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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