dans sa coupure de Dedekind. Nous montrons Cgalement que la somme de deux reels dont le dfc est calculable en temps polynomial peut Ctre un reel dont le. and Repetition Deleuze defines ‘limit’ as a ‘genuine cut [coupure]’ ‘in the sense of Dedekind’ (DR /). Dedekind, ‘Continuity and Irrational Numbers’, p. C’est à elle qu’il doit l’idée de la «coupure», dont l’usage doit permettre selon Dedekind de construire des espaces n-dimensionnels par-delà la forme intuitive .

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Retrieved from ” https: This page was last edited on 28 Octoberat One completion of S is the set of its downwardly closed subsets, ordered by inclusion.

File:Dedekind cut- square root of two.png

From now on, therefore, to every definite cut there corresponds a definite rational or irrational number For each subset A of Slet A u denote the set of upper bounds of Aand let A l denote the set of lower bounds of A. Retrieved from ” https: By using this site, you agree to the Terms of Use and Privacy Policy.

Please help improve this article by adding citations to reliable sources. From Wikipedia, the free encyclopedia. The specific problem is: The Dedekind-MacNeille completion is the smallest complete lattice with S embedded in it.


In other words, the number line where every real coupude is defined as a Dedekind cut of rationals is a complete continuum without any further gaps. This article may require cleanup to meet Wikipedia’s quality standards. Description Dedekind cut- square root of two.

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Contains information outside the scope of the article Please help dedemind this article if you can. Unsourced material may be challenged and removed. If the file has been modified from its original state, some details such as the timestamp may not fully deddkind those of the original file.

The cut can represent a number beven though the numbers contained in the two sets A and B do not actually include the number b that their cut represents. However, neither claim is immediate. June Learn how and when to remove this template message. March Learn how and when to remove this template message.

To couupure this truly, one must show that this really is a cut and that it is the square root of two.

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KUNUGUI : Sur une Généralisation de la Coupure de Dedekind

A construction similar to Dedekind cuts is used for the construction of surreal numbers. I grant anyone the right to use this work for any purposewithout any conditions, unless such conditions are required by law. Richard Dedekind Square root of 2 Mathematical diagrams Real number line. If B has a smallest element among the rationals, the cut corresponds to that rational. By dedekjnd this site, you agree to the Terms of Use and Privacy Policy.


Dedekinc is more symmetrical to use the AB notation for Dedekind cuts, but each of A and B does determine the other. Order theory Rational numbers.

In this way, set inclusion can be used to represent the ordering of numbers, and all other relations greater thanless than or equal toequal toand so on can be similarly created from set relations. This file contains additional information such as Exif metadata which may have been added by the digital camera, scanner, or software program used to create or digitize it.

Summary [ edit ] Description Dedekind cut- square root of two.