Is it legitimate to prove the fundamental theorem of calculus (FTC) using an epsilon-delta limit approach? I've been reading this set of notes https://math.berkeley.edu/~ogus/Math_1A/lectures/fundamental.pdf which provides a compelling argument, but I'm not entirely sure (I guess as I'm so used to seeing it proven using the extreme value theorem, or similar).
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Just choose the proof you like most. Here's one: http://math.stackexchange.com/questions/877907/is-this-proof-of-the-fundamental-theorem-of-calculus-correct – Feb 23 '15 at 16:55
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so is the one I linked to valid then? (sorry to be a pain, but I quite like it, so if it is correct that'd be great) – Will Feb 23 '15 at 17:50
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You have no idea of the can of worms you are opening up with questions like this. – Feb 23 '15 at 23:50
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Oh dear, is it a contentious subject then?! – Will Feb 24 '15 at 09:53
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Another way would to use the grunwald definition of the $n$th differintegral and the sum form of a definite integral to prove the FTC. – Simply Beautiful Art Aug 01 '16 at 23:23