Talk:Cauchy's equation

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DISAMBIGUATION: Cauchy's equation can also refer to a functional equation of form

find f(x,y) for all x,y \in N such that f(x)+f(y) = f(x+y)

Solution is f(x) = k x. This can be expanded by construction to sets Z and Q.

However, in reals additional requirements for the sole simple solution are for example one of the following:

• there exists a finite interval, where f is bounded
• in every finite interval, f is bounded
• f is continuous
• f is Lipschitz-continuous
• f'(x) exists for all x \in R

Proofs for these can be found in standard literature.