Big-Omega Proof So I'm trying to figure this one out, suppose this problem A.
$f(n) = n^2 - 2n$ and $g(n) = n^2$.
I want to prove that $f(n) \in \Omega(g(n))$ by showing a set of inequalities between $f(n)$ to $g(n)$ to derieve the $c > 0$ and $n_0 > 0$.
For example, say
$f(n) = n^2 + 2n$ and $g(n) = n^2$ and $f(n) \in O(g(n))$.
Clearly, $n^2 + 2n \le n^2 + 2n^2 = 3n^2 \quad \forall n_0>0$ Thus, if $c = 3$ and $n_0 > 0$, we have proved $f(n) \in O(g(n))$.
How do I do this for the former problem, problem A?
Thanks.

For large $n$,
$$f(n)=n^2-2n \ge \frac{1}{2} n^2 = \frac{1}{2} g(n).$$
To find $n_0$ explicitly, note
$$n^2-2n - \frac{1}{2}n^2= \frac{1}{2} n(n-4) > 0$$
for $n>4$.
