Comment on I dunno

• JackbyDev@programming.dev ⁨5⁩ ⁨weeks⁩ 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.

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  • SmartmanApps@programming.dev ⁨2⁩ ⁨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

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    • JackbyDev@programming.dev ⁨2⁩ ⁨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]

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      • SmartmanApps@programming.dev ⁨2⁩ ⁨weeks⁩ ago

        Please read this section of Wikipedia which talks about these topics better than I could

        Please read Maths textbooks which explain it better than Joe Blow Your next Door neighbour on Wikipedia. there’s plenty in here

        It shows that there is ambiguity in the order of operations

        and is wrong about that, as proven by Maths textbooks

        especially niche cases there is not a universally accepted order of operations when dealing with mixed division and multiplication

        That’s because Multiplication and Division can be done in any order

        It addresses everything you’ve mentioned

        wrongly, as per Maths textbooks

        Multiplication denoted by juxtaposition (also known as implied multiplication)

        Nope. Terms/Products is what they are called. “implied multiplication” is a “rule” made up by people who have forgotten the actual rules.

        s often given higher precedence than most other operations

        Always is, because brackets first. ab=(axb) by definition

        1 / 2n is interpreted to mean 1 / (2 · n)

        As per the definition that ab=(axb), 1/2n=1/(2xn).

        [2][10][14][15]

        Did you look at the references, and note that there are no Maths textbooks listed?

        the manuscript submission instructions for the Physical Review journals

        Which isn’t a Maths textbook

        the convention observed in physics textbooks

        Also not Maths textbooks

        mathematics textbooks such as Concrete Mathematics by Graham, Knuth, and Patashnik

        Actually that is a Computer Science textbook, written for programmers. Knuth is a very famous programmer

        More complicated cases are more ambiguous

        None of them are ambiguous.

        the notation 1 / 2π(a + b) could plausibly mean either 1 / [2π · (a + b)]

        It does as per the rules of Maths, but more precisely it actually means 1 / (2πa + 2πb)

        or [1 / (2π)] · (a + b).[18]

        No, it can’t mean that unless it was written (1 / 2π)(a + b), which it wasn’t

        Sometimes interpretation depends on context

        Nope, never

        more explicit expressions (a / b) / c or a / (b / c) are unambiguous

        a/b/c is already unambiguous - left to right. 🙄

        Image of two calculators getting different answers

        With the exception of Texas Instruments, all the other calculator manufacturers have gone back to doing it correctly, and Sharp have always done it correctly.

        6÷2(1+2) is interpreted as 6÷(2×(1+2))

        6÷(2x1+2x2) actually, as per The Distributive Law, a(b+c)=(ab+ac)

        (6÷2)×(1+2) by a TI-83 Plus calculator (lower)

        Yep, Texas Instruments is the only one still doing it wrong

        This ambiguity

        doesn’t exist, as per Maths textbooks

        “8 ÷ 2(2 + 2)”, for which there are two conflicting interpretations:

        No there isn’t - you MUST obey The Distributive Law, a(b+c)=(ab+ac)

        Mathematics education researcher Hung-Hsi Wu points out that “one never gets a computation of this type in real life”

        And he was wrong about that. 🙄

        calls such contrived examples

        Which notably can be found in Maths textbooks

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• Feathercrown@lemmy.world ⁨5⁩ ⁨weeks⁩ 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

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  • SmartmanApps@programming.dev ⁨2⁩ ⁨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

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    • Feathercrown@lemmy.world ⁨2⁩ ⁨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.

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      • SmartmanApps@programming.dev ⁨2⁩ ⁨weeks⁩ ago

        addressing the actual point (how those facts fit together)

        I did address the actual point - see Maths textbooks

        all you’ve done is confuse yourself

        I’m not confused at all. I’m the one who knows the difference between Distribution and Multiplication.

        what I was saying

        You lied about there being no such thing as “the Distribution step” (Brackets), proven wrong by the textbooks

        make arguments that don’t address it.

        Textbooks talking about The Distributive Law totally addresses your lie that no such step exists.

        Never mind that some of those micro-rebuttals aren’t even correct

        You think Maths textbooks aren’t correct?? 😂

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• MotoAsh@piefed.social ⁨5⁩ ⁨weeks⁩ 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.

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