• UnderpantsWeevil@lemmy.worldEnglish
    0·
    5 months ago

    There’s a Real Analysis proof for it and everything.

    Basically boils down to

    • If 0.(9) != 1 then there must be some value between 0.(9) and 1.
    • We know such a number cannot exist, because for any given discrete value (say 0.999…9) there is a number (0.999…99) that is between that discrete value and 0.(9)
    • Therefore, no value exists between 0.(9) and 1.
    • So 0.(9) = 1
    • Kairos@lemmy.todayEnglish
      0·
      5 months ago

      Even simpler: 1 = 3 * 1/3

      1/3 =0.333333…

      1/3 + 1/3 + 1/3 = 0.99999999… = 1

      • UnderpantsWeevil@lemmy.worldEnglish
        0·
        5 months ago

        Even simpler

        0.99999999… = 1

        But you’re just restating the premise here. You haven’t proven the two are equal.

        1/3 =0.333333…

        This step

        1/3 + 1/3 + 1/3 = 0.99999999…

        And this step

        Aren’t well-defined. You’re relying on division short-hand rather than a real proof.