The most fundamental doubt/question about calculus is: Can we use operators in association with the infinitesimal dX? The doubt araises because of the nature of the infinitesimal. If X decreases by an infinitesimal dX, then for obvious reasons we have no idea, whatsoever, about the change. Y is related to X. Every change in X CAUSES some 'predictable' change in Y. 'Predictable' because we express the relation between X and Y by a formula, say: XY=1. It means, 'if X increases Y decreases and the product XY=a constant.' OR 'if X decreases Y increases and the product is constant.' We can always justify the statement that X increases by dX and becomes X+dX. We are also sure that if XY=1 and X becomes X+dX, Y must have decreased, and that there must be an operator associated with dY. My question is: Is our assumption that if X becomes X+dX then Y must become Y-dY and that (X+dX)*(Y-dY)=1 true? Our ignorance about the rate at which Y would decrease compels us to say that dY=F(Y). I am right, or wrong?
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