the difference between big and small asymptotic notation

Question

I saw this example and i am a little confused.
$10n^2-5n+6046$=$ω(n^2)$
isn't that a mistake and it is necessary to use $Ω$?
because $n^2$=$n^2$

Answer 1

There is indeed a mistake in this example. $$\lim_{n\to\infty}\frac{10n^2-5n+6046}{n^2}=10\ne \infty$$ So $10n^2-5n+6046\ne \omega(n^2)$. However we can say that $10n^2-5n+6046=\Omega(n^2)$.