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  "body": "\n## Definition\n\nLet $D \\subseteq \\mathbb{R}$, let $f \\colon D \\to \\mathbb{R}$, and let $a \\in D$ be a limit point of $D$.\nThe point $a$ is a removable discontinuity of $f$ if the [[limit|0TXTSEMHR5]] $L = \\lim_{x \\to a} f(x)$ exists and $L \\ne f(a)$.\n\n## Remarks\n\nChange the value of $f$ at $a$ to $L$. The new function is [[continuous at|0EEE2CZB2A]] $a$.\nFor example, let $f(x) = 1$ for $x \\ne 0$ and $f(0) = 0$. Then $0$ is a removable discontinuity.\nSome texts also call $a$ removable when $a \\notin D$ and the limit exists. An example is $\\sin(x)/x$ at $0$.\n\n## Explanations\n\n### L1 human\n\nAt a removable discontinuity, the graph has a single misplaced point.\nMoving this one point repairs the continuity.\n",
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