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Integers

We are familiar with the number line. The set of whole numbers can be represented on a number
line as shown below.

0 1 2 3 4 5 6 7 8 9 10
This is actually a number ray as it starts with ‘0’ and goes endlessly to the right. Moreover, there
are many numbers which are on the left side of the number ray so that the concept of the number
line can be completed.

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

From the above number line, we can observe that corresponding to natural numbers 1, 2, 3, 4, 5, ...
there are – 1, –2, –3, –4, –5, ..., on the left side of 0. Here, −1 is called negative of 1 and they are
opposites of each other. They are equidistant from ‘0’. Similarly, +2 and –2 are opposite to each
other and are equidistant from ‘0’ and so on. Negative numbers are written with the ‘−’ symbol
whereas for positive numbers we generally omit the (+) sign before it.

Thus, the set of numbers –1, –2, –3, –4, –5, ... along with zero (0) and the collection of natural
numbers 1, 2, 3, 4, 5, … are called integers. Integers are denoted by the letter Z.
Integers = {…, –5, –4, –3, –2, –1, 0, 1, 2, 3, 4, 5, …}.

Numbers which are right of 0 are called positive integers and numbers which are left to ‘0’ are
called negative integers.
Negative Integers Positive Integers

–10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10
Left Side Right Side
From the above number line, we observe that:
Remember
• ‘0’ is at the centre.
The number ‘0’ is simply an
• Positive integers lie to the right of 0. integer which is neither positive
• Negative integers lie to the left of 0. nor negative.

• Every negative integer and its respective positive integer are at an equal distance from 0.
Example 1: Represent the following integers on a number line.

(a) +6 (b) –9
Solution: Draw a straight line, mark some divisions at equal distance on it and mark 0 at the centre
of this line. On the right side of the 0, we mark positive integers while on the left side, we mark
negative integers. Therefore,

(a) To mark +6 on the number line, we need to move 6 steps to the right of zero (0).

–5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8
(b) To mark –9 on the number line, we need to move 9 steps to the left of zero (0).

–10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5

281 The Other Side of Zero