Standard part function: Difference between revisions

Revision as of 14:47, 22 May 2011

Revision as of 14:52, 22 May 2011

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In [[non-standard analysis]], the '''standard part function''' "st" is a mathematical implementation of [[Pierre de Fermat]]'s [[adequality]]{{factCitation needed|date=May 2011}}. It is the key ingredient in [[Abraham Robinson]]'s formalisation of Leibniz's [[infinitesimal]] definition (see [[ghosts of departed quantities]]) of the derivative as the ratio of two infinitesimals

:<math>\frac{dy}{dx}</math>,

see more at [[non-standard calculus]].

==Definition==

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:<math>\,\mathrm{st}(x)=x_0</math>.

The standard part of any [[infinitesimal]] is 0. Thus if N is an infinite [[hypernatural]], then (0.1)^N is infinitesimal, and st(0.1^N)=0.

The standard part function "st" is not defined by an [[internal set]] {{cnCitation needed|date=May 2011}}.

==See also==

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*H. Jerome Keisler: Elementary Calculus: An Approach Using Infinitesimals. First edition 1976; 2nd edition 1986. (This book is now out of print. The publisher has reverted the copyright to the author, who has made available the 2nd edition in .pdf format available for downloading at http://www.math.wisc.edu/~keisler/calc.html.)

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[[Category:Calculus]]