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