翻訳と辞書 Words near each other ・ Internal security ・ Internal Security Act ・ Internal Security Act (Singapore) ・ Internal Security Act 1960 ・ Internal Security Act, 1982 ・ Internal Security Corps ・ Internal Security Department (Brunei) ・ Internal Security Department (Singapore) ・ Internal Security Forces ・ Internal Security Operations Command ・ Internal Security Organisation ・ Internal Security Service ・ Internal Security Unit ・ Internal security vehicle ・ Internal Services in the European Commission ・ Internal set ・ Internal set theory ・ Internal Settlement ・ Internal sin ・ Internal sort ・ Internal spermatic fascia ・ Internal sphincter muscle of urethra ・ Internal standard ・ Internal structure of the Moon ・ Internal Suffering ・ Internal Supervision Regulation ・ Internal thoracic artery ・ Internal thoracic vein ・ Internal thoracic vessels ・ Internal Thracian Revolutionary Organisation 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 Internal set ： ウィキペディア英語版 Internal set In mathematical logic, in particular in model theory and non-standard analysis, an internal set is a set that is a member of a model. The concept of internal sets is a tool in formulating the transfer principle, which concerns the logical relation between the properties of the real numbers R, and the properties of a larger field denoted *R called the hyperreal numbers. The field *R includes, in particular, infinitesimal ("infinitely small") numbers, providing a rigorous mathematical justification for their use. Roughly speaking, the idea is to express analysis over R in a suitable language of mathematical logic, and then point out that this language applies equally well to *R. This turns out to be possible because at the set-theoretic level, the propositions in such a language are interpreted to apply only to internal sets rather than to all sets (note that the term "language" is used in a loose sense in the above). Edward Nelson's internal set theory is an axiomatic approach to non-standard analysis (see also Palmgren at constructive non-standard analysis). Conventional infinitary accounts of non-standard analysis also use the concept of internal sets. ==Internal sets in the ultrapower construction== Relative to the ultrapower construction of the hyperreal numbers as equivalence classes of sequences $\backslash langle\; u\_n\backslash rangle$, an internal subset () of *R is one defined by a sequence of real sets $\backslash langle\; A\_n\; \backslash rangle$, where a hyperreal $()$ is said to belong to the set $()\backslash subset\; \backslash ;\; ^$ *\! if and only if the set of indices n such that $u\_n\; \backslash in\; A\_n$, is a member of the ultrafilter used in the construction of *R. More generally, an internal entity is a member of the natural extension of a real entity. Thus, every element of *R is internal; a subset of *R is internal if and only if it is a member of the natural extension $^$ * \mathcal(\mathbb) of the power set $\backslash mathcal(\backslash mathbb)$ of R; etc. 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「Internal set」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.