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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 Real-valued function ： ウィキペディア英語版 Real-valued function In mathematics, a real-valued function or real function is a function whose values are real numbers. In other words, it is a function that assigns a real number to each member of its domain. Many important function spaces are defined to consist of real functions. == In general == Let be an arbitrary set. Let $(X,)$ denote the set of all functions from to real numbers . Because is a field, $(X,)$ is a vector space and a commutative algebra (structure) over reals: *$\backslash \; f+g:\; x\; \backslash mapsto\; f(x)\; +\; g(x)$ – vector addition *$\backslash \; \backslash mathbf:\; x\; \backslash mapsto\; 0$ – additive identity *$\backslash \; c\; f:\; x\; \backslash mapsto\; c\; f(x),\backslash quad\; c\; \backslash in$ – scalar multiplication *$\backslash \; f\; g:\; x\; \backslash mapsto\; f(x)g(x)$ – pointwise multiplication Also, since is an ordered set, there is a partial order on $(X,)$: *$\backslash \; f\; \backslash le\; g\; \backslash quad\backslash iff\backslash quad\; \backslash forall\; x:\; f(x)\; \backslash le\; g(x)$. $(X,)$ is a partially ordered ring. 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「Real-valued 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.