Definition:Cauchy Functional Equation

Definition
Let $f: \R \to \R$ be a real function.

Then the Cauchy functional equation is:


 * $\forall x, y \in \R: \map f {x + y} = \map f x + \map f y$

Also see

 * The fifth problem on Hilbert's list is a generalisation of this equation.


 * Definition:Additive Function (Conventional): a real function that satisfies this equation