The word
zero came into the English language via
French from 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".
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 British English words
"nought" or "naught", and "
nil" are also synonymous. 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. Slang words for zero include "zip", "zilch", "nada", and "scratch". 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 , "the egg" – and "
duck" in
cricket, a shortening of "duck's egg". "Goose egg" is another general slang term used for zero. They used
hieroglyphs for the digits and were not
positional. In
one papyrus written around , 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. 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. 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 ), the scribe Bêl-bân-aplu used three hooks as a placeholder. By , a punctuation symbol (two slanted wedges) was repurposed as a placeholder. 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.” They were also not written at the end of a number (so 1 and 60 and 60×60 were all written as ).
Pre-Columbian Americas 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. 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
Olmecs. 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, 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.
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.
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. 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. 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. "The whole of the Greek universe rested on this pillar: There is no void." 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. 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. By AD150,
Ptolemy, influenced by
Hipparchus and the
Babylonians, was using a symbol for zero () in his work on
mathematical astronomy called the
Syntaxis Mathematica, also known as the
Almagest. 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 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, while the combination meant a zero angle. Minutes of immersion was also a continuous function (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. 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. 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. This use was repeated in 525 in an equivalent table, that was translated via the Latin ("none") by
Dionysius Exiguus, alongside
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—or his colleagues—around AD725.
China , based on the example provided by
A History of Mathematics. An empty space is used to represent zero. 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. The rods gave the decimal representation of a number, with an empty space denoting zero. 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. Chinese authors had been familiar with the idea of negative numbers, and decimal fractions, by the
Han dynasty , as seen in
The Nine Chapters on the Mathematical Art.
Qín Jiǔsháo's 1247
Mathematical Treatise in Nine Sections is the oldest surviving Chinese mathematical text using a round symbol '〇' for zero. The origin of this symbol is unknown; it may have been produced by modifying a square symbol. Zero was not treated as a number at that time, but as a "vacant position".
Chinese Epigraphy A variety of
Chinese characters have been used, through history, to represent zero: 空, 零, 洞, 〇.
India Pingala ( or 2nd century BC), a
Sanskrit prosody scholar, 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. Pingala used the
Sanskrit word
śūnya explicitly to refer to zero. A decimal place value
grapheme for zero was developed in
India. 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. The
Aryabhatiya ( 499), states
sthānāt sthānaṁ daśaguṇaṁ syāt "from place to place each is ten times the preceding". 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: 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, 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 There are numerous copper plate inscriptions with the same small 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,
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. 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. 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. followed by Hindu influences. 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; 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.
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 []. 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. From the 13th century, manuals on calculation (adding, multiplying, extracting roots, etc.) became common in Europe where they were called 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. The practice of calculating on paper using Hindu–Arabic numerals only gradually displaced calculation by
abacus and recording with
Roman numerals. In the 16th century, Hindu–Arabic numerals became the predominant numerals used in Europe. ==Symbols and representations==