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What if it's not random but π? https://github.com/philipl/pifs https://github.com/philipl/pifs

• cbd1984 11y ago
  > What if it's not random but π? π is known to never repeat (that is, it's irrational); it is not, however, known to be normal. That means the digits in its decimal expansion (to pick a base) are not known to be normally distributed. This means that it is not necessarily the case that every possible sequence of decimal digits is present in π. For example, for all we know it's the case that beyond a certain (massively huge) number of decimal places, π never contains another '7'. That would render some sequences impossible, while still preserving the proven-to-be-true property that π never repeats itself in its entirety (that is, that it's irrational).
  • leni536 11y ago
    > That means the digits in its decimal expansion (to pick a base) are not known to be normally distributed. You mean uniformly distributed. Being a normal number states more than that: any finite sequence of digits are uniformly distributed. While you are right that Pi isn't proven to be normal, constructing a normal number isn't exactly hard. I think the following number is proven to be normal (binary representation, I added spaces for clarity): 0.0 1 00 01 10 11 001 010 011 100 101 110 111 ... It's clear to see that this number contains all possible finite binary sequences.