Understanding Infinity: The Mathematics of Infinite Processes (Dover Books on Mathematics) Paperback – 28 Mar 2003
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Most Helpful Customer Reviews on Amazon.com (beta)
The book does a good job of taking the reader through the steps needed to explain "why the calculus works" -- and it really doesn't require calculus to understand most of this book, though you need calculus to understand the _motivation_ for a lot of what the book does. You need only have a decent grounding in high school geometry and algebra to understand the book. Still, it isn't an _easy_ read. I've found myself putting the book down and coming back to it later several times. Yet I can't say that the book is hard to read because it's badly written; I think it's written decently well. I think it's just that the topics it covers are harder going than a lot of the math I read.
So, while I don't _love_ this book, I'd recommend it to someone who wants to know something about the motivation for all those weird epsilons and deltas and the non-intuitive definitions of topics like continuity. It does that job, and does it as well as any book I know of.
Quite accessible for anyone who has done first year or even high school calculus