Editing 0 (section)

===Classical antiquity===
The [[Ancient Greece|ancient Greeks]] had no symbol for zero (μηδέν, pronounced 'midén'), and did not use a digit placeholder for it.<ref>{{Cite web |last=Wallin |first=Nils-Bertil |date=19 November 2002 |title=The History of Zero |url=http://yaleglobal.yale.edu/about/zero.jsp |archive-url=https://web.archive.org/web/20160825124525/http://yaleglobal.yale.edu/about/zero.jsp |archive-date=25 August 2016 |access-date=1 September 2016 |website=YaleGlobal online |publisher=The Whitney and Betty Macmillan Center for International and Area Studies at Yale.}}</ref> According to mathematician [[Charles Seife]], the ancient Greeks did begin to adopt the Babylonian placeholder zero for their work in [[Ancient Greek astronomy|astronomy]] after 500 BC, representing it with the lowercase Greek letter ''ό'' (''όμικρον'': [[omicron]]). However, after using the Babylonian placeholder zero for astronomical calculations they would typically convert the numbers back into [[Greek numerals]]. Greeks seemed to have a philosophical opposition to using zero as a number.<ref name="Seife2000">{{cite book | first = Charles | last = Seife | date = 1 September 2000 | title = Zero: The Biography of a Dangerous Idea | publisher = Penguin | page = 39 | isbn = 978-0-14-029647-1 | oclc = 1005913932 | url = https://books.google.com/books?id=obJ70nxVYFUC | access-date = 30 April 2022 | author-link= Charles Seife }}</ref> Other scholars give the Greek partial adoption of the Babylonian zero a later date, with neuroscientist Andreas Nieder giving a date of after 400 BC and mathematician Robert Kaplan dating it after the [[Wars of Alexander the Great|conquests of Alexander]].<ref name="Nieder2019">{{cite book | first = Andreas | last = Nieder | date = 19 November 2019 | title = A Brain for Numbers: The Biology of the Number Instinct | publisher = MIT Press | page = 286 | isbn = 978-0-262-35432-5 | url = https://books.google.com/books?id=x4y5DwAAQBAJ&pg=PA286 | access-date = 30 April 2022   }}</ref>{{sfn|Kaplan|2000|p=17}}

Greeks seemed unsure about the status of zero as a number. Some of them asked themselves, "How can not being be?", leading to philosophical and, by the [[medieval]] period, religious arguments about the nature and existence of zero and the [[vacuum]]. The [[Zeno's paradoxes|paradoxes]] of [[Zeno of Elea]] depend in large part on the uncertain interpretation of zero.<ref>{{cite encyclopedia |last=Huggett |first=Nick |title=Zeno's Paradoxes |date=2019 |url=https://plato.stanford.edu/archives/win2019/entries/paradox-zeno/ |encyclopedia=The Stanford Encyclopedia of Philosophy |editor-last=Zalta |editor-first=Edward N. |edition=Winter 2019 |publisher=Metaphysics Research Lab, Stanford University |access-date=2020-08-09 |archive-date=10 January 2021 |archive-url=https://web.archive.org/web/20210110135804/https://plato.stanford.edu/archives/win2019/entries/paradox-zeno/ |url-status=live }}</ref>

[[File:P. Lund, Inv. 35a.jpg|thumb|upright=1.4|alt=Fragment of papyrus with clear Greek script, lower-right corner suggests a tiny zero with a double-headed arrow shape above it|Example of the early Greek symbol for zero (lower right corner) from a 2nd-century papyrus]]
By AD{{nbsp}}150, [[Ptolemy]], influenced by [[Hipparchus]] and the [[Babylonia]]ns, was using a symbol for zero ({{overset|—|°}})<ref>{{Cite book |last=Neugebauer |first=Otto |url=https://archive.org/details/exactsciencesant00neug |title=The Exact Sciences in Antiquity |publisher=[[Dover Publications]] |year=1969 |isbn=978-0-486-22332-2 |edition=2  |pages=[https://archive.org/details/exactsciencesant00neug/page/n30 13]–14, plate 2  |author-link=Otto E. Neugebauer |orig-date=1957 |url-access=registration}}</ref><ref name="Mercier">{{cite web |last=Mercier |first=Raymond |title=Consideration of the Greek symbol 'zero' |url=http://www.raymondm.co.uk/prog/GreekZeroSign.pdf |work=Home of Kairos |access-date=28 March 2020 |archive-date=5 November 2020 |archive-url=https://web.archive.org/web/20201105113109/http://www.raymondm.co.uk/prog/GreekZeroSign.pdf |url-status=live }}{{self-published inline|date=November 2023}}</ref> in his work on [[mathematical astronomy]] called the ''Syntaxis Mathematica'', also known as the ''[[Almagest]]''.<ref name="Ptolemy">{{cite book |last=Ptolemy |title=Ptolemy's Almagest |pages=306–307 |year=1998 |orig-date=1984, {{circa}}150 |publisher=[[Princeton University Press]] |isbn=0-691-00260-6 |author-link=Ptolemy |translator-last=Toomer | title-link= Almagest |translator-first=G. J. |translator-link=Gerald J. Toomer}}</ref> This [[Greek numerals#Hellenistic zero|Hellenistic zero]] was perhaps the earliest documented use of a numeral representing zero in the Old World.<ref>{{cite web |last1=O'Connor |first1=J. J. |last2=Robertson |first2=E. F. |title=A history of Zero |url=http://mathshistory.st-andrews.ac.uk/HistTopics/Zero.html |url-status=live |archive-url=https://web.archive.org/web/20200407074239/http://mathshistory.st-andrews.ac.uk/HistTopics/Zero.html |archive-date=7 April 2020 |access-date=28 March 2020 |publisher=MacTutor History of Mathematics}}</ref> Ptolemy used it many times in his ''Almagest'' (VI.8) for the magnitude of [[solar eclipse|solar]] and [[lunar eclipse]]s. It represented the value of both [[digit (unit)|digit]]s and [[Minute and second of arc|minutes]] of immersion at first and last contact. Digits varied continuously from 0 to 12 to 0 as the Moon passed over the Sun (a triangular pulse), where twelve digits was the [[angular diameter]] of the Sun. Minutes of immersion was tabulated from 0{{prime}}0{{pprime}} to 31{{prime}}20{{pprime}} to 0{{prime}}0{{pprime}}, where 0{{prime}}0{{pprime}} used the symbol as a placeholder in two positions of his [[sexagesimal]] positional numeral system,{{efn|Each place in Ptolemy's sexagesimal system was written in [[Greek numerals]] from {{nowrap|0 to 59}}, where 31 was written λα meaning 30+1, and 20 was written κ meaning 20.}} while the combination meant a zero angle. Minutes of immersion was also a continuous function {{nowrap|{{sfrac|1|12}} 31{{prime}}20{{pprime}} {{radic|d(24−d)}}}} (a triangular pulse with [[convex lens|convex]] sides), where d was the digit function and 31{{prime}}20{{pprime}} was the sum of the radii of the Sun's and Moon's discs.<ref name="Pedersen">{{cite book |last=Pedersen |first=Olaf |title=A Survey of the Almagest |  series= Sources and Studies in the History of Mathematics and Physical Sciences | doi= 10.1007/978-0-387-84826-6_7 |pages=232–235 |year=2010 |orig-date=1974 |publisher=Springer |isbn=978-0-387-84825-9 |author-link=Olaf Pedersen | editor= Alexander Jones}}</ref> Ptolemy's symbol was a placeholder as well as a number used by two continuous mathematical functions, one within another, so it meant zero, not none. Over time, Ptolemy's zero tended to increase in size and lose the [[overline]], sometimes depicted as a large elongated 0-like omicron "Ο" or as omicron with overline "ō" instead of a dot with overline.<ref>{{cite web |title=Proposal to encode the Greek Zero in the UCS |url=https://www.unicode.org/L2/L2004/04054-greek-zero.pdf |date=2024-07-31 |archive-url=http://web.archive.org/web/20221007235444/https://unicode.org/L2/L2004/04054-greek-zero.pdf |archive-date=2022-10-07 |url-status=live}}</ref>

The earliest use of zero in the calculation of the [[Computus|Julian Easter]] occurred before AD{{spaces}}311, at the first entry in a table of [[epact]]s as preserved in an [[Ethiopia|Ethiopic]] document for the years 311 to 369, using a [[Geʽez]] word for "none" (English translation is "0" elsewhere) alongside Geʽez numerals (based on Greek numerals), which was translated from an equivalent table published by the [[Church of Alexandria]] in [[Medieval Greek]].<ref name="Neugebauer">{{cite book |last=Neugebauer |first=Otto |title=Ethiopic Astronomy and Computus |pages=25, 53, 93, 183, Plate I |year=2016 |publisher=Red Sea Press |orig-date=1979 |edition=Red Sea Press |isbn=978-1-56902-440-9 |author-link=Otto Neugebauer}}. The pages in this edition have numbers six less than the same pages in the original edition.</ref> This use was repeated in 525 in an equivalent table, that was translated via the Latin {{lang|la|nulla}} ("none") by [[Dionysius Exiguus]], alongside [[Roman numerals#Zero|Roman numerals]].<ref name="Dionysius">{{cite web |last=Deckers |first=Michael |title=Cyclus Decemnovennalis Dionysii |trans-title= Nineteen Year Cycle of Dionysius |url=http://hbar.phys.msu.ru/gorm/chrono/paschata.htm |year=2003 |orig-date=525 |archive-url=https://web.archive.org/web/20190115083618/http://hbar.phys.msu.ru/gorm/chrono/paschata.htm |archive-date=15 January 2019}}</ref> When division produced zero as a remainder, ''nihil'', meaning "nothing", was used. These medieval zeros were used by all future medieval [[computus|calculators of Easter]]. The initial "N" was used as a zero symbol in a table of Roman numerals by [[Bede]]—or his colleagues—around AD{{nbsp}}725.<ref name="zero">C. W. Jones, ed., ''Opera Didascalica'', vol. 123C in ''Corpus Christianorum, Series Latina''.</ref>

In most [[History of mathematics|cultures]], 0 was identified before the idea of negative things (i.e., quantities less than zero) was accepted.{{Citation needed |date=June 2024}}