Cardinal numbers are numbers used to describe how many individual units are present in a set. Cardinal numbers proceed similarly to traditional counting numbers, such as "1, 2, 3..."
A simple way to determine if a number is being used as a cardinal number is to determine whether it answers the question, "How many?" Cardinal numbers do not include any fractional or decimal numbers; rather, all cardinal numbers must be integers.
Cardinal numbers are different from ordinal numbers in that cardinal numbers explain the total number of items in the set, whereas ordinal numbers describe a particular item's position in a set. Therefore, ordinal numbers take the form of "1st, 2nd, 3rd..."
The underlying theory that cardinal numbers is based on is set theory. Cardinal numbers were originally developed by George Cantor in the late 1800s as a tool to compare finite sets. For example, if two sets each contain three unique items, the sets are not the same, but they are instead said to have the same cardinality. This means that even though the sets are different, they are similar because they each contain the same number of units. In this example, the cardinality of each set would be three.