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  "body": "\n## Definition\n\nLet $D \\subseteq \\mathbb{R}$, let $f \\colon D \\to \\mathbb{R}$ be a function, and let $a \\in D$.\nThe function $f$ is continuous at $a$ if the following holds.\nFor each open interval $V$ containing $f(a)$ there is an open interval $U$ containing $a$ with $f(x) \\in V$ for all $x \\in U \\cap D$.\n\n## Remarks\n\nIf $a$ is a limit point of $D$, then $f$ is continuous at $a$ if and only if $\\lim_{x \\to a} f(x) = f(a)$. See [[limit of a function|0TXTSEMHR5]].\nIf $a$ is an isolated point of $D$, then each function on $D$ is continuous at $a$.\nThe [[epsilon-delta form|0W8YHHGCJG]] states the same condition with numbers.\nMathlib defines it for topological spaces, as `ContinuousAt`.\n\n## Explanations\n\n### L1 human\n\nA function is continuous at $a$ if small changes of $x$ near $a$ give small changes of $f(x)$.\nThe graph has no jump or gap at $a$.\n",
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