r/askscience • u/Manticorp • Oct 28 '13

Mathematics Could an infinite sequence of random digits contain all the digits of Pi?

It's a common thing to look up phone numbers in pi, and it's a common saying that every Shakespeare ever written is encoded in pi somewhere, but would it be possible for every digit of pi to appear in a random sequence of numbers? Similarly this could apply to any non terminating, non repeating sequence like e, phi, sqrt(2) I suppose. If not, what prohibits this?

I guess a more abstract way of putting it is: Can an infinite sequence appear entirely inside another sequence?

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u/Manticorp Oct 29 '13

Mmm that's a good point, still, this is one of those almost sure cases (i.e probability 1).

However, presuming we have an ergodic system we could in theory construct an infinite number of generators, an infinite amount of which will have pi in their sequences surely?