Cardinal Numbers are Numbers that are used for counting something. They are also called the Cardinals. Cardinals are meant by how many of anything is existing in a group. In other words, cardinal numbers are a collection of ordinal numbers. Learn about the Cardinal Number of a Set Definition, Solved Examples explained in detail in the further modules.
Cardinal Number of a Set – Definition
The Number of Distinct Elements present in a finite set is called the Cardinal Number of a Set. Usually, we define the size of a set using cardinality. The Cardinal Number of a Set A is denoted as n(A) where A is any set and n(A) represents the number of members in Set A.
Consider a set of even numbers less than 15.
Set A = {2, 4, 6, 8, 10, 12, 14}
As Set A has 7 elements, the Cardinal Number of the Set is n(A) = 7
Note:
(i) Cardinal number of an infinite set is not defined.
(ii) Cardinal number of the empty set is 0 since it has no element.
Also, Check:
How to find the Cardinal Number of a Set?
1. Find the cardinal number of the following set
E = { x : x < 0, x ∈ N }
Solution:
x<0 means negative integers and they don’t fall under Natural Numbers.
Therefore, the above set will not have any elements
Cardinal Number of Set E is n(E) =0
2. Find the Cardinal Number of the Following Set
Q = { x : – 4 ≤ x ≤ 3, x ∈ Z }
Solution:
Given Q = { x : – 4 ≤ x ≤ 3, x ∈ Z }
x={-4, -3, -2, -1, 0, 1, 2, 3 }
Number of Elements in the above set is 8
Therefore, Cardinal Number of Set Q is n(Q) = 8
3. Find the Cardinal Number of the Set
A = { x : x is even prime number }
Solution:
Among all the prime numbers 2 is the only even prime number and the set has only one element
A ={2}
Cardinal Number of a Set n(A) = 1
4. Set D = {3, 4, 4, 5, 6, 7, 8, 8, 9}
Solution:
We know the cardinal number of a set is nothing but the number of distinct elements in the set
Cardinal Number of Set D is n(D) = 7
5. Find the Cardinal Number of a Set X = {letters in the word APPLE}
Solution:
Set X = {letters in the word APPLE}
We know the cardinal number of a set is nothing but the number of distinct elements in the set
x = {A, P, L, E}
Cardinal Number of Set n(X) = 4
6. Find the Cardinal Number of a Set
P = {x | x ∈ N and x2 <25}
Solution:
Given P = {x | x ∈ N and x2 <25}
Then P = {1, 2, 3, 4}
Cardinal Number of Set P is 4 and is denoted by n(P) = 4