How about ANY FINITE SEQUENCE AT ALL?

  • @[email protected]
    link
    fedilink
    English
    13 months ago

    Pi is often defined as 3.141 592 653… Does that mean Pi does not contain any 7s or 8s?

    • cosecantphi [he/him, they/them]
      link
      fedilink
      English
      1
      edit-2
      3 months ago

      That’s a decimal approximation of Pi with an ellipsis at the end to indicate its an approximation, not a definition. The way the ellipsis is used above is different. It’s being used to define a number via the decimal expansion by saying it’s an infinite sum of negative powers of 10 defined by the pattern before the ellipsis.

      So we have:

      0.101001000100001000001 . . . = 10^-1 + 10^-2 + 10^-3 + 10^-4 +10^-5+ . . .

      Pi, however, is not defined this way. Pi can be defined as twice the solution of the integral from -1 to 1 of the square root of (1-x^2), a function defining a unit semi-circle.