|
In mathematics, tiny and miny are operators that yield infinitesimal values when applied to numbers in combinatorial game theory. Given a positive number G, tiny G (denoted by ⧾G in many texts) is equal to for any game G, whereas miny G (analogously denoted ⧿G) is tiny G’s negative, or . Tiny and miny aren’t just abstract mathematical operators on combinatorial games: tiny and miny games do occur “naturally” in such games as toppling dominoes. Specifically, tiny ''n'', where ''n'' is a natural number, can be generated by placing two black dominoes outside ''n'' + 2 white dominoes. Tiny games and up have certain curious relational characteristics. Specifically, though ⧾G is infinitesimal with respect to ↑ for all positive values of ''x'', ⧾⧾⧾G is equal to up. Expansion of ⧾⧾⧾G into its canonical form yields . While the expression appears daunting, some careful and persistent expansion of the game tree of ⧾⧾⧾G + ↓ will show that it is a second player win, and that, consequently, ⧾⧾⧾G = ↑. Similarly curious, Conway noted, calling it “amusing,” that “↑ is the unique solution of ⧾G = G.” Conway’s assertion is also easily verifiable with canonical forms and game trees. == 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「Tiny and miny」の詳細全文を読む スポンサード リンク
|