In Mathematics, Number system consists of all types of numbers which are used to perform various calculations. These types of numbers include natural numbers and whole numbers, prime numbers and composite numbers, integers, real numbers and imaginary numbers etc.
Natural numbers and whole numbers, we have studied since our primary classes. Natural numbers are set of positive integers whereas natural numbers along with zero(0) are called as whole numbers, where zero is an undefined identity which produces a null result. Zero is the primary difference between natural and whole numbers.
Natural and whole numbers in Maths have equal importance. Suppose, if we have to count for a number of objects, then we start from number 1,2,3,4 and so on but once these objects are all vanished then what count does it gives is zero. There is a further classification of natural numbers. Let us have a look at the brief about both natural numbers and whole numbers in this article.
Natural numbers are the set of positive integers, from 1 to ∞ but it doesn’t include fractional and decimal numbers. They are also known as counting numbers.
Natural Numbers: 1, 2, 3, 4, 5, 6,…….,∞
Types of natural numbers:
- Prime Numbers
- Even and Odd numbers
- Composite numbers
- Co-prime numbers
- Perfect numbers
Whole numbers are also a set of positive integers including 0, i.e. from 0 to ∞. They also don’t include fractional and decimal part.
Whole Numbers: 0, 1, 2, 3, 4, 5, 6,…….,∞
Natural Numbers and Whole Numbers Properties
- Addition Property
When two natural numbers are added, it results in natural number only.
Eg: 34 + 45 = 79
When two whole numbers are added, it results in the whole number only.
Eg: 6 + 0 = 6
- Subtraction Property
When two natural numbers are subtracted it may or may not result in a natural number.
Eg: 5 – 2 = 3 is natural number
But 2 – 5 = -3 is not a natural number
Same is the condition for whole numbers. If two whole numbers are subtracted, then it is not necessary that it will result in the whole number.
- Multiplication Property
When two natural numbers or whole numbers are multiplied, then it always results in natural numbers and whole numbers respectively.
Eg: 2 X 6 = 12 is a natural number
4 X 0 = is a whole number, where 4 and 0 are also whole numbers.
- Division Property
Division of two natural numbers and whole numbers may or may not result in natural and whole numbers respectively. It means if the result is in fraction or decimal, then they are not considered as natural and whole numbers.
Eg: 4/2 = 2 is natural as well as the whole number
But 5/2 = 2.5 is neither a natural nor a whole number.