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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.

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  • $\begingroup$ There are punctuation marks other than !, you know. $\endgroup$ – Zev Chonoles Mar 1 '14 at 6:24
  • $\begingroup$ 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? $\endgroup$ – Zev Chonoles Mar 1 '14 at 6:26
  • $\begingroup$ 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 $\endgroup$ – user126885 Mar 1 '14 at 6:29
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    $\begingroup$ I found Marsden's "Elementary classical analysis" useful when developing my early real analysis skills. $\endgroup$ – copper.hat Mar 1 '14 at 6:31
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    $\begingroup$ 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 $\endgroup$ – Batman Mar 1 '14 at 6:34
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As other users have suggested you can do no harm to yourself by perusing through all related questions on this site. Attempting them on your own and then reading through the extensive and useful discussion can be immensely fruitful. I had similar issues and as I have mentioned here I believe it is the teacher's duty to make the student understand the logical concept behind it. So I urge you to keep nagging your tutors about questions you don't understand.

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:

All these books are excellent references for your particular problem but again I emphasise that the only way you are going to cement your knowledge in these proofs is through self-exploration.

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