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  "body": "\n## Summary\n\nA point of the domain where a real function is not [[continuous|0EEE2CZB2A]] is a discontinuity. Discontinuities are sorted by the behavior of the [[one-sided limits|0909PWZR62]] at the point.\n\n## Remarks\n\nAt a [[removable discontinuity|0QG9C579SR]], the limit exists but differs from the value.\nAt a [[jump discontinuity|05B0FKFXQA]], both one-sided limits exist but they differ.\nAt an essential discontinuity, at least one one-sided limit does not exist. An example is $\\sin(1/x)$ at $0$, with any value at $0$.\nA [[monotone function has countably many discontinuities|0WYTM4C9QG]], and all of them are jumps.\n\n## Explanations\n\n### L1 human\n\nA function can fail to be continuous in different ways.\nA hole in the graph can be repaired, a jump cannot, and some functions oscillate too wildly to have any limit.\n",
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