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  "body": "\n## Summary\n\nThe way-below relation $x \\ll y$ on a partially ordered set says that $x$ is a necessary part of every directed approximation of $y$.\nIt refines the order $x \\le y$ and formalizes the idea of \"a finite piece of information about $y$\".\nIt is used to define [[continuous lattices|RXBD58SGXZ]] and continuous domains, and an element is [[compact|9F7TYES4KE]] exactly when it is way below itself.\n\n## Explanations\n\n### L1 human\n\nSuppose $y$ is approached by a directed family of elements, for instance an increasing sequence.\nThen $x$ is way below $y$ if every such approach to $y$ passes above $x$ at some finite stage.\nIn the real interval $[0, 1]$, the number $0.4$ is way below $0.5$, because any increasing sequence with limit at least $0.5$ eventually exceeds $0.4$.\nBut $0.5$ is not way below itself, because the sequence $0.5 - 1/n$ approaches $0.5$ without reaching it.\n",
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