Standard part function: Difference between revisions

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In [[non-standard analysis]], the '''standard part function''' "st" associatesis tothe akey [[finite]]ingredient [[hyperrealin number|hyperreal]]Abraham Robinson''x'',s resolution of the standardparadox realof Leibniz''xs definition of the derivative as the ratio of two infinitesimals <submath>0\tfrac{dy}{dx}</submath>'' infinitely close to it, sosee thatmore weat can[[non-standard writecalculus]].

==Definition==

The standard part function associates to a [[finite]] [[hyperreal number|hyperreal]] ''x'', the standard real ''x₀'' infinitely close to it, so that we can write

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