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We know that there are an infinite number of primes (Euclid's theorem). We don't yet know whether or not every possible sequence of data occurs in the digits of
by shawnz 14y ago
We know that there are an infinite number of primes (Euclid's theorem). We don't yet know whether or not every possible sequence of data occurs in the digits of pi, but it's highly suspected (this would make pi a "normal number" if true).
- scarmig 14y agoIsn't a normal number ever so subtly different from that? In that not only does every possible sequence of data occur in the digits of a normal number, but each sequence occurs an infinite number of times with likelihood proportional to the number of digits. Infinities always mix up my intuitions, though, so they might be equivalent.
- sold 14y agoYou are correct, normality is a stronger criterion. See http://en.wikipedia.org/wiki/Disjunctive_sequence http://en.wikipedia.org/wiki/Disjunctive_sequence
- deleted 14y ago[deleted]
- Zenst 14y agoTrue, it was one of those `gravity` moments or feelings about it perhaps -- You know it is there but still have not proven how it fully works, though my a physics aspect but I do like to think of them hand in hand. Perhaps another bias perceptional thought process, sorry my bad.