Standard part

In non-standard analysis, the standard part function is a function from the limited (finite) hyperreal numbers to the real numbers. Briefly, the standard part function "rounds off" a finite hyperreal to the nearest real. It associates to every such hyperreal ${\displaystyle x}$, the unique real ${\displaystyle x_{0}}$ infinitely close to it, i.e. ${\displaystyle x-x_{0}}$ is infinitesimal. As such, it is a mathematical implementation of the historical concept of adequality introduced by Pierre de Fermat, as well as Leibniz's Transcendental law of homogeneity.

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