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  "body": "\n## Summary\n\nIn order theory, a completeness property of a partially ordered set says that every subset of a certain kind has a supremum, or an infimum.\nAll subsets give [[complete lattices|D7A0ZGZT5S]], and nonempty bounded subsets give [[conditionally complete lattices|CZPBQY67ZJ]].\nDirected subsets give [[directed-complete partial orders|7TSXP95QN6]].\nThese notions organize much of lattice theory and domain theory.\n\n## Explanations\n\n### L1 human\n\nAn ordered set is \"complete\" when some collections of its elements are sure to have a least upper bound.\nWhich collections are required depends on the context.\nAsking it for all finite nonempty sets gives a join-semilattice; asking it for every set gives a complete lattice.\nThe real numbers are complete for nonempty sets that are bounded above, and this is the form of completeness used in calculus.\n",
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