addition principle

加法原理

Combinatorics · Undergraduate · Mathematics Resources editorial compilation (AI-assisted)

Other names / variants: sum rule

Translation evidence: Literature usage

Meaning in context

For finitely many pairwise disjoint finite sets, the cardinality of their union equals the sum of their cardinalities.

有限个两两不交的有限集合，其并集的元素个数等于各集合元素个数之和。

Example

There are 3+4=73+4=7 symbols when choosing one symbol from disjoint alphabets of sizes 3 and 4.

Usage and distinctions

Cases must be both exhaustive and disjoint; overlapping cases require a correction.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Joy Morris — Combinatorics, version 2.1.1Sections 2.1–2.2, Theorems 2.1.2 and 2.2.4 · Checked 2026-10-14

Translation sources

  1. 上海交通大学 — CS0901 组合数学（2026）第1讲，开篇「加法原理与乘法原理」 · Checked 2026-10-14
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