連続の法則
WordNet
- the learned profession that is mastered by graduate study in a law school and that is responsible for the judicial system; "he studied law at Yale" (同)practice of law
- the collection of rules imposed by authority; "civilization presupposes respect for the law"; "the great problem for jurisprudence to allow freedom while enforcing order" (同)jurisprudence
- a generalization that describes recurring facts or events in nature; "the laws of thermodynamics" (同)law of nature
- a rule or body of rules of conduct inherent in human nature and essential to or binding upon human society (同)natural_law
- legal document setting forth rules governing a particular kind of activity; "there is a law against kidnapping"
- uninterrupted connection or union
- the property of a continuous and connected period of time (同)persistence
- a detailed script used in making a film in order to avoid discontinuities from shot to shot
- the syllable naming the sixth (submediant) note of a major or minor scale in solmization (同)lah
PrepTutorEJDIC
- 〈U〉《the ~》《集合的に》(法律・法規を総称して)『法』 / 〈U〉〈C〉(個々の)『法律』,法規 / 〈U〉法の[統制]力 / 〈U〉法律学 / 〈U〉弁護士[業] / 〈U〉《the law》警察[力],警官(police) / 〈U〉法の適用(発動);訴訟(legal action) / 〈C〉(科学・芸術などでの)法則,きまり / 〈C〉〈U〉(一般に従うべき)おきて,ならわし,規則
- 《所有・所属》…『の』,…のものである,…に属する・《材料・要素》…『でできた』,から成る・《部分》…『の』[『中の』] ・《数量・単位・種類を表す名詞に付いて》…の・《原因・動機》…『で』,のために(because of) ・《主格関係》…『の』,による,によって・《目的格関係》…『を』,の・《同格関係》…『という』・《関係・関連》…『についての』[『の』],の点で・《抽象名詞などと共に》…の[性質をもつ] ・《『It is』+『形』+『of』+『名』+『to』 doの形で,ofの後の名詞を意味上の主語として》・《分離》…『から』・《起原・出所》…『から』[『の』](out of) ・《『名』+『of』+『a』(『an』)+『名』の形で》…のような・《『名』+『of』+『mine』(『yours, his』など独立所有格)の形で》…の…・《時》(1)《副詞句を作って》…に《形容詞句を作って》…の・《時刻》《米》…前(to,《米》before)
- 〈U〉連続,断続,一貫性 / 〈U〉(映画・ラジオ・テレビの)コンテ,撮影(録音)用台本;〈C〉コンテに書かれた個々の指示
- ラ(全音階の第6音)
- OLD French古[代]フランス語
Wikipedia preview
出典(authority):フリー百科事典『ウィキペディア(Wikipedia)』「2015/08/30 22:04:52」(JST)
[Wiki en表示]
"Principle of continuity" redirects here. For other uses, see Dedekind cut.
The Law of Continuity is a heuristic principle introduced by Gottfried Leibniz based on earlier work by Nicholas of Cusa and Johannes Kepler. It is the principle that "whatever succeeds for the finite, also succeeds for the infinite".[1] Kepler used it to calculate the area of the circle by representing the latter as an infinite-sided polygon with infinitesimal sides, and adding the areas of infinitely many triangles with infinitesimal bases. Leibniz used the principle to extend concepts such as arithmetic operations, from ordinary numbers to infinitesimals, laying the groundwork for infinitesimal calculus. A mathematical implementation of the law of continuity is provided by the transfer principle in the context of the hyperreal numbers.
Leibniz's formulation
Leibniz expressed the law in the following terms in 1701:
- In any supposed continuous transition, ending in any terminus, it is permissible to institute a general reasoning, in which the final terminus may also be included (Cum Prodiisset).[2]
In a 1702 letter to French mathematician Pierre Varignon subtitled “Justification of the Infinitesimal Calculus by that of Ordinary Algebra," Leibniz adequately summed up the true meaning of his law, stating that "the rules of the finite are found to succeed in the infinite."[3]
The Law of Continuity became important to Leibniz's justification and conceptualization of the infinitesimal calculus.
See also
- Transcendental Law of Homogeneity
References
- ^ Karin Usadi Katz and Mikhail G. Katz (2011) A Burgessian Critique of Nominalistic Tendencies in Contemporary Mathematics and its Historiography. Foundations of Science. doi:10.1007/s10699-011-9223-1 [1] See arxiv
- ^ Child, J. M. (ed.): The early mathematical manuscripts of Leibniz. Translated from the Latin texts published by Carl Immanuel Gerhardt with critical and historical notes by J. M. Child. Chicago-London: The Open Court Publishing Co., 1920.
- ^ Leibniz, Gottfried Wilhelm, and Leroy E. Loemker. Philosophical Papers and Letters. 2d ed. Dordrecht: D. Reidel, 1970, p. 544
Gottfried Wilhelm Leibniz
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Mathematics and
philosophy
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- Alternating series test
- Best of all possible worlds
- Calculus ratiocinator
- Characteristica universalis
- Difference
- Identity of indiscernibles
- Law of Continuity
- Leibniz wheel
- Leibniz's gap
- Pre-established harmony
- Principle of sufficient reason
- Salva veritate
- Theodicy
- Transcendental law of homogeneity
- Vis viva
- Well-founded phenomenon
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Works |
- De Arte Combinatoria (1666)
- Discourse on Metaphysics (1686)
- New Essays on Human Understanding (1704)
- Théodicée (1710)
- Monadology (1714)
- Leibniz–Clarke correspondence (1715–1716)
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Other |
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Infinitesimals
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History |
- Adequality
- Leibniz's notation
- Integral symbol
- Criticism of non-standard analysis
- The Analyst
- The Method of Mechanical Theorems
- Cavalieri's principle
- Method of indivisibles
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Related branches |
- Non-standard analysis
- Non-standard calculus
- Internal set theory
- Synthetic differential geometry
- Constructive non-standard analysis
- Infinitesimal strain theory (physics)
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Formalizations |
- Differentials
- Hyperreal numbers
- Dual numbers
- Surreal numbers
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Individual concepts |
- Standard part function
- Transfer principle
- Hyperinteger
- Increment theorem
- Monad
- Internal set
- Levi-Civita field
- Hyperfinite set
- Law of Continuity
- Overspill
- Microcontinuity
- Transcendental law of homogeneity
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Scientists |
- Gottfried Wilhelm Leibniz
- Abraham Robinson
- Pierre de Fermat
- Augustin-Louis Cauchy
- Leonhard Euler
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Textbooks |
- Analyse des Infiniment Petits
- Elementary Calculus
- Cours d'Analyse
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UpToDate Contents
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English Journal
- Effect of microvascular distribution and its density on interstitial fluid pressure in solid tumors: A computational model.
- Mohammadi M1, Chen P2.
- Microvascular research.Microvasc Res.2015 Sep;101:26-32. doi: 10.1016/j.mvr.2015.06.001. Epub 2015 Jun 17.
- Solid tumors with different microvascular densities (MVD) have been shown to have different outcomes in clinical studies. Other studies have demonstrated the significant correlation between high MVD, elevated interstitial fluid pressure (IFP) and metastasis in cancers. Elevated IFP in solid tumors p
- PMID 26093178
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- Villarreal-Cervantes MG1, Guerrero-Castellanos JF2, Ramírez-Martínez S3, Sánchez-Santana JP4.
- ISA transactions.ISA Trans.2015 Jul 17. pii: S0019-0578(15)00149-4. doi: 10.1016/j.isatra.2015.06.013. [Epub ahead of print]
- Event-triggered control (ETC) is a sampling strategy that updates the control value only when some events related to the state of the system occurs. It therefore relaxes the periodicity of control updates without deteriorating the closed-loop performance. This paper develops a nonlinear ETC for the
- PMID 26190502
- Modeling of cell adhesion and deformation mediated by receptor-ligand interactions.
- Golestaneh AF1, Nadler B.
- Biomechanics and modeling in mechanobiology.Biomech Model Mechanobiol.2015 Jun 21. [Epub ahead of print]
- The current work is devoted to studying adhesion and deformation of biological cells mediated by receptors and ligands in order to enhance the existing models. Due to the sufficient in-plane continuity and fluidity of the phospholipid molecules, an isotropic continuum fluid membrane is proposed for
- PMID 26093646
Japanese Journal
- Specimen- and grain-size dependence of compression deformation behavior in nanocrystalline copper
- Okamoto Norihiko L.,Kashioka Daisuke,Hirato Tetsuji,Inui Haruyuki
- International Journal of
- … The compression deformation behavior of electrodeposited nanocrystalline copper pillars with average grain sizes (d) of 360, 100, and 34 nm has been investigated as a function of specimen size (D). …
- NAID 120005434967
- 東日本大震災における企業の危機管理・BCPの調査・研究
- 高野 一彦,蟻生 俊夫,桑山 三恵子,佐伯 隆博,杉田 純一,星野 邦夫,山中 裕
- 日本経営倫理学会誌 (21), 87-102, 2014-02-28
- … This study aims to examine whether the crisis management systems and business continuity plans (BCP) of Japanese industries functioned sufficiently during the Great East Japan Earthquake, by conducting interview surveys. … The study also aims to make proposals on the ideal state of new crisis management system and business leadership. … Based on interview surveys for 10 companies that had workable BCP, we found out that there are five key elements of BCP; …
- NAID 110009807364
- Experimental and numerical characterization of resin impregnation behavior in textile composites fabricated with micro-braiding technique
- KOBAYASHI Satoshi,MORIMOTO Tetsuya
- Mechanical Engineering Journal 1(4), SMM0031-SMM0031, 2014
- … Fiber reinforced thermoplastic composites has poorer matrix resin impregnation to fiber reinforcements, because of extreme high viscosity of molten thermoplastics. … Fabrication method of intermediate materials using micro-braiding technique has been developed to overcome these difficulties. … In order to predict the impregnation behavior, a simple model was proposed based on the Darcys law and the continuity equation. …
- NAID 130004684534
Related Links
- :a principle in philosophy: there is no break in nature and nothing passes from one state to another without passing through all the intermediate states ... Seen and Heard What made you want to look up law of continuity? Please tell ...
- As a fluid flows through a funnel-shaped conduit, like the one already described in the law of continuity discussion, the kinetic energy (1/2 Dv2) increases at the narrowing as manifested by the increased velocity of the flow at that point.
Related Pictures
★リンクテーブル★
[★]
- 同
- law of succession, law of continuity
SP.561
2007年後期生理学授業プリント
- (血管を剛体と見なすとき)直径が異なる管から構成される系において、容積流量はそれぞれの断面積にかかわらず一定
- Q = A・v
- Q:流量(=容量流量)
- A:断面積
- v:流速
[★]
- 関
- continuation、continue、continued、continuous、continuously、duration、last、persist、persistence、serial、serially、sustain
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- 関
- jurisprudence、litigation、method