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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 Thomae's function ： ウィキペディア英語版 Thomae's function Thomae's function, named after Carl Johannes Thomae, has many names: the popcorn function, the raindrop function, the countable cloud function, the modified Dirichlet function, the ruler function,〔"…the so-called ''ruler function'', a simple but provocative example that appeared in a work of Johannes Karl Thomae … The graph suggests the vertical markings on a ruler—hence the name." William Dunham, ''The Calculus Gallery'', chapter 10〕 the Riemann function, or the Stars over Babylon (John Horton Conway's name).〔http://mathforum.org/kb/message.jspa?messageID=1375516〕 This real-valued function ''f''(''x'') of the real variable ''x'' is defined as: :$f(x)\; =$ \begin 1 &\textx=0\\ \frac &\textx\textx=\tfrac\text q > 0\\ 0 &\textx\text \end It is a modification of the Dirichlet function, which is 1 at rational numbers and 0 elsewhere. ==Properties== The popcorn function has a complicated set of discontinuities: ''f'' is continuous at all irrational numbers and discontinuous at all rational numbers. The popcorn function also has a strict local maximum at each rational number. 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「Thomae's function」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.