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