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
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
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
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
