Thread

1. emil-lp · 1789585468 · focus · HN ↗

   What's surprising (to many) is that

   n! < exp(n log n)

   1. Someone · 1789587074 · focus · HN ↗

      > 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

      1. emil-lp · 1789587635 · focus · HN ↗

         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.
   2. [deleted] · 1789587431 · focus · HN ↗

      [deleted]

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