In combinatorial mathematics, Hall's marriage theorem, or simply Hall's Theorem, gives a necessary and sufficient condition for being able to select a distinct element from each of a collection of finite sets. It was proved by Philip Hall (1935).
Read more about Hall's Marriage Theorem: Definitions and Statement of The Theorem, Discussion and Examples, Graph Theoretic Formulation, Proof of The Graph Theoretic Version, Marshall Hall Jr. Variant, Applications, Marriage Condition Does Not Extend, Logical Equivalences
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“I was afraid the waking arm would break
From the loose earth and rub against his eyes
A fist of trees, and the whole country tremble
In the exultant labor of his rise;”
—Donald Hall (b. 1928)
“My husband sings Baa Baa black sheep and we pretend
that all’s certain and good, that the marriage won’t end.”
—Anne Sexton (1928–1974)
“To insure the adoration of a theorem for any length of time, faith is not enough, a police force is needed as well.”
—Albert Camus (1913–1960)