Dose there a function $f: \mathbb{R} \to \mathbb{R}$ satisfying $f(a+b) = f(a)+f(b)\quad\forall a,b\in\mathbb{R}$ But not of the form $f(x)= \lambda x$ ? Such $f$ must necessarily be discontinuous
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3@Ameryr Are you sure $e^{x+y}=e^x+e^y$? – C. Falcon Mar 22 '17 at 15:50
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1@C.Falcon I don't think those are duplicates the linked question asks for continuous functions. – kingW3 Mar 22 '17 at 16:02
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Oh sorry i deleted my comment – IrbidMath Mar 22 '17 at 18:55