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
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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 subalge ...
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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''" c ...
, 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 app ...
, 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 give ...
, 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 ma ...
, 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 a ...
, 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 ext ...
, 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 mathematics, a group extension is a general means of describing a group in terms of a particular normal subgroup and quotient group. If Q and N are two groups, then G is an extension of Q by N if there is a short exact sequence
:1\to N\;\ove ...
, in abstract algebra and homological algebra
Music
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Extension (music)
In music, an extension is a set of musical notes that lie outside the standard range or tessitura.
Staff
A note that lies outside the lines of a musical staff is an extension of the staff. The note will lie on a ledger line. Middle C, for ex ...
, 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)
Motion, the process of movement, is described using specific anatomical terms. Motion includes movement of organs, joints, limbs, and specific sections of the body. The terminology used describes this motion according to its direction relativ ...
, a movement at a
joint
A joint or articulation (or articular surface) is the connection made between bones, ossicles, or other hard structures in the body which link an animal's skeletal system into a functional whole.Saladin, Ken. Anatomy & Physiology. 7th ed. McGraw- ...
that increases the angle between the two ends of the joint; the opposite of
flexion
Motion, the process of movement, is described using specific anatomical terms. Motion includes movement of organs, joints, limbs, and specific sections of the body. The terminology used describes this motion according to its direction relativ ...
* Extension locus, the gene locus of
Melanocortin 1 receptor
The melanocortin 1 receptor (MC1R), also known as melanocyte-stimulating hormone receptor (MSHR), melanin-activating peptide receptor, or melanotropin receptor, is a G protein–coupled receptor that binds to a class of pituitary peptide hormones ...
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 ...
, 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 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 States and Canada.
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, 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" ...
, 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 plug on one end and one or more sockets on the other end (usually of the same type as the plug). The term usua ...
, power cable with a plug on one end and one or more sockets on the other end
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Eyelash extensions
Eyelash extensions are a cosmetics, cosmetic enhancement that involves attaching synthetic or natural hair fibers to the natural Eyelash, eyelashes to create a fuller, more dramatic look. They are applied by a professional using a specialized adhe ...
, 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
Agricultural extension is the application of scientific research and new knowledge to agricultural practices through farmer education. The field of 'extension' now encompasses a wider range of communication and learning activities organized for r ...
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Filename extension
A filename extension, file name extension or file extension is a suffix to the name of a computer file (e.g., .txt, .docx, .md). The extension indicates a characteristic of the file contents or its intended use. A filename extension is typically ...
, for computer file systems
See also
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Extensive (disambiguation)
{{Disambiguation