Concepts inPermutation betting markets: singleton betting with extra information
Singleton (mathematics)
In mathematics, a singleton, also known as a unit set, is a set with exactly one element. For example, the set {0} is a singleton. The term is also used for a 1-tuple (a sequence with one element).
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Permutation
In mathematics, the notion of permutation is used with several slightly different meanings, all related to the act of permuting (rearranging) objects or values. Informally, a permutation of a set of objects is an arrangement of those objects into a particular order. For example, 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). One might define an anagram of a word as a permutation of its letters.
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Bookmaker
A bookmaker, or bookie, is an organization or a person that takes bets on sporting and other events at agreed upon odds.
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P versus NP problem
The P versus NP problem is a major unsolved problem in computer science. Informally, it asks whether every problem whose solution can be quickly verified by a computer can also be quickly solved by a computer. It was introduced in 1971 by Stephen Cook in his seminal paper "The complexity of theorem proving procedures" and is considered by many to be the most important open problem in the field.
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Solvable group
In mathematics, more specifically in the field of group theory, a solvable group (or soluble group) is a group that can be constructed from abelian groups using extensions. That is, a solvable group is a group whose derived series terminates in the trivial subgroup. Historically, the word "solvable" arose from Galois theory and the proof of the general unsolvability of quintic equation.
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Necessity and sufficiency
In logic, necessity and sufficiency refer to the implicational relationships between statements. The assertion that one statement is a necessary and sufficient condition of another means that the former statement is true if and only if the latter is true.
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Order (group theory)
In group theory, a branch of mathematics, the term order is used in two closely related senses: The order of a group is its cardinality, i.e. , the number of elements in its set. The order, sometimes period, of an element a of a group is the smallest positive integer m such that a = e (where e denotes the identity element of the group, and a denotes the product of m copies of a). If no such m exists, a is said to have infinite order. All elements of finite groups have finite order.
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