Cardinal numbers describe the size of a setor collection, for instance how many dollars or how many days there are. The word cardinal comes from the Latin cardinalis for "most basic" or "most important," which underlines the significance people give to the idea of "how many."

When people count, they are actually using a combination of cardinal and ordinal numbers, two key mathematical concepts. Ordinal numbers also tell "how many" but in the context of "in what order"--for example, which day of the month it is. The Latin ordinalis means "order," as in a serial arrangement. Thus, when people count a collection of items, they are using cardinal numbers to tell how many, but the counting system itself is ordinal, because the numbers used for counting must be used in a specific sequence to be meaningful. It is possible for a set to contain only...