Extension, extend or extended may refer to:
Mathematics
Logic or set theory
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Axiom of extensionality
In axiomatic set theory and the branches of logic, mathematics, and computer science that use it, the axiom of extensionality, or axiom of extension, is one of the axioms of Zermelo–Fraenkel set theory. It says that sets having the same elements ...
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Extensible cardinal In mathematics, extendible cardinals are large cardinals introduced by , who was partly motivated by reflection principles. Intuitively, such a cardinal represents a point beyond which initial pieces of the universe of sets start to look simila ...
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Extension (model theory)
In mathematical logic, an (induced) substructure or (induced) subalgebra is a structure whose domain is a subset of that of a bigger structure, and whose functions and relations are restricted to the substructure's domain. Some examples of subal ...
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Extension (predicate logic)
The extension of a predicatea truth-valued functionis the set of tuples of values that, used as arguments, satisfy the predicate. Such a set of tuples is a relation.
Examples
For example, the statement "''d2'' is the weekday following ''d1''" can ...
, the set of tuples of values that satisfy the predicate
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Extension (semantics)
In any of several fields of study that treat the use of signs — for example, in linguistics, logic, mathematics, semantics, semiotics, and philosophy of language — the extension of a concept, idea, or sign consists of the things to which it ap ...
, the set of things to which a property applies
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Extension by definitions
In mathematical logic, more specifically in the proof theory of first-order theories, extensions by definitions formalize the introduction of new symbols by means of a definition. For example, it is common in naive set theory to introduce a symbol ...
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Extensional definition
In logic, extensional and intensional definitions are two key ways in which the objects, concepts, or referents a term refers to can be defined. They give meaning or denotation to a term.
Intensional definition
An intensional definition gives m ...
, a definition that enumerates every individual a term applies to
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Extensionality
In logic, extensionality, or extensional equality, refers to principles that judge objects to be equal if they have the same external properties. It stands in contrast to the concept of intensionality, which is concerned with whether the internal ...
Other uses
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Extension of a polyhedron In convex geometry and polyhedral combinatorics, the extension complexity is a convex polytope P is the smallest number of facets among convex polytopes Q that have P as a projection. In this context, Q is called an extended formulation of P; it m ...
, in geometry
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Exterior algebra
In mathematics, the exterior algebra, or Grassmann algebra, named after Hermann Grassmann, is an algebra that uses the exterior product or wedge product as its multiplication. In mathematics, the exterior product or wedge product of vectors is ...
, Grassmann's theory of extension, in geometry
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Homotopy extension property In mathematics, in the area of algebraic topology, the homotopy extension property indicates which homotopies defined on a subspace can be extended to a homotopy defined on a larger space. The homotopy extension property of cofibrations is dual ...
, in topology
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Kolmogorov extension theorem
In mathematics, the Kolmogorov extension theorem (also known as Kolmogorov existence theorem, the Kolmogorov consistency theorem or the Daniell-Kolmogorov theorem) is a theorem that guarantees that a suitably "consistent" collection of finite-di ...
, in probability theory
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Linear extension
In order theory, a branch of mathematics, a linear extension of a partial order is a total order (or linear order) that is compatible with the partial order. As a classic example, the lexicographic order of totally ordered sets is a linear extens ...
, in order theory
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Sheaf extension, in algebraic geometry
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Tietze extension theorem, in topology
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Whitney extension theorem, in differential geometry
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Group extension, in abstract algebra and homological algebra
Music
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Extension (music), notes that fit outside the standard range
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''Extended'' (Solar Fields album), 2005
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''Extension'' (George Braith album), 1964
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''Extension'' (Clare Fischer album), 1963
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''Extensions'' (Ahmad Jamal album), 1965
* ''Extensions'', a 1969 album by
Mystic Moods Orchestra
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''Extensions'' (McCoy Tyner album), 1970
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''Extensions'' (Dave Holland album), 1988
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''Extensions'' (The Manhattan Transfer album), 1979
Places
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Extension, British Columbia, a village near Regional District of Nanaimo, British Columbia, Canada
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Extension, Louisiana, unincorporated community, United States
Science
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Extension (geology), relating to the pulling apart of the Earth's crust and lithosphere
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Extension (anatomy), a movement at a
joint that increases the angle between the two ends of the joint; the opposite of
flexion
* Extension locus, the gene locus of
Melanocortin 1 receptor
Other uses
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Browser extension
A browser extension is a small software module for customizing a web browser. Browsers typically allow a variety of extensions, including user interface modifications, cookie management, ad blocking, and the custom scripting and styling of web p ...
, a small software module for customizing a web browser
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Building extension
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Continuing education
Continuing education (similar to further education in the United Kingdom and Republic of Ireland, Ireland) is an all-encompassing term within a broad list of post-secondary learning activities and programs. The term is used mainly in the United ...
, or extension school, a school for continuing education
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Cooperative State Research, Education, and Extension Service, a former division of the U.S. Department of Agriculture
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Extension (metaphysics) In metaphysics, extension signifies both 'stretching out' (Latin: ''extensio'') as well as later 'taking up space', and most recently, spreading one's internal mental cognition into the external world.
The history of thinking about ''extension'' ca ...
, the property of stretching out or taking up space
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Extension (telephone)
In residential telephony, an extension telephone is an additional telephone wired to the same telephone line as another. In middle 20th century telephone jargon, the first telephone on a line was a "Main Station" and subsequent ones "Extensions" o ...
, telephone line attached to a main line or to a PBX or Centrex system
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Extension cord
An extension cord (US), power extender, drop cord, or extension lead (UK) is a length of flexible electrical power cable (flex) with a AC power plugs and sockets, plug on one end and one or more sockets on the other end (usually of the same type ...
, power cable with a plug on one end and one or more sockets on the other end
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Eyelash extensions, material applied to eyelashes
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Hair extensions, strands of hair added to existing hair
* Extension, the building of community capacity by outsiders, for instance
agricultural extension
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Filename extension, for computer file systems
See also
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Extensive (disambiguation)
Extensive may refer to:
* Extensive property
* Extensive function
* Extensional In any of several fields of study that treat the use of signs — for example, in linguistics
Linguistics is the science, scientific study of human language. ...
{{Disambiguation