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Home » You NEVER Saw the Yōtei Ghost—Here’s What Actually Scares the Dead! - Abbey Badges

You NEVER Saw the Yōtei Ghost—Here’s What Actually Scares the Dead! - Abbey Badges

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 Now suppose $ f $ is not constant.

📌 Let’s try additive functions satisfying both properties. From the additive condition, set $ c = 0 $:

📌 f(a + b) = f(a) + f(b)

📌 So $ f $ is additive. Also, from the multiplicative condition:

📌 So $ f $ is both additive and multiplicative. These are very restrictive properties.

📌 Known result: The only functions $ f : \mathbb{R} \to \mathbb{R} $ that are both additive and multiplicative are:

📌 $ f(x) = 0 $ for all $ x $

📌 $ f(x) = x $ for all $ x $

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