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  "body": "\n## Summary\n\nThe germ of a function at a point records the behaviour of the function on arbitrarily small [[neighbourhoods|0ZCY0Z80B6]] of the point and forgets the rest.\nTwo functions have the same germ at $x$ when they agree on some neighbourhood of $x$.\nGerms make local properties, such as derivatives and local power series, into properties of single objects.\nThey are the stalks of the sheaf of functions and appear throughout analysis, geometry and singularity theory.\n\n## Explanations\n\n### L1 human\n\nLook at a function through a microscope at one point, and keep zooming in.\nTwo functions have the same germ at the point if, after enough zoom, they look identical.\nFor example, $t \\mapsto t$ and $t \\mapsto \\abs{t}$ on $\\R$ have the same germ at $1$, since they agree on $(0, 2)$.\nThey have different germs at $0$, because every interval around $0$ contains negative numbers, where they differ.\n",
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