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This is a 9GAG picture I saw tonight. The way it's put, it is evidently false, since 0.10100100010000… (the powers of 10 all in a row) is definitely decimal, infinite and nonrepeating (or in one word, irrational), but most surely doesn't contain every possible number combination. I was just wondering: can this be proved for pi? And more in general, are there sufficient conditions for a decimal number to contain, in its decimal expansion, all possible number sequences?

PS I wasn't sure how to tag this. I think this question deserves more than just the tag "pi". Any ideas on another tag for this question?

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marked as duplicate by Daniel Fischer, Mauro ALLEGRANZA, Carl Mummert, user147263, Ali Caglayan Nov 2 '14 at 21:38

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    $\begingroup$ I'm pretty sure this is a duplicate and has been answered here before. It is not known whether $\pi$ is normal in base $10$ (or in any base), but since almost all numbers are normal (in all bases) the chances aren't bad. $\endgroup$ – Daniel Fischer Nov 2 '14 at 20:01
  • $\begingroup$ @DanielFischer there is nothing random here, it is or is not ;) $\endgroup$ – mookid Nov 2 '14 at 20:07
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It is not known which patterns of numbers occur in the decimal expansion of $\pi$. I saw a reference that said we don't even know whether or not arbitrarily long strings of $9$'s, for example, occur.

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