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see more at [[non-standard calculus]].
==Definition==
The [[hyperreal number|hyperreal]] line is an extension of the real line. Thus, every real number is accompanied by a cluster ([[monad (mathematics)|monad]]) of hyperreals infinitely close, or [[adequality|adequal]], to it. The standard part function associates to a [[Wikt:finite|finite]] [[hyperreal number|hyperreal]] ''x'', the standard real ''x<sub>0</sub>'' infinitely close to it, so that we can write
:<math>\,\mathrm{st}(x)=x_0</math>.
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