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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 Ostrowski's theorem ： ウィキペディア英語版 Ostrowski's theorem In number theory, Ostrowski's theorem, due to Alexander Ostrowski (1916), states that every non-trivial absolute value on the rational numbers Q is equivalent to either the usual real absolute value or a absolute value.〔 for some prime or for .}}〕 == Definitions == Raising an absolute value to a power less than 1 always results in another absolute value. Two absolute values $|\backslash cdot|$ and $|\backslash cdot|\_$ on a field ''K'' are defined to be equivalent if there exists a real number such that :$|x|\_\; =\; |x|^\; \backslash text\; x\; \backslash in\; \backslash mathbf.$ The trivial absolute value on any field ''K'' is defined to be : The real absolute value on the rationals Q is the standard absolute value on the reals, defined to be : This is sometimes written with a subscript 1 instead of infinity. For a prime number , the -adic absolute value on Q is defined as follows: any non-zero rational , can be written uniquely as $x=p^\backslash dfrac$ with , and pairwise coprime and $n\backslash in\backslash mathbf$ some integer; so we define : 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「Ostrowski's theorem」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.