structural:summarization, structural:reformatting
Cardinality

The cardinality of a set is the number of elements of the set. For example, defining two sets: A = {a, b} and B = {5, 6}. Both set A and set B consist of two elements each. Their Cartesian product, written as A × B, results in a new set which has the following elements:

where each element of A is paired with each element of B, and where each pair makes up one element of the output set.The number of values in each element of the resulting set is equal to the number of sets whose Cartesian product is being taken; 2 in this case.The cardinality of the output set is equal to the product of the cardinalities of all the input sets. That is,

In this case, | A × B | = 4

Similarly,

and so on.

The set A × B is infinite if either A or B is infinite, and the other set is not the empty set.