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For all $\epsilon$ we have that $f(n)\le \epsilon n$ where n is a natural number. What can we say about the growth of $f(n)$? Clearly $f(n)=O(n)$, can we say anything sharper?

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    If$f$is a real-valued function then all we can say is that$f(n)$= 0 for all n, and nothing else. If$f$is a natural-number-values function, then simply f(n) = 0 for all n.2012-05-06

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