> What's surprising (to many) is that
> n! < exp(n log n)
Why would that be surprising? I can see that many wouldn’t know whether it’s true, but
exp(n × log n) =
exp(log(n) × n) =
exp(log(n))^n =
n^n
and it’s not surprising that 1 × 2 × 3 × 4 × … × n
< n × n × n × n × … × n
for n > 1
I don't know why that is surprising, but I'm teaching computer science at a university, and students seem surprised every time it comes up.