**Natural Numbers:** The set of all natural numbers, normally is denoted by math symbol N. Individual way of building the natural numbers is during an interactive process starting from the empty set.

**Natural numbers** happen naturally (hence the name) from counting objects.

Because of this fact, the fundamental operations of arithmetic are addition, subtraction, multiplication and division can be explained in naturally appealing ways for natural numbers before being extended to larger sets of numbers.

## What is a Natural Number?

The counting of objects in numbers 1, 2, 3 …. is known as natural numbers.

Then N = {1, 2, 3, 4 ….}

N = {+1, +2, +3 ….}

Clearly, the set N of natural number is an infinite set. The sum and product of two natural numbers are always a natural number. The natural numbers in the number line:

The order relations in Q can be exhibited pictorially by means of a straight line called the number line. For this, we draw a straight line, say l, which extends in both the directions endlessly as indicated by the arrowheads.

**Can Natural Numbers be Negative**

No, the natural numbers are all positive numbers that starts from 1 (Even they are called counting numbers).

**List of Natural Numbers**

- Natural numbers are beginning with 1 and increasing one by one.
- The set of natural numbers is denoted by the symbol N.
- In the set of natural numbers, 2 is called the successor of 1.
- 1 is called the predecessor of 2 and 3 is called successor of 2 and 2 is called predecessor of 3.
- After the element 3 to indicate that the other elements of N are listed following the pattern of 1, 2, 3.

## Natural Numbers Definition

The set of odd, even and prime numbers except zero is called as natural number. The result of addition and multiplication of numbers always gives natural number. The notation used for natural number to represent it mathematically is N.

The set of natural numbers may be finite or infinite. The finite defines the numbers in the set are countable. Infinite set means the numbers are uncountable. The natural numbers are well-ordered contains only positive integers.

## Is 0 a Natural Number?

No, zero is not a natural numbers. The natural numbers are always greater than zero. This natural numbers are used to count the things(thy are called counting numbers) so they wont consider zero a natural number.

Counting produced the numbers one, two, three, etc, which now are called set of natural numbers. The collection of all natural numbers are represented by the English letter N. Even though it is not possible to list all the elements of N, we write N = {1, 2, 3 …}.

## Properties of Natural Numbers

Natural numbers are involved in the following algebraic properties:

Property | Addition | Multiplication |

Closure | a + b | a × b |

Associative | a + (b + c) = (a + b) + c | a × (b × c) = (a × b) × c |

Commutative | a + b = b + a | a × b = b × a |

Identity | a + 0 = a | a × 1 = a |

Distributive | a × (b + c) = (a × b) + (a × c) | |

Zero divisor | a × b = 0 then a = 0 or b = 0 |

Following are the list of 4 important properties of Natural numbers:

- Closure Property.
- Associative Property.
- Commutative Property.
- Distributive Property.

## Natural Numbers Examples

Here are the natural numbers examples and solved examples:

Solution:

Closure Property for Addition states that a + b = b + a for any two whole numbers, putting the values a = 5 and b = 6,

a + b = 5 + 6 = 11

b + a = 6 + 5 = 11

So, a + b = b + a for a = 5, b =6.

So, closure property of addition holds for the numbers 5 and 6.

Solution:

Closure property for multiplication states that a x b, we multiplying two whole numbers.

Putting the values a = 5 and b = 6.

a x b = 5 x 6 = 30

So, closure property of multiplication holds for 5 and 6.

Question 3: With the given numbers 5, 4 and 3. Explain the associative property for addition of whole numbers.

Solution:

Associative property of addition states that a + (b + c) = (a + b) + c, where a = 5, b = 4 and c = 3.

a + (b + c) = (a + b) + c

5 + (4 + 3) = (5 + 4) + 3

5 + 7 = 9 + 3 12 = 12

So, associative property of addition holds true for 5, 4 and 3.

Question 4: With the given numbers 5, 4 and 3. Explain associative property for Multiplication of whole numbers.

Solution:

Associative property for multiplication of whole numbers is a x (b x c) = (a x b) x c, where a = 5, b = 4 and c = 3.

a x (b x c) = (a x b) x c

5 x (4 x 3) = (5 x 4) x 3

5 x 12 = 20 x 3

60 = 60

Question 5: With the given numbers 5 and 4. Explain commutative property for addition of whole numbers.

Solution:

Commutative property for addition of whole number is a + b = b + a, where a = 5 and b = 4.

a + b = b + a

5 + 4 = 4 + 5

9 = 9

So, commutative property for addition holds for 5 and 4.

Question 6: With the given numbers 5 and 4. Explain commutative property for multiplication of whole numbers.

Solution:

Commutative property for multiplication of whole numbers is a × b = a × b, where a = 5 and b = 4.

a × b = a × b

5 x 4 = 4 x 5

20 = 20

So, commutative property for multiplication holds for 5 and 4.

Question 7: With the given number 5. Explain identity property for addition of whole numbers.

Solution:

Identity property for addition of whole number is a + 0, where a = 5.

a + 0 = a

5 + 0 = 5

So, identity property for addition that holds for 5.

Question 8: With the given number 5. Explain identity property for multiplication of whole numbers.

Solution:

Identity property for multiplication is a × 1 = a , where a = 5.

a × 1 = a

5 x 1 = 5

So, identity property for multiplication that holds for 5.