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  text: 'The proof of (5) only goes through for $n\\in\\mathbb{N}$.\n\nYou can prove a version of (8) from (5), namely, $f(b)=1\\Rightarrow f(b^q)=q$ for $q\\in\\mathbb{Q}$, but this doesn't pin down $f$ completely, unless you include a continuity condition.',
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