Natural Numbers

We have learnt that counting numbers are called natural numbers. 1 is the smallest natural number. Natural numbers are denoted by N.

Thus, N = {1, 2, 3, 4, 5, 6, 7, ...}

Natural numbers are all the numbers from 1 onwards, i.e., 1, 2, 3, 4, 5, ………… and are used for counting.

We know since our childhood we are using numbers 1, 2, 3, 4, 5, 6, ……….. to count and calculate.

Definition of Natural Numbers:

Counting numbers {1, 2, 3, 4,...} are called natural numbers.

There are unlimited natural numbers starting with the smallest natural number 1.

For example: 3 apples, 7 mangoes, 2 balls,etc.

Here, apples, mangoes, balls, etc. are objects whereas three, seven, two, etc. indicate about the quantities of these objects.

When we count objects in a group of objects, we are counting from one and then go on to two, three, four etc. This is a natural way of counting objects.

Hence, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, …..….. are called natural numbers.

Since, we start counting with number 1, so 1 is the first natural number. If we add 1 to the first natural number 1, then we get 2, the second natural number. By adding 1 to 2, we get 3, the third natural number. In fact, by adding 1 to any natural number we get the next natural number.

It follows from the above discussion that 1 is the first natural number and there is no last natural number.

Thus, if we start counting natural numbers, we cannot complete the counting of all natural numbers even if we continue to count day and night for our whole life. This fact is expressed by saying that there are infinitely many natural numbers.

Properties of Natural Numbers

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