A number that indicates the total quantity of objects in the given set is referred to as a cardinality of the set. Cardinality always answers the question “How many?”

Cardinality Principle

The Cardinality Principle states that the last number word used in the process of counting indicates the total number of objects in a set.

Cardinal numbers always start from 1. Let us understand the cardinality concept with more illustrations.

Assume that there are 6 cupcakes in a box. Count a set by matching numbers to objects – 1, 2, 3, 4, 5, 6; this implies that each object is in its order but you do not know the total number of objects until we identify them. In this situation, cardinality helps to recognize the total number of cupcakes; 1, 2, 3, 4, 5, 6 – there are 6 cupcakes in the box.

Counting the cupcakes
Counting the cupcakes


You can try some more examples shown below for better understanding.

Illustration 1:
Can you tell me how many pencils are there?

Set of pencils
Set of pencils

Solution: To know the total number of pencils, we need to count the number pencils in the given image.

Counting the pencils
Counting the pencils

Therefore, the cardinality of the set of pencils is 5.

Illustration 2:
Can you count the number of balls?

Solution: Start from the first ball and count in the increasing order as 1, 2, 3, …. We get,

Therefore, the cardinality of the set of balls is 9.

Do it yourself.

Can you differentiate between the types of balls given in the image below? Hurry up! Start counting…


Type of Balls
Number of Balls

Math Facts

1. Cardinal numbers can also be referred to as Natural Numbers.
2. Cardinal numbers (or natural numbers) along with 0 forms a set of Whole numbers.


The concept of cardinality was discovered by Georg Cantor. He is well known as the originator of the Set Theory.

Georg Cantor
Georg Cantor

There was a great saying that “Hard work always pays off”. Cantor was a German mathematician, who is well known for his tremendous work on set theory which is considered as fundamental theory in mathematics. In his theory, he establishes the importance of one-to-one correspondence between items/members of two sets. He also proved the real numbers are more numerous than that of natural numbers. Most of his proofs of theorems indicate the existence of infinity of infinities. His theory was opposed and criticized by many other mathematical contemporaries. He went into a depression state from 1884 till the end of his life; he was suffering from bipolar disorder. In 1904, the Royal Society awarded Cantor Sylvester Medal, the highest honor it can confer for the work of mathematics.

Know more about other concepts of Number Sense on Counting Numbers, Number Line, Odd and Even Numbers, Rounding Numbers, and Ordering Numbers

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