cardinality of a set

基数

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

Other names / variants: cardinality

Translation evidence: Literature usage

Meaning in context

In ZFC, the least ordinal bijective with a set; equality of cardinalities is equivalently existence of a bijection.

在 ZFC 中，与给定集合等势的最小序数；两个集合基数相等等价于它们之间存在双射。

Example

∣{2,5,7}∣=3|\{2,5,7\}|=3 and ∣5N∣=∣N∣=ℵ0|5\mathbb N|=|\mathbb N|=\aleph_0.

Usage and distinctions

Cardinal size ignores order; ordinal type remembers an ordering.

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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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