• apolo399@lemmy.worldEnglish
    2·
    5 months ago

    Sure, let’s do it in base 3. 3 in base 3 is 10, and 3^(-1) is 10^(-1), so:

    1/3 in base 10 = 1/10 in base 3
    0.3… in base 10 = 0.1 in base 3

    Multiply by 3 on both sides:

    3 × 0.3… in base 10 = 10 × 0.1 in base 3
    0.9… in base 10 = 1 in base 3.

    But 1 in base 3 is also 1 in base 10, so:

    0.9… in base 10 = 1 in base 10

    • ColeSloth@discuss.tchncs.deEnglish
      25·
      5 months ago

      You’re having to use … to make your conversion again. If you need to to an irrational number to make your equation correct, it isn’t really correct.