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📅 May 14, 2026 👤 scraface

May 14, 2026

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📝 Recent Posts

So $ f $ is both additive and multiplicative. These are very restricti...
Known result: The only functions $ f : \mathbb{R} \to \mathbb{R} $ tha...
$ f(x) = 0 $ for all $ x $
$ f(x) = x $ for all $ x $
Let’s verify both:
$ f(x) = 0 $: $ f(a + b + c) = 0 = 0 + 0 + 0 = f(a) + f(b) + f(c) $, a...
$ f(x) = x $: $ f(a + b + c) = a + b + c = f(a) + f(b) + f(c) $, and $...
Are there any others? Suppose $ f $ is additive and multiplicative. Th...
If $ f(1) = 0 $, then $ f(n) = 0 $ for all integers $ n $, and by addi...
Hence, only two such functions exist.

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