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  "body": "\n## Definition\n\nLet $I$ be an open interval and let $f \\colon I \\to \\mathbb{R}$.\nThe function $f$ is smooth, or of class $C^{\\infty}$, if it is of [[class $C^k$|06SKCHDQT5]] for each natural number $k$.\n\n## Remarks\n\nSo a smooth function has derivatives of all orders.\nPolynomials, the exponential function, and the sine are smooth on $\\mathbb{R}$.\nA smooth function need not be [[analytic|0JD5ZNW0F4]]. See the [[smooth non-analytic function|09RTYYHXKA]].\nMathlib uses `ContDiff ℝ ⊤ f`.\n\n## Explanations\n\n### L1 human\n\nA smooth function can be differentiated as many times as we like.\nAll its derivatives exist and are continuous.\n",
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