Example

By this definition, g(n) = 1/2 n is asymptotically bigger than $f(n) = 8 \sqrt{n}$. Why? Well, give me any scaling factor c.

\begin{eqnarraystar} g(n_0) &\gt& c f(n_0) \ 1/2 n_0 &\gt& c (8 \sqrt{n_0}) \ ... ...{n_0} &\gt& 16 c \ \sqrt{n_0} &\gt& 16 c \ n_0 &\gt& 256 c^2\end{eqnarraystar}

So, any n0 at least that big will satisfy the conditions of the definition.

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