Editing Counting (section)

{{short description|Finding the number of elements of a finite set}}
{{for|its application to music|Counting (music)}}
[[File:Children's number blocks being used for learning to count - 51069936953.jpg|alt=A set of number blocks. The blocks 1, 2, and 3 are in the foreground; six other blocks can be seen in the background|thumb|Number blocks, which can be used for counting]]
'''Counting''' is the process of determining the [[number]] of [[Element (mathematics)|elements]] of a [[finite set]] of objects; that is, determining the [[size (mathematics)|size]] of a set. The traditional way of counting consists of continually increasing a (mental or spoken) counter by a [[1|unit]] for every element of the set, in some order, while marking (or displacing) those elements to avoid visiting the same element more than once, until no unmarked elements are left; if the counter was set to one after the first object, the value after visiting the final object gives the desired number of elements. The related term ''[[enumeration]]'' refers to uniquely identifying the elements of a [[Finite set|finite]] (combinatorial) [[Set (mathematics)|set]] or infinite set by assigning a number to each element.

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

There is archaeological evidence suggesting that humans have been counting for at least 50,000&nbsp;years.<ref>''An Introduction to the History of Mathematics'' (6th Edition) by [[Howard Eves]] (1990) p.9</ref> Counting was primarily used by ancient cultures to keep track of social and economic data such as the number of group members, prey animals, property, or debts (that is, [[accountancy]]). Notched bones were also found in the Border Caves in South Africa, which may suggest that the concept of counting was known to humans as far back as 44,000 BCE.<ref>{{Cite web|url=https://mathtimeline.weebly.com/early-human-counting-tools.html|title=Early Human Counting Tools|website=Math Timeline|access-date=2018-04-26}}</ref> The development of counting led to the development of [[mathematical notation]], [[numeral system]]s, and [[writing]].