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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 Kleene–Brouwer order ： ウィキペディア英語版 Kleene–Brouwer order In descriptive set theory, the Kleene–Brouwer order or Lusin–Sierpiński order is a linear order on finite sequences over some linearly ordered set , that differs from the more commonly used lexicographic order in how it handles the case when one sequence is a prefix of the other. In the Kleene–Brouwer order, the prefix is later than the longer sequence containing it, rather than earlier. The Kleene–Brouwer order generalizes the notion of a postorder traversal from finite trees to trees that are not necessarily finite. For trees over a well-ordered set, the Kleene–Brouwer order is itself a well-ordering if and only if the tree has no infinite branch. It is named after Stephen Cole Kleene, Luitzen Egbertus Jan Brouwer, Nikolai Luzin, and Wacław Sierpiński. ==Definition== If $t$ and $s$ are finite sequences of elements from $X$, we say that when there is an $n$ such that either: * $t\backslash upharpoonright\; n\; =\; s\backslash upharpoonright\; n$ and $t(n)$ is defined but $s(n)$ is undefined (i.e. $t$ properly extends $s$), or * both $s(n)$ and $t(n)$ are defined, Here, the notation $t\backslash upharpoonright\; n$ refers to the prefix of $t$ up to but not including $t(n)$. In simple terms, whenever $s$ is a prefix of $t$ (i.e. $s$ terminates before $t$, and they are equal up to that point) or $t$ is to the "left" of $s$ on the first place they differ.〔 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「Kleene–Brouwer order」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.