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Cauchy's functional equation is the functional equation of linear independence () = () Solutions to this are called additive functionsOver the rational numbers, it can be shown using elementary algebra that there is a single family of solutions, namely ↦ for any rational constant Over the real numbers, ↦, now with an arbitrary real constant, is likewise a family of solutions. Æ æ è/¸ M D á / û!K ö$ï h$ 3 !. L Ѓv C x C g E A C Q R s ` 3 0 Q ψ ͏o @.

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