## Definition of Cardinality of a Set

A set may contain a single element or multiple elements. The sets having multiple elements may be countable or uncountable. In other words, a set may contain a definite number of elements or an indefinite number of elements. The **Cardinality of a Set** is basically the count of the number of elements present in the set.

Therefore, the **Cardinality of a Set** may be defined as the size of the set or the number of elements present in the set.

For example, if the number of elements present in a set is 5, then the **Cardinality of the Set** will be 5.

The Cardinality of an Empty set is 0 and the **Cardinality** of an Infinite Set is not defined.

## Symbol for Cardinality of a Set

Let us consider two sets A and B as shown in the figure below.

The set A has 5 elements, i.e.,

A=\{1, 2, 3, 4, 5\}

The **Cardinality of the Set **A can be written as

n(A)=5

Also, as shown in the figure, set A and B has the same number of elements. For each element in set A, there is one element present in set B. Therefore, it can be said that the set A and B have same **Cardinality**.

\therefore n(A)=n(B)=5

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