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  "body": "\n## Summary\n\nA subadditive function is a function $f$ with $f(x + y) \\le f(x) + f(y)$ for all $x, y$ in its domain.\nThe triangle inequality says that every [[norm|0V2WP9B1MF]] is subadditive, and every [[sublinear function|K3356N0SAX]] is subadditive.\nFor subadditive sequences, [[Fekete's lemma|8A4GGX1MEY]] shows that $f(n)/n$ converges to its infimum, which may be $-\\infty$.\nThis makes subadditivity a basic tool for growth rates in analysis, combinatorics and ergodic theory.\n\n## Explanations\n\n### L1 human\n\nA function is subadditive when the whole costs at most the sum of its parts.\nShipping costs are a picture: sending two parcels together usually costs no more than sending them apart.\nThe square root is subadditive on $[0, \\infty)$: for example $\\sqrt{9 + 16} = 5 \\le 3 + 4$.\nThe absolute value on $\\R$ is subadditive by the triangle inequality.\n",
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