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Questions about asymptotic notations such as Big-O, Omega, etc.

44 votes

O(·) is not a function, so how can a function be equal to it?

$O$ is a function $$\begin{align} O : (\mathbb{N}\to \mathbb{R}) &\to \mathbf{P}(\mathbb{N}\to \mathbb{R}) \\ f &\mapsto O(f) \end{align}$$ i.e. it accepts a function $f$ and yields a set of functi …
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