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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 Euclidean relation ： ウィキペディア英語版 Euclidean relation In mathematics, Euclidean relations are a class of binary relations that satisfy a weakened form of transitivity that formalizes Euclid's "Common Notion 1" in ''The Elements'': ''things which equal the same thing also equal one another.'' ==Definition== A binary relation ''R'' on a set ''X'' is Euclidean (sometimes called right Euclidean) if it satisfies the following: for every ''a'', ''b'', ''c'' in ''X'', if ''a'' is related to ''b'' and ''c'', then ''b'' is related to ''c''.〔.〕 To write this in predicate logic: :$\backslash forall\; a,\; b,\; c\backslash in\; X\backslash ,(a\backslash ,R\backslash ,\; b\; \backslash land\; a\; \backslash ,R\backslash ,\; c\; \backslash to\; b\; \backslash ,R\backslash ,\; c).$ Dually, a relation ''R'' on ''X'' is left Euclidean if for every ''a'', ''b'', ''c'' in ''X'', if ''b'' is related to ''a'' and ''c'' is related to ''a'', then ''b'' is related to ''c'': :$\backslash forall\; a,\; b,\; c\backslash in\; X\backslash ,(b\backslash ,R\backslash ,\; a\; \backslash land\; c\; \backslash ,R\backslash ,\; a\; \backslash to\; b\; \backslash ,R\backslash ,\; c).$ 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「Euclidean relation」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.