It does not matter how slowly you go as long as you do not stop

Historically, the symbol dx was taken to represent an infinitesimally “small piece” of the independent variable x to be multiplied by the integrand and summed up in an infinite sense. While this notion is still heuristically useful, later mathematicians have deemed infinitesimal quantities to be untenable from the standpoint of the real number system. In introductory calculus, the expression dx is therefore not assigned an independent meaning.

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