Is Pi Truly Normal? Investigating the Occurrence of Finite Digit Strings

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The discussion centers on the question of whether any given finite string of digits appears in Pi. Currently, there is no proof or disproof confirming that all finite digit strings occur within Pi. This uncertainty relates to the concept of Pi being a "normal number," which remains unproven. The difficulty in establishing this property complicates the investigation into the occurrence of digit strings. Overall, the normality of Pi and its implications for digit strings remain unresolved.
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Is there a proof or disproof that any given finite string of digits will occur somewhere in Pi?
 
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No, there isn't. That would be equivalent, I think, to saying that \pi is a "normal number" and that has not been proved or disproved.
 
It smells equivalent to the property of normalness, but I'm not sure if it is easy to prove..
 

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