翻訳と辞書 Words near each other ・ Levi Yissar ・ Levi Yitzchak Horowitz ・ Levi Yitzchak Schneerson ・ Levi Yitzchok Bender ・ Levi Yitzchok of Berditchev ・ Levi Zililo Mumba ・ Levi's lemma ・ Levi's Plaza ・ Levi's Stadium ・ Levi, Estonia ・ Levi, Finland ・ Levi, Kentucky ・ Levi, Ray & Shoup ・ Levi-Civita (crater) ・ Levi-Civita connection ・ Levi-Civita field ・ Levi-Civita parallelogramoid ・ Levi-Civita symbol ・ Levi9 Global Sourcing ・ Levi9 Ukraine ・ Leviathan ・ Leviathan (1989 film) ・ Leviathan (2000 AD) ・ Leviathan (2012 film) ・ Leviathan (2014 film) ・ Leviathan (album) ・ Leviathan (audio drama) ・ Leviathan (Auster novel) ・ Leviathan (book) ・ LEVIATHAN (cipher) 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 Levi-Civita field ： ウィキペディア英語版 Levi-Civita field In mathematics, the Levi-Civita field, named after Tullio Levi-Civita, is a non-Archimedean ordered field; i.e., a system of numbers containing infinite and infinitesimal quantities. Its members can be constructed as formal series of the form : $$ \sum_ is the set of rational numbers, and $\backslash varepsilon$ is to be interpreted as a positive infinitesimal. The support of ''a'', i.e., the set of indices of the nonvanishing coefficients $\backslash ,$ must be a left-finite set: for any member of $\backslash mathbb$, there are only finitely many members of the set less than it; this restriction is necessary in order to make multiplication and division well defined and unique. The ordering is defined according to dictionary ordering of the list of coefficients, which is equivalent to the assumption that $\backslash varepsilon$ is an infinitesimal. The real numbers are embedded in this field as series in which all of the coefficients vanish except $a\_0\backslash ,$. ==Examples== * $7\backslash varepsilon$ is an infinitesimal that is greater than $\backslash varepsilon$, but less than every positive real number. * $\backslash varepsilon^2$ is less than $\backslash varepsilon$, and is also less than $r\backslash varepsilon$ for any positive real $r$. * $1+\backslash varepsilon$ differs infinitesimally from 1. * $\backslash varepsilon^\}$ is greater than $\backslash varepsilon$, but still less than every positive real number. * $1/\backslash varepsilon$ is greater than any real number. * $1+\backslash varepsilon+\backslash frac\backslash varepsilon^2+\backslash cdots+\backslash frac\backslash varepsilon^n+\backslash cdots$ is interpreted as $e^\backslash varepsilon$. * $1+\backslash varepsilon\; +\; 2\backslash varepsilon^2\; +\; \backslash cdots\; +\; n!\backslash varepsilon^n\; +\; \backslash cdots$ is a valid member of the field, because the series is to be construed formally, without any consideration of convergence. 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「Levi-Civita field」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.