Duality Law

A metatheorem stating that every theorem on partially ordered sets remains true if all inequalities are reversed. In this operation, supremum must be replaced by infimum, maximum with minimum, and conversely. In a lattice, this means that meet and join must be interchanged, and in a Boolean algebra, 1 and 0 must be switched.

Each of de Morgan's two laws can be derived from the other by duality.

See also

Duality Principle

This entry contributed by Margherita Barile

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Donnellan, T. "Duality." §10 in Lattice Theory. Oxford, England: Pergamon Press, pp. 75-76, 1968.Goodstein, R. L. "Duality." §2.5 in Boolean Algebra. Oxford, England: Pergamon Press, pp. 24-25, 1963.

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Duality Law

Cite this as:

Barile, Margherita. "Duality Law." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

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