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), or for well-ordered objects, to find the ordinal number of a particular object, or to find the object with a particular ordinal number. 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.) Euclid, Greek mathematician, 3rd century BC, as imagined by by Raphael in this detail from The School of Athens. ... An injective function. ... In mathematics, a well-order (or well-ordering) on a set S is a total order on S with the property that every non-empty subset of S has a least element in this ordering. ... Commonly, ordinal numbers, or ordinals for short, are numbers used to denote the position in an ordered sequence: first, second, third, fourth, etc. ... Different cultures have different traditional numeral systems used for writing numbers and for naming large numbers. ... A number is an abstract idea used in counting and measuring. ... In mathematics and theoretical computer science, an enumeration of a set is a procedure for listing all members of the set in some definite sequence. ... In mathematics, a set is called finite if and only if there is a bijection between the set and some set of the form {1, 2, ..., n} where is a natural number. ... In mathematics, a set can be thought of as any collection of distinct objects considered as a whole. ...

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. Image File history File linksMetadata Download high resolution version (442x888, 102 KB) Summary Super Crop showing only the sign. ... Image File history File linksMetadata Download high resolution version (442x888, 102 KB) Summary Super Crop showing only the sign. ... A sign warning hikers on the trail to Hanakapiai Beach. ... Quinquagesima is the name for the Sunday before Ash Wednesday. ...

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^[1], 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). Mathematical notation is used in mathematics, and throughout the physical sciences, engineering, and economics. ... A numeral is a symbol or group of symbols, or a word in a natural language that represents a number. ... Accountancy (profession) or accounting (methodology) is the measurement, disclosure or provision of assurance about financial information primarily used by managers, investors, tax authorities and other decision makers to make resource allocation decisions within companies, organizations, and public agencies. ...

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. A sign warning hikers on the trail to Hanakapiai Beach. ...

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. Finger counting, or dactylonomy, is the art of counting along ones fingers. ...

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

Finger counting, or dactylonomy, is the art of counting along ones fingers. ... Aleph-0, the smallest infinite cardinal In mathematics, cardinal numbers, or cardinals for short, are a generalized kind of number used to denote the size of a set. ... Combinatorics is a branch of pure mathematics concerning the study of discrete (and usually finite) objects. ... Introduction Kaufman et al. ... Tally marks are a variation of the unary numeral system. ... The unary numeral system is the simplest numeral system to represent natural numbers: in order to represent a number N, an arbitrarily chosen symbol is repeated N times. ... Elementary arithmetic is the most basic kind of mathematics: it concerns the operations of addition, subtraction, multiplication, and division. ... For a list of biographies of mathematicians, see list of mathematicians. ... Jetons were a token or coin-like medal produced across Europe during the 16th and 17th centuries. ...

References

1. ^ An Introduction to the History of Mathematics (6th Edition) by Howard Eves (1990)p.9

Howard Whitley Eves (10 January 1911 New Jersey - 6 June 2004) was an American mathematician, known for his work in geometry and the history of mathematics. ...

External Links

• History of Counting-PlainMath.Net