V2EX partial-order

Partial Order

Definition / 释义

偏序(关系):一种“只在部分元素之间可比较”的排序关系。它通常满足三条性质:自反性(每个元素与自身可比)、反对称性(若 a ≤ bb ≤ a,则 a = b)、传递性(若 a ≤ bb ≤ c,则 a ≤ c)。并非任意两元素都必须可比较;若任意两元素都可比较,则称为全序

Pronunciation / 发音

/prl rdr/

Examples / 例句

A subset relation () is a partial order.
子集关系()是一种偏序关系。

In this poset, some elements are incomparable, so it is not a total order.
在这个偏序集中,有些元素彼此不可比,因此它不是全序。

Etymology / 词源

partial 源自拉丁语 partialis(“部分的”),order 源自拉丁语 ordo(“排列、次序”)。合起来 partial order 字面义即“部分的次序/排序”,用来强调:这种“顺序”只对某些元素对成立,而不是对所有元素都能比较大小或先后。

Related Words / 相关词

Literary Works / 作品例证

  • 《Introduction to Lattices and Order》(B. A. Davey & H. A. Priestley):系统讲解偏序、格与序理论的经典教材。
  • 《Lattice Theory》(Garrett Birkhoff):在格论框架下大量使用并发展偏序概念。
  • 《Concrete Mathematics》(Graham, Knuth, Patashnik):在离散数学与组合数学语境中涉及偏序与相关结构。
  • 《The Art of Computer Programming》(Donald E. Knuth):在算法与组合结构讨论中出现偏序与可比性等概念。
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