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We saw that some common sets are numbers

N : the set of all natural numbers

Z : the set of all integers

Q : the set of all rational numbers

T : the set of irrational numbers

R : the set of real numbers


Let us check all the sets one by one.


Natural numbers

Natural numbers are numbers starting from 1.

Natural numbers = 1, 2, 3, 4, 5, …

So, N = {1, 2, 3, 4, 5, ….}



Integers are positive numbers, negative numbers and 0.

Integers = …., -3, -2, -1, 0, 1, 2, 3, …

So, Z = {…., -3, -2, -1, 0, 1, 2, 3, …}


Rational numbers

Rational numbers are those numbers which are of the form p/q

Example: 1/2, 2/3, …

So, we write set of rational numbers as

Subsets of real numbers - Subset

Irrational numbers

Irrational numbers are those numbers which are not of the form p/q

Example:  π, 1.10100100010000…

So, we write set of irrational numbers as

Representation of Irrational numbers as set.jpg


Real number

All numbers on number line are real numbers

It includes rational as well as irrational numbers

We write set of real numbers as  R

Writing as Subsets

So, we can now write subset

N ⊂ Z ⊂ Q ⊂ R

Natural number is a subset of Integers

Integer is a subset of Rational numbers

And Rational numbers is a subset of Real numbers


Also, T ⊂ R

Also, Irrational numbers is a subset of Real numbers


  1. Chapter 1 Class 11 Sets
  2. Concept wise

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.