Uses of Numbers

There are three ways in which we use numbers. Numbers are given three names to reflect these uses:

• Cardinal numbers are used to find how many "elements" (in other words, objects) are in a "set" (i.e. a collection). This is the most important use of numbers.
• Ordinal numbers are used to order the elements in a set. They give us information about the position of an element in a set, but provide no information about the number of elements in the set (i.e. the set's cardinal number). An example of ordinal numbers is street addresses. An address of 2201 Lakeshore Road, for example, doesn't indicate the number of houses on Lakeshore Road, but it does indicate that this house comes after 2177 Lakeshore Road and before 2235 Lakeshore Road. Some uses of numbers can be as both cardinal numbers and ordinal numbers at the same time.
• 
  This bus stop sign contains several examples of tag numbers.
  The third, and least important from a mathematical perspective, use of numbers is simply as a unique identifier of an object. These are tag numbers, or nominal numbers. Tag numbers give us no information either about how many objects are in a set or to the order of the set. For example, the number 7 bus doesn't necessarily leave before the number 8 bus. Tag numbers appear frequently in life, as phone numbers, credit card numbers, ZIP codes, airline flight numbers, and many others.

Here is a comparison of the uses of cardinal, ordinal, and tag numbers:

Cardinal	Ordinal	Tag
He worked 7 hours.	The time is 7 o'clock.	He took the route 7 bus.
1920 people attended the game.	She was born in 1920.	The last four digits of Joe's credit card number are 1920.
The gum costs 89 cents.	He lives on 281 Union Street.	His phone numbers is 209-8471.

Sources used (see bibliography page for titles corresponding to numbers): 35.