Home  Math_Discover  Dedekind Cuts 
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1. Dedekind Cut  From MathWorld Dedekind Cut. A set partition of has no greatest member. Real numberscan be defined using either dedekind cuts or Cauchy sequences. http://mathworld.wolfram.com/DedekindCut.html  

2. Dedekind Cut  Wikipedia, The Free Encyclopedia is a Dedekind cut that gets identified with a, so that the linearly ordered set Smay be regarded as embedded within the set of all dedekind cuts of S. If the http://en.wikipedia.org/wiki/Dedekind_cut  

3. PlanetMath: Dedekind Cuts dedekind cuts, (Definition). The purpose of dedekind cuts is to providea sound logical foundation for the real number system. Dedekind s http://planetmath.org/encyclopedia/DedekindCuts.html  

4. PlanetMath Example Of Definable Type See Also example of a universal structure, dedekind cuts Keywordsdense linear order. This object s parent. Crossreferences o http://planetmath.org/encyclopedia/ExampleOfDefinableType.html 
5. Dedekind Cut x a } } is a Dedekind cut that gets identified with a, so that the linearly orderedset S may be regarded as embedded within the set of all dedekind cuts of S http://www.factindex.com/d/de/dedekind_cut.html  

6. Construction Of Real Numbers 1. Construction by dedekind cuts. Real numbers can be constructed as Dedekindcuts of rational numbers. Construction by decimal expansions. http://www.factindex.com/c/co/construction_of_real_numbers.html  

7. Dedekind Cuts. Up Contents. Next Real numbers, other definitions. dedekind cuts. Wecall the set of all dedekind cuts, the set of reals, R. http://hemsidor.torget.se/users/m/mauritz/math/num/real.htm  

8. The Reals. As you may recall, one way of defining the reals was by using Dedekind scuts. We do now define the the real numbers to be a dedekind cuts. http://hemsidor.torget.se/users/m/mauritz/math/num/setreal.htm  

9. Theorem: R Via Dedekind Cuts Theorem R via dedekind cuts. The proof is not done, sorry. Context Context.Interactive Real Analysis, ver. 1.9.3 (c) 19942000, Bert G. Wachsmuth. http://www.shu.edu/projects/reals/infinity/proofs/r_dedek.html  

10. Dedekind Cuts Previous page (Some Early History of Set Theory), Contents, Next page (Farey sequences).dedekind cuts. Such a pair is called a Dedekind cut (Schnitt in German). http://www.gapsystem.org/~john/analysis/Lectures/A3.html  

11. Some Early History Of Set Theory MT2002 Analysis Previous page (Some definitions of the concept of continuity),Contents, Next page (dedekind cuts). Some Early History of Set Theory. http://www.gapsystem.org/~john/analysis/Lectures/A2.html  

12. Dedekind Cut Analysis about the problems, but between the time in the course (projects were also due soon),the lack of student understanding about the place of dedekind cuts in the http://gallery.carnegiefoundation.org/cbennett/Picture08/anal.htm  

13. Dedekind Cuts  Pedagogical dedekind cuts. Pedagogical Reasoning. At the classical definitions. HereI will emphasize the reasoning behind how I present dedekind cuts. http://gallery.carnegiefoundation.org/cbennett/Picture08/Pedreas.htm  

14. 2.15.1 Dedekind Cuts 2.15.1 dedekind cuts. A real number is represented by a cut , . Every cuthas the property that for all As presented, the cut represents . http://www.dgp.utoronto.ca/~mooncake/thesis/node61.html  

15. Dedekind Cuts Of Partial Orderings dedekind cuts of partial orderings. dedekind cuts are a clever trickfor defining the reals given the rationals. Such a cut considers http://www.caplore.com/MathPhys/Cuts.html  

16. 408 Course Notes Mar. 16, Karen, Countability of algebraic integers, Mar. 18, Brian, dedekind cuts,Mar. 30, Cynthia, Continued Fractions, Apr. 1, Dan, Quaternions and rotations,Apr. http://homepage.mac.com/vogtmann/projects.html  

17. Dedekind's Cuts Dedekind s cuts. post a message on this topic post a message on a new topic 29 Sep1998 Dedekind s cuts, by Alan Hill 3 Oct 1998 dedekind cuts, by todd trimble http://mathforum.org/epigone/alt.math.undergrad/dunyobe  

18. Re: On Defining Pi By John Conway John Conway conway@math.Princeton.EDU Date Thu, 16 Jan 1997 121808 0500 It strue of course that the problems of specifying dedekind cuts for root2 and http://mathforum.org/epigone/mathhistorylist/foubuhal  

19. [math/0305122] The Elementary Theory Of Dedekind Cuts In Polynomially Bounded St The elementary theory of dedekind cuts in polynomially bounded structures. AuthorsMarcus Tressl (University of Regensburg, Germany) Comments 16 pages. http://arxiv.org/abs/math.LO/0305122  

20. Dedekind Cut Dedekind Cut. Real Numbers can be defined using either dedekind cuts or CauchySequences. See also CantorDedekind Axiom, Cauchy Sequence. References. http://icl.pku.edu.cn/yujs/MathWorld/math/d/d068.htm  

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