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There are several types of numbers in Mathematics. They are:
- Natural numbers
- Whole numbers
- Integers
- Rational numbers
- Irrational numbers
- Complex numbers
These are the different numbers that have their individual format of representation. This article will go through the natural numbers and whole numbers in detail.
Natural Numbers
The number starting from 1 is known as a natural number. In other words, all counting numbers are referred to as natural numbers. For example, we use natural numbers to count the toffees, measuring things like height and weight. 1 is the smallest natural number. There is no endpoint of a natural number. It extends up to infinity. The natural number is represented by N, and the set for the same is {1, 2, 3, 4, 5, 6, …}.
Even Natural Numbers
The natural numbers divisible by 2 are known as even natural numbers. It starts from 2 and extends up to infinity. The series of even natural numbers is of the form {2, 4, 6, 8, 10,}.
Odd Natural Numbers
The natural numbers that are not divisible by 2 are known as odd natural numbers. 1 is the smallest odd natural number. The series starts from 1 and continues till infinity. The series of odd natural numbers is as follows- {1, 3, 5, 7 …}.
Whole Numbers
The number that starts from 0 and goes up to infinity is known as the whole number. The smallest whole number is 0. This is because they do not contain any negative terms in them.
For example: If we are putting 5 balls in the bag, then we start backwards, counting from 5, 4, 3, and so on. Then a time comes when all the balls are put in the bag, and there are zero balls left outside the bag. This is the use of the whole number 0. Therefore, 0 represents the null set.
The whole number is represented by the symbol W and the set for the same is {0, 1, 2, 3, 4 …}.
Natural Number and Whole Number: Difference
- The natural number starts from 1 and the whole number starts from 0.
- Every natural number is a whole number, but every whole number is not a natural number.
- When added, subtracted, divided, or multiplied, both a whole number and a natural number follow the same properties.
Properties of Whole Numbers and Natural Numbers
Closure Property: When we add, subtract, multiply, or divide a whole number with a whole number, the resulting number is also a whole number.
Similarly, when we add, subtract, multiply, or divide a natural number with a natural number, the resulting number is also a natural one.
This is known as closure property.
Associative Property: This property implies that when we add or multiply any number with any grouping, then the answer does not change.
For example, (7+6) + 9 = 22 and 7 +(6+9) = 22
Commutative Property: This property implies that even if we change the order of the numbers while subtracting or multiplying, the answer does not change.
For example, 6 X 2 = 2 X 6
Distributive Property: This property can be stated in the given form-
(a+b) * c = a*c + b*c
Conclusion
We have learned about the whole numbers and the natural numbers and the difference between the two through this guide. Natural numbers are counting numbers starting from 1, and whole numbers are numbers starting from 0. It should be noted that all natural numbers are whole numbers, but all whole numbers are not natural numbers. Reading this article will easily answer the differences between natural numbers and whole numbers.
