I was solving the problems provided in CLRS exercises and I came through this one which read: $\max(f(n), g(n)) = \Theta(f(n) + g(n))$
I got this interesting answer and understood everything: https://math.stackexchange.com/a/267255/492010
Except for one line which read: $\max(f(n), g(n)) \in \mathcal{\Omega}(f(n) + g(n))$
As far as I have read in CLRS definition for CLRS is defined as: $\Omega(g(n))= \{f(n):$ there exist positive constants c and $n_0$ such that $0\le c.g(n) \le f(n)$ for all $n\ge n_0$}
Coming to the answer provided. It had a line : $f(n) + g(n) \leq 2 \max(f(n),g(n))$ Following that I am confused that how come he proved that:
$max(f(n),g(n)) \in \Omega(f(n)+g(n))$
Does that mean: $0 \le c.(f(n)+g(n))\le max(f(n),g(n))$ ?
Please help. Thank you.