History of Zero [ 0 ]

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0 (Number)0 (zero) is both a numberand the numerical digit used to represent that number in numerals. It plays

a central role in mathematics as the additive identity of the integers, real numbers, and many otheralgebraic structures. As a digit, zero is used as a placeholder in place value systems. Historically, it

was the most recent digit to come into use. In the English language, zero may also be called null or

nil when a number, "oh" (IPA: [o]) or cipher (archaic) when a numeral, and nought or naught[1]

ineither context.

0 As A Number

0 is the integer between 1 and 1. In most systems, 0 was identified before the idea of 'negative

integers' was accepted. Zero is an even number.[2]

Zero is a number which quantifies a count or an amount of null size; that is, if the number of your

brothers is zero, that means the same thing as having no brothers, and if something has a weight of

zero, it has no weight. If the difference between the number of pieces in two piles is zero, it meansthe two piles have an equal number of pieces. Before counting starts, the result can be assumed to be

zero; that is the number of items counted before you count the first item and counting the first itembrings the result to one. And if there are no items to be counted, zero remains the final result.

While mathematicians accept zero as a number, some non-mathematicians would say that zero is not

a number, arguing that one cannot have zero of something (for example, 'zero oranges'). Others holdthat if one has a bank balance of zero, one has a specific quantity of money in that account, namely

none.

Almost all historians omit the year zero from the proleptic Gregorian and Julian calendars, butastronomers include it in these same calendars. However, the phrase Year Zero may be used to

describe any event considered so significant that it serves as a new base point in time.

0 As A Digit

The modern numerical digit 0 is usually written as a circle, an ellipse, or a rounded rectangle. While

the height of the 0 character is the same as the other digits in most modern typefaces, in typefaceswith text figures the character is often less tall (x-height).

On the seven-segment displays of calculators, watches, etc., 0 is usually

written with six line segments, though on some historical calculatormodels it was written with four line segments. The latter is less common

than the former.

The value, or number, zero (as in the "zero brothers" example above) is not the same as the digit

zero, used in numeral systems usingpositional 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 tothe preceding and following digits. A zero digit is not always necessary in a positional number

system:bijective numeration provides a possible counterexample.
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Distinguishing zero from O

The oval-shaped zero and circular letter O together came into use on

modern character displays. The zero with a dot in the centre seems to have

originated as an option on IBM 3270 displays (in theory this could beconfused with the Greek letter Theta on a badly focused display, but in

practice there was no confusion because theta was not a displayable

character). An alternative, the slashed zero (looking similar to the letter Oother than the slash), was primarily used in hand-written coding sheets before transcription to

punched cards or tape, and is also used in old-style ASCII graphic sets descended from the default

typewheel on the ASR-33 Teletype. This form is similar to the symbol , representing the empty

set, as well as to the letter used in several Scandinavian languages.

The convention which has the letter O with a slash and the zero without was used at IBM [citation needed]

and a few other early mainframe makers; this is even more problematic forScandinavians because itmeans two of their letters collide. Some Burroughs/Unisys equipment displays a zero with a reversed

slash. Another convention used on some early lineprinters left zero unornamented but added a tail or

hook to the letter-O so that it resembled an inverted Q or cursive capital letter-O ( )

The typeface used on some European number plates forcars distinguish the two symbols by making

the O rather egg-shaped and the zero more angular, but most of all by slitting open the zero on theupper right side, so the circle is not closed any more (as in German plates). The typeface chosen is

called flschungserschwerende Schrift (abbr.: FE Schrift), meaning "script which is harder to

falsify". Note that those used in the United Kingdom do not differentiate between the two as therecan never be any ambiguity if the design is correctly spaced; the same applies to UK Postcodes.

Sometimes the number zero is used exclusively or not at all to avoid confusion altogether. For

example, confirmation numbers used by Southwest Airlines use only the letters O and I instead of

the numbers 0 and 1.

Etymology

The word "zero" came via French zro from Venetian language zero, which (together with "cipher")

came via Italian zefiro from Arabic , afira = "it was empty", ifr = "zero", "nothing", which wasused to translate Sanskrit nya ( ), meaning void or empty.

Italian zefiro already meant "west wind" from Latin and Greek zephyrus; this may have influenced

the spelling when transcribing Arabic ifr.[3] The Italian mathematician Fibonacci (c.1170-1250),

who grew up in Arab North Africa and is credited with introducing the Hindu decimal system to

Europe, used the term zephyrum. This became zefiro in Italian, which was contracted to zero inVenetian, giving the modern English word.

As the Hindu decimal zero and its new mathematics spread from the Arab world to Europe in theMiddle Ages, words derived from sifr and zephyrus came to refer to calculation, as well as to

privileged knowledge and secret codes. According to Ifrah, "in thirteenth-century Paris, a 'worthlessfellow' was called a "... cifre en algorisme", i.e., an "arithmetical nothing"." [3] (Algorithm is also a

borrowing from the Arabic, in this case from the name of the 9th century mathematician al-

Khwarizmi.) From ifr also came French chiffre = "digit", "figure", "number", chiffrer = "to calculateor compute", chiffr= "encrypted". Today, the word in Arabic is still sifr, and cognates of sifr are

common throughout the languages of Europe and southwest Asia.
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History

By the mid 2nd millennium BC, the Babylonians had a sophisticated sexagesimal positional numeral

system. The lack of a positional value (or zero) was indicated by a space between sexagesimalnumerals. By 300 BC a punctuation symbol (two slanted wedges) was co-opted as a placeholder in

the same Babylonian system. In a tablet unearthed at Kish (dating from perhaps as far back as 700

BC), the scribe Bl-bn-aplu wrote his zeroes with three hooks, rather than two slanted wedges.[4]

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 (260), 3 and 180 (360), 4 and 240 (460), et al.,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: theyasked themselves "How can nothing be something?", leading tophilosophical 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.

Early use of something like zero by the Indian scholarPingala (circa 5th-2nd century BC), implied atfirst glance by his use ofbinary numbers, is only the modern binary representation using 0 and 1applied to Pingala's binary system, which used short and long syllables (the latter equal in length to

two short syllables), making it similar to Morse code.[5][6] Nevertheless, he and other Indian scholars

at the time used the Sanskrit word nya (the origin of the word zero after a series of transliterationsand a literal translation) to refer to zero or void.

History of zero

The use of a blank on a counting board to represent 0 dated

back in India to 4th century BC[8]. The Mesoamerican Long

Count calendardeveloped in south-central Mexico requiredthe use of zero as a place-holder within its vigesimal (base-

20) positional numeral system. A shell glyph was

used as a zero symbol for these Long Count dates, theearliest of which (on Stela 2 at Chiapa de Corzo, Chiapas)

has a date of 36 BC.[9] Since the eight earliest Long Count

dates appear outside the Maya homeland,[10] it is assumedthat the use of zero in the Americas predated the Maya and

was possibly the invention of the Olmecs. Indeed, many ofthe earliest Long Count dates were found within the Olmec

heartland, although the fact that the Olmec civilization hadcome to an end by the 4th century BC, several centuries

before the earliest known Long Count dates, argues against

the zero being an Olmec discovery.

Although zero became an integral part ofMaya numerals, it,of course, did not influence Old World numeral systems.

In China, counting rods were used for calculation since the 4th century BCE and Chinesemathematicians understood negative numbers and zero, though they had no symbol for the latter. [11]

The Nine Chapters on the Mathematical Art, which was mainly composed in the 1st century CE,

stated "[when subtracting] subtract same signed numbers, add differently signed numbers, subtract apositive number from zero to make a negative number, and subtract a negative number from zero to

make a positive number."[12]
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By 130, 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 alphabeticGreek 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 wereusually 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 his Syntaxis

Mathematica (Almagest), the Hellenistic zero had morphed into the Greek letteromicron (otherwisemeaning 70).

Another zero was used in tables alongside Roman numerals by 525 (first known use by DionysiusExiguus), 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 ofEaster). An isolated use of their initial, N, was used in a table ofRoman numerals by Bede or a colleague about 725, a zero symbol.

In 498 AD, Indian mathematician and astronomer Aryabhata stated that "Sthanam sthanam dasa

gunam" or place to place in ten times in value, which may be the origin of the modern decimal basedplace value notation.[13]

The oldest known text to use zero is the Jain text from India entitled the Lokavibhaaga, dated 458

AD.[14] it was first introduced to the world centuries later by Al-Khwarizmi, a Persian mathematician,astronomer and geographer[citation needed]. He was the founder of several branches and basic concepts of

mathematics. In the words of Philip Hitti, Al Khawarizmi's contribution to mathematics influencedmathematical thought to a greater extent. His work on algebra initiated the subject in a systematic

form and also developed it to the extent of giving analytical solutions of linear and quadratic

equations, which established him as the founder of Algebra. The very name Algebra has beenderived from his famous bookAl-Jabr wa-al-Muqabilah.

His arithmetic synthesized Greek and Hindu knowledge and also contained his own contribution of

fundamental importance to mathematics and science. Thus, he explained the use of zero, a numeralof fundamental importance developed by the Indians. And 'algorithm' or 'algorizm' is named after

him.

The first apparent appearance of a symbol for zero appears in 876 in India on a stone tablet in

Gwalior. Documents on copper plates, with the same small o in them, dated back as far as the sixth

century AD, abound.

Zero as a decimal digit

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 9th century. The glyph for the zero digitwas written in the shape of a dot, and consequently calledbindu ("dot").

The Indian numeral system(base 10) reached Europe in the 11th century, via the Iberian Peninsula

through SpanishMuslims the Moors, together with knowledge ofastronomy and instruments like theastrolabe, first imported by Gerbert of Aurillac. So in Europe they came to be known as "Arabic

numerals". The Italian mathematician Fibonacci or Leonardo of Pisa was instrumental in bringingthe 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 thePisan merchants who thronged to it, he took charge; and in view of its future usefulness andconvenience, 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
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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 placesthereafter, 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 asalmost 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 ofEuclid'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 displayedwith 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 ornecessary, 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 word sign "0", indicating it is like a sign to do operations like

addition or multiplication, but he did not recognize zero as a number in its own right. From the 13th

century, manuals on calculation (adding, multiplying, extracting roots etc.) became common inEurope where they were called algorimus after the Persian mathematician al-Khwarizmi. The most

popular was written by John ofSacrobosco about 1235 and was one of the earliest scientific books tobe printed in 1488. Hindu-Arabic numerals until the late 15th century seem to have predominated

among mathematicians, while merchants preferred to use the abacus. It was only from the 16thcentury that they became common knowledge in Europe.

In Mathematics

A) Elementary algebra

Zero (0) is the least non-negativeinteger. The natural numberfollowing zero is one and no naturalnumber precedes zero. Zero 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).

In set theory, the number zero is the cardinality of the empty set: if one does not have any apples,

then one has zero apples. In fact, in certain axiomatic developments ofmathematics from set theory,zero is defined to be the empty set. When this is done, the empty set is the Von Neumann cardinal

assignment for a set with no elements, which is the empty set. The cardinality function, applied to the

empty set, returns the empty set as a value, thereby assigning it zero elements.

Zero is neither positive nor negative, neither aprime numbernor a composite number, nor is it a unit.It is, however, even (see evenness of zero). If zero is excluded from the rational numbers, the real

numbers or the complex numbers, the remaining numbers form an abelian group undermultiplication.

The following are some basic (elementary) rules for dealing with the number zero. These rules apply

for any real orcomplex numberx, unless otherwise stated.

Addition: x + 0 = 0 + x = x. That is, 0 is an identity element (or neutral element) with respect

to addition.

Subtraction: x 0 = x and 0 x = x.

Multiplication: x 0 = 0 x = 0.

Division: 0/x = 0, for nonzero x. Butx/0 is undefined, because 0 has no multiplicative inverse,

a consequence of the previous rule. For positive x, as y in x/y approaches zero from positive

values, its quotient increases toward positive infinity, but as y approaches zero from negative
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values, the quotient increases toward negative infinity. It is also said that x/0 equals unsigned

infinity, see division by zero.

Exponentiation: x0 = 1, except that the case x = 0 may be left undefined in some contexts. For

all positive real x, 0x = 0.

The expression 0/0 is an "indeterminate form". That does not simply mean that it is undefined; rather,

it means that the limit of f(x)/g(x) is determined by the particular functions f and g as they both

approach 0. As x approaches some number, the limit may approach any finite number, 0, , or ,depending on the specific behavior of the functions. See l'Hpital's rule.

The sum of 0 numbers is 0, and the product of 0 numbers is 1.

B) Extended use of zero in mathematics

Zero is the identity element in an additive group or the additive identity of a ring.

A zero of a function is a point in the domain of the function whose image under the function

is zero. When there are finitely many zeros these are called the roots of the function. See zero(complex analysis).

In geometry, the dimension of apoint is 0. The concept of "almost" impossible inprobability. More generally, the concept ofalmost

nowhere in measure theory. For instance: if one chooses a point on a unit line interval [0,1) at

random, it is not impossible to choose 0.5 exactly, but the probability that you will get iszero.

A zero function (or zero map) is a constant function with 0 as its only possible output value;i.e., f(x) = 0 for all x defined. A particular zero function is a zero morphism in category

theory; e.g., a zero map is the identity in the additive group of functions. The determinant on

non-invertible square matrices is a zero map.

Zero is one of three possible return values of the Mbius function. Passed an integer of the

form x or xy (for x > 1, x and y are both integers), the Mbius function returns zero.

Zero is the first Perrin number.

Importance

The importance of the creation of the zero mark can never be exaggerated. This giving to airy

nothing, not merely a local habitation and a name, a picture, a symbol, but helpful power, is thecharacteristic of the Hindu race from whence it sprang. It is like coining the Nirvana into dynamos.

No single mathematical creation has been more potent for the general on-go of intelligence and

power. G.B. Halsted

Dividing by zero...allows you to prove, mathematically, anything in the universe. You can prove that

1+1=42, and from there you can prove that J. Edgar Hoover is a space alien, that WilliamShakespeare came from Uzbekistan, or even that the sky is polka-dotted. (See appendix A for a proofthat Winston Churchill was a carrot.) Charles Seife, from: Zero: The Biography of a Dangerous Idea

...a profound and important idea which appears so simple to us now that we ignore its true merit. Butits very simplicity and the great ease which it lent to all computations put our arithmetic in the first

rank of useful inventions. Pierre-Simon Laplace

The point about zero is that we do not need to use it in the operations of daily life. No one goes out tobuy zero fish. It is in a way the most civilized of all the cardinals, and its use is only forced on us by

the needs of cultivated modes of thought. Alfred North Whitehead

...a fine and wonderful refuge of the divine spirit--almost an amphibian between being and non-being. Gottfried Leibniz
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When a person is pointed out by others as a fool or a '0' he must take it in that sense that there is this

vast empty space within him which he has ignored or which he has found a little hard to fill i.e a weebit harder than the rest that he has filled.. He must be self-effacing though as it will do him good

because the biggest zeroes in life later come up from the marsh as fascinating white horses..Shiksha . S . Suvarna

In Science

A) Physics

The value zero plays a special role for many physical quantities. For some quantities, the zero levelis naturally distinguished from all other levels, whereas for others it is more or less arbitrarily

chosen. 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 isarbitrarily defined to be at the freezing point of water. Measuring sound intensity in decibels or

phons, the zero level is arbitrarily set at a reference valuefor example, at a value for the thresholdof hearing. See also Zero-point energy.

B) Chemistry

Zero has been proposed as the atomic number of the theoretical element tetraneutron. It has beenshown that a cluster of fourneutrons may be stable enough to be considered an atom in their own

right. This would create an element with noprotons and no charge on its nucleus.

As early as 1926 Professor Andreas von Antropoff coined the term neutronium for a conjecturedform ofmatter 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 classifyingthe chemical elements. It is at the centre of the Chemical Galaxy (2005).

Rules of Brahmagupta

The rules governing the use of zero appeared for the first time in Brahmagupta's bookBrahmasputha

Siddhanta, written in 628. Here Brahmagupta considers not only zero, but negative numbers, and thealgebraic rules for the elementary operations of arithmetic with such numbers. In some instances, his

rules differ from the modern standard. Here are the rules of Brahamagupta: [16]

The sum of zero and a negative number is negative

The sum of zero and a positive number is positive

The sum of zero and zero is zero.

The sum of a positive and a negative is their difference; or, if they are equal, zero

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.

In saying zero divided by zero is zero, Brahmagupta differs from the modern position.

Mathematicians normally do not assign a value, whereas computers and calculators will sometimesassignNaN, 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, ornegative infinity. Once again, these assignments are not numbers, and are associated more withcomputer science than pure mathematics, where in most contexts no assignment is done
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