4 ms·

Can pi be recursive then? Can it contain itself? I think not.

• vollmond 9y ago
  To be fair, no other filesystem could contain pi either, right?
• avian 9y ago
  No. If pi would contain itself it would be a rational number. We have a proof that pi is irrational, hence it cannot contain itself.
  • gowld 9y ago
    Specifically, if pi contains itself, that means "pi - pi/b^k" is a terminating fraction N in base b", where b is your choice of base (like base 10), and k is some positive integer. So pi = N/(1-b^k) which is rational. (And if you set k=0, you get that pi "contains itself" in the sense that pi from the 1st digit onward is of course pi)
• klmr 9y ago
  > Can it contain itself? Well it does, trivially. You’re probably thinking of set theory but the file system is about storing information in a sequence and an offset. Seen that way, π can be stored with offset 0.
• deleted 9y ago
  [deleted]
• gnulinux 9y ago
  If it's normal then it contains all finite strings uniformly in its base-b expansions. Pi is not a finite string so it wouldn't have to contain itself uniformly. More specifically if it contains itself then it's a rational number, but we know that pi is not a rational number. Note that we don't know whether pi is a normal real number.