Strangely enough, I took a whole degree in mathematics, and never felt comfortable with the epsilon-delta proofs for limits. It was only by reading Everything and More a Compact History of Infinity, by, of all people, David Foster Wallace that I understood the motivation behind it!
He explains how the ideas of infinity were developed, and which paradoxes and absurdities forced 19th century mathematicians like Cauchy to put the whole thing on a more rigorous footing.
He explains how the ideas of infinity were developed, and which paradoxes and absurdities forced 19th century mathematicians like Cauchy to put the whole thing on a more rigorous footing.