Zero Go Movie

[Henrietta Naughton]

0zero) is a number representing an empty quantity. Adding 0 to any number leaves that number unchanged. In mathematical terminology, 0 is the additive identity of the integers, rational numbers, real numbers, and complex numbers, as well as other algebraic structures. Multiplying any number by 0 has the result 0, and consequently, division by zero has no meaning in arithmetic.

As a numerical digit, 0 plays a crucial role in decimal notation: it indicates that the power of ten corresponding to the place containing a 0 does not contribute to the total. For example, "205" in decimal means two hundreds, no tens, and five ones. The same principle applies in place-value notations that uses a base other than ten, such as binary and hexadecimal. The modern use of 0 in this manner derives from Indian mathematics that was transmitted to Europe via medieval Islamic mathematicians and popularized by Fibonacci. It was independently used by the Maya.

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. The British English words "nought" or "naught", and "nil" are also synonymous.[5][6]

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 Canadian postal codes) may exclude the use of the letter O.[citation needed]

Ancient Egyptian numerals were of base 10.[8] They used hieroglyphs for the digits and were not positional. In one papyrus written around 1770 BC, a scribe recorded daily incomes and expenditures for the pharaoh's court, using the nfr hieroglyph to indicate cases where the amount of a foodstuff received was exactly equal to the amount disbursed. Egyptologist Alan Gardiner suggested that the nfr hieroglyph was being used as a symbol for zero. 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.[9]

By the middle of the 2nd millennium BC, Babylonian mathematics had a sophisticated base 60 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 Bl-bn-aplu used three hooks as a placeholder in the same Babylonian system.[10] By 300 BC, a punctuation symbol (two slanted wedges) was repurposed as a placeholder.[11][12]

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.[a][14]

Since the eight earliest Long Count dates appear outside the Maya homeland,[15] it is generally believed that the use of zero in the Americas predated the Maya and was possibly the invention of the Olmecs.[16] Many of the earliest Long Count dates were found within the Olmec heartland, although the Olmec civilization ended by the 4th century BC, several centuries before the earliest known Long Count dates.[citation needed]

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.[citation needed]

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.[17]

The ancient Greeks had no symbol for zero (μηδέν, pronounced 'midn'), and did not use a digit placeholder for it.[18] According to mathematician Charles Seife, the ancient Greeks did begin to adopt the Babylonian placeholder zero for their work in astronomy after 500 BC, representing it with the lowercase Greek letter ό (όμικρον: omicron). However, after using the Babylonian placeholder zero for astronomical calculations they would typically convert the numbers back into Greek numerals. Greeks seemed to have a philosophical opposition to using zero as a number.[19] Other scholars give the Greek partial adoption of the Babylonian zero a later date, with neuroscientist Andreas Nieder giving a date of after 400 BC and mathematician Robert Kaplan dating it after the conquests of Alexander.[20][21]

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.[22]

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.[48]

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:[52][53]

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.

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.[55][56]

The Arabic-language inheritance of science was largely Greek,[57] followed by Hindu influences.[58] 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;[58] 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.[59] 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.[58]

Muhammad ibn Ahmad al-Khwarizmi, in 976, stated that if no number appears in the place of tens in a calculation, a little circle should be used "to keep the rows". This circle was called ṣifr.[60]

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 [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.[61]

Today, the numerical digit 0 is usually written as a circle or ellipse. Traditionally, many print typefaces made the capital letter O more rounded than the narrower, elliptical digit 0.[65] Typewriters originally made no distinction in shape between O and 0; some models did not even have a separate key for the digit 0. The distinction came into prominence on modern character displays.[65]

The concept of zero plays multiple roles in mathematics: as a digit, it is an important part of positional notation for representing numbers, while it also plays an important role as a number in its own right in many algebraic settings.

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