7.
This one to one
correspondence gave
birth to many
mathematical symbols.
Some of these symbols
are now called as
NUMBERS.
8.
These
numbers/symbols, are
collectively called
counting numbers. And
mathematically they
are called
Natural Numbers.
9.
The collection of numbers 1,2,3,4,5… is
called as the set of NATURAL
NUMBERS, as these numbers are used
naturally for counting…
The symbol used for natural numbers is
10.
People from
different localities
and different
countries used
different symbols
to denote the
numbers…
13.
Babylonian numerals were written in
CUNEIFORM, using a wedge-tipped REED STYLUS
to make a mark on a soft CLAY tablet which
would be exposed in the SUN to harden to
create a permanent record.
14.
This system first appeared around 3100 BC. It is also
credited as being the first known
POSITIONAL NUMERAL SYSTEM,
in which the value of a particular digit depends both
on the digit itself and its position within the number
15.
Human’s
need for
numbers
seems to be
fulfilled
here…
16.
BUT its just the beginning…
His Need doesn't end.
NEED is the
MOTHER
of
INVENTIONS
and
DISCOVERIES
17.
One morning, he found
no animal
in the shed…
He was amazed to see the
empty shed…
18.
Suddenly a question came into
his mind…
No animal = no stone
No stone = what
symbol?
19.
Here he realized the need
for
“symbolizing NOTHING”
for the
first time…
NO
ANIMALS
20.
Many mathematicians of different
era has suggested for symbolizing
nothing but ARYABHATTA,
The INDIAN Mathematician was
the first who
Introduced the Symbol “0”
for symbolizing nothing, to the
world and made complicated
things easier.
21.
By the 9th century
AD, The number
system consists of
one more member
namely “0”…
The set of numbers
0,1,2,3,4,5…
is called as the set of
WHOLE NUMBERS.
Is used for
representing
the set of
whole
numbers
22.
But HUMAN NEEDS
DOESN’T FULFILLED HERE.
AS FAR AS THE HE
DEVELOPED THE SENSE
OF TRADE,
HE FOUND SOME OR THE
OTHER WAYS OF
EXCHANGE OF GOODS
AND SERVICES.ONE OF
THE WAY HE ADOPTED IS
THE BARTER SYSTEM
23.
The history of bartering dates all the way back to 6000 BC.
Introduced by Mesopotamia tribes, bartering was adopted by
Phoenicians. Phoenicians bartered goods to those located in
various other cities across oceans. Babylonian's also
developed an improved bartering system. Goods were
exchanged for food, tea, weapons, and spices. At times, human
skulls were used as well. Salt was another popular item
exchanged. Salt was so valuable that Roman soldiers' salaries
were paid with it. In the Middle Ages, Europeans traveled
around the globe to barter crafts and furs in exchange for silks
and perfumes. Colonial Americans exchanged musket balls,
deer skins, and wheat. When money was invented, bartering
did not end, it become more organized.
24.
Due to lack of money, bartering became
popular in the 1930s during the Great
Depression. It was used to obtain food and
various other services. It was done through
groups or between people who acted similar
to banks. If any items were sold, the owner
would receive credit (borrow) and the
buyer's account would be debited
(lending).
INFACT MONEY WASN’T ENOUGH
25.
This system of credits and debits introduced the
concept of borrowing in trade.
If I have nothing and I am borrowing money from
someone, it means I have a negative balance.
And, if I have a lot and someone else is
borrowing from me, I have positive balance…
26.
The positives and negatives in mathematics refer to positive numbers
and negative numbers.
These numbers are symbolized as
…-4,-3,-2,-1 etc.
27.
The collection of natural
numbers, zero and natural
numbers with –ve sign (called
as negative numbers) is defined
as the set of integers…
This symbol
used for the
set of
integers…
28.
With the flow of time, the
social relationships of
people improved. People
started sharing goods
with each other. This
sharing habit raise a
question in mathematics.
29.
Once, a boy was eating an apple. He
gave a part of the apple to his sister.
How much apple has he eaten?
And how much part his sister
received?
30.
Note that, part of the whole is
called as FRACTION. Thus, the
sister had a fraction of the Apple and the boy
also had another fraction of the same
Apple…
Sister’s
portion
Boy’s
portion
33.
The number written at the
above part of the fraction is
called as NUMERATOR and
the number written below the
bar is called as
DENOMINATOR.
NUMERATOR
DENOMINATOR
34.
… -327, -243, -137, -91, -86, -44, -30, -23, -5, -4, 0,
2,10, 34, 62, 97, 129, 294,892…
A handful of integers are written in the box
above.
Let us choose any two of them and write them
in the form of a fraction…
Eg:
__ __
, etc…
35.
A fraction in which numerator
and denominator are chosen
from the set of integers,
denominator non zero, is called
a RATIONAL NUMBER…
And, the collection of all such
rational numbers is called as
the set of RATIONAL
NUMBERS.
36.
We observe that any number can also be written in the form of
a decimal number. Further, A decimal number can be
categorized as follows…
DECIMAL
NUMBERS
TERMINATING NON-TERMINATING
RECURRING
DECIMALS
NON- RECURRING
DECIMALS
37.
TERMINATING
Eg: 4.5, 3.0, 22.75, 984.60, 2019.25 etc…
A number whose decimal representation
terminates.
NON-TERMINATING
A number whose decimal representation
does not terminates…
Eg: 7.333…, 6.494949…, 87.126126…,
3.142345667543277889665430045664…
78.909090…, 79.12356635679879… etc
3.142345667543277889665430045664…,
79.12356635679879…
7.333…, 6.494949…,
87.126126…,78.909090…
RECURRING
NON-RECURRING
38.
DECIMAL
NUMBERS
TERMINATING NON-TERMINATING
RECURRING
DECIMALS
NON- RECURRING
DECIMALS
Terminating decimals and non-terminating recurring
decimals together called as RATIONAL NUMBERS.
And Non-Terminating Non-Repeating decimals are
called IRRATIONAL NUMBERS.
39.
RATIONA
L
NUMBERS
(Q)
IRRATION
AL
NUMBERS
(QC )
REAL
NUMBERS
(R)
ALTOGETHER
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