Only the three people who finish the race fastest get a prize based on whether they ranked first, second, or third. Their respective numbers are nominal numbers. Difference Between Cardinal and Ordinal Numbers All the natural numbers are also referred to as cardinal numbers. The smallest cardinal number is 1 as 0 is not used for counting, so it is not a cardinal number. The participants in the race are assigned the numbers 1-15 depending on when they registered for the race. Examples of cardinal numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, and so on. They can be identified by using terms such as first, second, third, and fourth to represent the cardinal numbers 1, 2, 3, and 4.Īs an example that includes the use of all three types of numbers, imagine that there are 15 people running in a race.

Ordinal numbers, unlike cardinal or nominal numbers, tell us something about order, rank, or position. They do not represent a count of something as cardinal numbers do. Briefly, a nominal number differs from a cardinal number in that nominal numbers are only used for identification purposes, typically to distinguish elements within a set of similar objects. These three types of numbers are often discussed together since it is necessary to understand them in order to effectively communicate using numbers. There are various other properties of cardinal numbers, these are just a few. Cardinal multiplication also follows the respective rules for associativity and commutativity in ordinary multiplication. For example, cardinal addition is also associative and commutative.

Given the following sets of numbers:, the cardinality of the set is 0.Ĭardinal arithmetic follows many of the same rules and shares a number of properties of arithmetic operations with natural numbers.

Cardinal numbers