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 elemen ...
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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 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 i ...
, 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 ...
, 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 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 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 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 ...
, 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
The Mystic Moods Orchestra was a group known for mixing orchestral pop, environmental sounds, and pioneering recording techniques. It was created by audiophile Brad Miller. The first Mystic Moods Orchestra album, ''One Stormy Night'', was released ...
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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 Extension is an unincorporated community near the east coast of southern Vancouver Island, British Columbia. The location off BC Highway 19 is about by road northwest of Victoria, and south of Nanaimo.
Discovery
Louis Stark, an African Americ ...
, a village near Regional District of Nanaimo, British Columbia, Canada
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Extension, Louisiana
Extension is an unincorporated community in Franklin Parish, Louisiana, United States. Its ZIP code is 71243.
Notable people
Singer and songwriter Richard Berry was born in Extension. He is known for writing one of the world's most recorded son ...
, unincorporated community, United States
Science
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Extension (geology)
Extensional tectonics is concerned with the structures formed by, and the tectonic processes associated with, the stretching of a planetary body's crust or lithosphere.
Deformation styles
The types of structure and the geometries formed depend ...
, 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 pa ...
, 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), 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, 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
Artificial hair integrations, more commonly known as hair extensions, hair weaves, and fake hair add length and fullness to human hair. Hair extensions are usually clipped, glued, or sewn on natural hair by incorporating additional human or sy ...
, 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 ...
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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)
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