Integers

The notion of a number is connected with the act of counting. So, the natural numbers 1, 2, 3, 4, 5, …… are also called counting numbers. We use ten symbols or digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 to denote large numbers by using position of the digits in the given number.

What are integers?

The negative numbers, zero and the natural numbers together are called integers.

A collection of numbers which is written as …….. -4, -3, -2, -1, 0, 1, 2, 3, 4……… .

These numbers are called integers.

For example:

(i) -8, -2, 0, 2, 8

(ii) -7, -1, 0, 5, 12

(iii) -15, -9, 11, 21

(iv) -10, -3, 0, 9, 14

(v) -6, -4, 0, 7, 19

We usually represent numbers by making evenly spaced points one unit apart on a straight horizontal line which is called a number line. The line extends indefinitely to the left and to the right. A point O on the line, called the origin corresponds to the number 0. So, point A at a distance of 9 units to the right of zero represents the number 9 on the number line shown below.

$Positive Numbers$

What lies on the left of 0? Let us think about some of the familiar things to understand about the positive number and the negative number.

We very often hear that the temperature during winter went down to -2°. We know that the temperature in -2° is very cold, it is colder than 0°c. It means that -2 is smaller than 0. Let us see in a thermometer where -2 is located. It is marked below 0.

To measure the depth below the ground level we use negative numbers. Here, 0 indicated ground level. On a number line a number that is right to the 0 is positive and a number left side to the 0 is negative. So, we have a new set of numbers -1, -2, -3, -4, -5, ….. These are known as the negative numbers.

$Integers$

On the number line there are positive numbers, negative numbers and 0. These are called integers. 0 is neither positive nor negative.

$Integers on Number Line$

The sign before the number indicates its direction to the right or left of 0. For example +5 indicates that the number lies to the right of 0 and -5 indicates that the number lies to the left of 0. Thus, integers are also called directed numbers. If a number has no sign it means that it is a positive integer.

Negative Integers

The negative numbers ………. -5, -4, -3, -2, -1 are called negative integers.

Thus, examples of negative integers are ……… -5, -4, -3, -2, -1.

Note:

We use the symbol ‘-’ to denote negative integers and the same symbol is used to indicate subtraction. But the context will always make it clear whether we mean negative integer or subtraction.

Positive Integers

The natural numbers 1, 2, 3, 4, 5, ……… are called positive integers.

Thus, examples of positive integers are 1, 2, 3, 4, 5, ………. .

Note:

Positive integers are also written as +1, +2, +3, +4, +5, ………… however, the plus sign (+) is usually omitted and understood.

The number 0 is simply an integer. It is neither positive nor negative.

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