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  "body": "\n## Summary\n\nLet $L$ be a [[lattice|WH4SFAACAS]] with a least element $0$, and let $a \\in L$.\nThe pseudocomplement of $a$ is the largest element whose meet with $a$ is $0$, when such an element exists.\nIt is written $a^*$.\nIn a [[Boolean algebra|0XADJKM699]] it is the usual complement, and in a [[Heyting algebra|NG943XNQWH]] it is $a \\to 0$.\nPseudocomplements give a weak, intuitionistic form of negation.\n\n## Explanations\n\n### L1 human\n\nThe pseudocomplement of $a$ is the biggest thing that does not overlap $a$ at all.\nFor the open sets of the real line, the pseudocomplement of an open set $U$ is the interior of its complement.\nIf $U = (0, 1)$, this is $(-\\infty, 0) \\cup (1, \\infty)$.\nThe points $0$ and $1$ belong neither to $U$ nor to $U^*$, so $U \\cup U^*$ is not the whole line, unlike a true complement.\n",
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