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Continuum
Continuum may refer to: * Continuum (measurement), theories or models that explain gradual transitions from one condition to another without abrupt changes Mathematics * Continuum (set theory), the real line or the corresponding cardinal number * Linear continuum, any ordered set that shares certain properties of the real line * Continuum (topology), a nonempty compact connected metric space (sometimes Hausdorff space) * Continuum hypothesis, the hypothesis that no infinite sets are larger than the integers but smaller than the real numbers * Cardinality of the continuum, a cardinal number that represents the size of the set of real numbers Science * Continuum morphology, in plant morphology, underlining the continuum between morphological categories * Continuum concept, in psychology * Continuum mechanics, in physics, deals with continuous matter * Space-time continuum, any mathematical model that combines space and time into a single continuum * Continuum theory of specific he ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Continuum Mechanics
Continuum mechanics is a branch of mechanics that deals with the mechanical behavior of materials modeled as a continuous mass rather than as discrete particles. The French mathematician Augustin-Louis Cauchy was the first to formulate such models in the 19th century. Explanation A continuum model assumes that the substance of the object fills the space it occupies. Modeling objects in this way ignores the fact that matter is made of atoms, and so is not continuous; however, on length scales much greater than that of inter-atomic distances, such models are highly accurate. These models can be used to derive differential equations that describe the behavior of such objects using physical laws, such as mass conservation, momentum conservation, and energy conservation, and some information about the material is provided by constitutive relationships. Continuum mechanics deals with the physical properties of solids and fluids which are independent of any particular coordinate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Continuum (TV Series)
''Continuum'' is a Canadian science fiction television series created by Simon Barry that premiered on Showcase on May 27, 2012, and ran for four seasons. It was produced by Reunion Pictures, Boy Meets Girl Film Company, and Shaw Media. The plot centres around the conflict between a group of terrorists from the year 2077 who time travel to Vancouver, British Columbia, in 2012 and a police officer who unintentionally accompanies them. In spite of being many years early, the terrorist group decides to continue its violent campaign to stop corporations of the future from replacing governments, while the police officer endeavours to stop them without revealing to everyone that she and the terrorists are from the future. Premise City Protective Services (CPS) law enforcement officer Kiera Cameron lives with her husband and son in 2077-era Vancouver under the corporatocratic and oligarchic dystopia of the North American Union and its Corporate Congress, a technologically advanc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Continuum (topology)
In the mathematical field of point-set topology, a continuum (plural: "continua") is a nonempty compact connected metric space, or, less frequently, a compact connected Hausdorff space. Continuum theory is the branch of topology devoted to the study of continua. Definitions * A continuum that contains more than one point is called nondegenerate. * A subset ''A'' of a continuum ''X'' such that ''A'' itself is a continuum is called a subcontinuum of ''X''. A space homeomorphic to a subcontinuum of the Euclidean plane R2 is called a planar continuum. * A continuum ''X'' is homogeneous if for every two points ''x'' and ''y'' in ''X'', there exists a homeomorphism ''h'': ''X'' → ''X'' such that ''h''(''x'') = ''y''. * A Peano continuum is a continuum that is locally connected at each point. * An indecomposable continuum is a continuum that cannot be represented as the union of two proper subcontinua. A continuum ''X'' is hereditarily indecomposable if every subcontinuum of ''X'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Continuum Hypothesis
In mathematics, the continuum hypothesis (abbreviated CH) is a hypothesis about the possible sizes of infinite sets. It states that or equivalently, that In Zermelo–Fraenkel set theory with the axiom of choice (ZFC), this is equivalent to the following equation in aleph numbers: 2^=\aleph_1, or even shorter with beth numbers: \beth_1 = \aleph_1. The continuum hypothesis was advanced by Georg Cantor in 1878, and establishing its truth or falsehood is the first of Hilbert's 23 problems presented in 1900. The answer to this problem is independent of ZFC, so that either the continuum hypothesis or its negation can be added as an axiom to ZFC set theory, with the resulting theory being consistent if and only if ZFC is consistent. This independence was proved in 1963 by Paul Cohen, complementing earlier work by Kurt Gödel in 1940. The name of the hypothesis comes from the term '' the continuum'' for the real numbers. History Cantor believed the continuum hypothes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Continuum
In the mathematical field of order theory, a continuum or linear continuum is a generalization of the real line. Formally, a linear continuum is a linearly ordered set ''S'' of more than one element that is densely ordered, i.e., between any two distinct elements there is another (and hence infinitely many others), and complete, i.e., which "lacks gaps" in the sense that every nonempty subset with an upper bound has a least upper bound. More symbolically: ''S'' has the least upper bound property, and For each ''x'' in ''S'' and each ''y'' in ''S'' with ''x'' < ''y'', there exists ''z'' in ''S'' such that ''x'' < ''z'' < ''y'' A set has the least upper bound property, if every nonempty subset of the set that is bounded above has a least upper bound in the set. Linear continua are particularly important in the field of |
Continuum (John Mayer Album)
''Continuum'' is the third studio album by American singer-songwriter John Mayer, released on September 12, 2006, by Aware and Columbia Records. Recording sessions took place from November 2005 to September 2006 at The Village Recorder in Los Angeles, Avatar Studios and Right Track/Sound on Sound in New York City, and Royal Studios in Memphis, Tennessee.John Mayer and Steve Jordan discuss the writing and recording process . MixOnline. Retrieved on 2009-12-29. Produced by singer and drummer Steve Jordan, it marked a change in Mayer's musical style, incorporating elements of blues [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Continuum
Continuum may refer to: * Continuum (measurement), theories or models that explain gradual transitions from one condition to another without abrupt changes Mathematics * Continuum (set theory), the real line or the corresponding cardinal number * Linear continuum, any ordered set that shares certain properties of the real line * Continuum (topology), a nonempty compact connected metric space (sometimes Hausdorff space) * Continuum hypothesis, the hypothesis that no infinite sets are larger than the integers but smaller than the real numbers * Cardinality of the continuum, a cardinal number that represents the size of the set of real numbers Science * Continuum morphology, in plant morphology, underlining the continuum between morphological categories * Continuum concept, in psychology * Continuum mechanics, in physics, deals with continuous matter * Space-time continuum, any mathematical model that combines space and time into a single continuum * Continuum theory of specific he ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cardinality Of The Continuum
In set theory, the cardinality of the continuum is the cardinality or "size" of the set of real numbers \mathbb R, sometimes called the continuum. It is an infinite cardinal number and is denoted by \mathfrak c (lowercase fraktur "c") or , \mathbb R, . The real numbers \mathbb R are more numerous than the natural numbers \mathbb N. Moreover, \mathbb R has the same number of elements as the power set of \mathbb N. Symbolically, if the cardinality of \mathbb N is denoted as \aleph_0, the cardinality of the continuum is This was proven by Georg Cantor in his uncountability proof of 1874, part of his groundbreaking study of different infinities. The inequality was later stated more simply in his diagonal argument in 1891. Cantor defined cardinality in terms of bijective functions: two sets have the same cardinality if, and only if, there exists a bijective function between them. Between any two real numbers ''a'' \mathfrak c . Alternative explanation for 𝔠 = 2&al ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Triune Continuum Paradigm
The Triune Continuum Paradigm is a paradigm for general system modeling published in 2002.A. Naumenko''Triune Continuum Paradigm: a paradigm for general system modeling and its applications for UML and RM-ODP'' Doctoral thesis 2581, Swiss Federal Institute of Technology – Lausanne. EPFL, June 2002. The paradigm allows for building of rigorous conceptual frameworks employed for systems modeling in various application contexts (highly tailored as well as interdisciplinary). Overview As stated in the ''Cambridge Dictionary of Philosophy'':R. Audi (general editor). The Cambridge Dictionary of Philosophy, second edition; Cambridge University Press 1999. "Paradigm, as used by Thomas Kuhn (''The Structure of Scientific Revolutions'', 1962), refers to a set of scientific and metaphysical beliefs that make up a theoretical framework within which scientific theories can be tested, evaluated and if necessary revised." The Triune Continuum Paradigm holds true to this definition by definin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plant Morphology
Phytomorphology is the study of the physical form and external structure of plants.Raven, P. H., R. F. Evert, & S. E. Eichhorn. ''Biology of Plants'', 7th ed., page 9. (New York: W. H. Freeman, 2005). . This is usually considered distinct from plant anatomy, which is the study of the internal structure of plants, especially at the microscopic level. Plant morphology is useful in the visual identification of plants. Recent studies in molecular biology started to investigate the molecular processes involved in determining the conservation and diversification of plant morphologies. In these studies transcriptome conservation patterns were found to mark crucial ontogenetic transitions during the plant life cycle which may result in evolutionary constraints limiting diversification. Scope Plant morphology "represents a study of the development, form, and structure of plants, and, by implication, an attempt to interpret these on the basis of similarity of plan and origin". ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Continuum Concept
The continuum concept is an idea, coined by Jean Liedloff in her 1975 book ''The Continuum Concept'', that human beings have an innate set of expectations (which Liedloff calls the continuum) that our evolution as a species has designed us to meet in order to achieve optimal physical, mental, and emotional development and adaptability. According to Liedloff, in order to achieve this level of development, young humans (especially babies) require the kind of experience to which our species adapted during the long process of our evolution by natural selection. The continuum For infants, the experiences include: *Immediate placement, after birth, in their mothers' arms: Liedloff comments that the common hospital protocol of immediately separating a newborn from its mother may hormonally disrupt the mother, possibly explaining high rates of postpartum depression; *Constant carrying or physical contact with other people (usually their mothers or fathers) in the several months after ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Continuum (set Theory)
In the mathematical field of set theory, the continuum means the real numbers, or the corresponding (infinite) cardinal number, denoted by \mathfrak. Georg Cantor proved that the cardinality \mathfrak is larger than the smallest infinity, namely, \aleph_0. He also proved that \mathfrak is equal to 2^\!, the cardinality of the power set of the natural numbers. The ''cardinality of the continuum'' is the size of the set of real numbers. The continuum hypothesis is sometimes stated by saying that no cardinality lies between that of the continuum and that of the natural numbers, \aleph_0, or alternatively, that \mathfrak = \aleph_1. Linear continuum According to Raymond Wilder (1965), there are four axioms that make a set ''C'' and the relation < into a linear continuum: * ''C'' is simply ordered with respect to <. * If [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
