Dedekind complete | Article about Dedekind complete by The Free Dictionary
Dedekind Cut (redirected from Dedekind complete)
Also found in: Dictionary
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.
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.