翻訳と辞書 Words near each other ・ Pseudobiston ・ Pseudobithynia ・ Pseudobithynia pentheri ・ Pseudobithynia renei ・ Pseudobixadus marshalli ・ Pseudobixatoides nonveilleri ・ Pseudoblabes ・ Pseudoblabes oophora ・ Pseudo-modal energies ・ Pseudo-model ・ Pseudo-monotone operator ・ Pseudo-Nero ・ Pseudo-nitzschia ・ Pseudo-octave ・ Pseudo-operation ・ Pseudo-order ・ Pseudo-oxocarbon anion ・ Pseudo-penis ・ Pseudo-Philo ・ Pseudo-Phocylides ・ Pseudo-photograph ・ Pseudo-Plutarch ・ Pseudo-polynomial time ・ Pseudo-random number sampling ・ Pseudo-reductive group ・ Pseudo-Riemannian manifold ・ Pseudo-ring ・ Pseudo-runes ・ Pseudo-scholarship ・ Pseudo-Scymnus 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 Pseudo-order ： ウィキペディア英語版 Pseudo-order In constructive mathematics, a pseudo-order is a constructive generalisation of a linear order to the continuous case. The usual trichotomy law does not hold in the constructive continuum because of its indecomposability, so this condition is weakened. A pseudo-order is a binary relation satisfying the following conditions: # It is not possible for two elements to each be less than the other. That is, . # For all , , and , if then either or . That is, . # Every two elements for which neither one is less than the other must be equal. That is, This first condition is simply antisymmetry. It follows from the first two conditions that a pseudo-order is transitive. The second condition is often called ''co-transitivity'' or ''comparison'' and is the constructive substitute for trichotomy. In general, given two elements of a pseudo-ordered set, it is not always the case that either one is less than the other or else they are equal, but given any nontrivial interval, any element is either above the lower bound, or below the upper bound. The third condition is often taken as the definition of equality. The natural apartness relation on a pseudo-ordered set is given by : and equality is defined by the negation of apartness. The negation of the pseudo-order is a partial order which is close to a total order: if ''x'' ≤ ''y'' is defined as the negation of ''y'' < ''x'', then we have : $\backslash neg\backslash ;(\backslash neg\backslash ;(x\; \backslash le\; y)\; \backslash ;\backslash wedge\backslash ;\; \backslash neg\backslash ;(y\; \backslash le\; x))\; .$ Using classical logic one would then conclude that ''x'' ≤ ''y'' or ''y'' ≤ ''x'', so it would be a total order. However, this inference is not valid in the constructive case. The prototypical pseudo-order is that of the real numbers: one real number is less than another if there exists (one can construct) a rational number greater than the former and less than the latter. In other words, ''x'' < ''y'' if there exists a rational number ''z'' such that ''x'' < ''z'' < ''y''. ==References== * Arend Heyting (1966) Intuitionism: An introduction. Second revised edition North-Holland Publishing Co., Amsterdam. http://books.google.com/books/about/Intuitionism.html?id=4rhLAAAAMAAJ 〔 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「Pseudo-order」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.