I'm new to the $\delta$-$\epsilon$ proofs. I have been referencing Spivak's book to learn, but am having a hrd time with his theoretical approach. I find it difficult to answer any of the theoretical problems that do not involve numbers. I have an okay understanding of concepts involving numbers, but when I transition to proof-theoretic notions (involving "iff" statements, say), I get lost. I also have a hard time disproving things.
My difficulty is with the complexity of Spivak's examples. Instead of posting every single question I have, I was wondering if anyone had another source for learning about these ideas that is more intuitive but still rigorous. I want to be able to understand the underlying concepts and procedures.
I am aware that one of my difficulties is with the manipulation of logical quantifiers.