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In [[non-standard analysis]], the '''standard part function''' "st" is the key ingredient in [[Abraham Robinson]]'s resolution of the paradox of Leibniz's definition of the derivative as the ratio of two infinitesimals <math>\tfrac{dy}{dx}</math>, see more at [[non-standard calculus]].
==Definition==
The standard part function associates to a [[finite]] [[hyperreal number|hyperreal]] ''x'', the standard real ''x<sub>0</sub>'' infinitely close to it, so that we can write
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