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Extensive (other)
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. It is called a scientific study because it entails a comprehensive, systematic, obj ... See also * Extension (other) {{Dab ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Intensive And Extensive Properties
Physical properties of materials and systems can often be categorized as being either intensive or extensive, according to how the property changes when the size (or extent) of the system changes. According to IUPAC, an intensive quantity is one whose magnitude is independent of the size of the system, whereas an extensive quantity is one whose magnitude is additive for subsystems. The terms ''intensive and extensive quantities'' were introduced into physics by German writer Georg Helm in 1898, and by American physicist and chemist Richard C. Tolman in 1917. An intensive property does not depend on the system size or the amount of material in the system. It is not necessarily homogeneously distributed in space; it can vary from place to place in a body of matter and radiation. Examples of intensive properties include temperature, ''T''; refractive index, ''n''; density, ''ρ''; and hardness, ''η''. By contrast, extensive properties such as the mass, volume and entropy of syst ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Closure Operator
In mathematics, a closure operator on a set ''S'' is a function \operatorname: \mathcal(S)\rightarrow \mathcal(S) from the power set of ''S'' to itself that satisfies the following conditions for all sets X,Y\subseteq S : Closure operators are determined by their closed sets, i.e., by the sets of the form cl(''X''), since the closure cl(''X'') of a set ''X'' is the smallest closed set containing ''X''. Such families of "closed sets" are sometimes called closure systems or "Moore families", in honor of E. H. Moore who studied closure operators in his 1910 ''Introduction to a form of general analysis'', whereas the concept of the closure of a subset originated in the work of Frigyes Riesz in connection with topological spaces. Though not formalized at the time, the idea of closure originated in the late 19th century with notable contributions by Ernst Schröder, Richard Dedekind and Georg Cantor. Closure operators are also called "hull operators", which prevents confusion with the "c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Extensional
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 — an extensional context (or transparent context) is a syntactic environment in which a sub-sentential expression ''e'' can be replaced by an expression with the same extension and without affecting the truth-value of the sentence as a whole. Extensional contexts are contrasted with opaque contexts where truth-preserving substitutions are not possible. Take the case of Clark Kent, who is secretly Superman. Suppose that Lois Lane fell out of a window and Superman caught her. Thus the sentence "Superman caught Lois Lane" is true. Because this sentence is an extensional context, the sentence "Clark Kent caught Lois Lane" is also true. Anybody that Superman caught, Clark Kent caught. In opposition to extensional contexts are intensional contexts (which can involve modal operators and modal logic), where terms cannot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |