Question

# Are all whole numbers also natural numbers?

Hint: We should first consider and know about the definition of whole numbers and natural numbers, and then observe the basic difference between them.

Now, consider whole numbers:
Whole numbers are actually the set of positive integers including (0). Now, a set is a well defined collection of distinct objects. The objects that make up a set are known as its elements. Now, integers are numbers that can be written without a fractional component. Set of integers is denoted by â€˜Iâ€™ or â€˜ Zâ€™. Integers can be positive or negative and it includes (0), and as stated above, these positive integers along with (0) are known as whole numbers, whose set is denoted by â€˜Wâ€™. These are said whole numbers because they do not contain a fraction. Whole numbers are subsets of integers.

To understand subset we need to consider two sets, set A and set B. Now if every element of set B is also contained in set A then set B is called as subset of set A. It is symbolically written as B$\subset$A. Therefore, whole numbers are subset of integers.
$\therefore$ Symbolically, W$\subset$ Z.

Now, consider Natural numbers:
All whole numbers except (0) are called natural numbers. Therefore natural numbers are a subset of whole numbers. Set of natural numbers are denoted by â€˜Nâ€™. Therefore, N$\subset$W.
The set of natural numbers contains {1, 2, 3, 4â€¦â€¦â€¦}.
The set of whole numbers contains {0, 1, 2, 3, 4 â€¦â€¦â€¦}.
Therefore, we can conclude that all whole numbers are not natural numbers.

Note: We should know the definitions of mathematical terms properly. The basic difference between the terms should be properly known. In this question one may get confused only because of (0).