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# What is duality?

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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.

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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.

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## Related Questions

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The charge cloud model is an atomic model postulated by Erwin Schrödinger that takes into account the particle-wave duality of electrons orbiting an atomic nucleus. This model assigns a cloud of probability densities in regions around an atomic nucleus where electrons can be found with a high degree of certainty.

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Homographs are at least two words that are spelled exactly the same but have different meanings and sometimes different pronunciations, such as "moped," the past tense of mope or a type of motorbike. Another example is the word "bear," which either means to carry or a large wild animal.

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Underscore an email address by inputting the underscore character between two words; for example, John_Doe. The underscore joins two words or separates letters and numbers when the text cannot have a space. The underscore character also works to create a space in both IP addresses and website user names.