I am considering Stephen Abbott's Understanding Analysis and Walter Rudin's Principles of Mathematical Analysis. I am looking for a comparison between the two that addresses both of the following matters,
- Is one of the two substantially more mathematically rigorous than the other?
- Does one include substantially more challenging problems?
- Which provides a better introduction to Real Analysis?
- Would someone who has worked through Abbott's book be at a disadvantage compared to someone who has completed Rudin's text?