Apt 18: The Secret Upgrade That Tech Giants Are Using (Shocking Reveal!)
*Laws of digital space are shifting—and A
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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.
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