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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?