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Home » They’re More Than a Match – Mom & Daughter Shine Together in These Stunning Gowns! - go-checkin.com

They’re More Than a Match – Mom & Daughter Shine Together in These Stunning Gowns! - go-checkin.com

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Under the Axiom of Choice, there are **infinitely many** additive functions (including pathological ones), but if we restrict to **real-valued additive functions** (without further constraints), the number of such functions is uncountably infinite.

📌 However, in the context of a math olympiad, and given the phrasing find the number of functions, we assume the standard assumption of **linear solutions**, i.e., $ f(x) = kx $.

📌 Thus, the number of such functions is equal to the number of real constants $ k $, which is uncountably infinite. But if we are to count **distinct functions**, and assuming only linear solutions are acceptable, the number is infinite.

📌 However, if the problem is interpreted as asking for the number of **continuous** solutions, then the only such functions are linear: $ f(x) = kx $, and there are infinitely many such functions (one for each real $ k $).

📌 Hence, the number of such functions is $ \boxed{\infty} $, assuming no further restrictions.

📌 Question: Let $ x, y, z $ be positive real numbers such that $ x + y + z = 3 $. Find the minimum value of

📌 \frac{x^2}{y + z} + \frac{y^2}{z + x} + \frac{z^2}{x + y}.

📌 Solution: We are to minimize

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