翻訳と辞書 Words near each other ・ Hierarchical Music Specification Language ・ Hierarchical namespace ・ Hierarchical network model ・ Hierarchical organization ・ Hierarchical proportion ・ Hierarchical RBF ・ Hierarchical routing ・ Hierarchical state routing ・ Hierarchical storage management ・ Hierarchical structure of the Big Five ・ Hierarchical task network ・ Hierarchical temporal memory ・ Hierarchical value cache ・ Hierarchy ・ Hierarchy (disambiguation) ・ Hierarchy (mathematics) ・ Hierarchy and Free Expression in the Fight Against Racism ・ Hierarchy of angels ・ Hierarchy of beliefs ・ Hierarchy of death ・ Hierarchy of evidence ・ Hierarchy of genres ・ Hierarchy of hazard control ・ Hierarchy of precious substances ・ Hierarchy of roads ・ Hierarchy of the Catholic Church ・ Hierarchy of values ・ Hierarchy Open Service Interface Definition ・ Hierarchy problem ・ Hierarchy theory Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Hierarchy (mathematics) ： ウィキペディア英語版 Hierarchy (mathematics) In mathematics, a hierarchy is a set-theoretical object, consisting of a preorder defined on a set. This is often referred to as an ordered set, though that is an ambiguous term, which many authors reserve for partially ordered sets or totally ordered sets. The term ''pre-ordered set'' is unambiguous, and is always synonymous with a mathematical hierarchy. The term ''hierarchy'' is used to stress a ''hierarchical'' relation among the elements. Sometimes, a set comes equipped with a natural hierarchical structure. For example, the set of natural numbers ''N'' is equipped with a natural pre-order structure, where $n\; \backslash le\; n\text{'}$ whenever we can find some other number $m$ so that $n\; +\; m\; =\; n\text{'}$. That is, $n\text{'}$ is bigger than $n$ only because we can get to $n\text{'}$ from $n$ ''using'' $m$. This is true for any commutative monoid. On the other hand, the set of integers ''Z'' requires a more sophisticated argument for its hierarchical structure, since we can always solve the equation $n\; +\; m\; =\; n\text{'}$ by writing $m\; =\; (n\text{'}-n)$. A mathematical hierarchy (a pre-ordered set) should not be confused with the more general concept of a hierarchy in the social realm, particularly when one is constructing computational models which are used to describe real-world social, economic or political systems. These hierarchies, or complex networks, are much too rich to be described in the category (Set ) of sets.〔We may need a bigger topos.〕 This is not just a pedantic claim; there are also mathematical hierarchies which are not describable using set theory. Another natural hierarchy arises in computer science, where the word refers to partially ordered sets whose elements are classes of objects of increasing complexity. In that case, the preorder defining the hierarchy is the class-containment relation. Containment hierarchies are thus special cases of hierarchies. ==Related terminology== Individual elements of a hierarchy are often called levels and a hierarchy is said to be infinite if it has infinitely many distinct levels but said to collapse if it has only finitely many distinct levels. 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「Hierarchy (mathematics)」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.