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Cardinality of growth rates

$Let f=o(g)$ stand for $\lim_{x\to\infty} f(x)/g(x)=0$. It is simple to prove the following fact. Proposition. Let $f_0,f_1:\mathbb{R}\to(0,\infty)$ be such that $f_0=o(f_1)$. Then there is a family …
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