翻訳と辞書 Words near each other ・ Separation of powers in Australia ・ Separation of powers in Singapore ・ Separation of powers in the United Kingdom ・ Separation of powers under the United States Constitution ・ Separation of presentation and content ・ Separation of protection and security ・ Separation of Queensland ・ Separation of the elements ・ Separation of variables ・ Separation Party of Alberta ・ Separation principle ・ Separation process ・ Separation property ・ Separation property (finance) ・ Separation Range ・ Separation relation ・ Separation Road ・ Separation Sunday ・ Separation test ・ Separation theorem ・ Separations (album) ・ Separatism ・ Separatist (disambiguation) ・ Separatist feminism ・ Separatist movements of China ・ Separatist movements of India ・ Separatist movements of Pakistan ・ Separatista ・ Separatista flavida ・ Separatista helicoides Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Separation relation ： ウィキペディア英語版 Separation relation In mathematics, a separation relation is a formal way to arrange a set of objects in an unoriented circle. It is defined as a quaternary relation ''S''(''a'', ''b'', ''c'', ''d'') satisfying certain axioms, which is interpreted as asserting that ''a'' and ''c'' separate ''b'' from ''d''. Whereas a linear order endows a set with a positive end and a negative end, a separation relation forgets not only which end is which, but also where the ends are. In this way it is a final, further weakening of the concepts of a betweenness relation and a cyclic order. There is generally nothing else that can be forgotten: up to the relevant sense of interdefinability, these three relations are the only nontrivial reducts of the ordered set of rational numbers. ==Application== The separation may be used in showing the real projective plane is a complete space. The separation relation was described with axioms in 1898 by Giovanni Vailati.〔Bertrand Russell (1903) Principles of Mathematics, page 214〕 * ''abcd'' = ''badc'' * ''abcd'' = ''adcb'' * ''abcd'' ⇒ ¬ ''acbd'' * ''abcd'' ∨ ''acdb'' ∨ ''adbc'' * ''abcd'' ∧ ''acde'' ⇒ ''abde''. The relation of separation of points was written AC//BD by H. S. M. Coxeter in his textbook ''The Real Projective Plane''.〔H. S. M. Coxeter (1949) ''The Real Projective Plane'', Chapter 10: Continuity, McGraw Hill〕 The axiom of continuity used is "Every monotonic sequence of points has a limit." The separation relation is used to provide definitions: * is monotonic ≡ ∀ ''n'' > 1 $A\_0\; A\_n\; //\; A\_1\; A\_.$ * ''M'' is a limit ≡ (∀ ''n'' > 2 $A\_1\; A\_n\; //\; A\_2\; M$) ∧ (∀ P $A\_1P\; //\; A\_2\; M$ ⇒ ∃ ''n'' $A\_1\; A\_n\; //\; P\; M$ ). 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Separation relation」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.