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The infinite monkey theorem states that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type a given text, such as the complete works of William Shakespeare.
My question is actually if pi is a "random" sequence of numbers. (I've read in other posts that it's likely to be such a sequence, and that e.g. irrationality isn't a sufficient condition, as can be seen in 0.01001000100001...) But is there an elegant mathematical way to proof if a number is such a random sequence? Or can it be proven with statistics/numerical methods with a kind of certainty that it's such a number?
EDIT: people stated that the exact mathematical term for "random" that I was searching for, should've been "normal". So my questions boils down to:
Pi is likely to be a normal number; if it is, it contains every sequence of numbers. But if it isn't, does it then contain every sequence of numbers (although in this case not with the same likelihood)? Or is this not sure (or even a contradiction)?