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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 Conway chained arrow notation ： ウィキペディア英語版 Conway chained arrow notation Conway chained arrow notation, created by mathematician John Horton Conway, is a means of expressing certain extremely large numbers in googology. It is simply a finite sequence of positive integers separated by rightward arrows, e.g. 2 → 3 → 4 → 5 → 6. As with most combinatorial symbologies, the definition is recursive. In this case the notation eventually resolves to being the leftmost number raised to some (usually enormous) integer power. ==Definition and overview== A ''Conway chain'' (or ''chain'' for short) is defined as follows: * Any positive integer is a chain of length 1. * A chain of length ''n'', followed by a right-arrow → and a positive integer, together form a chain of length $n+1$. Any chain represents an integer, according to the four rules below. Two chains are said to be equivalent if they represent the same integer. If $p$ and $q$ are positive integers, and $X$ is a subchain, then: # An empty chain (or a chain of length 0) represents 1, and the chain $p$ represents the number $p$. # $p\; \backslash to\; q$ represents the exponential expression $p^q$. (Note that Conway in 〔John H. Conway & Richard K. Guy, The Book of Numbers, 1996, p.59-62〕 leaves the 2-tuple undefined, but has the 3d parameter count Knuth's arrows, so that this rule actually follows from the axiom to drop the $\backslash to\; 1$ from the right end.) # $X\; \backslash to\; 1$ is equivalent to $X$. # $X\; \backslash to\; p\; \backslash to\; (q\; +\; 1)$ is equivalent to $X\; \backslash to\; (\; X\; \backslash to\; (\; \backslash cdots\; (X\; \backslash to\; (\; X\; )\; \backslash to\; q)\backslash cdots\; )\; \backslash to\; q\; )\; \backslash to\; q$ (with ''p'' copies of ''X'', ''p'' − 1 copies of ''q'', and ''p'' − 1 pairs of parentheses; applies for ''q'' > 0). Note that the last rule can be restated recursively to avoid the ellipses: :4a. $X\; \backslash to\; 1\; \backslash to\; (q\; +\; 1)\; =\; X$ :4b. $X\; \backslash to\; (p\; +\; 1)\; \backslash to\; (q\; +\; 1)\; =\; X\; \backslash to\; (X\; \backslash to\; p\; \backslash to\; (q+1))\; \backslash to\; q$ 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「Conway chained arrow notation」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.