Counting

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 an injective function from the remaining objects to the natural numbers starting from two). Counting is also used (primarily by children) to demonstrate knowledge of the number names and the number system. In mathematics the term counting or enumeration also means finding the number of elements of a finite set.)

Counting using tally marks.

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. For example, the French word for fortnight is quinze jours (15 days), and similar words are present in Greek (δεκαπενθήμερο) and Spanish (quincena). This practice appears in other calendars as well; 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, counting out change, when "counting by twos" (2, 4, 6, 8, 10, 12…) or when "counting by fives" (5, 10, 15, 20, 25…).

There is archeological evidence suggesting that humans have been counting for at least 50,000 years, 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).

Forms

Counting can occur in a variety of forms.

Counting can be verbal; that is, speaking every number out loud (or mentally) to keep track of progress. This is often used to count objects that are present already, instead of counting a variety of things over time.

Counting can also be in the form of tally marks, making a mark for each number and then counting all of the marks when done tallying. This is useful when counting objects over time, such as the number of times something occurs during the course of a day.

Counting can also be in the form of finger counting, especially when counting small numbers. This is often used by children to facilitate counting and simple mathematical operations.

Various devices can also be used to facilitate counting, such as hand tally counters.

See also

• Finger counting
• Cardinal number
• Combinatorics
• Subitizing and counting
• Tally mark
• Unary numeral system
• Elementary arithmetic
• History of mathematics
• Jeton