[doo-al-i-tee, dyoo-] 
| 1. | a dual state or quality. |
| 2. | Mathematics. a symmetry within a mathematical system such that a theorem remains valid if certain objects, relations, or operations are interchanged, as the interchange of points and lines in a plane in projective geometry. |
| du·al·i·ty (dōō-āl'ĭ-tē, dyōō-) n. The quality or character of being twofold; dichotomy. |
duality
in mathematics, principle whereby one true statement can be obtained from another by merely interchanging two words. It is a property belonging to the branch of algebra known as lattice theory, which is involved with the concepts of order and structure common to different mathematical systems. A mathematical structure is called a lattice if it can be ordered in a specified way (see order). Projective geometry, set theory, and symbolic logic are examples of systems with underlying lattice structures, and therefore also have principles of duality.
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