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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