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For example, the union of three sets A, B, and C contains all elements of A, all elements of B, and all elements of C, and nothing else. Thus, x is an element of A ∪ B ∪ C if and only if x is in at least one of A, B, and C. A finite union is the union of a finite number of sets; the phrase does not imply that the union set is a finite set ...
Academic Games is a competition in the U.S. in which players win by out-thinking each other in mathematics, language arts, and social studies. Formal tournaments are organized by local leagues, and on a national level by the Academic Games Leagues of America (AGLOA). Member leagues in eight states hold a national tournament every year, in which ...
An example of the apportionment paradox known as "the Alabama paradox" was discovered in the context of United States congressional apportionment in 1880, [1]: 228–231 when census calculations found that if the total number of seats in the House of Representatives were hypothetically increased, this would decrease Alabama's seats from 8 to 7.
The Miller Analogies Test (MAT) was a standardized test used both for graduate school admissions in the United States and entrance to high I.Q. societies.Created and published by Harcourt Assessment (now a division of Pearson Education), the MAT consisted of 120 questions in 60 minutes (an earlier iteration was 100 questions in 50 minutes).
In probability theory, Boole's inequality, also known as the union bound, says that for any finite or countable set of events, the probability that at least one of the events happens is no greater than the sum of the probabilities of the individual events. This inequality provides an upper bound on the probability of occurrence of at least one ...
Fair division is the problem in game theory of dividing a set of resources among several people who have an entitlement to them so that each person receives their due share. . That problem arises in various real-world settings such as division of inheritance, partnership dissolutions, divorce settlements, electronic frequency allocation, airport traffic management, and exploitation of Earth ...
The Newton–Pepys problem is a probability problem concerning the probability of throwing sixes from a certain number of dice. [1]In 1693 Samuel Pepys and Isaac Newton corresponded over a problem posed to Pepys by a school teacher named John Smith. [2]
Then is a 𝜎-field over the set - to check closure under countable union, recall a -ring is closed under countable intersections. In fact A {\displaystyle {\mathcal {A}}} is the minimal 𝜎-field containing R {\displaystyle {\mathcal {R}}} since it must be contained in every 𝜎-field containing R . {\displaystyle {\mathcal {R}}.}