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  1. Vahsek

    Constructing the real number system by Dedekind cuts?

    Yeah I know, but my reason is that I'm more motivated to learn if the material isn't too easy. Anyway, I fully understand your point: if I run into another difficulty again while using this book, I'll order Pugh right away (which is highly probable).
  2. Vahsek

    Constructing the real number system by Dedekind cuts?

    Yeah, I've heard such things before. Nevertheless, I still wanted to give it a shot since a few schools use this book for a first course in analysis. I'm planning to fill in the gaps in my knowledge by using Pugh or Apostol after finishing Rudin.
  3. Vahsek

    Constructing the real number system by Dedekind cuts?

    Oh, all right. Now I get it. Thank you very much. It wasn't explained that explicitly in the book; it only proved that the real number system, so defined, is an ordered field with the least upper bound property, and that Q can be regarded as a subfield.
  4. Vahsek

    Constructing the real number system by Dedekind cuts?

    I understand your point about the "tricks". I saw something similar pertaining to definition of complex numbers (i.e. (a,b) instead of a + bi). However, my problem is as follows: suppose I choose a real number (say 5), then which "cut" in R represents that number 5?
  5. Vahsek

    Constructing the real number system by Dedekind cuts?

    Constructing the "real number system" by Dedekind cuts? Hi all, I've just been working through baby Rudin, and I've almost finished chapter 1. I am currently working through the appendix of chapter 1, which constructs the real number system from the rational number system by Dedekind cuts...
  6. Vahsek

    Dirac Delta function

    It's been quite some time now since I decided to stop self-studying physics and to pay more attention to the math behind. I'm working towards gaining an understanding of 100% rigorous mathematics for now. One thing that has always bothered me is the Dirac delta function. What I want to know...
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