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Home » Solving, subtract the second from the first: - RedTag Digital

Solving, subtract the second from the first: - RedTag Digital

📅 May 17, 2026 👤 scraface

May 17, 2026

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for all $ a, b, c \in \mathbb{R} $.
f(a + b + c) = f(a) + f(b) + f(c) \quad \forall a, b, c \in \mathbb{R}
Let’s set $ a = b = c = 0 $:
f(0) = 3f(0) \Rightarrow 2f(0) = 0 \Rightarrow f(0) = 0
Now, set $ c = 0 $:
This is the **Cauchy Functional Equation**, whose solutions over $ \ma...
Under the Axiom of Choice, there are **infinitely many** additive func...
However, in the context of a math olympiad, and given the phrasing fin...
Thus, the number of such functions is equal to the number of real cons...
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