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  "body": "\n## Summary\n\nThe standard part function sends each finite [[hyperreal number|421QMTFG9T]] $x$ to the unique [[real number|08J2M1JYAG]] $\\operatorname{st}(x)$ that is infinitely close to it.\nIt is the bridge back from the hyperreals to the reals in [[nonstandard analysis|WM62GKCBWN]].\nDerivatives, integrals and limits are defined as standard parts of hyperreal expressions.\n\n## Explanations\n\n### L1 human\n\nA finite hyperreal number is a real number plus an infinitely small error.\nThe standard part throws away the error and keeps the real number.\nFor example, if $\\varepsilon$ is a positive infinitesimal, then $\\operatorname{st}(3 + \\varepsilon) = 3$ and $\\operatorname{st}(\\varepsilon^2 - 5\\varepsilon) = 0$.\nAn infinite hyperreal such as $1/\\varepsilon$ has no standard part, because no real number is close to it.\n",
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