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0 (zero) is a
number A number is a mathematical object A mathematical object is an abstract concept arising in mathematics. In the usual language of mathematics, an ''object'' is anything that has been (or could be) formally defined, and with which one may do deduct ...

number
, and the
numerical digit A numerical digit (often shortened to just digit) is a single symbol used alone (such as "2") or in combinations (such as "25"), to represent number A number is a mathematical object A mathematical object is an abstract concept arising in mat ...
used to represent that number in
numerals A numeral is a figure, symbol, or group of figures or symbols denoting a number. It may refer to: * Numeral system used in mathematics * Numeral (linguistics), a part of speech denoting numbers (e.g. ''one'' and ''first'' in English) * Numerical di ...
. It fulfills a central role in
mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities and their changes (cal ...
as the
additive identity In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities and the ...
of the
integer An integer (from the Latin Latin (, or , ) is a classical language A classical language is a language A language is a structured system of communication Communication (from Latin ''communicare'', meaning "to share" or "to ...
s,
real number In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers ( and ), formulas and related structures (), shapes and spaces in which they are contained (), and quantities and their changes ( and ). There is no g ...
s, and many other
algebraic structure In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). It ...
s. As a digit, 0 is used as a placeholder in place value systems.
Names for the number 0 in English "Zero 0 (zero) is a number A number is a mathematical object A mathematical object is an abstract concept arising in mathematics. In the usual language of mathematics, an ''object'' is anything that has been (or could be) formally define ...
include zero, nought (UK), naught (US; ), nil, or—in contexts where at least one adjacent digit distinguishes it from the letter "O"—oh or o (). Informal or slang terms for zero include zilch and zip. ''Ought'' and ''aught'' (), as well as ''cipher'', have also been used historically.


Etymology

The word ''zero'' came into the English language via French from the
Italian Italian may refer to: * Anything of, from, or related to the country and nation of Italy ** Italians, an ethnic group or simply a citizen of the Italian Republic ** Italian language, a Romance language *** Regional Italian, regional variants of the ...

Italian
, a contraction of the Venetian form of Italian via ''ṣafira'' or ''ṣifr''. In pre-Islamic time the word (Arabic ) had the meaning "empty". evolved to mean zero when it was used to translate ( sa, शून्य) from
India India, officially the Republic of India (Hindi Hindi (Devanagari: , हिंदी, ISO 15919, ISO: ), or more precisely Modern Standard Hindi (Devanagari: , ISO 15919, ISO: ), is an Indo-Aryan language spoken chiefly in Hindi Belt, ...

India
.See: * Smithsonian Institution, , Annual Report of the Board of Regents of the Smithsonian Institution; Harvard University Archives, Quote="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., , p. 26, Quote = ''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, , p. 38, Quote = "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 first known English use of ''zero'' was in 1598. The Italian mathematician
Fibonacci Fibonacci (; also , ; – ), also known as Leonardo Bonacci, Leonardo of Pisa, or Leonardo Bigollo Pisano ('Leonardo the Traveller from Pisa'), was an Italian mathematician A mathematician is someone who uses an extensive knowledge of mathem ...

Fibonacci
(c. 1170–1250), who grew up in North Africa and is credited with introducing the decimal system to Europe, used the term ''zephyrum''. This became in Italian, and was then contracted to in Venetian. The Italian word was already in existence (meaning "west wind" from Latin and Greek ) and may have influenced the spelling when transcribing Arabic .


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" and "none" are often used. Sometimes, the word "nought" or "naught" is used. It is often called "oh" in the context of telephone numbers. Slang words for zero include "zip", "zilch", "nada", and "scratch."'Aught' synonyms
Thesaurus.com – Retrieved April 2013.
"Nil" is used for many sports in
British English British English (BrE) is the standard dialect A standard language (also standard variety, standard dialect, and standard) is a language variety that has undergone substantial codification of grammar and usage and is employed by a populatio ...
. Several sports have specific words for a score of zero, such as "
love Love encompasses a range of strong and positive emotion Emotions are mental state, psychological states brought on by neurophysiology, neurophysiological changes, variously associated with thoughts, feelings, behavioural responses, and ...
" in
tennis Tennis is a racket sport that can be played individually against a single opponent (Types of tennis match#Singles, singles) or between two teams of two players each (Types of tennis match#Doubles, doubles). Each player uses a tennis racket th ...
– from French ''l'oeuf'', "the egg" – and "
duck Duck is the common name for numerous species of waterfowl Anseriformes is an order (biology), order of birds that comprise about 180 living species in three families: Anhimidae (the 3 screamers), Anseranatidae (the magpie goose), and Anati ...
" in
cricket Cricket is a Bat-and-ball games, bat-and-ball game played between two teams of eleven players each on a cricket field, field at the centre of which is a cricket pitch, pitch with a wicket at each end, each comprising two Bail (cricket), bai ...
, a shortening of "duck's egg"; "goose egg" is another general slang term used for zero.


History


Ancient Near East

Ancient
Egyptian numerals The system of ancient Egyptian numerals was used in Ancient Egypt Ancient Egypt was a civilization of Ancient history, ancient North Africa, concentrated along the lower reaches of the Nile, Nile River, situated in the place that is now th ...
were of
base 10 The decimal numeral system A numeral system (or system of numeration) is a writing system A writing system is a method of visually representing verbal communication Communication (from Latin ''communicare'', meaning "to share") is t ...
. They used
hieroglyphs A hieroglyph (Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its population is approximately 10.7 million ...

hieroglyphs
for the digits and were not positional. By 1770 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. By the middle of the
2nd millennium BC The 2nd millennium BC spanned the years 2000 through 1001 BC. In the Ancient Near East The ancient Near East was the home of early civilization A civilization (or civilisation) is any complex society that is characterized by urban de ...
, the
Babylonian mathematics Babylonian mathematics (also known as ''Assyro-Babylonian mathematics'') denotes the mathematics developed or practiced by the people of Mesopotamia, from the days of the early Sumerians to the centuries following the fall of Babylon in 539 BC. Bab ...
had a sophisticated
sexagesimal Sexagesimal, also known as base 60 or sexagenary, is a numeral system A numeral system (or system of numeration) is a writing system A writing system is a method of visually representing verbal communication Communication (from Latin ...
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 (dating to as early as 700 BC), the scribe Bêl-bân-aplu used three hooks as a
placeholder Placeholder may refer to: Language * Placeholder name, a term or terms referring to something or somebody whose name is not known or, in that particular context, is not significant or relevant. * Filler text, text generated to fill space or provi ...
in the same .Kaplan, Robert. (2000). ''The Nothing That Is: A Natural History of Zero''. Oxford: Oxford University Press. By 300 BC, a punctuation symbol (two slanted wedges) was co-opted to serve as this placeholder. The Babylonian placeholder was not a true zero because it was not used alone, nor was it used at the end of a number. Thus numbers like 2 and 120 (2×60), 3 and 180 (3×60), 4 and 240 (4×60) looked the same, because the larger numbers lacked a final sexagesimal placeholder. Only context could differentiate them.


Pre-Columbian Americas

The
Mesoamerican Long Count calendar The Mesoamerican Long Count calendar is a non-repeating, vigesimal A vigesimal () or base-20 (base-score) numeral system is based on 20 (number), twenty (in the same way in which the decimal, decimal numeral system is based on 10 (number), t ...
developed in south-central Mexico and Central America required the use of zero as a placeholder within its
vigesimal A vigesimal () or base-20 (base-score) numeral system is based on 20 (number), twenty (in the same way in which the decimal, decimal numeral system is based on 10 (number), ten). ''wikt:vigesimal#English, Vigesimal'' is derived from the Latin adje ...
(base-20) positional numeral system. Many different glyphs, including this partial
quatrefoil A quatrefoil (anciently caterfoil) is a decorative element consisting of a symmetrical shape which forms the overall outline of four partially overlapping circles of the same diameter. It is found in art, architecture, heraldry and traditional C ...
——were used as a zero symbol for these Long Count dates, the earliest of which (on Stela 2 at Chiapa de Corzo,
Chiapas Chiapas (), officially the Free and Sovereign State of Chiapas ( es, Estado Libre y Soberano de Chiapas), is one of the states that make up the of . It comprises and its capital city is . Other important population centers in Chiapas include ...

Chiapas
) has a date of 36 BC. Since the eight earliest Long Count dates appear outside the Maya homeland, it is generally believed that the use of zero in the Americas predated the Maya and was possibly the invention of the
Olmec The Olmecs () were the earliest known major Mesoamerica Mesoamerica is a historical and important region In geography, regions are areas that are broadly divided by physical characteristics (physical geography), human impact characterist ...
s. Many of the earliest Long Count dates were found within the Olmec heartland, although the Olmec civilization ended by the , several centuries before the earliest known Long Count dates. Although zero became an integral part of
Maya numerals The Mayan numeral system was the system to represent number A number is a mathematical object used to counting, count, measurement, measure, and nominal number, label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. ...

Maya numerals
, with a different, empty
tortoise Tortoises () are reptiles Reptiles, as most commonly defined, are the animals in the class Class or The Class may refer to: Common uses not otherwise categorized * Class (biology), a taxonomic rank * Class (knowledge representation), a ...

tortoise
-like "" used for many depictions of the "zero" numeral, it is assumed not to have influenced
Old World The Old World consists of Africa Africa is the world's second-largest and second-most populous continent, after Asia in both cases. At about 30.3 million km2 (11.7 million square miles) including adjacent islands, it covers 6% o ...
numeral systems.
Quipu Quipu (also spelled khipu) are recording devices fashioned from historically used by a number of cultures in the region of . Knotted strings for collecting data, government management and keeping records were also used by the , and , but ...

Quipu
, a knotted cord device, used in the
Inca Empire The Inca Empire, also known as Incan Empire and the Inka Empire, and at the time known as the Realm of the Four Parts,,  "four parts together" was the largest empire in pre-Columbian America. The administrative, political and military c ...

Inca Empire
and its predecessor societies in the
Andean The Andes, Andes Mountains or Andean Mountains ( es, Cordillera de los Andes) are the longest continental mountain range in the world, forming a continuous highland along the western edge of South America South America is a continent e ...

Andean
region to record accounting and other digital data, is encoded in a
base ten The decimal numeral system (also called the base-ten positional numeral system, and occasionally called denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers of the Hi ...
positional system. Zero is represented by the absence of a knot in the appropriate position.


Classical antiquity

The
ancient Greeks Ancient Greece ( el, Ἑλλάς, Hellás) was a civilization belonging to a period of History of Greece, Greek history from the Greek Dark Ages of the 12th–9th centuries BC to the end of Classical Antiquity, antiquity ( AD 600). This era was ...
had no symbol for zero (μηδέν), and did not use a digit placeholder for it. 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 In the history of Europe The history of Europe concerns itself with the discovery and collection, the study, organization and presentation and the interpretation of past events and affairs of the people of Europe since the beginning of ...

medieval
period, religious arguments about the nature and existence of zero and the
vacuum A vacuum is a space Space is the boundless three-dimensional Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called parameter A parameter (from the Ancient Gr ...

vacuum
. The
paradoxes A paradox, also known as an antinomy, is a logically self-contradictory statement or a statement that runs contrary to one's expectation. It is a statement that, despite apparently valid reasoning from true premises, leads to a seemingly self-con ...
of depend in large part on the uncertain interpretation of zero. By AD 150,
Ptolemy Claudius Ptolemy (; grc-koi, Κλαύδιος Πτολεμαῖος, , ; la, Claudius Ptolemaeus; AD) was a mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Greek: ) includes ...
, influenced by
Hipparchus Hipparchus of Nicaea (; el, Ἵππαρχος, ''Hipparkhos'';  BC) was a Greek astronomer, geographer, and mathematician. He is considered the founder of trigonometry, but is most famous for his incidental discovery of precession of the ...
and the
Babylonia Babylonia () was an and based in central-southern which was part of Ancient Persia (present-day and ). A small -ruled state emerged in 1894 BCE, which contained the minor administrative town of . It was merely a small provincial town dur ...
ns, was using a symbol for zero () in his work on mathematical astronomy called the ''Syntaxis Mathematica'', also known as the ''
Almagest The ''Almagest'' is a 2nd-century Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its population is appr ...
''. This Hellenistic zero was perhaps the earliest documented use of a numeral representing zero in the Old World. Ptolemy used it many times in his ''Almagest'' (VI.8) for the magnitude of
solar Solar may refer to: Astronomy * Of or relating to the Sun. ** A solar telescope 175px, The Swedish 1-m Solar Telescope at Roque de los Muchachos Observatory, La Palma in the Canary Islands. A solar telescope is a special purpose telescope used ...

solar
and
lunar eclipse A lunar eclipse occurs when the moves into the . This can occur only when the , Earth, and Moon are exactly or very closely aligned (in ) with Earth between the other two, and only on the night of a . The type and length of a lunar eclipse dep ...

lunar eclipse
s. It represented the value of both
digit Digit may refer to: Mathematics and science * Numerical digit, as used in mathematics or computer science ** Arabic numerals, the most common modern representation of numerical digits * Digit (anatomy), one of several most distal parts of a limb ...
s and
minutes Minutes, also known as minutes of meeting (abbreviation MoM), protocols or, informally, notes, are the instant written record of a meeting A meeting is when two or more people A people is a plurality of person A person (plural people ...
of immersion at first and last contact. Digits varied continuously from as the Moon passed over the Sun (a triangular pulse), where twelve digits was the
angular diameter The angular diameter, angular size, apparent diameter, or apparent size is an angular distance Angular distance \theta (also known as angular separation, apparent distance, or apparent separation) is the angle In Euclidean geometry, an angle is ...

angular diameter
of the Sun. Minutes of immersion was tabulated from , where 0′0″ used the symbol as a placeholder in two positions of his
sexagesimal Sexagesimal, also known as base 60 or sexagenary, is a numeral system A numeral system (or system of numeration) is a writing system A writing system is a method of visually representing verbal communication Communication (from Latin ...
positional numeral system, while the combination meant a zero angle. Minutes of immersion was also a continuous function (a triangular pulse with
convex Convex means curving outwards like a sphere, and is the opposite of concave. Convex or convexity may refer to: Science and technology * Convex lens A lens is a transmissive optics, optical device which focuses or disperses a light beam by me ...

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. 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 Julian Easter occurred before AD311, at the first entry in a table of
epact The epact ( la, epactae, from grc, ἐπακται ἡμεραι () = added days), used to be described by medieval Computus, computists as the age of a Lunar phase, phase of the Moon in days on 22 March; in the newer Gregorian calendar, however, ...
s as preserved in an document for the years AD311 to 369, using a 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 The Church of Alexandria in Egypt is the Christian Church headed by the Patriarch of Alexandria. It is one of the Pentarchy, original Apostolic Sees of Christianity, alongside Rome, Antioch, Constantinople and Jerusalem. Tradition holds that the C ...
in
Medieval Greek Medieval Greek (also known as Middle Greek or Byzantine Greek) is the stage of the Greek language Greek ( el, label=Modern Greek Modern Greek (, , or , ''Kiní Neoellinikí Glóssa''), generally referred to by speakers simply as Greek ...
.. The pages in this edition have numbers six less than the same pages in the original edition. This use was repeated in AD525 in an equivalent table, that was translated via the Latin ''nulla'' or "none" by
Dionysius Exiguus Dionysius Exiguus (Latin Latin (, or , ) is a classical language belonging to the Italic branch of the Indo-European languages. Latin was originally spoken in the area around Rome, known as Latium. Through the power of the Roman Republ ...

Dionysius Exiguus
, alongside
Roman numerals Roman numerals are a that originated in and remained the usual way of writing numbers throughout Europe well into the . Numbers in this system are represented by combinations of letters from the . Modern style uses seven symbols, each with a ...

Roman numerals
. 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 Bede ( ; ang, Bǣda , ; 672/326 May 735), also known as Saint Bede, The Venerable Bede, and Bede the Venerable ( la, Beda Venerabilis), was an English Benedictine The Benedictines, officially the Order of Saint Benedict ( la, Ordo Sa ...

Bede
—or his colleagues—around AD 725.C. W. Jones, ed., ''Opera Didascalica'', vol. 123C in ''Corpus Christianorum, Series Latina''.


China

The '' Sūnzĭ Suànjīng'', of unknown date but estimated to be dated from the 1st to , and Japanese records dated from the 18th century, describe how the Chinese
counting rods Counting rods () are small bars, typically 3–14 cm long, that were used by mathematicians for calculation in ancient East Asia East Asia is the eastern region of Asia, which is defined in both Geography, geographical and culture, et ...
system enabled one to perform decimal calculations. As noted in 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, According to ''A History of Mathematics'', the rods "gave the decimal representation of a number, with an empty space denoting zero." The counting rod system is considered a
positional notation Positional notation (or place-value notation, or positional numeral system) usually denotes the extension to any base Base or BASE may refer to: Brands and enterprises * Base (mobile telephony provider), a Belgian mobile telecommunications ope ...
system. In AD 690, Empress Wǔ promulgated Zetian characters, one of which was "〇"; originally meaning 'star', it subsequently came to represent zero. Zero was not treated as a number at that time, but as a "vacant position". Qín Jiǔsháo's 1247 '' Mathematical Treatise in Nine Sections'' is the oldest surviving Chinese mathematical text using a round symbol for zero. Chinese authors had been familiar with the idea of negative numbers by the
Han Dynasty#REDIRECT Han dynasty The Han dynasty () was the second Dynasties in Chinese history, imperial dynasty of China (202 BC – 220 AD), established by the rebel leader Liu Bang and ruled by the House of Liu. Preceded by the short-lived Qin dynas ...

Han Dynasty
, as seen in ''
The Nine Chapters on the Mathematical Art ''The Nine Chapters on the Mathematical Art'' () is a Chinese mathematics book, composed by several generations of scholars from the 10th–2nd century BCE, its latest stage being from the 2nd century CE. This book is one of the earliest surv ...
''.Struik, Dirk J. (1987). ''A Concise History of Mathematics''. New York: Dover Publications. pp. 32–33. "''In these matrices we find negative numbers, which appear here for the first time in history.''"


India

Pingala Acharya Pingala ('; c. 3rd/2nd century BCE) was an ancient Indian poet and mathematician, and the author of the ' (also called ''Pingala-sutras''), the earliest known treatise on Sanskrit prosody. The ' is a work of eight chapters in the late Sū ...
(c. 3rd/2nd century BC), a
Sanskrit prosody Sanskrit prosody or Chandas refers to one of the six Vedanga The Vedanga ( sa, वेदाङ्ग ', "limbs of the Veda") are six auxiliary disciplines of Hinduism Hinduism () is an Indian religion and ''dharma'', or way of life. I ...
scholar, used
binary numbers In mathematics and digital electronics, a binary number is a number expressed in the base-2 numeral system or binary numeral system, which uses only two symbols: typically "0" (zero) and "1" (one). The base-2 numeral system is a positional notati ...
in the form of short and long syllables (the latter equal in length to two short syllables), a notation similar to
Morse code Morse code is a method used in telecommunication Telecommunication is the transmission of information by various types of technologies over wire A wire is a single usually cylindrical A cylinder (from Greek Greek may refer to: ...
. Pingala used the
Sanskrit Sanskrit (; attributively , ; nominalization, nominally , , ) is a classical language of South Asia that belongs to the Indo-Aryan languages, Indo-Aryan branch of the Indo-European languages. It arose in South Asia after its predecessor langua ...

Sanskrit
word '' śūnya'' explicitly to refer to zero. The concept of zero as a written digit in the decimal place value notation was developed in
India India, officially the Republic of India (Hindi Hindi (Devanagari: , हिंदी, ISO 15919, ISO: ), or more precisely Modern Standard Hindi (Devanagari: , ISO 15919, ISO: ), is an Indo-Aryan language spoken chiefly in Hindi Belt, ...
, presumably as early as during the
Gupta period The Gupta Empire was an empire which existed from the early 4th century CE to late 6th century CE. At its zenith, from approximately 319 to 467 CE, it covered much of the . This period is considered as the by historians. The ruling dynasty of ...
, with the oldest unambiguous evidence dating to the 7th century.Bourbaki, Nicolas ''Elements of the History of Mathematics'' (1998), p. 46. ''Britannica Concise Encyclopedia'' (2007), entry "Algebra" A symbol for zero, a large dot likely to be the precursor of the still-current hollow symbol, is used throughout the
Bakhshali manuscript The Bakhshali manuscript is an ancient Indian mathematical text written on birch bark that was found in 1881 in the village of Bakhshali, Mardan (near Peshawar Peshawar ( ps, پېښور ''Pēx̌awar'' ; hnd, ; ; ur, ) is the capita ...

Bakhshali manuscript
, a practical manual on arithmetic for merchants. In 2017, three samples from the manuscript were shown by
radiocarbon dating Radiocarbon dating (also referred to as carbon dating or carbon-14 dating) is a method for determining the age of an object containing organic material Organic matter, organic material, or natural organic matter refers to the large source of ...
to come from three different centuries: from AD 224–383, AD 680–779, and AD 885–993, making it South Asia's oldest recorded use of the zero symbol. It is not known how the
birch A birch is a thin-leaved deciduous hardwood tree of the genus ''Betula'' (), in the family Betulaceae, which also includes alders, hazels, and hornbeams. It is closely related to the beech-oak family Fagaceae. The genus ''Betula'' contains 30 ...

birch
bark fragments from different centuries forming the manuscript came to be packaged together. The '' Lokavibhāga'', a
Jain Jainism (), traditionally known as ''Jain Dharma'', is an ancient Indian religion Indian religions, sometimes also termed Dharmic religions or Indic religions, are the religions that originated in the Indian subcontinent. These religion ...

Jain
text on
cosmology Cosmology (from Greek#REDIRECT Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its population is appro ...
surviving in a medieval Sanskrit translation of the
Prakrit The Prakrits (; Early Brahmi 𑀧𑁆𑀭𑀸𑀓𑀾𑀢, ''prākṛta''; Devanagari Devanagari ( ; , , Sanskrit pronunciation: ), also called Nagari (),Kathleen Kuiper (2010), The Culture of India, New York: The Rosen Publishing Group, ...
original, which is internally dated to AD 458 (
Saka era 250px, Mohar of Gorkhali king Prithvi Narayan Shah dated Shaka era 1685 (AD 1763) The Shaka era (IAST The International Alphabet of Sanskrit Transliteration (IAST) is a transliteration scheme that allows the lossless romanisation of Brahmic ...
380), uses a decimal
place-value system Positional notation (or place-value notation, or positional numeral system) denotes usually the extension to any radix, base of the Hindu–Arabic numeral system (or decimal, decimal system). More generally, a positional system is a numeral system ...
, including a zero. In this text, '' śūnya'' ("void, empty") is also used to refer to zero. The ''
Aryabhatiya ''Aryabhatiya'' (IAST The International Alphabet of Sanskrit Transliteration (IAST) is a transliteration scheme that allows the lossless romanisation of Brahmic family, Indic scripts as employed by Sanskrit and related Indic languages. It is ...
'' (c. 500), states ''sthānāt sthānaṁ daśaguṇaṁ syāt'' "from place to place each is ten times the preceding."''Aryabhatiya of Aryabhata'', translated by
Walter Eugene Clark Walter Eugene Clark (September 8, 1881 – September 30, 1960), was an American philologist. He was the second Wales Professor of Sanskrit at Harvard University and editor of the volumes 38-44 of the Harvard Oriental Series The ''Harvard Ori ...
.
Rules governing the use of zero appeared in
Brahmagupta Brahmagupta ( – ) was an Indian Indian mathematics, mathematician and Indian astronomy, astronomer. He is the author of two early works on mathematics and astronomy: the ''Brāhmasphuṭasiddhānta'' (BSS, "correctly established Siddhanta, doc ...

Brahmagupta
's '' Brahmasputha Siddhanta'' (7th century), which states the sum of zero with itself as zero, and incorrectly
division by zero In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities a ...
as:''Algebra with Arithmetic of Brahmagupta and Bhaskara''
translated to English by Henry Thomas Colebrooke (1817) London
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.


Epigraphy

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. A stone tablet found in the ruins of a temple near Sambor on the
Mekong The Mekong or Mekong River is a trans-boundary river A transboundary river is a river that crosses at least one political border, either a border within a nation or an international boundary. Bangladesh has the highest number of these river ...

Mekong
, Kratié Province,
Cambodia Cambodia (; also Kampuchea ; km, កម្ពុជា, ), officially the Kingdom of Cambodia, is a country located in the southern portion of the Indochinese peninsula in Southeast Asia. It is in area, bordered by Thailand to Cambodia–T ...

Cambodia
, includes the inscription of "605" in
Khmer numerals Khmer numerals are the numerals A numeral is a figure, symbol, or group of figures or symbols denoting a number. It may refer to: * Numeral system used in mathematics * Numeral (linguistics), a part of speech denoting numbers (e.g. ''one'' and ...

Khmer numerals
(a set of numeral glyphs for the
Hindu–Arabic numeral system The Hindu–Arabic numeral system or Indo-Arabic numeral system Audun HolmeGeometry: Our Cultural Heritage 2000 (also called the Arabic numeral system or Hindu numeral system) is a positional notation, positional decimal numeral system, and is t ...
). The number is the year of the inscription in the
Saka era 250px, Mohar of Gorkhali king Prithvi Narayan Shah dated Shaka era 1685 (AD 1763) The Shaka era (IAST The International Alphabet of Sanskrit Transliteration (IAST) is a transliteration scheme that allows the lossless romanisation of Brahmic ...
, corresponding to a date of AD 683. Cœdès, George, "A propos de l'origine des chiffres arabes," Bulletin of the School of Oriental Studies, University of London, Vol. 6, No. 2, 1931, pp. 323–328. Diller, Anthony, "New Zeros and Old Khmer," The Mon-Khmer Studies Journal, Vol. 25, 1996, pp. 125–132. The first known use of special
glyph The term glyph is used in typography Typography is the art and technique of arranging type to make written language A written language is the representation of a spoken or gestural language A language is a structured system o ...
s 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 876. Zero is also used as a placeholder in the
Bakhshali manuscript The Bakhshali manuscript is an ancient Indian mathematical text written on birch bark that was found in 1881 in the village of Bakhshali, Mardan (near Peshawar Peshawar ( ps, پېښور ''Pēx̌awar'' ; hnd, ; ; ur, ) is the capita ...

Bakhshali manuscript
, portions of which date from AD 224–383.


Middle Ages


Transmission to Islamic culture

The
Arabic Arabic (, ' or , ' or ) is a Semitic language The Semitic languages are a branch of the Afroasiatic language family originating in the Middle East The Middle East is a list of transcontinental countries, transcontinental region ...

Arabic
-language inheritance of science was largely
Greek#REDIRECT Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its population is approximately 10.7 million as of ...

Greek
, followed by Hindu influences.Will Durant (1950), ''The Story of Civilization'', Volume 4, The Age of Faith: Constantine to Dante – A.D. 325–1300, Simon & Schuster, , p. 241, Quote = "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." In 773, at
Al-Mansur Al-Mansur or Abu Ja'far Abdallah ibn Muhammad al-Mansur (; ar, أبو جعفر عبدالله بن محمد المنصور‎; 95 AH – 158 AH (714 AD – 6 October 775 AD) was the second Abbasid The Abbasid Caliphate ( or ar, اَل ...

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 Persian may refer to: * People and things from Iran, historically called ''Persia'' in the English language ** Persians, Persian people, the majority ethnic group in Iran, not to be conflated with the Iranian peoples ** Persian language, an Iranian ...

Persian
mathematician,
Muḥammad ibn Mūsā al-Khwārizmī Muḥammad ibn Mūsā al-Khwārizmī ( fa, محمد بن موسی خوارزمی, Moḥammad ben Musā Khwārazmi; ), Arabized as al-Khwarizmi and formerly Latinisation of names, Latinized as ''Algorithmi'', was a Persians, Persian polymath who ...

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. This book was later translated into
Latin Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally spoken in the area around Rome, known as Latium. Through the power of the Roman Republic, it became ...

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 Muḥammad ibn al-ʿAbbās Abū Bakr al-Khwārazmī, better simply known as Abu Bakr al-Khwarazmi was a 10th-century Iranian Iranian may refer to: * Iran Iran ( fa, ایران ), also called Persia and officially the Islamic Republic of ...
, 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''.


Transmission to Europe

The
Hindu–Arabic numeral system The Hindu–Arabic numeral system or Indo-Arabic numeral system Audun HolmeGeometry: Our Cultural Heritage 2000 (also called the Arabic numeral system or Hindu numeral system) is a positional notation, positional decimal numeral system, and is t ...
(base 10) reached Western Europe in the 11th century, via , through Spanish
Muslim Muslims () are people who follow or practice Islam Islam (; ar, اَلْإِسْلَامُ, al-’Islām, "submission o God Oh God may refer to: * An exclamation; similar to "oh no", "oh yes", "oh my", "aw goodness", "ah gosh", ...

Muslim
s, the
Moors '' of Alfonso X, c. 1285 The term Moor is an Endonym and exonym, exonym first used by Christian Europeans to designate the Muslims, Muslim inhabitants of the Maghreb, the Iberian Peninsula, Sicily and Malta during the Middle Ages. The Moors init ...

Moors
, together with knowledge of classical
astronomy Astronomy (from el, ἀστρονομία, literally meaning the science that studies the laws of the stars) is a natural science that studies astronomical object, celestial objects and celestial event, phenomena. It uses mathematics, phys ...
and instruments like the
astrolabe An astrolabe ( grc, ἀστρολάβος ; ar, ٱلأَسْطُرلاب ; persian, ستاره‌یاب ) is an ancient astronomical instrument that was a handheld model of the universe. Its various functions also make it an elaborate inclinom ...

astrolabe
;
Gerbert of Aurillac Pope Sylvester II ( – 12 May 1003), originally known as Gerbert of Aurillac, was a French-born scholar and teacher who served as the bishop of Rome A bishop is an ordained, consecrated, or appointed member of the Clergy#Christianity, Christia ...

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 Fibonacci (; also , ; – ), also known as Leonardo Bonacci, Leonardo of Pisa, or Leonardo Bigollo Pisano ('Leonardo the Traveller from Pisa'), was an Italian mathematician A mathematician is someone who uses an extensive knowledge of mathem ...

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 Hindus (; ) are persons who regard themselves as culturally, ethnically, or religiously adhering to aspects of Hinduism Hinduism () is an Indian religion Indian religions, sometimes also termed Dharmic religions or Indic re ...

Hindus
(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.
Here Leonardo of Pisa uses the phrase "sign 0", indicating it is like a sign to do operations like addition or multiplication. From the 13th century, manuals on calculation (adding, multiplying, extracting roots, etc.) became common in Europe where they were called ''
algorism Algorism is the technique of performing basic arithmetic Arithmetic (from the Ancient Greek, Greek wikt:en:ἀριθμός#Ancient Greek, ἀριθμός ''arithmos'', 'number' and wikt:en:τική#Ancient Greek, τική wikt:en:τέχνη#Anci ...
us'' after the Persian mathematician al-Khwārizmī. The most popular was written by
Johannes de Sacrobosco Johannes de Sacrobosco, also written Ioannis de Sacro Bosco, later called John of Holywood or John of Holybush ( 1195 – 1256), was a scholar, monk A monk (, from el, μοναχός, ''monachos'', "single, solitary" via Latin Latin (, ...
, about 1235 and was one of the earliest scientific books to be ''printed'' in 1488. Until the late 15th century, Hindu–Arabic numerals seem to have predominated among mathematicians, while merchants preferred to use the
Roman numerals Roman numerals are a that originated in and remained the usual way of writing numbers throughout Europe well into the . Numbers in this system are represented by combinations of letters from the . Modern style uses seven symbols, each with a ...
. In the 16th century, they became commonly used in Europe.


Mathematics

0 is the
integer An integer (from the Latin Latin (, or , ) is a classical language A classical language is a language A language is a structured system of communication Communication (from Latin ''communicare'', meaning "to share" or "to ...
immediately preceding . Zero is an even number because it is divisible by with no remainder. 0 is neither positive nor negative, or both positive and negative. Many definitions include 0 as a
natural number In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and total order, ordering (as in "this is the ''third'' largest city in the country"). In common mathematical terminology, w ...
, in which case it is the only natural number that is not positive. Zero is a number which quantifies a count or an amount of size. In most
cultures Culture () is an umbrella term which encompasses the social behavior Social behavior is behavior Behavior (American English) or behaviour (British English; American and British English spelling differences#-our, -or, see spelling diff ...
, 0 was identified before the idea of negative things (i.e., quantities less than zero) was accepted. As a value or a ''number'', zero is not the same as the ''digit'' zero, used in
numeral system A numeral system (or system of numeration) is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using Numerical digit, digits or other symbols in a consistent manner. The same s ...
s with
positional notation Positional notation (or place-value notation, or positional numeral system) usually denotes the extension to any base Base or BASE may refer to: Brands and enterprises * Base (mobile telephony provider), a Belgian mobile telecommunications ope ...
. Successive positions of digits have higher weights, so the digit zero is used inside a numeral to skip a position and give appropriate weights to the preceding and following digits. A zero digit is not always necessary in a positional number system (e.g., the number 02). In some instances, a
leading zero In typography, leading ( ) is the space between adjacent lines of type; the exact definition varies. In hand typesetting, leading is the thin strips of lead (or aluminium) that were inserted between lines of type in the composing stick to incr ...
may be used to distinguish a number.


Elementary algebra

The number 0 is the smallest
non-negative In mathematics, the sign of a real number is its property of being either positive, negative number, negative, or zero. Depending on local conventions, zero may be considered as being neither positive nor negative (having no sign or a unique third ...
integer. The
natural number In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and total order, ordering (as in "this is the ''third'' largest city in the country"). In common mathematical terminology, w ...
following 0 is 1 and no natural number precedes 0. The number 0 may or may not be considered a natural number, but it is an integer, and hence a
rational number In mathematics, a rational number is a number that can be expressed as the quotient or fraction (mathematics), fraction of two integers, a numerator and a non-zero denominator . For example, is a rational number, as is every integer (e.g. ) ...
and a
real number In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers ( and ), formulas and related structures (), shapes and spaces in which they are contained (), and quantities and their changes ( and ). There is no g ...
(as well as an
algebraic number An algebraic number is any complex number In mathematics, a complex number is an element of a number system that contains the real numbers and a specific element denoted , called the imaginary unit, and satisfying the equation . Moreover, ev ...
and a
complex number In mathematics, a complex number is an element of a number system that contains the real numbers and a specific element denoted , called the imaginary unit, and satisfying the equation . Moreover, every complex number can be expressed in the for ...

complex number
). The number 0 is neither positive nor negative, and is usually displayed as the central number in a
number line In elementary mathematics 300px, Both groups are equal to 5. Apples are frequently used to explain arithmetic in textbooks for children. Elementary mathematics consists of mathematics Mathematics (from Ancient Greek, Greek: ) include ...

number line
. It is neither a
prime number A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime ...
nor a
composite number A composite number is a positive integer In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calcul ...
. It cannot be prime because it has an
infinite Infinite may refer to: Mathematics *Infinite set, a set that is not a finite set *Infinity, an abstract concept describing something without any limit Music *Infinite (band), a South Korean boy band *''Infinite'' (EP), debut EP of American musi ...

infinite
number of , and cannot be composite because it cannot be expressed as a product of prime numbers (as 0 must always be one of the factors). Zero is, however, even (i.e. a multiple of 2, as well as being a multiple of any other integer, rational, or real number). The following are some basic (elementary) 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 In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities and th ...
(or neutral element) with respect to addition. * Subtraction: ''x'' − 0 = ''x'' and 0 − ''x'' = −''x''. * Multiplication: ''x'' · 0 = 0 · ''x'' = 0. * Division: = 0, for nonzero ''x''. But is undefined, because 0 has no
multiplicative inverse Image:Hyperbola one over x.svg, thumbnail, 300px, alt=Graph showing the diagrammatic representation of limits approaching infinity, The reciprocal function: . For every ''x'' except 0, ''y'' represents its multiplicative inverse. The graph forms a r ...

multiplicative inverse
(no real number multiplied by 0 produces 1), a consequence of the previous rule. * Exponentiation: ''x''0 = = 1, except that the case ''x'' = 0 may be left undefined in some
contexts ''Contexts'': ''Understanding People in their Social Worlds'' is a quarterly Peer review, peer-reviewed academic journal and an official publication of the American Sociological Association. It is designed to be a more accessible source of sociolog ...
. For all positive real ''x'', . The expression , which may be obtained in an attempt to determine the limit of an expression of the form as a result of applying the limit of a function, lim operator independently to both operands of the fraction, is a so-called "indeterminate form". That does not simply mean that the limit sought is necessarily undefined; rather, it means that the limit of , if it exists, must be found by another method, such as l'Hôpital's rule. 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.


Other branches of mathematics

* In set theory, 0 is the cardinality of the empty set: 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 ''definition, defined'' to be the empty set. When this is done, the empty set is the von Neumann cardinal assignment for a set with no elements, which is the empty set. The cardinality function, applied to the empty set, returns the empty set as a value, thereby assigning it 0 elements. * Also in set theory, 0 is the lowest ordinal number, corresponding to the empty set viewed as a well-order, well-ordered set. * In propositional calculus, propositional logic, 0 may be used to denote the truth value false. * In abstract algebra, 0 is commonly used to denote a zero element, which is a Identity element, neutral element for addition (if defined on the structure under consideration) and an absorbing element for multiplication (if defined). * In lattice (order), lattice theory, 0 may denote the Greatest element, bottom element of a Lattice (order), bounded lattice. * In category theory, 0 is sometimes used to denote an initial and terminal objects, initial object of a category (mathematics), category. * In recursion theory, 0 can be used to denote the Turing degree of the computable function, partial computable functions.


Related mathematical terms

* A root of a function, zero of a function ''f'' is a point ''x'' in the domain of the function such that . When there are finitely many zeros these are called the roots of the function. This is related to zero (complex analysis), zeros of a holomorphic function. * The zero function (or zero map) on a domain ''D'' is the constant function with 0 as its only possible output value, i.e., the function ''f'' defined by for all ''x'' in ''D''. The zero function is the only function that is both Even function, even and Odd function, odd. A particular zero function is a zero morphism in category theory; e.g., a zero map is the identity in the additive group of functions. The determinant on non-invertible Matrix (mathematics), square matrices is a zero map. * Several branches of mathematics have zero elements, which generalize either the property , or the property or both.


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 Thermodynamic temperature, absolute temperature (as measured in kelvins), absolute zero, zero is the lowest possible value (negative temperatures are defined, but negative-temperature systems are not actually colder). This is in contrast to for example temperatures on the Celsius scale, where zero is arbitrarily defined to be at the Melting point, freezing point of water. 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. In physics, the zero-point energy is the lowest possible energy that a quantum mechanics, quantum mechanical physical system may possess and is the energy of the Stationary state, ground state of the system.


Chemistry

Zero has been proposed as the atomic number of the theoretical element tetraneutron. It has been shown that a cluster of four neutrons may be stable enough to be considered an atom in its own right. This would create an chemical element, element with no protons and no charge on its atomic nucleus, nucleus. As early as 1926, Andreas von Antropoff coined the term neutronium for a conjectured form of matter made up of neutrons with no protons, which he placed as the chemical element of atomic number zero at the head of his new version of the periodic table. It was subsequently placed as a noble gas in the middle of several spiral representations of the periodic system for classifying the chemical elements.


Computer science

The most common practice throughout human history has been to start counting at one, and this is the practice in early classic computer programming languages such as Fortran and COBOL. 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. For example, the elements of an Array data type, array are numbered starting from 0 in C (computer language), C, so that for an array of ''n'' items the sequence of array indices runs from 0 to . This permits an array element's location to be calculated by adding the index directly to address of the array, whereas 1-based languages precalculate the array's base address to be the position one element before the first. There can be confusion between 0- and 1-based indexing, for example Java's JDBC indexes parameters from 1 although Java (programming language), Java itself uses 0-based indexing. In databases, it is possible for a field not to have a value. It is then said to have a null (SQL), null value. 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 Ternary logic, 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. A null pointer is a pointer in a computer program that does not point to any object or function. In C, the integer constant 0 is converted into the null pointer at compile time when it appears in a pointer context, and so 0 is a standard way to refer to the null pointer in code. However, the internal representation of the null pointer may be any bit pattern (possibly different values for different data types). In mathematics both −0 and +0 represent exactly the same number, i.e., there is no "positive zero" or "negative zero" distinct from zero. 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 one's 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 floating point, IEEE 754 and IBM hexadecimal floating-point, IBM S/390 floating point formats). In binary, 0 represents the value for "off", which means no electricity flow. Zero is the value of false in many programming languages. The Unix epoch (the date and time associated with a zero timestamp) begins the midnight before the first of January 1970. The Classic Mac OS epoch (computing), epoch and Palm OS epoch (the date and time associated with a zero timestamp) begins the midnight before the first of January 1904. Many Application programming interface, 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 code, error or warning conditions. Programmers often use a Slashed zero#Usage, slashed zero to avoid confusion with the letter "O".


Other fields

* In zoology, 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. * In telephony, pressing 0 is often used for dialling out of a Business telephone system, company network or to a different Trunk prefix, city or region, and 00 is used for dialling International call prefix, abroad. In some countries, dialling 0 places a call for operator assistance. * DVDs that can be played in any region are sometimes referred to as being "region 0" * Roulette wheels usually feature a "0" space (and sometimes also a "00" space), whose presence is ignored when calculating payoffs (thereby allowing the house to win in the long run). * In Formula One, if the reigning List of Formula One World Drivers' Champions, World Champion no longer competes in Formula One in the year following their victory in the title race, 0 is given to one of the drivers of the team that the reigning champion won the title with. This happened in 1993 and 1994, with Damon Hill driving car 0, due to the reigning World Champion (Nigel Mansell and Alain Prost respectively) not competing in the championship. * On the U.S. Interstate Highway System, in most states exits are numbered based on the nearest milepost from the highway's western or southern terminus within that state. Several that are less than half a mile (800 m) from state boundaries in that direction are numbered as Exit 0.


Symbols and representations

The modern 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. 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 Visual display unit, displays. A slashed zero (0\!\!\!) can be used to distinguish the number from the letter (mostly used in computing, navigation and in the military). 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 one of the capital-O–digit-0 pair more rounded and the other more angular (closer to a rectangle). A further distinction is made in FE-Schrift, falsification-hindering typeface as used on Vehicle registration plates of Germany, German car number plates by slitting open the digit 0 on the upper right side. Sometimes the digit 0 is used either exclusively, or not at all, to avoid confusion altogether.


Year label

In the Before Christ, BC calendar era, the year 1 BC is the first year before AD 1; there is not a year zero. By contrast, in astronomical year numbering, the year 1 BC is numbered 0, the year 2 BC is numbered −1, and so forth.


See also

*
Brahmagupta Brahmagupta ( – ) was an Indian Indian mathematics, mathematician and Indian astronomy, astronomer. He is the author of two early works on mathematics and astronomy: the ''Brāhmasphuṭasiddhānta'' (BSS, "correctly established Siddhanta, doc ...

Brahmagupta
* Division by zero * Grammatical number * Gwalior Fort * Mathematical constant * Number theory * Peano axioms * Signed zero * 0th (disambiguation), Zeroth (zero as an ordinal number)


Notes


References


Bibliography

* * * *


Historical studies

* * * * *


External links


Searching for the World's First Zero



Zero Saga


* Edsger W. Dijkstra
Why numbering should start at zero
EWD831 (Portable Document Format, PDF of a handwritten manuscript) * * * {{DEFAULTSORT:0 (Number) 0 (number), Elementary arithmetic Integers, 00 Indian inventions