f(x+y) = f(x) + f(y). Continuous solutions: f(x) = cx. Without continuity: pathological solutions exist (need axiom-of-choice). D'Alembert 1747; Cauchy 1821. Foundation for characterising linear maps + entropy uniqueness.
f(x+y) = f(x) + f(y). Continuous solutions: f(x) = cx. Without continuity: pathological solutions exist (need axiom-of-choice). D'Alembert 1747; Cauchy 1821. Foundation for characterising linear maps + entropy uniqueness.