equinumerosity

等势

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

Other names / variants: equipollence

Translation evidence: Literature usage

Meaning in context

The relation between sets A and B that holds precisely when a bijection A→B exists.

集合 A 与 B 之间存在双射时成立的关系。

Example

N\mathbb N and {0,5,10,…}\{0,5,10,\ldots\} are equinumerous.

Usage and distinctions

Equal cardinality does not require sets to be equal or nested.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Avigad, Hua, Lewis and van Doorn — Logic and Proof§22.1 Equinumerosity; §22.2 Countably Infinite Sets; §22.3 Cantor’s Theorem; §22.5 The Cantor-Bernstein Theorem · 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「基数」：等势的定义；基数的定义 · Checked 2026-10-14
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