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Alternatively, if <math>y=f(x)</math>, one takes an infinitesimal increment <math>\Delta x</math>, and computes the corresponding <math>\Delta y=f(x+\Delta x)-f(x)</math>. One forms the ratio <math>\frac{\Delta y}{\Delta x}</math>. The derivative is then defined as the standard part of the ratio:
:<math>\frac{dy}{dx}=\mathrm{st}\left( \frac{\Delta y}{\Delta x} \right)</math>.
Similarly, one defines the integral as the standard part of an infinite Riemann sum when the value of $\Delta x$ is taken to be infinitesimal.
==See also==
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