thet,'' the collocations ''thet ane,'' ''thet one,'' ''thet a,'' ''thet o,'' became ''the tane,'' ''the tone,'' ''the ta,'' ''the to''.
See also
★
0.999...
References
1. Wells, D. ''The Penguin Dictionary of Curious and Interesting Numbers'' London: Penguin Group. (1987): 30 - 32
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