HOW TO IDENTITY WHETHER THE GIVEN SET IS FINITE OR INFINITE

The following definitions and examples of finite set and infinite set will tell us how to identify whether a set is finite set or infinite set.

Finite set :

If a set contains countable elements or finite number of sets, then the set is a finite set.

Example :

{2, 3, 5, 9}

Infinite set :

If a set contains uncountable elements or infinite number of sets, then the set is an infinite set.

Example :

{2, 3, 5, 9, ........}

State whether the following sets are finite or infinite.

Example 1 :

{x ∈ N : x is an even prime number}

Solution :

List out the elements of the given set. The set will contain even prime number.

2 is the only even prime number.

{2}

The above contains only one element, that is 2.

Hence the given set is a finite.

Example 2 :

{x ∈ N : x is an odd prime number}

Solution :

List out the elements of the given set. The set will contain odd prime number.

{3, 5, 7, 11, ..............}

The above set contains infinite number of elements.

Hence the given set is an infinite set.

Example 3 :

{x ∈ Z : x is positive, even and less than 10}.

Solution :

In math, Z stands for integers. Then, the given set is

{2, 4, 6, 8}

The above set contains finite number of elements.

Hence the given set is a finite set.

Example 4 :

{x ∈ N : x is a rational number}

Solution :

In math, N stands for natural number. All natural numbers are rational numbers and there are infinite natural numbers.

Hence the given set is an infinite set.

Example 4 :

{x ∈ R : x is a multiple of 5}

Solution :

In math, R stands for real numbers. There are infinite number of real numbers in which there are infinite number of multiples of 5.

Hence the given set is an infinite set.

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