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  "body": "\n## Statement\n\nLet $a_0, a_1, \\dots, a_n$ be real numbers.\nThen the function $p \\colon \\mathbb{R} \\to \\mathbb{R}$ given by $p(x) = a_0 + a_1 x + \\cdots + a_n x^n$ is [[continuous|0P27W9RW0G]].\n\n## Remarks\n\nConstant functions and the identity $x \\mapsto x$ are continuous. Sums and [[products of continuous functions are continuous|0VGMHCF4SC]], so induction on $n$ gives the result.\nMathlib states it as `Polynomial.continuous`.\n\n## Explanations\n\n### L1 human\n\nPolynomials are built from $x$ and constants by addition and multiplication.\nThese operations keep continuity, so each polynomial is continuous.\n",
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