Proving Big-Omega

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I have a tutorial sheet that asks:

Prove that $n^2 - 3$ is $\Omega(n^2)$

I understand that:

$$f(n) ≥ c g(n) $$

And that to $c > 0$ & $n > n_{0}$

The problem is that what ever $C$ value I use I keep ending up where the $n^2$ value shall fall into the negative domain.

Any help would be greatly appreciated

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1 Answer

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$\dfrac{n^2}2$ remains below $n^2-3$ as of $n=3$. Then you have it.

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