A number is an abstract entity used to describe quantity. There are lots of numbers; the most familiar numbers are the natural numbers = {1, 2, 3, 4, 5, ...}.

Natural numbers have two main purposes: they can be used for counting (there are three apples on the table), and they can be used for ordering (this is the third largest city in the country). Two generalizations of natural numbers arise from the two uses: ordinal numbers are used to describe the position of an element in an ordered sequence and cardinal numbers are used to specify the size of a given set.

The natural numbers are the first set of numbers used by ancient civilizations. Most did not have a symbol for zero (except the Chinese, Mayan and Indian civilizations), and only used the counting numbers.