I'm very confused when I see the following statement in the famous CLRS book Introduction to Algorithms (3rd), ch34.2, page 1063:...and therefore the running time is $\Omega(m!)=\Omega(\sqrt{n}!)=\Omega(2^{\sqrt{n}})$...How can the second inequality be possible since $n!$ is super-exponential and it grows always faster than $2^n$? Perhaps i'm making a too stupid mistake?
Is $\Omega(\sqrt{n}!)=\Omega(2^{\sqrt{n}})$ correct?
complexity theory;time complexity;asymptotics