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Counting is the mathematical action of repeatedly adding (or subtracting) one, usually to find out how many objects there are or to set aside a desired number of objects (starting with one for the first object and proceeding with a one-to-one correspondence). However, counting is also used (primarily by children) to demonstrate knowledge of the number names and the number system.

Inclusive counting is usually encountered when counting days in a calendar. Normally when counting 8 days from Sunday: Monday will be day 1, Tuesday day 2, and the following Monday will be the eighth day. When counting inclusively the Sunday (the start day) will be day 1 and therefore the following Sunday will be the eighth day. Examples: the French for fortnight is quinze jours (15 days), similarly in Greek (δεκαπενθήμερο) and Spanish (quincena) are all based on the number 15. The practice appears in other calendars: in the Roman calendar the nones (meaning nine) is 8 days before the ides; and in the Christian calendar Quinquagesima (meaning 50) is 49 days before Easter Sunday.

Counting sometimes involves numbers other than one -- for example, when counting money, or counting out change, or when "counting by twos" (2, 4, 6, 8, 10, 12, ...) or when "counting by fives" ( 5, 10, 15, 20, 25 ...).

There is archeological evidence that suggests that humans have been counting for at least 50,000 years [1 - p.9]; the development of counting led to the development of mathematical notation and numeral systems. Counting was primarily used by ancient cultures to keep track of economic data such as debts and capital (i.e., accountancy).

See also

• Cardinal number
• Combinatorics
• Subitizing and counting
• Tally mark
• Unary numeral system
• Elementary arithmetic

References

1. An Introduction to the History of Mathematics (6th Edition) by Howard Eves (1990)

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