Prepared by : Richa Agrawal

Importance0 (zero) is both a number and the numerical digit used to represent that number in numerals.

It fulfils 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

system.

History India

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 sunya to refer to zero or void. The use of a blank on a counting board to represent 0 dated back in India to 4th century BC. In 498 AD, Indian mathematician and astronomer Aryabhatta stated that "from place to place each is ten times the preceding "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 lokavibhaga, dated 458 AD, where shunya ("void" or "empty") was employed for this purpose .

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.

As a year label

0 (year)

In the BC calendar era ,the year 1 BC is the first year before AD 1; no room is reserved for a year zero. By contrast, in astronomical year numbering, the year 1 BC is numbered 0, the year 2 BC is numbered −1, and so on.

InventionThe credit for this goes to Indian

mathematicians and the number zero first appears in a book about ‘arithmetic’ written by an Indian mathematician ‘Brahamagupta’. Zero signifies ‘nothing’ and the current definition calls it an ‘additive identity’.

Aryabhatta

Aryabhatta, the greatest Indian mathematician of ancient era, has been famous for his mathematical works and theorems on astronomical bodies that have been found to be very accurate in terms of modern calculations. "Aryabhatiya", his only work to have survived has given the world innumerable theorems and research subjects.

Mathematicians

His two other major contributions are the, introduction of zero to the world and calculating the approximate value of pie. His works are also spread in fields like include algebra, arithmetic, trigonometry, quadratic equations and the sine table.

Ramanujam

Srinivasa Ramanujan Iyengar, the greatest Indian mathematician of 20th century, contributed

immensely in fields like number theory, mathematical analysis, string theory and

crystallography.

 

Although he lived for a short span of 32 years, he compiled nearly 3900 phenomenal results that leave even the best mathematical brains of today in sheer awe and wonder!

His genius has been admired by some greatest contemporary mathematicians of his time. He is hailed to be one of the most famous mathematicians in the field of number theory.

Archimedes

The greatest mathematicians of ancient era, Archimedes made phenomenal contribution in the field of mathematics. His works include integral calculus studies and finding various computation techniques to determine volume and area of several shapes including the conic section.

Euclid

Euclid, the 'father of Geometry', wrote the book ,"Euclid's Elements", that is considered to be the greatest piece of historical works in mathematics. The book is divided into 13 parts and in it, Euclid has discussed in details about geometry (what is now called Euclidean geometry).

His contributions are also famous in the fields of spherical geometry, conic sections and number theory.

Rules of Brahmagupta

• The rules governing the use of zero appeared for the first time in Brahmagupta's book Brahmasputha Siddhanta (The Opening of the Universe),written in 628 AD.

• 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 Brahmagupta:

• 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 their absolute values 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 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.

The most difficult concept in mathematics is operations involving zero. Zero is far from nothing, what exactly it is can be is difficult to explain and understand.

One of the most difficult concepts in mathematics is doing operations involving zero. Contrary to popular opinion zero is far from being nothing, but what exactly it is can be difficult to explain and understand.

• When we add or subtract using zero we generally think that what we are adding nothing, and in this situation we would be correct in using that thinking. However there are some cases when zero means something or what it means can't be accurately described.

Multiplication by zero does nothing to change the generally held concept of zero being "nothing". When we multiply any number by zero the result is simply zero.

While this result is understood as universal, multiplication in more advanced mathematics proves that this is not always so. Using exponents or raising a number to a power is one example where zero doesn't mean nothing.

One of the more interesting concepts involves the fact that division by zero is undefined. Proof of this statement can yield some amazing and interesting results.

Thank you