pigeonhole principle
An illustration of the pigeonhole principle: with 10 pigeons in 9 pigeonholes, one hole contains two pigeons
Meaning
Noun
- 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).
Related
Similar words
- Dirichlet's box principle, Dirichlet's drawer principle
Origin
- 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.
Modern English dictionary
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