A function satisfying $f(x+y)=f(x)+f(y)$ known as Cauchy's functional equation. # Properties - [[Additive Functions are q-Linear]] - [[Real Function That is Both Additive and Multiplicative is either Zero or The Identity]]. - [[Existence of non-linear additive real functions]]. - [[Real function satisfying the functional equation f(xy+x+y)=f(xy)+f(x)+f(y) is necessarily additive]].