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  "body": "\n## Summary\n\nA superadditive function is a function $f$ with $f(x + y) \\ge f(x) + f(y)$ for all $x, y$ in its domain.\nIt is the mirror image of a [[subadditive function|3X9DD9J3CV]]: $f$ is superadditive exactly when $-f$ is subadditive.\nFor superadditive sequences, [[Fekete's lemma|8A4GGX1MEY]] gives that $a_n / n$ converges to its supremum, which may be $+\\infty$.\nSuperadditivity describes situations where joining parts gains something, as for convex functions vanishing at $0$.\n\n## Explanations\n\n### L1 human\n\nA function is superadditive when the whole is worth at least the sum of its parts.\nThe square function on $[0, \\infty)$ is an example: $(3 + 4)^2 = 49$ is more than $3^2 + 4^2 = 25$.\nThe number of pairs that can be formed from a group of people is another: two groups merged have all the old pairs and some new ones.\n",
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