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This topic has appeared in the English Wikipedia rankings 1 time. It first appeared on 2026-05-17 and was most recently seen on 2026-05-17.
In mathematics, Dedekind cuts, named after German mathematician Richard Dedekind, are а method of constructing the real numbers from the rational numbers. A Dedekind cut is a partition of the rational numbers into two nonempty sets A and B, such that each element of A is less than every element of B, and A contains no greatest element. The set B may or may not have a smallest element among the rationals. If B has a smallest element among the rationals, the cut corresponds to that rational. Otherwise, that cut defines a unique irrational number which, loosely speaking, fills the "gap" between A and B. In other words, A contains every rational number less than the cut, and B contains every rational number greater than or equal to the cut. An irrational cut is equated to an irrational number which is in neither set. Every real number, rational or not, is equated to one and only one cut of rationals.
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