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 (see Ghosts of departed quantities) of the derivative as the ratio of two infinitesimals
see more at non-standard calculus.
The standard part function associates to a finite hyperreal x, the standard real x0 infinitely close to it, so that we can write
The standard part of any infinitesimal is 0. ...
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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 (see Ghosts of departed quantities) of the derivative as the ratio of two infinitesimals
see more at non-standard calculus.
The standard part function associates to a finite hyperreal x, the standard real x0 infinitely close to it, so that we can write
The standard part of any infinitesimal is 0. Thus if N is a hypernatural, then (.1) is infinitesimal, and st(.1)=0.
The existence of the standard part function is a consequence of the completeness of the reals or the fact that finite closed intervals of the reals are compact.
The standard part function "st" is not an internal object.
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