View source for 2

{{Short description|Integer number 2}}
{{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)]].}}
{{pp-vandalism|small=yes}}
{{Infobox number
|number=2
|ordinal=2nd (second)
|numeral=[[binary numeral system|binary]]
|gaussian integer factorization = <math>(1 + i)(1 - i)</math>
|prime=1st
|divisor=1, 2
|roman =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]], [[Central Kurdish|Kurdish]], [[Persian language|Persian]], [[Sindhi language|Sindhi]], [[Urdu numerals|Urdu]]
|lang2 symbol={{resize|150%|٢}}
|lang3=[[Ge'ez alphabet|Ge'ez]]
|lang3 symbol=፪
|lang4=[[Bengali numerals|Bengali]]
|lang4 symbol={{resize|150%|২}}
|lang5=[[Chinese numeral]]
|lang5 symbol=二，弍，貳
|lang6=[[Devanāgarī]]
|lang6 symbol={{resize|150%|२}}
|lang7=[[Indian numerals#Telugu numerals and their names|Telugu]]
|lang7 symbol={{resize|150%|౨}}
|lang8=[[Tamil numerals|Tamil]]
|lang8 symbol={{resize|150%|௨}}
|lang9=[[Kannada numerals|Kannada]]
|lang9 symbol={{resize|150%|೨}}
|lang10=[[Hebrew numerals|Hebrew]]
|lang10 symbol={{resize|150%|ב}}
|lang11=[[Armenian numerals|Armenian]]|lang11 symbol=Բ|lang12=[[Khmer numerals|Khmer]]
|lang12 symbol=២
|lang13=[[Maya numerals]]|lang13 symbol=••|lang14=[[Thai numerals|Thai]]
|lang14 symbol=๒
|lang15=[[Georgian numerals|Georgian]]	
|lang15 symbol={{resize|130%| Ⴁ/ⴁ/ბ}}([[Bani (letter)|Bani]])
|lang16=[[Malayalam numerals|Malayalam]]
|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]].

Because it forms the basis of a [[Dualistic cosmology|duality]], it has [[Religion|religious]] and [[Spirituality|spiritual]] significance in many [[Culture|cultures]].

== As a word ==
''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'' ===
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/>

== Mathematics ==
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> It is also the first [[superior highly composite number]],<ref>{{Cite web |title=A002201 - OEIS |url=https://oeis.org/A002201 |access-date=2024-11-28 |website=oeis.org}}</ref> and the first [[colossally abundant number]].<ref>{{Cite web |title=A004490 - OEIS |url=https://oeis.org/A004490 |access-date=2024-11-28 |website=oeis.org}}</ref>

=== Geometry ===
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 ===
A [[Set theory|set]] that is a [[field (mathematics)|field]] has a minimum of two [[Element (mathematics)|elements]].<ref>{{cite web| url=https://proofwiki.org/wiki/Field_Contains_at_least_2_Elements|title=Field Contains at least 2 Elements}}</ref> A [[Cantor space]] is a [[topological space]] <math>2^\mathbb{N}</math> [[homeomorphic]] to the [[Cantor set]].{{Citation needed|date=September 2024}}

== 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 ==
{|class="wikitable" style="text-align: center; background: white"
|+
![[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 (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]]
|[[200 (number)|200]]
|}

{|class="wikitable" style="text-align: center; background: white"
|-
!width="105px"|[[Division (mathematics)|Division]]
!1
!2
!3
!4
!5
!6
!7
!8
!9
!10
!width="5px"|
!11
!12
!13
!14
!15
!16
!17
!18
!19
!20
|-
|'''2 ÷ ''x'''''
|'''2'''
| rowspan="2"|[[1]]
|0.{{overline|6}}
|0.5
|0.4
|0.{{overline|3}}
|0.{{overline|285714}}
|0.25
|0.{{overline|2}}
|0.2
!
|0.{{overline|18}}
|0.1{{overline|6}}
|0.{{overline|153846}}
|0.{{overline|142857}}
|0.1{{overline|3}}
|0.125
|0.{{overline|1176470588235294}}
|0.{{overline|1}}
|0.{{overline|105263157894736842}}
|0.1
|-
|'''''x'' ÷ 2'''
|[[One half|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]]
|}

{|class="wikitable" style="text-align: center; background: white"
|-
!width="105px"|[[Exponentiation]]
!1
!2
!3
!4
!5
!6
!7
!8
!9
!10
!width="5px"|
!11
!12
!13
!14
!15
!16
!17
!18
!19
!20
|-
|'''2{{sup|''x''}}'''
|'''2'''
| rowspan="2" |[[4]]
|[[8]]
| rowspan="2" |[[16 (number)|16]]
|[[32 (number)|32]]
|[[64 (number)|64]]
|[[128 (number)|128]]
|[[256 (number)|256]]
|[[512 (number)|512]]
|[[1024 (number)|1024]]
!
|[[2048 (number)|2048]]
|[[4096 (number)|4096]]
|[[8192 (number)|8192]]
|16384
|32768
|[[65,536|65536]]
|131072
|262144
|524288
|1048576
|-
|'''''x''{{sup|2}}'''
|[[1]]
|[[9]]
|[[25 (number)|25]]
|[[36 (number)|36]]
|[[49 (number)|49]]
|[[64 (number)|64]]
|[[81 (number)|81]]
|[[100]]
!
|[[121 (number)|121]]
|[[144 (number)|144]]
|[[169 (number)|169]]
|[[196 (number)|196]]
|[[225 (number)|225]]
|[[256 (number)|256]]
|[[289 (number)|289]]
|[[324 (number)|324]]
|[[361 (number)|361]]
|[[400 (number)|400]]
|}

== Evolution of the Arabic digit ==
[[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}}

== In science ==
*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>

== See also ==
*[[Binary number]]

== References ==
{{Reflist}}

==External links==
{{Portal|Mathematics}}
{{Commons and category|2 (number)|2 (number)}}
*[http://primes.utm.edu/curios/page.php/2.html Prime curiosities: 2]

{{Wiktionary|two|both}}

{{Integers|zero}}

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