0 ( zero; ) is both a number and the numerical digit used to represent that number in numeral system. The number 0 fulfills a central role in mathematics as the additive identity of the , , and many other structures. As a digit, 0 is used as a placeholder in place value systems. Names for the number 0 in English 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.
The Italian mathematician 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 zefiro in Italian, and was then contracted to zero in Venetian. The Italian word was already in existence (meaning "west wind" from Latin and Greek Anemoi) and may have influenced the spelling when transcribing Arabic ṣifr.
By the middle of the 2nd millennium BC, the Babylonian mathematics had a sophisticated sexagesimal positional numeral system. The lack of a positional value (or zero) was indicated by a space between sexagesimal numerals. By 300 BC, a punctuation symbol (two slanted wedges) was coopted as a placeholder in the same Babylonian system. In a tablet unearthed at Kish (dating from about 700 BC), the scribe Bêlbânaplu wrote his zeros with three hooks, rather than two slanted wedges.Kaplan, Robert. (2000). The Nothing That Is: A Natural History of Zero. Oxford: Oxford University Press.
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.
Since the eight earliest Long Count dates appear outside the Maya homeland,Diehl, p. 186 it is generally believed that the use of zero in the Americas predated the Maya and was possibly the invention of the . 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 tortoiselike "Plastron" used for many depictions of the "zero" numeral, it is assumed to have not influenced Old World numeral systems.
Quipu, a knotted cord device, used in the Inca Empire and its predecessor societies in the Andes region to record accounting and other digital data, is encoded in a decimal positional system. Zero is represented by the absence of a knot in the appropriate position.
By 130 AD, Ptolemy, influenced by Hipparchus and the Babylonians, was using a symbol for zero (a small circle with a long overbar) in his work on mathematical astronomy called the Syntaxis Mathematica, also known as the Almagest. The way in which it is used can be seen in his table of chords in that book. Ptolemy's zero was used within a sexagesimal numeral system otherwise using alphabetic Greek numerals. Because it was used alone, not just as a placeholder, this Hellenistic zero was perhaps the earliest documented use of a numeral representing zero in the Old World. However, the positions were usually limited to the fractional part of a number (called minutes, seconds, thirds, fourths, etc.)—they were not used for the integral part of a number, indicating a concept perhaps better expressed as "none", rather than "zero" in the modern sense. In later Byzantine Empire manuscripts of Ptolemy's Almagest, the Hellenistic zero had morphed into the Greek letter omicron (otherwise meaning 70).
Another zero was used in tables alongside Roman numerals by 525 (first known use by Dionysius Exiguus), but as a word, nulla meaning "nothing", not as a symbol. When division produced zero as a remainder, nihil, also meaning "nothing", was used. These medieval zeros were used by all future medieval computus. The initial "N" was used as a zero symbol in a table of Roman numerals by Bede or his colleagues around 725.
In AD 690, Wu Zetian promulgated Zetian characters, one of which was "〇". The word is now used as a synonym for the number zero.
Zero was not treated as a number at that time, but as a "vacant position".
Qin Jiushao'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 , as seen in The Nine Chapters on the Mathematical Art,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." much earlier than the 15th century when they became wellestablished in Europe.
It was considered that the earliest text to use a decimal placevalue system, including a zero, is the Lokavibhaga, 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). In this text, śūnya ("void, empty") is also used to refer to zero.Ifrah, Georges (2000), p. 416.
A symbol for zero, a large dot likely to be the precursor of the stillcurrent hollow symbol, is used throughout the Bakhshali manuscript, a practical manual on arithmetic for merchants, the date of which was uncertain. In 2017 three samples from the manuscript were shown by radiocarbon dating to come from three different centuries: from 224383 AD, 680779 AD, and 885993 AD, making it the world's oldest recorded use of the zero symbol. It is not known how the birch bark fragments from different centuries that form the manuscript came to be packaged together.
The origin of the modern decimalbased place value notation can be traced to the Aryabhatiya (c. 500), which states sthānāt sthānaṁ daśaguṇaṁ syāt "from place to place each is ten times the preceding." Aryabhatiya of Aryabhata, translated by Walter Eugene Clark.
The concept of zero as a digit in the decimal place value notation was developed in India, presumably as early as during the Gupta period , 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"The rules governing the use of zero appeared for the first time in Brahmagupta's Brahmasputha Siddhanta (7th century). This work considers not only zero, but negative numbers, and the algebraic rules for the elementary operations of arithmetic with such numbers. In some instances, his rules differ from the modern standard, specifically the definition of the value of zero divided by zero as zero. Algebra with Arithmetic of Brahmagupta and Bhaskara, translated to English by Henry Thomas Colebrooke (1817) London
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 of the Hindu numerals family). The number is the year of the inscription in the Saka era, corresponding to a date of AD 683.Cœdès, Georges, "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 MonKhmer Studies Journal, Vol. 25, 1996, pp. 125–132.
The first known use of special 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 Chaturbhuja Temple at Gwalior in India, dated 876.Ifrah, Georges (2000), p. 400. Zero is also used as a placeholder in the Bakhshali manuscript, portions of which date from AD 224–383.
In AD 813, astronomical tables were prepared by a Persian people mathematician, Muḥammad ibn Mūsā alKhwārizmī, 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 in the 12th century under the title Algoritmi de numero Indorum. This title means "alKhwarizmi on the Numerals of the Indians". The word "Algoritmi" was the translator's Latinization of AlKhwarizmi's name, and the word "Algorithm" or "Algorism" started meaning any arithmetic based on decimals.Muhammad ibn Ahmad alKhwarizmi, 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.Will Durant (1950), The Story of Civilization, Volume 4, The Age of Faith, Simon & Schuster, , p. 241, Quote = "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."
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 giveandtake 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 Hinduism (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 preeminent 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, L., Fibonacci's Liber Abaci. English translation, Springer, 2003.Grimm, R.E., "The Autobiography of Leonardo Pisano", Fibonacci Quarterly 11/1 (February 1973), pp. 99–104.
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 after the Persian mathematician alKhwārizmī. The most popular was written by Johannes de Sacrobosco, 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. In the 16th century, they became commonly used in Europe.
The value, or number, zero is not the same as the digit zero, used in using positional notation. Successive positions of digits have higher weights, so inside a numeral the digit zero is used 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, for example, in the number 02. In some instances, a leading zero may be used to distinguish a number.
The number 0 is neither positive nor negative and is usually displayed as the central number in a number line. It is neither a prime number nor a composite number. It cannot be prime because it has an infinity number of divisor, and cannot be composite because it cannot be expressed as a product of prime numbers (0 must always be one of the factors).
Zero is, however, even (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.
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 lim operator independently to both operands of the fraction, is a socalled "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.
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.
There can be confusion between 0 and 1based indexing, for example Java's JDBC indexes parameters from 1 although Java itself uses 0based indexing.
In databases, it is possible for a field not to have a value. It is then said to have a 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. 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 754 and 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. Paul DuBois. "MySQL Cookbook: Solutions for Database Developers and Administrators" 2014. p. 204. Arnold Robbins; Nelson Beebe. "Classic Shell Scripting". 2005. p. 274 Iztok Fajfar. "Start Programming Using HTML, CSS, and JavaScript". 2015. p. 160.
The MacOS epoch and Palm OS epoch (the date and time associated with a zero timestamp) begins the midnight before the first of January 1904. Darren R. Hayes. "A Practical Guide to Computer Forensics Investigations". 2014. p. 399
Many APIs and that require applications to return an integer value as an exit status typically use zero to indicate success and nonzero values to indicate specific error code or warning conditions.
A slashed zero can be used to distinguish the number from the letter. 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 capitalO–digit0 pair more rounded and the other more angular (closer to a rectangle). A further distinction is made in FESchrift as used on 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.
