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{{Expand Spanish|date=September 2024}}{{Short description|Integer number 2}}
{{About|the number|the year|AD 2|other uses|2 (disambiguation)|and|II (disambiguation)|and|Number Two (disambiguation){{!}}Number Two}}
{{pp-vandalism|small=yes}}
{{Infobox number NUHA
{{Hatnote|This article is about the number. For the years, see [[2 BC]] and [[AD 2]]. For other uses, see [[II (disambiguation)]] and [[Number Two (disambiguation)]].}}
{{Infobox number
|number=2
|number=2
|ordinal=2nd (second / [[wikt:twoth|twoth]])
|ordinal=2nd (second / [[wikt:twoth|twoth]])
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|prime=1st
|prime=1st
|divisor=1, 2
|divisor=1, 2
|roman unicode=Ⅱ, ⅱ
|roman =II, ii
|greek prefix=[[Wiktionary:di-|di-]]
|greek prefix=[[Wiktionary:di-|di-]]
|latin prefix=[[Wiktionary:duo-|duo-]] [[Wiktionary:bi-|bi-]]
|latin prefix=[[Wiktionary:duo-|duo-]]/[[Wiktionary:bi-|bi-]]
|old english prefix=[[Wiktionary:twi-|twi-]]
|old english prefix=[[Wiktionary:twi-|twi-]]
|lang1=[[Greek numeral]]
|lang1=[[Greek numeral]]
|lang1 symbol=β'
|lang1 symbol=β'
|lang2=[[Eastern Arabic numerals|Arabic]] & [[Central Kurdish|Kurdish]]
|lang2=[[Eastern Arabic numerals|Arabic]], [[Central Kurdish|Kurdish]], [[Persian language|Persian]], [[Sindhi language|Sindhi]], [[Urdu numerals|Urdu]]
|lang2 symbol={{resize|150%|٢}}
|lang2 symbol={{resize|150%|٢}}
|lang3=[[Urdu]]
|lang3=[[Ge'ez alphabet|Ge'ez]]
|lang3 symbol={{Urdu numeral|2|20}}
|lang3 symbol=፪
|lang4=[[Ge'ez alphabet|Ge'ez]]
|lang4=[[Bengali numerals|Bengali]]
|lang4 symbol=፪
|lang4 symbol={{resize|150%|২}}
|lang5=[[Bengali numerals|Bengali]]
|lang5=[[Chinese numeral]]
|lang5 symbol={{resize|150%|২}}
|lang5 symbol=二，弍，貳
|lang6=[[Chinese numeral]]
|lang6=[[Devanāgarī]]
|lang6 symbol=二，弍，貳
|lang6 symbol={{resize|150%|२}}
|lang7=[[Indian numerals#Telugu numerals and their names|Telugu]]
|lang7=[[Devanāgarī]]
|lang7 symbol={{resize|150%|२}}
|lang7 symbol={{resize|150%|౨}}
|lang8=[[Indian numerals#Telugu numerals and their names|Telugu]]
|lang8=[[Tamil numerals|Tamil]]
|lang8 symbol={{resize|150%|౨}}
|lang8 symbol={{resize|150%|௨}}
|lang9=[[Tamil numerals|Tamil]]
|lang9=[[Kannada numerals|Kannada]]
|lang9 symbol={{resize|150%|௨}}
|lang9 symbol={{resize|150%|೨}}
|lang10=[[Hebrew numerals|Hebrew]]
|lang10=[[Hebrew numerals|Hebrew]]
|lang10 symbol={{resize|150%|ב}}
|lang10 symbol={{resize|150%|ב}}
|lang11=[[Armenian numerals|Armenian]]|lang11 symbol=Բ|lang12=[[Khmer numerals|Khmer]]
|lang11=[[Japanese numeral]]
|lang11 symbol=二/弐
|lang12=[[Khmer numerals|Khmer]]
|lang12 symbol=២
|lang12 symbol=២
|lang13=[[Korean numerals|Korean]]
|lang13=[[Maya numerals]]|lang13 symbol=••|lang14=[[Thai numerals|Thai]]
|lang13 symbol=이，둘
|lang14 symbol=๒
|lang14=[[Thai numerals|Thai]]
|lang15=[[Georgian numerals|Georgian]]
|lang15 symbol={{resize|130%| Ⴁ/ⴁ/ბ}}([[Bani (letter)|Bani]])
|lang14 symbol=๒}}
|lang16=[[Malayalam numerals|Malayalam]]
'''2''' ('''two''') is a [[number]], [[numeral system|numeral]], and [[glyph]]. It is the [[natural number]] following [[1]] and preceding [[3]].
|lang16 symbol=൨
|lang17=[[Babylonian cuneiform numerals|Babylonian numeral]]|lang17 symbol=𒐖|lang18=[[Egyptian numerals|Egyptian hieroglyph]], [[Aegean numerals|Aegean numeral]], [[counting rods|Chinese counting rod]]|lang18 symbol={{!}}{{!}}|lang19=[[Morse code]]|lang19 symbol={{resize|150%|.._ _ _}}}}


'''2''' ('''two''') is a [[number]], [[numeral (linguistics)|numeral]] and [[numerical digit|digit]]. It is the [[natural number]] following [[1]] and preceding [[3]]. It is the smallest and the only even [[prime number]].
==In mathematics==
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]], [[hexadecimal]], or in any other base that is even, 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.


Because it forms the basis of a [[Dualistic cosmology|duality]], it has [[Religion|religious]] and [[Spirituality|spiritual]] significance in many [[Culture|cultures]].
Two is the smallest [[prime number]], and the only even prime number (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|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]], and the first [[Ramanujan prime]].<ref>{{Cite web |url=https://oeis.org/A104272 |title=Sloane's A104272 : Ramanujan primes |last= |first= |date= |website=The On-Line Encyclopedia of Integer Sequences |publisher=OEIS Foundation |access-date=2016-06-01}}</ref>


== As a word ==
Two is the third (or fourth) [[Fibonacci number]].
''Two'' is most commonly a [[English determiners|determiner]] used with [[Grammatical number|plural]] countable nouns, as in ''two days'' or ''I'll take these two''.<ref>{{Cite book |last1=Huddleston |first1=Rodney D. |url=https://www.worldcat.org/oclc/1255524478 |title=A student's introduction to English grammar |last2=Pullum |first2=Geoffrey K. |last3=Reynolds |first3=Brett |publisher=[[Cambridge University Press]] |year=2022 |isbn=978-1-316-51464-1 |edition=2nd |location=Cambridge, United Kingdom |pages=117 |oclc= 1255524478|author-link=Rodney Huddleston |author-link2=Geoffrey K. Pullum}}</ref> ''Two'' is a [[English nouns|noun]] when it refers to the number two as in ''two plus two is four.''


=== Etymology of ''two'' ===
Two is the [[radix|base]] of [[Binary_number|the binary system]], the [[numeral system]] with the least number of tokens allowing to denote a natural number {{math|''n''}} substantially more concise ({{math|log<sub>2</sub> ''n'' }} tokens), compared to a direct representation by the corresponding count of a single token ({{math|''n''}} tokens). This binary number system is used extensively in [[Computer|computing]].
The word ''two'' is derived from the [[Old English]] words {{lang|ang|twā}} ([[Grammatical gender|feminine]]), {{lang|ang|tū}} (neuter), and {{lang|ang|twēġen}} (masculine, which survives today in the form [[wikt:twain|twain]]).<ref name=OED>{{Cite OED|two, adj., n., and adv.}}</ref>


The pronunciation {{IPA|/tuː/}}, like that of ''who'' is due to the [[labialization]] of the vowel by the ''w'', which then disappeared before the related sound. The successive stages of pronunciation for the Old English {{lang|ang|twā}} would thus be {{IPA|/twɑː/}}, {{IPA|/twɔː/}}, {{IPA|/twoː/}}, {{IPA|/twuː/}}, and finally {{IPA|/tuː/}}.<ref name=OED/>
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]]


== Mathematics ==
Extending this sequence of operations by introducing the notion of [[hyperoperation]]s, here denoted by "hyper(''a'',''b'',''c'')" with ''a'' and ''c'' being the first and second operand, and ''b'' being the ''level'' in the above sketched sequence of operations, the following holds in general:
An [[integer]] is determined to be [[Parity (mathematics)|even]] if it is [[Division (mathematics)|divisible]] by two. When written in base 10, all [[Multiple (mathematics)|multiples]] of 2 will end in [[0]], 2, 4, 6, or [[8]].<ref>{{Cite OEIS|A005843|The nonnegative even numbers|access-date=2022-12-15}}</ref> 2 is the smallest and the only even [[prime number]], and the first [[Ramanujan prime]].<ref>{{Cite web |title=Sloane's A104272 : Ramanujan primes |url=https://oeis.org/A104272 |url-status=dead |archive-url=https://web.archive.org/web/20110428165633/https://oeis.org/A104272 |archive-date=2011-04-28 |access-date=2016-06-01 |website=The On-Line Encyclopedia of Integer Sequences |publisher=OEIS Foundation}}</ref>
:hyper(''x'',''n'',''x'') = hyper(''x'',(''n'' + 1),2).


=== Geometry ===
Two has therefore the unique property that {{nowrap|1=2 + 2 = 2 · 2 = 2{{sup|2}} = 2↑↑2 = 2↑↑↑2 = ...}}, disregarding the level of the hyperoperation, here denoted by [[Knuth's up-arrow notation]]. The number of up-arrows refers to the level of the hyperoperation.
A [[digon]] is a polygon with two sides (or [[Edge (geometry)|edges]]) and two [[Vertex (geometry)|vertices]].<ref name="Wilson2014">{{cite book |last=Wilson |first=Robin |title=Four Colors Suffice |publisher=Princeton University Press |year=2014 |isbn=978-0-691-15822-8 |edition=Revised color}}</ref>{{rp|52}} Two distinct [[point (geometry)|points]] in a [[Plane (geometry)|plane]] are always [[Necessity and sufficiency|sufficient]] to define a unique [[line (geometry)|line]] in a nontrivial [[Euclidean space]].<ref>{{Cite book |last=Carrell |first=Jim |url=https://personal.math.ubc.ca/~carrell/307_chap1.pdf |title=MATH 307 Applied Linear Algebra |chapter=Chapter 1 {{!}} Euclidean Spaces and Their Geometry}}</ref>


=== Set Theory ===
Two is the only number ''x'' such that the sum of the reciprocals of the powers of ''x'' equals itself. In symbols
A [[Set theory|set]] that is a [[field (mathematics)|field]] has a minimum of two [[Element (mathematics)|elements]].{{Citation needed|date=September 2024}} A [[Cantor space]] is a [[topological space]] <math>2^\mathbb{N}</math> [[homeomorphic]] to the [[Cantor set]].{{Citation needed|date=September 2024}}
:<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>
== Base 2 ==
{{See also|Binary number}}
[[Binary number|Binary]] is a number system with a [[radix|base]] of two, it is used extensively in [[Computer|computing]].<ref>{{Cite web |title=How computers see the world - Binary - KS3 Computer Science Revision |url=https://www.bbc.co.uk/bitesize/guides/z26rcdm/revision/1 |access-date=2024-06-05 |website=BBC Bitesize |language=en-GB}}</ref>


== List of basic calculations ==
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 and other roots, may simply be left blank for square roots, as it is tacitly understood.

The [[square root of 2]] was the first known [[irrational number]].

The smallest [[field (mathematics)|field]] has two elements.

In a [[set theory|set-theoretical]] construction of the natural numbers, 2 is identified with the set <nowiki>{{∅},∅}</nowiki>. This latter set is important in [[category theory]]: it is a [[subobject classifier]] in the category of sets.

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

In any [[Dimension (mathematics and physics)|''n''-dimensional, euclidean space]] two distinct [[point (geometry)|points]] determine a [[line (geometry)|line]].

For any polyhedron homeomorphic to a sphere, the [[Euler characteristic]] is {{nowrap|1=''χ'' = ''V'' − ''E'' + ''F'' = 2}}, where ''V'' is the number of [[Vertex (geometry)|vertices]], ''E'' is the number of [[Edge (geometry)|edge]]s, and ''F'' is the number of [[Face (geometry)|face]]s.

===List of basic calculations===
{|class="wikitable" style="text-align: center; background: white"
{|class="wikitable" style="text-align: center; background: white"
|-
|+
!width="105px"|[[Multiplication]]
![[Multiplication]]
!1
!1
!2
!2
Line 116: Line 96:
!24
!24
!25
!25
!width="5px"|
!50
!50
!100
!100
!1000
|-
|-
|'''2 × ''x'''''
|'''2 × ''x'''''
|'''2'''
|'''2'''
|[[4 (number)|4]]
|[[4]]
|[[6 (number)|6]]
|[[6]]
|[[8 (number)|8]]
|[[8]]
|[[10 (number)|10]]
|[[10]]
|[[12 (number)|12]]
|[[12 (number)|12]]
|[[14 (number)|14]]
|[[14 (number)|14]]
Line 147: Line 125:
|[[48 (number)|48]]
|[[48 (number)|48]]
|[[50 (number)|50]]
|[[50 (number)|50]]
|[[100]]
!
|[[100 (number)|100]]
|[[200 (number)|200]]
|[[200 (number)|200]]
|[[2000 (number)|2000]]
|}
|}


Line 166: Line 142:
!9
!9
!10
!10
!width="5px"|
!11
!11
!12
!12
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!14
!14
!15
!15
!16
!17
!18
!19
!20
|-
|-
|'''2 ÷ ''x'''''
|'''2 ÷ ''x'''''
|'''2'''
|'''2'''
|[[1 (number)|1]]
| rowspan="2"|[[1]]
|0.{{overline|6}}
|0.{{overline|6}}
|[[one half|0.5]]
|0.5
|0.4
|0.4
|0.{{overline|3}}
|0.{{overline|3}}
|0.{{overline|285714}}
|0.{{overline|285714}}
|[[wikt:quarter|0.25]]
|0.25
|0.{{overline|2}}
|0.{{overline|2}}
|0.2
|0.2
!
|0.{{overline|18}}
|0.{{overline|18}}
|0.1{{overline|6}}
|0.1{{overline|6}}
Line 188: Line 171:
|0.{{overline|142857}}
|0.{{overline|142857}}
|0.1{{overline|3}}
|0.1{{overline|3}}
|0.125
|0.{{overline|1176470588235294}}
|0.{{overline|1}}
|0.{{overline|105263157894736842}}
|0.1
|-
|-
|'''''x'' ÷ 2'''
|'''''x'' ÷ 2'''
|0.5
|[[One half|0.5]]
|[[1 (number)|1]]
|1.5
|1.5
|'''2'''
|'''2'''
|2.5
|2.5
|[[3 (number)|3]]
|[[3]]
|3.5
|3.5
|[[4 (number)|4]]
|[[4]]
|4.5
|4.5
|[[5 (number)|5]]
|[[5]]
!
|5.5
|5.5
|[[6 (number)|6]]
|[[6]]
|6.5
|6.5
|[[7 (number)|7]]
|[[7]]
|7.5
|7.5
|[[8]]
|8.5
|[[9]]
|9.5
|[[10]]
|}
|}


Line 220: Line 213:
!9
!9
!10
!10
!width="5px"|
!11
!11
!12
!12
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|'''2{{sup|''x''}}'''
|'''2{{sup|''x''}}'''
|'''2'''
|'''2'''
|[[4 (number)|4]]
| rowspan="2" |[[4]]
|[[8 (number)|8]]
|[[8]]
|[[16 (number)|16]]
| rowspan="2" |[[16 (number)|16]]
|[[32 (number)|32]]
|[[32 (number)|32]]
|[[64 (number)|64]]
|[[64 (number)|64]]
Line 242: Line 236:
|[[512 (number)|512]]
|[[512 (number)|512]]
|[[1024 (number)|1024]]
|[[1024 (number)|1024]]
!
|[[2048 (number)|2048]]
|[[2048 (number)|2048]]
|[[4096 (number)|4096]]
|[[4096 (number)|4096]]
|[[8192 (number)|8192]]
|[[8192 (number)|8192]]
|[[:ko:16384|16384]]
|16384
|[[32768 (number)|32768]]
|32768
|[[65536 (number)|65536]]
|[[65,536|65536]]
|131072
|131072
|262144
|262144
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|-
|-
|'''''x''{{sup|2}}'''
|'''''x''{{sup|2}}'''
|[[1 (number)|1]]
|[[1]]
|[[4 (number)|4]]
|[[9]]
|[[9 (number)|9]]
|[[16 (number)|16]]
|[[25 (number)|25]]
|[[25 (number)|25]]
|[[36 (number)|36]]
|[[36 (number)|36]]
Line 263: Line 256:
|[[64 (number)|64]]
|[[64 (number)|64]]
|[[81 (number)|81]]
|[[81 (number)|81]]
|[[100 (number)|100]]
|[[100]]
!
|[[121 (number)|121]]
|[[121 (number)|121]]
|[[144 (number)|144]]
|[[144 (number)|144]]
Line 276: Line 270:
|}
|}


== Evolution of the Arabic digit ==
{{anchor|glyph}}
[[Image:Evolution2glyph.png|x50px|left]]
The digit used in the modern Western world to represent the number 2 traces its roots back to the Indic [[Brahmic script]], where "2" was written as two horizontal lines. The modern [[Chinese written language|Chinese]] and [[Japanese writing system|Japanese]] languages (and Korean [[Hanja]]) still use this method. The [[Gupta script]] rotated the two lines 45&nbsp;degrees, making them diagonal. The top line was sometimes also shortened and had its bottom end curve towards the center of the bottom line. In the [[Devanagari|Nagari]] script, the top line was written more like a curve connecting to the bottom line. In the Arabic [[Ghubār numerals|Ghubar]] writing, the bottom line was completely vertical, and the digit looked 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 digit.<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]], digit 2 usually is of [[x-height]], for example, [[Image:Text figures 256.svg]].{{citation needed|date=January 2024}}
==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 Indic [[Brahmic script]], where "2" was written as two horizontal lines. The modern [[Chinese written language|Chinese]] and [[Japanese writing system|Japanese]] languages still use this method. The [[Gupta script]] rotated the two lines 45&nbsp;degrees, making them diagonal. The top line was sometimes also shortened and had its bottom end curve towards the center of the bottom line. In the [[Devanagari|Nagari]] script, the top line was written more like a curve connecting to the bottom line. In the Arabic [[Ghubār numerals|Ghubar]] writing, the bottom line was completely vertical, and the glyph looked 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 science ==
In fonts with [[text figures]], 2 usually is of [[x-height]], for example, [[Image:Text figures 256.svg]].
*The number of [[polynucleotide]] strands in a [[DNA]] [[double helix]].<ref>{{Cite web|url=https://www.nature.com/scitable/content/double-stranded-dna-6834149/|title=Double-stranded DNA|work=Scitable|publisher=Nature Education|access-date=2019-12-22|archive-date=2020-07-24|archive-url=https://web.archive.org/web/20200724191225/https://www.nature.com/scitable/content/double-stranded-dna-6834149/|url-status=live}}</ref>
*The first [[Magic number (physics)|magic number]].<ref>{{Cite web|url=https://www.sjsu.edu/faculty/watkins/magicnumbers2.htm|title=The Complete Explanation of the Nuclear Magic Numbers Which Indicate the Filling of Nucleonic Shells and the Revelation of Special Numbers Indicating the Filling of Subshells Within Those Shells|website=www.sjsu.edu|access-date=2019-12-22|archive-date=2019-12-02|archive-url=https://web.archive.org/web/20191202130317/http://www.sjsu.edu/faculty/watkins/magicnumbers2.htm|url-status=dead}}</ref>
*The [[atomic number]] of [[helium]].<ref>{{Cite journal|last=Bezdenezhnyi|first=V. P.|date=2004|title=Nuclear Isotopes and Magic Numbers|bibcode=2004OAP....17...11B|journal=Odessa Astronomical Publications|volume=17|pages=11}}</ref>


==In science==
== See also ==
*[[Binary number]]
[[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]].
*The [[atomic mass]] of [[deuterium]], an isotope of [[hydrogen]].
*The [[ASCII]] code of "[[Start Of Text|Start of Text]]".
*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]].
*[[2 Pallas]], a large asteroid in the main belt and the second asteroid ever to be discovered.
*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]].
*The number of [[brain]] and [[cerebellum|cerebellar]] [[cerebral hemispheres|hemispheres]].


==In technology==
== References ==
[[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==
===Judaism===
The number 2 is important in [[Judaism]], with one of the earliest references being that God ordered Noah to put two of every [[unclean animals|unclean animal]] ([[Book of Genesis|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 {{lang|he|שמור וזכור}} ("guard" and "remember"), as in "Guard the Shabbat day to sanctify it" ([[Deuteronomy|Deut.]] 5:12) and "Remember the Shabbat day to sanctify it" ([[Book of Exodus|Ex.]] 20:8). Two [[challah|challot]] (''lechem mishneh'') 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 testimonies 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 [[Dualistic cosmology|dualism]] for an overview. In [[Georg Wilhelm Friedrich Hegel|Hegel]]ian [[dialectic]], the process of [[Thesis, antithesis, synthesis|synthesis]] reconciles two different perspectives into one.
The ancient Sanskrit language of India, does not only have a [[singular number|singular]] and [[plural]] form for [[noun]]s, as do many other languages, but instead has, a singular (1) form, a [[Dual (number)|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 ({{lang|zh|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 brand names, 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" ({{lang|zh|易}}) in [[Cantonese language|Cantonese]].

In [[Finland]], two [[candle]]s are lit on [[Independence Day (Finland)|Independence Day]] and put on a windowsill, to remind passersby of the sacrifices of past generations in the struggle for independence and democracy.<ref>{{Cite news |url=http://search.proquest.com/docview/1543054640?accountid=14757 |title=Candles light nation's way: MESSAGE |last=UUSI-VIDENOJA |first=Hannu |date=6 December 1994 |work=South China Morning Post |access-date=9 May 2017 }}</ref>

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==
*In [[baseball]] scorekeeping, 2 is the position of the catcher.
* In [[basketball]]:
** A standard basket, known in the rules as a "field goal", is worth 2 points.
** In the [[3x3 (basketball)|3x3]] variant, successful shots from behind the "three-point" arc are instead worth 2 points (all other successful shots are worth 1 point).
** In play diagrams, "2" typically denotes the [[shooting guard]].
* In [[ice hockey]]:
** A team typically has two [[Defenceman|defencemen]] on the ice at any given time.
** Minor [[Penalty (ice hockey)|penalties]] last for 2 minutes or until the non-penalized team scores a goal, whichever comes first.
* In most [[rugby league]] competitions (though not the [[Super League]], which uses static squad numbering), the starting right wing wears number 2.
* In [[rugby union]] and [[rugby sevens|its sevens variant]], the starting hooker wears number 2.
* In [[association football]], a player scoring two goals in one match is said to have recorded a brace.

==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}}
* [[AD 2]], the second year of the [[Common Era]]
* Groups of two:
** [[Lists of pairs]]
** [[List of twins]]

==See also==
{{Portal|Mathematics}}
*[[Square (algebra)]]&nbsp;– (2 [[superscript]])

==References==
{{Reflist}}
{{Reflist}}


==External links==
==External links==
{{Portal|Mathematics}}
*[https://web.archive.org/web/20140201161638/http://numdic.com/2 The Number 2]
{{Commons and category|2 (number)|2 (number)}}
*[http://www.positiveintegers.org/2 The Positive Integer 2]
*[http://primes.utm.edu/curios/page.php/2.html Prime curiosities: 2]
*[http://primes.utm.edu/curios/page.php/2.html Prime curiosities: 2]


{{Wiktionary|two|both}}
{{Wiktionary|two|both}}
{{Commons and category|2|2 (number)}}


{{Integers|zero}}
{{Integers|zero}}
{{Number systems|state=expanded}}


{{Authority control}}
{{DEFAULTSORT:2 (Number)}}
{{DEFAULTSORT:2 (Number)}}
[[Category:2 (number)]]
[[Category:2 (number)]]

Latest revision as of 17:23, 21 September 2024

This article is about the number. For the years, see 2 BC and AD 2. For other uses, see II (disambiguation) and Number Two (disambiguation).
← 1 2 3 →
−1 0 1 2 3 4 5 6 7 8 9 →
Cardinaltwo
Ordinal2nd (second / twoth)
Numeral systembinary
Factorizationprime
Gaussian integer factorization
Prime1st
Divisors1, 2
Greek numeralΒ´
Roman numeralII, ii
Greek prefixdi-
Latin prefixduo-/bi-
Old English prefixtwi-
Binary102
Ternary23
Senary26
Octal28
Duodecimal212
Hexadecimal216
Greek numeralβ'
Arabic, Kurdish, Persian, Sindhi, Urdu٢
Ge'ez፪
Bengali২
Chinese numeral二，弍，貳
Devanāgarī२
Telugu౨
Tamil௨
Kannada೨
Hebrewב
ArmenianԲ
Khmer២
Maya numerals••
Thai๒
Georgian Ⴁ/ⴁ/ბ(Bani)
Malayalam൨
Babylonian numeral𒐖
Egyptian hieroglyph, Aegean numeral, Chinese counting rod||
Morse code.._ _ _

2 (two) is a number, numeral and digit. It is the natural number following 1 and preceding 3. It is the smallest and the only even prime number.

Because it forms the basis of a duality, it has religious and spiritual significance in many cultures.

As a word

Two is most commonly a determiner used with plural countable nouns, as in two days or I'll take these two.[1] Two is a noun when it refers to the number two as in two plus two is four.

Etymology of two

The word two is derived from the Old English words twā (feminine), tū (neuter), and twēġen (masculine, which survives today in the form twain).[2]

The pronunciation /tuː/, like that of who is due to the labialization of the vowel by the w, which then disappeared before the related sound. The successive stages of pronunciation for the Old English twā would thus be /twɑː/, /twɔː/, /twoː/, /twuː/, and finally /tuː/.[2]

Mathematics

An integer is determined to be even if it is divisible by two. When written in base 10, all multiples of 2 will end in 0, 2, 4, 6, or 8.[3] 2 is the smallest and the only even prime number, and the first Ramanujan prime.[4]

Geometry

A digon is a polygon with two sides (or edges) and two vertices.[5]: 52  Two distinct points in a plane are always sufficient to define a unique line in a nontrivial Euclidean space.[6]

Set Theory

A set that is a field has a minimum of two elements.[citation needed] A Cantor space is a topological space homeomorphic to the Cantor set.[citation needed]

Base 2

See also: Binary number

Binary is a number system with a base of two, it is used extensively in computing.[7]

List 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
2 × x 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 100 200
Division 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
2 ÷ x 2 1 0.6 0.5 0.4 0.3 0.285714 0.25 0.2 0.2 0.18 0.16 0.153846 0.142857 0.13 0.125 0.1176470588235294 0.1 0.105263157894736842 0.1
x ÷ 2 0.5 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10
Exponentiation 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
2x 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 131072 262144 524288 1048576
x2 1 9 25 36 49 64 81 100 121 144 169 196 225 256 289 324 361 400

Evolution of the Arabic digit

The digit used in the modern Western world to represent the number 2 traces its roots back to the Indic Brahmic script, where "2" was written as two horizontal lines. The modern Chinese and Japanese languages (and Korean Hanja) still use this method. The Gupta script rotated the two lines 45 degrees, making them diagonal. The top line was sometimes also shortened and had its bottom end curve towards the center of the bottom line. In the Nagari script, the top line was written more like a curve connecting to the bottom line. In the Arabic Ghubar writing, the bottom line was completely vertical, and the digit looked 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 digit.[8]

In fonts with text figures, digit 2 usually is of x-height, for example, .[citation needed]

In science

See also

References

  1. ^ Huddleston, Rodney D.; Pullum, Geoffrey K.; Reynolds, Brett (2022). A student's introduction to English grammar (2nd ed.). Cambridge, United Kingdom: Cambridge University Press. p. 117. ISBN 978-1-316-51464-1. OCLC 1255524478.
  2. ^ a b "two, adj., n., and adv.". Oxford English Dictionary (Online ed.). Oxford University Press. (Subscription or participating institution membership required.)
  3. ^ Sloane, N. J. A. (ed.). "Sequence A005843 (The nonnegative even numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-12-15.
  4. ^ "Sloane's A104272 : Ramanujan primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on 2011-04-28. Retrieved 2016-06-01.
  5. ^ Wilson, Robin (2014). Four Colors Suffice (Revised color ed.). Princeton University Press. ISBN 978-0-691-15822-8.
  6. ^ Carrell, Jim. "Chapter 1 | Euclidean Spaces and Their Geometry". MATH 307 Applied Linear Algebra (PDF).
  7. ^ "How computers see the world - Binary - KS3 Computer Science Revision". BBC Bitesize. Retrieved 2024-06-05.
  8. ^ 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
  9. ^ "Double-stranded DNA". Scitable. Nature Education. Archived from the original on 2020-07-24. Retrieved 2019-12-22.
  10. ^ "The Complete Explanation of the Nuclear Magic Numbers Which Indicate the Filling of Nucleonic Shells and the Revelation of Special Numbers Indicating the Filling of Subshells Within Those Shells". www.sjsu.edu. Archived from the original on 2019-12-02. Retrieved 2019-12-22.
  11. ^ Bezdenezhnyi, V. P. (2004). "Nuclear Isotopes and Magic Numbers". Odessa Astronomical Publications. 17: 11. Bibcode:2004OAP....17...11B.
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