equivalence class

等价类

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

Translation evidence: Literature usage

Meaning in context

For an equivalence relation on X, the class [x] consists of all elements related to x.

对于 X 上的等价关系，x 的等价类 [x] 是所有与 x 等价的元素的集合。

Example

Modulo four, [2]={…,−2,2,6,…}[2]=\{\ldots,-2,2,6,\ldots\}.

Usage and distinctions

A class is a set of representatives, rather than one preferred representative.

Recommended reading in this subject · Preparation & skip guidance

Definition 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」 · 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」，等价类 [x] 的定义 · Checked 2026-10-14
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