It is very common in non-rigorous calculus classes to perform operations of the form $$\frac{dy}{dx} = f'\left(x\right) \implies dy = f'\left(x\right) dx$$ As if these are simply numbers. How is this formally dealt with? From the minimal understanding I have, people have gone out of their way to develop the hyperreal numbers to formalise procedures such as this. Is that all there is to it?
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6This question has been asked so many times before – tryst with freedom May 03 '22 at 07:26
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@Buraian . +1 Please vote to close . – Kurt G. May 03 '22 at 09:09
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See also this and many other similar questions. – Hans Lundmark May 03 '22 at 09:09