Cardinal numbers

A cardinal number is a natural number that is used to represent how many of something there are in a group. Given a set of objects, the cardinal number of the set is the number of elements in the set. In the set {1, 2, 3}, there are 3 elements, so the cardinal number is 3. We could also say that the cardinality of the set is 3.


Given the following sets of numbers: {1, 2, 3}, {4, 5, 6}, {7, 8, 9}, {10, 11, 12}, determine the cardinality of each set.

Although the numbers in each set of numbers above are different, they all have the same cardinality: 3.

We can also count that there are 4 sets of 3 numbers; 4 is another cardinal number.

Cardinal numbers are used for counting, so fractions, decimals, negative numbers, etc., are not considered cardinal numbers.

One real life example of a cardinal number is a team. A soccer team has 11 players on the field at any one time, a baseball team has 9, and so on. Players on the team may have the jersey numbers 11 and 9, but those numbers wouldn't be considered cardinal numbers, because they aren't actually counting anything, and are instead used as identification; these types of numbers are known as nominal numbers.