Editing 0 (section)

===China===
[[File:Zero in Rod Calculus.png|thumb|right|alt=Five illustrated boxes from left to right contain a T-shape, an empty box, three vertical bars, three lower horizontal bars with an inverted wide T-shape above, and another empty box. Numerals underneath left to right are six, zero, three, nine, and zero|This is a depiction of zero expressed in Chinese [[counting rods]], based on the example provided by ''A History of Mathematics''. An empty space is used to represent zero.<ref name="Hodgkin" />]]
The ''[[Sunzi Suanjing|Sūnzĭ Suànjīng]]'', of unknown date but estimated to be dated from the 1st to {{nowrap|5th centuries AD}}, describe how the{{nowrap| 4th century BC}} Chinese [[counting rods]] system enabled one to perform decimal calculations. As noted in the ''[[Xiahou Yang Suanjing]]'' (425–468 AD), to multiply or divide a number by 10, 100, 1000, or 10000, all one needs to do, with rods on the counting board, is to move them forwards, or back, by 1, 2, 3, or 4 places.<ref>{{MacTutor|class=HistTopics|id=Chinese_numerals |title=Chinese numerals |date=January 2004}}</ref> The rods gave the decimal representation of a number, with an empty space denoting zero.<ref name="Hodgkin">{{Cite book |last=Hodgkin |first=Luke |url=https://archive.org/details/historyofmathema0000hodg |title=A History of Mathematics: From Mesopotamia to Modernity |date=2005 |publisher=Oxford University Press |isbn=978-0-19-152383-0 |page=[https://archive.org/details/historyofmathema0000hodg/page/85 85] |url-access=registration}}</ref><ref>{{Cite web |title=Chinese numerals |url=https://mathshistory.st-andrews.ac.uk/HistTopics/Chinese_numerals/ |access-date=2024-04-28 |website=Maths History |language=en}}</ref> The counting rod system is a [[positional notation]] system.<ref>{{harvnb|Shen|Crossley|Lun|1999|p= 12}}: "the ancient Chinese system is a place notation system"</ref><ref>{{Citation |last=Eberhard-Bréard |first=Andrea |title=Mathematics in China |date=2008 |pages=1371–1378 |editor-last=Selin |editor-first=Helaine |place=Dordrecht |publisher=Springer Netherlands |language=en |doi=10.1007/978-1-4020-4425-0_9453 |isbn=978-1-4020-4425-0 |encyclopedia=Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures}}.</ref>

Zero was not treated as a number at that time, 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 |first2=John N.|last2= Crossley |first3=Anthony W.-C. | last3=Lun | author1-mask= Shen Kanshen |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}}</ref> [[Qin Jiushao|Qín Jiǔsháo]]'s 1247 ''[[Mathematical Treatise in Nine Sections]]'' is the oldest surviving Chinese mathematical text using a round symbol ‘〇’ for zero.<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 |website=grmath4.phpnet.us |page=262 |access-date=7 June 2012 |archive-date=4 November 2013 |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 |url-status=live }}</ref> The origin of this symbol is unknown; it may have been produced by modifying a square symbol.<ref>{{cite book |first=Jean-Claude |last=Martzloff |translator-first1=Stephen S. |translator-last1=Wilson |title=A History of Chinese Mathematics |publisher=Springer |year=2007 |isbn=978-3-540-33783-6 |page=208}}</ref> Chinese authors had been familiar with the idea of negative numbers by the [[Han dynasty]] {{nowrap|(2nd century AD)}}, as seen in ''[[The Nine Chapters on the Mathematical Art]]''.<ref name="struik33">Struik, Dirk J. (1987). ''A Concise History of Mathematics''. New York: Dover Publications. pp. 32–33. "''In these matrices we find negative numbers, which appear here for the first time in history.''"</ref>