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i.e. can we write

$\pi = 3.14159\dots X\dots$

where $X$ consists of (say) $10^{100}$ consecutive zeroes?

[Originally asked on reddit without response :-( ]

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    The exact outcome of the 2016 US presidential election is coded in there somewhere. But there's no way for us to find it, or recognize it. Every possible *false* result is in there too! (assuming pi is normal)2014-09-04

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To expand on Dan Brumleve's comment; it is widely believed, but not proved, that, given any finite string of digits, that finite string appears somewhere in the decimal for $\pi$, in fact, occurs infinitely often, in fact, occurs about once every $10^n$ digits, where $n$ is the length of the string. The same is believed to hold true for $e$, $\sqrt2$, in fact, for pretty much any number known to be irrational and not constructed specifically to falsify the belief, but, again, nothing has been proved. For all we know, all the digits of $\pi$ from some point on are sixes and sevens.

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    D'oh. Good point.2011-05-17