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Still Counting The Dead 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 [...More...]  "Still Counting The Dead" on: Wikipedia Yahoo 

Counting (music) In music, counting is a system of regularly occurring sounds that serve to assist with the performance or audition of music by allowing the easy identification of the beat. Commonly, this involves verbally counting the beats in each measure as they occur. In addition to helping to normalize the time taken up by each beat, counting allows easier identification of the beats that are stressed [...More...]  "Counting (music)" on: Wikipedia Yahoo 

Permutation In mathematics, the notion of permutation relates to the act of arranging all the members of a set into some sequence or order, or if the set is already ordered, rearranging (reordering) its elements, a process called permuting. These differ from combinations, which are selections of some members of a set where order is disregarded. For example, written as tuples, there are six permutations of the set 1,2,3 , namely: (1,2,3), (1,3,2), (2,1,3), (2,3,1), (3,1,2), and (3,2,1). These are all the possible orderings of this three element set. As another example, an anagram of a word, all of whose letters are different, is a permutation of its letters. In this example, the letters are already ordered in the original word and the anagram is a reordering of the letters. The study of permutations of finite sets is a topic in the field of combinatorics. Permutations occur, in more or less prominent ways, in almost every area of mathematics [...More...]  "Permutation" on: Wikipedia Yahoo 

Countably Infinite In mathematics, a countable set is a set with the same cardinality (number of elements) as some subset of the set of natural numbers. A countable set is either a finite set or a countably infinite set. Whether finite or infinite, the elements of a countable set can always be counted one at a time and, although the counting may never finish, every element of the set is associated with a unique natural number. Some authors use countable set to mean countably infinite alone.[1] To avoid this ambiguity, the term at most countable may be used when finite sets are included and countably infinite, enumerable,[2] or denumerable[3] otherwise. Georg Cantor Georg Cantor introduced the term countable set, contrasting sets that are countable with those that are uncountable (i.e., nonenumerable or nondenumerable[4]) [...More...]  "Countably Infinite" on: Wikipedia Yahoo 

Integer An integer (from the Latin Latin integer meaning "whole")[note 1] is a number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, 5 1⁄2, and √2 are not. The set of integers consists of zero (0), the positive natural numbers (1, 2, 3, …), also called whole numbers or counting numbers,[1][2] and their additive inverses (the negative integers, i.e., −1, −2, −3, …). This is often denoted by a boldface Z ("Z") or blackboard bold Z displaystyle mathbb Z ( Unicode Unicode U+2124 ℤ) standing for the German word Zahlen ([ˈtsaːlən], "numbers").[3][4] Z is a subset of the set of all rational numbers Q, in turn a subset of the real numbers R. Like the natural numbers, Z is countably infinite. The integers form the smallest group and the smallest ring containing the natural numbers [...More...]  "Integer" on: Wikipedia Yahoo 

Real Number In mathematics, a real number is a value that represents a quantity along a line. The adjective real in this context was introduced in the 17th century by René Descartes, who distinguished between real and imaginary roots of polynomials. The real numbers include all the rational numbers, such as the integer −5 and the fraction 4/3, and all the irrational numbers, such as √2 (1.41421356..., the square root of 2, an irrational algebraic number). Included within the irrationals are the transcendental numbers, such as π (3.14159265...). Real numbers can be thought of as points on an infinitely long line called the number line or real line, where the points corresponding to integers are equally spaced. Any real number can be determined by a possibly infinite decimal representation, such as that of 8.632, where each consecutive digit is measured in units one tenth the size of the previous one [...More...]  "Real Number" on: Wikipedia Yahoo 

Uncountable Set In mathematics, an uncountable set (or uncountably infinite set)[1] is an infinite set that contains too many elements to be countable. The uncountability of a set is closely related to its cardinal number: a set is uncountable if its cardinal number is larger than that of the set of all natural numbers.Contents1 Characterizations 2 Properties 3 Examples 4 Without the axiom of choice 5 See also 6 References 7 External linksCharacterizations[edit] There are many equivalent characterizations of uncountability. A set X is uncountable if and only if any of the following conditions holds:There is no injective function from X to the set of natural numbers. X is nonempty and for every ωsequence of elements of X, there exist at least one element of X not included in it [...More...]  "Uncountable Set" on: Wikipedia Yahoo 

Cardinality In mathematics, the cardinality of a set is a measure of the "number of elements of the set". For example, the set A = 2, 4, 6 contains 3 elements, and therefore A has a cardinality of 3. There are two approaches to cardinality – one which compares sets directly using bijections and injections, and another which uses cardinal numbers.[1] The cardinality of a set is also called its size, when no confusion with other notions of size[2] is possible. The cardinality of a set A is usually denoted A , with a vertical bar on each side; this is the same notation as absolute value and the meaning depends on context [...More...]  "Cardinality" on: Wikipedia Yahoo 

Set Theory Set theory Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics. The language of set theory can be used in the definitions of nearly all mathematical objects. The modern study of set theory was initiated by Georg Cantor Georg Cantor and Richard Dedekind Richard Dedekind in the 1870s [...More...]  "Set Theory" on: Wikipedia Yahoo 

Injective In mathematics, an injective function or injection or onetoone function is a function that preserves distinctness: it never maps distinct elements of its domain to the same element of its codomain. In other words, every element of the function's codomain is the image of at most one element of its domain. The term onetoone function must not be confused with onetoone correspondence (a.k.a [...More...]  "Injective" on: Wikipedia Yahoo 

Surjective In mathematics, a function f from a set X to a set Y is surjective (or onto), or a surjection, if for every element y in the codomain Y of f there is at least one element x in the domain X of f such that f(x) = y. It is not required that x is unique; the function f may map one or more elements of X to the same element of Y.A surjective function from domain X to codomain Y. The function is surjective because every point in the codomain is the value of f(x) for at least one point x in the domain.The term surjective and the related terms injective and bijective were introduced by Nicolas Bourbaki,[1] a group of mainly French 20thcentury mathematicians who under this pseudonym wrote a series of books presenting an exposition of modern advanced mathematics, beginning in 1935 [...More...]  "Surjective" on: Wikipedia Yahoo 

Pigeonhole Principle In mathematics, the pigeonhole principle states that if n items are put into m containers, with n > m, then at least one container must contain more than one item.[1] This theorem is exemplified in real life by truisms like "in any group of three gloves there must be at least two left gloves or two right gloves". It is an example of a counting argument. This seemingly obvious statement can be used to demonstrate possibly unexpected results; for example, that there are two people in London London who have the same number of hairs on their heads. The first formalization of the idea is believed to have been made by Peter Gustav Lejeune Dirichlet Peter Gustav Lejeune Dirichlet in 1834 under the name Schubfachprinzip ("drawer principle" or "shelf principle") [...More...]  "Pigeonhole Principle" on: Wikipedia Yahoo 

Enumerative Combinatorics Enumerative combinatorics is an area of combinatorics that deals with the number of ways that certain patterns can be formed. Two examples of this type of problem are counting combinations and counting permutations. More generally, given an infinite collection of finite sets Si indexed by the natural numbers, enumerative combinatorics seeks to describe a counting function which counts the number of objects in Sn for each n. Although counting the number of elements in a set is a rather broad mathematical problem, many of the problems that arise in applications have a relatively simple combinatorial description. The twelvefold way provides a unified framework for counting permutations, combinations and partitions. The simplest such functions are closed formulas, which can be expressed as a composition of elementary functions such as factorials, powers, and so on. For instance, as shown below, the number of different possible orderings of a deck of n cards is f(n) = n! [...More...]  "Enumerative Combinatorics" on: Wikipedia Yahoo 

Kirby Lester Pharmacy Automation Pharmacy automation Pharmacy automation involves the mechanical processes of handling and distributing medications. Any pharmacy task may be involved, including counting small objects (e.g., tablets, capsules); measuring and mixing powders and liquids for compounding; tracking and updating customer information in databases (e.g., personally identifiable information (PII), medical history, drug interaction risk detection); and inventory management [...More...]  "Kirby Lester Pharmacy Automation" on: Wikipedia Yahoo 

Natural Number In mathematics, the natural numbers are those used for counting (as in "there are six coins on the table") and ordering (as in "this is the third largest city in the country") [...More...]  "Natural Number" on: Wikipedia Yahoo 

Card Reading (bridge) In contract bridge, card reading (or counting the hand) is the process of inferring which remaining cards are held by each opponent. The reading is based on information gained in the bidding and the play to previous tricks.[1] The technique is used by the declarer and defenders primarily to determine the probable suit distribution and honor card holdings of each unseen hand; determination of the location of specific spotcards may be critical as well. Card reading is based on the fact that there are thirteen cards in each of four suits and thirteen cards in each of four hands.Contents1 General tips1.1 Basic 1.2 Advanced2 Counting suits2.1 Counting trumps3 See also 4 References 5 External linksGeneral tips[edit] Basic[edit] There are some basic tips:The player could memorize the common patterns of the 13 cards, in a suit, as held by the 4 players: 4432, 4333, 4441, 5332, 5431, 5422, 6322, 6331, etc [...More...]  "Card Reading (bridge)" on: Wikipedia Yahoo 