# Counting

Counting is the action of finding the number of elements of 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 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 (combinatorial) 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, 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. Counting was primarily used by ancient cultures to keep track of social and economic data such as number of group members, prey animals, property or debts (i.e., accountancy). The development of counting led to the development of mathematical notation, numeral systems and writing.

### Other articles related to "counting":

Counting in Mathematics
... In mathematics, the essence of counting a set and finding a result n, is that it establishes a one to one correspondence (or bijection) of the set with the set of numbers {1, 2.. ... that two bijections can be composed to give another bijection) ensures that counting the same set in different ways can never result in different numbers (unless an error is made) ... This is the fundamental mathematical theorem that gives counting its purpose however you count a (finite) set, the answer is the same ...
Measuring Principle
... Examples may range from counting fruit to reading a thermometer gauge to determine temperature ... Examples include counting fruit or using a ruler to measure length ... Distances between villages may be measured by counting the rotations of a Surveyor's wheel ...
Counting Up, Counting Down
... Counting Up, Counting Down is a collection of short stories by Harry Turtledove ... appearing in the book, one called Forty, Counting Down and the other named Twenty-One, Counting Up ... Agent of Byzantium Between the Rivers The Case of the Toxic Spell Dump Conan of Venarium Counting Up, Counting Down Departures A Different Flesh Down in the Bottomlands Earthgrip Every Inch a King Fort ...
... Counting Heads is a science fiction novel by David Marusek, published in 2005 by Tor Books ... Counting Heads is an expansion of Marusek's 1995 short story "We Were Out of Our Minds with Joy", which serves as the first chapter of Counting Heads (with minor revisions from its original ... Mind Over Ship, a sequel to Counting Heads, was released on January 20, 2009 ...
Card Reading (bridge) - Counting Suits - Counting Trumps
... As a declarer, an efficient way of counting the trump cards is instead of counting the number of trump rounds and cards trumped in, count the number of trumps in the opponents' hands ... An even better way, of counting trumps, is to get familiar with common distribution patterns ... Counting as a defender Counting HCP and winners ...

### Famous quotes containing the word counting:

But counting up to two
Is harder to do....
Philip Larkin (1922–1986)

If all power is in the people, if there is no higher law than their will, and if by counting their votes, their will may be ascertained—then the people may entrust all their power to anyone, and the power of the pretender and the usurper is then legitimate. It is not to be challenged since it came originally from the sovereign people.
Walter Lippmann (1889–1974)

Is it not manifest that our academic institutions should have a wider scope; that they should not be timid and keep the ruts of the last generation, but that wise men thinking for themselves and heartily seeking the good of mankind, and counting the cost of innovation, should dare to arouse the young to a just and heroic life; that the moral nature should be addressed in the school-room, and children should be treated as the high-born candidates of truth and virtue?
Ralph Waldo Emerson (1803–1882)