Number sequence is present in the decimal expansion of pi?

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SUMMARY

The discussion centers on the assertion that every possible finite number sequence is present in the decimal expansion of pi. While it is acknowledged that pi is a determined sequence to the nth digit, the ability to prove the presence of every finite subsequence remains unverified. The concept of a truly random infinite sequence suggests that any finite subsequence has a non-zero probability of occurrence, particularly under a uniform distribution where each digit from 0-9 has equal probability.

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  • Knowledge of probability theory, specifically uniform distribution
  • Basic comprehension of the decimal expansion of irrational numbers
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the4thamigo_uk
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Is it true that every possible finite number sequence is present in the decimal expansion of pi?
 
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the4thamigo_uk said:
Is it true that every possible finite number sequence is present in the decimal expansion of pi?

I don't think there's any way to prove that. It's a completely determined sequence to the nth digit. I think you can only talk about the characteristics of what actually has been calculated.

For a truly random infinite sequence, you could say that any finite subsequence of digits has a non-zero probability of occurring. For a uniform distribution (each digit 0-9 has the same probability of occurring), the probability of any given sequence of length k occurring is [tex](0.1)^{k}[/tex].
 
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