0 (zero; ) is both a number and the numerical digit used to represent that number in numerals. It fulfills a central role in mathematics as the additive identity of the integers, real numbers, and many other algebraic structures. As a digit, 0 is used as a placeholder in place value systems. In the English language, 0 may be called zero, nought or (US) naught(), nil, or "o". Informal or slang terms for zero include zilch and zip. ''Ought'' or ''aught'' (), have also been used.
The value, or ''number'', zero is not the same as the ''digit'' zero, used in numeral systems 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.
In 976 AD the Persian encyclopedist Muhammad ibn Ahmad al-Khwarizmi, in his "Keys of the Sciences", remarked that if, in a calculation, no number appears in the place of tens, then a little circle should be used "to keep the rows". This circle the Arabs called صفر ''ṣifr'', "empty". That was the earliest mention of the name ''ṣifr'' that eventually became ''zero''.
Italian ''zefiro'' already meant "west wind" from Latin and Greek ''zephyrus''; this may have influenced the spelling when transcribing Arabic ''ṣifr''. 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, which was contracted to ''zero'' in Venetian.
As the decimal zero and its new mathematics spread from the Arab world to Europe in the Middle Ages, words derived from ''ṣifr'' and ''zephyrus'' came to refer to calculation, as well as to privileged knowledge and secret codes. According to Ifrah, "in thirteenth-century Paris, a 'worthless fellow' was called a '... cifre en algorisme', i.e., an 'arithmetical nothing'." From ''ṣifr'' also came French ''chiffre'' = "digit", "figure", "number", ''chiffrer'' = "to calculate or compute", ''chiffré'' = "encrypted". Today, the word in Arabic is still ''ṣifr'', and cognates of ''ṣifr'' are common in the languages of Europe and southwest Asia.
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 displays.
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 the some modern computer typefaces such as Andalé Mono. 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 falsification-hindering typeface 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.
== History ==
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.
Records show that the ancient Greeks 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 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.
The concept of zero as a number and not merely a symbol for separation is attributed to India where by the 9th century AD practical calculations were carried out using zero, which was treated like any other number, even in case of division. The Indian scholar Pingala (circa 5th-2nd century BC) used binary numbers in the form of short and long syllables (the latter equal in length to two short syllables), making it similar to Morse code. He and his contemporary Indian scholars used the Sanskrit word ''śūnya'' to refer to zero or ''void''.
=== History of zero ===
The Mesoamerican Long Count calendar developed in south-central Mexico and Central America required the use of zero as a place-holder within its vigesimal (base-20) positional numeral system. Many different glyphs, including this partial quatrefoil—File:MAYA-g-num-0-inc-v1.svg—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 assumed 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 4th century BC, several centuries before the earliest known Long Count dates.
Although zero became an integral part of Maya numerals, it did not influence 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.
The use of a blank on a counting board to represent 0 dated back in India to 4th century BC.
In China, counting rods were used for decimal calculation since the 4th century BC including the use of blank spaces. Chinese mathematicians understood negative numbers and zero, some mathematicians used 無入, 空, 口 for the latter, until Gautama Siddha introduced the symbol 0. ''The Nine Chapters on the Mathematical Art'', which was mainly composed in the 1st century AD, stated "[when subtracting] subtract same signed numbers, add differently signed numbers, subtract a positive number from zero to make a negative number, and subtract a negative number from zero to make a positive number."
By 130 AD, Ptolemy, influenced by Hipparchus and the Babylonians, was using a symbol for zero (a small circle with a long overbar) 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 first documented use of a ''number'' 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. In later Byzantine manuscripts of Ptolemy's ''Syntaxis Mathematica'' (also known as the ''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 computists (calculators of Easter). The initial "N" was used as a zero symbol in a table of Roman numerals by Bede or his colleague around 725.
In 498 AD, Indian mathematician and astronomer Aryabhata stated that "Sthanam sthanam dasa gunam" or place to place in ten times in value, which is the origin of the modern decimal-based place value notation.
The oldest known text to use a decimal place-value system, including a zero, is the Jain text from India entitled the ''Lokavibhâga'', dated 458 AD. This text uses Sanskrit numeral words for the digits, with words such as the Sanskrit word for ''void'' for 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 Chaturbhuja Temple at Gwalior in India, dated 876 AD. There are many documents on copper plates, with the same small ''o'' in them, dated back as far as the sixth century AD, but their authenticity may be doubted.
The Hindu-Arabic numerals and the positional number system were introduced around 500 AD, and in 825 AD, it was introduced by a Persian scientist, al-Khwārizmī, in his book on arithmetic. This book synthesized Greek and Hindu knowledge and also contained his own fundamental contribution to mathematics and science including an explanation of the use of zero.
It was only centuries later, in the 12th century, that the Arabic numeral system was introduced to the Western world through Latin translations of his ''Arithmetic''.
In saying zero divided by zero is zero, Brahmagupta differs from the modern position. Mathematicians normally do not assign a value to this, whereas computers and calculators sometimes assign NaN, which means "not a number." Moreover, non-zero positive or negative numbers when divided by zero are either assigned no value, or a value of unsigned infinity, positive infinity, or negative infinity. Once again, these assignments are not numbers, and are associated more with computer science than pure mathematics, where in most contexts no assignment is done.
Positional notation without the use of zero (using an empty space in tabular arrangements, or the word ''kha'' "emptiness") is known to have been in use in India from the 6th century. The earliest certain use of zero as a ''decimal'' positional digit dates to the 5th century mention in the text Lokavibhaga. The glyph for the zero digit was written in the shape of a dot, and consequently called ''bindu'' ("dot"). The dot had been used in Greece during earlier ciphered numeral periods.
The Hindu-Arabic numeral system (base 10) reached Europe in the 11th century, via the Iberian Peninsula through Spanish Muslims, the Moors, together with knowledge of astronomy and instruments like the astrolabe, first imported by Gerbert of Aurillac. 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 (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 ''algorismus'' after the Persian mathematician al-Khwārizmī. 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 number 0 is neither positive nor negative and appears in the middle of a number line. It is neither a prime number nor a composite number. It cannot be prime because it has an infinite number of factors and cannot be composite because it cannot be expressed by multiplying prime numbers (0 must always be one of the factors). Zero is, however, even (see parity of zero).
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 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 is 0, and the product of 0 numbers is 1. The factorial 0! evaluates to 1.
As early as 1926, Professor 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 1 based indexing, for example Java's JDBC indexes parameters from 1 although 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 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 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. Asking for all records with value 0 or value not equal 0 will not yield all records, since the records with value null are excluded.
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 "negative zero" distinct from zero. In some signed number representations (but not the two's complement representation used to represent integers in most computers today) and most floating point number representations, zero has two distinct representations, one grouping it with the positive numbers and one with the negatives; this latter representation is known as negative zero.
Category:Elementary arithmetic 00 Category:Nothing Category:Indian inventions
am:0 ar:0 (عدد) az:0 (ədəd) ba:0 (һан) bo:༠ (གྲངས་ཀ།) bs:0 (broj) bg:Нула ca:Zero cs:Nula sn:Chipasina da:0 (tal) de:Null et:Null el:Μηδέν myv:Чаво es:Cero eo:Nulo eu:Zero fa:۰ (عدد) fo:0 (tal) fr:Zéro fur:0 (numar) gl:Cero gu:૦ (શૂન્ય) xal:0 ko:0 hi:शून्य hr:Nula io:Zero ig:0 (Ónúọgụgụ) id:0 (angka) ia:0 (numero) xh:Iqanda is:Núll it:0 (numero) he:0 (מספר) kn:ಸೊನ್ನೆ ka:ნული kk:Нөл rw:Ubusa rn:Ubusa ht:0 (nonm) ku:Sifir (hejmar) la:0 lv:Nulle lt:0 (skaičius) ln:Libúngútulú lg:Zeero lmo:Nümar 0 hu:0 (szám) mk:0 (број) ml:പൂജ്യം ms:0 (nombor) fj:Saiva nl:0 (getal) nds-nl:0 (getal) new:शून्य ja:0 no:Null nn:0 pa:੦ (ਅੰਕ) pnb:صفر pl:0 (liczba) pt:Zero ro:0 (cifră) qu:Ch'usaq yupay ru:0 (число) scn:Zeru simple:Zero sk:0 (číslo) sl:0 so:Eber srn:Numro 0 sr:0 (број) sh:0 (broj) fi:0 (luku) sv:0 (tal) tl:0 (bilang) ta:சுழியம் te:సున్న th:0 tr:0 (sayı) uk:0 (число) ur:صفر (عدد) vi:0 (số) vls:0 (getal) wo:Tus ts:Tandza yi:0 (נומער) yo:0 (nọ́mbà) zh-yue:0 zh:0This text is licensed under the Creative Commons CC-BY-SA License. This text was originally published on Wikipedia and was developed by the Wikipedia community.
Coordinates | 43°19′54″N45°38′41″N |
---|---|
name | The Fixx |
background | group_or_band |
origin | London, United Kingdom |
genre | New WavePop rockRock |
years active | 1980–present |
label | MCA, RCA, CMC, Rainman |
website | Official website |
current members | Cy CurninJamie West-OramRupert GreenallAdam WoodsDan K. Brown }} |
The Fixx is an English rock band formed in London in 1979. Their hits include "One Thing Leads to Another," "Red Skies," "Stand or Fall," "Saved by Zero," "Sign of Fire," "Are We Ourselves?," "Secret Separation," "Driven Out," "How Much Is Enough?," and "Deeper and Deeper," which was featured on the soundtrack of ''Streets of Fire''.
Later in 1980, McGrail left. At this point, the band added guitarist Jamie West-Oram (formerly of Phillip Rambow's band) and changed their name to The Fix. This iteration of the band recorded for 101 Records, releasing their first single ("Lost Planes") in February 1981. This track, along with several live tracks issued by 101 on various compilations, received some radio exposure on the BBC.
The Fix's raised profile eventually led to the group being offered a contract by MCA Records. Worried about the potential drug-user implication of the band's name, MCA insisted on a name change before signing them to the label. A compromise was reached as the band altered the spelling of their name to The Fixx, and a deal was duly inked.
Barret was replaced on bass by Alfie Agius for the ''Shuttered Room'' tour. Agius' stay in the band was short-lived, though, as he left during the 1983 recording of their next album ''Reach the Beach'', after having recorded three tracks. Agius is credited as co-writer on all the album's tracks, but the group for this album was officially credited as a quartet (Curnin, Greenall, West-Oram and Woods).
''Reach the Beach'' became (and remains) the group's most commercially successful album. Agius' bass work is featured on the album's first two singles "Saved by Zero" and "One Thing Leads to Another." Both these singles cracked the US top 40, and "One Thing Leads To Another" became the band's biggest-ever hit (#3 Canada, #4 US, and #33 Australia). Bassist Dan K. Brown performed on one album track, which was also the third US top 40 single from the album: "The Sign of Fire." Brown filled the bass spot in the Fixx for the subsequent tour, and was promoted to full membership status in the band.
The 1984 album ''Phantoms'' contained the hits "Are We Ourselves" and "Sunshine In The Shade." Another song from the period, "Deeper And Deeper," was released as the B-side of "Are We Ourselves" (and also appeared in an edited version on the soundtrack for the film ''Streets of Fire''). This track received substantial airplay on US modern rock radio stations.
In 1985 The Fixx recorded the song "A Letter to Both Sides" for the soundtrack of the film ''Fletch''. The next year they released their fourth album ''Walkabout'', containing "Secret Separation" (#1 on Billboard Magazine's "Album Rock" chart) and "Built for the Future." The 1987 album ''React'', containing both live and new studio material, was the last for MCA Records.
1988 saw their return with a new album ''Calm Animals'' and a new label RCA Records. This album contained another U.S. hit "Driven Out" (another #1 on Billboard's "Album Rock" chart).
The band returned to MCA for their next album, 1991's ''Ink''. The album featured "How Much Is Enough?" (#27 Canada, #35 US).
In 2002, The Fixx performed a cover version of Nancy Sinatra's 1960s classic "These Boots Are Made for Walkin'" for a special album called ''When Pigs Fly'', which featured unique remakes of songs from the 1960s through the 1990s.
In 2003, the band released their ninth studio album, ''Want That Life,'' with Gary Tibbs, formerly a member of Roxy Music, The Vibrators and Adam and the Ants on bass, replacing Tate.
Long-time bassist Dan K. Brown re-joined the band in 2008. The Fixx regularly tour the U.S., and recently celebrated 25 years of making music together, accompanied by the release of the 2 CD set ''Twentyfifth Anniversary Anthology'' compilation.
With the classic lineup back intact, The Fixx are recording their 10th studio album "Beautiful Friction" due for release in late summer 2011.
Year | Title | Chart Peak Position | Album | ||||||
UK Singles Chart>UK | Kent Report>Australia | Canadian Singles Chart>Canada | Billboard Hot 100>US | Modern Rock Tracks chart>MOD | Mainstream Rock Tracks chart>MSR | Hot Dance Club Play>Dance | |||
1979 | "Little Women" (as The Portraits) | ||||||||
1980 | "Hazards In The Home" (as The Portraits) | ||||||||
1981 | "Lost Planes" (as The Fix) | ||||||||
"Stand or Fall" | |||||||||
"Red Skies" | |||||||||
"Saved by Zero" | |||||||||
"One Thing Leads to Another" | |||||||||
"The Sign of Fire" | |||||||||
"Deeper And Deeper" | ''Streets of Fire'' ''Soundtrack'' § | ||||||||
"Are We Ourselves?" | rowspan="3" | ||||||||
"Sunshine in the Shade" | |||||||||
"Less Cities, More Moving People" | |||||||||
"Secret Separation" | rowspan="2" | ||||||||
"Built for the Future" | |||||||||
1987 | "Don't Be Scared" | ||||||||
"Driven Out" | |||||||||
"Precious Stone" | |||||||||
1991 | "How Much Is Enough?" | ||||||||
2000 | "One Thing Leads to Another (J. Benitez Remix)" |
Sources:
Category:British New Wave musical groups Category:English rock music groups Category:Musical groups from London Category:Musical groups established in 1980
de:The Fixx fr:The Fixx nl:The Fixx sv:The FixxThis text is licensed under the Creative Commons CC-BY-SA License. This text was originally published on Wikipedia and was developed by the Wikipedia community.
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