|
|
| (One intermediate revision by one other user not shown) |
| Line 1: |
Line 1: |
| {{Redirect4|II|Two}}
| | Let me first you must do introducing too. My name is Edwin Reagan although end up being not [http://www.adobe.com/cfusion/search/index.cfm?term=&common+history&loc=en_us&siteSection=home common history] on my birth official document. New Hampshire is where my [http://Property.org/ property] is but my spouse wants us to get. Since she was 18 she's been working like a bookkeeper. To fence place that I've done for a very long time. Check out current news on the website: http://www.pulsaraviation.com/wiki/index.php/User:DexterOCEX<br><br>Have a look at my homepage :: [http://www.pulsaraviation.com/wiki/index.php/User:DexterOCEX porn Blockers] |
| {{Infobox number
| |
| | number = 2
| |
| | ordinal = 2nd (second / [[wikt:twoth|twoth]])
| |
| | numeral = [[binary numeral system|binary]]
| |
| | factorization = [[prime number|prime]]
| |
| | gaussian integer factorization = <math>(1 + i)(1 - i)</math>
| |
| | prime = 1st
| |
| | divisor = 1, 2
| |
| | roman unicode = Ⅱ, ⅱ
| |
| | greek prefix = [[Wiktionary:di-|di-]]
| |
| | latin prefix = [[Wiktionary:duo-|duo-]] [[Wiktionary:bi-|bi-]]
| |
| | old english prefix = [[Wiktionary:twi-|twi-]]
| |
| | lang1 = [[Greek numeral]]
| |
| | lang1 symbol = β'
| |
| | lang2 = [[Eastern Arabic numerals|Arabic]]
| |
| | lang2 symbol = {{resize|150%|٢}}
| |
| | lang3 = [[Urdu]]
| |
| | lang3 symbol = {{Urdu numeral|2|20}}
| |
| | lang4 = [[Ge'ez alphabet|Ge'ez]]
| |
| | lang4 symbol = ፪
| |
| | lang5 = [[Bengali numerals|Bengali]]
| |
| | lang5 symbol = {{resize|150%|২}}
| |
| | lang6 = [[Chinese numeral]]
| |
| | lang6 symbol = 二，弍，贰，貳
| |
| | lang7 = [[Devanāgarī]]
| |
| | lang7 symbol = {{resize|150%|२}} (do)
| |
| | lang8 = [[Indian numerals#Telugu numerals and their names|Telugu]]
| |
| | lang8 symbol = {{resize|150%|౨}}
| |
| | lang9 = [[Tamil numerals|Tamil]]
| |
| | lang9 symbol = {{resize|150%|௨}}
| |
| | lang10 = [[Hebrew numerals|Hebrew]]
| |
| | lang10 symbol = {{resize|150%|ב}} (Bet)
| |
| | lang11 = [[Khmer numerals|Khmer]]
| |
| | lang11 symbol = ២
| |
| | lang12 = [[Korean numerals|Korean]]
| |
| | lang12 symbol = 이，둘
| |
| | lang13 = [[Thai numerals|Thai]]
| |
| | lang13 symbol = ๒
| |
| }}
| |
| '''2''' ('''Two'''; {{IPAc-en|audio=En-us-two.ogg|ˈ|t|uː}}) is a [[number]], [[numeral system|numeral]], and [[glyph]]. It is the [[natural number]] following [[1 (number)|1]] and preceding [[3 (number)|3]].
| |
| | |
| ==In mathematics==
| |
| The number two has many properties in [[mathematics]].<ref>Wells, D. ''[[The Penguin Dictionary of Curious and Interesting Numbers]]'' London: Penguin Group. (1987): 41–44</ref> An [[integer]] is called ''[[Parity (mathematics)|even]]'' if it is divisible by 2. For integers written in a numeral system based on an even number, such as [[decimal]] and [[hexadecimal]], divisibility by 2 is easily tested by merely looking at the last digit. If it is even, then the whole number is even. In particular, when written in the decimal system, all multiples of 2 will end in 0, 2, 4, 6, or 8.
| |
| | |
| Two is the smallest and the first [[prime number]], and the only even prime number <ref>Bryan Bunch, ''The Kingdom of Infinite Number''. New York: W. H. Freeman & Company (2000): 31</ref> (for this reason it is sometimes called "the oddest prime").<ref>John Horton Conway & Richard K. Guy, ''The Book of Numbers''. New York: Springer (1996): 25. ISBN 0-387-97993-X. "Two is celebrated as the only even prime, which in some sense makes it the oddest prime of all."</ref> The next prime is [[3 (number)|three]]. Two and three are the only two consecutive prime numbers. 2 is the first [[Sophie Germain prime]], the first [[factorial prime]], the first [[Lucas prime]], the first [[Ramanujan prime]], and the first [[Smarandache-Wellin prime]]. It is an [[Eisenstein prime]] with no imaginary part and real part of the form <math>3n - 1</math>. It is also a [[Stern prime]], a [[Pell number]], the first [[Fibonacci prime]], and a [[Markov number]]—appearing in infinitely many solutions to the Markov Diophantine equation involving odd-indexed Pell numbers.
| |
| | |
| It is the third [[Fibonacci number]], and the third and fifth [[Perrin number]]s.
| |
| | |
| Despite being a prime, two is also a [[highly composite number]], because it has more divisors than the number one. The next highly composite number is [[4 (number)|four]].
| |
| | |
| [[Vulgar fraction]]s with only 2 or 5 in the [[denominator]] do not yield infinite [[Decimal representation|decimal expansions]], as is the case with all other primes, because 2 and 5 are [[Divisor|factors]] of [[10 (number)|ten]], the decimal base.
| |
| | |
| Two is the [[radix|base]] of the simplest [[numeral system]] in which natural numbers can be written concisely, being the length of the number a logarithm of the value of the number (whereas in base 1 the length of the number is the value of the number itself); the binary system is used in [[computer]]s.
| |
| | |
| For any number ''x'':
| |
| :''x''+''x'' = 2·''x'' [[addition]] to [[multiplication]]
| |
| :''x''·''x'' = ''x''<sup>2</sup> [[multiplication]] to [[exponentiation]]
| |
| :''x''<sup>''x''</sup> = ''x''↑↑2 [[exponentiation]] to [[tetration]]
| |
| | |
| In general:
| |
| | |
| :hyper(''x'',n,''x'') = hyper(''x'',n-1,2)
| |
| | |
| Two also has the unique property that 2+2 = 2·2 = 2²=''2''↑↑2=''2''↑↑↑2, and so on, no matter how high the operation is.
| |
| | |
| Two is the only number ''x'' such that the sum of the reciprocals of the powers of ''x'' equals itself. In symbols
| |
| | |
| :<math>\sum_{k=0}^{\infin}\frac {1}{2^k}=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\cdots=2.</math> | |
| | |
| This comes from the fact that:
| |
| | |
| :<math>\sum_{k=0}^\infin \frac {1}{n^k}=1+\frac{1}{n-1} \quad\mbox{for all} \quad n\in\mathbb R > 1.</math>
| |
| | |
| [[Power of two|Powers of two]] are central to the concept of [[Mersenne prime]]s, and important to [[computer science]]. Two is the first Mersenne prime exponent.
| |
| | |
| Taking the [[square root]] of a number is such a common mathematical operation, that the spot on the root sign where the exponent would normally be written for cubic roots and other such roots, is left blank for square roots, as it is considered tacit.
| |
| | |
| The [[square root of 2]] was the first known [[irrational number]].
| |
| | |
| The smallest [[field (mathematics)|field]] has two elements.
| |
| | |
| In the [[set theory|set-theoretical]] construction of the natural numbers, 2 is identified with the set <math>\{\{\emptyset\},\emptyset\}</math>. This latter set is important in [[category theory]]: it is a [[subobject classifier]] in the category of sets.
| |
| | |
| Two is a [[primorials|primorial]], as well as its own [[factorial]]. Two often occurs in numerical sequences, such as the [[Fibonacci numbers|Fibonacci number]] sequence, but not quite as often as one does. Two is also a [[Motzkin number]], a [[Bell number]], an [[Harshad number|all-Harshad number]], a [[meandric number]], a [[semi-meandric number]], and an [[open meandric number]].
| |
| | |
| Two is the number of [[Eight queens puzzle|n-Queens Problem]] solutions for n = 4. With one exception, all known solutions to [[Znám's problem]] start with 2.
| |
| | |
| Two also has the unique property such that
| |
| | |
| :<math>\sum_{k=0}^{n-1} 2^k = 2^{n} - 1</math>
| |
| | |
| and also
| |
| | |
| :<math>\sum_{k=a}^{n-1} 2^k = 2^n - \sum_{k=0}^{a-1} 2^k - 1</math>
| |
| for ''a'' not equal to zero
| |
| | |
| The number of domino tilings of a 2×2 [[checkerboard]] is 2.
| |
| | |
| For any polyhedron homeomorphic to a sphere, the [[Euler characteristic]] is
| |
| :<math>\chi = V-E+F = 2.\ </math>
| |
| | |
| As of 2008, there are only two known [[Wieferich prime]]s.
| |
| | |
| ===List of basic calculations===
| |
| {|class="wikitable" style="text-align: center; background: white"
| |
| |-
| |
| !width="105px"|[[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
| |
| !width="5px"|
| |
| !50
| |
| !100
| |
| !1000
| |
| |-
| |
| |<math>2 \times x</math>
| |
| |'''2'''
| |
| |[[4 (number)|4]]
| |
| |[[6 (number)|6]]
| |
| |[[8 (number)|8]]
| |
| |[[10 (number)|10]]
| |
| |[[12 (number)|12]]
| |
| |[[14 (number)|14]]
| |
| |[[16 (number)|16]]
| |
| |[[18 (number)|18]]
| |
| |[[20 (number)|20]]
| |
| |[[22 (number)|22]]
| |
| |[[24 (number)|24]]
| |
| |[[26 (number)|26]]
| |
| |[[28 (number)|28]]
| |
| |[[30 (number)|30]]
| |
| |[[32 (number)|32]]
| |
| |[[34 (number)|34]]
| |
| |[[36 (number)|36]]
| |
| |[[38 (number)|38]]
| |
| |[[40 (number)|40]]
| |
| |[[42 (number)|42]]
| |
| |[[44 (number)|44]]
| |
| |[[46 (number)|46]]
| |
| |[[48 (number)|48]]
| |
| |[[50 (number)|50]]
| |
| !
| |
| |[[100 (number)|100]]
| |
| |[[200 (number)|200]]
| |
| |[[2000 (number)|2000]]
| |
| |}
| |
| | |
| {|class="wikitable" style="text-align: center; background: white"
| |
| |-
| |
| !width="105px"|[[Division (mathematics)|Division]]
| |
| !1
| |
| !2
| |
| !3
| |
| !4
| |
| !5
| |
| !6
| |
| !7
| |
| !8
| |
| !9
| |
| !10
| |
| !11
| |
| !12
| |
| !13
| |
| !14
| |
| !15
| |
| |-
| |
| |<math>2 \div x</math>
| |
| |'''2'''
| |
| |1
| |
| |0.{{overline|6}}
| |
| |[[one half|0.5]]
| |
| |0.4
| |
| |0.{{overline|3}}
| |
| |0.{{overline|285714}}
| |
| |[[4 (number)|0.25]]
| |
| |0.{{overline|2}}
| |
| |0.2
| |
| |0.{{overline|18}}
| |
| |0.1{{overline|6}}
| |
| |0.{{overline|153846}}
| |
| |0.{{overline|142857}}
| |
| |0.1{{overline|3}}
| |
| |-
| |
| |<math>x \div 2</math>
| |
| |0.5
| |
| |1
| |
| |1.5
| |
| |'''2'''
| |
| |2.5
| |
| |3
| |
| |3.5
| |
| |4
| |
| |4.5
| |
| |5
| |
| |5.5
| |
| |6
| |
| |6.5
| |
| |[[7 (number)|7]]
| |
| |7.5
| |
| |}
| |
| | |
| {|class="wikitable" style="text-align: center; background: white"
| |
| |-
| |
| !width="105px"|[[Exponentiation]]
| |
| !1
| |
| !2
| |
| !3
| |
| !4
| |
| !5
| |
| !6
| |
| !7
| |
| !8
| |
| !9
| |
| !10
| |
| !11
| |
| !12
| |
| !13
| |
| !14
| |
| |-
| |
| |<math>2 ^ x\,</math>
| |
| |'''2'''
| |
| |4
| |
| |8
| |
| |16
| |
| |32
| |
| |[[64 (number)|64]]
| |
| |[[128 (number)|128]]
| |
| |[[256 (number)|256]]
| |
| |[[512 (number)|512]]
| |
| |[[1024 (number)|1024]]
| |
| |2048
| |
| |4096
| |
| |8192
| |
| |16384
| |
| |-
| |
| |<math>x ^ 2\,</math>
| |
| |1
| |
| |4
| |
| |[[9 (number)|9]]
| |
| |16
| |
| |25
| |
| |36
| |
| |[[49 (number)|49]]
| |
| |64
| |
| |[[81 (number)|81]]
| |
| |[[100 (number)|100]]
| |
| |[[121 (number)|121]]
| |
| |[[144 (number)|144]]
| |
| |[[169 (number)|169]]
| |
| |[[196 (number)|196]]
| |
| |}
| |
| | |
| {{anchor|glyph}}
| |
| | |
| ==Evolution of the glyph==
| |
| [[Image:Evolution2glyph.png|x50px|right]]
| |
| The [[glyph]] used in the modern Western world to represent the number 2 traces its roots back to the Brahmin Indians, who wrote "2" as two horizontal lines. The modern [[Chinese written language|Chinese]] and [[Japanese writing system|Japanese]] languages still use this method. The [[Gupta script|Gupta]] rotated the two lines 45 degrees, making them diagonal, and sometimes also made the top line shorter and made its bottom end curve towards the center of the bottom line. Apparently for speed, the [[Nagari]] started making the top line more like a curve and connecting to the bottom line. The Ghubar Arabs made the bottom line completely vertical, and now the glyph looks like a dotless closing question mark. Restoring the bottom line to its original horizontal position, but keeping the top line as a curve that connects to the bottom line leads to our modern glyph.<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): 393, Fig. 24.62</ref>
| |
| | |
| In fonts with [[text figures]], 2 usually is of [[x-height]], for example, [[Image:Text figures 256.svg]].
| |
| | |
| ==In science==
| |
| [[Image:Seven-segment 2.svg|25px|right]]
| |
| *The number of [[polynucleotide]] strands in a [[DNA]] [[double helix]].
| |
| *The first [[Magic number (physics)|magic number]].
| |
| *The [[atomic number]] of [[helium]].
| |
| *Group '''2''' in the [[Periodic table]] of the elements consists of the [[alkaline earth]] metals whose usual [[valence (chemistry)|valence]] is +2.
| |
| *Period '''2''' in the Periodic table consists of the eight elements [[lithium]] through [[neon]].
| |
| | |
| ===Astronomy===
| |
| *[[Messier object]] [[Messier 2|M2]], a magnitude 6.5 [[globular cluster]] in the constellation [[Aquarius (constellation)|Aquarius]].
| |
| *The [[New General Catalogue]] [http://www.ngcic.org/ object] [[NGC 2]], a [[visual magnitude|magnitude]] 14.2 [[spiral galaxy]] in the [[constellation]] [[Pegasus (constellation)|Pegasus]]
| |
| *The [[Saros number|Saros]] [http://sunearth.gsfc.nasa.gov/eclipse/SEsaros/SEsaros1-175.html number] of the [[solar eclipse]] series which began on May 4, 2861 BC and ended on June 21, 1563 BC . The duration of Saros series 2 was 1298.1 years, and it contained 73 solar eclipses.
| |
| *The Saros [http://sunearth.gsfc.nasa.gov/eclipse/LEsaros/LEsaros1-175.html number] of the [[lunar eclipse]] series which began on February 21, 2541 BC and ended on April 22, 1225 BC. The duration of Saros series 2 was 1316.2 years, and it contained 74 lunar eclipses.
| |
| *The Roman numeral II stands for [[bright giant]] in the [[stellar classification|Yerkes spectral classification scheme]].
| |
| *The Roman numeral II (usually) stands for the second-discovered satellite of a planet or minor planet (e.g. [[Pluto II]] or [[(87) Sylvia II Remus]])
| |
| *A [[binary star]] is a [[Star system|stellar system]] consisting of two [[star]]s [[Planetary orbit|orbit]]ing around their [[center of mass]].
| |
| | |
| ==In technology==
| |
| [[Image:U+2674 DejaVu Sans.svg|50px|right|2 as a resin identification code, used in recycling.]]
| |
| * The [[resin identification code]] used in recycling to identify [[high-density polyethylene]].
| |
| | |
| ==In religion==
| |
| | |
| The number 2 is important in [[Judaism]], with one of the earliest reference being that God ordered Noah to put two of every [[unclean animals|unclean animal]] (Gen. 7:2) in his ark (see [[Noah's Ark]]). Later on, the [[Ten Commandments]] were given in the form of two tablets. The number also has ceremonial importance, such as the two candles that are traditionally kindled to usher in the [[Shabbat]], recalling the two different ways Shabbat is referred to in the two times the [[Ten Commandments]] are recorded in the [[Torah]]. These two expressions are known in [[Hebrew language|Hebrew]] as שמור וזכור ("guard" and "remember"), as in "Guard the Shabbat day to sanctify it" (Deut. 5:12) and "Remember the Shabbat day to sanctify it" (Ex. 20:8). Two [[challah]]s (''lechem mishnah'') are placed on the table for each [[Shabbat]] meal and a blessing made over them, to commemorate the double portion of [[manna]] which fell in the [[The Exodus|desert]] every Friday to cover that day's meals and the Shabbat meals
| |
| | |
| In [[Halakha|Jewish law]], the testimony of two witnesses are required to verify and validate events, such as [[Jewish view of marriage|marriage]], divorce, and a crime that warrants [[capital punishment]]
| |
| | |
| "Second-Day Yom Tov" (''Yom Tov Sheini Shebegaliyot'') is a rabbinical enactment that mandates a two-day celebration for each of the one-day [[Jewish holiday|Jewish festivals]] (i.e., the first and seventh day of [[Passover]], the day of [[Shavuot]], the first day of [[Sukkot]], and the day of [[Shemini Atzeret]]) outside the land of [[Israel]].
| |
| | |
| ==Numerological significance==
| |
| [[Image:2 playing cards.jpg|thumb|250px|The twos of all four suits in [[playing card]]s]]
| |
| | |
| The most common philosophical [[dichotomy]] is perhaps the one of [[Goodness and value theory|good]] and [[evil]], but there are many others. See [[dualism]] for an overview. In [[Georg Wilhelm Friedrich Hegel|Hegel]]ian [[dialectic]], the process of [[Thesis, antithesis, synthesis|synthesis]] creates two perspectives from one.
| |
|
| |
| The ancient Sanskrit language (संस्कृत भाषा) of India, does not only have a singular and dual form for nouns, as do most other languages, but instead has, a singular (1) form, a dual (2) form, and a plural (everything above 2)form, for all nouns, due to the significance of 2. It is viewed as important because of the anatomical significance of 2 (2 hands, 2 nostrils, 2 eyes, 2 legs, etc.)
| |
| | |
| Two (二, ''èr'') is a good [[number in Chinese culture]]. There is a Chinese saying, "good things come in pairs". It is common to use double symbols in product brandnames, e.g. double happiness, double coin, double elephants etc. [[Guangdong|Cantonese]] people like the number two because it sounds the same as the word "easy" (易) in [[Cantonese language|Cantonese]].
| |
| | |
| In [[Finland]], two [[candle]]s are lit on [[Independence Day (Finland)|Independence Day]]. Putting them on the windowsill invokes the symbolical meaning of division, and thus independence. {{Citation needed|date=May 2008}}
| |
| | |
| In pre-1972 [[Indonesian language|Indonesian]] and [[Malay language|Malay]] orthography, ''2'' was shorthand for the [[reduplication]] that forms plurals: ''orang'' "person", ''orang-orang'' or ''orang2'' "people". {{Citation needed|date=May 2008}}
| |
| | |
| In [[Astrology]], [[Taurus (constellation)|Taurus]] is the second [[astrological sign|sign]] of the [[Zodiac]].
| |
| | |
| ==In sports==
| |
| [[Football]]:
| |
| *In [[American football]], a safety has a two-point value. Also, a two-point conversion is a point after touchdown (PAT) attempt where the ball crosses the goal line via run or pass. (In [[six-man football]], however, the traditional PAT kick is worth two points, whereas a PAT via pass or run is only one point.)
| |
| *In [[Association football]], the scoring of two goals by one individual in a single match is referred to as a brace.
| |
| **The successor of a ''brace'' is the "'''[[hat-trick]]'''", three goals scored by one player.
| |
| | |
| [[Basketball]]:
| |
| * In standard basketball, the value of any made shot taken from inside the [[Three-point field goal|three-point arc]] in normal play is 2 points.
| |
| * In the half-court [[3x3 (basketball)|3x3]] variant, made shots taken from outside the "three-point" arc are worth 2 points.
| |
| | |
| ==In other fields==
| |
| {{Double image|right|ICS Pennant Two.svg|100|ICS Two.svg|100|[[Pennant (commissioning)|International maritime pennant]] for 2|[[International maritime signal flag]] for 2}}
| |
| Groups of two:
| |
| *[[Lists of pairs]]
| |
| **[[list of twins]]
| |
| | |
| *The name of several fictional characters: '''''[[Number Two (disambiguation)|Number Two]]'''''.
| |
| *The designation of the [[Trans-Canada Highway]] in most of the province of [[New Brunswick]].
| |
| *[[U.S. Route 2]], two separated highways in the northern tier of the United States, the western segment connecting [[Everett, Washington]] to [[St. Ignace, Michigan]] and the eastern route connecting [[Rouses Point, New York]] to [[Houlton, Maine]].
| |
| *The lowest channel of television in the United States, Canada, Argentina and Mexico on which television signals are broadcast.
| |
| *Brace is also used in [[hunting]] to refer to a pair. For example, "He shot a brace of pheasants".
| |
| * "Two turtle doves" is the gift on the second day of Christmas in the carol "[[The Twelve Days of Christmas (song)|The Twelve Days of Christmas]]"
| |
| | |
| In North American educational systems, the number 2.00 denotes a [[academic grading in North America|grade-point average]] of "C", which in some colleges and universities is the minimum required for good academic standing at the [[undergraduate]] level.<ref>''For a typical example'', ''see'' the [http://admissions.ou.edu/graderegs.htm#retention University of Oklahoma grading regulations].</ref>
| |
| | |
| == See also ==
| |
| {{Portal|Mathematics}}
| |
| * [[Square (algebra)]] — (2 [[superscript]])
| |
| | |
| ==References==
| |
| {{Reflist}}
| |
| | |
| ==External links==
| |
| * [http://www.numdic.com/2 The Number 2]
| |
| * [http://www.positiveintegers.org/2 The Positive Integer 2]
| |
| * [http://primes.utm.edu/curios/page.php/2.html Prime curiosities: 2]
| |
| | |
| {{Wiktionary|two|both}}
| |
| {{Commons and category|2|2 (number)}}
| |
| | |
| {{Integers|zero}}
| |
| | |
| {{DEFAULTSORT:2 (Number)}}
| |
| [[Category:2 (number)]]
| |
| [[Category:Integers|02]]
| |