Editing Numeral system (section)

==History==
{{see also|Numerical digit#History}}
{{Expand section|date=July 2024}}
<div style="float:right;">
{| class="wikitable zebra"
|-
!Western Arabic
|0 ||1 ||2 ||3 ||4 ||5 ||6 ||7 ||8 ||9
|-
!Eastern Arabic
|٠ ||١ ||٢ ||٣ ||٤ ||٥ ||٦ ||٧ ||٨ ||٩
|-
!Persian
|۰ ||۱ ||۲ ||۳ ||۴ ||۵ ||۶ ||۷ ||۸ ||۹
|-
!Devanagari
|० ||१ ||२ ||३ ||४ ||५ ||६ ||७ ||८ ||९
|}
</div>
Early numeral systems varied across civilizations, with the Babylonians using a base-60 system, the Egyptians developing hieroglyphic numerals, and the Chinese employing rod numerals. The Mayans independently created a vigesimal (base-20) system that included a symbol for zero. Indian mathematicians, such as Brahmagupta in the 7th century, played a crucial role in formalizing arithmetic rules and the concept of zero, which was later refined by scholars like Al-Khwarizmi in the Islamic world. As these numeral systems evolved, the efficiency of positional notation and the inclusion of zero helped shape modern numerical representation, influencing global commerce, science, and technology. The first true written [[positional numeral system]] is considered to be the [[Hindu–Arabic numeral system]]. This system was established by the 7th&nbsp;century in India,<ref name="O'Connor and Robertson">O'Connor, J. J. and Robertson, E. F. [http://www-history.mcs.st-andrews.ac.uk/HistTopics/Arabic_numerals.html Arabic Numerals]. January 2001. Retrieved on 2007-02-20.</ref> but was not yet in its modern form because the use of the digit [[zero]] had not yet been widely accepted. Instead of a zero sometimes the digits were marked with dots to indicate their significance, or a space was used as a placeholder. The first widely acknowledged use of zero was in 876.<ref>{{cite web|url=https://www.ams.org/featurecolumn/archive/india-zero.html |title=All for Nought |work=Feature Column |author=Bill Casselman |author-link=Bill Casselman (mathematician) |publisher=AMS |date=February 2007}}</ref> The original numerals were very similar to the modern ones, even down to the [[glyph]]s used to represent digits.<ref name="O'Connor and Robertson"/>

[[Image:Maya.svg|thumb|left|150px|The digits of the Maya numeral system]]
By the 13th century, [[Western Arabic numerals]] were accepted in European mathematical circles ([[Fibonacci]] used them in his {{Lang|la|[[Liber Abaci]]}}). Initially met with resistance, Hindu–Arabic numerals gained wider acceptance in Europe due to their efficiency in arithmetic operations, particularly in banking and trade. The invention of the printing press in the 15th century helped standardize their use, as printed mathematical texts favored this system over Roman numerals. They began to enter common use in the 15th&nbsp;century.<ref>{{Cite web|last=Bradley|first=Jeremy|title=How Arabic Numbers Were Invented|url=https://www.theclassroom.com/how-to-identify-numbers-on-brass-from-india-12082499.html|access-date=2020-07-22|website=www.theclassroom.com}}</ref> By the end of the 20th&nbsp;century virtually all non-computerized calculations in the world were done with Arabic numerals, which have replaced native numeral systems in most cultures. By the 17th century, the system had become dominant in scientific works, influencing mathematical advancements by figures like Isaac Newton and René Descartes. In the 19th and 20th centuries, the widespread adoption of Arabic numerals facilitated global finance, engineering, and technological developments, forming the foundation for modern computing and digital data representation.

===Other historical numeral systems using digits===
The exact age of the [[Maya numerals]] is unclear, but it is possible that it is older than the Hindu–Arabic system. The system was [[vigesimal]] (base&nbsp;20), so it has twenty digits. The Mayas used a shell symbol to represent zero. Numerals were written vertically, with the ones place at the bottom. The [[Mayas]] had no equivalent of the modern [[decimal separator]], so their system could not represent fractions.{{Citation needed|date=November 2024}}

The [[Thai numerals|Thai numeral system]] is identical to the [[Hindu–Arabic numeral system]] except for the symbols used to represent digits. The use of these digits is less common in [[Thailand]] than it once was, but they are still used alongside Arabic numerals.<ref>{{cite news |title=Wissanu rejects dumping Thai numerals |url=https://www.bangkokpost.com/thailand/general/2318442/wissanu-rejects-dumping-thai-numerals |access-date=27 November 2024 |work=Bangkok Post |date=31 May 2022}}</ref>

The rod numerals, the written forms of [[counting rods]] once used by [[China|Chinese]] and [[Japan]]ese mathematicians, are a decimal positional system used for performing decimal calculations. Rods were placed on a counting board and slid forwards or backwards to change the decimal place. The ''[[Sunzi Suanjing|Sūnzĭ Suànjīng]]'', a mathematical treatise dated to between the 3rd and 5th centuries AD, provides detailed instructions for the system, which is thought to have been in use since at least the 4th century BC.<ref>{{MacTutor|class=HistTopics|id=Chinese_numerals|title=Chinese numerals|date=January 2004}}</ref> Zero was not initially treated as a number, but as a vacant position.<ref name="Crossley">{{Cite book |last1=Shen |first1=Kangshen |url=https://books.google.com/books?id=eiTJHRGTG6YC |title=The Nine Chapters on the Mathematical Art: Companion and Commentary |last2=Crossley |first2=John N. |last3=Lun |first3=Anthony W.-C. |publisher=Oxford University Press |year=1999 |isbn=978-0-19-853936-0 |page=35 |quote=zero was regarded as a number in India ... whereas the Chinese employed a vacant position |author1-mask=Shen Kanshen}}</ref> Later sources introduced conventions for the expression of zero and negative numbers. The use of a round symbol {{Lang|zh|〇}} for zero is first attested in the ''[[Mathematical Treatise in Nine Sections]]'' of 1247 AD.<ref name="Qin">{{Cite web |title=Mathematics in the Near and Far East |url=http://grmath4.phpnet.us/istoria/the_history_of%20math_greece/the_history_of%20math_greece_3-5.pdf |url-status=live |archive-url=https://web.archive.org/web/20131104120005/http://grmath4.phpnet.us/istoria/the_history_of%20math_greece/the_history_of%20math_greece_3-5.pdf |archive-date=4 November 2013 |access-date=7 June 2012 |website=grmath4.phpnet.us |page=262}}</ref> The origin of this symbol is unknown; it may have been produced by modifying a square symbol.<ref>{{cite book |last=Martzloff |first=Jean-Claude |title=A History of Chinese Mathematics |publisher=Springer |year=2007 |isbn=978-3-540-33783-6 |page=208 |translator-last1=Wilson |translator-first1=Stephen S.}}</ref> The [[Suzhou numerals]], a descendant of rod numerals, are still used today for some commercial purposes.{{Citation needed|date=November 2024}}

{| class="wikitable" style="text-align:center"
|+ Rod numerals (vertical)
|-
! style="width:50px" | 0
! style="width:50px" | 1
! style="width:50px" | 2
! style="width:50px" | 3
! style="width:50px" | 4
! style="width:50px" | 5
! style="width:50px" | 6
! style="width:50px" | 7
! style="width:50px" | 8
! style="width:50px" | 9
|-
| [[Image:Counting rod 0.png]]
| [[Image:Counting rod v1.png]]
| [[Image:Counting rod v2.png]]
| [[Image:Counting rod v3.png]]
| [[Image:Counting rod v4.png]]
| [[Image:Counting rod v5.png]]
| [[Image:Counting rod v6.png]]
| [[Image:Counting rod v7.png]]
| [[Image:Counting rod v8.png]]
| [[Image:Counting rod v9.png]]
|-
! style="width:50px" | –0
! style="width:50px" | –1
! style="width:50px" | –2
! style="width:50px" | –3
! style="width:50px" | –4
! style="width:50px" | –5
! style="width:50px" | –6
! style="width:50px" | –7
! style="width:50px" | –8
! style="width:50px" | –9
|-
| [[Image:Counting rod -0.png]]
| [[Image:Counting rod v-1.png]]
| [[Image:Counting rod v-2.png]]
| [[Image:Counting rod v-3.png]]
| [[Image:Counting rod v-4.png]]
| [[Image:Counting rod v-5.png]]
| [[Image:Counting rod v-6.png]]
| [[Image:Counting rod v-7.png]]
| [[Image:Counting rod v-8.png]]
| [[Image:Counting rod v-9.png]]
|}