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I'm trying to determine to what degree digits can be predicted in irrational numbers in general.

I learned about normal numbers via this prior question: Predicting digits in $\pi$, which seems to imply that if numbers can be normal, digits may not be predictable.

If that's the case, is this an open question?

DukeZhou
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    From Wikipedia (https://en.wikipedia.org/wiki/Normal_number#Properties_and_examples): ". . . the normal number theorem: almost all real numbers are normal, in the sense that the set of non-normal numbers has Lebesgue measure zero". As a consequence, if $x$ is randomly chosen from the interval $(0,1)$ (uniform distribution), then the probability that it is not normal is zero. – quasi Aug 09 '19 at 03:38

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If $x$ is randomly chosen from the uniform distribution on the interval $(0,1)$, the decimal digits of $x$ are independent, and equally likely to be $0,1,2,\ldots,9$. In this sense, the digits of a random number are completely unpredictable.

Robert Israel
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