True or false: If $f(n)=\omega(g(n))$ then exists $h(n)$ so $h(n)=\omega(g(n))$ and $f(n)=\omega(h(n))$?
I think this is true but can't seem to prove it. I tried playing around with the definition that from some $n$: $f(n)>c\cdot g(n)$ but I didn't really get anywhere.