# Need help with fundamental understanding of $\delta$-$\epsilon$ proofs

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.

• There are punctuation marks other than !, you know. – Zev Chonoles Mar 1 '14 at 6:24
• Have you looked at any of the hundreds of other questions on this site about $\delta$-$\epsilon$ proofs? Have you looked at the Wikipedia page on them (link)? Can you point to anything specific in these resources that you don't understand? – Zev Chonoles Mar 1 '14 at 6:26
• I get the example there its basic Proving Limit laws is a whole different story! Disproving limits is confusing, Using arbitrary values is again confusing because again I dont know how to view them differently – user126885 Mar 1 '14 at 6:29
• I found Marsden's "Elementary classical analysis" useful when developing my early real analysis skills. – copper.hat Mar 1 '14 at 6:31
• There are ton of references on this. Kenneth Ross' book Elementary Analysis: The theory of calculus is a good one. Another is this note set: vex.net/~trebla/homework/epsilon-delta.html – Batman Mar 1 '14 at 6:34

You've been reading Spivak. And I read very few other books in grasping the $\epsilon$ - $\delta$ definition. Maybe a few other suggestions would be these: