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  "body": "\n## Statement\n\nLet $D \\subseteq \\mathbb{R}$ and let $f, g \\colon D \\to \\mathbb{R}$ be [[continuous|0P27W9RW0G]] functions.\nThen the sum $f + g$ and the product $f g$, given by $(f g)(x) = f(x) g(x)$, are continuous.\n\n## Remarks\n\nThe proof uses [[sequential continuity|0PAQM3H57X]] and the [[product rule for limits|0734RSVF2V]] of sequences.\nIn particular, $c f$ is continuous for each constant $c$.\nMathlib states it for topological monoids, as `Continuous.mul`.\n\n## Explanations\n\n### L1 human\n\nIf $f(x)$ and $g(x)$ change only a little when $x$ changes a little, so does $f(x) g(x)$.\n",
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