Find the values for n0 and the constant factor c such that f(n) = n log n is Ω(n)

Question

I was recently introduced to big O and big Omega, as well as big theta. I know that big O is the worse case scenario in terms of runtime, big Omega is the best case scenario, and big theta is in between. However, I'm still confused on how I would use it mathematically to prove that n log n = Ω(n). Also, I get that n0 is the lowest possible number for the equation to work, but where does the constant factor c come in? Any advice and help is greatly appreciated, thanks!

Answer 1

$\log(n) \ge 1$ for any $n>2$. Hence, if we choose $n_0=2$, then for any $n>n_0$ we have $n\log(n)\ge n\cdot 1 = n$. Thus, by the definition of $\Omega$, we have that $n\log(n) = \Omega(n)$.