countable set

可数集

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

Translation evidence: Literature usage

Meaning in context

A set that is finite or admits a bijection with the natural numbers, including the empty set.

有限或与自然数集之间存在双射的集合；本条约定包括空集。

Example

∅\emptyset, N\mathbb N, and Z\mathbb Z are countable; P(N)\mathcal P(\mathbb N) is not.

Usage and distinctions

Some Chinese and English texts use countable exclusively for the infinite case; this entry includes finite sets.

Read the encyclopedia explanation

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. 高等教育出版社 — 数学证明 通往高等数学的阶梯（第4版）影印版，官方中文目录官方中文目录：§11.2 可数集（名称证据，非正文定义证据） · Checked 2026-10-14
Edit source / propose a PRReport a correction

Original encyclopedia and terminology content: CC BY-SA 4.0. Contribute or report a correction.