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Inclusion–exclusion principle. In combinatorics, a branch of mathematics, the inclusion–exclusion principle is a counting technique which generalizes the familiar method of obtaining the number of elements in the union of two finite sets; symbolically expressed as. where A and B are two finite sets and | S | indicates the cardinality of a ...
Combinatorial principles. In proving results in combinatorics several useful combinatorial rules or combinatorial principles are commonly recognized and used. The rule of sum, rule of product, and inclusion–exclusion principle are often used for enumerative purposes. Bijective proofs are utilized to demonstrate that two sets have the same ...
In set theory, the union (denoted by ∪) of a collection of sets is the set of all elements in the collection. [1] It is one of the fundamental operations through which sets can be combined and related to each other. A nullary union refers to a union of zero ( ) sets and it is by definition equal to the empty set.
Disability. "The normalization principle means making available to all people with disabilities patterns of life and conditions of everyday living which are as close as possible to the regular circumstances and ways of life or society." [1] Normalization is a rigorous theory of human services that can be applied to disability services. [2]
Euclid's theorem. Euclid's theorem is a fundamental statement in number theory that asserts that there are infinitely many prime numbers. It was first proven by Euclid in his work Elements. There are several proofs of the theorem.
The inclusion/exclusion model [ edit ] A more specific model to predict assimilation and contrast effects with differences in categorizing information is the inclusion/exclusion model developed 1992 by Norbert Schwarz and Herbert Bless.< [ 7 ] It explains the mechanism through which effects occur. [ 8 ]
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 ...
Fundamental lemma of sieve theory. In number theory, the fundamental lemma of sieve theory is any of several results that systematize the process of applying sieve methods to particular problems. Halberstam & Richert [1] : 92–93 write: A curious feature of sieve literature is that while there is frequent use of Brun's method there are only a ...