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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. { k ɂ A g G A i ڂ j ɂāA V o A N Z T Ƀ} b W O y A O A l b N X ̃I _ C h s Ă moge i Q j 񂱂ƎR i A N Z T ́A ӂ A A ₳ Ԃ̗ ܂ B. } I Q @ X p A W F t b V Q w PR j E o Q ւ.

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