Cartesian product

笛卡尔积

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

Translation evidence: Literature usage

Meaning in context

For sets A and B, the set of ordered pairs with first coordinate in A and second in B.

集合 A 与 B 的笛卡尔积是所有第一分量属于 A、第二分量属于 B 的有序对的集合。

Example

{2}×{5,7}={(2,5),(2,7)}\{2\}\times\{5,7\}=\{(2,5),(2,7)\}.

Usage and distinctions

Coordinate order matters. Li calls this 积集; the university syllabus explicitly uses 笛卡尔积.

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. 鲍志强（北京大学）— 拓扑学2007年秋季教学纲要第1周9月12日，主要概念：笛卡尔积 · Checked 2026-10-14
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