Subadditivity

In mathematics, subadditivity is a property of a function that states, roughly, that evaluating the function for the sum of two elements of the domain always returns something less than or equal to the sum of the function's values at each element. There are numerous examples of subadditive functions in various areas of mathematics, particularly norms and square roots. Additive maps are special cases of subadditive functions.

A subadditive function is a function ${\displaystyle f\colon A\to B}$, having a domain A and an ordered codomain B that are both closed under addition, with the following property:

An example is the square root function, having the non-negative real numbers as domain and codomain, since ${\displaystyle \forall x,y\geq 0}$ we have:

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