Superadditive function

Summary

A superadditive function is a function $f$ with $f(x + y) \ge f(x) + f(y)$ for all $x, y$ in its domain. It is the mirror image of a subadditive function: $f$ is superadditive exactly when $-f$ is subadditive. For superadditive sequences, Fekete's lemma gives that $a_n / n$ converges to its supremum, which may be $+\infty$. Superadditivity describes situations where joining parts gains something, as for convex functions vanishing at $0$.