Number sequence is present in the decimal expansion of pi?

In summary, it is not possible to prove that every possible finite number sequence is present in the decimal expansion of pi. The sequence is completely determined to the nth digit and can only be described based on what has been calculated. However, for a random infinite sequence, there is a non-zero probability of any finite subsequence of digits occurring. For a uniform distribution, the probability of any given sequence of length k occurring is (0.1)^{k}.
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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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Related to Number sequence is present in the decimal expansion of pi?

1. What is the significance of number sequence in the decimal expansion of pi?

The number sequence in the decimal expansion of pi is significant because it is a never-ending, non-repeating pattern of digits that has been studied and calculated for centuries. It is also considered a fundamental constant in mathematics and plays a crucial role in many mathematical and scientific applications.

2. How many digits of pi have been calculated and what is the current record?

As of 2021, the current record for the most digits of pi calculated is 50 trillion digits. However, for practical purposes, only a few digits are needed for most mathematical and scientific calculations.

3. Is there a pattern to the number sequence in the decimal expansion of pi?

No, the number sequence in the decimal expansion of pi is considered to be random and does not follow any specific pattern or formula. It has been proven to be an irrational number, meaning it cannot be expressed as a ratio of two integers.

4. How is the number sequence in the decimal expansion of pi calculated?

The number sequence in the decimal expansion of pi is calculated using various mathematical methods and algorithms, such as the Chudnovsky algorithm and the Bailey-Borwein-Plouffe formula. These methods use advanced computing techniques to calculate more and more digits of pi.

5. Is there an end to the number sequence in the decimal expansion of pi?

No, there is no end to the number sequence in the decimal expansion of pi. It is an infinite, non-repeating pattern of digits. However, as mentioned earlier, for practical purposes, only a few digits are needed for most calculations and applications.

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