Whole Numbers and Natural Numbers

What are Whole Numbers ?

Whole numbers are the set of positive integers. They do not have any decimal or fractional part. Natural numbers along with zero(0) are whole numbers.
Closure Property Of Whole Numbers

•     Addition of whole numbers always gives a whole number. Thus whole numbers are closed under addition.
            Eg. 5+7 = 12
•     Subtraction of whole numbers does not always give a whole number. Thus whole numbers are not closed under subtraction.
           Eg. 5-7 = -2, which is a negative integer and not a whole number.
•     Multiplication of whole numbers always gives a whole number. Thus whole numbers are closed under multiplication.
           Eg. 5x7 = 35
•      Dividing a whole number by another does not always give a whole number. Thus whole numbers are not closed under division.
           Eg. 5÷7 = a fraction, thus it will not be a whole number.

Natural and Whole numbers on number line

What are Natural Numbers?

Natural numbers are the set of positive integers, that is, integers from 1 to ∞ excluding fractional n decimal part. They are whole numbers excluding zero. Natural Numbers are also called counting numbers.

Natural Numbers can further be sub-divided into different types :-

1)  Even and odd Numbers
2)  Prime Numbers
3)  Relatively prime/ co-prime numbers
4)  Composite numbers
5)  Perfect numbers

What is Zero ?
Zero is the only whole number which is not a natural number. It is represented by 0. "Zero is the only difference between natural and whole numbers."
 Properties of ZERO - 0
•     Zero added to any number gives the number itself. Hence, 0 is the additive identity for all numbers.
•     Multiplication with zero- 0 multiplied with any number always gives 0.
•     Zero divided my any number(except 0) gives 0.
•      Any number divided by 0 is not defined.
•      Zero raised to any power(except 0) gives 0.
•      Zero to the power 0 (0⁰) is not defined.

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