The cardinality of a set is a measure of the number of elements in the set. It is a way to describe the size of a set. The cardinality of a set is usually denoted by |A|, with vertical bars on each side. When a set is finite, its cardinality is simply the number of elements in the set. For example, the set A = {1, 2, 4} has a cardinality of 3 because it has three elements. When a set is infinite, its cardinality is represented by a cardinal number. For example, the set of all natural numbers has a cardinality of ℵ0 (aleph-null) .

The cardinality of a set can be used to compare the sizes of different sets. If two sets have the same cardinality, they are said to be equinumerous. The cardinality of a power set, which is the set of all subsets of a given set, is 2^n, where n is the number of elements in the original set.

In summary, the cardinality of a set is a measure of the number of elements in the set, and it is denoted by |A|. It can be used to compare the sizes of different sets, and the cardinality of a power set is 2^n.