Page 116 - Start Up Mathematics_6

6 Integers

Negative numbers are essential in everyday life. Their usefulness can be understood from the
following examples. The highest temperature ever recorded on earth was 58°C in Libya and the
coldest temperature recorded was 89.2°C in Antarctica. Symbolically, the two temperatures can
be denoted by +58°C and –89.2°C respectively. Similarly, it is very easy to represent the highest
point on the earth, Mount Everest which is 29,029 ft above sea level by + 29,029 ft and the lowest
point on the earth, Dead Sea which is 1,371 ft below sea level by –1,371 ft.
In Mathematics, the need to extend our number system arises, when we have to subtract a larger
number from a smaller number. To compute 3 – 5, we must find a number, say n such that
5 + n = 3. Since there is no such whole number we extend the number system to integers.

Before learning about integers, let’s review the definitions of natural numbers and whole numbers.

Natural Numbers

The numbers 1, 2, 3, 4, … are called natural numbers.

Whole Numbers

The numbers 0, 1, 2, 3, 4, … are called whole numbers.

Integers

The negative numbers …, –4, –3, –2, –1, along with whole numbers are called integers. In other
words, the numbers …, –4, –3, –2, –1, 0, 1, 2, 3, 4, ... are integers.

• The numbers …, –4, –3, –2, –1 are called negative integers.
• The numbers 1, 2, 3, 4, … are called positive integers.
• The number zero is an integer but it is neither positive nor negative.

Representation of Integers on a Number Line

Let’s draw a line and mark any point ‘O’ on it. Consider this point ‘O’ as zero. Now mark points
at equal distances on the right as well as on the left of ‘O’. Label the points on the right side of 0
as 1, 2, 3, 4, 5, ..., etc. and on left side of 0 as –1, –2, –3, –4, –5, ..., etc.

Negative Numbers O Positive Numbers

… –5 –4 –3 –2 –1 0 1 2 3 4 5 ...

Clearly, 1 and –1 are equidistant from 0 but in opposite directions. Similarly, 2 and –2 are equidistant
from 0 but in opposite directions and so on.

Note: The facts given above have been taken from Wikipedia.