> 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

    1 × 2 × 3 × 4 × … × n
  < n × n × n × n × … × n

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.