Phrase guide

pigeonhole principle

noun · 1 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

Sound

Pronunciation

Each Play button uses your device's default local English voice, or a natural local fallback. The selected voice name appears after playback. This is synthesized speech, not a source recording.

No pronunciation record was provided for this word.

1

noun

Meaning 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).

Definition source: English Wiktionary via Wiktextract

Usage: countable, uncountable

Topics: mathematics, sciences

Examples

  • 2012, Dov M. Gabbay, Akihiro Kanamori, John Woods (editors), Handbook of the History of Logic: Volume 6: Sets and Extensions in the Twentieth Century, Elevier (North-Holland), page 325, As we turn to look at various pigeonhole principles and how they are used to prove partition theorems, particularly for pairs, we keep in mind the slogan that is embedded in the Motzkin quote: complete disorder is impossible.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

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.

Across languages

Translations

4 source translations are retained for this English entry.

  • Finnish: kyyhkyslakkaperiaate — combinatorial theorem
  • German: Schubfachprinzip — combinatorial theorem
  • Polish: zasada szufladkowa (Dirichleta) — combinatorial theorem
  • Slovak: Dirichletov princíp — combinatorial theorem