Family of Sets - Hall's Marriage Theorem

Hall's Marriage Theorem

Hall's marriage theorem, due to Philip Hall gives necessary and sufficient conditions for a finite family of non-empty sets (repetitions allowed) to have a system of distinct representatives.

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Famous quotes containing the words hall, marriage and/or theorem:

    “Chipmunks jump, and
    Greensnakes slither.
    Rather burst than
    Not be with her.”
    —Donald Hall (b. 1928)

    “But not gold in commercial quantities,
    Just enough gold to make the engagement rings
    And marriage rings of those who owned the farm.
    What gold more innocent could one have asked for?”
    —Robert Frost (1874–1963)

    “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)