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 ?
We do not define what a dedekind complete poset is; in turn, we translate this concept in graph theoretic terms.
It is well known (taking into account that dedekind graphs correspond to dedekind complete finite posets) that, in this case, D is dedekind.
A vector lattice A is called laterally complete if every orthogonal system in A has a supremum in A and if A is Dedekind complete and laterally complete, A is said to be universally complete.