• nandeEbisu@lemmy.ml
      link
      fedilink
      English
      arrow-up
      3
      arrow-down
      9
      ·
      1 year ago

      Notation without a definition of what notation you’re using is always going to be ambiguous.

      If I wrote

      6 9 * 6 9 + +

      You wouldn’t know what that is, until I told you it was reverse polish notation, then you would know it resolves to 69 and does the same operations as the original equation.

      • Björn Tantau@swg-empire.de
        link
        fedilink
        English
        arrow-up
        8
        ·
        1 year ago

        You’re right, nobody defined the base of the numbers either. Come to think of it, what makes you think that those are numbers at all? That’s nothing but a random arrangement of pixels. I mean, who am I to tell you how to interpret the photons reaching your retina? You’re nothing but excitations in the electric fields in my neurons, anyways.

        • nandeEbisu@lemmy.ml
          link
          fedilink
          English
          arrow-up
          1
          arrow-down
          1
          ·
          1 year ago

          Its not that there’s no definition for the notation, but if you fall back to commonly held definitions, there is divergence in common definitions without the parenthesis. Plenty of calculators, especially old ones, don’t respect PEMDAS, so the so by adding brackets your expression is going to fit the intended operations in more commonly used systems than had you left the brackets out.

          I also do think its a bit more readable as your eyes are initially drawn to the first operation, you can start evaluating expressions without even parsing the rest of the equation, or you can just block out that entire chunk when you start looking at how many terms are in the equation. That’s subjective though, so to each their own.

  • nandeEbisu@lemmy.ml
    link
    fedilink
    arrow-up
    36
    ·
    edit-2
    1 year ago

    Huh, that’s true of any number that ends in 9.

    XY + X + Y = 10*X + Y

    Y’s cancel,

    XY = 9X => Y = 9 for any non-zero finite value of X.

    so for 69? X = 6, Y=9

    (6*9) + 6 + 9 = 10*6 + 9

    54 + 15 = 69

    69 = 69 (nice!)

    429? X = 42 Y = 9

    (42*9) + 42 + 9 =10*42 + 9

    (378) + 51 = 429

    429 = 429

    Even if 10X+Y doesn’t equal something that ends in 9 it works

    X=3.14 Y=9

    (3.14*9) + 3.14 + 9 = 10*3.14 + 9

    28.26 + 12.14 = 40.4

    40.4 = 40.4

    Doesn’t work if Y =\= 9:

    68? X = 6 Y = 8

    (6*8) + 6 + 8 ?= 10*6 + 8

    (48) + 14 ?= 68

    62 =\= 68

    • evilgiraffe666@ttrpg.network
      link
      fedilink
      arrow-up
      4
      ·
      1 year ago

      I wanted to try to properly prove that it didn’t work for y!=9, but I think you covered the edge cases - X=0 or unbounded. Well done!

      • nandeEbisu@lemmy.ml
        link
        fedilink
        arrow-up
        3
        ·
        1 year ago

        I’m an engineering major, we learn all of the edge cases as “well technically this isn’t always true, but we’ll just pretend it is because the results are close enough”