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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 Negligible function ： ウィキペディア英語版 Negligible function In mathematics, a negligible function is a function $\backslash mu(x):\backslash mathbb\backslash mathbb$ such that for every positive integer ''c'' there exists an integer ''N''''c'' such that for all ''x'' > ''N''''c'', : Equivalently, we may also use the following definition. A function $\backslash mu(x):\backslash mathbb\backslash mathbb$ is negligible, if for every positive polynomial poly(·) there exists an integer ''N''poly > 0 such that for all ''x'' > ''N''poly : ==History== The concept of ''negligibility'' can find its trace back to sound models of analysis. Though the concepts of "continuity" and "infinitesimal" became important in mathematics during Newton and Leibniz's time (1680s), they were not well-defined until the late 1810s. The first reasonably rigorous definition of ''continuity'' in mathematical analysis was due to Bernard Bolzano, who wrote in 1817 the modern definition of continuity. Later Cauchy, Weierstrass and Heine also defined as follows (with all numbers in the real number domain $\backslash mathbb$): :(Continuous function) A function $f(x):\backslash mathbb\backslash mathbb$ is ''continuous'' at $x=x\_0$ if for every $\backslash epsilon>0$, there exists a positive number $\backslash delta>0$ such that implies This classic definition of continuity can be transformed into the definition of negligibility in a few steps by changing parameters used in the definition. First, in the case $x\_0=\backslash infty$ with $f(x\_0)=0$, we must define the concept of "''infinitesimal function''": :(Infinitesimal) A continuous function $\backslash mu(x):\backslash mathbb\backslash mathbb$ is ''infinitesimal'' (as $x$ goes to infinity) if for every $\backslash epsilon>0$ there exists $N\_$ such that for all $x>N\_$ :: Next, we replace $\backslash epsilon>0$ by the functions $1/x^c$ where $c>0$ or by $1/poly(x)$ where $poly(x)$ is a positive polynomial. This leads to the definitions of negligible functions given at the top of this article. Since the constants $\backslash epsilon>0$ can be expressed as $1/poly(x)$ with a constant polynomial this shows that negligible functions are a subset of the infinitesimal functions. 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「Negligible 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.