Dedekind Cut

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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 ?
And indeed, it turns out that the Dedekind-MacNeille completion of [T.
where DM denotes the Dedekind-MacNeille completion.
In contrast, Dedekind-MacNeille completion inserts no elements at all, since P is already a lattice and hence the minimal lattice containing itself.
The Dedekind-MacNeille completion of P, denoted DM(P), is the least complete lattice containing P as an isomorphic subposet.