Textbook Recommendation for Functions

Question

I am currently in my first year introductory analysis course and I am struggling a lot with proofs for functions. I have gone through the examples in my textbook "Introduction to Real Analysis by R. Bartle and D. Sherbert" but the chapter on sets and functions wasn't long enough for me to fully comprehend it. I was wondering if anyone had any recommendations for books that go over these proofs for functions (e.g. Show that $f:A\to B$ is surjective) in more detail. Thanks!

Answer 1

Analysis With An Introduction to Proof by Lay is a good book for introductory real analysis, however if it's only functions that you're struggling with it's not really worth it to but a whole new book. I think most analysis courses assume that you have a basic understanding of sets and functions so it doesn't surprise me that they don't explain these topics in detail. I would just search the internet for example http://db.math.ust.hk/notes_download/elementary/algebra/ae_A1.pdf was the first link I found. And any specific questions or things you're struggling just ask here! Good luck!

Answer 2

You need a elementary book about Set theory (or Axiomatic set theory); the following books are useful to learn about that it:

• Book of proof (Hammack). You can get this book from here. (I suggest you start with this book, page 192.)
• How to prove it (Velleman).

Answer 3

Try the first chapter of Topology by Munkres.