# Who came up with the $\\varepsilon$-$\\delta$ definitions and the axioms in Real Analysis?

I've seen a lot of definitions of notions like boundary points, accumulation points, continuity, etc, and axioms for the set of the real numbers. But I have a hard time accepting these as "true" definitions or acceptable axioms and because of this it's awfully hard to believe that I can "prove" anything from them. It feels like I can create a close approximation to things found in calculus, but it feels like I'm constructing a forgery rather than proving. What I'm looking for is a way to discover these things on my own rather than have someone tell them to me. For instance, if I want to derive the area of a circle and I know the definition of $\\pi$ and an integral, I can figure it out.

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OChem, Calc, ACT/SAT/GRE-years of exp. w/all ages, former OChem TA@UCB

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