Numeration Systems

Numeration systems exist for three reasons: to identify, to order, and to tally.

Numeration systems are used to identify people and property, because they preserve confidentiality, increase security, and minimize errors caused when there are many people with the same name or many identical objects in the same production run in a factory assembly line. There are thousands of people named "John Jones," and even if John Jones uses his middle initial, he can still be confused with another John Jones with the same initial. Thus numeration systems are developed for credit cards, social security cards, bank accounts, serial numbers for products, and other reasons. These identification numbers might be very long to defeat a criminal who is randomly guessing at numbers in order to steal from someone's bank account or credit card account.

Numeration systems also define a person or unit's order in a series, for example, to determine who crosses a finish line in a race in first, second, or third place. Numbers that define order are known as the ordinal numbers (first, second, etc.) and contrast with the cardinal numbers (one, two, three, etc.) which express a tally or total of units.

Finally, numeration systems are used to tally or total; to find out how many items or units are involved in a calculation involving addition, subtraction, multiplication, or division.