pigeonhole principle

noun1

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).

   • 1. κ is a regular cardinal. 2. If we put κ pigeons into λ < κ pigeonholes, then some pigeonhole must contain κ pigeons. — 2009