# Cardinality of a Set

## 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.

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