What book to use to get familiar with the epsilon-delta stuff?

[theoristo]

What book do you recommend to use to get familiar with definitions that usually contain the phrase “given any positive epsilon, however small, delta can be found such that . . .”thank you

 

[Jorriss]

If I could go back I'd learn from Spivak, Calculus.

 

[verty]

There are many ways to answer this question.

Here are two cheap books that would give you a rather complete understanding. The first is more conceptual while the second includes multivariable topics. Both assume that you know calculus. But to get value from these, you'll probably need a logic or proof book as well as some dedication.

Without doing the whole proof thing, I'm not sure what to suggest. I'll let others who are more familiar with the calculus books that are out there answer.

Books:
https://www.amazon.com/dp/0486650383/?tag=pfamazon01-20
https://www.amazon.com/dp/0486457958/?tag=pfamazon01-20

PS. I should add that I interpret "get familiar with definitions that use epsilon and delta" to mean, getting familiar with the definitions, understanding them in the context of the theory of calculus.

 

[verty]

Regarding Spivak's book, I quote what I wrote in the more recent thread:

I have only read the first edition of Spivak and for me, the problems were a little too difficult and left me feeling beat up after solving them. But for the right reader, it would be a highly enjoyable read for sure.

 

[deluks917]

I learned the concept from spivak. It took me a very long time to understand the concept of a limit. However once I really got it it was surprisingly easy to apply the concept in more general settings (metric spaces, measure theory, etc).