• 🍉 DrRedOctopus 🐙🍉@lemmy.world
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    8 hours ago

    how the fuck i didn’t realize that!!!

    Fuck,

    so 1 in base pi is still 1, but 10 is pi

    makes sense,

    1 =pi ^ 0

    10=pi^1

    100 = pi^2

    my intuition kept telling me that using an irrational base system would end up with all integers being irrational. didn’t realize how easy it is to prove it otherwise

    ie, I had a very bad conjecture and I gained better understanding why it was wrong

      • setsubyou@lemmy.world
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        5 hours ago

        1 in base 10 isn’t 1/10 and in hexadecimal it’s not 1/16.

        Decimal integers in base pi are 1, 2, 3, 10.2201…, 11.2201…, 12.2201…, 20.2201… and so on.

        Basically: 10.2201… = 1 * pi^1 + 0 * pi^0 + 2 * pi^-1 + 2 * pi^-2 … which approaches 4 as you add digits.

        But 1 is just 1*pi^0