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{{Short description|Integer number 2}}
{{Short description|Natural number}}
{{Hatnote|This article is about the number. For the years, see [[2 BC]] and [[AD 2]]. For other uses, see [[2 (disambiguation)]], [[II (disambiguation)]], and [[Number Two (disambiguation)]].}}
{{Hatnote|This article is about the number. For the years, see [[2 BC]] and [[AD 2]]. For other uses, see [[2 (disambiguation)]], [[II (disambiguation)]], and [[Number Two (disambiguation)]].}}
{{pp-vandalism|small=yes}}
{{pp-vandalism|small=yes}}
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== Mathematics ==
== Mathematics ==
The number 2 is the second natural number after [[1]]. Each natural number, including 2, is constructed by succession, that is, by adding 1 to the previous natural number.<ref>{{cite book| last1=Colman| first1=Samuel| editor-last=Coan| editor-first=C. Arthur| title=''Nature's Harmonic Unity: A Treatise on Its Relation to Proportional Form''| publisher=G.P. Putnam's Sons| location=New York and London| year=1912| url=https://archive.org/details/naturesharmonic00coangoog/page/n26/mode/2up|page=10}}</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>
The number 2 is the second natural number, after [[1]]. Each natural number, including 2, is constructed by succession, that is, by adding 1 to the previous natural number.<ref>{{cite book| last1=Colman| first1=Samuel| editor-last=Coan| editor-first=C. Arthur| title=''Nature's Harmonic Unity: A Treatise on Its Relation to Proportional Form''| publisher=G.P. Putnam's Sons| location=New York and London| year=1912| url=https://archive.org/details/naturesharmonic00coangoog/page/n26/mode/2up|page=10}}</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 |archive-date=2010-12-29 |archive-url=https://web.archive.org/web/20101229032520/https://oeis.org/A002201 |url-status=live }}</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 |archive-date=2012-05-25 |archive-url=https://web.archive.org/web/20120525075430/https://oeis.org/A004490 |url-status=live }}</ref>


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> more generally, in any even base, even numbers will end with an even digit.
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> more generally, in any even base, even numbers will end with an even digit.


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>
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 |archive-date=2024-06-05 |access-date=2024-06-05 |archive-url=https://web.archive.org/web/20240605154649/https://personal.math.ubc.ca/~carrell/307_chap1.pdf |url-status=live }}</ref>


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 [[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>


[[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>
[[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"
! style="width:105px;" |[[Multiplication]]
!1
!2
!3
!4
!5
!6
!7
!8
!9
!10
!11
!12
!13
!14
!15
!16
!20
!25
!50
!100
!1000
|-
|'''2 * ''x'''''
|'''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]]
|[[40 (number)|40]]
|[[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
!width="5px"|
!11
!12
!13
!14
!15
!16
!17
!18
!19
!20
|-
|'''2 ÷ ''x'''''
|'''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.{{overline|16}}
|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'''
|0.5
|1
|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'''
|4
|8
|[[16 (number)|16]]
|[[32 (number)|32]]
|[[64 (number)|64]]
|128
|256
|512
|1024
!
|[[2048 (number)|2048]]
|[[4096]]
|[[8192]]
|16384
|32768
|65536
|131072
|262144
|524288
|1048576
|-
|'''''x''{{sup|2}}'''
|1
|4
|[[9 (number)|9]]
|16
|[[25 (number)|25]]
|[[36 (number)|36]]
|[[49 (number)|49]]
|64
|[[81 (number)|81]]
|100
!
|121
|[[144 (number)|144]]
|169
|196
|225
|256
|289
|324
|361
|400
|}


== As a word ==
== 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.''
''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. |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.''


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 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>
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== In science ==
== In science ==
* The first [[Magic number (physics)|magic number]] - number of electrons in the innermost electron shell of an atom.<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 first [[Magic number (physics)|magic number]] - number of electrons in the innermost electron shell of an atom.<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|last1=Watkins|first1=Thayer|publisher=San José State University|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 ==
== See also ==
*[[Binary number]]
*[[Binary number]]
*[[−2]]


== References ==
== References ==

Latest revision as of 18:24, 3 November 2025

Template:Short description Script error: No such module "Hatnote". Template:Pp-vandalism Template:Infobox number

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.

Mathematics

The number 2 is the second natural number, after 1. Each natural number, including 2, is constructed by succession, that is, by adding 1 to the previous natural number.[1] 2 is the smallest and the only even prime number, and the first Ramanujan prime.[2] It is also the first superior highly composite number,[3] and the first colossally abundant number.[4]

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;[5] more generally, in any even base, even numbers will end with an even digit.

A digon is a polygon with two sides (or edges) and two vertices.[6]Template:Rp Two distinct points in a plane are always sufficient to define a unique line in a nontrivial Euclidean space.[7]

A set that is a field has a minimum of two elements.[8]

Binary is a number system with a base of two, it is used extensively in computing.[9]

List of basic calculations

Multiplication 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 20 25 50 100 1000
2 * x 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 40 50 100 200 2000
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 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 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 289 324 361 400

As a word

Two is most commonly a determiner used with plural countable nouns, as in two days or I'll take these two.[10] Two is a noun when it refers to the number two as in two plus two is four.

The word two is derived from the Old English words Script error: No such module "Lang". (feminine), Script error: No such module "Lang". (neuter), and Script error: No such module "Lang". (masculine, which survives today in the form twain).[11]

Evolution of the Arabic digit

File:Evolution2glyph.png

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.[12]

In science

  • The first magic number - number of electrons in the innermost electron shell of an atom.[13]

See also

References

Template:Reflist

External links

Script error: No such module "Portal". Template:Sister project

Template:Sister project

Template:Integers

Template:Authority control

  1. ↑ Script error: No such module "citation/CS1".
  2. ↑ Script error: No such module "citation/CS1".
  3. ↑ Script error: No such module "citation/CS1".
  4. ↑ Script error: No such module "citation/CS1".
  5. ↑ Template:Cite OEIS
  6. ↑ Script error: No such module "citation/CS1".
  7. ↑ Script error: No such module "citation/CS1".
  8. ↑ Script error: No such module "citation/CS1".
  9. ↑ Script error: No such module "citation/CS1".
  10. ↑ Script error: No such module "citation/CS1".
  11. ↑ Script error: No such module "template wrapper". Template:OEDsub
  12. ↑ 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
  13. ↑ Script error: No such module "citation/CS1".
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