Dedekind Cut

(redirected from Dedekind-macneille completion)
Also found in: Dictionary.

Dedekind cut

[′dā·də·kint ‚kət]
(mathematics)
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.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

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.

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
References in periodicals archive ?
The construction is an application of the Dedekind-MacNeille completion known from lattice theory [MacNeille 1937; Birkhoff 1995; Davey and Priestley 1990].
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.