 Posted by Anjali Kaur on May 28, 2020 # What are the Different Types of Numbers?

A common question asked by the students is ‘what are the different types of numbers in Maths or Applied Mathematics’? Let’s discuss it, as it will also help you all in understanding ‘Set Theory‘ better.

The nature of numbers in mathematics is important to understand as it helps to solve several problems in a time-efficient manner. There are the following types of numbers that we should be clear about:

1. Natural Numbers: These are those numbers that you utter naturally. For example, counting generally starts from 1 onward. Hence, natural numbers start at 1. Remember, these numbers can’t be infractions like 1/2. So, (1,2,3,4,…..) are natural numbers. We generally use ‘N’ to represent natural numbers.
2. Whole Numbers: These numbers start with a hole, i.e., 0 onward. Remember, it can’t be in fractions or decimals. So, (0,1,2,3,…..) are whole numbers.
3. Integers: Whenever you hear integer numbers, think about the number line. So, (…..,-2,-1,0,1,2,……) are integer numbers. Remember, it can’t be in fractions or decimals. We generally use either ‘Z’ or ‘I’ to represent integers.
4. Rational Numbers: These are those numbers that can be written in the fractional form, i.e., in ‘P/Q’ form, where Q can not be zero, as it is in the denominator. Both P and Q are integers. What will happen, if Q is 0? Well, then ‘P/Q’ will become ‘not defined’. Remember, whenever ‘0’ comes in the denominator then the number becomes ‘not defined’. Although P can be 0 if 0 comes in the numerator than the rational number becomes 0. We generally use ‘Q’ to represent rational numbers. Rational numbers can be terminating like 1/2, if you solve it we get 0.5, it can also be repeating or non-terminating like 2/3, if you solve this fraction then the answer will be 0.66666 approximately, which is repeating and not going to terminate.
5. Irrational Numbers: These are those numbers that can not be represented in the ‘P/Q’ form. These are non-terminating as well as non-repeating. Take an example of π which is 22/7, if we divide this we will get 3.14285714 approximately, it is not going to terminate (not fully divisible) and it is non-repeating as numbers are different. Other examples include numbers that are not perfect squares like √2 whose value is 1.414 or √3 = 1.73205080756887729352, etc.
6. Real Numbers: It includes both rational as well as irrational numbers. Real numbers can be positive which is represented as R+ and the negative real numbers are represented by R-. 