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\\November 3, 2023 11:23 AM Surender Prajapati Proof 2 Reader _________________________ Date: ___________________74

Collectively, negative numbers, zero and counting numbers are called integers. It is denoted
by Z. Thus, Z = ..., –3, –2, –1, 0, 1, 2, 3, ...
If you observe any number on the number line, you find the number right to it is greater

than the number left of it.
Example: Represent the following negative numbers on a number line.
(a) –5 (b) –8 (c) –10

Solution: To represent negative numbers on a number line, start from 0 and move towards
the left of 0 to the show the given negative number.

Here to represent –5, –8 and –10, start from 0 and move 5, 8 and 10 steps
respectively.

Left side Right side
–11 –10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3

Knowledge Desk
Brahmagupta was an Ancient Indian astronomer and mathematician who lived
from 597 AD to 668 AD. He was born in the city of Bhinmal in Northwest
India. His one of the most significant work to mathematics was the
introduction of ‘zero’. By seventh century, Brahmagupta were describe the
use of negative numbers in mathematical calculations in his book ‘Brahma-
Sphuta-Siddhanta’.

OPPOSITENESS IN OUR DAILY LIFE

Suppose you have visited to Srinagar in the month of January.
In the month of January, the temperature of Srinagar goes
down to zero degree.
In the thermometer, the temperature below zero degree is
taken as negative of counting numbers such as –1°C, –2°C and
–3°C and so on. Similarly, we measure distance above sea level
as positive, i.e., counting number but if we want to represent
distance below the sea level, we take negative (–) of counting numbers.

Thus, to show a place 10 metres below the sea level, we will represent this distance as –10
metres.

Thus, we come across many such situations in our day-to-day life which are opposite to
each other. Such as gain and loss, deposit and withdrawn, above and below, height and
depth at a certain point or place, top and bottom, upstairs and downstairs, due east and
due west, etc. We can express such statements mathematically by the symbol + and –.
For example, the gain of `1000, means profit, and the sense is positive.

So, mathematically we can represent it as +1000. And, the loss of `1000 can be represent
mathematically, –1000 means loss, and the sense is negative.

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