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Quote from: imatfaal on 09/02/2012 12:01:15Mad mathematicians would tell you that the ratio of two infinitessimals can be anything you choose (kind of like the ration of two infinities it is not well defined).No, AFAIK that's definitely wrong. The reason that calculus works is that the LIMIT of dy/dx as you take the deltas towards zero is (in most normal cases) completely well defined. In some case limits can take two values in different directions where the curve jumps, so the curve has to be smooth where you differentiate; trying to differentiate a fractal doesn't do anything very good!

Mad mathematicians would tell you that the ratio of two infinitessimals can be anything you choose (kind of like the ration of two infinities it is not well defined).

yes - but when you deal with limits approaching zero or off to infinity things become very complicated - instantaneous measurements calculations etc can become very screwy .

Actually, isn't this, to some extent, what the OP was referring to?These points are interesting to the mathematically inclined, but to the average engineer who just wants to solve a stinking problem, they might appear slightly esoteric and academic. It's like any tool. The experts will test it to the limits and understand all of its corner-cases. The rest of us will use it like any other hammer, and, if it doesn't work, we'll get a bigger one.