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  "body": "\n## Summary\n\nA Darboux function is a real function on an interval that has the intermediate value property.\nIt never skips a value between two of its values.\nEvery [[continuous function|0P27W9RW0G]] on an interval is a Darboux function by the [[intermediate value theorem|00KAFBR32E]].\nBy [[Darboux's theorem|0Q5A47J48D]], every derivative is a Darboux function too, even when it is not continuous.\nSo the class of Darboux functions is much larger than the class of continuous functions.\n\n## Explanations\n\n### L1 human\n\nImagine driving along a road whose height is given by the function.\nA Darboux function cannot get from height $0$ to height $1$ without passing every height in between.\nContinuous functions behave like this, but so do some wild functions.\nFor example, $\\sin(1/x)$ with value $0$ at $0$ wiggles infinitely often near $0$ and is not continuous there, yet it skips no values.\n",
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