## 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.