Whole Numbers And Natural Numbers

A natural number is a part of number system which is also called as “counting numbers.”

NATURAL NUMBERS

Natural number includes all the positive integers, i.e. set of all the counting numbers i.e. \(1, 2, 3, 4, 5, 6…….\) (excluding 0).

It is to be noted that the natural numbers do not include fractions, decimals and negative numbers etc. Thus we can say that natural number are positive numbers which are part of an integers.

Natural numbers on a number line:

Natural numbers representation on a number line is as follows:

Natural numbers on a number line

The above number line represent natural numbers. All the integers on the right hand side of 0 represents the natural numbers, thus forming an infinite sets of numbers.

Difference between Natural Numbers and Whole numbers:

All natural numbers are whole numbers, but all whole numbers are not natural numbers.

Set representation of Natual and Whole Numbers

The above representation of sets shows two region,

\(A\cap B\) ie. Intersection of Natural Numbers and Whole Numbers (1,2,3,4,5,6,….. ) and the green region showing A-B, i.e. Part of Whole Number (0).

Thus a whole number is “a part of Integers consisting of all the Natural number including 0.”

Representing Natural numbers and Whole numbers:

Natural Numbers and Whole numbers on a Number line

Solve: Sort out the natural numbers from the following list.

\(20, 1555, 63.99, \frac{5}{2}, 60, -78, 0, -2, -\frac{3}{2}\)

Solution: Natural numbers are \(20, 1555, 60\)..

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Practise This Question

Which of the following is not a natural number?