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  "body": "\n## Summary\n\nEvery [[partially ordered set|011C29Q1S1]] has a dual, obtained by reversing the order.\nEach order-theoretic notion has a dual notion: upper bound and lower bound, supremum and infimum, greatest and least element.\nThe duality principle says that a statement true for all posets stays true when every notion in it is replaced by its dual.\nThis halves the work in many proofs.\n\n## Explanations\n\n### L1 human\n\nTurn a picture of an order upside down, and you get another order: its dual.\nWhat was the top is now the bottom, and what was above is now below.\nSo every theorem about orders comes with a mirror theorem for free.\nFor example, the divisors of $12$ ordered by divisibility have greatest element $12$; in the dual order, $12$ is the least element.\n",
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