well-order

良序

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

Translation evidence: Literature usage

Meaning in context

A total order on a set in which every nonempty subset has a least element.

一个全序，其中每个非空子集都有最小元素。

Example

The usual order well-orders N\mathbb N but not Z\mathbb Z.

Usage and distinctions

A least element of the whole set is insufficient; every nonempty subset must have one.

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「序结构与序数」，定义 def:well-ordered（良序集；每个非空子集有极小元） · 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:well-ordered 的定义「良序集」 · Checked 2026-10-14
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