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.

Cardinality of a set Venn Diagram

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

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

The Cardinality of the Set A can be written as


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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