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 :-( ]
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 :-( ]
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.