Comment on i and π

flyos@jlai.lu ⁨1⁩ ⁨year⁩ ago

• silent_water@hexbear.net ⁨1⁩ ⁨year⁩ ago

  it’s definitely 5-adicly rational

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  • flyos@jlai.lu ⁨1⁩ ⁨year⁩ ago

    Out of curiosity, I guess pi cannot be rational in any p-adic set, right?

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    • silent_water@hexbear.net ⁨1⁩ ⁨year⁩ ago

      yeah, the remainder of pi after p^2 for p>2 will always be the same as the remainder after division by p (p^2 if p=2), so it truncates to the left of the radix, and p-adic rationals can’t go off infinitely to the right of the radix.

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      • flyos@jlai.lu ⁨1⁩ ⁨year⁩ ago

        Not sure I understand all of it, but the last part about pi not being algebraic made sense to me, at least! Thanks!

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  • flyos@jlai.lu ⁨1⁩ ⁨year⁩ ago

    Haha, well done!

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• kogasa@programming.dev ⁨1⁩ ⁨year⁩ ago

  it’s an algebraic integer in C. So kinda.

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