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| {{Redirect2|One|No. 1|other uses|1 (disambiguation)}}
| | The title of the writer is Figures. I am a meter reader but I strategy on changing it. Playing baseball is the hobby he will by no means stop performing. Years ago we moved to North Dakota.<br><br>my web page :: [http://ref.pw/dietmealdelivery74619 healthy food delivery] |
| {{Refimprove|date=August 2007}}
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| {{Infobox number
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| | number = 1
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| | numeral = [[Unary numeral system|unary]]
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| | factorization = 1
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| | divisor = 1
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| | roman unicode = Ⅰ, ⅰ
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| | greek prefix = [[Wiktionary:mono-|mono-]] /[[Wiktionary:haplo-|haplo-]]
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| | latin prefix = [[Wiktionary:uni-|uni-]]
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| | lang1 = [[Greek numeral]]
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| | lang1 symbol = α'
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| | lang2 = [[Persian language|Persian]]
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| | lang2 symbol = {{resize|150%|١ - یک}}
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| | lang3 = [[Eastern Arabic numerals|Arabic]]
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| | lang3 symbol = {{resize|150%|١}}
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| | lang4 = [[Urdu]]
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| | lang4 symbol = {{Urdu numeral|1|20}}
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| | lang5 = [[Ge'ez alphabet|Ge'ez]]
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| | lang5 symbol = ፩
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| | lang6 = [[Bengali language|Bengali]] & [[Assamese language|Assamese]]
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| | lang6 symbol = {{resize|150%|১}}
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| | lang7 = [[Chinese numeral]]
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| | lang7 symbol = 一,弌,壹
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| | lang8 = [[Korean language|Korean]]
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| | lang8 symbol = 일, 하나
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| | lang9 = [[Devanāgarī]]
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| | lang9 symbol = {{resize|150%|१}} (ek)
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| | lang10 = [[Telugu language|Telugu]]
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| | lang10 symbol = {{resize|150%|೧}}
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| | lang11 = [[Tamil language|Tamil]]
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| | lang11 symbol = {{resize|150%|௧}}
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| | lang12 = [[Kannada language|Kannada]]
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| | lang12 symbol = {{resize|150%|೧}}
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| | lang13 = [[Hebrew numerals|Hebrew]]
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| | lang13 symbol = {{resize|150%|א}} ([[aleph|alef]])
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| | lang14 = [[Khmer numerals|Khmer]]
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| | lang14 symbol = ១
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| | lang15 = [[Thai numerals|Thai]]
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| | lang15 symbol = ๑
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| | lang16 = [[Malayalam]]
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| | lang16 symbol = ൧
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| | lang17 = [[counting rods|counting rod]]
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| | lang17 symbol = 𝍠
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| }}
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| '''1''' (also called "unity" or, in technical contexts, "monad") ('''one'''; {{IPAc-en|ˈ|w|ʌ|n}} or {{IPAc-en|UK|ˈ|w|ɒ|n}}) is a [[number]], a [[Numeral (linguistics)|numeral]], and the name of the [[glyph]] representing that number. 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.
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| ==As a number==
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| One, sometimes referred to as '''unity''', is the [[integer]] before [[2 (number)|two]] and after [[0 (number)|zero]]. One is the first non-zero number in the [[natural number]]s as well as the first [[odd number]] in the natural numbers.
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| Any number multiplied by one is that number, as one is the [[Identity element|identity]] for multiplication. As a result, one is its own [[factorial]], its own [[Square (algebra)|square]], its own [[Cube (algebra)|cube]], and so on. One is also the [[empty product]], as any number multiplied by one is itself.
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| ==As a digit==
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| [[Image:Evolution1glyph.svg|thumb|left]]
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| 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 [[Indian subcontinent|Indians]], who wrote 1 as a horizontal line, much like the [[Written Chinese|Chinese]] character [[一]]. The [[Gupta script|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 language|Gujarati]] and [[Punjabi language|Punjabi]] scripts). The [[Nepali language|Nepali]] also rotated it to the right but kept the circle small.<ref>Georges Ifrah, ''The Universal History of Numbers: From Prehistory to the Invention of the Computer'' transl. David Bellos et al. London: The Harvill Press (1998): 392, Fig. 24.61</ref> 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]] <math>\mathrm{I}</math>. In some European (e.g., [[Germany]]) and Asian (e.g., [[Israel]]) countries, 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.
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| While the shape of the 1 character has an [[Ascender (typography)|ascender]] in most modern [[typeface]]s, in typefaces with [[text figures]], the character usually is of [[x-height]], as, for example, in [[Image:TextFigs148.svg]].
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| [[File:Clock 24 J.jpg|thumb|The 24-hour tower clock in [[Venice]], using ''J'' as a symbol for 1.]]
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| Many older typewriters do not have a separate symbol for ''1'' and use the lowercase ''l'' instead. It is possible to find cases when the uppercase ''J'' is used, while it may be for decorative purposes.
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| ==Mathematics==
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| Mathematically, 1 is:
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| * in [[arithmetic]] ([[algebra]]) and [[calculus]], the [[natural number]] that follows [[0 (number)|0]] and precedes [[2 (number)|2]] and the multiplicative [[identity (mathematics)|identity]] of the [[integer]]s, [[real number]]s and [[complex number]]s;
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| * more generally, in [[abstract algebra]], the multiplicative identity ("unity"), usually of a [[ring (mathematics)|ring]].
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| One cannot be used as the base of a positional [[numeral system]]; sometimes [[tally mark|tallying]] is referred to as "base 1", since only one mark (the tally) is needed, but this is not a positional notation.
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| The [[logarithm]]s base 1 are undefined, since the function 1<sup>''x''</sup> always equals 1 and so has no unique [[inverse function|inverse]].
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| In the real-number system, 1 can be represented in two ways as a [[recurring decimal]]: as 1.000... and as [[0.999...]] (''[[q.v.]]'').
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| Formalizations of the natural numbers have their own representations of 1:
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| * in the [[Peano axioms]], 1 is the successor of 0;
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| * in [[Principia Mathematica]], 1 is defined as the set of all [[singleton (mathematics)|singleton]]s (sets with one element);
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| * in the [[Von Neumann cardinal assignment]] of natural numbers, 1 is defined as the [[Set (mathematics)|set]] {0}.
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| In a multiplicative [[group (mathematics)|group]] or [[monoid]], the [[identity element]] is sometimes denoted ''1'', especially in [[abelian group]]s, but ''e'' (from the German ''Einheit'', "unity") is more 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 (algebra)|characteristic]] ''n'' not equal to 0, the element called 1 has the property that ''n''1 = 1''n'' = 0 (where this 0 is the additive identity of the ring). Important examples are general [[Field (mathematics)|fields]].
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| One is the first [[figurate number]] of every kind, such as [[triangular number]], [[pentagonal number]] and [[centered hexagonal number]], to name just a few.
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| In many mathematical and engineering equations, numeric values are typically ''normalized''<!--need a good link for this--> to fall within the [[unit interval]] from 0 to 1, where 1 usually represents the maximum possible value in the range of parameters.
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| Because of the multiplicative identity, if ''f''(''x'') is a [[multiplicative function]], then ''f''(1) must equal 1.
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| It is also the first and second numbers in the [[Fibonacci number|Fibonacci]] sequence (0 is the zeroth) and is the first number in many other mathematical sequences. As a matter of convention, Sloane's early ''Handbook of Integer Sequences'' added an initial 1 to any sequence that did not 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.
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| One is neither a [[prime number]] nor a [[composite number]], but a [[unit (ring theory)|unit]], like −1 and, in the [[Gaussian integers]], ''[[imaginary unit|i]]'' and −''i''. The [[fundamental theorem of arithmetic]] guarantees [[factorization|unique factorization]] over the integers only up to units (e.g., 4 = 2<sup>2</sup> = (−1)<sup>6</sup>×1<sup>23</sup>×2<sup>2</sup>).
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| The definition of a [[field (mathematics)|field]] requires that 1 must not be equal to [[zero|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.
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| One 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). One was formerly considered prime by some mathematicians, using the definition that a prime is divisible only by one and itself. However, this complicates the fundamental theorem of arithmetic, so modern definitions exclude units.
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| One is one of three possible values of the [[Möbius function]]: it takes the value one for [[square-free integer]]s with an even number of distinct prime factors.
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| One is the only odd number in the range of [[Euler's totient function]] φ(''x''), in the cases ''x'' = 1 and ''x'' = 2.
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| One is the only 1-perfect number (see [[multiply perfect number]]).
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| By definition, 1 is the [[magnitude (mathematics)|magnitude]] or [[absolute value]] of a [[unit vector]] and a [[identity matrix|unit matrix]] (more usually called an identity matrix). Note that the term ''unit matrix'' is sometimes used to mean something [[Matrix of ones|quite different]].
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| By definition, 1 is the [[probability]] of an event that is [[almost certain]] to occur.
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| One is the most common leading digit in many sets of data, a consequence of [[Benford's law]].
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| The [[ancient Egypt]]ians represented all fractions (with the exception of 2/3) in terms of sums of fractions with [[numerator]] 1 and distinct [[denominator]]s. For example, <math>\frac{2}{5} = \frac{1}{3} + \frac{1}{15}</math>. Such representations are popularly known as [[Egyptian Fractions]] or [[Unit Fractions]]. <!-- Historical. -->
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| The [[Generating Function]] that has all coefficients 1 is given by
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| <math>\frac{1}{1-x} = 1 + x + x^2 + x^3 + \cdots</math>.
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| This power series converges and has finite value [[if and only if]], <math>| x | < 1</math>. <!-- Probably not needed, really should look at convergence theorem as there are other series that converge iff |x| < 1 -->
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| ===Table of basic calculations===
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| {|class="wikitable" style="text-align: center; background: white"
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| |-
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| ! style="width:105px;"|[[Multiplication]]
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| !1
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| !2
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| !3
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| !4
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| !5
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| !6
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| !7
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| !8
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| !9
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| !10
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| ! style="width:5px;"|
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| !11
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| | |
| !12
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| !13
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| !14
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| !15
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| !16
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| !17
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| !18
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| !19
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| !20
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| ! style="width:5px;"|
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| !21
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| !22
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| !23
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| !24
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| !25
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| ! style="width:5px;"|
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| !50
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| !100
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| !1000
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| |-
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| |<math>1 \times x</math>
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| |'''1'''
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| |[[2 (number)|2]]
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| |[[3 (number)|3]]
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| |[[4 (number)|4]]
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| |[[5 (number)|5]]
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| |[[6 (number)|6]]
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| |[[7 (number)|7]]
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| |[[8 (number)|8]]
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| |[[9 (number)|9]]
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| |[[10 (number)|10]]
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| !
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| |[[11 (number)|11]]
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| |[[12 (number)|12]]
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| |[[13 (number)|13]]
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| |[[14 (number)|14]]
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| |[[15 (number)|15]]
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| |[[16 (number)|16]]
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| |[[17 (number)|17]]
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| |[[18 (number)|18]]
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| |[[19 (number)|19]]
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| |[[20 (number)|20]]
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| !
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| |[[21 (number)|21]]
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| |[[22 (number)|22]]
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| |[[23 (number)|23]]
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| |[[24 (number)|24]]
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| |[[25 (number)|25]]
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| !
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| |[[50 (number)|50]]
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| |[[100 (number)|100]]
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| |[[1000 (number)|1000]]
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| |}
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| {|class="wikitable" style="text-align: center; background: white"
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| |-
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| ! style="width:105px;"|[[Division (mathematics)|Division]]
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| !1
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| !2
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| !3
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| !4
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| !5
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| !6
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| !7
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| !8
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| !9
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| !10
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| ! style="width:5px;"|
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| !11
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| !12
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| !13
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| !14
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| !15
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| |-
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| |<math>1 \div x</math>
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| |'''1'''
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| |0.5
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| |0.{{overline|3}}
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| |0.25
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| |0.2
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| |0.1{{overline|6}}
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| |0.{{overline|142857}}
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| |0.125
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| |0.{{overline|1}}
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| |0.1
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| !
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| |0.{{overline|09}}
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| |0.08{{overline|3}}
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| |0.{{overline|076923}}
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| |0.0{{overline|714285}}
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| |0.0{{overline|6}}
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| |-
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| |<math>x \div 1</math>
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| |'''1'''
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| |2
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| |3
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| |4
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| |5
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| |6
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| |7
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| |8
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| |9
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| |10
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| !
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| |11
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| |12
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| |13
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| |14
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| |15
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| |}
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| | |
| {|class="wikitable" style="text-align: center; background: white"
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| |-
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| ! style="width:105px;"|[[Exponentiation]]
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| !1
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| !2
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| !3
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| !4
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| !5
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| !6
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| !7
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| !8
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| !9
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| !10
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| ! style="width:5px;"|
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| !11
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| !12
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| !13
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| !14
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| !15
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| !16
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| !17
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| !18
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| !19
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| !20
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| |-
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| |<math>1 ^ x\,</math>
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| |'''1'''
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| |'''1'''
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| |'''1'''
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| |'''1'''
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| |'''1'''
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| |'''1'''
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| |'''1'''
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| |'''1'''
| |
| |'''1'''
| |
| |'''1'''
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| !
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| |'''1'''
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| |'''1'''
| |
| |'''1'''
| |
| |'''1'''
| |
| |'''1'''
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| |'''1'''
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| |'''1'''
| |
| |'''1'''
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| |'''1'''
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| |'''1'''
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| |-
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| |<math>x ^ 1\,</math>
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| |'''1'''
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| |2
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| |3
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| |4
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| |5
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| |6
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| |7
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| |8
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| |9
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| |10
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| !
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| |11
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| |12
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| |13
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| |14
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| |15
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| |16
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| |17
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| |18
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| |19
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| |20
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| |}
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| ==In technology==
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| [[Image:U+2673 DejaVu Sans.svg|50px|right|1 as a resin identification code, used in recycling]]
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| * The [[resin identification code]] used in recycling to identify [[polyethylene terephthalate]]<ref>{{cite web |url=http://www.americanchemistry.com/s_plastics/bin.asp?CID=1102&DID=4645&DOC=FILE.PDF |title=Plastic Packaging Resins |publisher=American Chemistry Council}}</ref>
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| * Used in [[binary code]] along with [[0 (number)|0]]
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| ==In science==
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| * The atomic number of [[hydrogen]]
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| ==In philosophy==
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| In the [[philosophy]] of [[Plotinus]] and a number of other [[neoplatonist]]s, [[Plotinus#One|The One]] is the ultimate reality and source of all existence.
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| [[Philo#Numbers|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]).
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| ==In sports==
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| * 1 is the lowest number permitted for use by players of the [[National Hockey League|National Hockey League (NHL)]], as the league has banned 00 and 0. (The highest number permitted is [[98 (number)|98]].)
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| * Many sports use 1 as their standard scoring increment—examples include goals in a large number of sports, runs in baseball and cricket, and points in volleyball. Examples where 1 is a non-standard increment, or used for one of several possible classes of scores, are listed below by sport.
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| * In [[Australian rules football]], 1 point is awarded to the attacking team for a [[Laws of Australian football#Scoring|behind]], scored when:
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| ** The ball is kicked by the attacking team and passes between a goal post (taller post) and the nearest behind post (shorter post) on the defensive side of the field without touching the behind post.
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| ** The ball passes between the defending team's goal posts, but either (1) was not kicked by the attacking team or (2) hit a goal post.
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| ** The defending team deliberately forces the ball between any two of its own posts. This particular score is officially called a "rushed behind".
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| * In [[baseball]] scoring, the number 1 is assigned to the [[pitcher]].
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| * In [[basketball]]:
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| ** 1 point is awarded for a successful [[free throw]].
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| ** In the [[3x3 (basketball)|3×3 variant]] of the game, shots made from inside the "three-point" arc are also worth 1 point. (Shots from outside the arc are worth 2 points.)
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| ** The number 1 is used to designate the [[point guard]] position.
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| * In [[association football]] (soccer) the number 1 is often given to the [[goalkeeper (association football)|goalkeeper]]
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| * In [[Gaelic football]], [[hurling]] and [[camogie]], a "point", with a scoring value of 1, is awarded when the attacking team legally sends the ball over the opponent's crossbar (above the goal).
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| * In [[gridiron football]] codes, one point is awarded under the following circumstances:
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| ** In almost all leagues, for [[Conversion (gridiron football)|a successful place kick after a touchdown]]. In [[American football]], the score is formally known as a "try", although the terms "extra point", "conversion", "PAT" (for "point after touchdown"), and "point after" are far more commonly used. In [[Canadian football]], the score is formally and popularly called a "convert". Conversions can also be scored by the now rare [[drop kick]]; in standard American and Canadian football, such a conversion is worth 1 point, while most forms of [[Indoor American football|indoor football]], including the [[Arena Football League]], award 2 points for a drop-kicked conversion.
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| ** In college football, if a point after "try" is blocked, if the blocked ball stayed in the field of play a defender may pick up and run the ball to his end zone at the other end of the field for a one point safety.
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| ** In [[six-man football]], one point is awarded for a successful conversion from scrimmage after a touchdown. Note that in standard 11-man (American) or 12-man (Canadian) football, place kicks are worth 1 point and conversions from scrimmage [[Two-point conversion|worth 2]]; this is reversed in six-man because the reduced number of players makes kicked conversions much more difficult.
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| ** In Canadian football only, a [[Single (football)|single]] or "rouge" is awarded when the ball is legally kicked into the opponent's end zone (except for a successful field goal), and the receiving team does not return, or kick, the ball out of its end zone. (In American football, the same play would result in a [[touchback]] and no points.)
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| ** Some forms of indoor football in the U.S. award a "single", similar to the Canadian score, on kickoffs only.
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| * In [[rugby league]]:
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| ** A [[drop goal]] is worth 1 point.
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| ** In most competitions (though not the European [[Super League]], which uses static squad numbering), the starting [[Fullback (rugby league)|fullback]] wears jersey number 1.
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| * In [[rugby union]]:
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| ** The starting [[Rugby union positions#Prop|loosehead prop]] wears the jersey number 1.
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| ** In the early years of the sport (prior to 1890), conversions, penalties, drop goals, and goals from mark were all worth 1 point. At that time, a try was worth no points, only giving the attacking team the right to attempt a conversion. In 1890–91, tries were rewarded with 1 point, while all other scores were increased in value. After that time, all scores have been worth at least 2 points (the goal from mark was abolished in 1977).
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| * The jersey number 1 has been retired by several [[Major professional sports leagues in the United States and Canada|North American sports]] teams in honor of past playing greats or other key figures (or, in one case, a team's fans):
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| ** In [[Major League Baseball]]:
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| *** The [[Boston Red Sox]], for [[National Baseball Hall of Fame and Museum|Hall of Famer]] [[Bobby Doerr]].
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| *** The [[Cincinnati Reds]], for [[manager (baseball)|manager]] [[Fred Hutchinson]].
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| *** The [[Los Angeles Dodgers]], for Hall of Famer [[Pee Wee Reese]].
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| *** The [[New York Yankees]], for [[Billy Martin]], who both played for and managed the team.
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| *** The [[Philadelphia Phillies]], for Hall of Famer [[Richie Ashburn]].
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| *** The [[Pittsburgh Pirates]], for manager [[Billy Meyer]].
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| *** The [[St. Louis Cardinals]], for Hall of Famer [[Ozzie Smith]].
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| ** In the [[National Basketball Association|NBA]]:
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| *** The [[Boston Celtics]], for founding owner [[Walter A. Brown|Walter Brown]], a member of the [[Naismith Memorial Basketball Hall of Fame|Hall of Fame]] as a [[List of members of the Naismith Memorial Basketball Hall of Fame#Contributors|contributor]].
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| *** The [[Milwaukee Bucks]], for Hall of Fame player [[Oscar Robertson]].
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| *** The [[Portland Trail Blazers]], for founding owner [[Larry Weinberg]]. Unlike most numbers so honored, this number remains in circulation for players.
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| *** The [[Sacramento Kings]], for Hall of Fame player [[Nate Archibald]], honoring the number's retirement when the team was known as the [[Sacramento Kings#Kansas City/Omaha|Kansas City Kings]].
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| *** The [[Seattle SuperSonics]], for [[Gus Williams (basketball)|Gus Williams]]. The team has since [[Seattle SuperSonics relocation to Oklahoma City|relocated]] to become the [[Oklahoma City Thunder]], but the Thunder have yet to issue any number retired by the franchise in Seattle.
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| *** The [[Utah Jazz]], for [[Frank Layden]], who served the team first as head coach and then as president.
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| ** In the [[National Football League|NFL]]:
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| *** The [[New York Giants]], for [[Pro Football Hall of Fame|Hall of Famer]] [[Ray Flaherty]].
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| *** The [[Tennessee Titans]], for Hall of Famer [[Warren Moon]], who played for the team in its past incarnation as the [[History of the Houston Oilers|Houston Oilers]].
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| ** In the [[National Hockey League|NHL]]:
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| *** The [[Chicago Blackhawks]], for [[Hockey Hall of Fame|Hall of Famer]] [[Glenn Hall]].
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| *** The [[Detroit Red Wings]], for Hall of Famer [[Terry Sawchuk]].
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| *** The [[Montreal Canadiens]], for Hall of Famer [[Jacques Plante]].
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| *** The [[New York Rangers]], for Hall of Famer [[Eddie Giacomin]].
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| *** The [[Minnesota Wild]], for their fans.
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| *** The [[Philadelphia Flyers]], for Hall of Famer [[Bernie Parent]].
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| *** The [[Toronto Maple Leafs]] have a policy of not retiring numbers unless the player honoured either died or suffered a career-ending incident while a member of the team. Other players whose numbers would otherwise be retired instead have their numbers enshrined by the team as "Honoured Numbers", which remain in circulation for future players. The number 1 is currently honoured for Hall of Famers [[Johnny Bower]] and [[Turk Broda]].
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| ==Etymology==
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| The word '''one''' can be used as a noun, an adjective and a pronoun.<ref name="etymonline">http://www.etymonline.com/index.php?term=one</ref>
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| It comes from the Old English word '''an''',<ref name="etymonline"/> which comes from the Proto-Germanic root '''*ainaz'''.<ref name="etymonline"/> The Proto-Germanic root '''*ainaz''' comes from the Proto-Indo-European root '''*oi-no-'''.<ref name="etymonline"/>
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| Compare the Proto-Germanic root '''*ainaz''' to [[Old Frisian]] '''an''', [[Gothic language|Gothic]] '''ains''', [[Danish language|Danish]] '''een''', [[Dutch language|Dutch]] '''een''', [[German language|German]] '''ein''' and [[Old Norse]] '''einn'''.
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| Compare the Proto-Indo-European root '''*oi-no-''' (which means one, single<ref name="etymonline"/>) to [[Greek language|Greek]] '''oinos''' (which means "ace" on dice<ref name="etymonline"/>), [[Latin]] '''unus''' (one<ref name="etymonline"/>), [[Old Persian]] '''aivam''', [[Old Church Slavonic]] '''-inu''' and '''ino-''', [[Lithuanian language|Lithuanian]] '''vienas''', [[Old Irish]] '''oin''' and [[Breton language|Breton]] '''un''' (one<ref name="etymonline"/>).
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| ==External links==
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| * [http://www.numdic.com/1 The Number 1]
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| * [http://www.positiveintegers.org/1 The Positive Integer 1]
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| * [http://primes.utm.edu/curios/page.php/1.html Prime curiosities: 1]
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| ==See also==
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| {{portal|Mathematics}}
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| * [[−1 (number)|−1]]
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| * [[BBC One]], which was BBC One's logo from 1991–1998.
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| * [[One (word)]]
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| * [[Root of unity]]
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| ==Notes==
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| {{Commons and category|1 (number)|1 (number)}}
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| {{reflist}}
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| {{Integers|zero}}
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| {{DEFAULTSORT:1 (Number)}}
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| [[Category:One| ]]
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| [[Category:Integers|01]]
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