Zero is a number that represents nothing or empty space. It was invented in ancient India and was an important development that allowed more advanced mathematics. Zero holds a central role and is the identity element in addition. It allows place-value systems like binary to function and is essential for computer science. Zero's existence was initially debated but is now widely used and crucial for science, mathematics, banking, and many other aspects of modern life.

1. INVENTION AND ROLE OF
ZERO
SUBMITTED BY SHASWATI SINGH
CLASS: TENTH ( X )
SCHOOL : VIKASH PUBLIC SCHOOL

2. 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!!

3. 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 ).

4. 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.

5. 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.

6. 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.

7. 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

8. 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.

11. 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”

12. 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.

13. 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’.

14. 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.

15. 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.

16. 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.