INVENTION AND ROLE OF ZERO

SUBMITTED BY SHASWATI SINGHCLASS: TENTH ( X )

SCHOOL : VIKASH PUBLIC SCHOOL

WHAT IS ZERO? Zero is a strange number and one of the greatest

paradoxes of human thoughts. it means both everything and nothing. It is both a number and numerical digit used to represent that numbers in numerals. It fulfills a central role in mathematics as the addive identity of integers, real numbers, and many other algebraic structures. Without zero, not just mathematics, but all branches of science would have struggled for clear definitions. As a digit zero is used as a placeholder in place value systems. The value of ZERO is well known today as it holds it’s highest value today. Without the invention of zero, the BINARY SYSTEM and computer are not possible. It is the greatest invention on which every calculation depends. Zero is a tiny number but cannot be ignored!!

UNIQUE NUMBER ZERO ZERO, the ingenuity of our fore fathers. The

number zero is neither positive nor negative. It appears on the middle of the number line. It is neither a prime nor a composite

number. It cannot be prime no. because it has infinite number of factors and cannot be expressed as multiplying prime numbers ( 0 must always be one of the factors ).

EXISTENCE OF ZERO Initially, zero was not considered a number. There was the idea of

empty space, which may be thought conceptually similar to zero. Babylonians around 700 BC used two hooks to denote an empty space in the positional notation. Records show that the ancient Greeks seemed unsure about the status of zero as a number. The concept a symbol of number and not merely a symbol of 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 concept of zero took some time for acceptance. It was only around 1600 that zero began to come into widespread use after encountering a lot of support and also criticism from mathematician around the world.

HISTORY OF ZERO It is said that the number zero was originated in

these three places – Ancient India, Ancient Babylon and the Mayan civilization . Historians believed that it came into existence from 458 AD. Zeroes were created at different times in each of these civilizations. But the one that people think was used first in ancient India by the Hindus and the Arabic's. Undoubtedly the complete credit goes to India for the invention of zero and it’s effects use as a number.

ZERO IN INDIA The number zero appear in the late 10th century in India. The concept of zero as a no. and not merely a symbol for separation is attributed to India, where by the ninth century CE, practical calculation were carried out using zero, which was treated like any other number, even in case of division. The word for zero in Hindu – India is “shunya” meaning void or empty. India is recognized with great respect for it’s invention for zero. These are the numbers that Hindus and Arabic's use.

ZERO IN BABYLON The Babylonians, who were famous for their astronomical observations and calculations used a sexagesimal (base-60) positional number system inherited from either the Sumerian or the Eblaite civilizations. The Babylonian system is credited as being the first known positional number system, in which the value of a particular digit depends both on the digit itself and its position within the number. This was an extremely important development, because non-place-value systems require unique symbols to represent each power of a base (ten, one hundred, one thousand, and so forth), making calculations difficult. The Babylonians did not technically have a digit for, nor a concept of, the number zero. Although they understood the idea of nothingness, it was not seen as a number—merely the lack of a number. What the Babylonians had instead was a space (and later a disambiguating placeholder symbol ) to mark the nonexistence of a digit in a certain place value

ZERO IN MAYAN CIVILIZATION• The Maya numeral system is a vegesimal (base-twenty) positional numeral

system used by the Pre Columbian Maya civilization.• The numerals are made up of three symbols; zero (shell shape, with

the plastron uppermost. The Maya calendar required the use of zero as a place-holder within its vigesimal positional numeral system. A shell glyph – – was used as a zero symbol for these Long Count dates, the earliest of which (on Stella 2 at Chiapa de Corzo, Chiapas) has a date of 36 BC. However, since the eight earliest Long Count dates appear outside the Maya homeland, it is assumed that the use of zero predated the Maya, and was possibly the invention of the Olmec. Indeed, many of the earliest Long Count dates were found within the Olmec heartland. However, the Olmec civilization had come to an end by the 4th century BC, several centuries before the earliest known Long Count dates—which suggests that zero was not an Olmec discovery.

EQUATIONS RELATED TO ZERO• The greatest mathematician of India , Brahmagupta

wrote on nature of zero in his book “Brahmagupta Siddhanth” 1) A + 0 = A 2) A – 0 = A 3) A x 0 = 0 4) A / 0 = 0 His first three equations were correct but he failed to

express the answer of fourth one. He told it as zero instead of infinity. Later it was solved by another famous Indian mathematician Bhaskar. It was mentioned in his famous book “Leelavathi”

THE RULES OF BRAHMAGUPTA• The sum or difference of zero and a zero is a zero.• The sum of zero and a negative number is a negative

number• The sum of zero and a positive number is a positive

number.• A positive or negative number when divided by zero

is a fraction with the zero as denominator.• Zero divided by either negative or a positive number

number is either zero or is expressed as zero as numerator and the finite quantity as denominator.

• Zero divided or multiplied by zero is always zero.

SYMBOL OF ZERO A Hindu astronomer and mathematician named Brahmagupta developed a symbol for zero –

a dot underneath numbers. This was recognized as a number of it’s own, as both an idea and a symbol. He also developed mathematical operations using zero, wrote rules for reaching zero through addition and subtraction, and the results of using zero in equations. The initial shape of zero was exactly the same thing as the letter ‘o’. It is only today that there is a distinction between zero and the letter ‘O’.

ROLE 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.

ROLE OF ZERO IN SCIENCE The value zero plays a special role for a large number of physical

quantities. For some quantities, the zero level is 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 is arbitrarily 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 value—for example, at a value for the threshold of hearing. The most common practice throughout human history has been to start counting at one. Nevertheless, in computer science zero has become the standard starting point. Many arithmetic concepts (such as hash tables) are less elegant to express in code unless the array starts at zero.

ROLE OF ZERO IN OUR LIFE• Zero is possibly one of the most important discoveries of all time, before its

discovery people rarely used numbers for anything beyond counting and so zero was not really required, you either had a number of sheep or none. Zero opened the way for more abstract ideas such as negative numbers, these let us solve geometric problems that would be impossible without negative numbers and zero. Without these numbers modern physics would be impossible there would be no theory of gravity as this requires negative potential energy, there would be no theories of movement as you need momentum calculations. Lending by banks to start businesses would be impossible without modern risk management relying on the sort of complex mathematics derived from the concept of zero.

Later on the concept of zero allowed modern mathematicians to think abstractly enough to develop the idea of "imaginary" numbers (the square roots of a negative number) finally leading to the ability to solve complex equations like the ones developed by the Greeks which started this search for new numbers off in the first place, this led to the ability to solve problems much more efficiently leading to among other things modern understanding of electronics and hence the modern computer.