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Extension By Zero
Extension, extend or extended may refer to: Mathematics Logic or set theory * Axiom of extensionality * Extensible cardinal * Extension (model theory) * Extension (predicate logic), the set of tuples of values that satisfy the predicate * Extension (semantics), the set of things to which a property applies * Extension by definitions * Extensional definition, a definition that enumerates every individual a term applies to * Extensionality Other uses * Extension of a polyhedron, in geometry * Exterior algebra, Grassmann's theory of extension, in geometry * Homotopy extension property, in topology * Kolmogorov extension theorem, in probability theory * Linear extension, in order theory * Sheaf extension, in algebraic geometry * Tietze extension theorem, in topology * Whitney extension theorem, in differential geometry * Group extension, in abstract algebra and homological algebra Music * Extension (music), notes that fit outside the standard range * ''Extended'' (Solar Fie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 are the same set. Formal statement In the formal language of the Zermelo–Fraenkel axioms, the axiom reads: :\forall A \, \forall B \, ( \forall X \, (X \in A \iff X \in B) \implies A = B) or in words: :Given any set ''A'' and any set ''B'', if for every set ''X'', ''X'' is a member of ''A'' if and only if ''X'' is a member of ''B'', then ''A'' is equal to ''B''. :(It is not really essential that ''X'' here be a ''set'' — but in ZF, everything is. See Ur-elements below for when this is violated.) The converse, \forall A \, \forall B \, (A = B \implies \forall X \, (X \in A \iff X \in B) ), of this axiom follows from the substitution property of equality. Interpretation To understand this axiom, note that the clause i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 example, is an extension note on both treble and bass clefs, however is not outside the grand staff. Soprano C and Deep C lie two ledger lines above treble and below bass respectively (as well as the grand staff). Instruments An instrumental extension is a range of playable notes outside the normal range of the instrument. A baritone horn, if played by a skillful player, can be played an octave above the normal range. Since this is not standard, these notes would be an extension. (See also: Crook (music)). With the bowed string instruments, lower pitches than the standard range are sometimes used through scordatura in which the lowest string is tuned down a note or two. The double bass sometimes uses a C extension extending the range of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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-Hill Connect. Webp.274/ref> They are constructed to allow for different degrees and types of movement. Some joints, such as the knee, elbow, and shoulder, are self-lubricating, almost frictionless, and are able to withstand compression and maintain heavy loads while still executing smooth and precise movements. Other joints such as sutures between the bones of the skull permit very little movement (only during birth) in order to protect the brain and the sense organs. The connection between a tooth and the jawbone is also called a joint, and is described as a fibrous joint known as a gomphosis. Joints are classified both structurally and functionally. Classification The number of joints depends on if sesamoids are included, age of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 relative to the anatomical position of the body parts involved. Anatomists and others use a unified set of terms to describe most of the movements, although other, more specialized terms are necessary for describing unique movements such as those of the hands, feet, and eyes. In general, motion is classified according to the anatomical plane it occurs in. ''Flexion'' and ''extension'' are examples of ''angular'' motions, in which two axes of a joint are brought closer together or moved further apart. ''Rotational'' motion may occur at other joints, for example the shoulder, and are described as ''internal'' or ''external''. Other terms, such as ''elevation'' and ''depression'', describe movement above or below the horizontal plane. Many anatomic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 on the amount of stretching involved. Stretching is generally measured using the parameter ''β'', known as the ''beta factor'', where : \beta = \frac \,, ''t''0 is the initial crustal thickness and ''t''1 is the final crustal thickness. It is also the equivalent of the strain parameter ''stretch''. Low beta factor In areas of relatively low crustal stretching, the dominant structures are high to moderate angle normal faults, with associated half grabens and tilted fault blocks. High beta factor In areas of high crustal stretching, individual extensional faults may become rotated to too low a dip to remain active and a new set of faults may be generated. Large displacements may juxtapose syntectonic sediments against metamorphic roc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 songs, "Louie Louie "Louie Louie" is a rhythm and blues song written and composed by American musician Richard Berry in 1955, recorded in 1956, and released in 1957. It is best known for the 1963 hit version by the Kingsmen and has become a standard in pop and r ...." Notes Unincorporated communities in Franklin Parish, Louisiana Unincorporated communities in Louisiana {{Louisiana-geo-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 American, lived in today's Colvilletown neighbourhood of south Nanaimo. Many suspected foul play when his body was found at the bottom of a cliff in 1895. One theory claimed he had refused to sell his coal rich land to Dunsmuir coal, desperately seeking new sources to replace its nearly exhausted Wellington mine. Another rumour suggested he was the discoverer of the coal seam on the southern slope of Mt. Benson. However, after the death, his close neighbour Ephraim (Edward) Hodgson claimed the credit and reward for the discovery. Murder charges against Hodgson were dropped. The Mt. Benson seam proved to be an extension of the Wellington one being worked by Dunsmuir, and the location was initially called Wellington Extension. Railway Thwarted i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Extensions (The Manhattan Transfer Album)
Extension, extend or extended may refer to: Mathematics Logic or set theory * Axiom of extensionality * Extensible cardinal * Extension (model theory) * Extension (predicate logic), the set of tuples of values that satisfy the predicate * Extension (semantics), the set of things to which a property applies * Extension by definitions * Extensional definition, a definition that enumerates every individual a term applies to * Extensionality Other uses * Extension of a polyhedron, in geometry * Exterior algebra, Grassmann's theory of extension, in geometry * Homotopy extension property, in topology * Kolmogorov extension theorem, in probability theory * Linear extension, in order theory * Sheaf extension, in algebraic geometry * Tietze extension theorem, in topology * Whitney extension theorem, in differential geometry * Group extension, in abstract algebra and homological algebra Music * Extension (music), notes that fit outside the standard range * ''Extended'' (Solar Field ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Extensions (Dave Holland Album)
''Extensions'' is an album by jazz bassist Dave Holland released on the ECM label in 1990. The record is Dave Holland's eighth album to be released on the ECM label. It features two members of his previous quintet— saxophonist Steve Coleman and drummer Marvin "Smitty" Smith—alongside guitarist Kevin Eubanks, in his first appearance on a Holland record. Holland recorded "Processional" again on his later sextet album '' Pass It On''. Reception The Allmusic review by Brian Olewnick awarded the album 4 stars, calling it a "tight and enjoyable quartet date" and "One of his better albums from this period, ''Extensions'' should please any Holland fan, and is an agreeable and non-threatening jumping in point for the curious".Olewnick, BAllmusic Reviewaccessed August 19, 2011. ''Extensions'' was voted Album of the Year (1989) by ''Downbeat Magazine''. Track listing # "Nemesis" (Kevin Eubanks) - 11:31 # "Processional" (Dave Holland) - 7:16 # "Black Hole" (Steve Coleman) - 10:10 # ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Extensions (McCoy Tyner Album)
''Extensions'' is an album by jazz pianist McCoy Tyner released on the Blue Note label. It was recorded on February 9, 1970 but not released until January of 1973. It has performances by Tyner with alto saxophonist Gary Bartz, tenor saxophonist Wayne Shorter, bassist Ron Carter, drummer Elvin Jones, and features Alice Coltrane playing harp on three of the four tracks. Reception In his AllMusic review Scott Yanow says, "The all-star sextet stretches out on lengthy renditions of four of Tyner's modal originals, and there is strong solo space for the leader and the two saxophonists... Stimulating music". Reviewing the album for jazz.com, Jared Pauley says, "McCoy Tyner finds himself among elite company on ''Extensions.'' Recorded as jazz was entering the fusion period, this is a great example of just how good straight-ahead swing can sound... This performance matches the superb quality of previous Shorter and Tyner albums where members of the Davis and Coltrane groups recorded tog ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 in 1966 through the label Philips. Throughout the rest of the 1960s and 1970s, the group continued to release similar styled recordings and their recordings continued to be reissued throughout the 1980s and 1990s. History Brad Miller was born in Burbank, California, and had developed an interest in railroading in his teens. After a few years of hanging around railyards and learning all the lore of steam and diesel engines, he decided to record the sounds of some of the last steam locomotives operating on a major rail line. Eventually, around 1958, he and his friend, Jim Connella, formed a company called Mobile Fidelity Records and started cutting records from these field recordings, which they released through railroading magazines and mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Extensions (Ahmad Jamal Album)
''Extensions'' is an album by American jazz pianist Ahmad Jamal featuring performances recorded in 1965 and released on the Argo label.Ahmad Jamal discography accessed May 18, 2012 Critical reception awarded the album 3 stars.Allmusic Reviewaccessed May 18, 20121 Track listing # "Extensions" (Ahmad Jamal) – 13:10 # "Dance to the Lady" () – 5:50 # "This Terr ...[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
