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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 with $g(x) \\ne 0$ for all $x \\in D$.\nThen the quotient $f/g$, given by $(f/g)(x) = f(x)/g(x)$, is continuous.\n\n## Remarks\n\nThe proof uses [[sequential continuity|0PAQM3H57X]] and the [[quotient rule for limits|03S6GWWKEZ]] of sequences.\nIf $g$ has zeros, then $f/g$ is continuous on the set where $g$ is not zero.\nMathlib states it as `Continuous.div`.\n\n## Explanations\n\n### L1 human\n\nDivision by a continuous function causes no problem away from its zeros.\nNear a point where $g$ is not zero, $g$ stays away from zero.\n",
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  "name": "Quotient of continuous functions is continuous",
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