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Dedekind Cuts: more detail 
1. Dedekind Cuts. dedekind cuts. If we choose a rational number q, we can use this to split the rationals in two sets, one larger than http://hemsidor.torget.se/users/m/mauritz/math/num/real.htm  

2. 2.15.1 Dedekind Cuts 2.15.1 dedekind cuts. A real number is represented by a cut , http://www.dgp.toronto.edu/people/mooncake/thesis/node61.html  

3. Dedekind Cuts Of Partial Orderings dedekind cuts of partial orderings dedekind cuts are a clever trick for defining the reals given the rationals. http://www.caplore.com/MathPhys/Cuts.html  

4. Dedekind Cuts dedekind cuts. The first construction of the Real numbers from the Rationalsis due to the German mathematician Richard Dedekind (1831 1916). http://www.gapsystem.org/~john/analysis/Lectures/A3.html 
5. 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 
6. PlanetMath: Dedekind Cuts The purpose of dedekind cuts is to provide a sound logical foundation for the real number system. http://www.planetmath.org/encyclopedia/DedekindCuts.html  

7. 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  

8. Dedekind CutsThe First Construction Of The Real Numbers From The Rationals Is Du Biography of Richard Dedekind (18311916) was his redefinition of irrational numbers in terms of dedekind cuts which, as we mentioned above, first came to him as http://wwwhistory.mcs.stand.ac.uk/~john/analysis/Lectures/A3.html 
9. D D. De Morgan's laws; De Morgan, Augustus (18061871); decreasing function;dedekind cuts; Dedekind's Theorem; density principle; derivative http://www.shu.edu/projects/reals/gloss/index_d.html  

10. Dedekind Cuts By Todd Trimble Subject dedekind cuts Author todd trimble trimble@math.luc.edu Date 3 Oct 98 185819 0400 (EDT) The idea is that http://forum.swarthmore.edu/epigone/alt.math.undergrad/dunyobe/x6e65pivbnzw@foru  

11. 2.15 Real Representations next up previous notation contents Next 2.15.1 dedekind cuts Up2 Numbers Previous 2.14 Variants 2.15 Real Representations. To http://www.dgp.toronto.edu/people/mooncake/thesis/node60.html  

12. Dedekind Cut  Wikipedia The Dedekind cut is named after Richard Dedekind, who invented this constructionin order to represent the real numbers as dedekind cuts of the rational numbers http://www.wikipedia.org/wiki/Dedekind_cut 
13. Real Number  Wikipedia This sense of completeness is most closely related to the construction of the realsfrom dedekind cuts, since that construction starts from an ordered field http://www.wikipedia.org/wiki/Real_number 
14. Dedekind's Cuts 3 Oct 1998 dedekind cuts, by todd trimble http://mathforum.com/epigone/alt.math.undergrad/dunyobe  

16. 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  

17. PlanetMath: decomposition (complementary subspace) owned by rmilson. decomposition group ownedby djao. dedekind cuts owned by rmilson. Dedekind domain owned by saforres. http://planetmath.org/encyclopedia/D/  

18. 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  

19. Reals Via Dedekind Cuts Theorem Real Numbers as dedekind cuts. The proof isnot done, sorry. To Theory Glossary Map (bgw). http://pirate.shu.edu/projects/reals/infinity/proofs/r_dedek.html  

20. Interactive Real Analysis Glossary D. De Morgan, Augustus (18061871); De Morgan's laws; decreasing function;dedekind cuts; Dedekind's Theorem; density principle; derivative http://pirate.shu.edu/projects/reals/gloss/index_d.html  

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