Question

what is cardinality?

Answer 1

Hint: To answer this theoretical problem we will follow the definition of cardinality. In a set the number of elements belong to the set we will count them and will find the cardinality of that set.

Complete step-by-step answer:
Definition 1: \[\left| A \right|{\text{ }} = {\text{ }}\left| B \right|\]
Two sets A and B have the same cardinality if there exists a bijection from A to B, that is, a function from A to B that is both injective and surjective. Such sets are said to be equipotent, equipollent, or equinumerous. This relationship can also be denoted \[A\; \approx \;B\]

Definition 2: \[\left| A \right|{\text{ }} \leqslant {\text{ }}\left| B \right|\]
A has cardinality less than or equal to the cardinality of B, if there exists an injective function from A into B

Definition 3: \[\left| A \right|{\text{ }} < {\text{ }}\left| B \right|\]
A has cardinality strictly less than the cardinality of B, if there is an injective function, but no bijective function, from A to B.

We know that the cardinality in math is defined as the number of elements or objects belonging to the set that number is called the cardinality of that set.
For example if there is a set \[A = \left\{ {2,{\text{ }}3,4,9,0,5,1} \right\}\] if we have to answer what is the cardinality of the set then the answer will be 7 because the set A contains the number of element in this set is equal to 7. So the cardinality of the set will be 7.

Note: Cardinality of a set can be any integer value from zero to infinity but it can not be negative and fraction, it must be a positive discrete value.