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).
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.
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.
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?
Constructing the "real number system" by Dedekind cuts?
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...
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...