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0 (број) — разлика између измена

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м Враћене измене 109.245.38.213 (разговор) на последњу измену корисника SimplyFreddie
ознака: враћање
.
ознака: везе до вишезначних одредница
Ред 1:
{{Short description|Број}}
{{Природни број
| број=0
Линија 18 ⟶ 19:
| мертенс = 0
}}
 
'''0''' ('''нула''' или '''ништица''') је [[број]],<ref>{{Cite web |last=Matson |first=John |date=21 August 2009 |title=The Origin of Zero |url=http://www.scientificamerican.com/article/history-of-zero/ |access-date=24 April 2016 |website=[[Scientific American]] |publisher=[[Springer Nature]]}}</ref> [[нумерал]] и име [[глиф]]а који представља тај број. То је цео број који следи после броја [[-1 (број)|-1]], а претходи броју [[1 (број)|1]].
 
== У математици ==
Линија 31 ⟶ 33:
:''-{x}-''<sup>0</sup> = 1, ако је ''-{x}-'' различито од 0
:0<sup>0</sup> = 1
 
== Историја ==
{{рут}}
===Ancient Near East===
{| style="float:right; clear:right; text-align:center; border: 1px solid" align=right cellspacing=0 cellpadding=8
|-
!nfr<br>&nbsp;
|heart with trachea<br>beautiful, pleasant, good
|<hiero>F35</hiero>
|}
Ancient [[Egyptian numerals]] were of [[decimal|base 10]].<ref>{{Cite web |title=Egyptian numerals |url=http://mathshistory.st-andrews.ac.uk/HistTopics/Egyptian_numerals.html |access-date=21 December 2019 |website=mathshistory.st-andrews.ac.uk}}</ref> They used [[hieroglyphs]] for the digits and were not [[positional notation|positional]]. By 1770&nbsp;BC, the Egyptians had a symbol for zero in accounting texts. The symbol nfr, meaning beautiful, was also used to indicate the base level in drawings of tombs and pyramids, and distances were measured relative to the base line as being above or below this line.<ref>{{Cite book |last=Joseph |first=George Gheverghese |url=https://archive.org/details/crestpeacocknone00jose |title=The Crest of the Peacock: Non-European Roots of Mathematics |publisher=Princeton UP |year=2011 |isbn=978-0-691-13526-7 |edition=Third |page=[https://archive.org/details/crestpeacocknone00jose/page/n116 86] |url-access=registration}}</ref>
 
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>
 
===Pre-Columbian Americas===
[[File:Estela C de Tres Zapotes.jpg|thumb|upright|alt=illustration of a fractured inscribed stone with pre-Columbian glyphs and icons|The back of [[Epi-Olmec culture|Epi-Olmec]] stela C from [[Tres Zapotes]], the second oldest [[Mesoamerican Long Count calendar|Long Count]] date discovered. The numerals 7.16.6.16.18 translate to September, 32&nbsp;BC (Julian). The glyphs surrounding the date are thought to be one of the few surviving examples of [[Isthmian script|Epi-Olmec script]].]]
The [[Mesoamerican Long Count calendar]] developed in south-central Mexico and Central America required the use of zero as a placeholder within its [[vigesimal]] (base-20) positional numeral system. Many different glyphs, including this partial [[quatrefoil]]—[[File:MAYA-g-num-0-inc-v1.svg|alt=small illustration of a partial quatrefoil in right half, whitespace in left half]]—were used as a zero symbol for these Long Count dates, the earliest of which (on Stela 2 at Chiapa de Corzo, [[Chiapas]]) has a date of 36&nbsp;BC.{{efn|No long count date actually using the number 0 has been found before the 3rd century AD, but since the long count system would make no sense without some placeholder, and since Mesoamerican glyphs do not typically leave empty spaces, these earlier dates are taken as indirect evidence that the concept of 0 already existed at the time.}}
 
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.
 
===Classical antiquity===
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>
 
===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}}, 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>
 
== Види још ==
* [[Ништа]]
 
== Напомене ==
{{notelist}}
 
== Референце ==
{{Reflist}}
 
== Литература ==
{{Refbegin}}
* {{Cite book |last=Aczel |first=Amir D. |title=Finding Zero |publisher=Palgrave Macmillan |year=2015 |isbn=978-1-137-27984-2 |location=New York |author-link=Amir D. Aczel}}
* {{Cite book |last=Asimov |first=Isaac |title=Asimov on Numbers |publisher=Pocket Books |year=1978 |isbn=978-0-671-82134-0 |location=New York |chapter=Nothing Counts |oclc=1105483009 |author-link=Isaac Asimov}}
* {{Cite book |last=Barrow |first=John D. |title=The Book of Nothing |publisher=Vintage |year=2001 |isbn=0-09-928845-1 |author-link=John D. Barrow}}
* {{Cite book |last=Woodford |first=Chris |url=https://books.google.com/books?id=My7Zr0aP2L8C&pg=PA9 |title=Digital Technology |date=2006 |publisher=Evans Brothers |isbn=978-0-237-52725-9 |ref={{sfnref|Chris Woodford|2006}}}}
* {{Cite book |last=Bourbaki |first=Nicolas |title=Elements of the History of Mathematics |publisher=Springer-Verlag |year=1998 |isbn=3-540-64767-8 |location=Berlin, Heidelberg, and New York |author-link=Nicolas Bourbaki}}
* {{Cite book |last=Diehl |first=Richard A. |title=The Olmecs: America's First Civilization |publisher=Thames & Hudson |year=2004 |location=London}}
* {{Cite book |last=Ifrah |first=Georges |title=The Universal History of Numbers: From Prehistory to the Invention of the Computer |publisher=Wiley |year=2000 |isbn=0-471-39340-1}}
* {{Cite book |last=Kaplan |first=Robert |title=The Nothing That Is: A Natural History of Zero |publisher=Oxford University Press |year=2000}}
* {{Cite book |last=Seife |first=Charles |title=Zero: The Biography of a Dangerous Idea |publisher=Penguin USA |year=2000 |isbn=0-14-029647-6 |author-link=Charles Seife}}
* {{Cite book |title=The Oxford Dictionary, Thesaurus and Wordpower Guide |publisher=[[Oxford University Press]] |year=2001 |isbn=978-0-19-860373-3 |editor-last=Soanes |editor-first=Catherine |edition=2nd |location=New York |type=Hardback |editor-last2=Waite |editor-first2=Maurice |editor-last3=Hawker |editor-first3=Sara}}
{{Refend}}
 
== Спољашње везе ==
{{Commonscat|0 (number)}}
* [http://www.b92.net/zivot/nauka.php?yyyy=2008&mm=11&dd=10&nav_id=327814 B92 Broj sa najviše muka]
* {{Cite web |title=aught (n.2) |url=https://www.etymonline.com/word/aught#etymonline_v_18939 |access-date=September 14, 2021 |website=[[Online Etymology Dictionary]]}}
* {{Cite web |title=Zero {{!}} Definition of Zero by Oxford Dictionary on Lexico.com also meaning of Zero |url=https://www.lexico.com/en/definition/zero |access-date=2020-08-09 |website=Lexico Dictionaries {{!}} English |language=en}}
 
{{клица-математика}}
Преузето из „https://sr.wikipedia.org/wiki/0_(број)”