A definition is a statement of the meaning of a term (a word, phrase, or other set of symbols). Definitions can be classified into two large categories, intensional definitions (which try to give the essence of a term) and extensional definitions (which list every single object that a term describes). A term may have many different senses and multiple meanings, and thus require multiple definitions.
In mathematics, a definition is used to give a precise meaning to a new term, instead of describing a pre-existing term. Definitions and axioms are the basis on which all of mathematics is constructed.
Intensional definitions vs extensional definitions
An Intensional definition, also called a connotative definition, specifies the necessary and sufficient conditions for a thing being a member of a specific set. Any definition that attempts to set out the essence of something, such as that by genus and differentia, is an intensional definition.
An extensional definition, also called a denotative definition, of a concept or term specifies its extension. It is a list naming every object that is a member of a specific set.
In calculus, the (ε, δ)-definition of limit ("epsilon-delta definition of limit") is a formalization of the notion of limit. It was first given by Bernard Bolzano in 1817. Augustin-Louis Cauchy never gave an () definition of limit in his Cours d'Analyse, but occasionally used
arguments in proofs. The definitive modern statement was ultimately provided by Karl Weierstrass.
History
Isaac Newton was aware, in the context of the derivative concept, that the limit of the ratio of evanescent quantities was not itself a ratio, as when he wrote:
Occasionally Newton explained limits in terms similar to the epsilon-delta definition.Augustin-Louis Cauchy gave a definition of limit in terms of a more primitive notion he called a variable quantity. He never gave an epsilon-delta definition of limit (Grabiner 1981). Some of Cauchy's proofs contain indications of the epsilon-delta method. Whether or not his foundational approach can be considered a harbinger of Weierstrass's is a subject of scholarly dispute. Grabiner feels that it is, while Schubring (2005) disagrees. Nakane concludes that Cauchy and Weierstrass gave the same name to different notions of limit.
Definition is the sixth album by the American crossover thrash band D.R.I., which was released in 1992.
Track listing
Bonus tracks
LP - "Out of Mind"
Cassette - "Hide Your Eyes"
CD - "Dry Heaves"
Credits
Canyon was a series of seven United States spy satellites launched between 1968 and 1977. Also known by its program number AFP-827, the satellites were developed with the participation of the Air Force. The Canyon project is credited as being the first American satellite system tasked for COMINT.
The satellites each had a mass of 700 kg and were launched from Atlas/Agena D rockets into near-geosynchronous orbits. They carried large parabolic reflecting dishes, estimated at 10m in diameter. The Canyon satellites were eventually replaced with the next generation of COMINT satellites, the Vortex/Chalet series. The program is still classified.
Seven Canyon satellites were launched from 1968 to 1977, all with Atlas Agena D vehicles from LC-13 at Cape Canaveral and there was one failure in 1971. The first four Canyons apparently remained attached to the Agena after achieving orbit, using its engine for maneuvering (the missions would have been concluded after Agena propellant depletion). Later Canyons were reputedly larger in size and did separate from the booster.
A canyon or gorge is a geographical feature.
Canyon may also refer to:
Places
Business
People
Films and television
Music
Others
Trance denotes any state of awareness or consciousness other than normal waking consciousness. Trance states may occur involuntarily and unbidden.
The term trance may be associated with hypnosis, meditation, magic, flow, and prayer. It may also be related to the earlier generic term, altered states of consciousness, which is no longer used in "consciousness studies" discourse.
Etymology
Trance in its modern meaning comes from an earlier meaning of "a dazed, half-conscious or insensible condition or state of fear", via the Old French transe "fear of evil", from the Latin transīre "to cross", "pass over". This definition is now obsolete.
Working models
Wier, in his 1995 book, Trance: from magic to technology, defines a simple trance (p. 58) as a state of mind being caused by cognitive loops where a cognitive object (thoughts, images, sounds, intentional actions) repeats long enough to result in various sets of disabled cognitive functions. Wier represents all trances (which include sleep and watching television) as taking place on a dissociated trance plane where at least some cognitive functions such as volition are disabled; as is seen in what is typically termed a 'hypnotic trance'. With this definition, meditation, hypnosis, addictions and charisma are seen as being trance states. In Wier's 2007 book, The Way of Trance, he elaborates on these forms, adds ecstasy as an additional form and discusses the ethical implications of his model, including magic and government use which he terms "trance abuse".
Trance is an album by American jazz pianist and composer Steve Kuhn recorded in 1974 and released on the ECM label.
Reception
The Allmusic review by Thom Jurek awarded the album 4 stars stating "This is jazz that touches on fusion, modal, and the new spirit of the music as ECM came into the 1970s as a player. There is restlessness and calm, tempestuousness and serenity, conflict and resolution, and -- above all -- creativity and vision".