I was recommended Rudin's "Principles of Mathematical Analysis" as a text that assumes you know nothing and takes it from there. And make no mistake, I think it's an amazing book. I've learned techniques and overcome some hurdles all on my own that make me feel quite good about myself. So this is not a criticism of Rudin's work. I just feel that it's not rigorous enough for my taste. While starting out, I tried to imagine that Rudin wasn't talking about "numbers" when using terms like "-x" and "0" etc, but this became impossible later on. For example, while constructing real numbers from the rationals using Dedekind cuts, he suddenly talks about the "Archimedean" property of the set of rationals Q which he hasn't mentioned before. In fact, he seems to take the set of rationals for granted entirely without defining what Integers are, what natural numbers are, and indeed what "numbers" are in the first place. He also doesn't define a "set" or how they're constructed. Now I know a lot of this since I've worked with analysis before, but for my own satisfaction I want to start with a completely blank slate. Basically assume that I have infinite intelligence (a rash proposition!) but know absolutely nothing. Can anyone help me out with a text that starts from scratch...absolutely from nothing and then builds up to the construction of the real numbers? Like I said, I love Rudin and plan to continue studying the book but I also feel "incomplete" without having a rigorous understanding of some of the fundamentals that Rudin seems to take for granted. Any suggestions would be greatly appreciated!