Question:
In my message about pi having lots of weird digits, I wanted to know if pi
contained every finite string of digits. Is the set of all such numbers
which have this property special? Is there a name for it. I am just
curious because it always seems that mathematicians have considered so
really oddball questions.

Replies:
No one knows if the decimal expansion of pi contains every finite string of
digits and no one ever will because only a finite number of digits may be
produced. Topics to look up for study include waiting times and expecta-
tions. The expected number decimal positions (starting at any unknown
value) before the onset of a string of 999 nines is 10^999 and then there is
only a reasonable probability (0.632) that the desired string will be found
in the 10^999 digits. A billion centuries is a small time interval compared
to the time it would take to try this out, given the best of modern comput-
ing speed.

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