Let’s begin with natural numbers.
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?
Only after adding ‘0’ to the set of natural numbers, 1 will have predecessor.
Important Note:
We represent whole numbers by ‘W’.
Or we can say W = {0, 1, 2, 3, 4...} (i.e. 0 to infinity)
Important Note:
Example: 6
Here, number is 6.
Successor = 6 + 1 = 7
Every whole number has its successor.
Example: 10
Here, number is 10.
Predecessor = 10 - 1 = 9
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).
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
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
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.