0 (број) — разлика између измена

▲By the middle of the [[2nd millennium BC]], the [[Babylonian mathematics]] had a sophisticated [[sexagesimal]] positional numeral system. The lack of a positional value (or zero) was indicated by a ''space'' between sexagesimal numerals. In a tablet unearthed at [[Kish (Sumer)|Kish]] (dating to as early as 700&nbsp;BC), the scribe Bêl-bân-aplu used three hooks as a [[Free variables and bound variables|placeholder]] in the same [[Babylonian numerals|Babylonian system]].<ref name="multiref1">Kaplan, Robert. (2000). ''The Nothing That Is: A Natural History of Zero''. Oxford: Oxford University Press.</ref> By 300&nbsp;BC, a punctuation symbol (two slanted wedges) was co-opted to serve as this placeholder.<ref>{{Cite web |title=Zero |url=https://mathshistory.st-andrews.ac.uk/HistTopics/Zero/ |access-date=2021-09-07 |website=Maths History |language=en}}</ref><ref>{{Cite web |title=Babylonian mathematics: View as single page |url=https://www.open.edu/openlearn/ocw/mod/oucontent/view.php?printable=1&id=1976 |access-date=2021-09-07 |website=www.open.edu}}</ref>

▲Since the eight earliest Long Count dates appear outside the Maya homeland,<ref>Diehl, p. 186</ref> it is generally believed that the use of zero in the Americas predated the Maya and was possibly the invention of the [[Olmec]]s.<ref>{{Cite news |last=Mortaigne |first=Véronique |date=28 November 2014 |title=The golden age of Mayan civilisation – exhibition review |work=[[The Guardian]] |url=https://www.theguardian.com/culture/2014/nov/28/mayan-civilisation-paris-exhibition |url-status=live |access-date=10 October 2015 |archive-url=https://web.archive.org/web/20141128222215/http://www.theguardian.com/culture/2014/nov/28/mayan-civilisation-paris-exhibition |archive-date=28 November 2014}}</ref> Many of the earliest Long Count dates were found within the Olmec heartland, although the Olmec civilization ended by the {{nowrap|4th century BC}}, several centuries before the earliest known Long Count dates.

▲The [[Ancient Greece|ancient Greeks]] had no symbol for zero (μηδέν), 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 |url-status=dead |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> They seemed unsure about the status of zero as a number. They asked themselves, "How can nothing ''be'' something?", 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>{{Citation |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}}</ref>

▲[[File:P. Lund, Inv. 35a.jpg|thumb|лево|300px|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 |journal=Acta Historica Scientiarum Naturalium et Medicinalium |publisher=[[Dover Publications]] |year=1969 |isbn=978-0-486-22332-2 |edition=2 |volume=9 |pages=[https://archive.org/details/exactsciencesant00neug/page/n30 13]–14, plate 2 |pmid=14884919 |author-link=Otto E. Neugebauer |orig-year=1957 |url-access=registration}}</ref><ref name="Mercier">{{Citation |last=Mercier |first=Raymond |title=Consideration of the Greek symbol 'zero' |url=http://www.raymondm.co.uk/prog/GreekZeroSign.pdf |work=Home of Kairos}}</ref> in his work on [[mathematical astronomy]] called the ''Syntaxis Mathematica'', also known as the ''[[Almagest]]''.<ref name="Ptolemy">{{Citation |last=Ptolemy |title=Ptolemy's Almagest |pages=306–307 |year=1998 |orig-year=1984, {{circa}}150 |publisher=[[Princeton University Press]] |isbn=0-691-00260-6 |author-link=Ptolemy |translator-last=Toomer |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>{{Citation |last1=O'Connor |first1=J J |title=A history of Zero |url=http://mathshistory.st-andrews.ac.uk/HistTopics/Zero.html |publisher=MacTutor History of Mathematics |last2=Robertson |first2=E F}}</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 [[continuous function|continuously]] from {{nowrap|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 {{nowrap|0′0″ to 31′20″ to 0′0″}}, where 0′0″ 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′20″ {{radic|d(24−d)}}}} (a triangular pulse with [[convex lens|convex]] sides), where d was the digit function and 31′20″ was the sum of the radii of the Sun's and Moon's discs.<ref name="Pedersen">{{Citation |last=Pedersen |first=Olaf |title=A Survey of the Almagest |pages=232–235 |year=2010 |orig-year=1974 |publisher=Springer |isbn=978-0-387-84825-9 |author-link=Olaf Pedersen}}</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.

▲The earliest use of zero in the calculation of the [[Computus|Julian Easter]] occurred before AD{{nbs}}311, at the first entry in a table of [[epact]]s as preserved in an [[Ethiopia|Ethiopic]] document for the years AD{{nbs}}311 to 369, using a [[Ge'ez]] word for "none" (English translation is "0" elsewhere) alongside Ge'ez numerals (based on Greek numerals), which was translated from an equivalent table published by the [[Church of Alexandria]] in [[Medieval Greek]].<ref name="Neugebauer">{{Citation |last=Neugebauer |first=Otto |title=Ethiopic Astronomy and Computus |pages=25, 53, 93, 183, Plate I |year=2016 |orig-year=1979 |edition=Red Sea Press |publisher=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 AD{{nbs}}525 in an equivalent table, that was translated via the Latin ''nulla'' or "none" by [[Dionysius Exiguus]], alongside [[Roman numerals#Zero|Roman numerals]].<ref name="Dionysius">{{Citation |last=Deckers |first=Michael |title=Cyclus Decemnovennalis Dionysii – Nineteen Year Cycle of Dionysius |url=http://hbar.phys.msu.ru/gorm/chrono/paschata.htm |year=2003 |orig-year=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>

▲[[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}}, and Japanese records dated from the 18th century, describe how the {{nowrap|c. 4th century BC}} Chinese [[counting rods]] system enabled one to perform decimal calculations. As noted in [[Xiahou Yang Suanjing|Xiahou Yang's Suanjing]] (425–468 AD) that states that 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>{{Cite web |last=O'Connor |first=J.J. |date=Jan 2004 |title=Chinese numerals |url=https://mathshistory.st-andrews.ac.uk/HistTopics/Chinese_numerals/ |access-date=14 June 2020 |website=Mac Tutor |publisher=School of Mathematics and Statistics University of St Andrews, Scotland}}</ref> According to ''A History of Mathematics'', 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: 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> The counting rod system is considered a [[positional notation]] system.<ref>Crossley, Lun. 1999, p. 12 "the ancient Chinese system is a place notation system"</ref>