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  "body": "\n## Summary\n\nIn a [[partially ordered set|0QV2JS9RJ3]], the join of two elements is their least upper bound and the meet is their greatest lower bound.\nThey are written $x \\vee y$ and $x \\wedge y$.\nJoin and meet are the [[supremum|0R3H5PANRQ]] and the [[infimum|0QF1MZ9FRG]] of a two-element set, seen as binary operations.\nThey are the basic operations of lattice theory: a poset in which all joins and meets of pairs exist is a lattice.\n\n## Explanations\n\n### L1 human\n\nThink of the elements of a poset as points of a diagram, with larger elements drawn higher.\nThe join of $x$ and $y$ is the lowest point that lies above both; the meet is the highest point below both.\nFor sets ordered by inclusion, the join of $A$ and $B$ is $A \\cup B$ and the meet is $A \\cap B$.\nFor positive integers ordered by divisibility, the join of $4$ and $6$ is $\\lcm(4, 6) = 12$ and the meet is $\\gcd(4, 6) = 2$.\nIn some posets a join or a meet can fail to exist.\n",
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