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  "body": "\n## Summary\n\nA directed-complete partial order, or dcpo, is a partially ordered set in which every directed subset has a supremum.\nDcpos are the basic objects of [[domain theory|Q2P5D74Q1V]], where elements are read as pieces of information and directed sets as consistent ways of collecting information.\nMany authors also ask for a least element and call the result a pointed dcpo or a cpo.\n\n## Explanations\n\n### L1 human\n\nThink of the elements as partial results of a computation, ordered by \"is less defined than\".\nA directed set is a collection of partial results in which any two have a common improvement inside the collection.\nIn a dcpo, such a collection always has a best combined result, its supremum.\nEvery complete lattice is a dcpo.\nThe partial functions from $\\N$ to $\\N$, ordered by extension, form a dcpo: the supremum of a directed family of partial functions is their union.\n",
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