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  "body": "\n## Summary\n\nThe Dedekind number $M(n)$ is the number of monotone [[Boolean functions|0X05GS525E]] of $n$ variables.\nIt also counts the [[antichains|03HF498P1J]] of subsets of an $n$-element set.\nFor $n \\ge 1$, $M(n) - 2$ is the number of elements of the [[free distributive lattice|T5GK6DH8BR]] on $n$ generators.\nThe first values are $M(0) = 2$, $M(1) = 3$, $M(2) = 6$, $M(3) = 20$, $M(4) = 168$ and $M(5) = 7581$.\nThe numbers grow very fast, and no closed formula for them is known; finding one is [[Dedekind's problem|RM64J2CP1M]].\n\n## Explanations\n\n### L1 human\n\nA monotone Boolean function is a yes/no rule on $n$ switches.\nIn such a rule, turning a switch on can never change the answer from yes to no.\nThe Dedekind number counts these rules.\nFor two switches $x$ and $y$ there are six: always no, always yes, $x$, $y$, \"$x$ and $y$\", and \"$x$ or $y$\".\nThe rule \"exactly one of $x$, $y$\" is not monotone.\nWith $x$ on, turning on $y$ changes the answer from yes to no.\n",
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