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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 Abuse of terminology ： ウィキペディア英語版 Abuse of notation In mathematics, abuse of notation occurs when an author uses a mathematical notation in a way that is not formally correct but that seems likely to simplify the exposition or suggest the correct intuition (while being unlikely to introduce errors or cause confusion). Abuse of notation should be contrasted with ''misuse'' of notation, which should be avoided. A related concept is abuse of language or abuse of terminology, when not notation but a ''term'' is misused. Abuse of language is an almost synonymous expression that is usually used for non-notational abuses. For example, while the word ''representation'' properly designates a group homomorphism from a group G to GL(V) where V is a vector space, it is common to call V "a representation of G". A common abuse of language consists in identifying two mathematical objects that are different but canonically isomorphic. For example, identifying a constant function and its value or identifying to $\backslash mathbb\; R^3$ the Euclidean space of dimension three equipped with a Cartesian coordinate system. The latter uses may achieve clarity in the new area in an unexpected way, but it may borrow arguments from the old area that do not carry over, creating a false analogy. ==Examples== Common examples occur when speaking of compound mathematical objects. For example, a topological space consists of a set $X$ (called the underlying set of the topological space) and a topology $\backslash mathcal$, and two topological spaces $(X,\; \backslash mathcal)$ and $(X,\; \backslash mathcal\text{'})$, even with the same underlying set $X$, can be quite different if they have different topologies. Nevertheless, it is common to refer to such a space simply as $X$ when there is no danger of confusion—that is, when it is implicitly clear what topology is being considered. Similarly, one often refers to a group $(G,\; \backslash star)$ as simply $G$ when the group operation is clear from context. 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「Abuse of notation」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.