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}

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