Factorial-time algorithms and P/NP

Question

It\'s quite easy to see that n! grows slower than almost anything to the N power (say, 100^N) and so, if a problems is considered NP complete and one happened upon a n! algorith

Answer 1

It's quite easy to see that the factorial is (approximately) exponential in behaviour.

It can be (very crudely) approximated as nⁿ (more specifically, sqrt(2πn)(n/e)ⁿ).

So if you have found any specific M where you think Mⁿ is a good approximation, you're (probably) wrong. 269! is larger than 100ⁿ and as n! will be multiplied by numbers larger than 100, it will continue to grow faster.