empty set

空集

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

Translation evidence: Literature usage

Meaning in context

The unique set with no members.

没有任何元素的唯一集合。

Example

$\{n\in\mathbb N:n<0\}=\emptyset$, with $\mathbb N=\{0,1,\ldots\}$.

Usage and distinctions

The empty set has zero elements; the singleton containing it has one.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

1. Avigad, Hua, Lewis and van Doorn — Logic and Proof§11.1 Elementary Set Theory; §11.4 Cartesian Product and Power Set · 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」 · Checked 2026-10-14

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