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.
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 It might be outdated or ideologically biased.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 ?
It is easy to show that the c-quotient relational structure (c/~, [less than or equal to]/~, [circle/~) is Dedekind-complete (since the magnitude set c is Dedekind-complete) and satisfies, in addition, axioms A(1.1), A(1.2), A(1.4), and A(1.5) [Garvin, 1987, pp.
It can be shown that if the decomposable structure [II.sub.i][c.sub.i] is Dedekind-complete, then each component magnitude set [c.sub.i] is Dedekind-complete (and conversely).
A(2.4): [II.sub.i][c.sub.i] is Dedekind-complete. A(2.5): [II.sub.i][c.sub.i] is unrestrictedly solvable.