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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 Well-defined ： ウィキペディア英語版 Well-defined In mathematics, an expression is called well-defined or ''unambiguous'' if its definition assigns it a unique interpretation or value. Otherwise, the expression is said to be ''not well-defined'' or ''ambiguous''. A function is well-defined if it gives the same result when the representation of the input is changed without changing the value of the input. For instance if ''f'' takes real numbers as input, and if ''f''(0.5) does not equal ''f''(1/2) then ''f'' is not well-defined (and thus: not a function).〔Joseph J. Rotman, ''The Theory of Groups: an Introduction'', p. 287 "... a function is "single-valued," or, as we prefer to say ... a function is ''well defined''.", Allyn and Bacon, 1965.〕 The term ''well-defined'' is also used to indicate whether a logical statement is unambiguous. A function that is not well-defined is not the same as a function that is undefined. For example, if ''f''(''x'') = 1/''x'', then ''f''(0) is undefined, but this has nothing to do with the question of whether ''f''(''x'') = 1/''x'' is well-defined. It is; 0 is simply not in the domain of the function. ==Simple example== Let $A\_0,A\_1$ be sets, let $A\; =\; A\_0\; \backslash bigcup\; A\_1$ and "define" $f:\; A\; \backslash rightarrow\; \backslash$ as $f(a)=0$ if $a\; \backslash in\; A\_0$ and $f(a)=1$ if $a\; \backslash in\; A\_1$. Then $f$ is well-defined if $A\_0\; \backslash bigcap\; A\_1\; =\; \backslash emptyset$. This is e. g. the case when $A\_0:=\backslash ,\; A\_1:=\backslash$ (then ''f''(''a'') happens to be $\backslash operatorname(a,2)$). If however $A\_0\; \backslash bigcap\; A\_1\; \backslash neq\; \backslash emptyset$ then $f$ is not well-defined because $f(a)$ is "ambiguous" for $a\; \backslash in\; A\_0\; \backslash bigcap\; A\_1$. This is e. g. the case when $A\_0:=\backslash$ and $A\_1:=\backslash$. Indeed, $A\_0\; \backslash bigcap\; A\_1=\backslash \backslash ni\; 2$ and ''f''(2) would have to be 0 as well as 1, which is impossible. Therefore, the latter ''f'' is not well-defined and thus not a function. 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「Well-defined」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.