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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク standard part function ： ウィキペディア英語版 standard part function In non-standard analysis, the standard part function is a function from the limited (finite) hyperreal numbers to the real numbers. Briefly, the standard part function "rounds off" a finite hyperreal to the nearest real. It associates to every such hyperreal $x$, the unique real $x\_0$ infinitely close to it, i.e. $x-x\_0$ is infinitesimal. As such, it is a mathematical implementation of the historical concept of adequality introduced by Pierre de Fermat,〔Karin Usadi Katz and Mikhail G. Katz (2011) A Burgessian Critique of Nominalistic Tendencies in Contemporary Mathematics and its Historiography. Foundations of Science. () See (arxiv ). The authors refer to the Fermat-Robinson standard part.〕 as well as Leibniz's Transcendental law of homogeneity. The standard part function was first defined by Abraham Robinson who used the notation $\{\}^\{\backslash circ\}x$ for the standard part of a hyperreal $x$ (see Robinson 1974). This concept plays a key role in defining the concepts of the calculus, such as continuity, the derivative, and the integral, in non-standard analysis. The latter theory is a rigorous formalisation of calculations with infinitesimals. The standard part of ''x'' is sometimes referred to as its shadow. ==Definition== Nonstandard analysis deals primarily with the pair $\backslash mathbb\backslash subset$, where the hyperreals $$ are an ordered field extension of the reals $\backslash mathbb$, and contain infinitesimals, in addition to the reals. In the hyperreal line every real number has a collection of numbers (called a monad (non-standard analysis) 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「standard part function」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.