When I first learned calculus and the “formal” definition popped up in the first chapter I must admit it looked quite scary. This delta epsilon definition ended up not being so bad of course, however one thing the author of my calc course book wrote caught my interest. That is, mathematicians apparently couldn’t decide on what a proper formal definition of some limit approaching an arbitrary value “a” should be and that after a lot of debate they stood on the delta epsilon definition.
Now I wonder, what were any alternatives back in the day that were so viable that they caused such debate. And, are they still of relevance to this day? How are they formulated and why is it that these definitions aren’t taught instead?
