equivalence relation

等价关系

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

Translation evidence: Literature usage

Meaning in context

A binary relation on a specified set that is reflexive, symmetric and transitive.

指定集合上满足反身性、对称性和传递性的二元关系。

Example

On Z\mathbb Z, a∼ba\sim b iff 4∣(a−b)4\mid(a-b).

Usage and distinctions

Reflexivity and symmetry alone are insufficient: distance at most one fails transitivity.

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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：「ZFC 公理一览」，等价关系及三条性质 · Checked 2026-10-14
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