>>11093080It's not horrible, it's just presented kind of idiotically and someone without a good amount of experience with proofs and general maturity won't see why Rudin is doing what he's doing at each step. Pugh, on the other hand, explains why EVERYTHING he tells you is important, and draws pictures to show you how to do arguments. Tao doesn't assume you know anything about math, and gradually, very carefully leads you into the subject, giving you room to grow.
Pugh and Tao are two wonderful teachers. Pugh's undergraduate analysis classes at Berkeley are regarded as some of the highest quality undergraduate analysis classes around. Rudin, on the other hand, is something many people use when they want to sound put together, and few people really learn how to think about mathematics from it since he hides away all the work he's done on each proof and just leaves you with the impeccable, seemingly god-given argument. PUGH TELLS YOU HOW HE FIGURES OUT WHICH DELTAS AND NS TO USE!
