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Jasper Deng (talk | contribs) →Non-trivial additive functions: wrong notion Tags: Mobile edit Mobile web edit Advanced mobile edit |
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{{See also|Cauchy's functional equation}}
A function <math>f : \Reals \to \Reals</math> is called an {{em|[[additive map|additive function]]}} if it satisfies [[Cauchy's functional equation]]:
<math display=block>f(x + y) = f(x) + f(y) \quad \text{ for all } x, y \in \Reals.</math>
For example, every map of form <math>x \mapsto c x,</math> where <math>c \in \Reals</math> is some constant, is additive (in fact, it is [[Linear map|linear]] and continuous). Furthermore, every linear map <math>L : \Reals \to \Reals</math> is of this form (by taking <math>c := L(1)</math>).
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