Dedekind Cut

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Related to Dedekind Cut: Cauchy sequences

Dedekind cut

[′dā·də·kint ‚kət]
A set of rational numbers satisfying certain properties, with which a unique real number may be associated; used to define the real numbers as an extension of the rationals.

Dedekind Cut


one of the arithmetic definitions of real numbers that does not introduce geometric concepts. It was first proposed in 1872 by the German mathematician J. W. R. Dedekind. The Dedekind cut expands the set of rational numbers to the set of all real numbers by introducing the new, irrational numbers, at the same time ordering them.

References in periodicals archive ?
a) Dedekind cuts whose purpose is to provide a sound logical foundation for the real number system.
We can, moreover, construct other kinds of numbers, for instance, non-rational real numbers with the help of Dedekind cuts.