Added: Much of the praise for baby Rudin suggests that trying to prove each theorem before having seen the proof, is one of the best ways to become a good mathematician. Can you comment on my thought that, after having read a more verbose book, I won’t have that same experience? Or is that approach going to work with most real analysis books, so that I could still try to prove everything before it is explained?
Yes, you can try to prove everything before it’s explained with pretty much any real analysis book. Just be reasonable about it, if you’ve gone a few hours without even making partial progress on a theorem, read the proof. A first exposure to analysis doesn’t just teach you analysis, it teaches you how to build theories from the bottom up. If you can do that on your first try, great. If you can’t (as is a lot more likely), learn how and save the “prove everything on your own” experience for a different subject.
That makes a lot of sense. Thank you.
Added: Much of the praise for baby Rudin suggests that trying to prove each theorem before having seen the proof, is one of the best ways to become a good mathematician. Can you comment on my thought that, after having read a more verbose book, I won’t have that same experience? Or is that approach going to work with most real analysis books, so that I could still try to prove everything before it is explained?
Yes, you can try to prove everything before it’s explained with pretty much any real analysis book. Just be reasonable about it, if you’ve gone a few hours without even making partial progress on a theorem, read the proof. A first exposure to analysis doesn’t just teach you analysis, it teaches you how to build theories from the bottom up. If you can do that on your first try, great. If you can’t (as is a lot more likely), learn how and save the “prove everything on your own” experience for a different subject.