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  "body": "\n## Summary\n\nA conditionally complete lattice is a lattice in which every nonempty bounded-above subset has a supremum and every nonempty bounded-below subset has an infimum.\nIt is the order-theoretic form of the completeness of the [[real numbers|08J2M1JYAG]].\nUnlike a [[complete lattice|D7A0ZGZT5S]], it need not have a least or a greatest element.\n\n## Explanations\n\n### L1 human\n\nThe real numbers are not a complete lattice, because the set of all integers has no upper bound.\nBut every nonempty set of reals that does have an upper bound has a least one.\nA conditionally complete lattice is an ordered set with this weaker property, together with the matching property for lower bounds.\nThe integers are another example: a nonempty set of integers that is bounded above has a largest element, which is its supremum.\nThe rational numbers are not an example, since the rationals below $\\sqrt{2}$ have no least rational upper bound.\n",
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