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.
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
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
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.
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.
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.
Ques. Why is Zero a Whole Number?
Well, the zero is neither negative nor positive, thus it is a neutral integer which falls in the middle of positive and negative numbers on the number line. Hence, it makes zero a whole number. This is why it is not considered as a natural number because of its neutral tendency on a number line. Except 0, every whole number has exactly one immediate predecessor—the number that comes before it. Also, this zero only creates the major yet basic difference between a natural numbers set and a whole numbers set. It is because all whole numbers set are natural numbers set but not all natural numbers set are whole numbers set.
Ques. How do you Check if a Number is a Whole Number?
To check you can multiply it by 10 and then do a "modulo" operation/division with 10, and check if the result of those two operations is zero. The result of those two operations will give you the first digit after the decimal point. If the result is equal to zero then the number is a whole number. Because all non-negative integers are whole numbers. Hence, to prove their tendency of being a whole number will only be proved when the result comes out to be a zero.