Book Recommendations and Proofs for a First Course in Real Analysis I am taking real analysis in university. I find that it is difficult to prove some certain questions. What I want to ask is:


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*How do we come out with a proof? Do we use some intuitive idea first and then write it down formally?

*What books do you recommended for an undergraduate who is studying real analysis? Are there any books which explain the motivation of theorems? 


I started studying Rudin's Principles of Mathematical Analysis book for analysis. I just couldn't understand it because I was thinking that definitions are some decorative blah blahs and proofs are some unintelligible mathematician sorceries. 
Then I have decided to learn something about proofs from the book An Introduction to Mathematical Reasoning. Just after three chapters all begin to make sense. It is a perfect book for people like me. 
