Could anyone give me a simple explanation of the Epsilon-Delta approach?
Before diving in, let me make a comment intended to reduce stress. This IS NOT an easy concept. It is very likely that previous exposure has been inadequate or premature. Please know that the founders of the calculus (Newton and Leibniz) had no epsilon-delta arguments, and the mathematical community lived without them for well over a hundred years. Eventually, in the 19th century, mathematicians became aware of some subtle oversights in the logic that had been accepted until then, and found that epsilon-delta arguments were the best way to fix these problems. So in the long run epsilon-delta are important, even though it may not be easy to see why. One of the things that changed to make epsilon-delta important is that the concept of what is a function changed dramatically. To illustrate, I’ll apply epsilon-delta arguments to the question of continuity for two functions: f(x) = x*x*x (usually written x superscript 3, meaning x cubed, but I can’t write superscripts here) and g(x) defined
