Whole Numbers

Let’s begin with natural numbers.

When we begin to count we naturally use counting numbers {1, 2, 3, 4...}. Hence, Natural numbers are the set of numbers ranging from 1 to infinity.

We represent natural numbers by ‘N’.

Or we can say N = {1, 2, 3, 4...} (i.e. 1 to infinity)

Every natural number has a predecessor and a successor such as predecessor of 2 is 1 and successor of 2 is 3.

What about 1? Does 1 have both a predecessor and a successor?

We found that the number 1 has no predecessor in natural numbers.

Only after adding ‘0’ to the set of natural numbers, 1 will have predecessor.

Important Note:

1. The smallest natural number is ‘1’.

2. There is no largest natural number.

3. Every natural number is a whole number.

4. Every natural number has its successor.

Basic Facts About Whole Numbers

The set of natural numbers along with zero are called whole numbers. The set of Whole numbers excludes decimal or fractional numbers.

We represent whole numbers by ‘W’.

Or we can say W = {0, 1, 2, 3, 4...} (i.e. 0 to infinity)

Important Note:

1. We can obtain successor of a whole number by adding 1 to the given whole number.

Example: 6

Here, number is 6.

Successor = 6 + 1 = 7

Every whole number has its successor.

2. We can obtain predecessor of whole number by subtracting 1 from    given whole number.

Example: 10

Here, number is 10.

Predecessor = 10 - 1 = 9

3. Zero has no predecessor.

4. The smallest whole number is ‘0’.

5. There is no largest number in set of whole numbers.

6. Every whole number excluding ‘zero’ is a natural number

Number Line

A line on which numbers are marked at equal intervals to show simple numerical operations is called a number line.

In order to represent whole numbers on a number line, we draw a straight line and mark a point O on it.

From ‘0’ point, mark points 1, 2, 3, 4, 5, 6, 7, 8, 9, etc. on the line at equal intervals to the right of ‘0’.

The arrow-head on the right-side on the number line shows that the numbers can continue up to infinity. With the help of number line we can compare two whole numbers (i.e. we can easily find out which number is greater or smaller).

On the number line we see that the number 6 is on the right of 3.

Hence 6 is greater than 3 (i.e. 6 > 3). Number 1 lies on the left of 3.

Therefore 1 is smaller than 3 (i.e. 1 < 3).

Addition on the number line

Here, 3 is added to the given number i.e. 2, so we will make 3 jumps to the right of 2.

i.e. 1st jump – from 2 to 3,

     2nd jump – 3 to 4

     And 3rd jump – 4 to 5

Therefore, the sum of 2 and 3 is 5

Subtraction on the number line

Here, 2 is subtracted from the given number i.e. 6, so we will make 2 jumps to the left of 6.

i.e. 1st jump – from 6 to 5,

     And 2nd jump – 5 to 4

     Therefore, we get 6 – 2 = 4

Multiplication on the number line

Start from 0, move 2 units at a time to the right, make such 3 moves. And we will reach 6.

So, we say, 2 × 3 = 6.