Give one example each to the following statements.

i. A number which is rational but not an integer

ii. A whole number which is not a natural number

iii. An integer which is not a whole number

iv. A number which is natural number, whole number, integer and rational number.

v. A number which is an integer but not a natural number.

(i). Integer is any number that can be written without a fractional component. So, write a rational number in which numerator and denominator doesn’t have any common factor.

For example: 99/98, 2/3, 57/2 etc…

(ii). Whole numbers are all positive natural numbers including zero.

Natural numbers are the set of positive integers from 1 to infinity, excluding fractional and decimal parts. Basically, they are whole numbers without 0.

This clearly implies that 0 is the only whole number which is not a natural number.

(iii). Integers are set of positive as well as negative numbers, that can be written without a fractional component. While whole numbers are natural numbers, including 0.

Thus, all negative non-fractional numbers are integers but not whole numbers.

For example: -1, -2, -3, etc…

(iv). Natural numbers are counting numbers (positive, non-fractional and non-decimal). (1, 2, 3, 4, …)

Whole numbers are all positive natural numbers, including 0. (0, 1, 2, 3, 4, …)

Integer is any number that can be written without a fractional component. (…, -4, -3, -2, -1, 0, 1, 2, 3, …)

And rational numbers are numbers that can be written in the form p/q, where p is a numerator and q ≠ 0 is a denominator. (1, 2/1, 3/2, 55/3, …)

Drawing out a common number from these set, we can say

1, 2, 3, … are numbers which are natural, whole, integer and rational numbers.

(v). Natural numbers are positive counting numbers, excluding fractions and decimals.

Integers are basically any numbers that can be written without fractional component.

So, numbers which are integers but not natural numbers are:

-3, -2, -44, -1, …