Duality is a mathematical principle whereby one true statement can be obtained from another by interchanging two words. Sometimes the wording of a statement needs to be modified so the corresponding dual statement is clear.
Duality is a property that belongs to the lattice theory branch of algebra. Lattice theory is involved with the concepts of order and structure, which is common to different mathematical systems. A mathematical structure is a lattice if it can be ordered in a specified way. Projective geometry, set theory and symbolic logic have principles of duality because they have underlying lattice structures. If the results of a structure to which duality is applied hold in both formations, it is called a dual formulation.