Who invented and/or discovered the "0" (ZERO), and who spread it around?

Question

Discovery and/or invention of the "ZERO" is one of the greatest things in mathematics. So who did humanity this great thing?

Short answers, please.

Answer 1

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 sexagesimal numerals. 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 Bêl-bân-aplu wrote his zeroes with three hooks, rather than two slanted wedges.[2]

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), etc. looked the same because the larger numbers lacked a final sexagesimal placeholder. Only context could differentiate them.

Records show[citation needed] that the ancient Greeks seemed unsure about the status of zero as a number: they asked themselves "How can nothing be something?",[citation needed] leading to interesting 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 ancient Greeks even questioned whether 1 was a number.[citation needed])

Early use of something like zero by the Indian scholar Pingala (circa 5th-2nd century BC), implied at first glance by his use of binary numbers, is only the modern binary representation using 0 and 1 applied 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.[3][4] Nevertheless, he and other Indian scholars at the time used the Sanskrit word śūnya (the origin of the word zero after a series of transliterations and a literal translation) to refer to zero or void.[5]


The back of Stela C from Tres Zapotes, an Olmec archaeological site
This is the second oldest Long Count date yet discovered. The numerals 7.16.6.16.18 translate to September 32 BCE (Julian). The glyphs surrounding the date are what is thought to be one of the few surviving examples of Epi-Olmec script.
[edit] History of zero
The Mesoamerican Long Count calendar developed in south-central Mexico required the 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, 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,[6] it is assumed that the use of zero in the Americas predated the Maya and was possibly the invention of the Olmecs. Indeed, many of the earliest Long Count dates were found within the Olmec heartland, although the fact that the Olmec civilization had come 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 of Maya numerals, it of course did not influence Old World numeral systems.

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 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 his Syntaxis Mathematica (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). An isolated use of their initial, N, was used in a table of Roman 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 based place value notation.[7]

The oldest known text to use zero is the Jain text from India entitled the Lokavibhaaga, dated 458 AD. [8]

The first indubitable 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.[9]


[edit] Rules of Brahmagupta
The rules governing the use of zero appeared for the first time in Brahmagupta's book Brahmasputha Siddhanta, written in 628. Here Brahmagupta 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. Here are the rules of Brahamagupta:[10]

The sum of two positive quantities is positive
The sum of two negative quantities is negative
The sum of zero and a negative number is negative
The sum of a positive number and zero 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
In subtraction, the less is to be taken from the greater, positive from positive
In subtraction, the less is to be taken from the greater, negative from negative
When the greater however, is subtracted from the less, the difference is reversed
When positive is to be subtracted from negative, and negative from positive, they must be added together
The product of a negative quantity and a positive quantity is negative
The product of a negative quantity and a negative quantity is positive
The product of two positive, is positive
Positive divided by positive or negative by negative is positive
Positive divided by negative is negative. Negative divided by positive is negative
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 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 made. (See division by zero)


[edit] Zero as a decimal digit
See also: History of the Hindu-Arabic numeral system.
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 digit was written in the shape of a dot, and consequently called bindu "dot".

The Hindu 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. So in Europe they came to be known 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.[11][12]

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 on its own right. From the 13th century, manuals on calculation (adding, multiplying, extracting roots etc.) became common in Europe where they were called algorimus after the Persian mathematician al-Khwarizmi. The most popular was written by John of Sacrobosco about 1235 and was one of the earliest scientific books to be 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 16th century that they became common knowledge in Europe.


[edit] In mathematics

[edit] Elementary algebra
Zero (0) is the lowest non-negative integer. The natural number following zero is one and no natural number precedes zero. Zero may or may not be counted as a natural number, depending on the definition of natural numbers.

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 of mathematics 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 a prime number nor a composite number, nor is it a unit. If zero is excluded from the rational numbers, the real numbers or the complex numbers, the remaining numbers form an abelian group under multiplication.

The following are some basic rules for dealing with the number zero. These rules apply for any complex number x, 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. But x / 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 values, the quotient increases toward negative infinity. The different quotients confirms that division by zero is undefined.
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 if f(x) and g(x) both approach 0 as x approaches some number, then f(x)/g(x) could approach any finite number or ∞ or −∞; it depends on which functions f and g are. See l'Hôpital's rule.

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


[edit] 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 a point is 0.
The concept of "almost" impossible in probability. More generally, the concept of almost 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 is zero.
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 Möbius function. Passed an integer of the form x2 or x2y (for x > 1), the Möbius function returns zero.
Zero is the first Perrin number.

Answer 2

The zero or the 'shunya' originated in India. The Arabs were given this informations by ancient Indians who then spread it to Europe in their trade travels. The Europeans the migrated to other parts of the world like Australia and America, carrying it with them.
Nobody knows exactly which Indian came up with this, but the first known Indian to research and apply it in his calculations was the ancient Indian astronomer, Aryabhatta.
The zero helped Europe in a big way. Till the Arabs arrived, they followed Roman numericals which stopped them from making huge calculations easily. The largest Roman number was 'M' whose value was 1000. One had to write 'M' 93000 times to express the distance between the sun and the earth!

Answer 3

That was one of the best pleas I've read in a long time and I sympathise with how you feel, even if I'm not gay. However I think it is a mistake to automatically associate hate with being put to death. Would you not put down your old crippled dog and still love him? Even the ArchDevil, Hitler, had them put to death. I would not advocate that and do not agree with the bible's statements on the subject. What I personally dislike is that, considering that there are well over 2 billion people on this planet that are religious and not in favour of 'gays', why you insist in affronting them with what they view as sin, and are always pressing for more tolerance, to the extent of having marriages and so on. So it can be no suprise to you that they react against it, even strongly. Wisdom would say stay in the closet and keep to yourselves. When things get rough, as they are going to over the next few years and beyond, it is well known that populations turn on minorities they dislike to give vent to their fear and anger. As Christ said, Let he who is without sin throw the first stone. I do not throw stones, but others will. Don't be a target seems commonsense and perhaps even wise.

Answer 4

zero was found out by indians though tey say that it was the chinees who invented it but i`ve got no idea how it got spread probably through talented mathematicians

Answer 5

http://en.wikipedia.org/wiki/0_%28number%29

Check out the history section.

Fibonacci was largely responsible for its acceptance in Europe.

Answer 6

Zero doesn't exist. It's a myth, just like eleventeen.

Answer 7

http://mathforum.org/library/drmath/view/52566.html

Answer 8

The Arabs, who are therefore good for nothing ;>)

(Oh, come on, you know it's funny)