Definition, Meaning & Synonyms | English word GENERALIZATION

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Definitions of GENERALIZATION

1. The formulation of general concepts from specific instances by abstracting common properties.
2. An oversimplified or exaggerated conception, opinion, or image of the members of a group.
3. An act or instance of generalizing; concluding that something true of a subclass is true of the entire class
4. Inductive reasoning from detailed facts to general principles
5. (mathematics) A proof, axiom, problem, or definition that includes another's cases, and also some additional cases; a conclusion reached by inferring from specific cases to more general cases or principles.

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Examples of Using GENERALIZATION in a Sentence

• With addition as an operation, the integers and the real numbers form abelian groups, and the concept of an abelian group may be viewed as a generalization of these examples.
• A Boolean algebra can be seen as a generalization of a power set algebra or a field of sets, or its elements can be viewed as generalized truth values.
• One such generalization is that a topological space is sequentially compact if every infinite sequence of points sampled from the space has an infinite subsequence that converges to some point of the space.
• Conjugate element (field theory), a generalization of the preceding conjugations to roots of a polynomial of any degree.
• In probability theory, the expected value (also called expectation, expectancy, expectation operator, mathematical expectation, mean, expectation value, or first moment) is a generalization of the weighted average.
• In mathematics, more specifically in ring theory, a Euclidean domain (also called a Euclidean ring) is an integral domain that can be endowed with a Euclidean function which allows a suitable generalization of the Euclidean division of integers.
• A generalization is a form of abstraction whereby common properties of specific instances are formulated as general concepts or claims.
• Partially ordered set#Intervals, its generalization from numbers to arbitrary partially ordered sets.
• Philosophy professor Bradley Dowden explains the fallacy as an "ad hoc rescue" of a refuted generalization attempt.
• The method can be extended to prove statements about more general well-founded structures, such as trees; this generalization, known as structural induction, is used in mathematical logic and computer science.
• In mathematics, the concept of a measure is a generalization and formalization of geometrical measures (length, area, volume) and other common notions, such as magnitude, mass, and probability of events.
• A large generalization of this formula applies to summation over an arbitrary locally finite partially ordered set, with Möbius' classical formula applying to the set of the natural numbers ordered by divisibility: see incidence algebra.
• A polyhedron is a generalization of a 2-dimensional polygon and a 3-dimensional specialization of a polytope, a more general concept in any number of dimensions.
• the set of all stars within the Milky Way galaxy) or a hypothetical and potentially infinite group of objects conceived as a generalization from experience (e.
• Separable algebra, a generalization to associative algebras of the notion of a separable field extension.
• Stokes' theorem was formulated in its modern form by Élie Cartan in 1945, following earlier work on the generalization of the theorems of vector calculus by Vito Volterra, Édouard Goursat, and Henri Poincaré.
• The carpet is a generalization of the Cantor set to two dimensions; another such generalization is the Cantor dust.
• In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions.
• In mathematics, an -sphere or hypersphere is an -dimensional generalization of the -dimensional circle and -dimensional sphere to any non-negative integer.
• In a generalized digroup or g-digroup, a generalization due to Salazar-Díaz, Velásquez, and Wills-Toro (2016), each element has a left inverse and a right inverse instead of one two-sided inverse.

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