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I just got through reading the first chapter of principles of mathematical analysis by Walter Rudin, the first chapter goes on and on about Dedekind cuts and then starts defining properties of them, talking about how there closed under certain mathematical operations and such, I just don't understand how defining the notion of a Dedkind cut is at all useful or interesting, and when I say useful I don't mean practical. I mean in the sense that it could contribute to other areas of mathematics, not including itself, I kind of had the same experience when I started studying parts of linear algebra, I know that notation and rigour is important but some of the parts seem like over kill in terms of rigor and the results don't seem very meaningful to me. I have only read the first chapter and don't know if I should continue, I would appreciate any advice.

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    Rudin puts the proof in the Appendix for a reason. If you don't find it interesting, don't read it. (I don't say this to be rude - when I first got to this section, I skipped a lot of it.)2012-11-02
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    My professor mentioned that it is included for the intellectually curious. I don't think any of my friends have had a professor that rigorously covered Dedkind cuts. The usual reason is because it contributes to a deeper understand of mathematics, but you can get through a first course in analysis without ever knowing exactly how the Dedkind cuts work.2012-11-02
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    You can question the value of dedekind cuts, but it's difficult to question the value of linear algebra, which is used constantly in science and engineering (and so much of advanced math).2012-11-02
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    Knowing the idea behind Dedekind cuts should be part of any well rounded mathematical education. The details in verifying all the algebraic rules are messy and not very interesting, so just try to get the big picture.2012-11-02
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    Dedekind cuts is one approach (among others) to construct $\mathbb{R}$. Often this book is the first rigorous book that a student encounters and I would guess Rudin wished to be self-contained.2012-11-02
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    See also this question: [Can I skip the first chapter in Rudin's Principles of Mathematical Analysis?](http://math.stackexchange.com/questions/3617/can-i-skip-the-first-chapter-in-rudins-principles-of-mathematical-analysis). (It was shown between related questions on the right.)2012-11-02

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