4 ms·

No, this proves pi can not be written as a fraction. But not being a fraction does not imply that a number contains all sequences of digits.

• dragonwriter 3y ago
  As a fairly simple example, consider the number wirtten in decimal notation as: 0.101001000100001000001... (with an increasing-by-one sequence of zeroes between each successive 1.) It doesn't contain all sequences of digits, or even all digits, yet it cannot be written as a fraction.
  • constantcrying 3y ago
    >yet it cannot be written as a fraction. Is that trivial?
    • dragonwriter 3y ago
      > Is that trivial? My understanding is that it is a trivial (or at least well-known) result that a rational will always have a finite, infinitely-repeating terminal sequence in any base.
    • xigoi 3y ago
      Yes. It can quite easily (depending on your knowledge of basic number theory) be proven that a number is rational if and only if its digits (in any base) eventually become periodic.