Understanding Delta Epsilon Proofs: Recommended Calc Textbooks

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Can anyone recommend me a book that better explains delta epsilon proofs. We skimmed it in beginning calc class and I would like to understand it better.

Also I would like to know if there are any good books out there for learning calc. I do not like the stewart textbook we are using that much.



The folly of mistaking a paradox for a discovery, a metaphor for a proof, a torrent of verbiage for a string of capital truths, and ourselves for an oracle, is inborn in us- Paul Valerey
 
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I haven't read Stewart's Book, but I've only heard good things. A great book is "Calculus" by Michael Spivak, arguably the best calc book written to date! It has a wonderful explanation of the epsilon delta definition of limits. The exercises are probably more challenging than Stewarts though, so this book isn't for the faint of heart.
 
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Thanks for yuor reply. I will certainly give it a look!-Darius
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...

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