Natural Numbers
The counting numbers are known as Natural Numbers.
Example
1, 2, 3, 4, 5, 6, 7, 8, . . . . . are natural numbers
Predecessor and Successor
Predecessor of a Number
The number that comes just before a number is called the Predecessor of that number.
Example
(a) Number 4 comes just before the number 5, so 4 is the predecessor of the number 5.
(b) Number 7 comes just before the number 8, so 7 is the predecessor of the number 8.
(c) Number 10 comes just before the number 11, so 10 is the predecessor of the number 11.
(d) Number 1 comes just before the number 2, so 1 is the predecessor of the number 2.
(e) Number 20 comes just before the number 21, so 20 is the predecessor of the number 21.
Calculation of Predecessor of a Number
By subtracting 1 from a number, we can find the predecessor of the number.
Example
(a) Find the predecessor of number 15
Solution
Since we can find the predecessor of a number by subtracting 1 from the given number.
So, predecessor of 15
= 15 – 1 = 14
Thus, 14 is the predecessor of 15.
(b) Find the predecessor of number 31
Solution
Since we can find the predecessor of a number by subtracting 1 from the given number.
So, predecessor of 31
= 31 – 1 = 30
Thus, 30 is the predecessor of 31
(c) Find the predecessor of number 50
Solution
Since we can find the predecessor of a number by subtracting 1 from the given number.
So, predecessor of 50
= 50 – 1 = 49
Thus, 49 is the predecessor of 50
Successor of a Number
The number that comes just after a number is called the Successor of that number.
Example
(a) Number 4 comes just after the number 3, so 4 is the successor of the number 3.
(b) Number 5 comes just after the number 4, so 5 is the successor of the number 4.
(c) Number 10 comes just after the number 9, so 10 is the successor of the number 9.
(d) Number 50 comes just after the number 49, so 50 is the successor of the number 49.
Calculation of Successor of a Number
By addition of 1 to a number, we can find the successor of the number.
Example
(a) Find the successor of number 15
Solution
Since we can find the successor of a number by adding 1 to the given number.
So, the successor of 15
= 15 + 1 = 16
Thus, 16 is the successor of the number 15.
(b) Find the successor of number 5
Solution
Since we can find the successor of a number by adding 1 to the given number.
So, the successor of 5
= 5 + 1 = 6
Thus, 6 is the successor of the number 5.
(c) Find the successor of number 8
Solution
Since we can find the successor of a number by adding 1 to the given number.
So, the successor of 8
= 8 + 1 = 9
Thus, 9 is the successor of the number 8
(d) Find the successor of number 51
Solution
Since we can find the successor of a number by adding 1 to the given number.
So, the successor of 51
= 51 + 1 = 52
Thus, 52 is the successor of the number 51
Solution of Try These Exercise
Question (1) Write the predecessor and successor of 19; 1997; 12000; 49; 100000.
Solution
(a) Predecessor of 19
We know that the predecessor of a number can be find by subtracting 1 from the given number.
Thus, predecessor of 19
= 19 – 1 = 18
Thus, the predecessor of 19 is the number 18 Answer
(b) Predecessor of 1997
We know that the predecessor of a number can be find by subtracting 1 from the given number.
Thus, predecessor of 1997
= 1997 – 1 = 1998
Thus, the predecessor of 1997 is the number 1998 Answer
(c) Predecessor of 12000
We know that the predecessor of a number can be find by subtracting 1 from the given number.
Thus, predecessor of 12000
= 12000 – 1 = 11999
Thus, the predecessor of 12000 is the number 11999 Answer
(d) Predecessor of 49
We know that the predecessor of a number can be find by subtracting 1 from the given number.
Thus, predecessor of 49
= 49 – 1 = 48
Thus, the predecessor of 49 is the number 48 Answer
(e) Predecessor of 100000
We know that the predecessor of a number can be find by subtracting 1 from the given number.
Thus, predecessor of 100000
= 100000 – 1 = 99999
Thus, the predecessor of 100000 is the number 99999 Answer
Question (2) Is there any natural number that has no predecessor?
Answer
Yes, the natural number 1 has no predecessor. Answer
Explanation
We know that the predecessor of a number can be find by subtracting 1 from the given number.
Thus, if we will subtract 1 from 1, then we will find zero (0).
And we also know that natural numbers are 1, 2, 3, 4, 5, 6, . . . .
This means the first natural number is 1 (one), i.e. there is no number before this. This means zero (0) is not a natural number.
And hence, there is no predecessor of the natural number 1.
Thus, yes the natural number 1 has no predecessor. Answer
Question (3) (a) Is there any natural number which has no successor? Is there a last natural number?
Answer
No. There is no natural number which has no successor.
Question (3) (b) Is there a last natural number?
Answer
There is no last natural number.
Explanation
The number of natural numbers is countless. This means we can indefinitely find the successor of a natural numbers by adding 1 to a natural number.
Thus, there is no last natural number.