The Dedekind cut is named after Richard Dedekind, who invented this construction in order to represent the real numbers as Dedekind cuts of the rational numbers. A typical Dedekind cut of the rational numbers is given by A = { a in Q : a^{2} < 2 }, B = { b in Q : b^{2} ≥ 2 }. This cut represents the real number √ 2 in Dedekind's construction.
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