• Kogasa@programming.dev
    link
    fedilink
    arrow-up
    7
    arrow-down
    18
    ·
    edit-2
    1 year ago

    It is, in fact, completely arbitrary. There is no reason why we should read 1+2*3 as 1 + (2*3) instead of (1 + 2) * 3 except that it is conventional and having a convention facilitates communication. No, it has nothing to do with set theory or mathematical foundations. It is literally just a notational convention, and not the only one that is still currently used.

    Edit: I literally have an MSc in math, but good to see Lemmy is just as much on board with the Dunning-Kruger effect as Reddit.

    • Uphillbothways@lemmy.world
      link
      fedilink
      arrow-up
      11
      arrow-down
      1
      ·
      edit-2
      1 year ago

      If you don’t accept adding and subtracting numbers as allowed mathematical transactions, multiplication doesn’t make sense at all. It isn’t arbitrary. It’s fundamental basic accounting.

      • Kogasa@programming.dev
        link
        fedilink
        arrow-up
        1
        arrow-down
        2
        ·
        edit-2
        1 year ago

        What you just said is at best irrelevant and at worst meaningless. No, the fact that multiplication is defined in terms of addition does not mean that it is required or natural to evaluate multiplication before addition when parsing a mathematical expression. The latter is a purely syntactic convention. It is arbitrary. It isn’t “accounting.”

    • nLuLukna @sh.itjust.works
      link
      fedilink
      arrow-up
      5
      ·
      edit-2
      1 year ago

      Yeah I haven no idea what I was saying when I said that, I’ve edited my comment a bit.

      On that note though using your example I think I can illistarte the point I was trying to make earlier.

      1 + (2*3) by always doing multiplication first we can remove those brackets.

      (1 + 2) * 3 can be rewritten as (1 * 3 )+ (2 * 3) so using the first rule again makes a sense. That is a crappy explaination but I think you get my gist.

      • Kogasa@programming.dev
        link
        fedilink
        arrow-up
        1
        arrow-down
        2
        ·
        1 year ago

        Your point is not clear.

        1 + (2 * 3) by always doing addition first we can remove those brackets.

        (1 * 3) + (2 * 3) can be rewritten as (1 + 2) * 3 so using the first rule again makes sense.

        Do you see the issue?

        • nLuLukna @sh.itjust.works
          link
          fedilink
          arrow-up
          1
          ·
          1 year ago

          I don’t see it mate. So you’re going to have to tell me, sorry.

          The point I’m trying to make is that using Pemdas/Bedmas is the most effiecent way of removing brackets - I actually don’t 100% know that but I doubt it creates hundreds of brackets - if thats slightly clearer.

          • Kogasa@programming.dev
            link
            fedilink
            arrow-up
            1
            ·
            1 year ago

            I don’t know how else to explain it. I used your own argument verbatim but with the opposite assumption, that addition takes priority over multiplication. In either case, some expressions can be written without parentheses which require parentheses in the other case.

            • nLuLukna @sh.itjust.works
              link
              fedilink
              arrow-up
              1
              ·
              1 year ago

              Right well that makes sense. And is also a very good point. I don’t really see why you couldn’t do that. So I guess it is arbitrary. Although you then have the question of which case occurs more commonly, which is imo actually quite interesting, but also entirely pointless, since good luck showing one case to be more than the other. It’s like that door and wheel question.