partial order

偏序

Foundations & Logic · Undergraduate · Mathematics Resources editorial compilation (AI-assisted)

Translation evidence: Literature usage

Meaning in context

A reflexive, antisymmetric and transitive binary relation on a set.

集合上满足反身性、反对称性和传递性的二元关系。

Example

Inclusion orders P({2,5})\mathcal P(\{2,5\}); {2}\{2\} and {5}\{5\} are incomparable.

Usage and distinctions

A partial order (偏序) is the relation; a partially ordered set or poset (偏序集) is the set equipped with that relation. Antisymmetry says mutual comparison forces equality; it is not the negation of symmetry.

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Definition sources

  1. Avigad, Hua, Lewis and van Doorn — Logic and Proof§13.1 Order Relations; §13.3 Equivalence Relations and Equality · Checked 2026-10-14

Translation sources

  1. 李文威 — 代数学方法，第一卷（作者源码）第1章：「序结构与序数」，带源码标签 def:partial-order 的定义；正文称「偏序」 · Checked 2026-10-14
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