Extension, extend or extended may refer to:
Mathematics
Logic or set theory
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Axiom of extensionality
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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), the set of things to which a property applies
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Extension by definitions
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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
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, 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 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