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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 Gelfond–Schneider constant ： ウィキペディア英語版 Gelfond–Schneider constant The Gelfond–Schneider constant or Hilbert number is :$2^\{\backslash sqrt\{2\}\}=2.6651441426902251886502972498731\backslash ldots$ which was proved to be a transcendental number by Rodion Kuzmin in 1930. In 1934, Aleksandr Gelfond proved the more general ''Gelfond–Schneider theorem'', which solved the part of Hilbert's seventh problem described below. ==Properties== The square root of the Gelfond–Schneider constant is the transcendental number :$\backslash sqrt=\backslash sqrt^^^\}=\backslash left(\backslash sqrt\backslash right)^\backslash left(\backslash sqrt\; \backslash sqrt\backslash right)=\backslash left(\backslash sqrt\backslash right)^2=2$ is an irrational to an irrational power that is rational, which proves the theorem.〔}=\sqrt^^^}=\left(\sqrt\right)^\left(\sqrt \sqrt\right)=\left(\sqrt\right)^2=2 is an irrational to an irrational power that is rational, which proves the theorem.〔.〕〔,〕 The proof is not constructive, as it does not say which of the two cases is true, but it is much simpler than Kuzmin's proof. 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「Gelfond–Schneider constant」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.