Counting

Counting is the process of determining the number of elements in a finite set of objects. The traditional way of counting consists of continually increasing a (mental or spoken) counter by a 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 counting ends with the last object on a number that is then called the number of elements in the set.

History of Counting

Counting, in terms of a more concrete understanding, involves the history of number systems. Ancient cultures such as those in Egypt and Greece used a tally system where separate marks were either grouped by five or ten. In East Asia, a decimal system was developed, similar to the one used worldwide today. Counting Rods were used that could be placed in configurations to represent numbers.

Counting in Mathematics

In mathematics, counting is considered an initial step of enumerating concepts including integers, real numbers, and topological spaces. Counting also plays a crucial role in statistics, where it is important to determine sets of precise count data. Counting can be done in a variety of ways ranging from the simple, where objects in a set are tagged to avoid double counting, to more complex techniques such as the inclusion-exclusion principle.

Counting in Computer Science

In computer science, counting is considered an important aspect as well. It is necessary to be able to count the number of operations that a particular algorithm takes in order to ensure that it runs in a reasonable amount of time. Counting is also used in counting sort, a sorting algorithm that takes advantage of the fact that the number of integers is small.

See Also

• Number
• Mathematics
• Computer Science
• Statistics
• Counting Rods

References

Counting Resources
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