Difference Between a Finite Set And an Infinite Set

There are two different types of sets Finite and infinite sets. The word ‘Finite ‘means it is countable and the word ‘Infinite’ means uncountable or it is not finite.

In this article learn about finite and infinite sets, their definition, properties, and other details of these two types of sets along with different examples.

What is a Finite Set?

Finite sets are sets having a countable number of elements. Finite sets are also said as countable sets as they can be counted. The process will run out of members to list if the members of this set have a finite number of members.

For example:

A={1,2,3,4,5}

B={X: X=whole number1<X<10}

C=A set of all English Alphabets (because it is countable).

Set of even numbers less than 11

Properties Finite Set

The following finite set conditions are always finite.

• A subset of a finite set is finite
• The union of two finite sets is also finite
• The power set of a finite set  is a finite set
• The intersection of two finite sets is finite.
• The Cartesian product of finite sets is finite.

What is an Infinite Set?

infinite sets are sets having an uncountable number of elements. If a set is also said an infinite set because the number of members or elements in that set is not countable and also we cannot indicate it in Roster form. Thus, infinite sets are also called uncountable sets.

For example:

A =the set of natural number

A={1,2,3,4,5,…}

B=the set of even number

B={2,4,6,8,10,…}

Property of infinite set

• The union of two infinite sets is also infinite
• The power set of an infinite set is infinite.
• The superset of an infinite set is also infinite.
• The intersection of two infinite sets is infinite.

Difference between a finite set and an infinite set

Finite set	Infinite set
Finite sets are sets having a countable number of elements.	infinite sets are sets having an uncountable number of members
n(A) = n, n is the number of members in the set	n(A) = ∞ as the number of members are uncountable
The union of two finite sets is also finite	The union of two infinite sets is also infinite
The intersection of two finite sets is a finite set	The intersection of two infinite sets is infinite.