0

Whole number Zero other uses 0 (disambiguation) and Zero (disambiguation) For technical reasons, "0#" and ":0" redirect here. For the concept in set theory, see Zero sharp. For the keyboard symbols, see List of emoticons. the letter O December 2019 0 0, zero, nought, naught, nil, "oh" (oʊ) Zeroth, noughth, 0th nulli- Arabic, Kurdish, Persian, Sindhi, Urdu 150% ٠ Hindu numerals 150% ० Santali 150% ᱐ Chinese 零, 〇 Burmese ၀ Khmer ០ Thai ๐ Assamese, Bengali ০ Maya numerals 𝋠 Morse code _ _ _ _ _ 0 (zero, ˈ z iː . ɹ oʊ) is a number representing an empty quantity. Adding zero to or subtracting zero from any number leaves that number unchanged. In mathematical terminology, 0 is the additive identity of the integers, rational numbers, real numbers, complex numbers, and algebraic structures. Multiplying any number by 0 results in 0; therefore, division by zero is generally regarded as undefined in arithmetic. Any number to the power of 0 equals 1, except that zero to the power of zero is sometimes regarded as undefined. As a numerical digit, 0 plays a crucial role in positional notation (i.e., place value notation): it means that the zero position does not increase or decrease the number's total value. For example, 205 in decimal notation means two hundreds, no tens, and five ones, which equals two hundreds plus five ones. The same principle applies in place-value notations that uses a base other than ten, such as binary and hexadecimal notations. This use of zero derives from Indian mathematics, which was transmitted to Europe by medieval Islamic mathematicians and popularized by Fibonacci. It was independently used by the Maya civilization. Common names for the number 0 in English include zero, nought, naught (n ɔː t), and nil. In contexts where at least one adjacent digit distinguishes it from the letter O, the number is sometimes pronounced as oh or o (oʊ). Informal or slang terms for 0 include zilch and zip. Historically, ought, aught (ɔː t), and cipher have also been used. Etymology Names for the number 0 Names for the number 0 in English The word zero came into the English language via French fr zéro from the Italian it zero, a contraction of the Venetian vec zevero form of Italian it zefiro, itself borrowed from Arabic ar ṣafira or ar ṣifr. Douglas Harper 2011 https://www.etymonline.com/index.php?allowed_in_frame=0&search=zero&searchmode=none Zero https://web.archive.org/web/20170703014638/http://www.etymonline.com/index.php?allowed_in_frame=0&search=zero&searchmode=none 3 July 2017 Etymonline ""figure which stands for naught in the Arabic notation," also "the absence of all quantity considered as quantity", c. 1600, from French zéro or directly from Italian zero, from Medieval Latin zephirum, from Arabic sifr "cipher", translation of Sanskrit sunya-m "empty place, desert, naught" none Menninger Karl https://books.google.com/books?id=BFJHzSIj2u0C Number Words and Number Symbols: A cultural history of numbers Courier Dover Publications 1992 978-0-486-27096-8 399–404 5 January 2016 none December 2011 zero, n. http://www.oed.com/view/Entry/232803?rskey=zGcSoq&result=1&isAdvanced=false live https://www.webcitation.org/65yd7ur9u?url=http://www.oed.com/view/Entry/232803?rskey=zGcSoq&result=1&isAdvanced=false 7 March 2012 4 March 2012 OED Online Oxford University Press French zéro (1515 in Hatzfeld & Darmesteter) or its source Italian zero, for *zefiro, Arabic çifr. none In pre-Islamic time the word ar ṣifr (Arabic ar صفر) had the meaning "empty". ar Sifr evolved to mean zero when it was used to translate sa śūnya (sa शून्य) from India.Smithsonian Institution. 0_UyAQAAMAAJ Oriental Elements of Culture in the Occident 518. Annual Report of the Board of Regents of the Smithsonian Institution; Harvard University Archives. "Sifr occurs in the meaning of "empty" even in the pre-Islamic time. ... Arabic sifr in the meaning of zero is a translation of the corresponding India sunya." Jan Gullberg 1997 Mathematics: From the Birth of Numbers W.W. Norton & Co. 978-0-393-04002-9 26 Zero derives from Hindu sunya – meaning void, emptiness – via Arabic sifr, Latin cephirum, Italian zevero. Robert Logan 2010 The Poetry of Physics and the Physics of Poetry World Scientific 978-981-4295-92-5 38 The idea of sunya and place numbers was transmitted to the Arabs who translated sunya or "leave a space" into their language as sifr. The earliest known use of zero as a loanword in English literature was 1598.The Origin Of The Word 'Zero' https://www.sciencefriday.com/articles/the-origin-of-the-word-zero/ Science Friday 17 July 2018 2025-11-27 en-US The Italian mathematician Fibonacci (1170 1250), who grew up in North Africa and is credited with introducing the decimal system to Europe, used the term la-x-medieval zephyrum. This became it zefiro in Italian, and was then contracted to vec zero via the Venetian form vec zevero. The Italian word it Wikt:zefiro zefiro was already in existence (meaning "west wind" from Latin and Greek la Zephyrus) and may have influenced the spelling when transcribing Arabic ar ṣifr.Ifrah 2000 589. Modern usage Depending on the context, there may be different words used for the number zero, or the concept of zero. For the simple notion of lacking, the words "nothing" (although this is not accurate) and "none" are often used. The English words "nought" or "naught", "nil", and null are also synonymous.Collins – Free online dictionary 19 May 2026 https://www.collinsdictionary.com/dictionary/english/noughtCollins – Free online dictionary, thesaurus and reference materials – nill 19 May 2026 https://www.collinsdictionary.com/dictionary/english/nil It is often called "oh" in the context of reading out a string of digits, such as telephone numbers, street addresses, credit card numbers, military time, or years. For example, the area code 201 may be pronounced "two oh one", and the year 1907 is often pronounced "nineteen oh seven". The presence of other digits, indicating that the string contains only numbers, avoids confusion with the letter O. For this reason, systems that include strings with both letters and numbers (such as postcodes in the UK) may exclude the use of the letter O.Appendix C - Valid Postcode Format https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/611951/Appendix_C_ILR_2017_to_2018_v1_Published_28April17.pdf gov.uk 24 July 2025 28 April 2017 Slang words for zero include "zip", "zilch", "nada", and "scratch". http://thesaurus.com/browse/aught#visualthesaurus 'Aught' synonyms https://web.archive.org/web/20140823071642/http://thesaurus.com/browse/aught#visualthesaurus 23 August 2014 Thesaurus.com 23 April 2013 In the context of sports, "nil" is sometimes used, especially in British English. Several sports have specific words for a score of zero, such as "love" in tennis – possibly from French fr l'œuf, "the egg" – and "duck" in cricket, a shortening of "duck's egg". "Goose egg" is another general slang term used for zero. Mathematics Null (mathematics) The concept of zero plays multiple roles in mathematics: as a digit, it is an important part of positional notation for representing numbers, while it also plays an important role as a number in its own right in many algebraic settings. As a digit Positional notation In positional number systems (such as the usual decimal notation for representing numbers), the digit 0 plays the role of a placeholder, indicating that certain powers of the base do not contribute. For example, the decimal number 205 is the sum of two hundreds and five ones, with the 0 digit indicating that no tens are added. The digit plays the same role in decimal fractions and in the decimal representation of other real numbers (indicating whether any tenths, hundredths, thousandths, etc., are present) and in bases other than 10 (for example, in binary, where it indicates which powers of 2 are omitted).Reimer 2014 156,199–204 Elementary algebra thumb|upright=1.4|A number line from −3 to 3, with 0 in the middle The number 0 is the smallest nonnegative integer, and the largest nonpositive integer. The natural number following 0 is 1 and no natural number precedes 0. The number 0 may or may not be considered a natural number,Bunt Lucas Nicolaas Hendrik https://books.google.com/books?id=7xArILpcndYC The historical roots of elementary mathematics Jones Phillip S. Bedient Jack D. Courier Dover Publications 1976 978-0-486-13968-5 254–255 5 January 2016 23 June 2016 https://web.archive.org/web/20160623174716/https://books.google.com/books?id=7xArILpcndYC live , Extract of pp. 254–255 https://web.archive.org/web/20160510195505/https://books.google.com/books?id=7xArILpcndYC&pg=PA255 10 May 2016 Cheng 2017 32 but it is an integer, and hence a rational number and a real number.Cheng 2017 41, 48–53 Zero is evenLemma B.2.2, The integer 0 is even and is not odd, in Penner Robert C. https://archive.org/details/discretemathemat0000penn Discrete Mathematics: Proof Techniques and Mathematical Structures World Scientific 1999 978-981-02-4088-2 34 (that is, a multiple of 2), and is also an integer multiple of any other integer.Cummings Jay Proofs: a long-form mathematics textbook 2021 Amazon Fulfillment 979-8-5952-6597-3 Wrocław It is neither a prime number nor a composite number.Prime and Composite Numbers https://www.aaamath.com/fra63ax2.htm 2026-06-18 www.aaamath.com The number 0 is regarded as neither positive nor negative,Weisstein, Eric W. Zero http://mathworld.wolfram.com/Zero.html 4 April 2018 Wolfram en 1 June 2013 https://web.archive.org/web/20130601190920/http://mathworld.wolfram.com/Zero.html live and is usually displayed as the origin of a number line.Moise Edwin E. Calculus 1996 Addison-Wesley Publishing Company, Inc. part 1 18 When the real numbers are extended to form the complex numbers, 0 becomes the origin of the complex plane.Foerster 1980 283 alt=A collection of five dots and one of zero dots merge into one of five dots.|thumb|193x193px|5+0=5 illustrated with collections of dots. The following are some basic rules for dealing with the number 0. These rules apply for any real or complex number x, unless otherwise stated. Addition: x + 0 = 0 + x = x. That is, 0 is an identity element (or neutral element) with respect to addition.Foerster 1980 3 Subtraction: x − 0 = x and 0 − x = −x.Subtracting Integers Rules: Definition and Rules with Examples https://testbook.com/maths/subtracting-integers-rules 2026-06-18 Testbook en Multiplication: x · 0 = 0 · x = 0.Foerster 1980 21 The converse also holds: If x · y = 0 then x=0 or y=0. Division: 0 x = 0, for nonzero x. But x 0 is undefined, because 0 has no multiplicative inverse (no real number multiplied by 0 produces 1), a consequence of the previous rule.Cheng 2017 47 Exponentiation: x0 = x x = 1, except that the case x = 0 is considered undefined in some contexts. For all positive real x, 0x 0.Foerster 1980 136 The expression 0 0, which may be obtained in an attempt to determine the limit of an expression of the form f(x) g(x) as a result of applying the lim operator independently to both operands of the fraction, is a so-called "indeterminate form". That does not mean that the limit sought is necessarily undefined; rather, it means that the limit of f(x) g(x), if it exists, must be found by another method, such as l'Hôpital's rule.Herman Edwin https://openstax.org/details/books/calculus-volume-1 Calculus 1 Strang Gilbert 2017 OpenStax 978-1-938168-02-4 Houston, Texas 1022848630 etal Gilbert Strang 26 July 2022 23 September 2022 https://web.archive.org/web/20220923230919/https://openstax.org/details/books/calculus-volume-1 live 454–459 The sum of 0 numbers (the empty sum) is 0, and the product of 0 numbers (the empty product) is 1. The factorial 0! evaluates to 1, as a special case of the empty product.Ronald L. Graham Ronald Graham Donald E. Knuth Donald Knuth Oren Patashnik Oren Patashnik 1988 Concrete Mathematics Addison-Wesley Reading, MA 0-201-14236-8 Concrete Mathematics 111 Other uses in mathematics thumb|upright=0.4|alt={}|The empty set has zero elementsThe role of 0 as the smallest counting number can be generalized or extended in various ways. In set theory, 0 is the cardinality of the empty set (notated as "{ }", "", or "∅"): if one does not have any apples, then one has 0 apples. In fact, in certain axiomatic developments of mathematics from set theory, 0 is defined to be the empty set.Cheng 2017 60 When this is done, the empty set is the von Neumann cardinal assignment for a set with no elements, which is the empty set.Booher Jeremy CONSTRUCTING THE INTEGERS: N, ORDINAL NUMBERS, AND TRANSFINITE ARITHMETIC https://people.clas.ufl.edu/jeremybooher/files/ordinals_promys.pdf University of Florida Also in set theory, 0 is the lowest ordinal number, corresponding to the empty set viewed as a well-ordered set. In order theory (and especially its subfield lattice theory), 0 may denote the least element of a lattice or other partially ordered set. The role of 0 as additive identity generalizes beyond elementary algebra. In abstract algebra, 0 is commonly used to denote a zero element, which is the identity element for addition (if defined on the structure under consideration) and an absorbing element for multiplication (if defined). Examples include identity elements of additive groups and vector spaces. Another example is the zero function (or zero map) on a domain D. This is the constant function with 0 as its only possible output value, that is, it is the function f defined by f(x) 0 for all x in D. As a function from the real numbers to the real numbers, the zero function is the only function that is both even and odd. The number 0 is also used in several other ways within various branches of mathematics: A zero of a function f is a point x in the domain of the function such that f(x) 0. In propositional logic, 0 may be used to denote the truth value false. In probability theory, 0 is the smallest allowed value for the probability of any event.Kardar 2007 35 Category theory introduces the idea of a zero object, often denoted 0, and the related concept of zero morphisms, which generalize the zero function.Riehl Emily Category Theory in Context Emily Riehl 103 https://math.jhu.edu/~eriehl/context/ Dover 2016 978-0-486-80903-8 History Ancient Near East nfr heart with tracheabeautiful, pleasant, goodF35 Ancient Egyptian numerals were of base 10.O'Connor J. J. Robertson E. F. 2000 Egyptian numerals http://mathshistory.st-andrews.ac.uk/HistTopics/Egyptian_numerals.html live https://web.archive.org/web/20191115221313/http://mathshistory.st-andrews.ac.uk/HistTopics/Egyptian_numerals.html 15 November 2019 21 December 2019 mathshistory.st-andrews.ac.uk University of St Andrews They used hieroglyphs for the digits and were not positional. In one papyrus written around 1770 BC, a scribe recorded daily incomes and expenditures for the pharaoh's court, using the nfr hieroglyph to indicate cases where the amount of a foodstuff received was exactly equal to the amount disbursed. Egyptologist Alan Gardiner suggested that the nfr hieroglyph was being used as a symbol for zero.eg. Alan Gardiner. “§357. Other Modes of Negation” Egyptian Grammar (1927). p. 266 etc. et al. Cites: Cairo 20003. Turin 1447. British Museum MS 152. The same symbol 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.Beatrice Lumpkin 10.1007/BF03024613 Mathematics Used in Egyptian Construction and Bookkeeping The Mathematical Intelligencer 2002 24 2 20–25 120648746 By the middle of the 2nd millennium BC, Babylonian mathematics had a sophisticated base 60 positional numeral system, but a positional value of zero was indicated by a space between numerals. In a tablet unearthed at Kish (dating to as early as 700 BC), the scribe Bêl-bân-aplu used three hooks as a placeholder.Kaplan 2000 By 300 BC, a punctuation symbol (two slanted wedges) was repurposed as a placeholder.O'Connor J. J. Robertson E. F. 2000 Zero https://mathshistory.st-andrews.ac.uk/HistTopics/Zero/ live https://web.archive.org/web/20210921191118/https://mathshistory.st-andrews.ac.uk/HistTopics/Zero/ 21 September 2021 2021-09-07 Maths History University of St Andrews enBabylonian mathematics 2016 https://www.open.edu/openlearn/ocw/mod/oucontent/view.php?printable=1&id=1976 2021-09-07 The Open University 7 September 2021 https://web.archive.org/web/20210907135356/https://www.open.edu/openlearn/ocw/mod/oucontent/view.php?printable=1&id=1976 live Significantly, however, these placeholder signs were not considered a numerical value, they were never used alone “Therefore, they cannot be interpreted as representations of the concept or the number zero.”Nieder, Andreas (19 November 2019). A Brain for Numbers: The Biology of the Number Instinct. MIT Press. p. 286. They were also not written at the end of a number (so 1 and 60 and 60×60 were all written as 20px).Reimer 2014 172 Pre-Columbian Americas thumb|alt=𝋠|Maya numeral zero 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 the partial quatrefoil 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 BC.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.Cyclical views of time https://www.mexicolore.co.uk/aztecs/calendar/cyclical-views-of-time 2024-01-20 www.mexicolore.co.uk Since the eight earliest Long Count dates appear outside the Maya homeland,Diehl 2004 186 it is generally believed that the use of zero in the Americas predated the Maya and was possibly the invention of the Olmecs.Mortaigne Véronique 28 November 2014 The golden age of Mayan civilisation – exhibition review The Guardian https://www.theguardian.com/culture/2014/nov/28/mayan-civilisation-paris-exhibition live 10 October 2015 https://web.archive.org/web/20141128222215/http://www.theguardian.com/culture/2014/nov/28/mayan-civilisation-paris-exhibition 28 November 2014 Many of the earliest Long Count dates were found within the Olmec heartland, although the Olmec civilization ended by the 4th century BC,Cyphers Ann The Olmec, 1800–400 BCE 2014 The Cambridge World Prehistory 1005–1025 Renfrew Colin https://www.cambridge.org/core/books/cambridge-world-prehistory/olmec-1800400-bce/2C66AF7B3D041260EE2BFC94DF085029 2024-08-13 Cambridge Cambridge University Press 978-0-521-11993-1 Bahn Paul several centuries before the earliest known Long Count dates.Expedition Magazine Time, Kingship, and the Maya Universe Maya Calendars https://www.penn.museum/sites/expedition/time-kingship-and-the-maya-universe-maya-calendars/ 2024-08-13 Expedition Magazine en Although zero became an integral part of Maya numerals, with a different, empty tortoise-like "shell shape" used for many depictions of the "zero" numeral, it is assumed not to have influenced Old World numeral systems.Birchak Gabrielle 2025-06-03 Mayan Mathematics https://mathsciencehistory.com/mayan-mathematics/ 2025-09-30 Math! Science! History!™ en-US Historian Georges Ifrah calls the Mayan use of zero “one of the most striking inventions ever to emerge in a mathematical culture isolated from the Old World.” Quipu, a knotted cord device, used in the Inca Empire and its predecessor societies in the Andean region to record accounting and other digital data, is encoded in a base ten positional system. Zero is represented by the absence of a knot in the appropriate position.Leon Manuel de 2022-12-20 Knots representing numbers: The mathematics of the Incas https://english.elpais.com/science-tech/2022-12-20/knots-representing-numbers-the-mathematics-of-the-incas.html 2024-06-05 EL PAÍS English en-us Classical antiquity The earliest confidently cited exemplar of the Greek use of the Hellenistic zero appears in Hipparchus in 140 CE. The archaic Greece had no symbol for zero (μηδέν, pronounced mēdén), and did not use a digit placeholder for it.Wallin Nils-Bertil 19 November 2002 The History of Zero http://yaleglobal.yale.edu/about/zero.jsp https://web.archive.org/web/20160825124525/http://yaleglobal.yale.edu/about/zero.jsp 25 August 2016 1 September 2016 YaleGlobal online The Whitney and Betty Macmillan Center for International and Area Studies at Yale. According to mathematician Charles Seife, after the Babylonian placeholder zero shows up sometime shortly after 500 BC, Greek astronomers began to use the lowercase Greek letter ό (όμικρον: omicron) as a placeholder or representation of ground-level/null degree value.Kaplan Robert http://archive.org/details/nothingthatisnat0000kapl The nothing that is : a natural history of zero 1999 Allen Lane London Internet Archive 978-0-7139-9284-7 18 However, after using the Babylonian placeholder zero for astronomical calculations they would typically convert the numbers back into Greek numerals. As with the rejection of infinitesimals by Pythagoras, Greeks appear to maintain to a philosophical opposition to using zero as a number.Seife 2000 39 "The whole of the Greek universe rested on this pillar: There is no void."Seife 2000 25 Nieder dates the appearance of zero in Greek astronomical texts after 400 BC and mathematician Robert Kaplan further specifies that it must have been after the conquests of Alexander. Andreas Nieder 19 November 2019 A Brain for Numbers: The Biology of the Number Instinct MIT Press 286 978-0-262-35432-5 https://books.google.com/books?id=x4y5DwAAQBAJ&pg=PA286 30 April 2022 Kaplan 2000 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 paradoxes of Zeno of Elea depend in large part on the uncertain interpretation of zero.Huggett Nick Zeno's Paradoxes 2019 https://plato.stanford.edu/archives/win2019/entries/paradox-zeno/ The Stanford Encyclopedia of Philosophy Zalta Edward N. Winter 2019 Metaphysics Research Lab, Stanford University 2020-08-09 10 January 2021 https://web.archive.org/web/20210110135804/https://plato.stanford.edu/archives/win2019/entries/paradox-zeno/ live 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 AD150, Ptolemy, influenced by Hipparchus and the Babylonians, was using a symbol for zero (— °)Neugebauer Otto https://archive.org/details/exactsciencesant00neug The Exact Sciences in Antiquity Dover Publications 1969 978-0-486-22332-2 2 13–14, plate 2 Otto E. Neugebauer 1957 registrationMercier Raymond Consideration of the Greek symbol 'zero' http://www.raymondm.co.uk/prog/GreekZeroSign.pdf Home of Kairos 28 March 2020 5 November 2020 https://web.archive.org/web/20201105113109/http://www.raymondm.co.uk/prog/GreekZeroSign.pdf live November 2023 in his work on mathematical astronomy called the Syntaxis Mathematica, also known as the Almagest.Ptolemy Ptolemy's Almagest 306–307 1998 1984, 150 Princeton University Press 0-691-00260-6 Ptolemy Toomer Almagest G. J. Gerald J. Toomer This Hellenistic zero was perhaps the earliest documented use of a numeral representing zero in the Old World.O'Connor J. J. Robertson E. F. A history of Zero http://mathshistory.st-andrews.ac.uk/HistTopics/Zero.html live https://web.archive.org/web/20200407074239/http://mathshistory.st-andrews.ac.uk/HistTopics/Zero.html 7 April 2020 28 March 2020 MacTutor History of Mathematics Ptolemy used it many times in his Almagest (VI.8) for the magnitude of solar and lunar eclipses. It represented the value of both digits and 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 00 to 3120 to 00, where 00 used the symbol as a placeholder in two positions of his sexagesimal positional numeral system,Each place in Ptolemy's sexagesimal system was written in Greek numerals from 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 1 12 3120 d(24−d) (a triangular pulse with convex sides), where d was the digit function and 3120 was the sum of the radii of the Sun's and Moon's discs.Pedersen Olaf A Survey of the Almagest Sources and Studies in the History of Mathematics and Physical Sciences 10.1007/978-0-387-84826-6_7 232–235 2010 1974 Springer 978-0-387-84825-9 Olaf Pedersen Alexander Jones 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.Proposal to encode the Greek Zero in the UCS https://www.unicode.org/L2/L2004/04054-greek-zero.pdf 2024-07-31 https://web.archive.org/web/20221007235444/https://unicode.org/L2/L2004/04054-greek-zero.pdf 2022-10-07 live The earliest use of zero in the calculation of the Julian Easter occurred before AD311, at the first entry in a table of epacts as preserved in an 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.Neugebauer Otto Ethiopic Astronomy and Computus 25, 53, 93, 183, Plate I 2016 Red Sea Press 1979 Red Sea Press 978-1-56902-440-9 Otto Neugebauer. The pages in this edition have numbers six less than the same pages in the original edition. This use was repeated in 525 in an equivalent table, that was translated via the Latin la nulla ("none") by Dionysius Exiguus, alongside Roman numerals.Deckers Michael Cyclus Decemnovennalis Dionysii Nineteen Year Cycle of Dionysius http://hbar.phys.msu.ru/gorm/chrono/paschata.htm 2003 525 https://web.archive.org/web/20190115083618/http://hbar.phys.msu.ru/gorm/chrono/paschata.htm 15 January 2019 When division produced zero as a remainder, nihil, meaning "nothing", was used. These medieval zeros were used by all future medieval calculators of Easter. The initial "N" was used as a zero symbol in a table of Roman numerals by Bede—or his colleagues—around AD725.C. W. Jones, ed., Opera Didascalica, vol. 123C in Corpus Christianorum, Series Latina. China 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.Hodgkin Luke https://archive.org/details/historyofmathema0000hodg A History of Mathematics: From Mesopotamia to Modernity 2005 Oxford University Press 978-0-19-152383-0 85 registration The Sūnzĭ Suànjīng, of unknown date but estimated to be dated from the 1st to 5th centuries AD, describe how the 4th century BC Chinese counting rods system enabled one to perform positional decimal calculations.Shen Crossley Lun 1999 12: "the ancient Chinese system is a place notation system"Eberhard-Bréard Andrea Mathematics in China 2008 1371–1378 Selin Helaine Selin Helaine Dordrecht Springer Netherlands en 10.1007/978-1-4020-4425-0_9453 978-1-4020-4425-0 Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures. 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.HistTopics Chinese_numerals Chinese numerals January 2004 cs1 The rods gave the decimal representation of a number, with an empty space denoting zero.Chinese numerals https://mathshistory.st-andrews.ac.uk/HistTopics/Chinese_numerals/ 2024-04-28 Maths History en J J O'Connor E F Robertson A circa 190 AD, manual, the "Supplementary Notes on the Art of Figures", by Xu Yue, also outlines the techniques to add, subtract, multiply, and divide numbers, containing zero values in a decimal power, on counting devices, that include counting rods, and abacus.K. Volkov Alexeï 1994 Large Numbers and Counting Rods https://www.persee.fr/doc/oroc_0754-5010_1994_num_16_16_991 Extrême-Orient, Extrême-Occident 16 16 71–92 10.3406/oroc.1994.991City News Service Shanghai and China City News Service and Life Guide https://www.citynewsservice.cn/shine/2cecaa99-45e6-4f3f-9703-189199c07f3e 2025-07-01 www.citynewsservice.cn en Chinese authors had been familiar with the idea of negative numbers, and decimal fractions, by the Han dynasty (2nd century AD), as seen in The Nine Chapters on the Mathematical Art.Dirk Struik Struik Dirk J. 1987 A Concise History of Mathematics New York Dover Publications 32–33 In these matrices we find negative numbers, which appear here for the first time in history. Qín Jiǔsháo's 1247 Mathematical Treatise in Nine Sections is the oldest surviving Chinese mathematical text using a round symbol '〇' for zero.Mathematics in the Near and Far East http://grmath4.phpnet.us/istoria/the_history_of%20math_greece/the_history_of%20math_greece_3-5.pdf grmath4.phpnet.us 262 7 June 2012 4 November 2013 https://web.archive.org/web/20131104120005/http://grmath4.phpnet.us/istoria/the_history_of%20math_greece/the_history_of%20math_greece_3-5.pdf live The origin of this symbol is unknown; it may have been produced by modifying a square symbol.Jean-Claude Martzloff Stephen S. Wilson A History of Chinese Mathematics Springer 2007 978-3-540-33783-6 208 Zero was not treated as a number at that time, but as a "vacant position".Shen Kangshen https://books.google.com/books?id=eiTJHRGTG6YC The Nine Chapters on the Mathematical Art: Companion and Commentary John N. Crossley Anthony W.-C. Lun Shen Kanshen Oxford University Press 1999 978-0-19-853936-0 35 zero was regarded as a number in India ... whereas the Chinese employed a vacant position Chinese Epigraphy A variety of Chinese characters have been used, through history, to represent zero: 空, 零, 洞, 〇. India Pingala (3rd or 2nd century BC),Plofker Kim Kim Plofker Mathematics in India Mathematics in India (book) Princeton University Press 2009 978-0-691-12067-6 54–56 In the Chandah-sutra of Pingala, dating perhaps the third or second century BC, [ ...] Pingala's use of a zero symbol [śūnya] as a marker seems to be the first known explicit reference to zero. ... In the Chandah-sutra of Pingala, dating perhaps the third or second century BC, there are five questions concerning the possible meters for any value "n". [ ...] The answer is (2)7 = 128, as expected, but instead of seven doublings, the process (explained by the sutra) required only three doublings and two squarings – a handy time saver where "n" is large. Pingala's use of a zero symbol as a marker seems to be the first known explicit reference to zero. a Sanskrit prosody scholar,Vaman Shivaram Apte https://books.google.com/books?id=4ArxvCxV1l4C&pg=PA648 The Student's Sanskrit-English Dictionary Sanskrit Prosody and Important Literary and Geographical Names in the Ancient History of India Motilal Banarsidass 1970 978-81-208-0045-8 648–649 21 April 2017 used binary sequences, in the form of short and long syllables (the latter equal in length to two short syllables), to identify the possible valid Sanskrit meters, a notation similar to Morse code.Math for Poets and Drummers: The Mathematics of Rhythm Rachel Hall Saint Joseph's University February 15, 2005 slideshow http://people.sju.edu/~rhall/Rhythms/Poets/arcadia.pdf https://web.archive.org/web/20190122014628/http://people.sju.edu/~rhall/Rhythms/Poets/arcadia.pdf 22 January 2019 20 December 2015 dead Pingala used the Sanskrit word śūnya explicitly to refer to zero. thumb|Bakhshali manuscript, with the numeral "zero" represented by a black dot; its date is uncertain.Chivall David 2024 Radiocarbon dating of the Bakhshālī manuscript https://ora.ox.ac.uk/objects/uuid:5a6d1dd7-f20c-4209-adb6-33849f5b08f4/files/snp193c210 A decimal place value grapheme for zero was developed in India.Bourbaki 1998 46. The Lokavibhāga, a Jain text on cosmology surviving in a medieval Sanskrit translation of the Prakrit original, which is internally dated to AD 458 (Saka era 380), uses a decimal place-value system, including a zero. In this text, śūnya ("void, empty") is also used to refer to zero.Ifrah 2000 416 The Aryabhatiya ( 499), states sthānāt sthānaṁ daśaguṇaṁ syāt "from place to place each is ten times the preceding".Aryabhatiya of Aryabhata, translated by Walter Eugene Clark.O'Connor J. J. Robertson E. F. 2000 Aryabhata the Elder http://www-history.mcs.st-andrews.ac.uk/Biographies/Aryabhata_I.html live https://web.archive.org/web/20150711055702/http://www-history.mcs.st-andrews.ac.uk/Biographies/Aryabhata_I.html 11 July 2015 26 May 2013 School of Mathematics and Statistics, University of St. Andrews Scotlandhttps://books.google.com/books?id=cuN7rH6RzikC&pg=PA97 The Britannica Guide to Numbers and Measurement (Math Explained) 15 August 2010 The Rosen Publishing Group 978-1-61530-108-9 Hosch William L. 97–98 26 September 2016 Rules governing the use of zero appeared in Brahmagupta's Brahmasputha Siddhanta (7th century), which states the sum of zero with itself as zero, and incorrectly describes division by zero in the following way:https://archive.org/details/algebrawitharith00brahuoft Algebra, with Arithmetic and Mensuration from the Sanscrit of Brahmegupta and Bháscara 1817 John Murray London, England Henry Thomas Colebrooke 1039515732Kaplan 2000 68–75 A positive or negative number when divided by zero is a fraction with the zero as denominator. Zero divided by a negative or positive number is either zero or is expressed as a fraction with zero as numerator and the finite quantity as denominator. Zero divided by zero is zero. Bhāskara II's 12th century treatise Līlāvatī instead proposed that division by zero results in an infinite quantity,Roy Rahul Resonance 8 1 January 2003 Babylonian Pythagoras' Theorem, the Early History of Zero and a Polemic on the Study of the History of Science 30–40 https://www.ias.ac.in/describe/article/reso/008/01/0030-0040 10.1007/BF02834448 A quantity divided by zero becomes a fraction the denominator of which is zero. This fraction is termed an infinite quantity. In this quantity consisting of that which has zero for its divisor, there is no alteration, though many may be inserted or extracted; as no change takes place in the infinite and immutable God when worlds are created or destroyed, though numerous orders of beings are absorbed or put forth. Early Asian Epigraphy 2 330 right Sambor Inscription First zero 1.jpg Khmer Numerals - 605 from the Sambor inscriptions.jpg 03-National Museum of Cambodia-nX-1.jpg The oldest, firmly dated use of zero as a decimal figure, found on the Sambor Inscription. The number "605" is written in Khmer numerals (top), referring to the year it was made: 605 Saka era (683 CE). The fragment, inscribed in Old Khmer, was once part of a temple doorway, and was found in Kratié province, Cambodia. There are numerous copper plate inscriptions with the same small o in them, some of them possibly dated to the 6th century, but their date or authenticity may be open to doubt.Kaplan 2000 A stone tablet found in the ruins of a temple near Sambor on the Mekong, Kratié Province, Cambodia, includes the inscription of "605" in Khmer numerals (a set of numeral glyphs for the Hindu–Arabic numeral system). The number is the year of the inscription in the Saka era, corresponding to a date of AD 683.George Cœdès Cœdès George A propos de l'origine des chiffres arabes Bulletin of the School of Oriental Studies, University of London 6 2 1931 323–328 607661 Cambridge University Press fr 10.1017/S0041977X00092806 130482979 Diller Anthony New Zeros and Old Khmer Mon-Khmer Studies 25 1996 125–132 http://sealang.net/sala/archives/pdf8/diller1996new.pdf The first known use of special glyphs for the decimal digits that includes the indubitable appearance of a symbol for the digit zero, a small circle, appears on a stone inscription found at the Chaturbhuj Temple, Gwalior, in India, dated AD 876.Casselman Bill Bill Casselman (mathematician) All for Nought http://www.ams.org/samplings/feature-column/fcarc-india-zero ams.org University of British Columbia), American Mathematical Society 20 December 2015 6 December 2015 https://web.archive.org/web/20151206184352/http://www.ams.org/samplings/feature-column/fcarc-india-zero live Ifrah 2000 400 A symbol for zero, a black dot, is used throughout the Bakhshali manuscript, a practical manual on arithmetic for merchants. The Bodleian Library reported radiocarbon dating results for six folio from the manuscript, indicating that they came from different centuries, but date the manuscript to AD 799 – 1102. Middle Ages Transmission to Islamic culture History of the Hindu–Arabic numeral system The Arabic-language inheritance of science was largely Greek,Pannekoek Anton A History of Astronomy George Allen & Unwin 1961 165 840043 Anton Pannekoek https://archive.org/details/historyofastrono0000pann followed by Hindu influences. Will Durant 1950 The Story of Civilization, Volume IV, The Age of Faith: Constantine to Dante – A.D. 325–1300 Simon & Schuster 241 The Arabic inheritance of science was overwhelmingly Greek, but Hindu influences ranked next. In 773, at Mansur's behest, translations were made of the Siddhantas – Indian astronomical treatises dating as far back as 425 BC; these versions may have the vehicle through which the "Arabic" numerals and the zero were brought from India into Islam. In 813, al-Khwarizmi used the Hindu numerals in his astronomical tables. Will Durant https://archive.org/details/ageoffaithahisto012288mbp In 773, at Al-Mansur's behest, translations were made of many ancient treatises including Greek, Roman, Indian, and others. In AD 813, astronomical tables were prepared by a Persian mathematician, Muḥammad ibn Mūsā al-Khwārizmī, using Hindu numerals; and about 825, he published a book synthesizing Greek and Hindu knowledge and also contained his own contribution to mathematics including an explanation of the use of zero.Brezina Corona https://books.google.com/books?id=955jPgAACAAJ Al-Khwarizmi: The Inventor of Algebra The Rosen Publishing Group 2006 978-1-4042-0513-0 26 September 2016 This book was later translated into Latin in the 12th century under the title Algoritmi de numero Indorum. This title means "al-Khwarizmi on the Numerals of the Indians". The word "Algoritmi" was the translator's Latinization of Al-Khwarizmi's name, and the word "Algorithm" or "Algorism" started to acquire a meaning of any arithmetic based on decimals. Muhammad ibn Ahmad al-Khwarizmi, in 976, stated that if no number appears in the place of tens in a calculation, a little circle should be used "to keep the rows". This circle was called ṣifr.Durant 1950 241: "In 976, Muhammad ibn Ahmad, in his Keys of the Sciences, remarked that if, in a calculation, no number appears in the place of tens, a little circle should be used "to keep the rows". This circle the Mosloems called ṣifr, "empty" whence our cipher". Transmission to Europe The Hindu–Arabic numeral system (base 10) reached Western Europe in the 11th century, via Al-Andalus, through Spanish Muslims, the Moors, together with knowledge of classical astronomy and instruments like the astrolabe. Gerbert of Aurillac is credited with reintroducing the lost teachings into Catholic Europe. For this reason, the numerals came to be known in Europe as "Arabic numerals". The Italian mathematician Fibonacci or Leonardo of Pisa was instrumental in bringing the system into European mathematics in 1202, stating: After my father's appointment by his homeland as state official in the customs house of Bugia for the Pisan merchants who thronged to it, he took charge; and in view of its future usefulness and convenience, had me in my boyhood come to him and there wanted me to devote myself to and be instructed in the study of calculation for some days. There, following my introduction, as a consequence of marvelous instruction in the art, to the nine digits of the Hindus, the knowledge of the art very much appealed to me before all others, and for it I realized that all its aspects were studied in Egypt, Syria, Greece, Sicily, and Provence, with their varying methods; and at these places thereafter, while on business. I pursued my study in depth and learned the give-and-take of disputation. But all this even, and the algorism, as well as the art of Pythagoras, I considered as almost a mistake in respect to the method of the Hindus [la-x-medieval Modus Indorum]. Therefore, embracing more stringently that method of the Hindus, and taking stricter pains in its study, while adding certain things from my own understanding and inserting also certain things from the niceties of Euclid's geometric art. I have striven to compose this book in its entirety as understandably as I could, dividing it into fifteen chapters. Almost everything which I have introduced I have displayed with exact proof, in order that those further seeking this knowledge, with its pre-eminent method, might be instructed, and further, in order that the Latin people might not be discovered to be without it, as they have been up to now. If I have perchance omitted anything more or less proper or necessary, I beg indulgence, since there is no one who is blameless and utterly provident in all things. The nine Indian figures are: 9 8 7 6 5 4 3 2 1. With these nine figures, and with the sign 0... any number may be written.Sigler Laurence E. Fibonacci's Liber Abaci: A Translation into Modern English of Leonardo Pisano's Book of Calculation Springer 2003 978-1-4613-0079-3 10.1007/978-1-4613-0079-3 Sources and Studies in the History of Mathematics and Physical Sciences Sigler Laurence Grimm Richard E. The Autobiography of Leonardo Pisano Fibonacci Quarterly 11 1 February 1973 99–104 https://web.archive.org/web/20231126180044/https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=318a17253f745e2af400eb2ebb4dc4e762560a5b 26 November 2023 live https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=318a17253f745e2af400eb2ebb4dc4e762560a5b Hansen Alice https://books.google.com/books?id=COJsbuUI1h8C&pg=PT31 Primary Mathematics: Extending Knowledge in Practice 2008 SAGE 10.4135/9781446276532 978-0-85725-233-3 en 7 November 2020 7 March 2021 https://web.archive.org/web/20210307234959/https://books.google.com/books?id=COJsbuUI1h8C&q=%22Therefore%2C+embracing+more+stringently+that+method+of+the+Hindus%2C+and+taking+stricter+pains+in+its+study%2C+while+adding+certain+things+from+my+own+understanding+and+inserting+also+certain+things+from+the+niceties+of+Euclid%27s+geometric+art.%22&pg=PT31 live From the 13th century, manuals on calculation (adding, multiplying, extracting roots, etc.) became common in Europe where they were called la-x-medieval algorismus after the Persian mathematician al-Khwārizmī. One popular manual was written by Johannes de Sacrobosco in the early 1200s and was one of the earliest scientific books to be printed, in 1488.D. E. Smith L. C. Karpinski 1911 The spread of the [Hindu–Arabic] numerals in Europe The Hindu–Arabic Numerals 134–136 Ginn and Company Internet Archive https://archive.org/stream/hinduarabicnume02karpgoog#page/n145/mode/1upPedersen Olaf 1985 In Quest of Sacrobosco Journal for the History of Astronomy 16 3 175–221 10.1177/002182868501600302 1985JHA....16..175P 118227787 The practice of calculating on paper using Hindu–Arabic numerals only gradually displaced calculation by abacus and recording with Roman numerals.Ifrah 2000 588–590 In the 16th century, Hindu–Arabic numerals became the predominant numerals used in Europe. Symbols and representations Symbols for zero 71px|alt=horizontal guidelines with a zero touching top and bottom, a three dipping below, and a six cresting above the guidelines, from left to right|left|class=skin-invert-image thumb|Oslo airport train station, Platform 0 Today, the numerical digit 0 is usually written as a circle or ellipse. Traditionally, many print typefaces made the capital letter O more rounded than the narrower, elliptical digit 0.Bemer R. W. 1967 Towards standards for handwritten zero and oh: much ado about nothing (and a letter), or a partial dossier on distinguishing between handwritten zero and oh Communications of the ACM 10 8 513–518 10.1145/363534.363563 294510 Typewriters originally made no distinction in shape between O and 0; some models did not even have a separate key for the digit 0. The distinction came into prominence on modern character displays. A slashed zero () is often used to distinguish the number from the letter (mostly in computing, navigation and in the military, for example). The digit 0 with a dot in the center seems to have originated as an option on IBM 3270 displays and has continued with some modern computer typefaces such as Andalé Mono, and in some airline reservation systems. One variation uses a short vertical bar instead of the dot. Some fonts designed for use with computers made the "0" character more squared at the edges, like a rectangle, and the "O" character more rounded. A further distinction is made in falsification-hindering typeface as used on German car number plates by slitting open the digit 0 on the upper right side. In some systems either the letter O or the numeral 0, or both, are excluded from use, to avoid confusion.March 2026 Physics The value zero plays a special role for many physical quantities. For some quantities, the zero level is naturally distinguished from all other levels, whereas for others it is more or less arbitrarily chosen. For example, for an absolute temperature (typically measured in kelvins), zero is the lowest possible value. (Negative temperatures can be defined for some physical systems, but negative-temperature systems are not actually colder.) This is in contrast to temperatures on the Celsius scale, for example, where zero is arbitrarily defined to be at the freezing point of water.Andrew Rex C. B. P. Finn Finn's Thermal Physics 3rd CRC Press 2017 978-1-4987-1887-5 8–16Kardar 2007 4–5,103–104 Measuring sound intensity in decibels or phons, the zero level is arbitrarily set at a reference value—for example, at a value for the threshold of hearing.McGowan — Paul 2024-11-13 When zero means something https://www.psaudio.com/blogs/pauls-posts/when-zero-means-something 2026-06-18 PS Audio enUnderstanding The Silence: What Does 0 Db Sound Really Mean? SoundCy https://soundcy.com/article/what-is-0-db-sound 2026-06-18 soundcy.com Computer science Modern computers store information in binary, that is, using an "alphabet" that contains only two symbols, usually chosen to be "0" and "1". Binary coding is convenient for digital electronics, where "0" and "1" can stand for the absence or presence of electrical current in a wire.Woodford 2006 9 Computer programmers typically use high-level programming languages that are more intelligible to humans than the binary instructions that are directly executed by the central processing unit. 0 plays various important roles in high-level languages. For example, a Boolean variable stores a value that is either true or false, and 0 is often the numerical representation of false.Hill 2020 20 0 also plays a role in array indexing. The most common practice throughout human history has been to start counting at one, and this is the practice in early classic programming languages such as Fortran and COBOL.Overland Brian https://books.google.com/books?id=bW6MiHxPULUC&dq=cobol+array+index&pg=PT132 C++ Without Fear: A Beginner's Guide That Makes You Feel Smart 2004-09-14 Pearson Education 978-0-7686-8488-9 132 en However, in the late 1950s LISP introduced zero-based numbering for arrays while Algol 58 introduced completely flexible basing for array subscripts (allowing any positive, negative, or zero integer as base for array subscripts), and most subsequent programming languages adopted one or other of these positions.June 2024 For example, the elements of an array are numbered starting from 0 in C, so that for an array of n items the sequence of array indices runs from 0 to n−1.Oliveira Suely https://books.google.com/books?id=E6a8oZOS8noC&dq=C+array+index+zero&pg=PA64 Writing Scientific Software: A Guide to Good Style Stewart David E. 2006-09-07 Cambridge University Press 978-1-139-45862-7 64 en Since C arrays are accessed by the array's first element memory address plus an offset, the initial pointer plus with offset zero refers to the first element of the array. There can be confusion between 0- and 1-based indexing; for example, Java's JDBC indexes parameters from 1 although Java itself uses 0-based indexing.ResultSet (Java Platform SE 8 ) https://docs.oracle.com/javase/8/docs/api/java/sql/ResultSet.html 2022-05-09 docs.oracle.com 9 May 2022 https://web.archive.org/web/20220509185749/https://docs.oracle.com/javase/8/docs/api/java/sql/ResultSet.html live In C, a byte containing the value 0 serves to indicate where a string of characters ends. Also, 0 is a standard way to refer to a null pointer in code.Reese Richard M. Understanding and Using C Pointers: Core Techniques for Memory Management 2013 978-1-449-34455-9 O'Reilly Media https://books.google.com/books?id=-U155tRMLJgC&dq=C%20%22null%20pointer%22%200&pg=PT26 In databases, it is possible for a field not to have a value. It is then said to have a null value.Wu X. https://books.google.com/books?id=SdLsCgAAQBAJ&q=%C2%A0In+databases%2C+it+is+possible+for+a+field+not+to+have+a+value+%28null%29&pg=PT197 Knowledge-Base Assisted Database Retrieval Systems Ichikawa T. Cercone N. 25 October 1996 World Scientific 978-981-4501-75-0 en 7 November 2020 31 March 2022 https://web.archive.org/web/20220331032618/https://books.google.com/books?id=SdLsCgAAQBAJ&q=%C2%A0In+databases%2C+it+is+possible+for+a+field+not+to+have+a+value+%28null%29&pg=PT197 live For numeric fields it is not the value zero. For text fields this is not blank nor the empty string. The presence of null values leads to three-valued logic. No longer is a condition either true or false, but it can be undetermined. Any computation including a null value delivers a null result. https://www.ibm.com/docs/en/rbd/9.5.1?topic=parts-null-values-nullable-type Null values and the nullable type 12 December 2018 IBM 23 November 2021 In regard to services, sending a null value as an argument in a remote service call means that no data is sent. Because the receiving parameter is nullable, the receiving function creates a new, uninitialized value for the missing data then passes it to the requested service function. 23 November 2021 https://web.archive.org/web/20211123185142/https://www.ibm.com/docs/en/rbd/9.5.1?topic=parts-null-values-nullable-type live In mathematics, there is no "positive zero" or "negative zero" distinct from zero; both −0 and +0 represent exactly the same number. However, in some computer hardware signed number representations, zero has two distinct representations, a positive one grouped with the positive numbers and a negative one grouped with the negatives. This kind of dual representation is known as signed zero, with the latter form sometimes called negative zero. These representations include the signed magnitude and ones' complement binary integer representations (but not the two's complement binary form used in most modern computers), and most floating-point number representations (such as IEEE 754 and IBM S/360 floating-point formats). An epoch, in computing terminology, is the date and time associated with a zero timestamp. The Unix epoch begins the midnight before the first of January 1970.Paul DuBois. "MySQL Cookbook: Solutions for Database Developers and Administrators". https://web.archive.org/web/20170224134429/https://books.google.com/books?id=lFsaBAAAQBAJ 24 February 2017, 2014. p. 204.Arnold Robbins; Nelson Beebe. "Classic Shell Scripting". https://web.archive.org/web/20170224134147/https://books.google.com/books?id=J9WbAgAAQBAJ 24 February 2017. 2005. p. 274.Iztok Fajfar. "Start Programming Using HTML, CSS, and JavaScript". https://web.archive.org/web/20170224134155/https://books.google.com/books?id=eHq9CgAAQBAJ 24 February 2017. 2015. p. 160. The Classic Mac OS epoch and Palm OS epoch begin the midnight before the first of January 1904.Darren R. Hayes. "A Practical Guide to Computer Forensics Investigations". https://web.archive.org/web/20170224134341/https://books.google.com/books?id=0qPfBQAAQBAJ 24 February 2017. 2014. p. 399. Many APIs and operating systems that require applications to return an integer value as an exit status typically use zero to indicate success and non-zero values to indicate specific error or warning conditions.Rochkind Marc J. Advanced UNIX Programming Prentice Hall 1985 0-13-011818-4 Prentice-Hall Software Series Englewood Cliffs, New Jersey Section 5.5, "Exit system call", p.114. Programmers often use a slashed zero to avoid confusion with the letter "O".18 August 2010 Font Survey: 42 of the Best Monospaced Programming Fonts https://www.codeproject.com/Articles/30040/Font-Survey-42-of-the-Best-Monospaced-Programming live 22 July 2021 codeproject.com https://web.archive.org/web/20120124051919/http://www.codeproject.com:80/Articles/30040/Font-Survey-42-of-the-Best-Monospaced-Programming 24 January 2012 Other fields Biology In comparative zoology and cognitive science, recognition that some animals display awareness of the concept of zero leads to the conclusion that the capability for numerical abstraction arose early in the evolution of species.Cepelewicz Jordana https://www.quantamagazine.org/animals-can-count-and-use-zero-how-far-does-their-number-sense-go-20210809/ Animals Count and Use Zero. How Far Does Their Number Sense Go? https://web.archive.org/web/20210818042926/https://www.quantamagazine.org/animals-can-count-and-use-zero-how-far-does-their-number-sense-go-20210809/ 18 August 2021 Quanta Magazine August 9, 2021 Dating systems Year zero In the BC calendar era, the year 1BC is the first year before AD1; there is not a year zero. By contrast, in astronomical year numbering, the year 1BC is numbered 0, the year 2BC is numbered −1, and so forth.Steel Duncan https://archive.org/details/markingtimeepicq00stee_0/page/113 Marking Time: The epic quest to invent the perfect calendar John Wiley & Sons 2000 978-0-471-29827-4 113 In the B.C./A.D. scheme there is no year zero. After 31 December 1BC came 1 January AD 1. ... If you object to that no-year-zero scheme, then don't use it: use the astronomer's counting scheme, with negative year numbers. registration 1135427740 See also Grammatical number Mathematical constant Number theory Peano axioms Notes References Bibliography Aczel Amir D. Finding Zero Palgrave Macmillan 2015 978-1-137-27984-2 New York Amir D. Aczel https://archive.org/details/findingzeromathe0000acze none Asimov Isaac Asimov on Numbers Pocket Books 1978 978-0-671-82134-0 New York Nothing Counts 1105483009 Isaac Asimov https://archive.org/details/asimovonnumbers00isaa none Barrow John D. The Book of Nothing Vintage 2001 0-09-928845-1 John D. Barrow https://archive.org/details/bookofnothing0000barr none Eugenia Cheng Eugenia Cheng Beyond Infinity: An Expedition to the Outer Limits of Mathematics Basic Books 2017 978-1-5416-4413-7 Mehran Kardar Mehran Kardar Statistical Physics of Particles Statistical Physics of Particles 2007 Cambridge University Press 978-0-521-87342-0 David Reimer Count Like an Egyptian 2014 Princeton University Press 978-0-691-16012-2 Woodford Chris Chris Woodford (author) https://books.google.com/books?id=My7Zr0aP2L8C&pg=PA9 Digital Technology 2006 Evans Brothers 978-0-237-52725-9 24 March 2016 17 August 2019 https://web.archive.org/web/20190817150242/https://books.google.com/books?id=My7Zr0aP2L8C&pg=PA9 live Hill Christian Learning Scientific Programming with Python Cambridge University Press 2020 978-1-10707541-2 2nd Historical studies Bourbaki Nicolas Elements of the History of Mathematics Springer-Verlag 1998 3-540-64767-8 Berlin, Heidelberg, and New York Nicolas Bourbaki Diehl Richard A. The Olmecs: America's First Civilization Thames & Hudson 2004 London, England 978-0-500-28503-9 Ifrah Georges The Universal History of Numbers: From Prehistory to the Invention of the Computer Wiley 2000 0-471-39340-1 Kaplan Robert The Nothing That Is: A Natural History of Zero Oxford University Press 2000 978-0-198-02945-8 Seife Charles Zero: The Biography of a Dangerous Idea Penguin USA 2000 0-14-029647-6 Charles Seife Foerster Paul A. Algebra and Trigonometry Addison-Wesley Innovative Division 1980 0-201-20239-5 External links zero y zero Zero no no no no Searching for the World's First Zero A History of Zero Zero Saga The History of Algebra Edsger W. Dijkstra: Why numbering should start at zero, EWD831 (PDF of a handwritten manuscript) Zero p004y254 Zero 0 0 Zero x x Zero x x zero expand Category:Elementary arithmetic 00 Category:Indian inventions