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  "body": "\n## Definition\n\nLet $c \\in \\mathbb{C}$ and let $f$ be a complex function.\nThe point $c$ is an isolated singularity of $f$ if there is $r \u003e 0$ such that $f$ is defined and [[holomorphic|0DG0Z72CQD]] on the punctured disc $\\{z : 0 \u003c |z - c| \u003c r\\}$.\nThe value of $f$ at $c$, if there is one, plays no role.\n\n## Remarks\n\nEach isolated singularity is of exactly one of three types: [[removable|0P18JC72RE]], a [[pole|0WPQYW8MTE]], or [[essential|0YKDJBV26S]].\nFor example, $0$ is an isolated singularity of $1/z$, of $\\frac{\\sin z}{z}$ and of $e^{1/z}$.\nThe point $0$ is not an isolated singularity of $\\frac{1}{\\sin(1/z)}$, because the poles $\\frac{1}{k\\pi}$ accumulate at $0$. It is not an isolated singularity of $\\operatorname{Log} z$ either, because $\\operatorname{Log}$ is not holomorphic on any punctured disc around $0$.\n\n## Explanations\n\n### L1 human\n\nAn isolated singularity is a single bad point of a function, with only good points around it.\nThe function is holomorphic on a small disc around the point, with only the center removed.\n",
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