Counting numbers are known as Natural numbers.
Example: 1, 2, 3, 4, …∞ are all natural numbers.
0 and negative numbers are not natural numbers. 1 is the smallest natural number. The natural numbers are called nominal numbers.
The set of natural numbers when added with zero (0) then the resultant set is known as whole numbers set.
Example: 0,1,2,3,4,…∞are all whole numbers.
0 is the smallest whole number. In mathematics, the most basic set is that of whole numbers. These whole numbers are an integral part of the real number set which comprises various other number sets like integers, rational numbers among others.
Except 0, every whole number has exactly one immediate predecessor that is the number that comes before a whole number. Every whole number has exactly one immediate successor that is the number that comes after a whole number.
The basic difference between natural numbers and whole numbers is that the whole numbers set includes 0 Instead natural numbers set doesn’t include 0. Let us talk about other differences as shown below.
Difference Between Whole Numbers and Natural Numbers
Difference Between Natural and whole Numbers
All Whole numbers are represented by ‘W’
In whole numbers counting starts from ‘0’ ZERO
When 0 is added to a number the answer is just the number you start with: 24+0=24.
For this reason, 0 is called the identity element for addition. Identity element is absent from the natural numbers for addition property.
All whole numbers are also integers. For each whole number, there is a negative number that corresponds with it. For instance -5 corresponds to the whole number 5 and -120 corresponds to the whole number 120.
Within the set of integers, the sum of two numbers can be 0.
For eg. 20+(−20)=0 and 135+(−135)=0.
20 and -20 will be termed as the additive inverses.
All Natural numbers are represented by ‘N’
In natural numbers counting starts from ‘1’
When you add two or more natural numbers, you get a natural number again.
When you multiply two or more natural numbers, you get a natural number again
The maths way to say it is that “The system of natural numbers is closed under addition and multiplication”. It means that when subtraction or division is performed on natural numbers the result may not always be a natural number.
Examples of Whole Numbers and Natural Numbers
Example 1. Find whole numbers from given numbers. 14,0,8,48,-6,-9,2
Sol. Whole numbers: 14,0,8,48,2
Example 2.Find natural numbers from given numbers.
Sol. natural numbers: 24,6,40
Explanation of Addition Property of Natural and Whole Numbers :
When two natural numbers are added, it results in a natural number only.
Eg: 34+45 = 79
Adding two whole numbers will give you a whole number.
Eg: 6+0= 6
Explanation of Subtraction Property of Natural and Whole Numbers :
Subtraction of two natural numbers doesn’t necessarily result in a natural number
Eg: 8 – 5 = 3 is natural number
But 5 – 8 = -3 is not a natural number
Similar is the condition for whole numbers. Subtracting two whole numbers need not result in a whole number.
Explanation of Multiplication Property of Natural and Whole Numbers :
Multiplication of a natural number with a natural number and whole number with another whole number results in a natural number and whole number respectively.
Eg: 4 X 3 = 12 is a natural number
8 X 5 = 40 is a whole number, where 8 and 0 are also whole numbers.
Explanation of Division Property for Natural and Whole Numbers:
Division property also does not hold for the natural numbers and whole numbers for instance.
Eg: 10/2 = 5 is natural as well as the whole number
But 7/2 = 3.5 is neither natural nor the whole number.
Similarly, the difference between natural numbers and whole numbers can be understood by representing them on a number line.
Whole numbers are located on the right side of the number line including zero.
Natural numbers are located on the right side excluding zero.