Introduction to Real Analysis (Proof Based Course) Spivak vs Baby Rudin? I'm a second year math major and I don't know which is the right book for me?
I hope that only someone who studied both or has a strong background in analysis attempts to answer my question because random answers are shared pretty much everywhere.
Please note that I only know: elementary set theory aka discrete mathematics and calculus
Thanks!
 A: I have looked at some different textbooks, but the one that I learned out of was Ethan Bloch's "The Real Numbers and Real Analysis." I liked it for the following reasons:
-It makes atypically rigorous arguments utilizing the least upper bound property on real numbers
-The book minimizes dependence on sequences for many of the "big proofs" of real analysis (Sometimes sequences take away from the heart of what is going on.)
-Bloch introduces the Riemann integral without specific reference to Darboux integrals (upper and lower sums) so that the "intro calculus" intuition is intact when first dealing with integration. In fact, all of the topics are introduced in the order that a typical calculus course would cover them.
-There is a really interesting sub-chapter proving that the Riemann Integral is indeed the "area" under a curve, given by a rather abstract (but intuitive) notion of area.
A: I think Baby Rudin is a better introduction. I would advise that and there's also an excellent video series by Professor Su of Harvey Mudd College with an accompanying website called Rudinium which has over 200 problems to go along with the videos. 
The video quality isn't great but I think he's an excellent instructor. 
