# Cardinality

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.

### CAN YOU READ IT OUT LOUD?

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

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

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

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… Solution:

## 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.

## Mathemagician

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