# Finite Sets and Infinite Sets – Definition and Examples

Here you will learn what are finite and infinite sets, cardinality of a finite set and examples based on it.

Let’s begin –

## Finite and Infinite Sets

#### (i) Finite Sets

A set is called a finite set if it is either void set or its element can be listed (counted, labelled) by natural numbers 1, 2, 3, ….. and the process of listing terminates at a certain natural number n (say).

#### Cardinal Number of a Finite Set

The number n in the above definition is called the cardinal number or order of a finite set A and is denoted by n(A).

Example : Each one of the following sets is a finite set :

(i)  Set of even natural numbers less than 100.

(ii)  Set of soldiers in Indian army

(iii) Set of even prime natural numbers

(iii) Set of all persons on the earth

#### (ii) Infinite Set

A set whose elements cannot be listed by the natural numbers 1, 2, 3, …. n for any natural number n is called an infinite set.

Example : Each one of the following sets is an infinite set :

(i)  Set of all points in a plane.

(ii)  Set of lines in a plane

(iii) {x $$\in$$ R : 0 < x < 1}