V2EX partial order

Partial Order

定义 Definition

partial order(偏序关系):一种在集合上定义的关系,满足自反性(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)。称为“偏序”是因为并非任意两个元素都必须可比较(有的元素“不可比”)。

发音 Pronunciation

/prl rdr/

例句 Examples

A partial order can compare some elements, but not necessarily all of them.
偏序关系可以比较某些元素,但不一定能比较所有元素。

The subset relation () forms a partial order on the power set of a given set, producing a structure used in lattice theory.
在某个集合的幂集上,“子集关系”() 构成偏序关系,并产生一种在格论中常用的结构。

词源 Etymology

partial 来自拉丁语 partialis(“部分的”),强调“不是全部”;order 来自拉丁语 ordo(“排列、秩序”)。合在一起,partial order 字面意思是“部分的秩序/排序”,用来表示一种“只对部分元素能排出先后”的数学关系。

相关词 Related Words

文学与著作 Literary Works

  • B. A. Davey & H. A. Priestley, Introduction to Lattices and Order(系统介绍偏序、格等概念)
  • S. Roman, Lattices and Ordered Sets(围绕偏序集与相关结构展开)
  • G. Grtzer, General Lattice Theory(大量使用偏序与格论语言)
  • Paul R. Halmos, Naive Set Theory(以集合论背景自然引入关系与序的思想)
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