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Whole Numbers

The whole numbers are the counting numbers including 0.

In our daily life we come across many solutions where the result cannot be represented by a natural number. Suppose Ranjan has 12 ice-cream. He gave 8 ice-creams to her sister and 4 ice-creams to his brother. How many ice-creams were left with him? Certainly there were no ice-cream left with him. To denote 'no' or 'nothing one more symbol is introduced, which is called zero (0).

It is not part of natural number. The set of natural numbers along with zero gives a set of numbers called whole numbers. Whole numbers are denoted by W.

Thus, W = {0, 1, 2, 3, 4, ...)

Definition of Whole Numbers:

All natural numbers along with 0 are called whole numbers. There are unlimited whole numbers starting with the smallest whole number 0.

We have seen that the numbers 1, 2, 3, 4, 5, 6………. etc. are natural numbers. These natural numbers along with the number zero from the collection of whole numbers. The numbers 0, 1, 2, 3, 4, …………… are called whole numbers.

The smallest whole number is 0.

The first 100 whole numbers are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25,26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99.

Thus, a whole numbers is either 0 or a natural number.

REMEMBER:

I: Every natural number is a whole number.

II: Zero is the only number which is a whole number but not a natural number.

1. State True or False:

(i) Zero is the smallest natural number.

(ii) 1 is the smallest whole number.

(iii) All natural numbers are not whole numbers.

(iv) All whole numbers are natural numbers.

Answer:

1. (i) False

(ii) False