About zero apr balance transfer  zero_apr_balance_transfer
"Towards standards for handwritten zero and oh: much ado about nothing (and a letter), or a partial dossier on distinguishing between handwritten zero and oh".
"from place to place each is ten times the preceding"[14] which is the origin of the modern decimalbased place value notation.
A further distinction is made in falsificationhindering typeface as used on German car number plates by slitting open the digit 0 on the upper right side.
A zero digit is not always necessary in a positional number system, for example, in the number 02.
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.
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.
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.
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).
But x⁄0 is undefined, because 0 has no multiplicative inverse (no real number multiplied by 0 produces 1), a consequence of the previous rule; see division by zero.
By 300 BC, a punctuation symbol (two slanted wedges) was coopted as a placeholder in the same Babylonian system.
By contrast, in astronomical year numbering, the year 1 BC is numbered 0, the year 2 BC is numbered −1, and so on.
By most definitions[27] 0 is a natural number, and then the only natural number not to be positive.
For example, on the Kelvin temperature scale, zero is the coldest possible temperature (negative temperatures exist but are not actually colder), whereas on the Celsius scale, zero is arbitrarily defined to be at the freezing point of water.
For example, the elements of an array are numbered starting from 0 in C, so that for an array of n items the sequence of array indices runs from 0 to n−1.
For some quantities, the zero level is naturally distinguished from all other levels, whereas for others it is more or less arbitrarily chosen.
Here Brahmagupta considers not only zero, but negative numbers, and the algebraic rules for the elementary operations of arithmetic with such numbers.
However, in the late 1950s LISP introduced zerobased 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.
However, the internal representation of the null pointer may be any bit pattern (possibly different values for different data types).
However, the positions were usually limited to the fractional part of a number (called minutes, seconds, thirds, fourths, etc.
I have striven to compose this book in its entirety as understandably as I could, dividing it into fifteen chapters.
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.
If you object to that noyearzero scheme, then don't use it: use the astronomer's counting scheme, with negative year numbers.
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.
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.
In fact, in certain axiomatic developments of mathematics from set theory, 0 is defined to be the empty set.
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).
In most cultures, 0 was identified before the idea of negative things (quantities) that go lower than zero was accepted.
In physics, the zeropoint energy is the lowest possible energy that a quantum mechanical physical system may possess and is the energy of the ground state of the system.
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.
In the English language, 0 may be called zero, nought or (US) naught ( /ˈnɔːt/), nil, or — in contexts where at least one adjacent digit distinguishes it from the letter "O" — oh or o ( /ˈoʊ/).
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).
It fulfils a central role in mathematics as the additive identity of the integers, real numbers, and many other algebraic structures.
It has been shown that a cluster of four neutrons may be stable enough to be considered an atom in its own right.
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 treatise Arithmetic.
It was subsequently placed as a noble gas in the middle of several spiral representations of the periodic system for classifying the chemical elements.
Many different glyphs, including this 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.
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.
Mathematicians normally do not assign a value to this, whereas computers and calculators sometimes assign NaN, which means "not a number.
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.
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.
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.
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).
Sometimes the digit 0 is used either exclusively, or not at all, to avoid confusion altogether.
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.
That does not simply mean that the limit sought is necessarily undefined; rather, it means that the limit of f(x)⁄g(x), if it exists, must be found by another method, such as l'Hôpital's rule.
The Italian mathematician Fibonacci or Leonardo of Pisa was instrumental in bringing the system into European mathematics in 1202, stating:
The cardinality function, applied to the empty set, returns the empty set as a value, thereby assigning it 0 elements.
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.
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 glyphs surrounding the date are thought to be one of the few surviving examples of EpiOlmec script.
The initial "N" was used as a zero symbol in a table of Roman numerals by Bede or his colleague around 725.
The lack of a positional value (or zero) was indicated by a space between sexagesimal numerals.
The most popular was written by Johannes de Sacrobosco, about 1235 and was one of the earliest scientific books to be printed in 1488.
The number 0 may or may not be considered a natural number, but it is a whole number and hence a rational number and a real number (as well as an algebraic number and a complex number).
The paradoxes of Zeno of Elea depend in large part on the uncertain interpretation of zero.
The use of a blank on a counting board to represent 0 dated back in India to 4th century BC.
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.
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.
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.
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.
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.
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.
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.
Today, the word in Arabic is still ṣifr, and cognates of ṣifr are common in the languages of Europe and southwest Asia.
Traditionally, many print typefaces made the capital letter O more rounded than the narrower, elliptical digit 0.
Until the late 15th century, HinduArabic numerals seem to have predominated among mathematicians, while merchants preferred to use the Roman numerals.
When this is done, the empty set is the Von Neumann cardinal assignment for a set with no elements, which is the empty set.
" Moreover, nonzero positive or negative numbers when divided by zero are either assigned no value, or a value of unsigned infinity, positive infinity, or negative infinity.
"[19] The word wúrù (無入) (rendered here as zero, its standard translation by mathematical historians) literally means "no entry" or "null enters".
"[29] From ṣifr also came French chiffre = "digit", "figure", "number", chiffrer = "to calculate or compute", chiffré = "encrypted".
0 (zero; BrE: /ˈzɪərəʊ/, ZIRRoh or AmE: /ˈziːroʊ/, ZEERoh) is both a number[1] and the numerical digit used to represent that number in numerals.
1170–1250), who grew up in North Africa and is credited with introducing the decimal system to Europe, used the term zephyrum.
A null pointer is a pointer in a computer program that does not point to any object or function.
A positive or negative number when divided by zero is a fraction with the zero as denominator.
A zero of a function f is a point x in the domain of the function such that f(x) = 0.
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.
Along with negative numbers, Chinese mathematicians understood zero[when?], and some of them indicated it with wúrù (無入 "no entry"), kōng (空 "empty") and the framelike symbol[vague] 口/囗,[vague] Gautama Siddha introduced the symbol 0[vague] in the 8th century.
Also in set theory, 0 is the lowest ordinal number, corresponding to the empty set viewed as a wellordered set.
Although zero became an integral part of Maya numerals, it did not influence Old World numeral systems.
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.
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.
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.
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.
By the middle of the 2nd millennium BC, the Babylonian mathematics had a sophisticated sexagesimal positional numeral system.
Ch’in Chushao's 1247 Mathematical Treatise in Nine Sections is the oldest surviving Chinese mathematical text using a round symbol for zero,[22] and Chinese authors were familiar with the idea of negative numbers well before the fifteenth century[when?] when they became well established in Europe.
DVDs that can be played in any region are sometimes referred to as being "region 0"
Example of the early Greek symbol for zero (lower right corner) from a 2nd century papyrus
Exponentiation: x0 = x/x = 1, except that the case x = 0 may be left undefined in some contexts; see Zero to the zero power.
Here Leonardo of Pisa uses the phrase "sign 0", indicating it is like a sign to do operations like addition or multiplication.
If an internal link led you here, you may wish to change the link to point directly to the intended article.
Ifrah, Georges (2000) The Universal History of Numbers: From Prehistory to the Invention of the Computer, Wiley.
In 976 AD the Persian encyclopedist Muhammad ibn Ahmad alKhwarizmi, 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".
In Formula One, if the reigning 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.
In abstract algebra, 0 is commonly used to denote a zero element, which is a neutral element for addition (if defined on the structure under consideration) and an absorbing element for multiplication (if defined).
In game design, balance is the concept and the practice of tuning relationships between a game's component systems.
In grammar, balancing refers to the use in subordinate clauses of verb forms identical to those in main clauses
In recursion theory, 0 can be used to denote the Turing degree of the partial computable functions.
In set theory, 0 is the cardinality of the empty set: if one does not have any apples, then one has 0 apples.
In some countries and some company phone networks, dialing 0 on a telephone places a call for operator assistance.
In the BC calendar era, the year 1 BC is the first year before AD 1; no room is reserved for a year zero.
Italian zefiro already meant "west wind" from Latin and Greek zephyrus; this may have influenced the spelling when transcribing Arabic ṣifr.
Kaplan, Robert (2000) The Nothing That Is: A Natural History of Zero, Oxford: Oxford University Press.
Language transfer, where native language grammar and pronunciation influence the learning and use of a second language
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.
Records show that the ancient Greeks seemed unsure about the status of zero as a number.
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).
Several branches of mathematics have zero elements, which generalise either the property 0 + x = x, or the property 0 × x = 0, or both.
Since the 4th century BC, counting rods were used in China for decimal calculations including the use of blank spaces.
The Chief Scouts' Advance Party Report, a review of Scouting, with international implications, that took place in the UK in 1966
The HinduArabic 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.
The HinduArabic numerals and the positional number system were introduced around 500 AD, and in 825 AD, it was introduced by a Persian scientist, alKhwārizmī,[23] in his book on arithmetic.
The Mesoamerican Long Count calendar developed in southcentral Mexico and Central America required the use of zero as a placeholder within its vigesimal (base20) positional numeral system.
The back of Olmec stela C from Tres Zapotes, the second oldest Long Count date discovered.
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 expression 0⁄0, which may be obtained in an attempt to determine the limit of an expression of the form f(x)⁄g(x) as a result of applying the lim operator independently to both operands of the fraction, is a socalled "indeterminate form".
The most common practice throughout human history has been to start counting at one, and this is the practice in early classic computer science programming languages such as Fortran and COBOL.
The number 0 is neither positive nor negative and appears in the middle of a number line.
The oldest known text to use a decimal placevalue system, including a zero, is the Jain text from India entitled the Lokavibhâga, dated 458 AD, where shunya ("void" or "empty") was employed for this purpose.
The rules governing the use of zero appeared for the first time in Brahmagupta's book Brahmasputha Siddhanta (The Opening of the Universe),[31] written in 628 AD.
The sum of a positive and a negative is their difference; or, if their absolute values are equal, zero.
The value, or number, zero is not the same as the digit zero, used in numeral systems using positional notation.
The word zero came via French zéro from Venetian zero, which (together with cypher) came via Italian zefiro from Arabic صفر, ṣafira = "it was empty", ṣifr = "zero", "nothing".
The zero function (or zero map) on a domain D is the constant function with 0 as its only possible output value, i.
There can be confusion between 0 and 1 based indexing, for example Java's JDBC indexes parameters from 1 although Java itself uses 0based indexing.
This article is based on material taken from the Free Online Dictionary of Computing prior to 1 November 2008 and incorporated under the "relicensing" terms of the GFDL, version 1.
Tire balance, the distribution of mass within an automobile tire and/or the wheel to which it is attached.
Transfer (public transit), a ticket that allows a passenger to use multiple conveyances in a single trip
Transfer DNA, the transferred DNA of the tumorinducing (Ti) plasmid of some species of bacteria such as Agrobacterium tumefaciens
Weighing scale, also known as a balance, a type of device used to measure the mass of an object.
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.
[11][12] He and his contemporary Indian scholars used the Sanskrit word śūnya to refer to zero or void.
[13] In 498 AD, Indian mathematician and astronomer Aryabhata stated that "sthānāt sthānaṁ daśaguņaṁ syāt"[14] (literally, "place to place in ten times in value"),[citation needed] i.
[15] 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[disambiguation needed] at Gwalior in India, dated 876 AD.
[16][17] 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.
[18] instructed "[when subtracting] subtract samesigned numbers,[vague] 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.
[24] Since the eight earliest Long Count dates appear outside the Maya homeland,[25] it is assumed that the use of zero in the Americas predated the Maya and was possibly the invention of the Olmecs.
[30] Typewriters originally made no distinction in shape between O and 0; some models did not even have a separate key for the digit 0.
[9][10] The Indian scholar Pingala (circa 5th2nd 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.
^ "Chapter 8" includes 正負術曰: 同名相除，異名相益，正無入負之，負無入正之。其異名相除，同名相益，正無入正之，負無入負之。 This may be found in context in Chinese text of The Nine Chapters on the Mathematical Art.
^ Its known text survives as a commentary on its fragments, prepared by Liu Hui in A.
^ No long count date actually using the number 0 has been found before the 3rd century AD, but since the long count system would make no sense without some placeholder, and since Mesoamerican glyphs do not typically leave empty spaces, these earlier dates are taken as indirect evidence that the concept of 0 already existed at the time.
^ a b Algebra with Arithmetic of Brahmagupta and Bhaskara, translated to English by Henry Thomas Colebrooke, London1817
^ a b Will Durant, 'The Story of Civilization', Volume 4, The Age of Faith, pp.
