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When I write the asymptotic approximation of a function, does the sign convention matter? i.e. suppose I have (though the formula might not make sense) $$f_n(x)=x^2+\dots-O(n),$$ If my function is actually $\mathbf{-}O(n)$, do I write $-$ or is it convention to write $+$, no matter what?

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If you use the absolute value based definition, then it does not matter and normally $+$ is used.

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