Natural numbers space a part of the number mechanism which includes all the positive integers indigenous 1 till infinity and also are likewise used because that counting purpose. It does not encompass zero (0). In fact, 1,2,3,4,5,6,7,8,9…., are also called counting numbers.

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Natural number are part of actual numbers, that include only the positive integers i.e. 1, 2, 3, 4,5,6, ………. Not included zero, fractions, decimals and negative numbers.

Note: natural numbers do not include an adverse numbers or zero.

## Natural Number Definition

As explained in the arrival part, organic numbers are the numbers which are positive integers and includes numbers from 1 it rotates infinity(∞). This numbers space countable and also are usually used because that calculation purpose. The set of organic numbers is represented by the letter “N”.

N = 1,2,3,4,5,6,7,8,9,10…….

## Natural Numbers and also Whole Numbers

Natural numbers incorporate all the entirety numbers not included the number 0. In other words, all natural numbers are totality numbers, but all totality numbers room not natural numbers.

Natural numbers = 1,2,3,4,5,6,7,8,9,…..Whole number = 0,1,2,3,4,5,7,8,9,….

Check the end the difference between natural and whole number to know an ext about the distinguishing properties that these 2 sets the numbers.

The above representation that sets shows two regions. A ∩ B i.e. Intersection of natural numbers and also whole number (1, 2, 3, 4, 5, 6, ……..) and also the green region showing A-B, i.e. Component of the whole number (0).

Thus, a totality number is “a component of Integers consisting of all the natural number including 0.”

### Is ‘0’ a organic Number?

The answer to this question is ‘No’. Together we understand already, natural numbers begin with 1 come infinity and also are confident integers. Yet when we incorporate 0 with a optimistic integer such as 10, 20, etc. It becomes a natural number. In fact, 0 is a entirety number which has a null value.

### Every organic Number is a entirety Number. True or False?

Every organic number is a totality number. The declare is true since natural numbers space the confident integers that begin from 1 and also goes till infinity whereas entirety numbers likewise include all the hopeful integers together with 0.

## Representing organic Numbers ~ above a Number Line

Natural numbers representation on a number heat is together follows:

The over number heat represents natural numbers and also whole numbers. All the integers on the right-hand next of 0 represent the herbal numbers, thus creating an infinite set of numbers. Once 0 is included, this numbers become whole number which are likewise an infinite collection of numbers.

### Set of organic Numbers

In a set notation, the symbol of herbal number is “N” and also it is stood for as offered below.

Statement:

N = collection of every numbers beginning from 1.

In Roster Form:

N = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ………………………………

In collection Builder Form:

N = x : x is one integer starting from 1

### Natural number Examples

The herbal numbers incorporate the positive integers (also recognized as non-negative integers) and also a few examples encompass 1, 2, 3, 4, 5, 6, …∞. In other words, organic numbers room a collection of every the whole numbers not included 0.

23, 56, 78, 999, 100202, etc. Space all examples of natural numbers.

## Properties of organic Numbers

Natural number properties room segregated into 4 main properties which include:

Closure home Commutative propertyAssociative propertyDistributive property

Each of this properties is explained below in detail.

### Closure Property

Natural number are constantly closed under addition and multiplication. The addition and multiplication of 2 or more natural number will always yield a herbal number. In the case of subtraction and division, herbal numbers do not obey closure property, which way subtracting or splitting two herbal numbers can not give a herbal number as a result.

Addition: 1 + 2 = 3, 3 + 4 = 7, etc. In each of this cases, the result number is constantly a natural number.Multiplication: 2 × 3 = 6, 5 × 4 = 20, etc. In this instance also, the result is constantly a organic number.Subtraction: 9 – 5 = 4, 3 – 5 = -2, etc. In this case, the result may or might not be a natural number.Division: 10 ÷ 5 = 2, 10 ÷ 3 = 3.33, etc. In this case, also, the resultant number might or may not it is in a natural number.

Note: Closure residential property does no hold, if any of the number in case of multiplication and division, is no a organic number. However for enhancement and subtraction, if the an outcome is a hopeful number, then just closure property exists.

For example:

-2 x 3 = -6; no a natural number6/-2 = -3; no a herbal number

### Associative Property

The associative residential property holds true in situation of enhancement and multiplication of organic numbers i.e. A + ( b + c ) = ( a + b ) + c and also a × ( b × c ) = ( a × b ) × c. On the various other hand, because that subtraction and division of natural numbers, the associative residential or commercial property does not organize true. An example of this is provided below.

Addition: a + ( b + c ) = ( a + b ) + c => 3 + (15 + 1 ) = 19 and also (3 + 15 ) + 1 = 19.Multiplication: a × ( b × c ) = ( a × b ) × c => 3 × (15 × 1 ) = 45 and ( 3 × 15 ) × 1 = 45.Subtraction: a – ( b – c ) ≠ ( a – b ) – c => 2 – (15 – 1 ) = – 12 and ( 2 – 15 ) – 1 = – 14.Division: a ÷ ( b ÷ c ) ≠ ( a ÷ b ) ÷ c => 2 ÷( 3 ÷ 6 ) = 4 and ( 2 ÷ 3 ) ÷ 6 = 0.11.

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### Commutative Property

For commutative property

Addition and also multiplication of organic numbers display the commutative property. Because that example, x + y = y + x and also a × b = b × aSubtraction and division of organic numbers execute not display the commutative property. For example, x – y ≠ y – x and x ÷ y ≠ y ÷ x

### Distributive Property

Multiplication of natural numbers is constantly distributive end addition. For example, a × (b + c) = abdominal muscle + acMultiplication of herbal numbers is likewise distributive end subtraction. Because that example, a × (b – c) = abdominal muscle – ac