Cardinality is a mathematical term that describes the size of a specific set of elements. A cardinal number, then, is represented as a non-negative integer that identifies the exact number of elements in a finite set. It is frequently used in mathematics to compare sets, as two sets may not be equal, but have identical cardinality. The process for determining the cardinal number of a set is very simple and applicable for any finite set of elements.

Obtain a finite set of elements. Elements within a set are not limited to numbers and may include symbols and letters. For example, suppose a set R is defined as:

R = {a, 1, 3, 7, @}

Count the number of elements in the set and identify this value as the cardinal number. There are five elements within the set R; therefore, the cardinality of the example set R is 5.

Realize that the order of the set does not affect the cardinality. The elements within the example set, R, can be arranged in any order and still have the same cardinality of 5. In addition, two sets may not be equal but have identical cardinality. For example, the sets R and S that follow are not equal but have the same cardinality of 5:

R = {a, 1, 3, 7, @}

S = {1, 2, b, 3, 9}