# pigeonhole principle

> English word · Noun

## Definitions
1. The theorem which states that any partition of a finite set of n elements into m (< n) subsets (allowing empty subsets) must include a subset with two or more elements; any of certain reformulations concerning the partition of infinite sets where the cardinality of the unpartitioned set exceeds that of the partition (so there is no one-to-one correspondence).

## Etymology
From the commonly used expository example that if n+1 pigeons are placed in n pigeonholes, at least one pigeonhole must contain two (or more) pigeons.

## Source
Compiled from Wiktionary via kaikki.org (CC BY-SA). Data vintage: 2026-05-06.
Canonical page: https://plainspell.com/en/word/pigeonhole-principle