Comment on I dunno

a + b
-----
c + d

a + b + d
    -
    c

• CannonFodder@lemmy.world ⁨1⁩ ⁨month⁩ ago

  Or
  12 / 2(6) And trying to argue this is 36.

  source

  • JackbyDev@programming.dev ⁨1⁩ ⁨month⁩ ago

    Now that’s a good troll math thing because it gets really deep into the weeds of mathematical notation. There isn’t one true order of operations that is objectively correct, and in top of that, that’s hardly the way most people would write that. As in, if you wrote that by hand, you wouldn’t use the / symbol. You’d either use ÷ or a proper fraction.

    It’s a good candidate for nerd sniping.

    Personally, I’d call that 36 as written given the context you’re saying it in, instead of calling it 1. But I’d say it’s ambiguous and you should notate in a way to avoid ambiguities. Especially if you’re in the camp of multiplication like a(b) being different from ab and/or a × b.

    source

    • SmartmanApps@programming.dev ⁨5⁩ ⁨weeks⁩ ago

      There isn’t one true order of operations that is objectively correct

      Yes there is, as found in Maths textbooks the world over

      that’s hardly the way most people would write that

      Maths textbooks write it that way

      you wouldn’t use the / symbol

      Yes you would.

      You’d either use ÷

      Same same

      It’s a good candidate for nerd sniping.

      Here’s one I prepared earlier to save you the trouble

      I’d call that 36

      And you’d be wrong

      as written given the context you’re saying it in

      The context is Maths, you have to obey the rules of Maths. a(b+c)=(ab+ac), 5(8-5)=(5x8-5x5).

      But I’d say it’s ambiguous

      And you’d be wrong about that too

      you should notate in a way to avoid ambiguities

      It already is notated in a way that avoids all ambiguities!

      Especially if you’re in the camp of multiplication like a(b)

      That’s not Multiplication, it’s Distribution, a(b+c)=(ab+ac), a(b)=(axb).

      being different from ab

      Nope, that’s exactly the same, ab=(axb) by definition

      and/or a × b

      (axb) is most certainly different to axb. 1/ab=1/(axb), 1/axb=b/a

      source

      • JackbyDev@programming.dev ⁨5⁩ ⁨weeks⁩ ago

        Please read this section of Wikipedia which talks about these topics better than I could. It shows that there is ambiguity in the order of operations and that for especially niche cases there is not a universally accepted order of operations when dealing with mixed division and multiplication. It addresses everything you’ve mentioned.

        en.wikipedia.org/wiki/Order_of_operations#Mixed_d…

        There is no universal convention for interpreting an expression containing both division denoted by ‘÷’ and multiplication denoted by ‘×’. Proposed conventions include assigning the operations equal precedence and evaluating them from left to right, or equivalently treating division as multiplication by the reciprocal and then evaluating in any order;[10] evaluating all multiplications first followed by divisions from left to right; or eschewing such expressions and instead always disambiguating them by explicit parentheses.[11]

        Beyond primary education, the symbol ‘÷’ for division is seldom used, but is replaced by the use of algebraic fractions,[12] typically written vertically with the numerator stacked above the denominator – which makes grouping explicit and unambiguous – but sometimes written inline using the slash or solidus symbol ‘/’.[13]

        Multiplication denoted by juxtaposition (also known as implied multiplication) creates a visual unit and is often given higher precedence than most other operations. In academic literature, when inline fractions are combined with implied multiplication without explicit parentheses, the multiplication is conventionally interpreted as having higher precedence than division, so that e.g. 1 / 2n is interpreted to mean 1 / (2 · n) rather than (1 / 2) · n.[2][10][14][15] For instance, the manuscript submission instructions for the Physical Review journals directly state that multiplication has precedence over division,[16] and this is also the convention observed in physics textbooks such as the Course of Theoretical Physics by Landau and Lifshitz[c] and mathematics textbooks such as Concrete Mathematics by Graham, Knuth, and Patashnik.[17] However, some authors recommend against expressions such as a / bc, preferring the explicit use of parenthesis a / (bc).[3]

        More complicated cases are more ambiguous. For instance, the notation 1 / 2π(a + b) could plausibly mean either 1 / [2π · (a + b)] or [1 / (2π)] · (a + b).[18] Sometimes interpretation depends on context. The Physical Review submission instructions recommend against expressions of the form a / b / c; more explicit expressions (a / b) / c or a / (b / c) are unambiguous.[16]

        Image of two calculators getting different answers: 6÷2(1+2) is interpreted as 6÷(2×(1+2)) by a fx-82MS (upper), and (6÷2)×(1+2) by a TI-83 Plus calculator (lower), respectively.

        This ambiguity has been the subject of Internet memes such as “8 ÷ 2(2 + 2)”, for which there are two conflicting interpretations: 8 ÷ [2 · (2 + 2)] = 1 and (8 ÷ 2) · (2 + 2) = 16.[15][19] Mathematics education researcher Hung-Hsi Wu points out that “one never gets a computation of this type in real life”, and calls such contrived examples “a kind of Gotcha! parlor game designed to trap an unsuspecting person by phrasing it in terms of a set of unreasonably convoluted rules”.[12]

        source

        • -> View More Comments
  • Feathercrown@lemmy.world ⁨1⁩ ⁨month⁩ ago

    The P in PEMDAS means to solve everything within parentheses first; there is no “distribution” step or rule that says multiplying without a visible operator other than parentheses comes first. So yes, 36 is valid here. It’s mostly because PEMDAS never shows up in the same context as this sort of multiplication or large fractions

    source

    • SmartmanApps@programming.dev ⁨5⁩ ⁨weeks⁩ ago

      The P in PEMDAS means to solve everything within parentheses first

      and without a(b+c)=(ab+ac), now solve (ab+ac)

      there is no “distribution” step or rule

      It’s a LAW of Maths actually, The Distributive Law.

      Image

      that says multiplying without a visible operator

      It’s not “Multiplying”, it’s Distributing, a(b+c)=(ab+ac)

      So yes, 36 is valid here

      No it isn’t. To get 36 you have disobeyed The Distributive Law, thus it is a wrong answer

      It’s mostly because

      people like you try to gaslight others that there’s no such thing as The Distributive Law

      source

      • Feathercrown@lemmy.world ⁨5⁩ ⁨weeks⁩ ago

        Are you under the impression that atomizing your opponents statements and making a comment about each part individually without addressing the actual point (how those facts fit together) is a good debate tactic? Because it seems like all you’ve done is confuse yourself about what I was saying and make arguments that don’t address it.

        source

        • -> View More Comments
  • MotoAsh@piefed.social ⁨1⁩ ⁨month⁩ ago

    Well, now you might be running into syntax issues instead of PEMDAS issues depending on what they’re confused about. If it’s 12 over 2*6, it’s 1. If it’s 12 ÷ 2 x 6, it’s 36.

    A lot of people try a bunch of funky stuff to represent fractions in text form (like mixing spaces and no spaces) when they should just be treating it like a programmer has to, and use parenthesis if it’s a complex fraction in basic text form.

    source
• SmartmanApps@programming.dev ⁨5⁩ ⁨weeks⁩ ago

  Because people never use that after they learn fractions,

  Yes they do, because not every division is a fraction

  source

  • JackbyDev@programming.dev ⁨5⁩ ⁨weeks⁩ ago

    math.berkeley.edu/~wu/order5.pdf

    Image

    source

    • SmartmanApps@programming.dev ⁨5⁩ ⁨weeks⁩ ago

      math.berkeley.edu/~wu/order5.pdf

      I already said he was wrong about that. Quoting him saying it doesn’t change that he’s wrong about it

      source

      • JackbyDev@programming.dev ⁨5⁩ ⁨weeks⁩ ago

        Take it up with Berkeley then.

        source

        • -> View More Comments
• sukhmel@programming.dev ⁨1⁩ ⁨month⁩ ago

  Treat a + b/c + d as a + b/(c + d) I can almost understand, I was guilty of doing that in school with multiplication, but auto-parenthesising the first part is really crazy take, imo

  source

  • SmartmanApps@programming.dev ⁨5⁩ ⁨weeks⁩ ago

    Treat a + b/c + d as a + b/(c + d)

    No don’t. That rule was changed more than 130 years ago. a+b/c+d=a+(b/c)+d, Division before Addition

    source
  • JackbyDev@programming.dev ⁨1⁩ ⁨month⁩ ago

    That’s a really odd way to parse it.

    a +   b
        -----
        c + b
    

    source