# Is this a true statement? [duplicate]

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?

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

• 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. – Daniel Fischer Nov 2 '14 at 20:01
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.