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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 Banach game ： ウィキペディア英語版 Banach game In mathematics, the Banach game is a topological game introduced by Stefan Banach in 1935 in the second addendum to problem 43 of the Scottish book as a variation of the Banach–Mazur game. Given a subset $X$ of real numbers, two players alternatively write down arbitrary (not necessarily in $X$) positive real numbers $x\_0,\; x\_1,\; x\_2,\backslash ldots$ such that $x\_0\; >\; x\_1\; >\; x\_2\; >\backslash cdots$ Player one wins if and only if $\backslash sum^\backslash infty\_\; x\_i$ exists and is in $X$.〔 at 242.〕 One observation about the game is that if $X$ is a countable set, then either of the players can cause the final sum to avoid the set. Thus in this situation the second player can win. == References == 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「Banach game」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.