WordNet
- rule of personal conduct (同)precept
- a basic generalization that is accepted as true and that can be used as a basis for reasoning or conduct; "their principles of composition characterized all their works" (同)rule
- a rule or law concerning a natural phenomenon or the function of a complex system; "the principle of the conservation of mass"; "the principle of jet propulsion"; "the right-hand rule for inductive fields" (同)rule
- a basic truth or law or assumption; "the principles of democracy"
- a rule or standard especially of good behavior; "a man of principle"; "he will not violate his principles"
- 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
- based on or manifesting objectively defined standards of rightness or morality; "principled pragmatism and unprincipled expediency"; "a principled person"
PrepTutorEJDIC
- 〈C〉『原理,原則』;法則 / 〈C〉『主義,信条』,基本方針,行動指針 / 〈U〉道義,節繰
- 《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
- 「…主義の(をもった)」の意を表す
- 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)』「2016/11/29 17:14:08」(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 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
- Upgrading short read animal genome assemblies to chromosome level using comparative genomics and a universal probe set.
- Damas J1, O'Connor R2, Farré M1, Lenis VP3, Martell HJ2, Mandawala A4, Fowler K5, Joseph S2, Swain MT3, Griffin DK2, Larkin DM6.
- Genome research.Genome Res.2016 Nov 30. pii: gr.213660.116. [Epub ahead of print]
- Most recent initiatives to sequence and assemble new species' genomes de-novo fail to achieve the ultimate endpoint to produce contigs, each representing one whole chromosome. Even the best-assembled genomes (using contemporary technologies) consist of sub-chromosomal sized scaffolds. To circumvent
- PMID 27903645
- Effect of continuity of care on health-related quality of life in adult patients with hypertension: a cohort study in China.
- Ye T1, Sun X1, Tang W2, Miao Y1, Zhang Y1, Zhang L3.
- BMC health services research.BMC Health Serv Res.2016 Nov 28;16(1):674.
- BACKGROUND: Continuity of care is widely considered a principle of primary care that decreases healthcare utilization and mortality. However, the effect of continuity of care on health-related quality of life (HRQoL) for adult patients with hypertension remains unclear.METHODS: To further evaluate t
- PMID 27894298
Japanese Journal
- 家畜の個体性再考 : 河南蒙旗におけるツェタル実践(<特集>自然と社会の民族誌-動物と人間の連続性)
- シンジルト
- 文化人類学 76(4), 439-462, 2012-03-31
- 他のチベット仏教系の牧畜地域と同様に、河南蒙旗でも、ある家畜個体を屠らず売らず、その命を自由にするツェタル実践がみられる。ツェタル実践の動機は多様であるが、そのほとんどは、牧畜民と家畜個体との間に共有される日常的な喜怒哀楽に基づく経験である。家畜の種を問わず、原理的にあらゆる個体がツェタルの対象になりうる。この実践は、仏教の教義に基づく放生や功徳を目的としたものだとする説明もありえよう。だが河南蒙 …
- NAID 110009436712
- 乙訓 稔
- 実践女子大学生活科学部紀要 49, 65-80, 2012-03-10
- … It is said that the kindergarten education theory of Sozo Kurahashi had a great influence onthe infant educational fronts of Japan from the Taisho era period to World War II. … His idea ofhis kindergarten education criticized the doctrinairism of Froebelian in the nurture world ofJapan at that time and the immobilization of the usage of Gabe. …
- NAID 110008916599
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- 関
- continuation、continue、continued、continuous、continuously、duration、last、persist、persistence、serial、serially、sustain
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- 関
- belief、fundamentals、philosophy、rationale