# Are all whole numbers also natural numbers?

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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 ‘I’ or ‘ Z’. 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 ‘W’. 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 ‘N’. Therefore, N$\subset $W.

The set of natural numbers contains {1, 2, 3, 4………}.

The set of whole numbers contains {0, 1, 2, 3, 4 ………}.

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).

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 ‘I’ or ‘ Z’. 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 ‘W’. 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 ‘N’. Therefore, N$\subset $W.

The set of natural numbers contains {1, 2, 3, 4………}.

The set of whole numbers contains {0, 1, 2, 3, 4 ………}.

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).

Last updated date: 18th Sep 2023

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